diff --git a/ABACUS.develop/source/Makefile.Objects b/ABACUS.develop/source/Makefile.Objects index 10825db039..e2e652597e 100644 --- a/ABACUS.develop/source/Makefile.Objects +++ b/ABACUS.develop/source/Makefile.Objects @@ -26,7 +26,6 @@ xc_2.o\ xc_3.o \ vdwd2.o\ vdwd2_parameters.o\ -dftd3_subroutine.o\ vdwd3.o\ vdwd3_parameters.o\ pseudopot_upf.o\ @@ -350,4 +349,4 @@ lsame.o\ psort_w.o\ s_cmp.o\ s_copy.o\ -xerbla.o\ +xerbla.o\ \ No newline at end of file diff --git a/ABACUS.develop/source/Makefile.system b/ABACUS.develop/source/Makefile.system index 80237901c1..b8ca7926c2 100644 --- a/ABACUS.develop/source/Makefile.system +++ b/ABACUS.develop/source/Makefile.system @@ -36,7 +36,7 @@ CEREAL_INCLUDE_DIR = ${CEREAL_DIR}/include # comment out by mohan 2021-02-06 #LIBS = -lifcore -lm -lpthread ${LAPACK_LIB} ${FFTW_LIB} ${ELPA_LIB} ${LIBXC_LIB} LIBS = -lifcore -lm -lpthread ${LAPACK_LIB} ${FFTW_LIB} ${ELPA_LIB} -#LIBS = -liomp5 -lpthread -lm -ldl ${BOOST_LIB} ${LAPACK_LIB} ${FFTW_LIB} ${LPA_LIB} ${LIBXC_LIB} +#LIBS = -liomp5 -lpthread -lm -ldl ${BOOST_LIB} ${LAPACK_LIB} ${FFTW_LIB} ${ELPA_LIB} ${LIBXC_LIB} INCLUDES = -I. -Icommands -I${BOOST_INCLUDE_DIR} -I${LAPACK_INCLUDE_DIR} -I${FFTW_INCLUDE_DIR} -I${LIBXC_INCLUDE_DIR} -I${CEREAL_INCLUDE_DIR} diff --git a/ABACUS.develop/source/input_conv.cpp b/ABACUS.develop/source/input_conv.cpp index 8903aaba06..900bc93e6e 100644 --- a/ABACUS.develop/source/input_conv.cpp +++ b/ABACUS.develop/source/input_conv.cpp @@ -10,7 +10,7 @@ #include "src_pw/efield.h" #include "src_lcao/global_fp.h" #include "src_pw/vdwd2_parameters.h" -#include "src_pw/vdwd3.h" +#include "src_pw/vdwd3_parameters.h" #include "src_io/chi0_hilbert.h" #include "src_io/chi0_standard.h" #include "src_io/epsilon0_pwscf.h" @@ -213,46 +213,24 @@ void Input_Conv::Convert(void) } if(INPUT.vdw_method=="d3_0" || INPUT.vdw_method=="d3_bj") { - vdwd3.vdwD3 = true; - vdwd3.s6 = std::stod(INPUT.vdw_s6); - vdwd3.s18 = std::stod(INPUT.vdw_s8); - vdwd3.rs6 = std::stod(INPUT.vdw_a1); - vdwd3.rs18 = std::stod(INPUT.vdw_a2); - vdwd3.abc = INPUT.vdw_abc; - if(INPUT.vdw_method=="d3_0") - { - vdwd3.version = 1; - } - if(INPUT.vdw_method=="d3_bj") - { - vdwd3.version = 2; - } - vdwd3.model = INPUT.vdw_model; - if(INPUT.vdw_model=="radius") - { - if(INPUT.vdw_radius_unit=="Bohr") - { - vdwd3.rthr2 = pow(std::stod(INPUT.vdw_radius),2); - } - else - { - vdwd3.rthr2 = pow((std::stod(INPUT.vdw_radius) * BOHR_TO_A),2); - } - if(INPUT.vdw_cn_thr_unit=="Bohr") - { - vdwd3.cn_thr2 = pow(INPUT.vdw_cn_thr,2); - } - else - { - vdwd3.cn_thr2 = pow((INPUT.vdw_cn_thr * BOHR_TO_A),2); - } - } - else if(INPUT.vdw_model=="period") - { - vdwd3.rep_vdw[0] = INPUT.vdw_period.x; - vdwd3.rep_vdw[1] = INPUT.vdw_period.y; - vdwd3.rep_vdw[2] = INPUT.vdw_period.z; - } + vdwd3_para.flag_vdwd3 = true; + vdwd3_para.s6 = std::stod(INPUT.vdw_s6); + vdwd3_para.s18 = std::stod(INPUT.vdw_s8); + vdwd3_para.rs6 = std::stod(INPUT.vdw_a1); + vdwd3_para.rs18 = std::stod(INPUT.vdw_a2); + vdwd3_para.abc = INPUT.vdw_abc; + vdwd3_para.version = INPUT.vdw_method; + vdwd3_para.model = INPUT.vdw_model; + if(INPUT.vdw_radius_unit=="Bohr") + vdwd3_para.rthr2 = pow(std::stod(INPUT.vdw_radius),2); + else + vdwd3_para.rthr2 = pow((std::stod(INPUT.vdw_radius) * BOHR_TO_A),2); + if(INPUT.vdw_cn_thr_unit=="Bohr") + vdwd3_para.cn_thr2 = pow(INPUT.vdw_cn_thr,2); + else + vdwd3_para.cn_thr2 = pow((INPUT.vdw_cn_thr * BOHR_TO_A),2); + if(INPUT.vdw_model=="period") + vdwd3_para.period = INPUT.vdw_period; } //---------------------------------------------------------- diff --git a/ABACUS.develop/source/src_global/matrix3.h b/ABACUS.develop/source/src_global/matrix3.h index 7729fe5cde..451bb28aec 100644 --- a/ABACUS.develop/source/src_global/matrix3.h +++ b/ABACUS.develop/source/src_global/matrix3.h @@ -46,7 +46,7 @@ Matrix3 operator -(const Matrix3 &m1, const Matrix3 &m2); //m1-m2 Matrix3 operator /(const Matrix3 &m,const double &s); //m/s Matrix3 operator *(const Matrix3 &m1,const Matrix3 &m2); //m1*m2 Matrix3 operator *(const Matrix3 &m,const double &s); //m*s -Matrix3 operator *(double &s, const Matrix3 &m); //s*m +Matrix3 operator *(const double &s, const Matrix3 &m); //s*m template Vector3 operator *(const Matrix3 &m, const Vector3 &u); //m*u // Peize Lin change Vector3 2017-01-10 template Vector3 operator *(const Vector3 &u, const Matrix3 &m); //u*m // Peize Lin change Vector3 2017-01-10 diff --git a/ABACUS.develop/source/src_lcao/FORCE_STRESS.cpp b/ABACUS.develop/source/src_lcao/FORCE_STRESS.cpp index 770a3d4bf9..2bfaae3595 100644 --- a/ABACUS.develop/source/src_lcao/FORCE_STRESS.cpp +++ b/ABACUS.develop/source/src_lcao/FORCE_STRESS.cpp @@ -5,6 +5,7 @@ // new #include "../src_pw/H_XC_pw.h" #include "src_pw/vdwd2.h" +#include "src_pw/vdwd3.h" double Force_Stress_LCAO::force_invalid_threshold_ev = 0.00; double Force_Stress_LCAO::output_acc = 1.0e-8; @@ -154,13 +155,28 @@ void Force_Stress_LCAO::getForceStress( stress_vdw = vdwd2.get_stress().to_matrix(); } } - // jiyy add 2019-05-18 - else if(vdwd3.vdwD3) + // jiyy add 2019-05-18, update 2021-04-25 + else if(vdwd3_para.flag_vdwd3) { - if(isforce) force_vdw.create(nat,3); - if(isstress) stress_vdw.create(3,3); - vdwd3.force(isforce, isstress, force_vdw, stress_vdw); - } + if(isforce) + { + force_vdw.create(nat,3); + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_force(); + for(int iat=0; iatprint_force("EFIELD FORCE",fefield,1,ry); } - if(vdwd2_para.flag_vdwd2||vdwd3.vdwD3) + if(vdwd2_para.flag_vdwd2||vdwd3_para.flag_vdwd3) { this->print_force("VDW FORCE",force_vdw,1,ry); } @@ -358,7 +374,7 @@ void Force_Stress_LCAO::getForceStress( + sigmahar(i,j);// hartree stress //VDW stress from linpz and jiyy - if(vdwd2_para.flag_vdwd2||vdwd3.vdwD3) + if(vdwd2_para.flag_vdwd2||vdwd3_para.flag_vdwd3) { scs(i,j) += stress_vdw(i , j); } @@ -414,7 +430,7 @@ void Force_Stress_LCAO::getForceStress( sc_pw.print_stress("cc STRESS",sigmacc,TEST_STRESS,ry); // sc_pw.print_stress("NLCC STRESS",sigmacc,TEST_STRESS,ry); sc_pw.print_stress("XC STRESS",sigmaxc,TEST_STRESS,ry); - if(vdwd2_para.flag_vdwd2||vdwd3.vdwD3) + if(vdwd2_para.flag_vdwd2||vdwd3_para.flag_vdwd3) { sc_pw.print_stress("VDW STRESS",sigmaxc,TEST_STRESS,ry); } diff --git a/ABACUS.develop/source/src_lcao/LOOP_elec.cpp b/ABACUS.develop/source/src_lcao/LOOP_elec.cpp index bc22cd4735..e7a1bbc9f8 100644 --- a/ABACUS.develop/source/src_lcao/LOOP_elec.cpp +++ b/ABACUS.develop/source/src_lcao/LOOP_elec.cpp @@ -20,6 +20,7 @@ #include "src_ri/exx_abfs.h" #include "src_ri/exx_opt_orb.h" #include "src_pw/vdwd2.h" +#include "src_pw/vdwd3.h" void LOOP_elec::solve_elec_stru(const int &istep) @@ -147,11 +148,12 @@ void LOOP_elec::solver(const int &istep) vdwd2.cal_energy(); en.evdw = vdwd2.get_energy(); } - // jiyy add 2019-05-18 - else if(vdwd3.vdwD3) + // jiyy add 2019-05-18, 2021-04-25 + else if(vdwd3_para.flag_vdwd3) { - vdwd3.energy(); - en.evdw = vdwd3.energy_result; + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_energy(); + en.evdw = vdwd3.get_energy(); } // self consistent calculations for electronic ground state diff --git a/ABACUS.develop/source/src_lcao/LOOP_ions.cpp b/ABACUS.develop/source/src_lcao/LOOP_ions.cpp index 779652d5cf..16e6239661 100644 --- a/ABACUS.develop/source/src_lcao/LOOP_ions.cpp +++ b/ABACUS.develop/source/src_lcao/LOOP_ions.cpp @@ -13,6 +13,7 @@ #include "ELEC_scf.h" #include "src_global/sltk_atom_arrange.h" #include "src_pw/vdwd2.h" +#include "src_pw/vdwd3.h" #include "LCAO_descriptor.h" LOOP_ions::LOOP_ions() @@ -447,10 +448,11 @@ void LOOP_ions::final_scf(void) vdwd2.cal_energy(); en.evdw = vdwd2.get_energy(); } - else if(vdwd3.vdwD3) //jiyy add 2019-05-18 + else if(vdwd3_para.flag_vdwd3) //jiyy add 2019-05-18, update 2021-04-25 { - vdwd3.energy(); - en.evdw = vdwd3.energy_result; + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_energy(); + en.evdw = vdwd3.get_energy();; } diff --git a/ABACUS.develop/source/src_lcao/run_md.cpp b/ABACUS.develop/source/src_lcao/run_md.cpp index 92f0f20d52..95f0caf396 100644 --- a/ABACUS.develop/source/src_lcao/run_md.cpp +++ b/ABACUS.develop/source/src_lcao/run_md.cpp @@ -13,6 +13,7 @@ #include "ELEC_scf.h" #include "src_global/sltk_atom_arrange.h" #include "src_pw/vdwd2.h" +#include "src_pw/vdwd3.h" Run_MD::Run_MD() {} @@ -447,10 +448,11 @@ void Run_MD::final_scf(void) vdwd2.cal_energy(); en.evdw = vdwd2.get_energy(); } - else if(vdwd3.vdwD3) //jiyy add 2019-05-18 + else if(vdwd3_para.flag_vdwd3) //jiyy add 2019-05-18, update 2021-04-25 { - vdwd3.energy(); - en.evdw = vdwd3.energy_result; + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_energy(); + en.evdw = vdwd3.get_energy(); } ELEC_scf es; diff --git a/ABACUS.develop/source/src_pw/dftd3_subroutine.f b/ABACUS.develop/source/src_pw/dftd3_subroutine.f deleted file mode 100644 index c78878c2d2..0000000000 --- a/ABACUS.develop/source/src_pw/dftd3_subroutine.f +++ /dev/null @@ -1,2719 +0,0 @@ - subroutine setr0ab(max_elem,autoang,r) - implicit none - integer max_elem,i,j,k - real*8 r(max_elem,max_elem),autoang - real*8 r0ab(4465) - r0ab( 1: 70)=(/ - . 2.1823, 1.8547, 1.7347, 2.9086, 2.5732, 3.4956, 2.3550 - ., 2.5095, 2.9802, 3.0982, 2.5141, 2.3917, 2.9977, 2.9484 - ., 3.2160, 2.4492, 2.2527, 3.1933, 3.0214, 2.9531, 2.9103 - ., 2.3667, 2.1328, 2.8784, 2.7660, 2.7776, 2.7063, 2.6225 - ., 2.1768, 2.0625, 2.6395, 2.6648, 2.6482, 2.5697, 2.4846 - ., 2.4817, 2.0646, 1.9891, 2.5086, 2.6908, 2.6233, 2.4770 - ., 2.3885, 2.3511, 2.2996, 1.9892, 1.9251, 2.4190, 2.5473 - ., 2.4994, 2.4091, 2.3176, 2.2571, 2.1946, 2.1374, 2.9898 - ., 2.6397, 3.6031, 3.1219, 3.7620, 3.2485, 2.9357, 2.7093 - ., 2.5781, 2.4839, 3.7082, 2.5129, 2.7321, 3.1052, 3.2962 - ./) - r0ab( 71: 140)=(/ - . 3.1331, 3.2000, 2.9586, 3.0822, 2.8582, 2.7120, 3.2570 - ., 3.4839, 2.8766, 2.7427, 3.2776, 3.2363, 3.5929, 3.2826 - ., 3.0911, 2.9369, 2.9030, 2.7789, 3.3921, 3.3970, 4.0106 - ., 2.8884, 2.6605, 3.7513, 3.1613, 3.3605, 3.3325, 3.0991 - ., 2.9297, 2.8674, 2.7571, 3.8129, 3.3266, 3.7105, 3.7917 - ., 2.8304, 2.5538, 3.3932, 3.1193, 3.1866, 3.1245, 3.0465 - ., 2.8727, 2.7664, 2.6926, 3.4608, 3.2984, 3.5142, 3.5418 - ., 3.5017, 2.6190, 2.4797, 3.1331, 3.0540, 3.0651, 2.9879 - ., 2.9054, 2.8805, 2.7330, 2.6331, 3.2096, 3.5668, 3.3684 - ., 3.3686, 3.3180, 3.3107, 2.4757, 2.4019, 2.9789, 3.1468 - ./) - r0ab( 141: 210)=(/ - . 2.9768, 2.8848, 2.7952, 2.7457, 2.6881, 2.5728, 3.0574 - ., 3.3264, 3.3562, 3.2529, 3.1916, 3.1523, 3.1046, 2.3725 - ., 2.3289, 2.8760, 2.9804, 2.9093, 2.8040, 2.7071, 2.6386 - ., 2.5720, 2.5139, 2.9517, 3.1606, 3.2085, 3.1692, 3.0982 - ., 3.0352, 2.9730, 2.9148, 3.2147, 2.8315, 3.8724, 3.4621 - ., 3.8823, 3.3760, 3.0746, 2.8817, 2.7552, 2.6605, 3.9740 - ., 3.6192, 3.6569, 3.9586, 3.6188, 3.3917, 3.2479, 3.1434 - ., 4.2411, 2.7597, 3.0588, 3.3474, 3.6214, 3.4353, 3.4729 - ., 3.2487, 3.3200, 3.0914, 2.9403, 3.4972, 3.7993, 3.6773 - ., 3.8678, 3.5808, 3.8243, 3.5826, 3.4156, 3.8765, 4.1035 - ./) - r0ab( 211: 280)=(/ - . 2.7361, 2.9765, 3.2475, 3.5004, 3.4185, 3.4378, 3.2084 - ., 3.2787, 3.0604, 2.9187, 3.4037, 3.6759, 3.6586, 3.8327 - ., 3.5372, 3.7665, 3.5310, 3.3700, 3.7788, 3.9804, 3.8903 - ., 2.6832, 2.9060, 3.2613, 3.4359, 3.3538, 3.3860, 3.1550 - ., 3.2300, 3.0133, 2.8736, 3.4024, 3.6142, 3.5979, 3.5295 - ., 3.4834, 3.7140, 3.4782, 3.3170, 3.7434, 3.9623, 3.8181 - ., 3.7642, 2.6379, 2.8494, 3.1840, 3.4225, 3.2771, 3.3401 - ., 3.1072, 3.1885, 2.9714, 2.8319, 3.3315, 3.5979, 3.5256 - ., 3.4980, 3.4376, 3.6714, 3.4346, 3.2723, 3.6859, 3.8985 - ., 3.7918, 3.7372, 3.7211, 2.9230, 2.6223, 3.4161, 2.8999 - ./) - r0ab( 281: 350)=(/ - . 3.0557, 3.3308, 3.0555, 2.8508, 2.7385, 2.6640, 3.5263 - ., 3.0277, 3.2990, 3.7721, 3.5017, 3.2751, 3.1368, 3.0435 - ., 3.7873, 3.2858, 3.2140, 3.1727, 3.2178, 3.4414, 2.5490 - ., 2.7623, 3.0991, 3.3252, 3.1836, 3.2428, 3.0259, 3.1225 - ., 2.9032, 2.7621, 3.2490, 3.5110, 3.4429, 3.3845, 3.3574 - ., 3.6045, 3.3658, 3.2013, 3.6110, 3.8241, 3.7090, 3.6496 - ., 3.6333, 3.0896, 3.5462, 2.4926, 2.7136, 3.0693, 3.2699 - ., 3.1272, 3.1893, 2.9658, 3.0972, 2.8778, 2.7358, 3.2206 - ., 3.4566, 3.3896, 3.3257, 3.2946, 3.5693, 3.3312, 3.1670 - ., 3.5805, 3.7711, 3.6536, 3.5927, 3.5775, 3.0411, 3.4885 - ./) - r0ab( 351: 420)=(/ - . 3.4421, 2.4667, 2.6709, 3.0575, 3.2357, 3.0908, 3.1537 - ., 2.9235, 3.0669, 2.8476, 2.7054, 3.2064, 3.4519, 3.3593 - ., 3.2921, 3.2577, 3.2161, 3.2982, 3.1339, 3.5606, 3.7582 - ., 3.6432, 3.5833, 3.5691, 3.0161, 3.4812, 3.4339, 3.4327 - ., 2.4515, 2.6338, 3.0511, 3.2229, 3.0630, 3.1265, 2.8909 - ., 3.0253, 2.8184, 2.6764, 3.1968, 3.4114, 3.3492, 3.2691 - ., 3.2320, 3.1786, 3.2680, 3.1036, 3.5453, 3.7259, 3.6090 - ., 3.5473, 3.5327, 3.0018, 3.4413, 3.3907, 3.3593, 3.3462 - ., 2.4413, 2.6006, 3.0540, 3.1987, 3.0490, 3.1058, 2.8643 - ., 2.9948, 2.7908, 2.6491, 3.1950, 3.3922, 3.3316, 3.2585 - ./) - r0ab( 421: 490)=(/ - . 3.2136, 3.1516, 3.2364, 3.0752, 3.5368, 3.7117, 3.5941 - ., 3.5313, 3.5164, 2.9962, 3.4225, 3.3699, 3.3370, 3.3234 - ., 3.3008, 2.4318, 2.5729, 3.0416, 3.1639, 3.0196, 3.0843 - ., 2.8413, 2.7436, 2.7608, 2.6271, 3.1811, 3.3591, 3.3045 - ., 3.2349, 3.1942, 3.1291, 3.2111, 3.0534, 3.5189, 3.6809 - ., 3.5635, 3.5001, 3.4854, 2.9857, 3.3897, 3.3363, 3.3027 - ., 3.2890, 3.2655, 3.2309, 2.8502, 2.6934, 3.2467, 3.1921 - ., 3.5663, 3.2541, 3.0571, 2.9048, 2.8657, 2.7438, 3.3547 - ., 3.3510, 3.9837, 3.6871, 3.4862, 3.3389, 3.2413, 3.1708 - ., 3.6096, 3.6280, 3.6860, 3.5568, 3.4836, 3.2868, 3.3994 - ./) - r0ab( 491: 560)=(/ - . 3.3476, 3.3170, 3.2950, 3.2874, 3.2606, 3.9579, 2.9226 - ., 2.6838, 3.7867, 3.1732, 3.3872, 3.3643, 3.1267, 2.9541 - ., 2.8505, 2.7781, 3.8475, 3.3336, 3.7359, 3.8266, 3.5733 - ., 3.3959, 3.2775, 3.1915, 3.9878, 3.8816, 3.5810, 3.5364 - ., 3.5060, 3.8097, 3.3925, 3.3348, 3.3019, 3.2796, 3.2662 - ., 3.2464, 3.7136, 3.8619, 2.9140, 2.6271, 3.4771, 3.1774 - ., 3.2560, 3.1970, 3.1207, 2.9406, 2.8322, 2.7571, 3.5455 - ., 3.3514, 3.5837, 3.6177, 3.5816, 3.3902, 3.2604, 3.1652 - ., 3.7037, 3.6283, 3.5858, 3.5330, 3.4884, 3.5789, 3.4094 - ., 3.3473, 3.3118, 3.2876, 3.2707, 3.2521, 3.5570, 3.6496 - ./) - r0ab( 561: 630)=(/ - . 3.6625, 2.7300, 2.5870, 3.2471, 3.1487, 3.1667, 3.0914 - ., 3.0107, 2.9812, 2.8300, 2.7284, 3.3259, 3.3182, 3.4707 - ., 3.4748, 3.4279, 3.4182, 3.2547, 3.1353, 3.5116, 3.9432 - ., 3.8828, 3.8303, 3.7880, 3.3760, 3.7218, 3.3408, 3.3059 - ., 3.2698, 3.2446, 3.2229, 3.4422, 3.5023, 3.5009, 3.5268 - ., 2.6026, 2.5355, 3.1129, 3.2863, 3.1029, 3.0108, 2.9227 - ., 2.8694, 2.8109, 2.6929, 3.1958, 3.4670, 3.4018, 3.3805 - ., 3.3218, 3.2815, 3.2346, 3.0994, 3.3937, 3.7266, 3.6697 - ., 3.6164, 3.5730, 3.2522, 3.5051, 3.4686, 3.4355, 3.4084 - ., 3.3748, 3.3496, 3.3692, 3.4052, 3.3910, 3.3849, 3.3662 - ./) - r0ab( 631: 700)=(/ - . 2.5087, 2.4814, 3.0239, 3.1312, 3.0535, 2.9457, 2.8496 - ., 2.7780, 2.7828, 2.6532, 3.1063, 3.3143, 3.3549, 3.3120 - ., 3.2421, 3.1787, 3.1176, 3.0613, 3.3082, 3.5755, 3.5222 - ., 3.4678, 3.4231, 3.1684, 3.3528, 3.3162, 3.2827, 3.2527 - ., 3.2308, 3.2029, 3.3173, 3.3343, 3.3092, 3.2795, 3.2452 - ., 3.2096, 3.2893, 2.8991, 4.0388, 3.6100, 3.9388, 3.4475 - ., 3.1590, 2.9812, 2.8586, 2.7683, 4.1428, 3.7911, 3.8225 - ., 4.0372, 3.7059, 3.4935, 3.3529, 3.2492, 4.4352, 4.0826 - ., 3.9733, 3.9254, 3.8646, 3.9315, 3.7837, 3.7465, 3.7211 - ., 3.7012, 3.6893, 3.6676, 3.7736, 4.0660, 3.7926, 3.6158 - ./) - r0ab( 701: 770)=(/ - . 3.5017, 3.4166, 4.6176, 2.8786, 3.1658, 3.5823, 3.7689 - ., 3.5762, 3.5789, 3.3552, 3.4004, 3.1722, 3.0212, 3.7241 - ., 3.9604, 3.8500, 3.9844, 3.7035, 3.9161, 3.6751, 3.5075 - ., 4.1151, 4.2877, 4.1579, 4.1247, 4.0617, 3.4874, 3.9848 - ., 3.9280, 3.9079, 3.8751, 3.8604, 3.8277, 3.8002, 3.9981 - ., 3.7544, 4.0371, 3.8225, 3.6718, 4.3092, 4.4764, 2.8997 - ., 3.0953, 3.4524, 3.6107, 3.6062, 3.5783, 3.3463, 3.3855 - ., 3.1746, 3.0381, 3.6019, 3.7938, 3.8697, 3.9781, 3.6877 - ., 3.8736, 3.6451, 3.4890, 3.9858, 4.1179, 4.0430, 3.9563 - ., 3.9182, 3.4002, 3.8310, 3.7716, 3.7543, 3.7203, 3.7053 - ./) - r0ab( 771: 840)=(/ - . 3.6742, 3.8318, 3.7631, 3.7392, 3.9892, 3.7832, 3.6406 - ., 4.1701, 4.3016, 4.2196, 2.8535, 3.0167, 3.3978, 3.5363 - ., 3.5393, 3.5301, 3.2960, 3.3352, 3.1287, 2.9967, 3.6659 - ., 3.7239, 3.8070, 3.7165, 3.6368, 3.8162, 3.5885, 3.4336 - ., 3.9829, 4.0529, 3.9584, 3.9025, 3.8607, 3.3673, 3.7658 - ., 3.7035, 3.6866, 3.6504, 3.6339, 3.6024, 3.7708, 3.7283 - ., 3.6896, 3.9315, 3.7250, 3.5819, 4.1457, 4.2280, 4.1130 - ., 4.0597, 3.0905, 2.7998, 3.6448, 3.0739, 3.2996, 3.5262 - ., 3.2559, 3.0518, 2.9394, 2.8658, 3.7514, 3.2295, 3.5643 - ., 3.7808, 3.6931, 3.4723, 3.3357, 3.2429, 4.0280, 3.5589 - ./) - r0ab( 841: 910)=(/ - . 3.4636, 3.4994, 3.4309, 3.6177, 3.2946, 3.2376, 3.2050 - ., 3.1847, 3.1715, 3.1599, 3.5555, 3.8111, 3.7693, 3.5718 - ., 3.4498, 3.3662, 4.1608, 3.7417, 3.6536, 3.6154, 3.8596 - ., 3.0301, 2.7312, 3.5821, 3.0473, 3.2137, 3.4679, 3.1975 - ., 2.9969, 2.8847, 2.8110, 3.6931, 3.2076, 3.4943, 3.5956 - ., 3.6379, 3.4190, 3.2808, 3.1860, 3.9850, 3.5105, 3.4330 - ., 3.3797, 3.4155, 3.6033, 3.2737, 3.2145, 3.1807, 3.1596 - ., 3.1461, 3.1337, 3.4812, 3.6251, 3.7152, 3.5201, 3.3966 - ., 3.3107, 4.1128, 3.6899, 3.6082, 3.5604, 3.7834, 3.7543 - ., 2.9189, 2.6777, 3.4925, 2.9648, 3.1216, 3.2940, 3.0975 - ./) - r0ab( 911: 980)=(/ - . 2.9757, 2.8493, 2.7638, 3.6085, 3.1214, 3.4006, 3.4793 - ., 3.5147, 3.3806, 3.2356, 3.1335, 3.9144, 3.4183, 3.3369 - ., 3.2803, 3.2679, 3.4871, 3.1714, 3.1521, 3.1101, 3.0843 - ., 3.0670, 3.0539, 3.3890, 3.5086, 3.5895, 3.4783, 3.3484 - ., 3.2559, 4.0422, 3.5967, 3.5113, 3.4576, 3.6594, 3.6313 - ., 3.5690, 2.8578, 2.6334, 3.4673, 2.9245, 3.0732, 3.2435 - ., 3.0338, 2.9462, 2.8143, 2.7240, 3.5832, 3.0789, 3.3617 - ., 3.4246, 3.4505, 3.3443, 3.1964, 3.0913, 3.8921, 3.3713 - ., 3.2873, 3.2281, 3.2165, 3.4386, 3.1164, 3.1220, 3.0761 - ., 3.0480, 3.0295, 3.0155, 3.3495, 3.4543, 3.5260, 3.4413 - ./) - r0ab( 981:1050)=(/ - . 3.3085, 3.2134, 4.0170, 3.5464, 3.4587, 3.4006, 3.6027 - ., 3.5730, 3.4945, 3.4623, 2.8240, 2.5960, 3.4635, 2.9032 - ., 3.0431, 3.2115, 2.9892, 2.9148, 2.7801, 2.6873, 3.5776 - ., 3.0568, 3.3433, 3.3949, 3.4132, 3.3116, 3.1616, 3.0548 - ., 3.8859, 3.3719, 3.2917, 3.2345, 3.2274, 3.4171, 3.1293 - ., 3.0567, 3.0565, 3.0274, 3.0087, 2.9939, 3.3293, 3.4249 - ., 3.4902, 3.4091, 3.2744, 3.1776, 4.0078, 3.5374, 3.4537 - ., 3.3956, 3.5747, 3.5430, 3.4522, 3.4160, 3.3975, 2.8004 - ., 2.5621, 3.4617, 2.9154, 3.0203, 3.1875, 2.9548, 2.8038 - ., 2.7472, 2.6530, 3.5736, 3.0584, 3.3304, 3.3748, 3.3871 - ./) - r0ab(1051:1120)=(/ - . 3.2028, 3.1296, 3.0214, 3.8796, 3.3337, 3.2492, 3.1883 - ., 3.1802, 3.4050, 3.0756, 3.0478, 3.0322, 3.0323, 3.0163 - ., 3.0019, 3.3145, 3.4050, 3.4656, 3.3021, 3.2433, 3.1453 - ., 3.9991, 3.5017, 3.4141, 3.3520, 3.5583, 3.5251, 3.4243 - ., 3.3851, 3.3662, 3.3525, 2.7846, 2.5324, 3.4652, 2.8759 - ., 3.0051, 3.1692, 2.9273, 2.7615, 2.7164, 2.6212, 3.5744 - ., 3.0275, 3.3249, 3.3627, 3.3686, 3.1669, 3.0584, 2.9915 - ., 3.8773, 3.3099, 3.2231, 3.1600, 3.1520, 3.4023, 3.0426 - ., 3.0099, 2.9920, 2.9809, 2.9800, 2.9646, 3.3068, 3.3930 - ., 3.4486, 3.2682, 3.1729, 3.1168, 3.9952, 3.4796, 3.3901 - ./) - r0ab(1121:1190)=(/ - . 3.3255, 3.5530, 3.5183, 3.4097, 3.3683, 3.3492, 3.3360 - ., 3.3308, 2.5424, 2.6601, 3.2555, 3.2807, 3.1384, 3.1737 - ., 2.9397, 2.8429, 2.8492, 2.7225, 3.3875, 3.4910, 3.4520 - ., 3.3608, 3.3036, 3.2345, 3.2999, 3.1487, 3.7409, 3.8392 - ., 3.7148, 3.6439, 3.6182, 3.1753, 3.5210, 3.4639, 3.4265 - ., 3.4075, 3.3828, 3.3474, 3.4071, 3.3754, 3.3646, 3.3308 - ., 3.4393, 3.2993, 3.8768, 3.9891, 3.8310, 3.7483, 3.3417 - ., 3.3019, 3.2250, 3.1832, 3.1578, 3.1564, 3.1224, 3.4620 - ., 2.9743, 2.8058, 3.4830, 3.3474, 3.6863, 3.3617, 3.1608 - ., 3.0069, 2.9640, 2.8427, 3.5885, 3.5219, 4.1314, 3.8120 - ./) - r0ab(1191:1260)=(/ - . 3.6015, 3.4502, 3.3498, 3.2777, 3.8635, 3.8232, 3.8486 - ., 3.7215, 3.6487, 3.4724, 3.5627, 3.5087, 3.4757, 3.4517 - ., 3.4423, 3.4139, 4.1028, 3.8388, 3.6745, 3.5562, 3.4806 - ., 3.4272, 4.0182, 3.9991, 4.0007, 3.9282, 3.7238, 3.6498 - ., 3.5605, 3.5211, 3.5009, 3.4859, 3.4785, 3.5621, 4.2623 - ., 3.0775, 2.8275, 4.0181, 3.3385, 3.5379, 3.5036, 3.2589 - ., 3.0804, 3.0094, 2.9003, 4.0869, 3.5088, 3.9105, 3.9833 - ., 3.7176, 3.5323, 3.4102, 3.3227, 4.2702, 4.0888, 3.7560 - ., 3.7687, 3.6681, 3.6405, 3.5569, 3.4990, 3.4659, 3.4433 - ., 3.4330, 3.4092, 3.8867, 4.0190, 3.7961, 3.6412, 3.5405 - ./) - r0ab(1261:1330)=(/ - . 3.4681, 4.3538, 4.2136, 3.9381, 3.8912, 3.9681, 3.7909 - ., 3.6774, 3.6262, 3.5999, 3.5823, 3.5727, 3.5419, 4.0245 - ., 4.1874, 3.0893, 2.7917, 3.7262, 3.3518, 3.4241, 3.5433 - ., 3.2773, 3.0890, 2.9775, 2.9010, 3.8048, 3.5362, 3.7746 - ., 3.7911, 3.7511, 3.5495, 3.4149, 3.3177, 4.0129, 3.8370 - ., 3.7739, 3.7125, 3.7152, 3.7701, 3.5813, 3.5187, 3.4835 - ., 3.4595, 3.4439, 3.4242, 3.7476, 3.8239, 3.8346, 3.6627 - ., 3.5479, 3.4639, 4.1026, 3.9733, 3.9292, 3.8667, 3.9513 - ., 3.8959, 3.7698, 3.7089, 3.6765, 3.6548, 3.6409, 3.5398 - ., 3.8759, 3.9804, 4.0150, 2.9091, 2.7638, 3.5066, 3.3377 - ./) - r0ab(1331:1400)=(/ - . 3.3481, 3.2633, 3.1810, 3.1428, 2.9872, 2.8837, 3.5929 - ., 3.5183, 3.6729, 3.6596, 3.6082, 3.5927, 3.4224, 3.2997 - ., 3.8190, 4.1865, 4.1114, 4.0540, 3.6325, 3.5697, 3.5561 - ., 3.5259, 3.4901, 3.4552, 3.4315, 3.4091, 3.6438, 3.6879 - ., 3.6832, 3.7043, 3.5557, 3.4466, 3.9203, 4.2919, 4.2196 - ., 4.1542, 3.7573, 3.7039, 3.6546, 3.6151, 3.5293, 3.4849 - ., 3.4552, 3.5192, 3.7673, 3.8359, 3.8525, 3.8901, 2.7806 - ., 2.7209, 3.3812, 3.4958, 3.2913, 3.1888, 3.0990, 3.0394 - ., 2.9789, 2.8582, 3.4716, 3.6883, 3.6105, 3.5704, 3.5059 - ., 3.4619, 3.4138, 3.2742, 3.7080, 3.9773, 3.9010, 3.8409 - ./) - r0ab(1401:1470)=(/ - . 3.7944, 3.4465, 3.7235, 3.6808, 3.6453, 3.6168, 3.5844 - ., 3.5576, 3.5772, 3.5959, 3.5768, 3.5678, 3.5486, 3.4228 - ., 3.8107, 4.0866, 4.0169, 3.9476, 3.6358, 3.5800, 3.5260 - ., 3.4838, 3.4501, 3.4204, 3.3553, 3.6487, 3.6973, 3.7398 - ., 3.7405, 3.7459, 3.7380, 2.6848, 2.6740, 3.2925, 3.3386 - ., 3.2473, 3.1284, 3.0301, 2.9531, 2.9602, 2.8272, 3.3830 - ., 3.5358, 3.5672, 3.5049, 3.4284, 3.3621, 3.3001, 3.2451 - ., 3.6209, 3.8299, 3.7543, 3.6920, 3.6436, 3.3598, 3.5701 - ., 3.5266, 3.4904, 3.4590, 3.4364, 3.4077, 3.5287, 3.5280 - ., 3.4969, 3.4650, 3.4304, 3.3963, 3.7229, 3.9402, 3.8753 - ./) - r0ab(1471:1540)=(/ - . 3.8035, 3.5499, 3.4913, 3.4319, 3.3873, 3.3520, 3.3209 - ., 3.2948, 3.5052, 3.6465, 3.6696, 3.6577, 3.6388, 3.6142 - ., 3.5889, 3.3968, 3.0122, 4.2241, 3.7887, 4.0049, 3.5384 - ., 3.2698, 3.1083, 2.9917, 2.9057, 4.3340, 3.9900, 4.6588 - ., 4.1278, 3.8125, 3.6189, 3.4851, 3.3859, 4.6531, 4.3134 - ., 4.2258, 4.1309, 4.0692, 4.0944, 3.9850, 3.9416, 3.9112 - ., 3.8873, 3.8736, 3.8473, 4.6027, 4.1538, 3.8994, 3.7419 - ., 3.6356, 3.5548, 4.8353, 4.5413, 4.3891, 4.3416, 4.3243 - ., 4.2753, 4.2053, 4.1790, 4.1685, 4.1585, 4.1536, 4.0579 - ., 4.1980, 4.4564, 4.2192, 4.0528, 3.9489, 3.8642, 5.0567 - ./) - r0ab(1541:1610)=(/ - . 3.0630, 3.3271, 4.0432, 4.0046, 4.1555, 3.7426, 3.5130 - ., 3.5174, 3.2884, 3.1378, 4.1894, 4.2321, 4.1725, 4.1833 - ., 3.8929, 4.0544, 3.8118, 3.6414, 4.6373, 4.6268, 4.4750 - ., 4.4134, 4.3458, 3.8582, 4.2583, 4.1898, 4.1562, 4.1191 - ., 4.1069, 4.0639, 4.1257, 4.1974, 3.9532, 4.1794, 3.9660 - ., 3.8130, 4.8160, 4.8272, 4.6294, 4.5840, 4.0770, 4.0088 - ., 3.9103, 3.8536, 3.8324, 3.7995, 3.7826, 4.2294, 4.3380 - ., 4.4352, 4.1933, 4.4580, 4.2554, 4.1072, 5.0454, 5.1814 - ., 3.0632, 3.2662, 3.6432, 3.8088, 3.7910, 3.7381, 3.5093 - ., 3.5155, 3.3047, 3.1681, 3.7871, 3.9924, 4.0637, 4.1382 - ./) - r0ab(1611:1680)=(/ - . 3.8591, 4.0164, 3.7878, 3.6316, 4.1741, 4.3166, 4.2395 - ., 4.1831, 4.1107, 3.5857, 4.0270, 3.9676, 3.9463, 3.9150 - ., 3.9021, 3.8708, 4.0240, 4.1551, 3.9108, 4.1337, 3.9289 - ., 3.7873, 4.3666, 4.5080, 4.4232, 4.3155, 3.8461, 3.8007 - ., 3.6991, 3.6447, 3.6308, 3.5959, 3.5749, 4.0359, 4.3124 - ., 4.3539, 4.1122, 4.3772, 4.1785, 4.0386, 4.7004, 4.8604 - ., 4.6261, 2.9455, 3.2470, 3.6108, 3.8522, 3.6625, 3.6598 - ., 3.4411, 3.4660, 3.2415, 3.0944, 3.7514, 4.0397, 3.9231 - ., 4.0561, 3.7860, 3.9845, 3.7454, 3.5802, 4.1366, 4.3581 - ., 4.2351, 4.2011, 4.1402, 3.5381, 4.0653, 4.0093, 3.9883 - ./) - r0ab(1681:1750)=(/ - . 3.9570, 3.9429, 3.9112, 3.8728, 4.0682, 3.8351, 4.1054 - ., 3.8928, 3.7445, 4.3415, 4.5497, 4.3833, 4.3122, 3.8051 - ., 3.7583, 3.6622, 3.6108, 3.5971, 3.5628, 3.5408, 4.0780 - ., 4.0727, 4.2836, 4.0553, 4.3647, 4.1622, 4.0178, 4.5802 - ., 4.9125, 4.5861, 4.6201, 2.9244, 3.2241, 3.5848, 3.8293 - ., 3.6395, 3.6400, 3.4204, 3.4499, 3.2253, 3.0779, 3.7257 - ., 4.0170, 3.9003, 4.0372, 3.7653, 3.9672, 3.7283, 3.5630 - ., 4.1092, 4.3347, 4.2117, 4.1793, 4.1179, 3.5139, 4.0426 - ., 3.9867, 3.9661, 3.9345, 3.9200, 3.8883, 3.8498, 4.0496 - ., 3.8145, 4.0881, 3.8756, 3.7271, 4.3128, 4.5242, 4.3578 - ./) - r0ab(1751:1820)=(/ - . 4.2870, 3.7796, 3.7318, 3.6364, 3.5854, 3.5726, 3.5378 - ., 3.5155, 4.0527, 4.0478, 4.2630, 4.0322, 4.3449, 4.1421 - ., 3.9975, 4.5499, 4.8825, 4.5601, 4.5950, 4.5702, 2.9046 - ., 3.2044, 3.5621, 3.8078, 3.6185, 3.6220, 3.4019, 3.4359 - ., 3.2110, 3.0635, 3.7037, 3.9958, 3.8792, 4.0194, 3.7460 - ., 3.9517, 3.7128, 3.5474, 4.0872, 4.3138, 4.1906, 4.1593 - ., 4.0973, 3.4919, 4.0216, 3.9657, 3.9454, 3.9134, 3.8986 - ., 3.8669, 3.8289, 4.0323, 3.7954, 4.0725, 3.8598, 3.7113 - ., 4.2896, 4.5021, 4.3325, 4.2645, 3.7571, 3.7083, 3.6136 - ., 3.5628, 3.5507, 3.5155, 3.4929, 4.0297, 4.0234, 4.2442 - ./) - r0ab(1821:1890)=(/ - . 4.0112, 4.3274, 4.1240, 3.9793, 4.5257, 4.8568, 4.5353 - ., 4.5733, 4.5485, 4.5271, 2.8878, 3.1890, 3.5412, 3.7908 - ., 3.5974, 3.6078, 3.3871, 3.4243, 3.1992, 3.0513, 3.6831 - ., 3.9784, 3.8579, 4.0049, 3.7304, 3.9392, 3.7002, 3.5347 - ., 4.0657, 4.2955, 4.1705, 4.1424, 4.0800, 3.4717, 4.0043 - ., 3.9485, 3.9286, 3.8965, 3.8815, 3.8500, 3.8073, 4.0180 - ., 3.7796, 4.0598, 3.8470, 3.6983, 4.2678, 4.4830, 4.3132 - ., 4.2444, 3.7370, 3.6876, 3.5935, 3.5428, 3.5314, 3.4958 - ., 3.4730, 4.0117, 4.0043, 4.2287, 3.9939, 4.3134, 4.1096 - ., 3.9646, 4.5032, 4.8356, 4.5156, 4.5544, 4.5297, 4.5083 - ./) - r0ab(1891:1960)=(/ - . 4.4896, 2.8709, 3.1737, 3.5199, 3.7734, 3.5802, 3.5934 - ., 3.3724, 3.4128, 3.1877, 3.0396, 3.6624, 3.9608, 3.8397 - ., 3.9893, 3.7145, 3.9266, 3.6877, 3.5222, 4.0448, 4.2771 - ., 4.1523, 4.1247, 4.0626, 3.4530, 3.9866, 3.9310, 3.9115 - ., 3.8792, 3.8641, 3.8326, 3.7892, 4.0025, 3.7636, 4.0471 - ., 3.8343, 3.6854, 4.2464, 4.4635, 4.2939, 4.2252, 3.7169 - ., 3.6675, 3.5739, 3.5235, 3.5126, 3.4768, 3.4537, 3.9932 - ., 3.9854, 4.2123, 3.9765, 4.2992, 4.0951, 3.9500, 4.4811 - ., 4.8135, 4.4959, 4.5351, 4.5105, 4.4891, 4.4705, 4.4515 - ., 2.8568, 3.1608, 3.5050, 3.7598, 3.5665, 3.5803, 3.3601 - ./) - r0ab(1961:2030)=(/ - . 3.4031, 3.1779, 3.0296, 3.6479, 3.9471, 3.8262, 3.9773 - ., 3.7015, 3.9162, 3.6771, 3.5115, 4.0306, 4.2634, 4.1385 - ., 4.1116, 4.0489, 3.4366, 3.9732, 3.9176, 3.8983, 3.8659 - ., 3.8507, 3.8191, 3.7757, 3.9907, 3.7506, 4.0365, 3.8235 - ., 3.6745, 4.2314, 4.4490, 4.2792, 4.2105, 3.7003, 3.6510 - ., 3.5578, 3.5075, 3.4971, 3.4609, 3.4377, 3.9788, 3.9712 - ., 4.1997, 3.9624, 4.2877, 4.0831, 3.9378, 4.4655, 4.7974 - ., 4.4813, 4.5209, 4.4964, 4.4750, 4.4565, 4.4375, 4.4234 - ., 2.6798, 3.0151, 3.2586, 3.5292, 3.5391, 3.4902, 3.2887 - ., 3.3322, 3.1228, 2.9888, 3.4012, 3.7145, 3.7830, 3.6665 - ./) - r0ab(2031:2100)=(/ - . 3.5898, 3.8077, 3.5810, 3.4265, 3.7726, 4.0307, 3.9763 - ., 3.8890, 3.8489, 3.2706, 3.7595, 3.6984, 3.6772, 3.6428 - ., 3.6243, 3.5951, 3.7497, 3.6775, 3.6364, 3.9203, 3.7157 - ., 3.5746, 3.9494, 4.2076, 4.1563, 4.0508, 3.5329, 3.4780 - ., 3.3731, 3.3126, 3.2846, 3.2426, 3.2135, 3.7491, 3.9006 - ., 3.8332, 3.8029, 4.1436, 3.9407, 3.7998, 4.1663, 4.5309 - ., 4.3481, 4.2911, 4.2671, 4.2415, 4.2230, 4.2047, 4.1908 - ., 4.1243, 2.5189, 2.9703, 3.3063, 3.6235, 3.4517, 3.3989 - ., 3.2107, 3.2434, 3.0094, 2.8580, 3.4253, 3.8157, 3.7258 - ., 3.6132, 3.5297, 3.7566, 3.5095, 3.3368, 3.7890, 4.1298 - ./) - r0ab(2101:2170)=(/ - . 4.0190, 3.9573, 3.9237, 3.2677, 3.8480, 3.8157, 3.7656 - ., 3.7317, 3.7126, 3.6814, 3.6793, 3.6218, 3.5788, 3.8763 - ., 3.6572, 3.5022, 3.9737, 4.3255, 4.1828, 4.1158, 3.5078 - ., 3.4595, 3.3600, 3.3088, 3.2575, 3.2164, 3.1856, 3.8522 - ., 3.8665, 3.8075, 3.7772, 4.1391, 3.9296, 3.7772, 4.2134 - ., 4.7308, 4.3787, 4.3894, 4.3649, 4.3441, 4.3257, 4.3073 - ., 4.2941, 4.1252, 4.2427, 3.0481, 2.9584, 3.6919, 3.5990 - ., 3.8881, 3.4209, 3.1606, 3.1938, 2.9975, 2.8646, 3.8138 - ., 3.7935, 3.7081, 3.9155, 3.5910, 3.4808, 3.4886, 3.3397 - ., 4.1336, 4.1122, 3.9888, 3.9543, 3.8917, 3.5894, 3.8131 - ./) - r0ab(2171:2240)=(/ - . 3.7635, 3.7419, 3.7071, 3.6880, 3.6574, 3.6546, 3.9375 - ., 3.6579, 3.5870, 3.6361, 3.5039, 4.3149, 4.2978, 4.1321 - ., 4.1298, 3.8164, 3.7680, 3.7154, 3.6858, 3.6709, 3.6666 - ., 3.6517, 3.8174, 3.8608, 4.1805, 3.9102, 3.8394, 3.8968 - ., 3.7673, 4.5274, 4.6682, 4.3344, 4.3639, 4.3384, 4.3162 - ., 4.2972, 4.2779, 4.2636, 4.0253, 4.1168, 4.1541, 2.8136 - ., 3.0951, 3.4635, 3.6875, 3.4987, 3.5183, 3.2937, 3.3580 - ., 3.1325, 2.9832, 3.6078, 3.8757, 3.7616, 3.9222, 3.6370 - ., 3.8647, 3.6256, 3.4595, 3.9874, 4.1938, 4.0679, 4.0430 - ., 3.9781, 3.3886, 3.9008, 3.8463, 3.8288, 3.7950, 3.7790 - ./) - r0ab(2241:2310)=(/ - . 3.7472, 3.7117, 3.9371, 3.6873, 3.9846, 3.7709, 3.6210 - ., 4.1812, 4.3750, 4.2044, 4.1340, 3.6459, 3.5929, 3.5036 - ., 3.4577, 3.4528, 3.4146, 3.3904, 3.9014, 3.9031, 4.1443 - ., 3.8961, 4.2295, 4.0227, 3.8763, 4.4086, 4.7097, 4.4064 - ., 4.4488, 4.4243, 4.4029, 4.3842, 4.3655, 4.3514, 4.1162 - ., 4.2205, 4.1953, 4.2794, 2.8032, 3.0805, 3.4519, 3.6700 - ., 3.4827, 3.5050, 3.2799, 3.3482, 3.1233, 2.9747, 3.5971 - ., 3.8586, 3.7461, 3.9100, 3.6228, 3.8535, 3.6147, 3.4490 - ., 3.9764, 4.1773, 4.0511, 4.0270, 3.9614, 3.3754, 3.8836 - ., 3.8291, 3.8121, 3.7780, 3.7619, 3.7300, 3.6965, 3.9253 - ./) - r0ab(2311:2380)=(/ - . 3.6734, 3.9733, 3.7597, 3.6099, 4.1683, 4.3572, 4.1862 - ., 4.1153, 3.6312, 3.5772, 3.4881, 3.4429, 3.4395, 3.4009 - ., 3.3766, 3.8827, 3.8868, 4.1316, 3.8807, 4.2164, 4.0092 - ., 3.8627, 4.3936, 4.6871, 4.3882, 4.4316, 4.4073, 4.3858 - ., 4.3672, 4.3485, 4.3344, 4.0984, 4.2036, 4.1791, 4.2622 - ., 4.2450, 2.7967, 3.0689, 3.4445, 3.6581, 3.4717, 3.4951 - ., 3.2694, 3.3397, 3.1147, 2.9661, 3.5898, 3.8468, 3.7358 - ., 3.9014, 3.6129, 3.8443, 3.6054, 3.4396, 3.9683, 4.1656 - ., 4.0394, 4.0158, 3.9498, 3.3677, 3.8718, 3.8164, 3.8005 - ., 3.7662, 3.7500, 3.7181, 3.6863, 3.9170, 3.6637, 3.9641 - ./) - r0ab(2381:2450)=(/ - . 3.7503, 3.6004, 4.1590, 4.3448, 4.1739, 4.1029, 3.6224 - ., 3.5677, 3.4785, 3.4314, 3.4313, 3.3923, 3.3680, 3.8698 - ., 3.8758, 4.1229, 3.8704, 4.2063, 3.9987, 3.8519, 4.3832 - ., 4.6728, 4.3759, 4.4195, 4.3952, 4.3737, 4.3551, 4.3364 - ., 4.3223, 4.0861, 4.1911, 4.1676, 4.2501, 4.2329, 4.2208 - ., 2.7897, 3.0636, 3.4344, 3.6480, 3.4626, 3.4892, 3.2626 - ., 3.3344, 3.1088, 2.9597, 3.5804, 3.8359, 3.7251, 3.8940 - ., 3.6047, 3.8375, 3.5990, 3.4329, 3.9597, 4.1542, 4.0278 - ., 4.0048, 3.9390, 3.3571, 3.8608, 3.8056, 3.7899, 3.7560 - ., 3.7400, 3.7081, 3.6758, 3.9095, 3.6552, 3.9572, 3.7436 - ./) - r0ab(2451:2520)=(/ - . 3.5933, 4.1508, 4.3337, 4.1624, 4.0916, 3.6126, 3.5582 - ., 3.4684, 3.4212, 3.4207, 3.3829, 3.3586, 3.8604, 3.8658 - ., 4.1156, 3.8620, 4.1994, 3.9917, 3.8446, 4.3750, 4.6617 - ., 4.3644, 4.4083, 4.3840, 4.3625, 4.3439, 4.3253, 4.3112 - ., 4.0745, 4.1807, 4.1578, 4.2390, 4.2218, 4.2097, 4.1986 - ., 2.8395, 3.0081, 3.3171, 3.4878, 3.5360, 3.5145, 3.2809 - ., 3.3307, 3.1260, 2.9940, 3.4741, 3.6675, 3.7832, 3.6787 - ., 3.6156, 3.8041, 3.5813, 3.4301, 3.8480, 3.9849, 3.9314 - ., 3.8405, 3.8029, 3.2962, 3.7104, 3.6515, 3.6378, 3.6020 - ., 3.5849, 3.5550, 3.7494, 3.6893, 3.6666, 3.9170, 3.7150 - ./) - r0ab(2521:2590)=(/ - . 3.5760, 4.0268, 4.1596, 4.1107, 3.9995, 3.5574, 3.5103 - ., 3.4163, 3.3655, 3.3677, 3.3243, 3.2975, 3.7071, 3.9047 - ., 3.8514, 3.8422, 3.8022, 3.9323, 3.7932, 4.2343, 4.4583 - ., 4.3115, 4.2457, 4.2213, 4.1945, 4.1756, 4.1569, 4.1424 - ., 4.0620, 4.0494, 3.9953, 4.0694, 4.0516, 4.0396, 4.0280 - ., 4.0130, 2.9007, 2.9674, 3.8174, 3.5856, 3.6486, 3.5339 - ., 3.2832, 3.3154, 3.1144, 2.9866, 3.9618, 3.8430, 3.9980 - ., 3.8134, 3.6652, 3.7985, 3.5756, 3.4207, 4.4061, 4.2817 - ., 4.1477, 4.0616, 3.9979, 3.6492, 3.8833, 3.8027, 3.7660 - ., 3.7183, 3.6954, 3.6525, 3.9669, 3.8371, 3.7325, 3.9160 - ./) - r0ab(2591:2660)=(/ - . 3.7156, 3.5714, 4.6036, 4.4620, 4.3092, 4.2122, 3.8478 - ., 3.7572, 3.6597, 3.5969, 3.5575, 3.5386, 3.5153, 3.7818 - ., 4.1335, 4.0153, 3.9177, 3.8603, 3.9365, 3.7906, 4.7936 - ., 4.7410, 4.5461, 4.5662, 4.5340, 4.5059, 4.4832, 4.4604 - ., 4.4429, 4.2346, 4.4204, 4.3119, 4.3450, 4.3193, 4.3035 - ., 4.2933, 4.1582, 4.2450, 2.8559, 2.9050, 3.8325, 3.5442 - ., 3.5077, 3.4905, 3.2396, 3.2720, 3.0726, 2.9467, 3.9644 - ., 3.8050, 3.8981, 3.7762, 3.6216, 3.7531, 3.5297, 3.3742 - ., 4.3814, 4.2818, 4.1026, 4.0294, 3.9640, 3.6208, 3.8464 - ., 3.7648, 3.7281, 3.6790, 3.6542, 3.6117, 3.8650, 3.8010 - ./) - r0ab(2661:2730)=(/ - . 3.6894, 3.8713, 3.6699, 3.5244, 4.5151, 4.4517, 4.2538 - ., 4.1483, 3.8641, 3.7244, 3.6243, 3.5589, 3.5172, 3.4973 - ., 3.4715, 3.7340, 4.0316, 3.9958, 3.8687, 3.8115, 3.8862 - ., 3.7379, 4.7091, 4.7156, 4.5199, 4.5542, 4.5230, 4.4959 - ., 4.4750, 4.4529, 4.4361, 4.1774, 4.3774, 4.2963, 4.3406 - ., 4.3159, 4.3006, 4.2910, 4.1008, 4.1568, 4.0980, 2.8110 - ., 2.8520, 3.7480, 3.5105, 3.4346, 3.3461, 3.1971, 3.2326 - ., 3.0329, 2.9070, 3.8823, 3.7928, 3.8264, 3.7006, 3.5797 - ., 3.7141, 3.4894, 3.3326, 4.3048, 4.2217, 4.0786, 3.9900 - ., 3.9357, 3.6331, 3.8333, 3.7317, 3.6957, 3.6460, 3.6197 - ./) - r0ab(2731:2800)=(/ - . 3.5779, 3.7909, 3.7257, 3.6476, 3.5729, 3.6304, 3.4834 - ., 4.4368, 4.3921, 4.2207, 4.1133, 3.8067, 3.7421, 3.6140 - ., 3.5491, 3.5077, 3.4887, 3.4623, 3.6956, 3.9568, 3.8976 - ., 3.8240, 3.7684, 3.8451, 3.6949, 4.6318, 4.6559, 4.4533 - ., 4.4956, 4.4641, 4.4366, 4.4155, 4.3936, 4.3764, 4.1302 - ., 4.3398, 4.2283, 4.2796, 4.2547, 4.2391, 4.2296, 4.0699 - ., 4.1083, 4.0319, 3.9855, 2.7676, 2.8078, 3.6725, 3.4804 - ., 3.3775, 3.2411, 3.1581, 3.1983, 2.9973, 2.8705, 3.8070 - ., 3.7392, 3.7668, 3.6263, 3.5402, 3.6807, 3.4545, 3.2962 - ., 4.2283, 4.1698, 4.0240, 3.9341, 3.8711, 3.5489, 3.7798 - ./) - r0ab(2801:2870)=(/ - . 3.7000, 3.6654, 3.6154, 3.5882, 3.5472, 3.7289, 3.6510 - ., 3.6078, 3.5355, 3.5963, 3.4480, 4.3587, 4.3390, 4.1635 - ., 4.0536, 3.7193, 3.6529, 3.5512, 3.4837, 3.4400, 3.4191 - ., 3.3891, 3.6622, 3.8934, 3.8235, 3.7823, 3.7292, 3.8106 - ., 3.6589, 4.5535, 4.6013, 4.3961, 4.4423, 4.4109, 4.3835 - ., 4.3625, 4.3407, 4.3237, 4.0863, 4.2835, 4.1675, 4.2272 - ., 4.2025, 4.1869, 4.1774, 4.0126, 4.0460, 3.9815, 3.9340 - ., 3.8955, 2.6912, 2.7604, 3.6037, 3.4194, 3.3094, 3.1710 - ., 3.0862, 3.1789, 2.9738, 2.8427, 3.7378, 3.6742, 3.6928 - ., 3.5512, 3.4614, 3.4087, 3.4201, 3.2607, 4.1527, 4.0977 - ./) - r0ab(2871:2940)=(/ - . 3.9523, 3.8628, 3.8002, 3.4759, 3.7102, 3.6466, 3.6106 - ., 3.5580, 3.5282, 3.4878, 3.6547, 3.5763, 3.5289, 3.5086 - ., 3.5593, 3.4099, 4.2788, 4.2624, 4.0873, 3.9770, 3.6407 - ., 3.5743, 3.5178, 3.4753, 3.3931, 3.3694, 3.3339, 3.6002 - ., 3.8164, 3.7478, 3.7028, 3.6952, 3.7669, 3.6137, 4.4698 - ., 4.5488, 4.3168, 4.3646, 4.3338, 4.3067, 4.2860, 4.2645 - ., 4.2478, 4.0067, 4.2349, 4.0958, 4.1543, 4.1302, 4.1141 - ., 4.1048, 3.9410, 3.9595, 3.8941, 3.8465, 3.8089, 3.7490 - ., 2.7895, 2.5849, 3.6484, 3.0162, 3.1267, 3.2125, 3.0043 - ., 2.9572, 2.8197, 2.7261, 3.7701, 3.2446, 3.5239, 3.4696 - ./) - r0ab(2941:3010)=(/ - . 3.4261, 3.3508, 3.1968, 3.0848, 4.1496, 3.6598, 3.5111 - ., 3.4199, 3.3809, 3.5382, 3.2572, 3.2100, 3.1917, 3.1519 - ., 3.1198, 3.1005, 3.5071, 3.5086, 3.5073, 3.4509, 3.3120 - ., 3.2082, 4.2611, 3.8117, 3.6988, 3.5646, 3.6925, 3.6295 - ., 3.5383, 3.4910, 3.4625, 3.4233, 3.4007, 3.2329, 3.6723 - ., 3.6845, 3.6876, 3.6197, 3.4799, 3.3737, 4.4341, 4.0525 - ., 3.9011, 3.8945, 3.8635, 3.8368, 3.8153, 3.7936, 3.7758 - ., 3.4944, 3.4873, 3.9040, 3.7110, 3.6922, 3.6799, 3.6724 - ., 3.5622, 3.6081, 3.5426, 3.4922, 3.4498, 3.3984, 3.4456 - ., 2.7522, 2.5524, 3.5742, 2.9508, 3.0751, 3.0158, 2.9644 - ./) - r0ab(3011:3080)=(/ - . 2.8338, 2.7891, 2.6933, 3.6926, 3.1814, 3.4528, 3.4186 - ., 3.3836, 3.2213, 3.1626, 3.0507, 4.0548, 3.5312, 3.4244 - ., 3.3409, 3.2810, 3.4782, 3.1905, 3.1494, 3.1221, 3.1128 - ., 3.0853, 3.0384, 3.4366, 3.4562, 3.4638, 3.3211, 3.2762 - ., 3.1730, 4.1632, 3.6825, 3.5822, 3.4870, 3.6325, 3.5740 - ., 3.4733, 3.4247, 3.3969, 3.3764, 3.3525, 3.1984, 3.5989 - ., 3.6299, 3.6433, 3.4937, 3.4417, 3.3365, 4.3304, 3.9242 - ., 3.7793, 3.7623, 3.7327, 3.7071, 3.6860, 3.6650, 3.6476 - ., 3.3849, 3.3534, 3.8216, 3.5870, 3.5695, 3.5584, 3.5508 - ., 3.4856, 3.5523, 3.4934, 3.4464, 3.4055, 3.3551, 3.3888 - ./) - r0ab(3081:3150)=(/ - . 3.3525, 2.7202, 2.5183, 3.4947, 2.8731, 3.0198, 3.1457 - ., 2.9276, 2.7826, 2.7574, 2.6606, 3.6090, 3.0581, 3.3747 - ., 3.3677, 3.3450, 3.1651, 3.1259, 3.0147, 3.9498, 3.3857 - ., 3.2917, 3.2154, 3.1604, 3.4174, 3.0735, 3.0342, 3.0096 - ., 3.0136, 2.9855, 2.9680, 3.3604, 3.4037, 3.4243, 3.2633 - ., 3.1810, 3.1351, 4.0557, 3.5368, 3.4526, 3.3699, 3.5707 - ., 3.5184, 3.4085, 3.3595, 3.3333, 3.3143, 3.3041, 3.1094 - ., 3.5193, 3.5745, 3.6025, 3.4338, 3.3448, 3.2952, 4.2158 - ., 3.7802, 3.6431, 3.6129, 3.5853, 3.5610, 3.5406, 3.5204 - ., 3.5036, 3.2679, 3.2162, 3.7068, 3.4483, 3.4323, 3.4221 - ./) - r0ab(3151:3220)=(/ - . 3.4138, 3.3652, 3.4576, 3.4053, 3.3618, 3.3224, 3.2711 - ., 3.3326, 3.2950, 3.2564, 2.5315, 2.6104, 3.2734, 3.2299 - ., 3.1090, 2.9942, 2.9159, 2.8324, 2.8350, 2.7216, 3.3994 - ., 3.4475, 3.4354, 3.3438, 3.2807, 3.2169, 3.2677, 3.1296 - ., 3.7493, 3.8075, 3.6846, 3.6104, 3.5577, 3.2052, 3.4803 - ., 3.4236, 3.3845, 3.3640, 3.3365, 3.3010, 3.3938, 3.3624 - ., 3.3440, 3.3132, 3.4035, 3.2754, 3.8701, 3.9523, 3.8018 - ., 3.7149, 3.3673, 3.3199, 3.2483, 3.2069, 3.1793, 3.1558 - ., 3.1395, 3.4097, 3.5410, 3.5228, 3.5116, 3.4921, 3.4781 - ., 3.4690, 4.0420, 4.1759, 4.0078, 4.0450, 4.0189, 3.9952 - ./) - r0ab(3221:3290)=(/ - . 3.9770, 3.9583, 3.9434, 3.7217, 3.8228, 3.7826, 3.8640 - ., 3.8446, 3.8314, 3.8225, 3.6817, 3.7068, 3.6555, 3.6159 - ., 3.5831, 3.5257, 3.2133, 3.1689, 3.1196, 3.3599, 2.9852 - ., 2.7881, 3.5284, 3.3493, 3.6958, 3.3642, 3.1568, 3.0055 - ., 2.9558, 2.8393, 3.6287, 3.5283, 4.1511, 3.8259, 3.6066 - ., 3.4527, 3.3480, 3.2713, 3.9037, 3.8361, 3.8579, 3.7311 - ., 3.6575, 3.5176, 3.5693, 3.5157, 3.4814, 3.4559, 3.4445 - ., 3.4160, 4.1231, 3.8543, 3.6816, 3.5602, 3.4798, 3.4208 - ., 4.0542, 4.0139, 4.0165, 3.9412, 3.7698, 3.6915, 3.6043 - ., 3.5639, 3.5416, 3.5247, 3.5153, 3.5654, 4.2862, 4.0437 - ./) - r0ab(3291:3360)=(/ - . 3.8871, 3.7741, 3.6985, 3.6413, 4.2345, 4.3663, 4.3257 - ., 4.0869, 4.0612, 4.0364, 4.0170, 3.9978, 3.9834, 3.9137 - ., 3.8825, 3.8758, 3.9143, 3.8976, 3.8864, 3.8768, 3.9190 - ., 4.1613, 4.0566, 3.9784, 3.9116, 3.8326, 3.7122, 3.6378 - ., 3.5576, 3.5457, 4.3127, 3.1160, 2.8482, 4.0739, 3.3599 - ., 3.5698, 3.5366, 3.2854, 3.1039, 2.9953, 2.9192, 4.1432 - ., 3.5320, 3.9478, 4.0231, 3.7509, 3.5604, 3.4340, 3.3426 - ., 4.3328, 3.8288, 3.7822, 3.7909, 3.6907, 3.6864, 3.5793 - ., 3.5221, 3.4883, 3.4649, 3.4514, 3.4301, 3.9256, 4.0596 - ., 3.8307, 3.6702, 3.5651, 3.4884, 4.4182, 4.2516, 3.9687 - ./) - r0ab(3361:3430)=(/ - . 3.9186, 3.9485, 3.8370, 3.7255, 3.6744, 3.6476, 3.6295 - ., 3.6193, 3.5659, 4.0663, 4.2309, 4.0183, 3.8680, 3.7672 - ., 3.6923, 4.5240, 4.4834, 4.1570, 4.3204, 4.2993, 4.2804 - ., 4.2647, 4.2481, 4.2354, 3.8626, 3.8448, 4.2267, 4.1799 - ., 4.1670, 3.8738, 3.8643, 3.8796, 4.0575, 4.0354, 3.9365 - ., 3.8611, 3.7847, 3.7388, 3.6826, 3.6251, 3.5492, 4.0889 - ., 4.2764, 3.1416, 2.8325, 3.7735, 3.3787, 3.4632, 3.5923 - ., 3.3214, 3.1285, 3.0147, 2.9366, 3.8527, 3.5602, 3.8131 - ., 3.8349, 3.7995, 3.5919, 3.4539, 3.3540, 4.0654, 3.8603 - ., 3.7972, 3.7358, 3.7392, 3.8157, 3.6055, 3.5438, 3.5089 - ./) - r0ab(3431:3500)=(/ - . 3.4853, 3.4698, 3.4508, 3.7882, 3.8682, 3.8837, 3.7055 - ., 3.5870, 3.5000, 4.1573, 4.0005, 3.9568, 3.8936, 3.9990 - ., 3.9433, 3.8172, 3.7566, 3.7246, 3.7033, 3.6900, 3.5697 - ., 3.9183, 4.0262, 4.0659, 3.8969, 3.7809, 3.6949, 4.2765 - ., 4.2312, 4.1401, 4.0815, 4.0580, 4.0369, 4.0194, 4.0017 - ., 3.9874, 3.8312, 3.8120, 3.9454, 3.9210, 3.9055, 3.8951 - ., 3.8866, 3.8689, 3.9603, 3.9109, 3.9122, 3.8233, 3.7438 - ., 3.7436, 3.6981, 3.6555, 3.5452, 3.9327, 4.0658, 4.1175 - ., 2.9664, 2.8209, 3.5547, 3.3796, 3.3985, 3.3164, 3.2364 - ., 3.1956, 3.0370, 2.9313, 3.6425, 3.5565, 3.7209, 3.7108 - ./) - r0ab(3501:3570)=(/ - . 3.6639, 3.6484, 3.4745, 3.3492, 3.8755, 4.2457, 3.7758 - ., 3.7161, 3.6693, 3.6155, 3.5941, 3.5643, 3.5292, 3.4950 - ., 3.4720, 3.4503, 3.6936, 3.7392, 3.7388, 3.7602, 3.6078 - ., 3.4960, 3.9800, 4.3518, 4.2802, 3.8580, 3.8056, 3.7527 - ., 3.7019, 3.6615, 3.5768, 3.5330, 3.5038, 3.5639, 3.8192 - ., 3.8883, 3.9092, 3.9478, 3.7995, 3.6896, 4.1165, 4.5232 - ., 4.4357, 4.4226, 4.4031, 4.3860, 4.3721, 4.3580, 4.3466 - ., 4.2036, 4.2037, 3.8867, 4.2895, 4.2766, 4.2662, 4.2598 - ., 3.8408, 3.9169, 3.8681, 3.8250, 3.7855, 3.7501, 3.6753 - ., 3.5499, 3.4872, 3.5401, 3.8288, 3.9217, 3.9538, 4.0054 - ./) - r0ab(3571:3640)=(/ - . 2.8388, 2.7890, 3.4329, 3.5593, 3.3488, 3.2486, 3.1615 - ., 3.1000, 3.0394, 2.9165, 3.5267, 3.7479, 3.6650, 3.6263 - ., 3.5658, 3.5224, 3.4762, 3.3342, 3.7738, 4.0333, 3.9568 - ., 3.8975, 3.8521, 3.4929, 3.7830, 3.7409, 3.7062, 3.6786 - ., 3.6471, 3.6208, 3.6337, 3.6519, 3.6363, 3.6278, 3.6110 - ., 3.4825, 3.8795, 4.1448, 4.0736, 4.0045, 3.6843, 3.6291 - ., 3.5741, 3.5312, 3.4974, 3.4472, 3.4034, 3.7131, 3.7557 - ., 3.7966, 3.8005, 3.8068, 3.8015, 3.6747, 4.0222, 4.3207 - ., 4.2347, 4.2191, 4.1990, 4.1811, 4.1666, 4.1521, 4.1401 - ., 3.9970, 3.9943, 3.9592, 4.0800, 4.0664, 4.0559, 4.0488 - ./) - r0ab(3641:3710)=(/ - . 3.9882, 4.0035, 3.9539, 3.9138, 3.8798, 3.8355, 3.5359 - ., 3.4954, 3.3962, 3.5339, 3.7595, 3.8250, 3.8408, 3.8600 - ., 3.8644, 2.7412, 2.7489, 3.3374, 3.3950, 3.3076, 3.1910 - ., 3.0961, 3.0175, 3.0280, 2.8929, 3.4328, 3.5883, 3.6227 - ., 3.5616, 3.4894, 3.4241, 3.3641, 3.3120, 3.6815, 3.8789 - ., 3.8031, 3.7413, 3.6939, 3.4010, 3.6225, 3.5797, 3.5443 - ., 3.5139, 3.4923, 3.4642, 3.5860, 3.5849, 3.5570, 3.5257 - ., 3.4936, 3.4628, 3.7874, 3.9916, 3.9249, 3.8530, 3.5932 - ., 3.5355, 3.4757, 3.4306, 3.3953, 3.3646, 3.3390, 3.5637 - ., 3.7053, 3.7266, 3.7177, 3.6996, 3.6775, 3.6558, 3.9331 - ./) - r0ab(3711:3780)=(/ - . 4.1655, 4.0879, 4.0681, 4.0479, 4.0299, 4.0152, 4.0006 - ., 3.9883, 3.8500, 3.8359, 3.8249, 3.9269, 3.9133, 3.9025 - ., 3.8948, 3.8422, 3.8509, 3.7990, 3.7570, 3.7219, 3.6762 - ., 3.4260, 3.3866, 3.3425, 3.5294, 3.7022, 3.7497, 3.7542 - ., 3.7494, 3.7370, 3.7216, 3.4155, 3.0522, 4.2541, 3.8218 - ., 4.0438, 3.5875, 3.3286, 3.1682, 3.0566, 2.9746, 4.3627 - ., 4.0249, 4.6947, 4.1718, 3.8639, 3.6735, 3.5435, 3.4479 - ., 4.6806, 4.3485, 4.2668, 4.1690, 4.1061, 4.1245, 4.0206 - ., 3.9765, 3.9458, 3.9217, 3.9075, 3.8813, 3.9947, 4.1989 - ., 3.9507, 3.7960, 3.6925, 3.6150, 4.8535, 4.5642, 4.4134 - ./) - r0ab(3781:3850)=(/ - . 4.3688, 4.3396, 4.2879, 4.2166, 4.1888, 4.1768, 4.1660 - ., 4.1608, 4.0745, 4.2289, 4.4863, 4.2513, 4.0897, 3.9876 - ., 3.9061, 5.0690, 5.0446, 4.6186, 4.6078, 4.5780, 4.5538 - ., 4.5319, 4.5101, 4.4945, 4.1912, 4.2315, 4.5534, 4.4373 - ., 4.4224, 4.4120, 4.4040, 4.2634, 4.7770, 4.6890, 4.6107 - ., 4.5331, 4.4496, 4.4082, 4.3095, 4.2023, 4.0501, 4.2595 - ., 4.5497, 4.3056, 4.1506, 4.0574, 3.9725, 5.0796, 3.0548 - ., 3.3206, 3.8132, 3.9720, 3.7675, 3.7351, 3.5167, 3.5274 - ., 3.3085, 3.1653, 3.9500, 4.1730, 4.0613, 4.1493, 3.8823 - ., 4.0537, 3.8200, 3.6582, 4.3422, 4.5111, 4.3795, 4.3362 - ./) - r0ab(3851:3920)=(/ - . 4.2751, 3.7103, 4.1973, 4.1385, 4.1129, 4.0800, 4.0647 - ., 4.0308, 4.0096, 4.1619, 3.9360, 4.1766, 3.9705, 3.8262 - ., 4.5348, 4.7025, 4.5268, 4.5076, 3.9562, 3.9065, 3.8119 - ., 3.7605, 3.7447, 3.7119, 3.6916, 4.1950, 4.2110, 4.3843 - ., 4.1631, 4.4427, 4.2463, 4.1054, 4.7693, 5.0649, 4.7365 - ., 4.7761, 4.7498, 4.7272, 4.7076, 4.6877, 4.6730, 4.4274 - ., 4.5473, 4.5169, 4.5975, 4.5793, 4.5667, 4.5559, 4.3804 - ., 4.6920, 4.6731, 4.6142, 4.5600, 4.4801, 4.0149, 3.8856 - ., 3.7407, 4.1545, 4.2253, 4.4229, 4.1923, 4.5022, 4.3059 - ., 4.1591, 4.7883, 4.9294, 3.3850, 3.4208, 3.7004, 3.8800 - ./) - r0ab(3921:3990)=(/ - . 3.9886, 3.9040, 3.6719, 3.6547, 3.4625, 3.3370, 3.8394 - ., 4.0335, 4.2373, 4.3023, 4.0306, 4.1408, 3.9297, 3.7857 - ., 4.1907, 4.3230, 4.2664, 4.2173, 4.1482, 3.6823, 4.0711 - ., 4.0180, 4.0017, 3.9747, 3.9634, 3.9383, 4.1993, 4.3205 - ., 4.0821, 4.2547, 4.0659, 3.9359, 4.3952, 4.5176, 4.3888 - ., 4.3607, 3.9583, 3.9280, 3.8390, 3.7971, 3.7955, 3.7674 - ., 3.7521, 4.1062, 4.3633, 4.2991, 4.2767, 4.4857, 4.3039 - ., 4.1762, 4.6197, 4.8654, 4.6633, 4.5878, 4.5640, 4.5422 - ., 4.5231, 4.5042, 4.4901, 4.3282, 4.3978, 4.3483, 4.4202 - ., 4.4039, 4.3926, 4.3807, 4.2649, 4.6135, 4.5605, 4.5232 - ./) - r0ab(3991:4060)=(/ - . 4.4676, 4.3948, 4.0989, 3.9864, 3.8596, 4.0942, 4.2720 - ., 4.3270, 4.3022, 4.5410, 4.3576, 4.2235, 4.6545, 4.7447 - ., 4.7043, 3.0942, 3.2075, 3.5152, 3.6659, 3.8289, 3.7459 - ., 3.5156, 3.5197, 3.3290, 3.2069, 3.6702, 3.8448, 4.0340 - ., 3.9509, 3.8585, 3.9894, 3.7787, 3.6365, 4.1425, 4.1618 - ., 4.0940, 4.0466, 3.9941, 3.5426, 3.8952, 3.8327, 3.8126 - ., 3.7796, 3.7635, 3.7356, 4.0047, 3.9655, 3.9116, 4.1010 - ., 3.9102, 3.7800, 4.2964, 4.3330, 4.2622, 4.2254, 3.8195 - ., 3.7560, 3.6513, 3.5941, 3.5810, 3.5420, 3.5178, 3.8861 - ., 4.1459, 4.1147, 4.0772, 4.3120, 4.1207, 3.9900, 4.4733 - ./) - r0ab(4061:4130)=(/ - . 4.6157, 4.4580, 4.4194, 4.3954, 4.3739, 4.3531, 4.3343 - ., 4.3196, 4.2140, 4.2339, 4.1738, 4.2458, 4.2278, 4.2158 - ., 4.2039, 4.1658, 4.3595, 4.2857, 4.2444, 4.1855, 4.1122 - ., 3.7839, 3.6879, 3.5816, 3.8633, 4.1585, 4.1402, 4.1036 - ., 4.3694, 4.1735, 4.0368, 4.5095, 4.5538, 4.5240, 4.4252 - ., 3.0187, 3.1918, 3.5127, 3.6875, 3.7404, 3.6943, 3.4702 - ., 3.4888, 3.2914, 3.1643, 3.6669, 3.8724, 3.9940, 4.0816 - ., 3.8054, 3.9661, 3.7492, 3.6024, 4.0428, 4.1951, 4.1466 - ., 4.0515, 4.0075, 3.5020, 3.9158, 3.8546, 3.8342, 3.8008 - ., 3.7845, 3.7549, 3.9602, 3.8872, 3.8564, 4.0793, 3.8835 - ./) - r0ab(4131:4200)=(/ - . 3.7495, 4.2213, 4.3704, 4.3300, 4.2121, 3.7643, 3.7130 - ., 3.6144, 3.5599, 3.5474, 3.5093, 3.4853, 3.9075, 4.1115 - ., 4.0473, 4.0318, 4.2999, 4.1050, 3.9710, 4.4320, 4.6706 - ., 4.5273, 4.4581, 4.4332, 4.4064, 4.3873, 4.3684, 4.3537 - ., 4.2728, 4.2549, 4.2032, 4.2794, 4.2613, 4.2491, 4.2375 - ., 4.2322, 4.3665, 4.3061, 4.2714, 4.2155, 4.1416, 3.7660 - ., 3.6628, 3.5476, 3.8790, 4.1233, 4.0738, 4.0575, 4.3575 - ., 4.1586, 4.0183, 4.4593, 4.5927, 4.4865, 4.3813, 4.4594 - ., 2.9875, 3.1674, 3.4971, 3.6715, 3.7114, 3.6692, 3.4446 - ., 3.4676, 3.2685, 3.1405, 3.6546, 3.8579, 3.9637, 4.0581 - ./) - r0ab(4201:4270)=(/ - . 3.7796, 3.9463, 3.7275, 3.5792, 4.0295, 4.1824, 4.1247 - ., 4.0357, 3.9926, 3.4827, 3.9007, 3.8392, 3.8191, 3.7851 - ., 3.7687, 3.7387, 3.9290, 3.8606, 3.8306, 4.0601, 3.8625 - ., 3.7269, 4.2062, 4.3566, 4.3022, 4.1929, 3.7401, 3.6888 - ., 3.5900, 3.5350, 3.5226, 3.4838, 3.4594, 3.8888, 4.0813 - ., 4.0209, 4.0059, 4.2810, 4.0843, 3.9486, 4.4162, 4.6542 - ., 4.5005, 4.4444, 4.4196, 4.3933, 4.3741, 4.3552, 4.3406 - ., 4.2484, 4.2413, 4.1907, 4.2656, 4.2474, 4.2352, 4.2236 - ., 4.2068, 4.3410, 4.2817, 4.2479, 4.1921, 4.1182, 3.7346 - ., 3.6314, 3.5168, 3.8582, 4.0927, 4.0469, 4.0313, 4.3391 - ./) - r0ab(4271:4340)=(/ - . 4.1381, 3.9962, 4.4429, 4.5787, 4.4731, 4.3588, 4.4270 - ., 4.3957, 2.9659, 3.1442, 3.4795, 3.6503, 3.6814, 3.6476 - ., 3.4222, 3.4491, 3.2494, 3.1209, 3.6324, 3.8375, 3.9397 - ., 3.8311, 3.7581, 3.9274, 3.7085, 3.5598, 4.0080, 4.1641 - ., 4.1057, 4.0158, 3.9726, 3.4667, 3.8802, 3.8188, 3.7989 - ., 3.7644, 3.7474, 3.7173, 3.9049, 3.8424, 3.8095, 4.0412 - ., 3.8436, 3.7077, 4.1837, 4.3366, 4.2816, 4.1686, 3.7293 - ., 3.6709, 3.5700, 3.5153, 3.5039, 3.4684, 3.4437, 3.8663 - ., 4.0575, 4.0020, 3.9842, 4.2612, 4.0643, 3.9285, 4.3928 - ., 4.6308, 4.4799, 4.4244, 4.3996, 4.3737, 4.3547, 4.3358 - ./) - r0ab(4341:4410)=(/ - . 4.3212, 4.2275, 4.2216, 4.1676, 4.2465, 4.2283, 4.2161 - ., 4.2045, 4.1841, 4.3135, 4.2562, 4.2226, 4.1667, 4.0932 - ., 3.7134, 3.6109, 3.4962, 3.8352, 4.0688, 4.0281, 4.0099 - ., 4.3199, 4.1188, 3.9768, 4.4192, 4.5577, 4.4516, 4.3365 - ., 4.4058, 4.3745, 4.3539, 2.8763, 3.1294, 3.5598, 3.7465 - ., 3.5659, 3.5816, 3.3599, 3.4024, 3.1877, 3.0484, 3.7009 - ., 3.9451, 3.8465, 3.9873, 3.7079, 3.9083, 3.6756, 3.5150 - ., 4.0829, 4.2780, 4.1511, 4.1260, 4.0571, 3.4865, 3.9744 - ., 3.9150, 3.8930, 3.8578, 3.8402, 3.8073, 3.7977, 4.0036 - ., 3.7604, 4.0288, 3.8210, 3.6757, 4.2646, 4.4558, 4.2862 - ./) - r0ab(4411:4465)=(/ - . 4.2122, 3.7088, 3.6729, 3.5800, 3.5276, 3.5165, 3.4783 - ., 3.4539, 3.9553, 3.9818, 4.2040, 3.9604, 4.2718, 4.0689 - ., 3.9253, 4.4869, 4.7792, 4.4918, 4.5342, 4.5090, 4.4868 - ., 4.4680, 4.4486, 4.4341, 4.2023, 4.3122, 4.2710, 4.3587 - ., 4.3407, 4.3281, 4.3174, 4.1499, 4.3940, 4.3895, 4.3260 - ., 4.2725, 4.1961, 3.7361, 3.6193, 3.4916, 3.9115, 3.9914 - ., 3.9809, 3.9866, 4.3329, 4.1276, 3.9782, 4.5097, 4.6769 - ., 4.5158, 4.3291, 4.3609, 4.3462, 4.3265, 4.4341 - ./) - - k=0 - do i=1,max_elem - do j=1,i - k=k+1 - r(i,j)=r0ab(k)/autoang - r(j,i)=r0ab(k)/autoang - enddo - enddo - - end subroutine setr0ab - - - - SUBROUTINE SET_CRITERIA(rthr,lat,tau_max) - - REAL*8 :: r_cutoff,rthr - REAL*8 :: lat(3,3) - REAL*8 :: tau_max(3) - REAL*8 :: norm1(3),norm2(3),norm3(3) - REAL*8 :: cos10,cos21,cos32 - real*8,external :: vectorsize - - r_cutoff=sqrt(rthr) -c ! write(*,*) 'lat',lat - !c find normal to the plane... - call kreuzprodukt(lat(:,2),lat(:,3),norm1) - call kreuzprodukt(lat(:,3),lat(:,1),norm2) - call kreuzprodukt(lat(:,1),lat(:,2),norm3) -c !write(*,*) 'norm2',norm2 - !c ...normalize it... - norm1=norm1/VECTORSIZE(norm1) - norm2=norm2/VECTORSIZE(norm2) - norm3=norm3/VECTORSIZE(norm3) -c !write(*,*) 'norm2_',norm2 - !c cos angles between normals and lattice vectors - cos10=SUM(norm1*lat(:,1)) - cos21=SUM(norm2*lat(:,2)) - cos32=SUM(norm3*lat(:,3)) - !write(*,*) 'cos32',cos32 - !tau_max(1)=abs(2*r_cutoff/cos10) - !tau_max(2)=abs(2*r_cutoff/cos21) - !tau_max(3)=abs(2*r_cutoff/cos32) - !write(*,*) 'r_cutoff',r_cutoff - tau_max(1)=abs(r_cutoff/cos10) - tau_max(2)=abs(r_cutoff/cos21) - tau_max(3)=abs(r_cutoff/cos32) -c !write(*,'(3f8.4)')tau_max(1),tau_max(2),tau_max(3) - END SUBROUTINE SET_CRITERIA - - - SUBROUTINE kreuzprodukt(A,B,C) - IMPLICIT NONE - - REAL*8 :: A(3),B(3) - REAL*8 :: X,Y,Z - REAL*8 :: C(3) - - X=A(2)*B(3)-B(2)*A(3) - Y=A(3)*B(1)-B(3)*A(1) - Z=A(1)*B(2)-B(1)*A(2) - C=(/X,Y,Z/) - END SUBROUTINE kreuzprodukt - - FUNCTION VECTORSIZE(VECT) - - REAL*8 :: VECT(3) - REAL*8 :: SVECT(3) - REAL*8 :: VECTORSIZE - - SVECT=VECT*VECT - VECTORSIZE=SUM(SVECT) - VECTORSIZE=VECTORSIZE**(0.5) - END FUNCTION VECTORSIZE - - subroutine getc6(maxc,max_elem,c6ab,mxc,iat,jat,nci,ncj,c6) - implicit none - integer maxc,max_elem - integer iat,jat,i,j,mxc(max_elem) - real*8 nci,ncj,c6,c6mem - real*8 c6ab(max_elem,max_elem,maxc,maxc,3) - real*8 cn1,cn2,r,rsum,csum,tmp,tmp1 - real*8 r_save - include 'param' - - c6mem=-1.d+99 - rsum=0.0d0 - csum=0.0d0 - c6 =0.0d0 - r_save=1.0d99 - do i=1,mxc(iat) - do j=1,mxc(jat) - c6=c6ab(iat,jat,i,j,1) - if(c6.gt.0)then -! c6mem=c6 - cn1=c6ab(iat,jat,i,j,2) - cn2=c6ab(iat,jat,i,j,3) - r=(cn1-nci)**2+(cn2-ncj)**2 - if (r.lt.r_save) then - r_save=r - c6mem=c6 - endif - tmp1=exp(k3*r) - rsum=rsum+tmp1 - csum=csum+tmp1*c6 - endif - enddo - enddo - - if(rsum.gt.1.0d-99)then - c6=csum/rsum - else - c6=c6mem - endif - - end subroutine getc6 - - subroutine pbcncoord(natoms,rcov,iz,xyz,cn,lat,rep_cn,crit_cn) - implicit none - include 'param' - integer,intent(in) :: natoms,iz(*) - real*8,intent(in) :: rcov(94) - - integer i,max_elem,rep_cn(3) - real*8 xyz(3,*),cn(*),lat(3,3) - - integer iat,taux,tauy,tauz - real*8 dx,dy,dz,r,damp,xn,rr,rco,tau(3) - real*8, INTENT(IN) :: crit_cn - - do i=1,natoms - xn=0.0d0 - do iat=1,natoms - do taux=-rep_cn(1),rep_cn(1) - do tauy=-rep_cn(2),rep_cn(2) - do tauz=-rep_cn(3),rep_cn(3) - if(iat.eq.i .and. taux.eq.0 .and. tauy.eq.0 .and. - . tauz.eq.0) cycle - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - dx=xyz(1,iat)-xyz(1,i)+tau(1) - dy=xyz(2,iat)-xyz(2,i)+tau(2) - dz=xyz(3,iat)-xyz(3,i)+tau(3) - r=(dx*dx+dy*dy+dz*dz) - if (r.gt.crit_cn) cycle - r=sqrt(r) - rco=rcov(iz(i))+rcov(iz(iat)) - rr=rco/r - damp=1.d0/(1.d0+exp(-k1*(rr-1.0d0))) - xn=xn+damp - - enddo !tauz - enddo !tauy - enddo !taux - enddo !iat - cn(i)=xn - enddo !i - - end subroutine pbcncoord - - subroutine pbcedisp(max_elem,maxc,n,xyz,iz,c6ab,mxc,r2r4,r0ab, - . rcov,rs6,rs8,rs10,alp6,alp8,alp10,version,noabc, - . e6,e8,e10,e12,e63,lat,rthr,rep_vdw,cn_thr,rep_cn) - implicit none - integer max_elem,maxc - real*8 r2r4(max_elem),rcov(max_elem) - real*8 rs6,rs8,rs10,alp6,alp8,alp10 - real*8 rthr,cn_thr,crit_cn - integer rep_vdw(3),rep_cn(3) - integer n,iz(*),version,mxc(max_elem) - - real*8 xyz(3,*),r0ab(max_elem,max_elem),lat(3,3)!,r2r4(*) -! real*8 rs6,rs8,rs10,alp6,alp8,alp10,rcov(max_elem) - real*8 c6ab(max_elem,max_elem,maxc,maxc,3) - real*8 e6, e8, e10, e12, e63!,crit_vdw,crit_cn - logical noabc - - integer iat,jat,kat - real*8 r,r2,r6,r8,tmp,dx,dy,dz,c6,c8,c10,ang,rav,R0 - real*8 damp6,damp8,damp10,rr,thr,c9,r42,c12,r10,c14 - real*8 cn(n),rxyz(3),dxyz(3) - real*8 r2ab(n*n),cc6ab(n*n),dmp(n*n),d2(3),t1,t2,t3,tau(3) - integer lin,ij,ik,jk - integer taux,tauy,tauz,counter - real*8 a1,a2 !BJ-parameter - real*8 bj_dmp6,bj_dmp8 - real*8 tmp1,tmp2 - - e6 =0 - e8 =0 - e10=0 - e12=0 - e63=0 - tau=(/0.0,0.0,0.0/) - counter=0 - crit_cn=cn_thr -c Becke-Johnson parameters - a1=rs6 - a2=rs8 - - if(version.eq.1)then -C DFT-D3(zero-damping) - !write(*,*)"1 open" - call pbcncoord(n,rcov,iz,xyz,cn,lat,rep_cn,crit_cn) - - do iat=1,n-1 - do jat=iat+1,n -c get C6 - call getc6(maxc,max_elem,c6ab,mxc,iz(iat),iz(jat), - . cn(iat),cn(jat),c6) - - if(.not.noabc)then - ij=lin(jat,iat) -c store C6 for C9, calc as sqrt - cc6ab(ij)=sqrt(c6) - endif - do taux=-rep_vdw(1),rep_vdw(1) - do tauy=-rep_vdw(2),rep_vdw(2) - do tauz=-rep_vdw(3),rep_vdw(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - dx=xyz(1,iat)-xyz(1,jat)+tau(1) - dy=xyz(2,iat)-xyz(2,jat)+tau(2) - dz=xyz(3,iat)-xyz(3,jat)+tau(3) - r2=dx*dx+dy*dy+dz*dz -c cutoff - - if(r2.gt.rthr) cycle - r =sqrt(r2) - R0=r0ab(iz(jat),iz(iat)) - rr=R0/r -C DFT-D3 zero-damp - tmp=rs6*rr - damp6 =1.d0/( 1.d0+6.d0*tmp**alp6 ) - tmp=rs8*rr - damp8 =1.d0/( 1.d0+6.d0*tmp**alp8 ) - - - r6=r2**3 - e6 =e6+damp6/r6* c6 - - -c stored in main as sqrt - c8 =3.0d0*r2r4(iz(iat))*r2r4(iz(jat))*c6 - r8 =r6*r2 - - e8 =e8+c8*damp8/r8 - - enddo !tauz - enddo !tauy - enddo !taux - enddo !jat - enddo !iat - - do iat=1,n - jat=iat -c get C6 - call getc6(maxc,max_elem,c6ab,mxc,iz(iat),iz(jat), - . cn(iat),cn(jat),c6) - - if(.not.noabc)then - ij=lin(jat,iat) -c store C6 for C9, calc as sqrt - cc6ab(ij)=sqrt(c6) - endif - do taux=-rep_vdw(1),rep_vdw(1) - do tauy=-rep_vdw(2),rep_vdw(2) - do tauz=-rep_vdw(3),rep_vdw(3) - if (taux.eq.0 .and. tauy.eq.0 .and. tauz.eq.0) cycle - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - dx=tau(1) - dy=tau(2) - dz=tau(3) - r2=dx*dx+dy*dy+dz*dz -c cutoff - if(r2.gt.rthr) cycle - r =sqrt(r2) - R0=r0ab(iz(jat),iz(iat)) - rr=R0/r - -C DFT-D3 zero-damp - tmp=rs6*rr - damp6 =1.d0/( 1.d0+6.d0*tmp**alp6 ) - tmp=rs8*rr - damp8 =1.d0/( 1.d0+6.d0*tmp**alp8 ) - - - - r6=r2**3 - - e6 =e6+damp6/r6*0.50d0 *C6 - -c stored in main as sqrt - c8 =3.0d0*r2r4(iz(iat))*r2r4(iz(jat)) *C6 - r8 =r6*r2 - - e8 =e8+c8*damp8/r8*0.50d0 - counter=counter+1 - - enddo !tauz - enddo !tauy - enddo !taux - enddo !iat -! write(*,*)'counter(edisp): ',counter - else if(version.eq.2) then - !write(*,*)"open 2" - -C DFT-D3(BJ-damping) - call pbcncoord(n,rcov,iz,xyz,cn,lat,rep_cn,crit_cn) - - do iat=1,n - do jat=iat+1,n -c get C6 - call getc6(maxc,max_elem,c6ab,mxc,iz(iat),iz(jat), - . cn(iat),cn(jat),c6) - - rxyz=xyz(:,iat)-xyz(:,jat) - r42=r2r4(iz(iat))*r2r4(iz(jat)) - bj_dmp6=(a1*dsqrt(3.0d0*r42)+a2)**6 - bj_dmp8=(a1*dsqrt(3.0d0*r42)+a2)**8 - - if(.not.noabc)then - ij=lin(jat,iat) -c store C6 for C9, calc as sqrt - cc6ab(ij)=sqrt(c6) - endif - do taux=-rep_vdw(1),rep_vdw(1) - do tauy=-rep_vdw(2),rep_vdw(2) - do tauz=-rep_vdw(3),rep_vdw(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - dxyz=rxyz+tau - - r2=sum(dxyz*dxyz) -c cutoff - if(r2.gt.rthr) cycle - r =sqrt(r2) - rr=r0ab(iz(jat),iz(iat))/r - - - r6=r2**3 - - e6 =e6+c6/(r6+bj_dmp6) - -c stored in main as sqrt - c8 =3.0d0*c6*r42 - r8 =r6*r2 - - e8 =e8+c8/(r8+bj_dmp8) - - counter=counter+1 - - enddo !tauz - enddo !tauy - enddo !taux - enddo !jat - -! Now the self interaction - jat=iat -c get C6 - call getc6(maxc,max_elem,c6ab,mxc,iz(iat),iz(jat), - . cn(iat),cn(jat),c6) - r42=r2r4(iz(iat))*r2r4(iz(iat)) - bj_dmp6=(a1*dsqrt(3.0d0*r42)+a2)**6 - bj_dmp8=(a1*dsqrt(3.0d0*r42)+a2)**8 - - if(.not.noabc)then - ij=lin(jat,iat) -c store C6 for C9, calc as sqrt - cc6ab(ij)=dsqrt(c6) - endif - - do taux=-rep_vdw(1),rep_vdw(1) - do tauy=-rep_vdw(2),rep_vdw(2) - do tauz=-rep_vdw(3),rep_vdw(3) - if (taux.eq.0 .and. tauy.eq.0 .and. tauz.eq.0) cycle - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - r2=sum(tau*tau) -c cutoff - if(r2.gt.rthr) cycle - r =sqrt(r2) - rr=r0ab(iz(jat),iz(iat))/r - - - r6=r2**3 - - e6 =e6+c6/(r6+bj_dmp6)*0.50d0 - -c stored in main as sqrt - c8 =3.0d0*c6*r42 - r8 =r6*r2 - - e8 =e8+c8/(r8+bj_dmp8)*0.50d0 - counter=counter+1 - - enddo !tauz - enddo !tauy - enddo !taux - enddo !iat - - - endif !version - - if(noabc)return - -C compute non-additive third-order energy using averaged C6 - call pbcthreebody(max_elem,xyz,lat,n,iz,rep_cn,crit_cn, - . cc6ab,r0ab,e63) - - end subroutine pbcedisp - - - SUBROUTINE pbcthreebody(max_elem,xyz,lat,n,iz,repv,cnthr,cc6ab, - . r0ab,eabc) - IMPLICIT NONE - integer max_elem - INTEGER :: n,i,j,k,jtaux,jtauy,jtauz,iat,jat,kat - INTEGER :: ktaux,ktauy,ktauz,counter,ij,ik,jk,idum - REAL*8 :: dx,dy,dz,rij2,rik2,rjk2,c9,rr0ij,rr0ik - REAL*8 :: rr0jk,geomean,fdamp,rik,rjk,rij - REAL*8 :: r0ij,r0ik,r0jk - REAL*8,INTENT(OUT)::eabc - REAL*8 :: tmp,tmp1,tmp2,tmp3,tmp4,ang - - REAL*8 ,DIMENSION(3,3),INTENT(IN)::lat - REAL*8 ,DIMENSION(3,*),INTENT(IN) :: xyz - INTEGER,DIMENSION(*),INTENT(IN)::iz - REAL*8,DIMENSION(3):: jtau,ktau,jxyz,kxyz,ijvec,ikvec,jkvec,dumvec - INTEGER,DIMENSION(3):: repv - REAL*8,INTENT(IN) ::cnthr - REAL*8,DIMENSION(n*n),INTENT(IN)::cc6ab - REAL*8,DIMENSION(max_elem,max_elem),INTENT(IN):: r0ab - REAL*8,PARAMETER::sr9=0.75d0 !reciprocal radii scaling parameter for damping function (s_r=4/3) - REAL*8,PARAMETER::alp9=-16.0d0 !alpha saved with "-" sign - INTEGER,EXTERNAL :: lin - REAL*8 :: abcthr - INTEGER, DIMENSION(3) :: repmin,repmax -! REAL*8 :: time1,time2 - - counter=0 - eabc=0.0d0 - abcthr=cnthr -! abcthr=1.0d99 -! write(*,*)'thr:',(abcthr) - -! call cpu_time(time1) - - do iat=3,n - do jat=2,iat-1 - ijvec=xyz(:,jat)-xyz(:,iat) - ij=lin(iat,jat) - r0ij=r0ab(iz(iat),iz(jat)) - do kat=1,jat-1 - ik=lin(iat,kat) - jk=lin(jat,kat) - ikvec=xyz(:,kat)-xyz(:,iat) - jkvec=xyz(:,kat)-xyz(:,jat) - c9=-1.0d0*(cc6ab(ij)*cc6ab(ik)*cc6ab(jk)) - - r0ik=r0ab(iz(iat),iz(kat)) - r0jk=r0ab(iz(jat),iz(kat)) - - - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=ijvec+jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - - rr0ij=DSQRT(rij2)/r0ij - - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ikvec+ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=DSQRT(rik2)/r0ik - - dumvec=jkvec+ktau-jtau - rjk2=SUM(dumvec*dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=DSQRT(rjk2)/r0jk - - - geomean=(rr0ij*rr0ik*rr0jk)**(1.0d0/3.0d0) -! write(*,*)'geomean:',geomean - fdamp=1./(1.+6.*(sr9*geomean)**alp9) !alp9 is already saved with "-" - tmp1 = (rij2+rjk2-rik2) - tmp2 = (rij2+rik2-rjk2) - tmp3 = (rik2+rjk2-rij2) - tmp4=rij2*rjk2*rik2 - ang=(0.375d0*tmp1*tmp2*tmp3/tmp4+1.0d0)/tmp4**1.5d0 - - eabc=eabc+ang*c9*fdamp - - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - - ENDDO !kat - ENDDO !jat - ENDDO !iat - - DO iat=2,n - jat=iat - ij=lin(iat,jat) - ijvec=0.0d0 - r0ij=r0ab(iz(iat),iz(jat)) - DO kat=1,iat-1 - jk=lin(jat,kat) - ik=jk - ikvec=xyz(:,kat)-xyz(:,iat) - jkvec=ikvec - c9=-(cc6ab(ij)*cc6ab(ik)*cc6ab(jk)) - - r0ik=r0ab(iz(iat),iz(kat)) - r0jk=r0ab(iz(jat),iz(kat)) - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - IF (jtaux.eq.0 .and. jtauy.eq.0 .and. jtauz.eq.0) cycle - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=ijvec+jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - - rr0ij=DSQRT(rij2)/r0ij - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) -! every result * 0.5 - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ikvec+ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=DSQRT(rik2)/r0ik - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=DSQRT(rjk2)/r0jk - - - geomean=(rr0ij*rr0ik*rr0jk)**(1./3.) - fdamp=1./(1.+6.*(sr9*geomean)**alp9) - tmp1 = (rij2+rjk2-rik2) - tmp2 = (rij2+rik2-rjk2) - tmp3 = (rik2+rjk2-rij2) - tmp4=rij2*rjk2*rik2 - ang=(0.375d0*tmp1*tmp2*tmp3/tmp4+1.0d0)/tmp4**1.5d0 - - eabc=eabc+c9*fdamp*ang/2.0 - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - ENDDO !kat - ENDDO !iat - ! And now kat=jat, but cycling throug all imagecells without jtau=ktau. and jat>iat going though all cells - ! But this counts only 1/2 - - DO iat=2,n - DO jat=1,iat-1 - kat=jat - ij=lin(iat,jat) - jk=lin(jat,kat) - ik=ij - ikvec=xyz(:,kat)-xyz(:,iat) - ijvec=ikvec - jkvec=0.0d0 - c9=-(cc6ab(ij)*cc6ab(ik)*cc6ab(jk)) - - r0ij=r0ab(iz(iat),iz(jat)) - r0ik=r0ij - r0jk=r0ab(iz(jat),iz(kat)) - - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=ijvec+jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - - rr0ij=DSQRT(rij2)/r0ij - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) -! every result * 0.5 - IF (jtaux.eq.ktaux .and. jtauy.eq.ktauy - . .and. jtauz.eq.ktauz) cycle - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ikvec+ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=DSQRT(rik2)/r0ik - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=DSQRT(rjk2)/r0jk - - - geomean=(rr0ij*rr0ik*rr0jk)**(1./3.) - fdamp=1./(1.+6.*(sr9*geomean)**alp9) - tmp1 = (rij2+rjk2-rik2) - tmp2 = (rij2+rik2-rjk2) - tmp3 = (rik2+rjk2-rij2) - tmp4=rij2*rjk2*rik2 - ang=(0.375d0*tmp1*tmp2*tmp3/tmp4+1.0d0)/tmp4**1.5d0 - - eabc=eabc+c9*fdamp*ang/2.0 - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - ENDDO !kat - ENDDO !iat - - -! And finally the self interaction iat=jat=kat all - - idum=0 - DO iat=1,n - jat=iat - kat=iat - ijvec=0.0d0 - ij=lin(iat,iat) - ik=ij - jk=ij - ikvec=ijvec - jkvec=ikvec - c9=-(cc6ab(ij)*cc6ab(ik)*cc6ab(jk)) - - r0ij=r0ab(iz(iat),iz(iat)) - r0ik=r0ij - r0jk=r0ij - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - IF (jtaux.eq.0 .and. jtauy.eq.0 .and. jtauz.eq.0) cycle - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - rr0ij=DSQRT(rij2)/r0ij - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) - IF ((ktaux.eq.0) .and.( ktauy.eq.0) .and.( ktauz.eq.0))cycle !IF iat and kat are the same then cycle - IF ((ktaux.eq.jtaux) .and. (ktauy.eq.jtauy) - . .and. (ktauz.eq.jtauz)) cycle !If kat and jat are the same then cycle - -! every result * 1/6 becaues every triple is counted twice due to the two loops jtau and ktau going from -repv to repv -> *1/2 -! -!plus 1/3 becaues every triple is three times in each unitcell - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=DSQRT(rik2)/r0ik - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=DSQRT(rjk2)/r0jk - - - geomean=(rr0ij*rr0ik*rr0jk)**(1./3.) - fdamp=1./(1.+6.*(sr9*geomean)**alp9) - tmp1 = (rij2+rjk2-rik2) - tmp2 = (rij2+rik2-rjk2) - tmp3 = (rik2+rjk2-rij2) - tmp4=rij2*rjk2*rik2 - ang=(0.375d0*tmp1*tmp2*tmp3/tmp4+1.0d0)/tmp4**1.5d0 - - eabc=eabc+c9*fdamp*ang/6.0d0 - - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - - - ENDDO !iat - - END SUBROUTINE pbcthreebody - - integer function lin(i1,i2) - integer i1,i2,idum1,idum2 - idum1=max(i1,i2) - idum2=min(i1,i2) - lin=idum2+idum1*(idum1-1)/2 - return - end function lin - - subroutine get_dC6_dCNij(maxc,max_elem,c6ab,mxci,mxcj,cni,cnj, - . izi,izj,iat,jat,c6check,dc6i,dc6j) - - IMPLICIT NONE - include 'param' - integer maxc,max_elem - real*8 c6ab(max_elem,max_elem,maxc,maxc,3) - integer mxci,mxcj !mxc(iz(iat)) - real*8 cni,cnj,term - integer iat,jat,izi,izj - real*8 dc6i,dc6j,c6check - - - integer i,j,a,b - real*8 zaehler,nenner,dzaehler_i,dnenner_i,dzaehler_j,dnenner_j - real*8 expterm,cn_refi,cn_refj,c6ref,r - real*8 c6mem,r_save - - - - c6mem=-1.d99 - r_save=9999.0 - zaehler=0.0d0 - nenner=0.0d0 - - dzaehler_i=0.d0 - dnenner_i=0.d0 - dzaehler_j=0.d0 - dnenner_j=0.d0 - - - DO a=1,mxci - DO b=1,mxcj - c6ref=c6ab(izi,izj,a,b,1) - if (c6ref.gt.0) then -! c6mem=c6ref - cn_refi=c6ab(izi,izj,a,b,2) - cn_refj=c6ab(izi,izj,a,b,3) - r=(cn_refi-cni)*(cn_refi-cni)+(cn_refj-cnj)*(cn_refj-cnj) - if (r.lt.r_save) then - r_save=r - c6mem=c6ref - endif - expterm=exp(k3*r) - zaehler=zaehler+c6ref*expterm - nenner=nenner+expterm - expterm=expterm*2.d0*k3 - term=expterm*(cni-cn_refi) - dzaehler_i=dzaehler_i+c6ref*term - dnenner_i =dnenner_i + term - - term=expterm*(cnj-cn_refj) - dzaehler_j=dzaehler_j+c6ref*term - dnenner_j =dnenner_j + term - endif - ENDDO !b - ENDDO !a - - if (nenner.gt.1.0d-99) then - c6check=zaehler/nenner - dc6i=((dzaehler_i*nenner)-(dnenner_i*zaehler)) - . /(nenner*nenner) - dc6j=((dzaehler_j*nenner)-(dnenner_j*zaehler)) - . /(nenner*nenner) - else - c6check=c6mem - dc6i=0.0d0 - dc6j=0.0d0 - endif - end subroutine get_dC6_dCNij - - - subroutine pbcgdisp(max_elem,maxc,n,xyz,iz,c6ab,mxc,r2r4,r0ab, - . rcov,s6,s18,rs6,rs8,rs10,alp6,alp8,alp10,noabc, - . version,g,disp,stress,sigma,lat,rep_v,rep_cn, - . crit_vdw,crit_cn) - - implicit none - include 'param' - integer n,iz(*),max_elem,maxc,version,mxc(max_elem) - real*8 xyz(3,*),r0ab(max_elem,max_elem),r2r4(*) - real*8 c6ab(max_elem,max_elem,maxc,maxc,3) - real*8 g(3,*),s6,s18,rcov(max_elem) - real*8 rs6,rs8,rs10,alp10,alp8,alp6 - real*8 a1,a2 !BJ-parameters - real*8 bj_dmp6,bj_dmp8 ! precalculated dampingterms - logical noabc -c coversion factors - REAL*8, parameter ::autoang =0.52917726d0 - REAL*8, parameter ::autokcal=627.509541d0 - REAL*8, parameter ::autoev=27.211652d0 - - integer iat,jat,i,j,kat,my,ny,a,b,idum,tau2 - real*8 R0,C6,alp,R42,disp,x1,y1,z1,x2,y2,z2,rr,e6abc,fdum - real*8 dx,dy,dz,r2,r,r4,r6,r8,r10,r12,t6,t8,t10,damp1 - real*8 damp6,damp8,damp9,e6,e8,e10,e12,tmp1 - real*8 s10,s8,gC6(3),term,step,dispr,displ,r235,tmp2 - real*8 cn(n),gx1,gy1,gz1,gx2,gy2,gz2,rthr,testsum - real*8, DIMENSION(3,3) :: lat,stress,sigma,virialstress,lat_1 - real*8, DIMENSION(3,3) :: gC6_stress - integer, DIMENSION(3) :: rep_v,rep_cn - real*8 crit_vdw,crit_cn - integer taux,tauy,tauz - real*8, DIMENSION(3) :: tau,vec12,dxyz,dxyz0 - real*8,external ::volume - real*8 ::outpr(3,3) - real*8, DIMENSION(3,3):: outerprod - - real*8 rij(3),rik(3),rjk(3),r7,r9 - real*8 rik_dist,rjk_dist - real*8 drik,drjk - real*8 rcovij - real*8 dc6,c6chk !d(C6ij)/d(r_ij) - real*8 expterm,dcni - real*8, allocatable,dimension(:,:,:,:) :: drij !d(E)/d(r_ij) derivative wrt. dist. iat-jat - real*8, allocatable,dimension(:,:,:,:) :: dcn !dCN(iat)/d(r_ij) is equal to - real*8 dcnn - !dCN(jat)/d(r_ij) - real*8 :: dc6_rest - integer,external :: lin - real*8,external ::vectorsize - real*8 vec(3),vec2(3),dummy - real*8 dc6i(n) !dC6i(iat) saves dE_dsp/dCN(iat) - real*8 dc6ij(n,n) !dC6(iat,jat)/cCN(iat) in dc6ij(i,j) for ABC-grad - real*8 dc6_rest_sum(n*(n+1)/2) - integer linij,linik,linjk - real*8 abc(3,n) - - real*8 eabc - real*8 gabc(3,n),glatabc(3,3) !threebody gradient - real*8 sigma_abc(3,3) - real*8 labc,rabc - real*8 ,dimension(3) ::ijvec,ikvec,jkvec,jtau,ktau,dumvec - integer jtaux,jtauy,jtauz,ktaux,ktauy,ktauz,mtaux,mtauy,mtauz - integer,dimension(3) :: taumin,taumax - integer mat,linim,linjm,linkm - real*8 rij2,rik2,rjk2,c9,c6ij,c6ik,c6jk,geomean,geomean3 - real*8 rr0ij,rr0jk,rr0ik,dc6iji,dc6ijj - real*8 :: sr9=0.75d0 !inverse of 4/3 - real*8, parameter :: alp9=-16.0d0 - real*8,DIMENSION(n*(n+1)) ::c6save - real*8 abcthr,time1,time2,geomean2,r0av,dc9,dfdmp,dang,ang - integer,dimension(3) ::repv,repmin,repmax,repmin2,repmax2 - -c R^2 cut-off - rthr=crit_vdw - abcthr=crit_cn -! write(*,*)'abcthr:', abcthr**(1./1.) - sigma=0.0d0 - virialstress=0.0d0 - stress=0.0d0 - gabc=0.0d0 - glatabc=0.0d0 - -c testsum=0.0d0 - - if (version.eq.1) then -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -! -! begin ZERO DAMPING GRADIENT -! -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! - -c precompute for analytical part - call pbcncoord(n,rcov,iz,xyz,cn,lat,rep_cn,crit_cn) - - - s8 =s18 - s10=s18 - allocate(drij(-rep_v(3):rep_v(3),-rep_v(2):rep_v(2), - . -rep_v(1):rep_v(1),n*(n+1)/2)) - - disp=0 - - drij=0.0d0 - dc6_rest=0.0d0 - dc6_rest_sum=0.0d0 - c6save=0.0d0 - kat=0 - dc6i=0.0d0 - - - do iat=1,n - call get_dC6_dCNij(maxc,max_elem,c6ab,mxc(iz(iat)), - . mxc(iz(iat)),cn(iat),cn(iat),iz(iat),iz(iat),iat,iat, - . c6,dc6iji,dc6ijj) - - c6save(lin(iat,iat))=c6 - dc6ij(iat,iat)=dc6iji - r0=r0ab(iz(iat),iz(iat)) - r42=r2r4(iz(iat))*r2r4(iz(iat)) - rcovij=rcov(iz(iat))+rcov(iz(iat)) - - - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - -!first dE/d(tau) saved in drij(i,i,counter) - rij=tau - r2=sum(rij*rij) -! if (r2.gt.rthr) cycle - - if (r2.gt.0.1.and.r2.lt.rthr) then - - - r=dsqrt(r2) - r6=r2*r2*r2 - r7=r6*r - r8=r6*r2 - r9=r8*r - -! -! Calculates damping functions: -C DGAS Edit - t6 = (r/(rs6*R0))**(-alp6) - damp6 =1.d0/( 1.d0+6.d0*t6 ) - t8 = (r/(rs8*R0))**(-alp8) - damp8 =1.d0/( 1.d0+6.d0*t8 ) - - drij(tauz,tauy,taux,lin(iat,iat))=drij(tauz,tauy,taux,lin(iat, - . iat)) - . +(-s6*(6.0/(r7)*C6*damp6) ! d(r^(-6))/d(tau) - . -s8*(24.0/(r9)*C6*r42*damp8))*0.5d0 - - - drij(tauz,tauy,taux,lin(iat,iat))=drij(tauz,tauy,taux,lin(iat, - . iat)) - . +(s6*C6/r7*6.d0*alp6*t6*damp6*damp6 !d(f_dmp)/d(tau) - . +s8*C6*r42/r9*18.d0*alp8*t8*damp8*damp8)*0.5d0 - -! -! in dC6_rest all terms BUT C6-term is saved for the kat-loop -! - dc6_rest= - . (s6/r6*damp6+3.d0*s8*r42/r8*damp8)*0.50d0 - - - disp=disp-dc6_rest*c6 ! calculate E_disp for sanity check - - dc6i(iat)=dc6i(iat)+dc6_rest*(dc6iji+dc6ijj) -! if (r2.lt.crit_cn) - dc6_rest_sum(lin(iat,iat))=dc6_rest_sum(lin(iat,iat))+dc6_rest - - - else !r2 < 0.1>rthr - drij(tauz,tauy,taux,lin(iat,iat))=0.0d0 - endif - - - ENDDO !tauz - ENDDO !tauy - ENDDO !taux - -!!!!!!!!!!!!!!!!!!!!!!!!!! -! B E G I N jat L O O P -!!!!!!!!!!!!!!!!!!!!!!!!!! - do jat=1,iat-1 -! -! get_dC6_dCNij calculates the derivative dC6(iat,jat)/dCN(iat) and -! dC6(iat,jat)/dCN(jat). these are saved in dC6ij for the kat loop -! - call get_dC6_dCNij(maxc,max_elem,c6ab,mxc(iz(iat)), - . mxc(iz(jat)),cn(iat),cn(jat),iz(iat),iz(jat),iat,jat, - . c6,dc6iji,dc6ijj) - - r0=r0ab(iz(jat),iz(iat)) - r42=r2r4(iz(iat))*r2r4(iz(jat)) - rcovij=rcov(iz(iat))+rcov(iz(jat)) - linij=lin(iat,jat) - - dc6ij(iat,jat)=dc6iji - dc6ij(jat,iat)=dc6ijj - c6save(linij)=c6 - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - - rij=xyz(:,jat)-xyz(:,iat)+tau - r2=sum(rij*rij) - if (r2.gt.rthr) cycle - - - r=dsqrt(r2) - r6=r2*r2*r2 - r7=r6*r - r8=r6*r2 - r9=r8*r - -! -! Calculates damping functions: - t6 = (r/(rs6*R0))**(-alp6) - damp6 =1.d0/( 1.d0+6.d0*t6 ) - t8 = (r/(rs8*R0))**(-alp8) - damp8 =1.d0/( 1.d0+6.d0*t8 ) - - drij(tauz,tauy,taux,linij)=drij(tauz,tauy,taux, - . linij) - . -s6*(6.0/(r7)*C6*damp6) ! d(r^(-6))/d(r_ij) - . -s8*(24.0/(r9)*C6*r42*damp8) - - drij(tauz,tauy,taux,linij)=drij(tauz,tauy,taux, - . linij) - . +s6*C6/r7*6.d0*alp6*t6*damp6*damp6 !d(f_dmp)/d(r_ij) - . +s8*C6*r42/r9*18.d0*alp8*t8*damp8*damp8 - -! -! in dC6_rest all terms BUT C6-term is saved for the kat-loop -! - dc6_rest= - . (s6/r6*damp6+3.d0*s8*r42/r8*damp8) - - - disp=disp-dc6_rest*c6 ! calculate E_disp for sanity check - - dc6i(iat)=dc6i(iat)+dc6_rest*dc6iji - dc6i(jat)=dc6i(jat)+dc6_rest*dc6ijj -! if (r2.lt.crit_cn) - dc6_rest_sum(linij)=dc6_rest_sum(linij) - . +dc6_rest - - - enddo !tauz - enddo !tauy - enddo !taux - - enddo !jat - - enddo !iat - - elseif (version.eq.2) then - - - -!!!!!!!!!!!!!!!!!!!!!!! -! NOW THE BJ Gradient ! -!!!!!!!!!!!!!!!!!!!!!!! - - - call pbcncoord(n,rcov,iz,xyz,cn,lat,rep_cn,crit_cn) - - a1 =rs6 - a2 =rs8 - s8 =s18 - - allocate(drij(-rep_v(3):rep_v(3),-rep_v(2):rep_v(2), - . -rep_v(1):rep_v(1),n*(n+1)/2)) - disp=0 - drij=0.0d0 - dc6_rest=0.0d0 - dc6_rest_sum=0.0d0 - kat=0 - dc6i=0.0d0 - - do iat=1,n - call get_dC6_dCNij(maxc,max_elem,c6ab,mxc(iz(iat)), - . mxc(iz(iat)),cn(iat),cn(iat),iz(iat),iz(iat),iat,iat, - . c6,dc6iji,dc6ijj) - - dc6ij(iat,iat)=dc6iji - c6save(lin(iat,iat))=c6 - r42=r2r4(iz(iat))*r2r4(iz(iat)) - rcovij=rcov(iz(iat))+rcov(iz(iat)) - - R0=a1*sqrt(3.0d0*r42)+a2 - - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - -!first dE/d(tau) saved in drij(i,i,counter) - rij=tau - r2=sum(rij*rij) -! if (r2.gt.rthr) cycle - -! if (r2.gt.0.1) then - if (r2.gt.0.1.and.r2.lt.rthr) then -! -! get_dC6_dCNij calculates the derivative dC6(iat,jat)/dCN(iat) and -! dC6(iat,jat)/dCN(jat). these are saved in dC6ij for the kat loop -! - r=dsqrt(r2) - r4=r2*r2 - r6=r4*r2 - r7=r6*r - r8=r6*r2 - r9=r8*r - -! -! Calculates damping functions: - - t6=(r6+R0**6) - t8=(r8+R0**8) - - drij(tauz,tauy,taux,lin(iat,iat))=drij(tauz,tauy,taux,lin(iat, - . iat)) - . -s6*C6*6.0d0*r4*r/(t6*t6)*0.5d0 ! d(1/(r^(6)+R0^6)/d(r) - . -s8*C6*24.0d0*r42*r7/(t8*t8)*0.5d0 - - -! -! in dC6_rest all terms BUT C6-term is saved for the kat-loop -! - dc6_rest= - . (s6/t6+3.d0*s8*r42/t8)*0.50d0 - - - disp=disp-dc6_rest*c6 ! calculate E_disp for sanity check - - dc6i(iat)=dc6i(iat)+dc6_rest*(dc6iji+dc6ijj) - !if(iat.eq.29)then - !endif - -! if (r2.lt.crit_cn) - dc6_rest_sum(lin(iat,iat))=dc6_rest_sum(lin(iat,iat))+ - . dc6_rest - - - else !r2 < 0.1>rthr - drij(tauz,tauy,taux,lin(iat,iat))=0.0d0 - endif - - - ENDDO !tauz - ENDDO !tauy - ENDDO !taux - -!!!!!!!!!!!!!!!!!!!!!!!!!! -! B E G I N jat L O O P -!!!!!!!!!!!!!!!!!!!!!!!!!! - do jat=1,iat-1 -! -! get_dC6_dCNij calculates the derivative dC6(iat,jat)/dCN(iat) and -! dC6(iat,jat)/dCN(jat). these are saved in dC6ij for the kat loop -! - call get_dC6_dCNij(maxc,max_elem,c6ab,mxc(iz(iat)), - . mxc(iz(jat)),cn(iat),cn(jat),iz(iat),iz(jat),iat,jat, - . c6,dc6iji,dc6ijj) - - r42=r2r4(iz(iat))*r2r4(iz(jat)) - rcovij=rcov(iz(iat))+rcov(iz(jat)) - - R0=a1*dsqrt(3.0d0*r42)+a2 - - linij=lin(iat,jat) - dc6ij(iat,jat)=dc6iji - dc6ij(jat,iat)=dc6ijj - c6save(linij)=c6 - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - - rij=xyz(:,jat)-xyz(:,iat)+tau - r2=sum(rij*rij) - if (r2.gt.rthr) cycle - - - r=dsqrt(r2) - r4=r2*r2 - r6=r4*r2 - r7=r6*r - r8=r6*r2 - r9=r8*r - -! -! Calculates damping functions: - t6=(r6+R0**6) - t8=(r8+R0**8) - - - drij(tauz,tauy,taux,linij)=drij(tauz,tauy,taux, - . linij) - . -s6*C6*6.0d0*r4*r/(t6*t6) - . -s8*C6*24.0d0*r42*r7/(t8*t8) - -! -! in dC6_rest all terms BUT C6-term is saved for the kat-loop -! - dc6_rest= - . (s6/t6+3.d0*s8*r42/t8) - - - disp=disp-dc6_rest*c6 ! calculate E_disp for sanity check - - dc6i(iat)=dc6i(iat)+dc6_rest*dc6iji - dc6i(jat)=dc6i(jat)+dc6_rest*dc6ijj -! if (r2.lt.crit_cn) - dc6_rest_sum(lin(iat,jat))=dc6_rest_sum(linij) - . +dc6_rest - - - enddo !tauz - enddo !tauy - enddo !taux - - enddo !jat - - enddo !iat - - endif ! version=1 or 2 - - -! -!!!!!!!!!!!!!!!!!!!!!!! -!! BEGIN Threebody gradient -!!!!!!!!!!!!!!!!!!!!!!! - if (.not.noabc) then - -! write(*,*)'!!!!!!!!!! THREEBODY GRADIENT !!!!!!!!!!' - sr9=0.75d0 - eabc=0.0d0 - abcthr=crit_cn - repv=rep_cn -! write(*,*)'thr:',sqrt(abcthr) - - - do iat=3,n - do jat=2,iat-1 - linij=lin(iat,jat) - ijvec=xyz(:,jat)-xyz(:,iat) - - c6ij=c6save(linij) - do kat=1,jat-1 - linik=lin(iat,kat) - linjk=lin(jat,kat) - ikvec=xyz(:,kat)-xyz(:,iat) - jkvec=xyz(:,kat)-xyz(:,jat) - - c6ik=c6save(linik) - c6jk=c6save(linjk) - c9=-1.0d0*dsqrt(c6ij*c6ik*c6jk) - - do jtaux=-rep_cn(1),rep_cn(1) - repmin(1)=max(-rep_cn(1),jtaux-rep_cn(1)) - repmax(1)=min(rep_cn(1),jtaux+rep_cn(1)) - do jtauy=-rep_cn(2),rep_cn(2) - repmin(2)=max(-rep_cn(2),jtauy-rep_cn(2)) - repmax(2)=min(rep_cn(2),jtauy+rep_cn(2)) - do jtauz=-rep_cn(3),rep_cn(3) - repmin(3)=max(-rep_cn(3),jtauz-rep_cn(3)) - repmax(3)=min(rep_cn(3),jtauz+rep_cn(3)) - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - rij2=SUM((ijvec+jtau)*(ijvec+jtau)) - if(rij2.gt.abcthr)cycle - - rr0ij=DSQRT(rij2)/r0ab(iz(iat),iz(jat)) - - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - rik2=SUM((ikvec+ktau)*(ikvec+ktau)) - if(rik2.gt.abcthr)cycle - - dumvec=jkvec+ktau-jtau - rjk2=SUM(dumvec*dumvec) - if(rjk2.gt.abcthr)cycle - rr0ik=dsqrt(rik2)/r0ab(iz(iat),iz(kat)) - rr0jk=dsqrt(rjk2)/r0ab(iz(jat),iz(kat)) - geomean2=(rij2*rjk2*rik2) -! first calculate the three components for the energy calculation fdmp -! and ang - r0av=(rr0ij*rr0ik*rr0jk)**(1.0d0/3.0d0) - damp9=1./(1.+6.*(sr9*r0av)**alp9) !alp9 is already saved with "-" - - geomean=dsqrt(geomean2) - geomean3=geomean*geomean2 - ang=0.375d0*(rij2+rjk2-rik2)*(rij2-rjk2+rik2) - . *(-rij2+rjk2+rik2)/(geomean3*geomean2) - . +1.0d0/(geomean3) - - dc6_rest=ang*damp9 - eabc=eabc+dc6_rest*c9 -! -!start calculating the gradient components dfdmp, dang and dc9 - -!dfdmp is the same for all three distances - dfdmp=2.d0*alp9*(0.75d0*r0av)**(alp9)*damp9*damp9 - -!start calculating the derivatives of each part w.r.t. r_ij - r=dsqrt(rij2) - - - dang=-0.375d0*(rij2**3+rij2**2*(rjk2+rik2) - . +rij2*(3.0d0*rjk2**2+2.0*rjk2*rik2+3.0*rik2**2) - . -5.0*(rjk2-rik2)**2*(rjk2+rik2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(jtauz,jtauy,jtaux,linij)= - . drij(jtauz,jtauy,jtaux,linij)-tmp1 - -!start calculating the derivatives of each part w.r.t. r_ik - - r=dsqrt(rik2) - - - dang=-0.375d0*(rik2**3+rik2**2*(rjk2+rij2) - . +rik2*(3.0d0*rjk2**2+2.0*rjk2*rij2+3.0*rij2**2) - . -5.0*(rjk2-rij2)**2*(rjk2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang -! tmp1=-dc9 - drij(ktauz,ktauy,ktaux,linik)= - . drij(ktauz,ktauy,ktaux,linik)-tmp1 - -! -!start calculating the derivatives of each part w.r.t. r_jk - - r=dsqrt(rjk2) - - dang=-0.375d0*(rjk2**3+rjk2**2*(rik2+rij2) - . +rjk2*(3.0d0*rik2**2+2.0*rik2*rij2+3.0*rij2**2) - . -5.0*(rik2-rij2)**2*(rik2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)= - . drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)-tmp1 - -!calculating the CN derivative dE_disp(ijk)/dCN(i) - - dc9=dc6ij(iat,jat)/c6ij+dc6ij(iat,kat)/c6ik - dc9=0.5d0*c9*dc9 - dc6i(iat)=dc6i(iat)+dc6_rest*dc9 - - dc9=dc6ij(jat,iat)/c6ij+dc6ij(jat,kat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(jat)=dc6i(jat)+dc6_rest*dc9 - - dc9=dc6ij(kat,iat)/c6ik+dc6ij(kat,jat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(kat)=dc6i(kat)+dc6_rest*dc9 - - - enddo !ktauz - enddo !ktauy - enddo !ktauz - enddo !jtauz - enddo !jtauy - enddo !jtaux - enddo !kat - enddo !jat - enddo !iat - -! Now the interaction with jat=iat of the triples iat,iat,kat - DO iat=2,n - jat=iat - linij=lin(iat,jat) - ijvec=0.0d0 - - c6ij=c6save(linij) - DO kat=1,iat-1 - linjk=lin(jat,kat) - linik=linjk - - c6ik=c6save(linik) - c6jk=c6ik - ikvec=xyz(:,kat)-xyz(:,iat) - jkvec=ikvec - c9=-dsqrt(c6ij*c6ik*c6jk) - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - IF (jtaux.eq.0 .and. jtauy.eq.0 .and. jtauz.eq.0) cycle - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=jtau - rij2=SUM(dumvec*dumvec) - if(rij2.gt.abcthr)cycle - - rr0ij=DSQRT(rij2)/r0ab(iz(iat),iz(jat)) - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) -! every result * 0.5 - - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ikvec+ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0ik=DSQRT(rik2)/r0ab(iz(iat),iz(kat)) - rr0jk=DSQRT(rjk2)/r0ab(iz(jat),iz(kat)) - - - geomean2=(rij2*rjk2*rik2) - r0av=(rr0ij*rr0ik*rr0jk)**(1.0d0/3.0d0) - damp9=1./(1.+6.*(sr9*r0av)**alp9) !alp9 is already saved with "-" - - geomean=dsqrt(geomean2) - geomean3=geomean*geomean2 - ang=0.375d0*(rij2+rjk2-rik2)*(rij2-rjk2+rik2) - . *(-rij2+rjk2+rik2)/(geomean3*geomean2) - . +1.0d0/(geomean3) - - - dc6_rest=ang*damp9/2.0d0 !factor 1/2 for doublecounting - eabc=eabc+dc6_rest*c9 - -! iat=jat - dfdmp=2.d0*alp9*(0.75d0*r0av)**(alp9)*damp9*damp9 - -!start calculating the derivatives of each part w.r.t. r_ij - r=dsqrt(rij2) - - dang=-0.375d0*(rij2**3+rij2**2*(rjk2+rik2) - . +rij2*(3.0d0*rjk2**2+2.0*rjk2*rik2+3.0*rik2**2) - . -5.0*(rjk2-rik2)**2*(rjk2+rik2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(jtauz,jtauy,jtaux,linij)= - . drij(jtauz,jtauy,jtaux,linij)-tmp1/2.0 - -!start calculating the derivatives of each part w.r.t. r_ik - r=dsqrt(rik2) - - - dang=-0.375d0*(rik2**3+rik2**2*(rjk2+rij2) - . +rik2*(3.0d0*rjk2**2+2.0*rjk2*rij2+3.0*rij2**2) - . -5.0*(rjk2-rij2)**2*(rjk2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(ktauz,ktauy,ktaux,linik)= - . drij(ktauz,ktauy,ktaux,linik)-tmp1/2.0 -! -!start calculating the derivatives of each part w.r.t. r_ik - r=dsqrt(rjk2) - - dang=-0.375d0*(rjk2**3+rjk2**2*(rik2+rij2) - . +rjk2*(3.0d0*rik2**2+2.0*rik2*rij2+3.0*rij2**2) - . -5.0*(rik2-rij2)**2*(rik2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - - drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)= - . drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)-tmp1/2.0 - - dc9=dc6ij(iat,jat)/c6ij+dc6ij(iat,kat)/c6ik - dc9=0.5d0*c9*dc9 - dc6i(iat)=dc6i(iat)+dc6_rest*dc9 - - dc9=dc6ij(jat,iat)/c6ij+dc6ij(jat,kat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(jat)=dc6i(jat)+dc6_rest*dc9 - - dc9=dc6ij(kat,iat)/c6ik+dc6ij(kat,jat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(kat)=dc6i(kat)+dc6_rest*dc9 - - - - - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - ENDDO !kat - ENDDO !iat - ! And now kat=jat, but cycling throug all imagecells without jtau=ktau. and jat>iat going though all cells (iat,jat,jat) - ! But this counts only 1/2 - - DO iat=2,n - DO jat=1,iat-1 - kat=jat - linij=lin(iat,jat) - linjk=lin(jat,kat) - linik=linij - - c6ij=c6save(linij) - c6ik=c6ij - - c6jk=c6save(linjk) - ikvec=xyz(:,kat)-xyz(:,iat) - ijvec=ikvec - jkvec=0.0d0 - - c9=-1.0d0*dsqrt(c6ij*c6ik*c6jk) - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=ijvec+jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - - rr0ij=SQRT(rij2)/r0ab(iz(iat),iz(jat)) - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) -! every result * 0.5 - IF (jtaux.eq.ktaux .and. jtauy.eq.ktauy - . .and. jtauz.eq.ktauz) cycle - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ikvec+ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=SQRT(rik2)/r0ab(iz(iat),iz(kat)) - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=SQRT(rjk2)/r0ab(iz(jat),iz(kat)) - -! if (rij*rjk*rik.gt.abcthr)cycle - - geomean2=(rij2*rjk2*rik2) - r0av=(rr0ij*rr0ik*rr0jk)**(1.0d0/3.0d0) - damp9=1./(1.+6.d0*(sr9*r0av)**alp9) !alp9 is already saved with "-" - - geomean=dsqrt(geomean2) - geomean3=geomean*geomean2 - ang=0.375d0*(rij2+rjk2-rik2)*(rij2-rjk2+rik2) - . *(-rij2+rjk2+rik2)/(geomean2*geomean3) - . +1.0d0/(geomean3) - dc6_rest=ang*damp9/2.0d0 !factor 1/2 for doublecounting - eabc=eabc+dc6_rest*c9 - - -! jat=kat - dfdmp=2.d0*alp9*(0.75d0*r0av)**(alp9)*damp9*damp9 -!start calculating the derivatives of each part w.r.t. r_ij - r=dsqrt(rij2) - - dang=-0.375d0*(rij2**3+rij2**2*(rjk2+rik2) - . +rij2*(3.0d0*rjk2**2+2.0d0*rjk2*rik2+3.0d0*rik2**2) - . -5.0d0*(rjk2-rik2)**2*(rjk2+rik2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(jtauz,jtauy,jtaux,linij)= - . drij(jtauz,jtauy,jtaux,linij)-tmp1/2.0d0 - -!start calculating the derivatives of each part w.r.t. r_ik - r=dsqrt(rik2) - - - dang=-0.375d0*(rik2**3+rik2**2*(rjk2+rij2) - . +rik2*(3.0d0*rjk2**2+2.0*rjk2*rij2+3.0*rij2**2) - . -5.0*(rjk2-rij2)**2*(rjk2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang -! tmp1=-dc9 - drij(ktauz,ktauy,ktaux,linik)= - . drij(ktauz,ktauy,ktaux,linik)-tmp1/2.0d0 -! -!start calculating the derivatives of each part w.r.t. r_jk - r=dsqrt(rjk2) - - dang=-0.375d0*(rjk2**3+rjk2**2*(rik2+rij2) - . +rjk2*(3.0d0*rik2**2+2.0*rik2*rij2+3.0*rij2**2) - . -5.0d0*(rik2-rij2)**2*(rik2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)= - . drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)-tmp1/2.0d0 - -!calculating the CN derivative dE_disp(ijk)/dCN(i) - - dc9=dc6ij(iat,jat)/c6ij+dc6ij(iat,kat)/c6ik - dc9=0.5d0*c9*dc9 - dc6i(iat)=dc6i(iat)+dc6_rest*dc9 - - dc9=dc6ij(jat,iat)/c6ij+dc6ij(jat,kat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(jat)=dc6i(jat)+dc6_rest*dc9 - - dc9=dc6ij(kat,iat)/c6ik+dc6ij(kat,jat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(kat)=dc6i(kat)+dc6_rest*dc9 - - - - - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - ENDDO !kat - ENDDO !iat - - -! And finally the self interaction iat=jat=kat all - - idum=0 - DO iat=1,n - jat=iat - kat=iat - ijvec=0.0d0 - linij=lin(iat,jat) - linik=lin(iat,kat) - linjk=lin(jat,kat) - ikvec=ijvec - jkvec=ikvec - c6ij=c6save(linij) - c6ik=c6ij - c6jk=c6ij - c9=-(DSQRT(c6ij*c6ij*c6ij)) - - do jtaux=-repv(1),repv(1) - repmin(1)=max(-repv(1),jtaux-repv(1)) - repmax(1)=min(repv(1),jtaux+repv(1)) - do jtauy=-repv(2),repv(2) - repmin(2)=max(-repv(2),jtauy-repv(2)) - repmax(2)=min(repv(2),jtauy+repv(2)) - do jtauz=-repv(3),repv(3) - repmin(3)=max(-repv(3),jtauz-repv(3)) - repmax(3)=min(repv(3),jtauz+repv(3)) - IF ((jtaux.eq.0) .and.(jtauy.eq.0) .and.(jtauz.eq.0))cycle !IF iat and jat are the same then cycle - jtau=jtaux*lat(:,1)+jtauy*lat(:,2)+jtauz*lat(:,3) - dumvec=jtau - dumvec=dumvec*dumvec - rij2=SUM(dumvec) - if(rij2.gt.abcthr)cycle - rr0ij=SQRT(rij2)/r0ab(iz(iat),iz(jat)) - - do ktaux=repmin(1),repmax(1) - do ktauy=repmin(2),repmax(2) - do ktauz=repmin(3),repmax(3) - IF ((ktaux.eq.0) .and.( ktauy.eq.0) .and.( ktauz.eq.0))cycle !IF iat and kat are the same then cycle - IF ((ktaux.eq.jtaux) .and. (ktauy.eq.jtauy) - . .and. (ktauz.eq.jtauz)) cycle !If kat and jat are the same then cycle - -! every result * 1/6 becaues every triple is counted twice due to the two loops jtau and ktau going from -repv to repv -> *1/2 -! -!plus 1/3 becaues every triple is three times in each unitcell - ktau=ktaux*lat(:,1)+ktauy*lat(:,2)+ktauz*lat(:,3) - dumvec=ktau - dumvec=dumvec*dumvec - rik2=SUM(dumvec) - if(rik2.gt.abcthr)cycle - rr0ik=SQRT(rik2)/r0ab(iz(iat),iz(kat)) - - dumvec=jkvec+ktau-jtau - dumvec=dumvec*dumvec - rjk2=SUM(dumvec) - if(rjk2.gt.abcthr)cycle - rr0jk=SQRT(rjk2)/r0ab(iz(jat),iz(kat)) - - geomean2=(rij2*rjk2*rik2) - r0av=(rr0ij*rr0ik*rr0jk)**(1.0d0/3.0d0) - damp9=1./(1.+6.*(sr9*r0av)**alp9) !alp9 is already saved with "-" - - geomean=dsqrt(geomean2) - geomean3=geomean*geomean2 - ang=0.375d0*(rij2+rjk2-rik2)*(rij2-rjk2+rik2) - . *(-rij2+rjk2+rik2)/(geomean2*geomean3) - . +1.0d0/(geomean3) - dc6_rest=ang*damp9/6.0d0 - eabc=eabc+c9*dc6_rest - -! iat=jat=kat - dfdmp=2.d0*alp9*(0.75d0*r0av)**(alp9)*damp9*damp9 -!start calculating the derivatives of each part w.r.t. r_ij - - r=dsqrt(rij2) - dang=-0.375d0*(rij2**3+rij2**2*(rjk2+rik2) - . +rij2*(3.0d0*rjk2**2+2.0*rjk2*rik2+3.0*rik2**2) - . -5.0*(rjk2-rik2)**2*(rjk2+rik2)) - . /(r*geomean3*geomean2) - - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(jtauz,jtauy,jtaux,linij)= - . drij(jtauz,jtauy,jtaux,linij)-tmp1/6.0d0 - -!start calculating the derivatives of each part w.r.t. r_ik - - r=dsqrt(rik2) - - dang=-0.375d0*(rik2**3+rik2**2*(rjk2+rij2) - . +rik2*(3.0d0*rjk2**2+2.0*rjk2*rij2+3.0*rij2**2) - . -5.0*(rjk2-rij2)**2*(rjk2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(ktauz,ktauy,ktaux,linik)= - . drij(ktauz,ktauy,ktaux,linik)-tmp1/6.0d0 -! -!start calculating the derivatives of each part w.r.t. r_jk - - r=dsqrt(rjk2) - dang=-0.375d0*(rjk2**3+rjk2**2*(rik2+rij2) - . +rjk2*(3.0d0*rik2**2+2.0*rik2*rij2+3.0*rij2**2) - . -5.0*(rik2-rij2)**2*(rik2+rij2)) - . /(r*geomean3*geomean2) - - tmp1=-dang*c9*damp9+dfdmp/r*c9*ang - drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)= - . drij(ktauz-jtauz,ktauy-jtauy,ktaux-jtaux,linjk)-tmp1/6.0d0 - - -!calculating the CN derivative dE_disp(ijk)/dCN(i) - - dc9=dc6ij(iat,jat)/c6ij+dc6ij(iat,kat)/c6ik - dc9=0.5d0*c9*dc9 - dc6i(iat)=dc6i(iat)+dc6_rest*dc9 - - dc9=dc6ij(jat,iat)/c6ij+dc6ij(jat,kat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(jat)=dc6i(jat)+dc6_rest*dc9 - - dc9=dc6ij(kat,iat)/c6ik+dc6ij(kat,jat)/c6jk - dc9=0.5d0*c9*dc9 - dc6i(kat)=dc6i(kat)+dc6_rest*dc9 - - - - - - ENDDO !ktauz - ENDDO !ktauy - ENDDO !ktaux - ENDDO !jtauz - ENDDO !jtauy - ENDDO !jtaux - - - ENDDO !iat - - - - -! write(*,*)' eabc(gdisp): ',eabc -! write(*,'('' time(abc) '',f6.1)')time2-time1 - disp=disp-eabc ! cbannwarth: the minus is correct here, because the angular term is calculated with 0.375d0 instead of -0.375d0 (c.f., non-periodic code) -! write(*,*)'gdisp:',disp - endif !.not.noabc - - - - sigma_abc=0.0d0 - sigma=0.0d0 - -! After calculating all derivatives dE/dr_ij w.r.t. distances, -! the grad w.r.t. the coordinates is calculated dE/dr_ij * dr_ij/dxyz_i - do iat=2,n - do jat=1,iat-1 - linij=lin(iat,jat) -! write(*,'(3E17.6,XX,2I2)'),drij(0,0,-1:1,lin(iat,jat)),iat,jat - rcovij=rcov(iz(iat))+rcov(iz(jat)) - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - - rij=xyz(:,jat)-xyz(:,iat)+tau - r2=sum(rij*rij) - if (r2.gt.rthr.or.r2.lt.0.5) cycle - r=dsqrt(r2) - - if (r2.lt.crit_cn) then - expterm=exp(-k1*(rcovij/r-1.d0)) - dcnn=-k1*rcovij*expterm/ - . (r2*(expterm+1.d0)*(expterm+1.d0)) - else - dcnn=0.0d0 - endif - x1=drij(tauz,tauy,taux,linij)+dcnn*(dc6i(iat)+dc6i(jat)) - - vec=x1*rij/r - g(:,iat)=g(:,iat)+vec - g(:,jat)=g(:,jat)-vec - do i=1,3 - do j=1,3 - sigma(j,i)=sigma(j,i)+vec(j)*rij(i) - enddo !j - enddo !i - - - - enddo !tauz - enddo !tauy - enddo !taux - enddo !jat - enddo !iat - - do iat=1,n - rcovij=rcov(iz(iat))+rcov(iz(iat)) - do taux=-rep_v(1),rep_v(1) - do tauy=-rep_v(2),rep_v(2) - do tauz=-rep_v(3),rep_v(3) - if (taux.eq.0.and.tauy.eq.0.and.tauz.eq.0) cycle - - tau=taux*lat(:,1)+tauy*lat(:,2)+tauz*lat(:,3) - r2=(sum(tau*tau)) - r=dsqrt(r2) - if (r2.lt.crit_cn) then - expterm=exp(-k1*(rcovij/r-1.d0)) - dcnn=-k1*rcovij*expterm/ - . (r2*(expterm+1.d0)*(expterm+1.d0)) - else - dcnn=0.0d0 - endif - x1=drij(tauz,tauy,taux,lin(iat,iat))+dcnn*dc6i(iat) - vec=x1*tau/r - vec2(1)=taux - vec2(2)=tauy - vec2(3)=tauz - do i=1,3 - do j=1,3 - sigma(j,i)=sigma(j,i)+vec(j)*tau(i) - enddo !j - enddo !i - - - enddo !tauz - enddo !tauy - enddo !taux - - - - enddo !iat - - - - stress=0.0d0 - glatabc=0.0d0 - call inv_cell(lat,lat_1) - do a=1,3 - do b=1,3 - do my=1,3 - stress(a,b)=stress(a,b)-sigma(a,my)*lat_1(b,my) - enddo - enddo !b - enddo !a - - deallocate(drij) - - end subroutine pbcgdisp - - subroutine inv_cell(x,a) !x is normal lat, a is lat^(-1) - IMPLICIT NONE - real*8, intent(in) :: x(3,3) !unitcell vectors in direct space - real*8, intent(out) :: a(3,3) !unitcell vectors in reciprocal space - integer i - real*8 det - - a=0.0 - det=x(1,1)*x(2,2)*x(3,3)+x(1,2)*x(2,3)*x(3,1)+x(1,3)*x(2,1)* - . x(3,2)-x(1,3)*x(2,2)*x(3,1)-x(1,2)*x(2,1)*x(3,3)-x(1,1)* - . x(2,3)*x(3,2) -! write(*,*)'Det:',det - a(1,1)=x(2,2)*x(3,3)-x(2,3)*x(3,2) - a(2,1)=x(2,3)*x(3,1)-x(2,1)*x(3,3) - a(3,1)=x(2,1)*x(3,2)-x(2,2)*x(3,1) - a(1,2)=x(1,3)*x(3,2)-x(1,2)*x(3,3) - a(2,2)=x(1,1)*x(3,3)-x(1,3)*x(3,1) - a(3,2)=x(1,2)*x(3,1)-x(1,1)*x(3,2) - a(1,3)=x(1,2)*x(2,3)-x(1,3)*x(2,2) - a(2,3)=x(1,3)*x(2,1)-x(1,1)*x(2,3) - a(3,3)=x(1,1)*x(2,2)-x(1,2)*x(2,1) - a=a/det - end subroutine inv_cell diff --git a/ABACUS.develop/source/src_pw/energy.cpp b/ABACUS.develop/source/src_pw/energy.cpp index 8e77ff7f89..e6975222d4 100644 --- a/ABACUS.develop/source/src_pw/energy.cpp +++ b/ABACUS.develop/source/src_pw/energy.cpp @@ -141,9 +141,9 @@ void energy::print_etot( { this->print_format("E_vdwD2",evdw); } - if(vdwd3.vdwD3) //jiyy add 2019-05 + if(vdwd3_para.flag_vdwd3) //jiyy add 2019-05, update 2021-04-25 { - this->print_format("E_vdwD3",vdwd3.energy_result); + this->print_format("E_vdwD3",evdw); } this->print_format("E_exx",exx); } diff --git a/ABACUS.develop/source/src_pw/forces.cpp b/ABACUS.develop/source/src_pw/forces.cpp index 580e51581b..d5b28996fe 100644 --- a/ABACUS.develop/source/src_pw/forces.cpp +++ b/ABACUS.develop/source/src_pw/forces.cpp @@ -51,9 +51,16 @@ void Forces::init(matrix& force) Forces::print("VDW FORCE (Ry/Bohr)", force_vdw); } } - else if(vdwd3.vdwD3) //jiyy add 2019-05-18 + else if(vdwd3_para.flag_vdwd3) //jiyy add 2019-05-18, update 2021.04.25 { - vdwd3.force(1, 0, force_vdw, stress_vdw_pw); + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_force(); + for(int iat=0; iat5 might lead to bumps in the potential - parameter (k3=-4.) - diff --git a/ABACUS.develop/source/src_pw/stress_pw.cpp b/ABACUS.develop/source/src_pw/stress_pw.cpp index 127f913b54..e69de19aaf 100644 --- a/ABACUS.develop/source/src_pw/stress_pw.cpp +++ b/ABACUS.develop/source/src_pw/stress_pw.cpp @@ -1,6 +1,7 @@ #include "./stress_pw.h" #include "./H_XC_pw.h" #include "src_pw/vdwd2.h" +#include "src_pw/vdwd3.h" void Stress_PW::cal_stress(matrix& sigmatot) { @@ -117,9 +118,11 @@ void Stress_PW::stress_vdw(matrix& sigma) vdwd2.cal_stress(); sigma = vdwd2.get_stress().to_matrix(); } - if(vdwd3.vdwD3) //jiyy add 2019-05-18 + if(vdwd3_para.flag_vdwd3) //jiyy add 2019-05-18, update 2021-04-25 { - vdwd3.force(0, 1, force, sigma); + Vdwd3 vdwd3(ucell,vdwd3_para); + vdwd3.cal_stress(); + sigma = vdwd3.get_stress().to_matrix(); } return; } diff --git a/ABACUS.develop/source/src_pw/vdwd3.cpp b/ABACUS.develop/source/src_pw/vdwd3.cpp index 431d228556..96feb40e7c 100644 --- a/ABACUS.develop/source/src_pw/vdwd3.cpp +++ b/ABACUS.develop/source/src_pw/vdwd3.cpp @@ -1,275 +1,1236 @@ -#include"vdwd3.h" -#include"../src_global/element_name.h" -#include"../src_global/constants.h" -#include"../src_global/global_function.h" -#include -#include - -Vdwd3::Vdwd3( const UnitCell_pseudo &unitcell): - energy_result(0), - noabc(true), - alp(14.0), - max_elem(94), - maxc(5), - nline(32385), - ucell(unitcell), - init_set(false) -{ - disp = 0.0; - init_C6_tmp(); - init_r2r4(); - add_r2r4=VECTOR_TO_PTR(r2r4); - init_rcov(); - add_rcov=VECTOR_TO_PTR(rcov); -} - -void Vdwd3::atomkind (const UnitCell_pseudo &unitcell) -{ - atom_kind.resize(unitcell.ntype) ; - for ( vector::size_type i=0 ; i!=unitcell.ntype ; i++ ) - { - for (int j=0; j!=element_name.size(); j++) - { - if ( unitcell.atoms[i].psd == element_name[j] ) - { - atom_kind[i] = j ; - break; - } - } - } - return ; -} - - -void Vdwd3::XYZ( const UnitCell_pseudo &unitcell,double (*xyz)[3],int *iz) -{ - int k = 0; - for(int it=0 ; it=100) - { - i-=100; - icn+=1; - } - return icn; -} - -void Vdwd3::loadc6() -{ - init_mxc(); - int k = 0,iat,jat,iatcn,jatcn; - for(int n=0;n(C6_tmp[k+1])-1; - jat = static_cast(C6_tmp[k+2])-1; - iatcn = limit(iat); - jatcn = limit(jat); - - mxc[iat] = max(mxc[iat],iatcn); - mxc[jat] = max(mxc[jat],jatcn); - - c6ab[0][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k]; - c6ab[1][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k+3]; - c6ab[2][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k+4]; - - c6ab[0][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k]; - c6ab[1][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k+4]; - c6ab[2][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k+3]; - - } - return; -} - -void Vdwd3::setlat( const UnitCell_pseudo &unitcell) -{ - lat[0][0] = unitcell.latvec.e11* unitcell.lat0; - lat[0][1] = unitcell.latvec.e12* unitcell.lat0; - lat[0][2] = unitcell.latvec.e13* unitcell.lat0; - - lat[1][0] = unitcell.latvec.e21* unitcell.lat0; - lat[1][1] = unitcell.latvec.e22* unitcell.lat0; - lat[1][2] = unitcell.latvec.e23* unitcell.lat0; - - lat[2][0] = unitcell.latvec.e31* unitcell.lat0; - lat[2][1] = unitcell.latvec.e32* unitcell.lat0; - lat[2][2] = unitcell.latvec.e33* unitcell.lat0; - - return; -} - -/* void Vdwd3::setfuncpar(int &ver) -{ - if(ver==1) - { - s6 = 1.0; - rs6 = 1.217; - s18 = 0.722; - rs18 = 1.0; - } - else if(ver==2) - { - s6 = 1.0; - rs6 = 0.4289; - s18 = 0.7875; - rs18 = 4.4407; - } - return; -} */ - -void Vdwd3::initset() -{ - if(!init_set) - { - if(abc) - { - noabc = !abc; - } - atomkind(ucell); - loadc6(); - setlat(ucell); - setr0ab_(&max_elem,&BOHR_TO_A,r0ab); -/* if((s6==0)&&(rs6==0)&&(s18==0)&&(rs18==0)&&(rthr2==0)) - { - setfuncpar(version); - rthr2=95**2; - } */ - for(int i=0 ; i<3 ; i++) - { - tau_max[i] = 0; - } - if(model=="radius") - { - set_criteria_(&rthr2,lat,tau_max); - for(int i=0 ; i<3 ; i++) - { - rep_vdw[i] = int(tau_max[i])+1; - } - } - set_criteria_(&cn_thr2,lat,tau_max); - for(int i=0 ; i<3 ; i++) - { - rep_cn[i] = int(tau_max[i])+1; - } - for(int i=0 ; i<3 ; i++) - { - for(int j=0 ; j<3 ; j++) - { - stress[i][i] = 0; - sigma[i][i] = 0; - } - } - - init_set = true; - } - return; -} - -double Vdwd3::energy() -{ - TITLE("Vdwd3","energy"); - initset(); - double xyz[ucell.nat][3]; - int iz[ucell.nat]; - - XYZ(ucell,xyz,iz); - - double alp2 = alp+2; - double alp4 = alp+4; - pbcedisp_(&max_elem,&maxc,&ucell.nat,xyz,iz,c6ab,mxc,add_r2r4, - r0ab,add_rcov,&rs6,&rs18,&rs18,&alp,&alp2,&alp4, - &version,&noabc,&e6,&e8,&e10,&e12,&e63,lat, - &rthr2,rep_vdw,&cn_thr2,rep_cn); - - energy_result = (-s6*e6-s18*e8-e63)*2; - return energy_result; -} - -vector< vector > Vdwd3::force( - const bool force_for_vdw, - const bool stress_for_vdw, - matrix &force_vdw, - matrix &stress_result -) -{ - TITLE("Vdwd3","force"); - initset(); - double xyz[ucell.nat][3]; - int iz[ucell.nat]; - XYZ(ucell,xyz,iz); - double g[ucell.nat][3]; - for(int iat=0; iat!=ucell.nat; ++iat) - { - for(int j=0; j!=3; ++j) - { - g[iat][j] = 0; - } - } - - force_result.resize(ucell.nat); - for( int iat=0; iat!=ucell.nat; ++iat ) - { - force_result[iat].assign(3,0); - } - if(stress_for_vdw) stress_result.zero_out(); - - double alp2 = alp+2; - double alp4 = alp+4; - pbcgdisp_(&max_elem,&maxc,&ucell.nat,xyz,iz,c6ab,mxc,add_r2r4, - r0ab,add_rcov,&s6,&s18,&rs6,&rs18,&rs18,&alp,&alp2,&alp4, - &noabc,&version,g,&disp,stress,sigma,lat,rep_vdw,rep_cn, - &rthr2,&cn_thr2); - - for(int iat=0 ; iat> &lat, vector &tau_max) +{ + tau_max.resize(3); + double r_cutoff = sqrt(rthr); + Vector3 norm1 = (lat[1] ^ lat[2]).normalize(); + Vector3 norm2 = (lat[2] ^ lat[0]).normalize(); + Vector3 norm3 = (lat[0] ^ lat[1]).normalize(); + double cos10 = norm1 * lat[0]; + double cos21 = norm2 * lat[1]; + double cos32 = norm3 * lat[2]; + tau_max[0] = abs(r_cutoff/cos10); + tau_max[1] = abs(r_cutoff/cos21); + tau_max[2] = abs(r_cutoff/cos32); +} + +void Vdwd3::init(const UnitCell_pseudo &ucell) +{ + lat.resize(3); + lat[0] = ucell.a1*ucell.lat0; + lat[1] = ucell.a2*ucell.lat0; + lat[2] = ucell.a3*ucell.lat0; + + vectoratom_kind = atomkind(ucell); + iz.reserve(ucell.nat); + xyz.reserve(ucell.nat); + for(size_t it=0; it!=ucell.ntype; it++) + for(size_t ia=0; ia!=ucell.atoms[it].na; ia++) + { + iz.push_back(atom_kind[it]); + xyz.push_back(ucell.atoms[it].tau[ia] * ucell.lat0); + } + + vector tau_max(3); + if(para.model=="radius") + { + rep_vdw.resize(3); + set_criteria(para.rthr2,lat,tau_max); + for(size_t i=0 ; i<3 ; i++) + rep_vdw[i] = ceil(tau_max[i]); + } + else if(para.model=="period") + rep_vdw = {para.period.x, para.period.y, para.period.z}; + rep_cn.resize(3); + set_criteria(para.cn_thr2,lat,tau_max); + for(size_t i=0 ; i<3 ; i++) + rep_cn[i] = ceil(tau_max[i]); +} + +vector Vdwd3::atomkind (const UnitCell_pseudo &ucell) +{ + vectoratom_kind(ucell.ntype); + for(size_t i=0 ; i!=ucell.ntype ; i++) + for(int j=0; j!=element_name.size(); j++) + if (ucell.atoms[i].psd == element_name[j]) + { + atom_kind[i] = j; + break; + } + return atom_kind; +} + +void Vdwd3::getc6(int &iat, int &jat, double &nci, double &ncj, double &c6) +{ + double c6mem = -1e99, rsum = 0.0, csum = 0.0, r_save = 1e99; + double cn1 = 0.0, cn2 = 0.0, r = 0.0; + for(size_t i=0; i!=para.mxc[iat]; i++) + for(size_t j=0; j!=para.mxc[jat]; j++) + { + c6 = para.c6ab[0][j][i][jat][iat]; + if(c6 > 0) + { + cn1 = para.c6ab[1][j][i][jat][iat]; + cn2 = para.c6ab[2][j][i][jat][iat]; + r = pow((cn1-nci), 2)+pow((cn2-ncj), 2); + if(r < r_save) + { + r_save = r; + c6mem = c6; + } + double tmp1 = exp(para.k3*r); + rsum += tmp1; + csum += tmp1*c6; + } + } + c6 = (rsum > 1e-99) ? csum/rsum : c6mem; +} + +void Vdwd3::pbcncoord(vector &cn) +{ + for(size_t i=0; i!=ucell.nat; i++) + { + double xn = 0.0; + Vector3 tau; + double r2 = 0.0, rr = 0.0; + for(size_t iat=0; iat!=ucell.nat; iat++) + for(int taux=-rep_cn[0]; taux<=rep_cn[0]; taux++) + for(int tauy=-rep_cn[1]; tauy<=rep_cn[1]; tauy++) + for(int tauz=-rep_cn[2]; tauz<=rep_cn[2]; tauz++) + { + if(iat==i && taux==0 && tauy==0 && tauz==0) continue; + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = (xyz[iat]-xyz[i]+tau).norm2(); + if(r2 > para.cn_thr2) continue; + rr = (para.rcov[iz[i]]+para.rcov[iz[iat]])/sqrt(r2); + xn += 1.0/(1.0+exp(-para.k1*(rr-1.0))); + } + cn[i] = xn; + } +} + +void Vdwd3::pbcthreebody(vector &iz, vector> &lat, vector> &xyz, vector &rep_cn, vector &cc6ab, double &eabc) +{ + double sr9=0.75, alp9=-16.0; + int ij, ik, jk; + double r0ij, r0ik, r0jk, c9, rij2, rik2, rjk2, rr0ij, rr0ik, rr0jk, geomean, fdamp, tmp1, tmp2, tmp3, tmp4, ang; + Vector3 ijvec, ikvec, jkvec, jtau, ktau; + vector repmin(3), repmax(3); + for(int iat=2; iat!=ucell.nat; iat++) + for(int jat=1; jat!=iat; jat++) + { + ijvec = xyz[jat]-xyz[iat]; + ij = lin(iat, jat); + r0ij = para.r0ab[iz[jat]][iz[iat]]; + for(int kat=0; kat!=jat; kat++) + { + ik = lin(iat, kat); + jk = lin(jat, kat); + ikvec = xyz[kat]-xyz[iat]; + jkvec = xyz[kat]-xyz[jat]; + c9 = -cc6ab[ij]*cc6ab[ik]*cc6ab[jk]; + + r0ik = para.r0ab[iz[kat]][iz[iat]]; + r0jk = para.r0ab[iz[kat]][iz[jat]]; + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = (ijvec+jtau).norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/r0ij; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/r0ik; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/r0jk; + + geomean = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + fdamp = 1.0/(1.0+6.0*pow(sr9*geomean, alp9)); + tmp1 = (rij2+rjk2-rik2); + tmp2 = (rij2+rik2-rjk2); + tmp3 = (rik2+rjk2-rij2); + tmp4=rij2*rjk2*rik2; + + ang = (0.375*tmp1*tmp2*tmp3/tmp4+1.0)/pow(tmp4, 1.5); + + eabc += ang*c9*fdamp; + } // end ktau + } // end jtauz + } // end jtauy + } // end jtaux + } // end kat + } // end jat + //end iat + + for(int iat=1; iat!=ucell.nat; iat++) + { + int jat = iat; + ij = lin(iat, jat); + ijvec.set(0, 0, 0); + r0ij = para.r0ab[iz[jat]][iz[iat]]; + for(int kat=0; kat!=iat; kat++) + { + jk = lin(jat, kat); + ik = jk; + ikvec = xyz[kat] - xyz[iat]; + jkvec = ikvec; + c9 = -cc6ab[ij]*cc6ab[ik]*cc6ab[jk]; + + r0ik = para.r0ab[iz[kat]][iz[iat]]; + r0jk = para.r0ab[iz[kat]][iz[jat]]; + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + if(jtaux == 0 && jtauy == 0 && jtauz == 0) continue; + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = (ijvec+jtau).norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/r0ij; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/r0ik; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/r0jk; + + geomean = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + fdamp = 1.0/(1.0+6.0*pow(sr9*geomean, alp9)); + tmp1 = (rij2+rjk2-rik2); + tmp2 = (rij2+rik2-rjk2); + tmp3 = (rik2+rjk2-rij2); + tmp4=rij2*rjk2*rik2; + + ang = (0.375*tmp1*tmp2*tmp3/tmp4+1.0)/pow(tmp4, 1.5); + + eabc += ang*c9*fdamp/2.0; + } // end ktau + } //end jtauz + } // end jtauy + } // end jtaux + } // end kat + } // end iat + + for(int iat=1; iat!=ucell.nat; iat++) + for(int jat=0; jat!=iat; jat++) + { + int kat = jat; + ij = lin(iat, jat); + jk = lin(jat, kat); + ik = ij; + ikvec = xyz[kat] - xyz[iat]; + ijvec = ikvec; + jkvec.set(0, 0, 0); + c9 = -cc6ab[ij]*cc6ab[ik]*cc6ab[jk]; + + r0ij = para.r0ab[iz[jat]][iz[iat]]; + r0ik = r0ij; + r0jk = para.r0ab[iz[kat]][iz[jat]]; + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = (ijvec+jtau).norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/r0ij; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + if(jtaux == ktaux && jtauy == ktauy && jtauz == ktauz) continue; + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/r0ik; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/r0jk; + + geomean = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + fdamp = 1.0/(1.0+6.0*pow(sr9*geomean, alp9)); + tmp1 = (rij2+rjk2-rik2); + tmp2 = (rij2+rik2-rjk2); + tmp3 = (rik2+rjk2-rij2); + tmp4=rij2*rjk2*rik2; + + ang = (0.375*tmp1*tmp2*tmp3/tmp4+1.0)/pow(tmp4, 1.5); + + eabc += ang*c9*fdamp/2.0; + } // end ktau + } //end jtauz + } // end jtauy + } // end jtaux + } // end jat + // end iat + + for(int iat=0; iat!=ucell.nat; iat++) + { + int jat = iat; + int kat = iat; + ijvec.set(0, 0, 0); + ij = lin(iat, iat); + ik = ij; + jk = ij; + ikvec = ijvec; + jkvec = ikvec; + c9 = -cc6ab[ij]*cc6ab[ik]*cc6ab[jk]; + + r0ij = para.r0ab[iz[iat]][iz[iat]]; + r0ik = r0ij; + r0jk = r0ij; + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + if(jtaux == 0 && jtauy == 0 && jtauz == 0) continue; + rij2 = jtau.norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/r0ij; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + if(ktaux == 0 && ktauy == 0 && ktauz == 0) continue; + if(jtaux == ktaux && jtauy == ktauy && jtauz == ktauz) continue; + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = ktau.norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/r0ik; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/r0jk; + + geomean = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + fdamp = 1.0/(1.0+6.0*pow(sr9*geomean, alp9)); + tmp1 = (rij2+rjk2-rik2); + tmp2 = (rij2+rik2-rjk2); + tmp3 = (rik2+rjk2-rij2); + tmp4=rij2*rjk2*rik2; + + ang = (0.375*tmp1*tmp2*tmp3/tmp4+1.0)/pow(tmp4, 1.5); + + eabc += ang*c9*fdamp/6.0; + } // end ktau + } //end jtauz + } // end jtauy + } // end jtaux + + } // end iat +} + +void Vdwd3::cal_energy() +{ + TITLE("Vdwd3","cal_energy"); + init(ucell); + + int ij; + double c6 = 0.0, c8 = 0.0, r2 = 0.0, r6 = 0.0, r8 = 0.0, rr = 0.0, damp6 = 0.0, damp8 = 0.0; + double e6 = 0.0, e8 = 0.0, eabc = 0.0; + vector cc6ab(ucell.nat*ucell.nat), cn(ucell.nat); + pbcncoord(cn); + Vector3 tau; + if(para.version == "d3_0") // DFT-D3(zero-damping) + { + double tmp; + for(int iat=0; iat!=ucell.nat-1; iat++) + for(int jat=iat+1; jat!=ucell.nat; jat++) + { + getc6(iz[iat], iz[jat], cn[iat], cn[jat], c6); + if(para.abc) + { + ij = lin(iat, jat); + cc6ab[ij] = sqrt(c6); + } + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = (xyz[iat]-xyz[jat]+tau).norm2(); + if(r2 > para.rthr2) continue; + rr = para.r0ab[iz[iat]][iz[jat]]/sqrt(r2); + // zero-damping function + tmp = para.rs6*rr; + damp6 = 1.0/(1.0+6.0*pow(tmp, para.alp6)); + tmp = para.rs18*rr; + damp8 = 1.0/(1.0+6.0*pow(tmp, para.alp8)); + + r6 = pow(r2, 3); + e6 += damp6/r6*c6; + + c8 = 3.0*para.r2r4[iz[iat]]*para.r2r4[iz[jat]]*c6; + r8 = r6*r2; + e8 += c8*damp8/r8; + } // end tau + } // end jat + + for(int iat=0; iat!=ucell.nat; iat++) + { + int jat = iat; + getc6(iz[iat], iz[jat], cn[iat], cn[jat], c6); + if(para.abc) + { + ij = lin(iat, jat); + cc6ab[ij] = sqrt(c6); + } + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + if(taux==0 && tauy==0 && tauz==0) continue; + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = tau.norm2(); + if(r2 > para.rthr2) continue; + rr = para.r0ab[iz[iat]][iz[jat]]/sqrt(r2); + + // zero-damping function + tmp = para.rs6*rr; + damp6 = 1.0/(1.0+6.0*pow(tmp,para.alp6)); + tmp = para.rs18*rr; + damp8 = 1.0/(1.0+6.0*pow(tmp, para.alp8)); + + r6 = pow(r2, 3); + e6 += damp6/r6*c6*0.5; + + c8 = 3.0*para.r2r4[iz[iat]]*para.r2r4[iz[jat]]*c6; + r8 = r6*r2; + e8 += c8*damp8/r8*0.5; + } // end tau + } // end iat + } // end d3_0 + else if(para.version == "d3_bj") // DFT-D3(BJ-damping) + { + double r42; + for(int iat=0; iat!=ucell.nat; iat++) + { + for(int jat=iat+1; jat!=ucell.nat; jat++) + { + getc6(iz[iat], iz[jat], cn[iat], cn[jat], c6); + if(para.abc) + { + ij = lin(iat, jat); + cc6ab[ij] = sqrt(c6); + } + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = (xyz[iat]-xyz[jat]+tau).norm2(); + if(r2 > para.rthr2) continue; + rr = para.r0ab[iz[iat]][iz[jat]]/sqrt(r2); + + // BJ-damping function + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[jat]]; + damp6 = pow((para.rs6*sqrt(3.0*r42)+para.rs18), 6); + damp8 = pow((para.rs6*sqrt(3.0*r42)+para.rs18), 8); + + r6 = pow(r2, 3); + e6 += c6/(r6+damp6); + + c8 = 3.0*c6*r42; + r8 = r6*r2; + e8 += c8/(r8+damp8); + } // end tau + } // end jat + int jat = iat; + getc6(iz[iat], iz[jat], cn[iat], cn[jat], c6); + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[jat]]; + damp6 = pow((para.rs6*sqrt(3.0*r42)+para.rs18), 6); + damp8 = pow((para.rs6*sqrt(3.0*r42)+para.rs18), 8); + if(para.abc) + { + ij = lin(iat, jat); + cc6ab[ij] = sqrt(c6); + } + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + if(taux==0 && tauy==0 && tauz==0) continue; + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = tau.norm2(); + if(r2 > para.rthr2) continue; + rr = para.r0ab[iz[iat]][iz[jat]]/sqrt(r2); + + r6 = pow(r2, 3); + e6 += c6/(r6+damp6)*0.5; + + c8 = 3.0*c6*r42; + r8 = r6*r2; + e8 += c8/(r8+damp8)*0.5; + } // end tau + } // end iat + } // end d3_bj + + if(para.abc) + { + pbcthreebody(iz, lat, xyz, rep_cn, cc6ab, eabc); + } + energy = (-para.s6*e6-para.s18*e8-eabc)*2; +} + +void Vdwd3::get_dc6_dcnij(int &mxci, int &mxcj, double &cni, double &cnj, int &izi, int &izj, int &iat, int &jat, double &c6check, double &dc6i, double &dc6j) +{ + double r_save = 9999.0, c6mem = -1e99, zaehler = 0.0, nenner = 0.0; + double dzaehler_i = 0.0, dnenner_i = 0.0, dzaehler_j = 0.0, dnenner_j = 0.0; + double c6ref = 0.0, cn_refi = 0.0, cn_refj = 0.0, r = 0.0, expterm = 0.0, term = 0.0; + for(size_t a=0; a!=mxci; a++) + for(size_t b=0; b!=mxcj; b++) + { + c6ref = para.c6ab[0][b][a][izj][izi]; + if(c6ref > 0) + { + cn_refi = para.c6ab[1][b][a][izj][izi]; + cn_refj = para.c6ab[2][b][a][izj][izi]; + r = (cn_refi-cni)*(cn_refi-cni)+(cn_refj-cnj)*(cn_refj-cnj); + if(r < r_save) + { + r_save = r; + c6mem = c6ref; + } + expterm = exp(para.k3*r); + zaehler += c6ref*expterm; + nenner += expterm; + expterm *= 2.0*para.k3; + term = expterm*(cni-cn_refi); + dzaehler_i += c6ref*term; + dnenner_i += term; + + term = expterm*(cnj-cn_refj); + dzaehler_j += c6ref*term; + dnenner_j += term; + } + } + + if(nenner > 1e-99) + { + c6check = zaehler/nenner; + dc6i = ((dzaehler_i*nenner)-(dnenner_i*zaehler))/(nenner*nenner); + dc6j = ((dzaehler_j*nenner)-(dnenner_j*zaehler))/(nenner*nenner); + } + else + { + c6check = c6mem; + dc6i = 0.0; + dc6j = 0.0; + } +} + +void Vdwd3::pbcgdisp(vector> &g, matrix &sigma) +{ + init(ucell); + vector c6save(ucell.nat*(ucell.nat+1)), dc6_rest_sum(ucell.nat*(ucell.nat+1)/2), dc6i(ucell.nat), cn(ucell.nat); + pbcncoord(cn); + vector> dc6ij(ucell.nat, vector(ucell.nat)); + double c6 = 0.0, dc6iji = 0.0, dc6ijj = 0.0; + double r = 0.0, r0 = 0.0, r2 = 0.0, r6 = 0.0, r7 = 0.0, r8 = 0.0, r9 = 0.0; + double r42 = 0.0, rcovij = 0.0, t6 = 0.0, t8 = 0.0, dc6_rest = 0.0; + int linii = 0, linij = 0; + Vector3 tau; + vector>>> drij(ucell.nat*(ucell.nat+1)/2, vector>>(2*rep_vdw[0]+1, vector>(2*rep_vdw[1]+1, vector(2*rep_vdw[2]+1)))); + if(para.version == "d3_0") + { + double damp6 = 0.0, damp8 = 0.0; + for(int iat=0; iat!=ucell.nat; iat++) + { + get_dc6_dcnij(para.mxc[iz[iat]], para.mxc[iz[iat]], cn[iat], cn[iat], iz[iat], iz[iat], iat, iat, c6, dc6iji, dc6ijj); + + linii = lin(iat, iat); + c6save[linii] = c6; + dc6ij[iat][iat] = dc6iji; + r0 = para.r0ab[iz[iat]][iz[iat]]; + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[iat]]; + rcovij = para.rcov[iz[iat]]+para.rcov[iz[iat]]; + + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + + // first dE/d(tau) + r2 = tau.norm2(); + if(r2 > 0.1 && r2 < para.rthr2) + { + r = sqrt(r2); + r6 = pow(r2, 3); + r7 = r6*r; + r8 = r6*r2; + r9 = r8*r; + + t6 = pow(r/(para.rs6*r0), -para.alp6); + damp6 = 1.0/(1.0+6.0*t6); + t8 = pow(r/(para.rs18*r0), -para.alp8); + damp8 = 1.0/(1.0+6.0*t8); + + // d(r^(-6))/d(tau) + drij[linii][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += (-para.s6*(6.0/(r7)*c6*damp6)-para.s18*(24.0/(r9)*c6*r42*damp8))*0.5; + // d(f_dmp)/d(tau) + drij[linii][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += (para.s6*c6/r7*6.0*para.alp6*t6*damp6*damp6+para.s18*c6*r42/r9*18.0*para.alp8*t8*damp8*damp8)*0.5; + + dc6_rest = (para.s6/r6*damp6+3.0*para.s18*r42/r8*damp8)*0.5; + dc6i[iat] += dc6_rest*(dc6iji+dc6ijj); + dc6_rest_sum[linii] += dc6_rest; + } + } // end tau + for(int jat=0; jat!=iat; jat++) + { + get_dc6_dcnij(para.mxc[iz[iat]], para.mxc[iz[jat]], cn[iat], cn[jat], iz[iat], iz[jat], iat, jat, c6, dc6iji, dc6ijj); + + linij = lin(iat, jat); + c6save[linij] = c6; + r0 = para.r0ab[iz[iat]][iz[jat]]; + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[jat]]; + rcovij = para.rcov[iz[iat]]+para.rcov[iz[jat]]; + dc6ij[jat][iat] = dc6iji; + dc6ij[iat][jat] = dc6ijj; + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = (xyz[jat]-xyz[iat]+tau).norm2(); + if(r2 > para.rthr2) continue; + + r = sqrt(r2); + r6 = pow(r2, 3); + r7 = r6*r; + r8 = r6*r2; + r9 = r8*r; + + t6 = pow(r/(para.rs6*r0), -para.alp6); + damp6 = 1.0/(1.0+6.0*t6); + t8 = pow(r/(para.rs18*r0), -para.alp8); + damp8 = 1.0/(1.0+6.0*t8); + + // d(r^(-6))/d(r_ij) + drij[linij][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += -para.s6*(6.0/(r7)*c6*damp6)-para.s18*(24.0/(r9)*c6*r42*damp8); + // d(f_dmp)/d(r_ij) + drij[linij][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += para.s6*c6/r7*6.0*para.alp6*t6*damp6*damp6+para.s18*c6*r42/r9*18.0*para.alp8*t8*damp8*damp8; + + dc6_rest = para.s6/r6*damp6+3.0*para.s18*r42/r8*damp8; + dc6i[iat] += dc6_rest*dc6iji; + dc6i[jat] += dc6_rest*dc6ijj; + dc6_rest_sum[linij] += dc6_rest; + } // end tau + } // end jat + } // end iat + } // end d3_0 + else if(para.version == "d3_bj") + { + double r4; + for(int iat=0; iat!=ucell.nat; iat++) + { + get_dc6_dcnij(para.mxc[iz[iat]], para.mxc[iz[iat]], cn[iat], cn[iat], iz[iat], iz[iat], iat, iat, c6, dc6iji, dc6ijj); + + linii = lin(iat, iat); + c6save[linii] = c6; + dc6ij[iat][iat] = dc6iji; + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[iat]]; + r0 = para.rs6*sqrt(3.0*r42)+para.rs18; + rcovij = para.rcov[iz[iat]]+para.rcov[iz[iat]]; + + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + + // first dE/d(tau) + r2 = tau.norm2(); + if(r2 > 0.1 && r2 < para.rthr2) + { + r = sqrt(r2); + r4 = r2*r2; + r6 = pow(r2, 3); + r7 = r6*r; + r8 = r6*r2; + r9 = r8*r; + + t6 = r6+pow(r0, 6); + t8 = r8+pow(r0, 8); + + // d(1/r^(-6)+r0^6)/d(r) + drij[linii][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += -para.s6*c6*6.0*r4*r/(t6*t6)*0.5-para.s18*c6*24.0*r42*r7/(t8*t8)*0.5; + + dc6_rest = (para.s6/t6+3.0*para.s18*r42/t8)*0.5; + dc6i[iat] += dc6_rest*(dc6iji+dc6ijj); + dc6_rest_sum[linii] += dc6_rest; + } + } // end tau + for(int jat=0; jat!=iat; jat++) + { + get_dc6_dcnij(para.mxc[iz[iat]], para.mxc[iz[jat]], cn[iat], cn[jat], iz[iat], iz[jat], iat, jat, c6, dc6iji, dc6ijj); + + linij = lin(iat, jat); + c6save[linij] = c6; + r42 = para.r2r4[iz[iat]]*para.r2r4[iz[jat]]; + r0 = para.rs6*sqrt(3.0*r42)+para.rs18; + rcovij = para.rcov[iz[iat]]+para.rcov[iz[jat]]; + dc6ij[jat][iat] = dc6iji; + dc6ij[iat][jat] = dc6ijj; + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = (xyz[jat]-xyz[iat]+tau).norm2(); + if(r2 > para.rthr2) continue; + + r = sqrt(r2); + r4 = r2*r2; + r6 = pow(r2, 3); + r7 = r6*r; + r8 = r6*r2; + r9 = r8*r; + + t6 = r6+pow(r0, 6); + t8 = r8+pow(r0, 8); + + drij[linij][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]] += -para.s6*c6*6.0*r4*r/(t6*t6)-para.s18*c6*24.0*r42*r7/(t8*t8); + + dc6_rest = para.s6/t6+3.0*para.s18*r42/t8; + dc6i[iat] += dc6_rest*dc6iji; + dc6i[jat] += dc6_rest*dc6ijj; + dc6_rest_sum[linij] += dc6_rest; + } // end tau + } // end jat + } // end iat + } // end d3_bj + + if(para.abc) + { + Vector3 ijvec, ikvec, jkvec, jtau, ktau; + vector repmin(3), repmax(3); + double sr9=0.75, alp9=-16.0; + double linik, linjk, rij2, rik2, rjk2, rr0ij, rr0ik, rr0jk, geomean2, geomean, geomean3, r0av, r; + double c6ij, c6ik, c6jk, c9, damp9, ang, dfdmp, dang, tmp1, dc9; + for(int iat=2; iat!=ucell.nat; iat++) + for(int jat=1; jat!=iat; jat++) + { + linij = lin(iat, jat); + ijvec = xyz[jat] - xyz[iat]; + + c6ij = c6save[linij]; + for(int kat=0; kat!=jat; kat++) + { + linik = lin(iat, kat); + linjk = lin(jat, kat); + ikvec = xyz[kat] - xyz[iat]; + jkvec = xyz[kat] - xyz[jat]; + + c6ik = c6save[linik]; + c6jk = c6save[linjk]; + c9 = -1.0*sqrt(c6ij*c6ik*c6jk); + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = (ijvec+jtau).norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/para.r0ab[iz[jat]][iz[iat]]; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/para.r0ab[iz[kat]][iz[iat]]; + rr0jk = sqrt(rjk2)/para.r0ab[iz[kat]][iz[jat]]; + + geomean2 = rij2*rjk2*rik2; + r0av = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + damp9 = 1.0/(1.0+6.0*pow(sr9*r0av, alp9)); + geomean = sqrt(geomean2); + geomean3 = geomean*geomean2; + ang = 0.375*(rij2+rjk2-rik2)*(rij2-rjk2+rik2)*(-rij2+rjk2+rik2)/(geomean3*geomean2)+1.0/geomean3; + dc6_rest = ang*damp9; + dfdmp = 2.0*alp9*pow(0.75*r0av, alp9)*damp9*damp9; + + r = sqrt(rij2); + dang = -0.375*(pow(rij2, 3)+pow(rij2, 2)*(rjk2+rik2)+rij2*(3.0*pow(rjk2, 2)+2.0*rjk2*rik2+3.0*pow(rik2, 2))-5.0*pow(rjk2-rik2, 2)*(rjk2+rik2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linij][jtaux+rep_vdw[0]][jtauy+rep_vdw[1]][jtauz+rep_vdw[2]] -= tmp1; + + r = sqrt(rik2); + dang = -0.375*(pow(rik2, 3)+pow(rik2, 2)*(rjk2+rij2)+rik2*(3.0*pow(rjk2, 2)+2.0*rjk2*rij2+3.0*pow(rij2, 2))-5.0*pow(rjk2-rij2, 2)*(rjk2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linik][ktaux+rep_vdw[0]][ktauy+rep_vdw[1]][ktauz+rep_vdw[2]] -= tmp1; + + r = sqrt(rjk2); + dang = -0.375*(pow(rjk2, 3)+pow(rjk2, 2)*(rik2+rij2)+rjk2*(3.0*pow(rik2, 2)+2.0*rik2*rij2+3.0*pow(rij2, 2))-5.0*pow(rik2-rij2, 2)*(rik2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linjk][ktaux-jtaux+rep_vdw[0]][ktauy-jtauy+rep_vdw[1]][ktauz-jtauz+rep_vdw[2]] -= tmp1; + + dc9 = (dc6ij[jat][iat]/c6ij+dc6ij[kat][iat]/c6ik)*c9*0.5; + dc6i[iat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][jat]/c6ij+dc6ij[kat][jat]/c6jk)*c9*0.5; + dc6i[jat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][kat]/c6ik+dc6ij[jat][kat]/c6jk)*c9*0.5; + dc6i[kat] += dc6_rest*dc9; + } // end ktau + } // end jtauz + } //end jtauy + } // end jtaux + } // end kat + } // end jat + + for(int iat=1; iat!=ucell.nat; iat++) + { + int jat = iat; + linij = lin(iat, jat); + ijvec.set(0, 0, 0); + + c6ij = c6save[linij]; + for(int kat=0; kat!=iat; kat++) + { + linjk = lin(jat, kat); + linik = linjk; + ikvec = xyz[kat] - xyz[iat]; + jkvec = ikvec; + + c6ik = c6save[linik]; + c6jk = c6ik; + c9 = -1.0*sqrt(c6ij*c6ik*c6jk); + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + if(jtaux == 0 && jtauy == 0 && jtauz == 0) continue; + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = jtau.norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/para.r0ab[iz[jat]][iz[iat]]; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/para.r0ab[iz[kat]][iz[iat]]; + rr0jk = sqrt(rjk2)/para.r0ab[iz[kat]][iz[jat]]; + + geomean2 = rij2*rjk2*rik2; + r0av = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + damp9 = 1.0/(1.0+6.0*pow(sr9*r0av, alp9)); + geomean = sqrt(geomean2); + geomean3 = geomean*geomean2; + ang = 0.375*(rij2+rjk2-rik2)*(rij2-rjk2+rik2)*(-rij2+rjk2+rik2)/(geomean3*geomean2)+1.0/geomean3; + dc6_rest = ang*damp9/2.0; + dfdmp = 2.0*alp9*pow(0.75*r0av, alp9)*damp9*damp9; + + r = sqrt(rij2); + dang = -0.375*(pow(rij2, 3)+pow(rij2, 2)*(rjk2+rik2)+rij2*(3.0*pow(rjk2, 2)+2.0*rjk2*rik2+3.0*pow(rik2, 2))-5.0*pow(rjk2-rik2, 2)*(rjk2+rik2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linij][jtaux+rep_vdw[0]][jtauy+rep_vdw[1]][jtauz+rep_vdw[2]] -= tmp1/2.0; + + r = sqrt(rik2); + dang = -0.375*(pow(rik2, 3)+pow(rik2, 2)*(rjk2+rij2)+rik2*(3.0*pow(rjk2, 2)+2.0*rjk2*rij2+3.0*pow(rij2, 2))-5.0*pow(rjk2-rij2, 2)*(rjk2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linik][ktaux+rep_vdw[0]][ktauy+rep_vdw[1]][ktauz+rep_vdw[2]] -= tmp1/2.0; + + r = sqrt(rjk2); + dang = -0.375*(pow(rjk2, 3)+pow(rjk2, 2)*(rik2+rij2)+rjk2*(3.0*pow(rik2, 2)+2.0*rik2*rij2+3.0*pow(rij2, 2))-5.0*pow(rik2-rij2, 2)*(rik2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linjk][ktaux-jtaux+rep_vdw[0]][ktauy-jtauy+rep_vdw[1]][ktauz-jtauz+rep_vdw[2]] -= tmp1/2.0; + + dc9 = (dc6ij[jat][iat]/c6ij+dc6ij[kat][iat]/c6ik)*c9*0.5; + dc6i[iat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][jat]/c6ij+dc6ij[kat][jat]/c6jk)*c9*0.5; + dc6i[jat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][kat]/c6ik+dc6ij[jat][kat]/c6jk)*c9*0.5; + dc6i[kat] += dc6_rest*dc9; + } // end ktau + } // end jtauz + } //end jtauy + } // end jtaux + } // end kat + } // end iat + + for(int iat=1; iat!=ucell.nat; iat++) + for(int jat=0; jat!=iat; jat++) + { + int kat = jat; + linij = lin(iat, jat); + linjk = lin(jat, kat); + linik = linij; + ikvec = xyz[kat] - xyz[iat]; + ijvec = ikvec; + jkvec.set(0, 0, 0); + + c6ij = c6save[linij]; + c6ik = c6ij; + c6jk = c6save[linjk]; + c9 = -1.0*sqrt(c6ij*c6ik*c6jk); + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = (ijvec+jtau).norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/para.r0ab[iz[jat]][iz[iat]]; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + if(jtaux == ktaux && jtauy == ktauy && jtauz == ktauz) continue; + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = (ikvec+ktau).norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/para.r0ab[iz[kat]][iz[iat]]; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/para.r0ab[iz[kat]][iz[jat]]; + + geomean2 = rij2*rjk2*rik2; + r0av = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + damp9 = 1.0/(1.0+6.0*pow(sr9*r0av, alp9)); + geomean = sqrt(geomean2); + geomean3 = geomean*geomean2; + ang = 0.375*(rij2+rjk2-rik2)*(rij2-rjk2+rik2)*(-rij2+rjk2+rik2)/(geomean3*geomean2)+1.0/geomean3; + dc6_rest = ang*damp9/2.0; + dfdmp = 2.0*alp9*pow(0.75*r0av, alp9)*damp9*damp9; + + r = sqrt(rij2); + dang = -0.375*(pow(rij2, 3)+pow(rij2, 2)*(rjk2+rik2)+rij2*(3.0*pow(rjk2, 2)+2.0*rjk2*rik2+3.0*pow(rik2, 2))-5.0*pow(rjk2-rik2, 2)*(rjk2+rik2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linij][jtaux+rep_vdw[0]][jtauy+rep_vdw[1]][jtauz+rep_vdw[2]] -= tmp1/2.0; + + r = sqrt(rik2); + dang = -0.375*(pow(rik2, 3)+pow(rik2, 2)*(rjk2+rij2)+rik2*(3.0*pow(rjk2, 2)+2.0*rjk2*rij2+3.0*pow(rij2, 2))-5.0*pow(rjk2-rij2, 2)*(rjk2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linik][ktaux+rep_vdw[0]][ktauy+rep_vdw[1]][ktauz+rep_vdw[2]] -= tmp1/2.0; + + r = sqrt(rjk2); + dang = -0.375*(pow(rjk2, 3)+pow(rjk2, 2)*(rik2+rij2)+rjk2*(3.0*pow(rik2, 2)+2.0*rik2*rij2+3.0*pow(rij2, 2))-5.0*pow(rik2-rij2, 2)*(rik2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linjk][ktaux-jtaux+rep_vdw[0]][ktauy-jtauy+rep_vdw[1]][ktauz-jtauz+rep_vdw[2]] -= tmp1/2.0; + + dc9 = (dc6ij[jat][iat]/c6ij+dc6ij[kat][iat]/c6ik)*c9*0.5; + dc6i[iat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][jat]/c6ij+dc6ij[kat][jat]/c6jk)*c9*0.5; + dc6i[jat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][kat]/c6ik+dc6ij[jat][kat]/c6jk)*c9*0.5; + dc6i[kat] += dc6_rest*dc9; + } // end ktau + } // end jtauz + } //end jtauy + } // end jtaux + } // end jat + // end iat + + for(int iat=0; iat!=ucell.nat; iat++) + { + int jat = iat; + int kat = iat; + ijvec.set(0, 0, 0); + linij = lin(iat, jat); + linik = lin(iat, kat); + linjk = lin(jat, kat); + ikvec = ijvec; + jkvec = ikvec; + c6ij = c6save[linij]; + c6ik = c6ij; + c6jk = c6ij; + c9 = -1.0*sqrt(c6ij*c6ik*c6jk); + + for(int jtaux=-rep_cn[0]; jtaux<=rep_cn[0]; jtaux++) + { + repmin[0] = max(-rep_cn[0], jtaux-rep_cn[0]); + repmax[0] = min(rep_cn[0], jtaux+rep_cn[0]); + for(int jtauy=-rep_cn[1]; jtauy<=rep_cn[1]; jtauy++) + { + repmin[1] = max(-rep_cn[1], jtauy-rep_cn[1]); + repmax[1] = min(rep_cn[1], jtauy+rep_cn[1]); + for(int jtauz=-rep_cn[2]; jtauz<=rep_cn[2]; jtauz++) + { + repmin[2] = max(-rep_cn[2], jtauz-rep_cn[2]); + repmax[2] = min(rep_cn[2], jtauz+rep_cn[2]); + if(jtaux == 0 && jtauy == 0 && jtauz == 0) continue; + jtau = static_cast(jtaux)*lat[0]+static_cast(jtauy)*lat[1]+static_cast(jtauz)*lat[2]; + rij2 = jtau.norm2(); + if(rij2>para.cn_thr2) continue; + rr0ij = sqrt(rij2)/para.r0ab[iz[jat]][iz[iat]]; + + for(int ktaux=repmin[0]; ktaux<=repmax[0]; ktaux++) + for(int ktauy=repmin[1]; ktauy<=repmax[1]; ktauy++) + for(int ktauz=repmin[2]; ktauz<=repmax[2]; ktauz++) + { + if(ktaux == 0 && ktauy == 0 && ktauz == 0) continue; + if(jtaux == ktaux && jtauy == ktauy && jtauz == ktauz) continue; + ktau = static_cast(ktaux)*lat[0]+static_cast(ktauy)*lat[1]+static_cast(ktauz)*lat[2]; + rik2 = ktau.norm2(); + if(rik2>para.cn_thr2) continue; + rr0ik = sqrt(rik2)/para.r0ab[iz[kat]][iz[iat]]; + + rjk2 = (jkvec+ktau-jtau).norm2(); + if(rjk2>para.cn_thr2) continue; + rr0jk = sqrt(rjk2)/para.r0ab[iz[kat]][iz[jat]]; + + geomean2 = rij2*rjk2*rik2; + r0av = pow(rr0ij*rr0ik*rr0jk, 1.0/3.0); + damp9 = 1.0/(1.0+6.0*pow(sr9*r0av, alp9)); + geomean = sqrt(geomean2); + geomean3 = geomean*geomean2; + ang = 0.375*(rij2+rjk2-rik2)*(rij2-rjk2+rik2)*(-rij2+rjk2+rik2)/(geomean3*geomean2)+1.0/geomean3; + dc6_rest = ang*damp9/6.0; + dfdmp = 2.0*alp9*pow(0.75*r0av, alp9)*damp9*damp9; + + r = sqrt(rij2); + dang = -0.375*(pow(rij2, 3)+pow(rij2, 2)*(rjk2+rik2)+rij2*(3.0*pow(rjk2, 2)+2.0*rjk2*rik2+3.0*pow(rik2, 2))-5.0*pow(rjk2-rik2, 2)*(rjk2+rik2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linij][jtaux+rep_vdw[0]][jtauy+rep_vdw[1]][jtauz+rep_vdw[2]] -= tmp1/6.0; + + r = sqrt(rik2); + dang = -0.375*(pow(rik2, 3)+pow(rik2, 2)*(rjk2+rij2)+rik2*(3.0*pow(rjk2, 2)+2.0*rjk2*rij2+3.0*pow(rij2, 2))-5.0*pow(rjk2-rij2, 2)*(rjk2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linik][ktaux+rep_vdw[0]][ktauy+rep_vdw[1]][ktauz+rep_vdw[2]] -= tmp1/6.0; + + r = sqrt(rjk2); + dang = -0.375*(pow(rjk2, 3)+pow(rjk2, 2)*(rik2+rij2)+rjk2*(3.0*pow(rik2, 2)+2.0*rik2*rij2+3.0*pow(rij2, 2))-5.0*pow(rik2-rij2, 2)*(rik2+rij2))/(r*geomean3*geomean2); + tmp1 = -dang*c9*damp9+dfdmp/r*c9*ang; + drij[linjk][ktaux-jtaux+rep_vdw[0]][ktauy-jtauy+rep_vdw[1]][ktauz-jtauz+rep_vdw[2]] -= tmp1/6.0; + + dc9 = (dc6ij[jat][iat]/c6ij+dc6ij[kat][iat]/c6ik)*c9*0.5; + dc6i[iat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][jat]/c6ij+dc6ij[kat][jat]/c6jk)*c9*0.5; + dc6i[jat] += dc6_rest*dc9; + + dc9 = (dc6ij[iat][kat]/c6ik+dc6ij[jat][kat]/c6jk)*c9*0.5; + dc6i[kat] += dc6_rest*dc9; + } // end ktau + } // end jtauz + } // end jtauy + } // jtaux + } // end iat + } + + // dE/dr_ij * dr_ij/dxyz_i + double expterm, dcnn, x1; + Vector3 rij, vec3; + for(int iat=1; iat!=ucell.nat; iat++) + for(int jat=0; jat!=iat; jat++) + { + linij = lin(iat, jat); + rcovij = para.rcov[iz[iat]]+para.rcov[iz[jat]]; + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + rij = xyz[jat]-xyz[iat]+tau; + r2 = rij.norm2(); + if(r2 > para.rthr2 || r2 < 0.5) continue; + r = sqrt(r2); + if(r2 < para.cn_thr2) + { + expterm = exp(-para.k1*(rcovij/r-1.0)); + dcnn = -para.k1*rcovij*expterm/(r2*(expterm+1.0)*(expterm+1.0)); + } + else + dcnn = 0.0; + x1 = drij[linij][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]]+dcnn*(dc6i[iat]+dc6i[jat]); + vec3 = x1*rij/r; + g[iat] += vec3; + g[jat] -= vec3; + + vector vec = {vec3.x, vec3.y, vec3.z}; + vector rij_vec = {rij.x, rij.y, rij.z}; + for(size_t i=0; i!=3; i++) + for(size_t j=0; j!=3; j++) + { + sigma(i, j) += vec[j]*rij_vec[i]; + } + } // end tau + } // end iat, jat + for(int iat=0; iat!=ucell.nat; iat++) + { + linii = lin(iat, iat); + rcovij = para.rcov[iz[iat]]+para.rcov[iz[iat]]; + for(int taux=-rep_vdw[0]; taux<=rep_vdw[0]; taux++) + for(int tauy=-rep_vdw[1]; tauy<=rep_vdw[1]; tauy++) + for(int tauz=-rep_vdw[2]; tauz<=rep_vdw[2]; tauz++) + { + if(taux == 0 && tauy == 0 && tauz == 0) continue; + tau = static_cast(taux)*lat[0]+static_cast(tauy)*lat[1]+static_cast(tauz)*lat[2]; + r2 = tau.norm2(); + r = sqrt(r2); + if(r2 < para.cn_thr2) + { + expterm = exp(-para.k1*(rcovij/r-1.0)); + dcnn = -para.k1*rcovij*expterm/(r2*(expterm+1.0)*(expterm+1.0)); + } + else + dcnn = 0.0; + x1 = drij[linii][taux+rep_vdw[0]][tauy+rep_vdw[1]][tauz+rep_vdw[2]]+dcnn*dc6i[iat]; + + vec3 = x1*tau/r; + vector vec = {vec3.x, vec3.y, vec3.z}; + vector tau_vec = {tau.x, tau.y, tau.z}; + for(size_t i=0; i!=3; i++) + for(size_t j=0; j!=3; j++) + { + sigma(i, j) += vec[j]*tau_vec[i]; + } + } // end tau + } // end iat +} + +void Vdwd3::cal_force() +{ + TITLE("Vdwd3","cal_force"); + + force.clear(); + force.resize(ucell.nat); + + vector> g; + g.clear(); + g.resize(ucell.nat); + matrix sigma(3, 3); + + pbcgdisp(g, sigma); + + for(size_t iat=0; iat!=ucell.nat; iat++) + force[iat] = -2.0*g[iat]; + +} + +void Vdwd3::cal_stress() +{ + TITLE("Vdwd3","cal_stress"); + + vector> g; + g.clear(); + g.resize(ucell.nat); + matrix sigma(3, 3); + + pbcgdisp(g, sigma); + + stress = Matrix3( + 2.0*sigma(0, 0), 2.0*sigma(0, 1), 2.0*sigma(0, 2), + 2.0*sigma(1, 0), 2.0*sigma(1, 1), 2.0*sigma(1, 2), + 2.0*sigma(2, 0), 2.0*sigma(2, 1), 2.0*sigma(2, 2) + )/ucell.omega; + +} diff --git a/ABACUS.develop/source/src_pw/vdwd3.h b/ABACUS.develop/source/src_pw/vdwd3.h index 52586beb97..792f6d1f8a 100644 --- a/ABACUS.develop/source/src_pw/vdwd3.h +++ b/ABACUS.develop/source/src_pw/vdwd3.h @@ -1,137 +1,54 @@ //========================================================== -// AUTHOR : jiyy +// AUTHOR : Yuyang Ji // DATE : 2019-04-22 +// UPDATE : 2021-4-19 //========================================================== #ifndef VDWD3_H #define VDWD3_H - -#include"unitcell_pseudo.h" -#include -#include"../input_conv.h" - -#ifdef __cplusplus -extern "C"{ -#endif -void setr0ab_(const int *max_elem,const double *autoang, - double (*r0ab)[94]); -void set_criteria_(double *rthr2,double (*lat)[3],double *tau_max); -void pbcedisp_(const int *max_elem,const int *maxc,const int *n, - double (*xyz)[3],int *iz,double (*c6ab)[5][5][94][94], - int *mxc,double *r2r4,double (*r0ab)[94], - double *rcov,double *rs6,double *rs8, - double *rs10,double *alp6,double *alp8,double *alp10, - int *version,bool *noabc, double *e6,double *e8,double *e10, - double *e12,double *e63,double (*lat)[3],double *rthr2, - int *rep_vdw,double *cn_thr2,int *rep_cn); -void pbcgdisp_(const int *max_elem,const int *maxc,const int *n, - double (*xyz)[3],int *iz,double (*c6ab)[5][5][94][94], - int *mxc,double *r2r4,double (*r0ab)[94], - double *rcov,double *s6,double *s18,double *rs6, - double *rs8,double *rs10,double *alp6,double *alp8, - double *alp10,bool *noabc,int *version,double (*g)[3],double *disp, - double (*stress)[3],double (*sigma)[3],double (*lat)[3],int *rep_v, - int *rep_cn,double *crit_vdw,double *crit_cn); -#ifdef __cplusplus -} -#endif +#include "src_pw/vdwd3_parameters.h" +#include "src_pw/unitcell_pseudo.h" +#include "src_global/vector3.h" +#include +#include class Vdwd3 { - public: - Vdwd3( const UnitCell_pseudo &unitcell); - - bool vdwD3; - - double energy_result; - double energy(); - - vector< vector > force_result; - vector< vector > force( - const bool force_for_vdw, - const bool stress_for_vdw, - matrix &force_vdw, - matrix &stress_result - ); - - private: - //third-order term? - bool abc; - bool noabc; - //R^2 distance neglect threshold (important for speed in case of large systems) (a.u.) - double rthr2; - //R^2 distance to cutoff for CN_calculation (a.u.) - double cn_thr2; - - string model; - - double s6; - double rs6; - double s18; - double alp; - double rs18; - - //energies - double e6; - double e8; - double e10; - double e12; - //3_th energy - double e63; - - - const int max_elem; - //maximum coordination number references per element - const int maxc; - const int nline; - - const UnitCell_pseudo &ucell; - vector atom_kind; - void atomkind(const UnitCell_pseudo &unitcell); - - void XYZ(const UnitCell_pseudo &unitcell,double (*xyz)[3],int *iz); - - //C6 for all element pairs - vector C6_tmp; - void init_C6_tmp(); - double c6ab[3][5][5][94][94]; - //how many different C6 for one element - int mxc[94]; - void init_mxc(); - int limit(int &i); - void loadc6(); - - //lattice in au - double lat[3][3]; - void setlat( const UnitCell_pseudo &unitcell); - - int version; - //void setfuncpar(int &ver); - - //atomic / values - vector r2r4; - void init_r2r4(); - double* add_r2r4; - //covalent radii - vector rcov; - void init_rcov(); - double* add_rcov; - - //cut-off radii for all element pairs - double r0ab[94][94]; - double tau_max[3]; - //repetitions of the unitcell to match the rthr and c_thr - int rep_vdw[3]; - int rep_cn[3]; - - bool init_set; - void initset(); - - //force and stress - double stress[3][3]; - double sigma[3][3]; - double disp; - - friend void Input_Conv::Convert(); +public: + + Vdwd3(const UnitCell_pseudo &unit_in, Vdwd3_Parameters ¶_in); + + void cal_energy(); + void cal_force(); + void cal_stress(); + + const double &get_energy()const{ return energy; } + const vector> &get_force() const{ return force; } + const Matrix3 &get_stress()const{ return stress; } + +private: + + const UnitCell_pseudo &ucell; + Vdwd3_Parameters ¶ + + double energy = 0; + vector> force; + Matrix3 stress; + + vector> lat; + vector iz; + vector> xyz; + vector rep_vdw; + vector rep_cn; + + void init(const UnitCell_pseudo &ucell); + void set_criteria(double &rthr, vector> &lat, vector &tau_max); + vector atomkind(const UnitCell_pseudo &ucell); + void getc6(int &iat, int &jat, double &nci, double &ncj, double &c6); + void pbcncoord(vector &cn); + //void pbcthreebody(vector &cc6ab, double &e63); + void pbcgdisp(vector> &g, matrix &sigma); + void get_dc6_dcnij(int &mxci, int &mxcj, double &cni, double &cnj, int &izi, int &izj, int &iat, int &jat, double &c6check, double &dc6i, double &dc6j); + int lin(int &i1, int &i2) {int idum1 = max(i1+1, i2+1); int idum2 = min(i1+1, i2+1); int res = idum2+idum1*(idum1-1)/2-1; return res;} }; -#endif +#endif \ No newline at end of file diff --git a/ABACUS.develop/source/src_pw/vdwd3_parameters.cpp b/ABACUS.develop/source/src_pw/vdwd3_parameters.cpp index f5c2b486a4..90bad85fa9 100644 --- a/ABACUS.develop/source/src_pw/vdwd3_parameters.cpp +++ b/ABACUS.develop/source/src_pw/vdwd3_parameters.cpp @@ -1,32445 +1,33149 @@ -#include "../src_pw/vdwd3.h" - -void Vdwd3::init_C6_tmp() -{ - C6_tmp={ - 0.30267000E+1,0.100E+1,0.100E+1,0.91180000E+0,0.91180000E+0 - ,0.20835000E+1,0.200E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.15583000E+1,0.200E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.38944800E+2,0.300E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.22150800E+2,0.300E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.11634454E+4,0.300E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.24441500E+2,0.400E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.14824600E+2,0.400E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.49461900E+3,0.400E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.25748630E+3,0.400E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.17314300E+2,0.500E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.11097500E+2,0.500E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.28373080E+3,0.500E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.16159710E+3,0.500E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.10717770E+3,0.500E+1,0.500E+1,0.00000000E+0,0.00000000E+0 - ,0.12140200E+2,0.600E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.81841000E+1,0.600E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.16990300E+3,0.600E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.10295600E+3,0.600E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.71279400E+2,0.600E+1,0.500E+1,0.00000000E+0,0.00000000E+0 - ,0.49113000E+2,0.600E+1,0.600E+1,0.00000000E+0,0.00000000E+0 - ,0.87171000E+1,0.700E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.61380000E+1,0.700E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.10848540E+3,0.700E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.68645800E+2,0.700E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.49113200E+2,0.700E+1,0.500E+1,0.00000000E+0,0.00000000E+0 - ,0.34814600E+2,0.700E+1,0.600E+1,0.00000000E+0,0.00000000E+0 - ,0.25268500E+2,0.700E+1,0.700E+1,0.00000000E+0,0.00000000E+0 - ,0.67180000E+1,0.800E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.48949000E+1,0.800E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.76961300E+2,0.800E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.50125200E+2,0.800E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.36724700E+2,0.800E+1,0.500E+1,0.00000000E+0,0.00000000E+0 - ,0.26592900E+2,0.800E+1,0.600E+1,0.00000000E+0,0.00000000E+0 - ,0.19654600E+2,0.800E+1,0.700E+1,0.00000000E+0,0.00000000E+0 - ,0.15505900E+2,0.800E+1,0.800E+1,0.00000000E+0,0.00000000E+0 - ,0.51616000E+1,0.900E+1,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.38825000E+1,0.900E+1,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.55093300E+2,0.900E+1,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.36745300E+2,0.900E+1,0.400E+1,0.00000000E+0,0.00000000E+0 - ,0.27482100E+2,0.900E+1,0.500E+1,0.00000000E+0,0.00000000E+0 - ,0.20282700E+2,0.900E+1,0.600E+1,0.00000000E+0,0.00000000E+0 - ,0.15241800E+2,0.900E+1,0.700E+1,0.00000000E+0,0.00000000E+0 - ,0.12183400E+2,0.900E+1,0.800E+1,0.00000000E+0,0.00000000E+0 - ,0.96916000E+1,0.900E+1,0.900E+1,0.00000000E+0,0.00000000E+0 - ,0.40112000E+1,0.100E+2,0.100E+1,0.00000000E+0,0.91180000E+0 - ,0.31025000E+1,0.100E+2,0.200E+1,0.00000000E+0,0.00000000E+0 - ,0.40473100E+2,0.100E+2,0.300E+1,0.00000000E+0,0.00000000E+0 - ,0.27486700E+2,0.100E+2,0.400E+1,0.00000000E+0,0.00000000E+0 - 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,0.25908200E+3,0.482E+3,0.227E+3,0.39098000E+1,0.29263000E+1 - ,0.24194730E+3,0.482E+3,0.228E+3,0.39098000E+1,0.65458000E+1 - ,0.33891650E+3,0.482E+3,0.231E+3,0.39098000E+1,0.19315000E+1 - ,0.35857470E+3,0.482E+3,0.232E+3,0.39098000E+1,0.19447000E+1 - ,0.33082030E+3,0.482E+3,0.233E+3,0.39098000E+1,0.19793000E+1 - ,0.30911340E+3,0.482E+3,0.234E+3,0.39098000E+1,0.19812000E+1 - ,0.46550130E+3,0.482E+3,0.238E+3,0.39098000E+1,0.19143000E+1 - ,0.45081160E+3,0.482E+3,0.239E+3,0.39098000E+1,0.28903000E+1 - ,0.45551320E+3,0.482E+3,0.240E+3,0.39098000E+1,0.39106000E+1 - ,0.44042440E+3,0.482E+3,0.241E+3,0.39098000E+1,0.29225000E+1 - ,0.39158340E+3,0.482E+3,0.242E+3,0.39098000E+1,0.11055600E+2 - ,0.34719340E+3,0.482E+3,0.243E+3,0.39098000E+1,0.95402000E+1 - ,0.32867310E+3,0.482E+3,0.244E+3,0.39098000E+1,0.88895000E+1 - ,0.33331550E+3,0.482E+3,0.245E+3,0.39098000E+1,0.29696000E+1 - ,0.34765890E+3,0.482E+3,0.246E+3,0.39098000E+1,0.57095000E+1 - ,0.43817200E+3,0.482E+3,0.249E+3,0.39098000E+1,0.19378000E+1 - ,0.47608450E+3,0.482E+3,0.250E+3,0.39098000E+1,0.19505000E+1 - ,0.45091710E+3,0.482E+3,0.251E+3,0.39098000E+1,0.19523000E+1 - ,0.43638380E+3,0.482E+3,0.252E+3,0.39098000E+1,0.19639000E+1 - ,0.56401480E+3,0.482E+3,0.256E+3,0.39098000E+1,0.18467000E+1 - ,0.58633110E+3,0.482E+3,0.257E+3,0.39098000E+1,0.29175000E+1 - ,0.43725330E+3,0.482E+3,0.272E+3,0.39098000E+1,0.38840000E+1 - ,0.45578380E+3,0.482E+3,0.273E+3,0.39098000E+1,0.28988000E+1 - ,0.42555250E+3,0.482E+3,0.274E+3,0.39098000E+1,0.10915300E+2 - ,0.38809680E+3,0.482E+3,0.275E+3,0.39098000E+1,0.98054000E+1 - ,0.36629140E+3,0.482E+3,0.276E+3,0.39098000E+1,0.91527000E+1 - ,0.37206660E+3,0.482E+3,0.277E+3,0.39098000E+1,0.29424000E+1 - ,0.39108870E+3,0.482E+3,0.278E+3,0.39098000E+1,0.66669000E+1 - ,0.46992250E+3,0.482E+3,0.281E+3,0.39098000E+1,0.19302000E+1 - ,0.49666200E+3,0.482E+3,0.282E+3,0.39098000E+1,0.19356000E+1 - ,0.50715130E+3,0.482E+3,0.283E+3,0.39098000E+1,0.19655000E+1 - ,0.50436840E+3,0.482E+3,0.284E+3,0.39098000E+1,0.19639000E+1 - ,0.62120410E+3,0.482E+3,0.288E+3,0.39098000E+1,0.18075000E+1 - ,0.11907380E+3,0.482E+3,0.305E+3,0.39098000E+1,0.29128000E+1 - ,0.10755120E+3,0.482E+3,0.306E+3,0.39098000E+1,0.29987000E+1 - ,0.81781000E+2,0.482E+3,0.307E+3,0.39098000E+1,0.29903000E+1 - ,0.26273830E+3,0.482E+3,0.313E+3,0.39098000E+1,0.29146000E+1 - ,0.31386840E+3,0.482E+3,0.314E+3,0.39098000E+1,0.29407000E+1 - ,0.26230480E+3,0.482E+3,0.315E+3,0.39098000E+1,0.29859000E+1 - ,0.23191300E+3,0.482E+3,0.327E+3,0.39098000E+1,0.77785000E+1 - ,0.25285690E+3,0.482E+3,0.328E+3,0.39098000E+1,0.62918000E+1 - ,0.27961360E+3,0.482E+3,0.331E+3,0.39098000E+1,0.29233000E+1 - ,0.32256300E+3,0.482E+3,0.332E+3,0.39098000E+1,0.29186000E+1 - ,0.31909300E+3,0.482E+3,0.333E+3,0.39098000E+1,0.29709000E+1 - ,0.37612340E+3,0.482E+3,0.349E+3,0.39098000E+1,0.29353000E+1 - ,0.43071080E+3,0.482E+3,0.350E+3,0.39098000E+1,0.29259000E+1 - ,0.43559950E+3,0.482E+3,0.351E+3,0.39098000E+1,0.29315000E+1 - ,0.42108940E+3,0.482E+3,0.381E+3,0.39098000E+1,0.29420000E+1 - ,0.48797400E+3,0.482E+3,0.382E+3,0.39098000E+1,0.29081000E+1 - ,0.49291380E+3,0.482E+3,0.383E+3,0.39098000E+1,0.29500000E+1 - ,0.11222540E+3,0.482E+3,0.405E+3,0.39098000E+1,0.45856000E+1 - ,0.88703000E+2,0.482E+3,0.406E+3,0.39098000E+1,0.39844000E+1 - ,0.26034680E+3,0.482E+3,0.414E+3,0.39098000E+1,0.38677000E+1 - ,0.28611790E+3,0.482E+3,0.432E+3,0.39098000E+1,0.38972000E+1 - ,0.39112500E+3,0.482E+3,0.450E+3,0.39098000E+1,0.39123000E+1 - ,0.45528540E+3,0.482E+3,0.482E+3,0.39098000E+1,0.39098000E+1 - }; - return ; -} - -void Vdwd3::init_r2r4() -{ - r2r4={ - 2.00734898, 1.56637132, 5.01986934, 3.85379032, 3.64446594, - 3.10492822, 2.71175247, 2.59361680, 2.38825250, 2.21522516, - 6.58585536, 5.46295967, 5.65216669, 4.88284902, 4.29727576, - 4.04108902, 3.72932356, 3.44677275, 7.97762753, 7.07623947, - 6.60844053, 6.28791364, 6.07728703, 5.54643096, 5.80491167, - 5.58415602, 5.41374528, 5.28497229, 5.22592821, 5.09817141, - 6.12149689, 5.54083734, 5.06696878, 4.87005108, 4.59089647, - 4.31176304, 9.55461698, 8.67396077, 7.97210197, 7.43439917, - 6.58711862, 6.19536215, 6.01517290, 5.81623410, 5.65710424, - 5.52640661, 5.44263305, 5.58285373, 7.02081898, 6.46815523, - 5.98089120, 5.81686657, 5.53321815, 5.25477007, 11.02204549, - 10.15679528, 9.35167836, 9.06926079, 8.97241155, 8.90092807, - 8.85984840, 8.81736827, 8.79317710, 7.89969626, 8.80588454, - 8.42439218, 8.54289262, 8.47583370, 8.45090888, 8.47339339, - 7.83525634, 8.20702843, 7.70559063, 7.32755997, 7.03887381, - 6.68978720, 6.05450052, 5.88752022, 5.70661499, 5.78450695, - 7.79780729, 7.26443867, 6.78151984, 6.67883169, 6.39024318, - 6.09527958, 11.79156076, 11.10997644, 9.51377795, 8.67197068, - 8.77140725, 8.65402716, 8.53923501, 8.85024712 - }; - return ; -} - -void Vdwd3::init_rcov() -{ - rcov={ - 0.80628308, 1.15903197, 3.02356173, 2.36845659, 1.94011865, - 1.88972601, 1.78894056, 1.58736983, 1.61256616, 1.68815527, - 3.52748848, 3.14954334, 2.84718717, 2.62041997, 2.77159820, - 2.57002732, 2.49443835, 2.41884923, 4.43455700, 3.88023730, - 3.35111422, 3.07395437, 3.04875805, 2.77159820, 2.69600923, - 2.62041997, 2.51963467, 2.49443835, 2.54483100, 2.74640188, - 2.82199085, 2.74640188, 2.89757982, 2.77159820, 2.87238349, - 2.94797246, 4.76210950, 4.20778980, 3.70386304, 3.50229216, - 3.32591790, 3.12434702, 2.89757982, 2.84718717, 2.84718717, - 2.72120556, 2.89757982, 3.09915070, 3.22513231, 3.17473967, - 3.17473967, 3.09915070, 3.32591790, 3.30072128, 5.26603625, - 4.43455700, 4.08180818, 3.70386304, 3.98102289, 3.95582657, - 3.93062995, 3.90543362, 3.80464833, 3.82984466, 3.80464833, - 3.77945201, 3.75425569, 3.75425569, 3.72905937, 3.85504098, - 3.67866672, 3.45189952, 3.30072128, 3.09915070, 2.97316878, - 2.92277614, 2.79679452, 2.82199085, 2.84718717, 3.32591790, - 3.27552496, 3.27552496, 3.42670319, 3.30072128, 3.47709584, - 3.57788113, 5.06446567, 4.56053862, 4.20778980, 3.98102289, - 3.82984466, 3.85504098, 3.88023730, 3.90543362 - }; - return ; -} \ No newline at end of file +//========================================================== +// AUTHOR, Yuyang Ji +// DATE , 2021-04-19 +//========================================================== + +#include "vdwd3_parameters.h" +#include "src_global/constants.h" + +Vdwd3_Parameters::Vdwd3_Parameters(): + mxc(max_elem, 1), + r0ab(max_elem, vector(max_elem)), + c6ab(3, vector>>>(5, vector>>(5, vector>(max_elem, vector(max_elem))))) +{ + init_C6(); + init_r2r4(); + init_rcov(); + init_r0ab(); +} + +void Vdwd3_Parameters::init_C6() +{ + vector C6_tmp={ + 0.30267000E+1,0.100E+1,0.100E+1,0.91180000E+0,0.91180000E+0 + ,0.20835000E+1,0.200E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.15583000E+1,0.200E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.38944800E+2,0.300E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.22150800E+2,0.300E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.11634454E+4,0.300E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.24441500E+2,0.400E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.14824600E+2,0.400E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.49461900E+3,0.400E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.25748630E+3,0.400E+1,0.400E+1,0.00000000E+0,0.00000000E+0 + ,0.17314300E+2,0.500E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.11097500E+2,0.500E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.28373080E+3,0.500E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.16159710E+3,0.500E+1,0.400E+1,0.00000000E+0,0.00000000E+0 + ,0.10717770E+3,0.500E+1,0.500E+1,0.00000000E+0,0.00000000E+0 + ,0.12140200E+2,0.600E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.81841000E+1,0.600E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.16990300E+3,0.600E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.10295600E+3,0.600E+1,0.400E+1,0.00000000E+0,0.00000000E+0 + ,0.71279400E+2,0.600E+1,0.500E+1,0.00000000E+0,0.00000000E+0 + ,0.49113000E+2,0.600E+1,0.600E+1,0.00000000E+0,0.00000000E+0 + ,0.87171000E+1,0.700E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.61380000E+1,0.700E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.10848540E+3,0.700E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.68645800E+2,0.700E+1,0.400E+1,0.00000000E+0,0.00000000E+0 + ,0.49113200E+2,0.700E+1,0.500E+1,0.00000000E+0,0.00000000E+0 + ,0.34814600E+2,0.700E+1,0.600E+1,0.00000000E+0,0.00000000E+0 + ,0.25268500E+2,0.700E+1,0.700E+1,0.00000000E+0,0.00000000E+0 + ,0.67180000E+1,0.800E+1,0.100E+1,0.00000000E+0,0.91180000E+0 + ,0.48949000E+1,0.800E+1,0.200E+1,0.00000000E+0,0.00000000E+0 + ,0.76961300E+2,0.800E+1,0.300E+1,0.00000000E+0,0.00000000E+0 + ,0.50125200E+2,0.800E+1,0.400E+1,0.00000000E+0,0.00000000E+0 + ,0.36724700E+2,0.800E+1,0.500E+1,0.00000000E+0,0.00000000E+0 + ,0.26592900E+2,0.800E+1,0.600E+1,0.00000000E+0,0.00000000E+0 + 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,0.43071080E+3,0.482E+3,0.350E+3,0.39098000E+1,0.29259000E+1 + ,0.43559950E+3,0.482E+3,0.351E+3,0.39098000E+1,0.29315000E+1 + ,0.42108940E+3,0.482E+3,0.381E+3,0.39098000E+1,0.29420000E+1 + ,0.48797400E+3,0.482E+3,0.382E+3,0.39098000E+1,0.29081000E+1 + ,0.49291380E+3,0.482E+3,0.383E+3,0.39098000E+1,0.29500000E+1 + ,0.11222540E+3,0.482E+3,0.405E+3,0.39098000E+1,0.45856000E+1 + ,0.88703000E+2,0.482E+3,0.406E+3,0.39098000E+1,0.39844000E+1 + ,0.26034680E+3,0.482E+3,0.414E+3,0.39098000E+1,0.38677000E+1 + ,0.28611790E+3,0.482E+3,0.432E+3,0.39098000E+1,0.38972000E+1 + ,0.39112500E+3,0.482E+3,0.450E+3,0.39098000E+1,0.39123000E+1 + ,0.45528540E+3,0.482E+3,0.482E+3,0.39098000E+1,0.39098000E+1 + }; + + int k = 0, nline = 32385; + int iat, jat, iatcn, jatcn; + for(size_t n=0; n!=nline; n++) + { + k = n*5; + + iat = static_cast(C6_tmp[k+1])-1; + jat = static_cast(C6_tmp[k+2])-1; + iatcn = limit(iat); + jatcn = limit(jat); + + mxc[iat] = max(mxc[iat], iatcn); + mxc[jat] = max(mxc[jat], jatcn); + + c6ab[0][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k]; + c6ab[1][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k+3]; + c6ab[2][jatcn-1][iatcn-1][jat][iat] = C6_tmp[k+4]; + + c6ab[0][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k]; + c6ab[1][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k+4]; + c6ab[2][iatcn-1][jatcn-1][iat][jat] = C6_tmp[k+3]; + + } + + return ; +} + +int Vdwd3_Parameters::limit(int &i) +{ + int icn = 1; + while(i>=100) + { + i-=100; + icn+=1; + } + return icn; +} + +void Vdwd3_Parameters::init_r2r4() +{ + r2r4={ + 2.00734898, 1.56637132, 5.01986934, 3.85379032, 3.64446594, + 3.10492822, 2.71175247, 2.59361680, 2.38825250, 2.21522516, + 6.58585536, 5.46295967, 5.65216669, 4.88284902, 4.29727576, + 4.04108902, 3.72932356, 3.44677275, 7.97762753, 7.07623947, + 6.60844053, 6.28791364, 6.07728703, 5.54643096, 5.80491167, + 5.58415602, 5.41374528, 5.28497229, 5.22592821, 5.09817141, + 6.12149689, 5.54083734, 5.06696878, 4.87005108, 4.59089647, + 4.31176304, 9.55461698, 8.67396077, 7.97210197, 7.43439917, + 6.58711862, 6.19536215, 6.01517290, 5.81623410, 5.65710424, + 5.52640661, 5.44263305, 5.58285373, 7.02081898, 6.46815523, + 5.98089120, 5.81686657, 5.53321815, 5.25477007, 11.02204549, + 10.15679528, 9.35167836, 9.06926079, 8.97241155, 8.90092807, + 8.85984840, 8.81736827, 8.79317710, 7.89969626, 8.80588454, + 8.42439218, 8.54289262, 8.47583370, 8.45090888, 8.47339339, + 7.83525634, 8.20702843, 7.70559063, 7.32755997, 7.03887381, + 6.68978720, 6.05450052, 5.88752022, 5.70661499, 5.78450695, + 7.79780729, 7.26443867, 6.78151984, 6.67883169, 6.39024318, + 6.09527958, 11.79156076, 11.10997644, 9.51377795, 8.67197068, + 8.77140725, 8.65402716, 8.53923501, 8.85024712 + }; +} + +void Vdwd3_Parameters::init_rcov() +{ + rcov={ + 0.80628308, 1.15903197, 3.02356173, 2.36845659, 1.94011865, + 1.88972601, 1.78894056, 1.58736983, 1.61256616, 1.68815527, + 3.52748848, 3.14954334, 2.84718717, 2.62041997, 2.77159820, + 2.57002732, 2.49443835, 2.41884923, 4.43455700, 3.88023730, + 3.35111422, 3.07395437, 3.04875805, 2.77159820, 2.69600923, + 2.62041997, 2.51963467, 2.49443835, 2.54483100, 2.74640188, + 2.82199085, 2.74640188, 2.89757982, 2.77159820, 2.87238349, + 2.94797246, 4.76210950, 4.20778980, 3.70386304, 3.50229216, + 3.32591790, 3.12434702, 2.89757982, 2.84718717, 2.84718717, + 2.72120556, 2.89757982, 3.09915070, 3.22513231, 3.17473967, + 3.17473967, 3.09915070, 3.32591790, 3.30072128, 5.26603625, + 4.43455700, 4.08180818, 3.70386304, 3.98102289, 3.95582657, + 3.93062995, 3.90543362, 3.80464833, 3.82984466, 3.80464833, + 3.77945201, 3.75425569, 3.75425569, 3.72905937, 3.85504098, + 3.67866672, 3.45189952, 3.30072128, 3.09915070, 2.97316878, + 2.92277614, 2.79679452, 2.82199085, 2.84718717, 3.32591790, + 3.27552496, 3.27552496, 3.42670319, 3.30072128, 3.47709584, + 3.57788113, 5.06446567, 4.56053862, 4.20778980, 3.98102289, + 3.82984466, 3.85504098, 3.88023730, 3.90543362 + }; +} + +void Vdwd3_Parameters::init_r0ab() +{ + vector r={ + 2.1823, 1.8547, 1.7347, 2.9086, 2.5732, 3.4956, 2.3550, + 2.5095, 2.9802, 3.0982, 2.5141, 2.3917, 2.9977, 2.9484, + 3.2160, 2.4492, 2.2527, 3.1933, 3.0214, 2.9531, 2.9103, + 2.3667, 2.1328, 2.8784, 2.7660, 2.7776, 2.7063, 2.6225, + 2.1768, 2.0625, 2.6395, 2.6648, 2.6482, 2.5697, 2.4846, + 2.4817, 2.0646, 1.9891, 2.5086, 2.6908, 2.6233, 2.4770, + 2.3885, 2.3511, 2.2996, 1.9892, 1.9251, 2.4190, 2.5473, + 2.4994, 2.4091, 2.3176, 2.2571, 2.1946, 2.1374, 2.9898, + 2.6397, 3.6031, 3.1219, 3.7620, 3.2485, 2.9357, 2.7093, + 2.5781, 2.4839, 3.7082, 2.5129, 2.7321, 3.1052, 3.2962, + 3.1331, 3.2000, 2.9586, 3.0822, 2.8582, 2.7120, 3.2570, + 3.4839, 2.8766, 2.7427, 3.2776, 3.2363, 3.5929, 3.2826, + 3.0911, 2.9369, 2.9030, 2.7789, 3.3921, 3.3970, 4.0106, + 2.8884, 2.6605, 3.7513, 3.1613, 3.3605, 3.3325, 3.0991, + 2.9297, 2.8674, 2.7571, 3.8129, 3.3266, 3.7105, 3.7917, + 2.8304, 2.5538, 3.3932, 3.1193, 3.1866, 3.1245, 3.0465, + 2.8727, 2.7664, 2.6926, 3.4608, 3.2984, 3.5142, 3.5418, + 3.5017, 2.6190, 2.4797, 3.1331, 3.0540, 3.0651, 2.9879, + 2.9054, 2.8805, 2.7330, 2.6331, 3.2096, 3.5668, 3.3684, + 3.3686, 3.3180, 3.3107, 2.4757, 2.4019, 2.9789, 3.1468, + 2.9768, 2.8848, 2.7952, 2.7457, 2.6881, 2.5728, 3.0574, + 3.3264, 3.3562, 3.2529, 3.1916, 3.1523, 3.1046, 2.3725, + 2.3289, 2.8760, 2.9804, 2.9093, 2.8040, 2.7071, 2.6386, + 2.5720, 2.5139, 2.9517, 3.1606, 3.2085, 3.1692, 3.0982, + 3.0352, 2.9730, 2.9148, 3.2147, 2.8315, 3.8724, 3.4621, + 3.8823, 3.3760, 3.0746, 2.8817, 2.7552, 2.6605, 3.9740, + 3.6192, 3.6569, 3.9586, 3.6188, 3.3917, 3.2479, 3.1434, + 4.2411, 2.7597, 3.0588, 3.3474, 3.6214, 3.4353, 3.4729, + 3.2487, 3.3200, 3.0914, 2.9403, 3.4972, 3.7993, 3.6773, + 3.8678, 3.5808, 3.8243, 3.5826, 3.4156, 3.8765, 4.1035, + 2.7361, 2.9765, 3.2475, 3.5004, 3.4185, 3.4378, 3.2084, + 3.2787, 3.0604, 2.9187, 3.4037, 3.6759, 3.6586, 3.8327, + 3.5372, 3.7665, 3.5310, 3.3700, 3.7788, 3.9804, 3.8903, + 2.6832, 2.9060, 3.2613, 3.4359, 3.3538, 3.3860, 3.1550, + 3.2300, 3.0133, 2.8736, 3.4024, 3.6142, 3.5979, 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4.3260, + 4.2725, 4.1961, 3.7361, 3.6193, 3.4916, 3.9115, 3.9914, + 3.9809, 3.9866, 4.3329, 4.1276, 3.9782, 4.5097, 4.6769, + 4.5158, 4.3291, 4.3609, 4.3462, 4.3265, 4.4341 + }; + + int k = 0; + for (size_t i=0; i!=max_elem; i++) + for (size_t j=0; j<=i; j++) + { + r0ab[j][i] = r[k]/BOHR_TO_A; + r0ab[i][j] = r[k]/BOHR_TO_A; + k += 1; + } +} \ No newline at end of file diff --git a/ABACUS.develop/source/src_pw/vdwd3_parameters.h b/ABACUS.develop/source/src_pw/vdwd3_parameters.h new file mode 100644 index 0000000000..32ce01b630 --- /dev/null +++ b/ABACUS.develop/source/src_pw/vdwd3_parameters.h @@ -0,0 +1,51 @@ +//========================================================== +// AUTHOR: Yuyang Ji +// DATE: 2021-04-19 +//========================================================== + +#ifndef VDWD3_PARAMETERS_H +#define VDWD3_PARAMETERS_H + +#include +#include +#include "src_global/vector3.h" +#include "src_global/matrix3.h" +#include "src_pw/unitcell_pseudo.h" + +class Vdwd3_Parameters +{ +public: + Vdwd3_Parameters(); + + void init_C6(); + void init_r2r4(); + void init_rcov(); + void init_r0ab(); + + bool flag_vdwd3; + bool abc; //third-order term? + double rthr2; //R^2 distance neglect threshold (important for speed in case of large systems) (a.u.) + double cn_thr2; //R^2 distance to cutoff for CN_calculation (a.u.) + double s6; + double rs6; + double s18; + double rs18; + string version; + string model; + Vector3 period; + + // internal used + int max_elem = 94; + vector mxc; + vector>>>> c6ab; + vector r2r4; + vector rcov; + vector> r0ab; + double k1 = 16.0, k2 = 4.0/3.0, k3 = -4.0; + double alp6 = 14.0, alp8 = alp6+2, alp10 = alp8+2; + +private: + int limit(int &i); +}; + +#endif // define VDWD3_PARAMETERS_H \ No newline at end of file