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!
! Copyright (C) 2004-2014 Quantum ESPRESSO group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
!-------------------------------------------------------------------
module funct
!-------------------------------------------------------------------
! This module contains data defining the DFT functional in use
! and a number of functions and subroutines to manage them.
! Data are PRIVATE and are accessed and set only by function calls.
! Basic drivers to compute XC quantities are also included.
!
! setting routines: set_dft_from_name (previously which_dft)
! set_dft_from_indices
! enforce_input_dft
! start_exx
! stop_exx
! set_finite_size_volume
! retrieve functions: get_dft_name
! get_iexch
! get_icorr
! get_igcx
! get_igcc
! get_exx_fraction
! write_dft_name
! logical functions: dft_is_gradient
! dft_is_meta
! dft_is_hybrid
! dft_is_nonlocc
! exx_is_active
! dft_has_finite_size_correction
!
! XC computation drivers: xc, xc_spin, gcxc, gcx_spin, gcc_spin, gcc_spin_more
! derivatives of XC computation drivers: dmxc, dmxc_spin, dmxc_nc, dgcxc,
! dgcxc_spin
!
USE io_global, ONLY: stdout
USE kinds, ONLY: DP
IMPLICIT NONE
PRIVATE
SAVE
! subroutines/functions managing dft name and indices
PUBLIC :: set_dft_from_indices, set_dft_from_name
PUBLIC :: enforce_input_dft, write_dft_name, dft_name
PUBLIC :: get_dft_name
PUBLIC :: get_iexch, get_icorr, get_igcx, get_igcc, get_meta, get_inlc
PUBLIC :: dft_is_gradient, dft_is_meta, dft_is_hybrid, dft_is_nonlocc, igcc_is_lyp
! additional subroutines/functions for hybrid functionals
PUBLIC :: start_exx, stop_exx, get_exx_fraction, exx_is_active
PUBLIC :: set_exx_fraction
PUBLIC :: set_screening_parameter, get_screening_parameter
PUBLIC :: set_gau_parameter, get_gau_parameter
! additional subroutines/functions for finite size corrections
PUBLIC :: dft_has_finite_size_correction, set_finite_size_volume
! rpa specific
PUBLIC :: init_dft_exxrpa, enforce_dft_exxrpa
! driver subroutines computing XC
PUBLIC :: xc, xc_spin, gcxc, gcx_spin, gcc_spin, gcc_spin_more
PUBLIC :: tau_xc , tau_xc_spin, dmxc, dmxc_spin, dmxc_nc
PUBLIC :: dgcxc, dgcxc_spin
PUBLIC :: nlc
! vector XC driver
PUBLIC :: evxc_t_vec, gcx_spin_vec
!
! PRIVATE variables defining the DFT functional
!
PRIVATE :: dft, dft_shortname, iexch, icorr, igcx, igcc, imeta, inlc
PRIVATE :: discard_input_dft
PRIVATE :: isgradient, ismeta, ishybrid
PRIVATE :: exx_fraction, exx_started
PRIVATE :: has_finite_size_correction, &
finite_size_cell_volume, finite_size_cell_volume_set
!
character (len=25) :: dft = 'not set'
character (len=6) :: dft_shortname = ' '
!
! "dft" is the exchange-correlation functional label, described either
! by short names listed below, or by a series of keywords (everything
! is case-insensitive). "dft_shortname" contains one of the short names
! listed below (deduced from from "dft" as read from input or PP files)
!
! short name complete name Short description
! "pz" = "sla+pz" = Perdew-Zunger LDA
! "bp" = "b88+p86" = Becke-Perdew grad.corr.
! "pw91" = "sla+pw+ggx+ggc" = PW91 (aka GGA)
! "blyp" = "sla+b88+lyp+blyp" = BLYP
! "pbe" = "sla+pw+pbx+pbc" = PBE
! "revpbe"= "sla+pw+rpb+pbc" = revPBE (Zhang-Yang)
! "pw86pbe" = "sla+pw+pw86+pbc" = PW86 exchange + PBE correlation
! "b86bpbe" = "sla+pw+b86b+pbc" = B86b exchange + PBE correlation
! "pbesol"= "sla+pw+psx+psc" = PBEsol
! "q2d" = "sla+pw+q2dx+q2dc" = PBEQ2D
! "hcth" = "nox+noc+hcth+hcth" = HCTH/120
! "olyp" = "nox+lyp+optx+blyp" = OLYP
! "wc" = "sla+pw+wcx+pbc" = Wu-Cohen
! "sogga" = "sla+pw+sox+pbec" = SOGGA
! "optbk88"="sla+pw+obk8+p86" = optB88
! "optb86b"="sla+pw+ob86+p86" = optB86
! "ev93" = "sla+pw+evx+nogc" = Engel-Vosko
! "tpss" = "sla+pw+tpss+tpss" = TPSS Meta-GGA
! "m06l" = "nox+noc+m6lx+m6lc" = M06L Meta-GGA
! "tb09" = "sla+pw+tb09+tb09" = TB09 Meta-GGA
! "pbe0" = "pb0x+pw+pb0x+pbc" = PBE0
! "hse" = "sla+pw+hse+pbc" = Heyd-Scuseria-Ernzerhof (HSE 06, see note below)
! "b3lyp" = "b3lp+b3lp+b3lp+b3lp"= B3LYP
! "b3lypv1r" = "b3lp+b3lpv1r+b3lp+b3lp"= B3LYP-VWN1-RPA
! "x3lyp" = "x3lp+x3lp+x3lp+x3lp"= X3LYP
! "vwn-rpa" = "sla+vwn-rpa" = VWN LDA using vwn1-rpa parametriz
! "gaupbe"= "sla+pw+gaup+pbc" = Gau-PBE (also "gaup")
! "vdw-df" ="sla+pw+rpb +vdw1" = vdW-DF1
! "vdw-df2" ="sla+pw+rw86+vdw2" = vdW-DF2
! "vdw-df-x" ="sla+pw+????+vdwx" = vdW-DF-x, reserved Thonhauser, not implemented
! "vdw-df-y" ="sla+pw+????+vdwy" = vdW-DF-y, reserved Thonhauser, not implemented
! "vdw-df-z" ="sla+pw+????+vdwz" = vdW-DF-z, reserved Thonhauser, not implemented
! "vdw-df-c09" ="sla+pw+c09x+vdw1" = vdW-DF-C09
! "vdw-df2-c09" ="sla+pw+c09x+vdw2" = vdW-DF2-C09
! "vdw-df-cx" ="sla+pw+cx13+vdW1" = vdW-DF-cx
! "vdw-df-obk8" ="sla+pw+obk8+vdw1" = vdW-DF-obk8 (optB88-vdW)
! "vdw-df-ob86" ="sla+pw+ob86+vdw1" = vdW-DF-ob86 (optB86b-vdW)
! "vdw-df2-b86r" ="sla+pw+b86r+vdw2" = vdW-DF2-B86R (rev-vdw-df2)
! "rvv10" = "sla+pw+rw86+pbc+vv10" = rVV10
!
! Any nonconflicting combination of the following keywords is acceptable:
!
! Exchange: "nox" none iexch=0
! "sla" Slater (alpha=2/3) iexch=1 (default)
! "sl1" Slater (alpha=1.0) iexch=2
! "rxc" Relativistic Slater iexch=3
! "oep" Optimized Effective Potential iexch=4
! "hf" Hartree-Fock iexch=5
! "pb0x" PBE0 (Slater*0.75+HF*0.25) iexch=6
! "b3lp" B3LYP(Slater*0.80+HF*0.20) iexch=7
! "kzk" Finite-size corrections iexch=8
! "x3lp" X3LYP(Slater*0.782+HF*0.218) iexch=9
!
! Correlation: "noc" none icorr=0
! "pz" Perdew-Zunger icorr=1 (default)
! "vwn" Vosko-Wilk-Nusair icorr=2
! "lyp" Lee-Yang-Parr icorr=3
! "pw" Perdew-Wang icorr=4
! "wig" Wigner icorr=5
! "hl" Hedin-Lunqvist icorr=6
! "obz" Ortiz-Ballone form for PZ icorr=7
! "obw" Ortiz-Ballone form for PW icorr=8
! "gl" Gunnarson-Lunqvist icorr=9
! "kzk" Finite-size corrections icorr=10
! "vwn-rpa" Vosko-Wilk-Nusair, alt param icorr=11
! "b3lp" B3LYP (0.19*vwn+0.81*lyp) icorr=12
! "b3lpv1r" B3LYP-VWN-1-RPA
! (0.19*vwn_rpa+0.81*lyp) icorr=13
! "x3lp" X3LYP (0.129*vwn_rpa+0.871*lyp)icorr=14
!
! Gradient Correction on Exchange:
! "nogx" none igcx =0 (default)
! "b88" Becke88 (beta=0.0042) igcx =1
! "ggx" Perdew-Wang 91 igcx =2
! "pbx" Perdew-Burke-Ernzenhof exch igcx =3
! "rpb" revised PBE by Zhang-Yang igcx =4
! "hcth" Cambridge exch, Handy et al igcx =5
! "optx" Handy's exchange functional igcx =6
! "pb0x" PBE0 (PBE exchange*0.75) igcx =8
! "b3lp" B3LYP (Becke88*0.72) igcx =9
! "psx" PBEsol exchange igcx =10
! "wcx" Wu-Cohen igcx =11
! "hse" HSE screened exchange igcx =12
! "rw86" revised PW86 igcx =13
! "pbe" same as PBX, back-comp. igcx =14
! "c09x" Cooper 09 igcx =16
! "sox" sogga igcx =17
! "q2dx" Q2D exchange grad corr igcx =19
! "gaup" Gau-PBE hybrid exchange igcx =20
! "pw86" Perdew-Wang (1986) exchange igcx =21
! "b86b" Becke (1986) exchange igcx =22
! "obk8" optB88 exchange igcx =23
! "ob86" optB86b exchange igcx =24
! "evx" Engel-Vosko exchange igcx =25
! "b86r" revised Becke (b86b) igcx =26
! "cx13" consistent exchange igcx =27
! "x3lp" X3LYP (Becke88*0.542 +
! Perdew-Wang91*0.167) igcx =28
!
! Gradient Correction on Correlation:
! "nogc" none igcc =0 (default)
! "p86" Perdew86 igcc =1
! "ggc" Perdew-Wang 91 corr. igcc =2
! "blyp" Lee-Yang-Parr igcc =3
! "pbc" Perdew-Burke-Ernzenhof corr igcc =4
! "hcth" Cambridge corr, Handy et al igcc =5
! "b3lp" B3LYP (Lee-Yang-Parr*0.81) igcc =7
! "psc" PBEsol corr igcc =8
! "pbe" same as PBX, back-comp. igcc =9
! "q2dc" Q2D correlation grad corr igcc =12
! "x3lp" X3LYP (Lee-Yang-Parr*0.871) igcc =13
!
! Meta-GGA functionals
! "tpss" TPSS Meta-GGA imeta=1
! "m6lx" M06L Meta-GGA imeta=2
! "tb09" TB09 Meta-GGA imeta=3
!
! Van der Waals functionals (nonlocal term only)
! "nonlc" none inlc =0 (default)
! "vdw1" vdW-DF1 inlc =1
! "vdw2" vdW-DF2 inlc =2
! "vv10" rVV10 inlc =3
! "vdwx" vdW-DF-x inlc =4, reserved Thonhauser, not implemented
! "vdwy" vdW-DF-y inlc =5, reserved Thonhauser, not implemented
! "vdwz" vdW-DF-z inlc =6, reserved Thonhauser, not implemented
!
! Note: as a rule, all keywords should be unique, and should be different
! from the short name, but there are a few exceptions.
!
! References:
! pz J.P.Perdew and A.Zunger, PRB 23, 5048 (1981)
! vwn S.H.Vosko, L.Wilk, M.Nusair, Can.J.Phys. 58,1200(1980)
! vwn1-rpa S.H.Vosko, L.Wilk, M.Nusair, Can.J.Phys. 58,1200(1980)
! wig E.P.Wigner, Trans. Faraday Soc. 34, 67 (1938)
! hl L.Hedin and B.I.Lundqvist, J. Phys. C4, 2064 (1971)
! gl O.Gunnarsson and B.I.Lundqvist, PRB 13, 4274 (1976)
! pw J.P.Perdew and Y.Wang, PRB 45, 13244 (1992)
! obpz G.Ortiz and P.Ballone, PRB 50, 1391 (1994)
! obpw as above
! b88 A.D.Becke, PRA 38, 3098 (1988)
! p86 J.P.Perdew, PRB 33, 8822 (1986)
! pw86 J.P.Perdew, PRB 33, 8800 (1986)
! b86b A.D.Becke, J.Chem.Phys. 85, 7184 (1986)
! ob86 Klimes, Bowler, Michaelides, PRB 83, 195131 (2011)
! b86r I. Hamada, Phys. Rev. B 89, 121103(R) (2014)
! pbe J.P.Perdew, K.Burke, M.Ernzerhof, PRL 77, 3865 (1996)
! pw91 J.P.Perdew and Y. Wang, PRB 46, 6671 (1992)
! blyp C.Lee, W.Yang, R.G.Parr, PRB 37, 785 (1988)
! hcth Handy et al, JCP 109, 6264 (1998)
! olyp Handy et al, JCP 116, 5411 (2002)
! revPBE Zhang and Yang, PRL 80, 890 (1998)
! pbesol J.P. Perdew et al., PRL 100, 136406 (2008)
! q2d L. Chiodo et al., PRL 108, 126402 (2012)
! rw86 E. Amonn D. Murray et al, J. Chem. Theory comp. 5, 2754 (2009)
! wc Z. Wu and R. E. Cohen, PRB 73, 235116 (2006)
! kzk H.Kwee, S. Zhang, H. Krakauer, PRL 100, 126404 (2008)
! pbe0 J.P.Perdew, M. Ernzerhof, K.Burke, JCP 105, 9982 (1996)
! hse Heyd, Scuseria, Ernzerhof, J. Chem. Phys. 118, 8207 (2003)
! Heyd, Scuseria, Ernzerhof, J. Chem. Phys. 124, 219906 (2006).
! b3lyp P.J. Stephens,F.J. Devlin,C.F. Chabalowski,M.J. Frisch
! J.Phys.Chem 98, 11623 (1994)
! x3lyp X. Xu, W.A Goddard III, PNAS 101, 2673 (2004)
! vdW-DF M. Dion et al., PRL 92, 246401 (2004)
! T. Thonhauser et al., PRL 115, 136402 (2015)
! vdW-DF2 Lee et al., Phys. Rev. B 82, 081101 (2010)
! rev-vdW-DF2 I. Hamada, Phys. Rev. B 89, 121103(R) (2014)
! vdW-DF-cx K. Berland and P. Hyldgaard, PRB 89, 035412 (2014)
! vdW-DF-obk8 Klimes et al, J. Phys. Cond. Matter, 22, 022201 (2010)
! vdW-DF-ob86 Klimes et al, Phys. Rev. B, 83, 195131 (2011)
! c09x V. R. Cooper, Phys. Rev. B 81, 161104(R) (2010)
! tpss J.Tao, J.P.Perdew, V.N.Staroverov, G.E. Scuseria,
! PRL 91, 146401 (2003)
! tb09 F Tran and P Blaha, Phys.Rev.Lett. 102, 226401 (2009)
! sogga Y. Zhao and D. G. Truhlar, JCP 128, 184109 (2008)
! m06l Y. Zhao and D. G. Truhlar, JCP 125, 194101 (2006)
! gau-pbe J.-W. Song, K. Yamashita, K. Hirao JCP 135, 071103 (2011)
! rVV10 R. Sabatini et al. Phys. Rev. B 87, 041108(R) (2013)
! ev93 Engel-Vosko, Phys. Rev. B 47, 13164 (1993)
!
! NOTE ABOUT HSE: there are two slight deviations with respect to the HSE06
! functional as it is in Gaussian code (that is considered as the reference
! in the chemistry community):
! - The range separation in Gaussian is precisely 0.11 bohr^-1,
! instead of 0.106 bohr^-1 in this implementation
! - The gradient scaling relation is a bit more complicated
! [ see: TM Henderson, AF Izmaylov, G Scalmani, and GE Scuseria,
! J. Chem. Phys. 131, 044108 (2009) ]
! These two modifications accounts only for a 1e-5 Ha difference for a
! single He atom. Info by Fabien Bruneval
!
integer, parameter:: notset = -1
!
! internal indices for exchange-correlation
! iexch: type of exchange
! icorr: type of correlation
! igcx: type of gradient correction on exchange
! igcc: type of gradient correction on correlation
! inlc: type of non local correction on correlation
! inlc: type of meta-GGA
integer :: iexch = notset
integer :: icorr = notset
integer :: igcx = notset
integer :: igcc = notset
integer :: imeta = notset
integer :: inlc = notset
!
real(DP):: exx_fraction = 0.0_DP
real(DP):: screening_parameter = 0.0_DP
real(DP):: gau_parameter = 0.0_DP
logical :: islda = .false.
logical :: isgradient = .false.
logical :: ismeta = .false.
logical :: ishybrid = .false.
logical :: isnonlocc = .false.
logical :: exx_started = .false.
logical :: has_finite_size_correction = .false.
logical :: finite_size_cell_volume_set = .false.
real(DP):: finite_size_cell_volume = notset
logical :: discard_input_dft = .false.
!
integer, parameter:: nxc=8, ncc=10, ngcx=27, ngcc=12, nmeta=3, ncnl=6
character (len=4) :: exc, corr, gradx, gradc, meta, nonlocc
dimension :: exc (0:nxc), corr (0:ncc), gradx (0:ngcx), gradc (0:ngcc), &
meta(0:nmeta), nonlocc (0:ncnl)
data exc / 'NOX', 'SLA', 'SL1', 'RXC', 'OEP', 'HF', 'PB0X', 'B3LP', 'KZK' /
data corr / 'NOC', 'PZ', 'VWN', 'LYP', 'PW', 'WIG', 'HL', 'OBZ', &
'OBW', 'GL' , 'KZK' /
data gradx / 'NOGX', 'B88', 'GGX', 'PBX', 'RPB', 'HCTH', 'OPTX',&
'xxxx', 'PB0X', 'B3LP','PSX', 'WCX', 'HSE', 'RW86', 'PBE', &
'xxxx', 'C09X', 'SOX', 'xxxx', 'Q2DX', 'GAUP', 'PW86', 'B86B', &
'OBK8', 'OB86', 'EVX', 'B86R', 'CX13' /
data gradc / 'NOGC', 'P86', 'GGC', 'BLYP', 'PBC', 'HCTH', 'NONE',&
'B3LP', 'PSC', 'PBE', 'xxxx', 'xxxx', 'Q2DC' /
data meta / 'NONE', 'TPSS', 'M06L', 'TB09' /
data nonlocc/'NONE', 'VDW1', 'VDW2', 'VV10', 'VDWX', 'VDWY', 'VDWZ' /
CONTAINS
!-----------------------------------------------------------------------
subroutine set_dft_from_name( dft_ )
!-----------------------------------------------------------------------
!
! translates a string containing the exchange-correlation name
! into internal indices iexch, icorr, igcx, igcc
!
implicit none
character(len=*), intent(in) :: dft_
integer :: len, l, i
character (len=50):: dftout
logical :: dft_defined = .false.
character (len=1), external :: capital
integer :: save_iexch, save_icorr, save_igcx, save_igcc, save_meta, save_inlc
!
! Exit if discard_input_dft
!
if ( discard_input_dft ) return
!
! save current status of XC indices
!
save_iexch = iexch
save_icorr = icorr
save_igcx = igcx
save_igcc = igcc
save_meta = imeta
save_inlc = inlc
!
! convert to uppercase
!
len = len_trim(dft_)
dftout = ' '
do l = 1, len
dftout (l:l) = capital (dft_(l:l) )
enddo
!
! ----------------------------------------------
! FIRST WE CHECK ALL THE SHORT NAMES
! Note: comparison is done via exact matching
! ----------------------------------------------
!
! special cases : PZ (LDA is equivalent to PZ)
IF (('PZ' .EQ. TRIM(dftout) ).OR.('LDA' .EQ. TRIM(dftout) )) THEN
dft_defined = set_dft_values(1,1,0,0,0,0)
! special cases : VWN-RPA
else IF ('VWN-RPA' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(1,11,0,0,0,0)
! special cases : OEP no GC part (nor LDA...) and no correlation by default
else IF ('OEP' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(4,0,0,0,0,0)
! special cases : HF no GC part (nor LDA...) and no correlation by default
else IF ('HF' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(5,0,0,0,0,0)
else if ('PBE' .EQ. TRIM(dftout) ) then
! special case : PBE
dft_defined = set_dft_values(1,4,3,4,0,0)
! special case : BP = B88 + P86
else if ('BP'.EQ. TRIM(dftout) ) then
dft_defined = set_dft_values(1,1,1,1,0,0)
! special case : PW91 = GGX + GGC
else if ('PW91'.EQ. TRIM(dftout) ) then
dft_defined = set_dft_values(1,4,2,2,0,0)
elseif ( 'REVPBE' .EQ. TRIM(dftout) ) then
! special case : revPBE
dft_defined = set_dft_values(1,4,4,4,0,0)
else if ('PBESOL'.EQ. TRIM(dftout) ) then
! special case : PBEsol
dft_defined = set_dft_values(1,4,10,8,0,0)
! special cases : BLYP (note, BLYP=>B88)
else IF ('BLYP' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(1,3,1,3,0,0)
else if ('OPTBK88' .EQ. TRIM(dftout)) then
! Special case optB88
dft_defined = set_dft_values(1,4,23,1,0,0)
else if ('OPTB86B' .EQ. TRIM(dftout)) then
! Special case optB86b
dft_defined = set_dft_values(1,4,24,1,0,0)
else if ('PBC'.EQ. TRIM(dftout) ) then
! special case : PBC = PW + PBC
dft_defined = set_dft_values(1,4,0,4,0,0)
! special case : HCTH
else if ('HCTH'.EQ. TRIM(dftout)) then
dft_defined = set_dft_values(0,0,5,5,0,0)
! special case : OLYP = OPTX + LYP
else if ('OLYP'.EQ. TRIM(dftout)) then
dft_defined = set_dft_values(0,3,6,3,0,0)
else if ('WC' .EQ. TRIM(dftout) ) then
! special case : Wu-Cohen
dft_defined = set_dft_values(1,4,11,4,0,0)
elseif ('PW86PBE' .EQ. TRIM(dftout) ) then
! special case : PW86PBE
dft_defined = set_dft_values(1,4,21,4,0,0)
elseif ('B86BPBE' .EQ. TRIM(dftout) ) then
! special case : B86BPBE
dft_defined = set_dft_values(1,4,22,4,0,0)
else if ('PBEQ2D' .EQ. TRIM(dftout) .OR. 'Q2D'.EQ. TRIM(dftout) ) then
! special case : PBEQ2D
dft_defined = set_dft_values(1,4,19,12,0,0)
! special case : SOGGA = SOX + PBEc
else if ('SOGGA' .EQ. TRIM(dftout) ) then
dft_defined = set_dft_values(1,4,17,4,0,0)
! special case : Engel-Vosko
else if ( 'EV93' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(1,4,25,0,0,0)
else if ('RPBE' .EQ. TRIM(dftout) ) then
! special case : RPBE
call errore('set_dft_from_name', &
& 'RPBE (Hammer-Hansen-Norskov) not implemented (revPBE is)',1)
else if ('PBE0'.EQ. TRIM(dftout) ) then
! special case : PBE0
dft_defined = set_dft_values(6,4,8,4,0,0)
else if ('HSE' .EQ. TRIM( dftout) ) then
! special case : HSE
dft_defined = set_dft_values(1,4,12,4,0,0)
else if ( 'GAUP' .EQ. TRIM(dftout) .OR. 'GAUPBE' .EQ. TRIM(dftout) ) then
! special case : GAUPBE
dft_defined = set_dft_values(1,4,20,4,0,0)
else if ('VDW-DF' .EQ. TRIM(dftout)) then
! Special case vdW-DF
dft_defined = set_dft_values(1,4,4,0,1,0)
else if ('VDW-DF-X' .EQ. TRIM(dftout) ) then
call errore('set_dft_from_name','functional not yet implemented',1)
else if ('VDW-DF-Y' .EQ. TRIM(dftout) ) then
call errore('set_dft_from_name','functional not yet implemented',1)
else if ('VDW-DF-Z' .EQ. TRIM(dftout) ) then
call errore('set_dft_from_name','functional not yet implemented',1)
else if ('VDW-DF-CX' .EQ. TRIM(dftout)) then
! Special case vdW-DF-CX
dft_defined = set_dft_values(1,4,27,0,1,0)
else if ('VDW-DF-C09' .EQ. TRIM(dftout) ) then
! Special case vdW-DF with C09 exchange
dft_defined = set_dft_values(1,4,16,0,1,0)
else if ('VDW-DF-OBK8' .EQ. TRIM(dftout)) then
! Special case vdW-DF-obk8, or vdW-DF + optB88
dft_defined = set_dft_values(1,4,23,0,1,0)
else if ('VDW-DF3' .EQ. TRIM(dftout) ) then
call errore('set_dft_from_name','obsolete XC label, use VDW-DF-OBK8',1)
else if ('VDW-DF-OB86' .EQ. TRIM(dftout) ) then
! Special case vdW-DF-ob86, or vdW-DF + optB86
dft_defined = set_dft_values(1,4,24,0,1,0)
else if ('VDW-DF4'.EQ.TRIM(dftout) .OR. 'OPTB86B-VDW'.EQ.TRIM(dftout) ) then
call errore('set_dft_from_name','obsolete XC label, use VDW-DF-OB86',1)
else if ('VDW-DF2-C09' .EQ. TRIM(dftout) ) then
! Special case vdW-DF2 with C09 exchange
dft_defined = set_dft_values(1,4,16,0,2,0)
else if ('VDW-DF2' .EQ. TRIM(dftout) ) then
! Special case vdW-DF2
dft_defined = set_dft_values(1,4,13,0,2,0)
else if ('VDW-DF2-B86R' .EQ. TRIM(dftout) ) then
! Special case vdW-DF2 with B86R
dft_defined = set_dft_values(1,4,26,0,2,0)
else if ('REV-VDW-DF2' .EQ. TRIM(dftout) ) then
call errore('set_dft_from_name','obsolete XC label, use VDW-DF2-B86R',1)
else if ('RVV10' .EQ. TRIM(dftout) ) then
! Special case rVV10
dft_defined = set_dft_values(1,4,13,4,3,0)
else if ('B3LYP'.EQ. TRIM(dftout) ) then
! special case : B3LYP hybrid
dft_defined = set_dft_values(7,12,9,7,0,0)
else if ('B3LYP-V1R'.EQ. TRIM(dftout) ) then
! special case : B3LYP-VWN-1-RPA hybrid
dft_defined = set_dft_values(7,13,9,7,0,0)
else if ('X3LYP'.EQ. TRIM(dftout) ) then
! special case : X3LYP hybrid
dft_defined = set_dft_values(9,14,28,13,0,0)
! special case : TPSS meta-GGA Exc
else IF ('TPSS'.EQ. TRIM(dftout ) ) THEN
dft_defined = set_dft_values(1,4,7,6,0,1)
! special case : M06L Meta GGA
else if ( 'M06L' .EQ. TRIM(dftout) ) THEN
dft_defined = set_dft_values(0,0,0,0,0,2)
! special case : TB09 meta-GGA Exc
else IF ('TB09'.EQ. TRIM(dftout ) ) THEN
dft_defined = set_dft_values(0,0,0,0,0,3)
END IF
!
! ----------------------------------------------------------------
! If the DFT was not yet defined, check every part of the string
! ----------------------------------------------------------------
!
if (.not. dft_defined) then
iexch = matching (dftout, nxc, exc)
icorr = matching (dftout, ncc, corr)
igcx = matching (dftout, ngcx,gradx)
igcc = matching (dftout, ngcc,gradc)
imeta = matching (dftout,nmeta, meta)
inlc = matching (dftout, ncnl, nonlocc)
endif
! ----------------------------------------------------------------
! Last check
! No more defaults, the code exits if the dft is not defined
! ----------------------------------------------------------------
! Back compatibility - TO BE REMOVED
if (igcx == 14) igcx = 3 ! PBE -> PBX
if (igcc == 9) igcc = 4 ! PBE -> PBC
if (igcx == 6) &
call errore('set_dft_from_name','OPTX untested! please test',-igcx)
! check for unrecognized labels
if ( iexch<=0.and.icorr<=0.and.igcx<=0.and.igcc<= 0.and.imeta<=0 ) then
if ( inlc <= 0 .and. trim(dftout) /= 'NOX-NOC') then
call errore('set_dft_from_name',trim(dftout)//': unrecognized dft',1)
else
! if inlc is the only nonzero index the label is likely wrong
call errore('set_dft_from_name',trim(dftout)//': strange dft, please check',inlc)
endif
endif
!
! Fill variables and exit
!
dft = dftout
dftout = exc (iexch) //'-'//corr (icorr) //'-'//gradx (igcx) //'-' &
&//gradc (igcc) //'-'// nonlocc(inlc)
call set_auxiliary_flags
!
! check dft has not been previously set differently
!
if (save_iexch .ne. notset .and. save_iexch .ne. iexch) then
write (stdout,*) iexch, save_iexch
call errore('set_dft_from_name',' conflicting values for iexch',1)
end if
if (save_icorr .ne. notset .and. save_icorr .ne. icorr) then
write (stdout,*) icorr, save_icorr
call errore('set_dft_from_name',' conflicting values for icorr',1)
end if
if (save_igcx .ne. notset .and. save_igcx .ne. igcx) then
write (stdout,*) igcx, save_igcx
call errore('set_dft_from_name',' conflicting values for igcx',1)
end if
if (save_igcc .ne. notset .and. save_igcc .ne. igcc) then
write (stdout,*) igcc, save_igcc
call errore('set_dft_from_name',' conflicting values for igcc',1)
end if
if (save_meta .ne. notset .and. save_meta .ne. imeta) then
write (stdout,*) inlc, save_meta
call errore('set_dft_from_name',' conflicting values for imeta',1)
end if
if (save_inlc .ne. notset .and. save_inlc .ne. inlc) then
write (stdout,*) inlc, save_inlc
call errore('set_dft_from_name',' conflicting values for inlc',1)
end if
return
end subroutine set_dft_from_name
!
integer function matching(dft, n, name)
implicit none
integer, intent(in):: n
character(len=*), intent(in):: name(0:n)
character(len=*), intent(in):: dft
logical, external :: matches
integer :: i
matching = notset
do i = n, 0, -1
if (matches (name (i), trim(dft)) ) then
if ( matching == notset ) then
! write(*, '("matches",i2,2X,A,2X,A)') i, name(i), trim(dft)
matching = i
else
write(*, '(2(2X,i2,2X,A))') i, trim(name(i)), &
matching, trim(name(matching))
call errore ('set_dft', 'two conflicting matching values', 1)
end if
endif
end do
if (matching == notset) matching = 0
!
end function matching
!
!-----------------------------------------------------------------------
subroutine set_auxiliary_flags
!-----------------------------------------------------------------------
! set logical flags describing the complexity of the xc functional
! define the fraction of exact exchange used by hybrid fuctionals
!
isnonlocc = (inlc > 0)
ismeta = (imeta > 0)
isgradient= (igcx > 0) .or. (igcc > 0) .or. ismeta .or. isnonlocc
islda = (iexch> 0) .and. (icorr > 0) .and. .not. isgradient
! PBE0
IF ( iexch==6 .or. igcx ==8 ) exx_fraction = 0.25_DP
! HSE
IF ( igcx ==12 ) THEN
exx_fraction = 0.25_DP
screening_parameter = 0.106_DP
END IF
! gau-pbe
IF ( igcx ==20 ) THEN
exx_fraction = 0.24_DP
gau_parameter = 0.150_DP
END IF
! HF or OEP
IF ( iexch==4 .or. iexch==5 ) exx_fraction = 1.0_DP
! B3LYP or B3LYP-VWN-1-RPA
IF ( iexch == 7 ) exx_fraction = 0.2_DP
! X3LYP
IF ( iexch == 9 ) exx_fraction = 0.218_DP
!
ishybrid = ( exx_fraction /= 0.0_DP )
has_finite_size_correction = ( iexch==8 .or. icorr==10)
return
end subroutine set_auxiliary_flags
!
!-----------------------------------------------------------------------
logical function set_dft_values (i1,i2,i3,i4,i5,i6)
!-----------------------------------------------------------------------
!
implicit none
integer :: i1,i2,i3,i4,i5,i6
iexch=i1
icorr=i2
igcx =i3
igcc =i4
inlc =i5
imeta=i6
set_dft_values = .true.
return
end function set_dft_values
!-----------------------------------------------------------------------
subroutine enforce_input_dft (dft_, nomsg)
!
! translates a string containing the exchange-correlation name
! into internal indices and force any subsequent call to set_dft_from_name
! to return without changing them
!
implicit none
character(len=*), intent(in) :: dft_
logical, intent(in), optional :: nomsg
call set_dft_from_name (dft_)
if (dft == 'not set') call errore('enforce_input_dft','cannot fix unset dft',1)
discard_input_dft = .true.
if ( present (nomsg) ) return
write (stdout,'(/,5x,a)') "IMPORTANT: XC functional enforced from input :"
call write_dft_name
write (stdout,'(5x,a)') "Any further DFT definition will be discarded"
write (stdout,'(5x,a/)') "Please, verify this is what you really want"
return
end subroutine enforce_input_dft
!-----------------------------------------------------------------------
subroutine enforce_dft_exxrpa ( )
!
implicit none
!
!character(len=*), intent(in) :: dft_
!logical, intent(in), optional :: nomsg
iexch = 0; icorr = 0; igcx = 0; igcc = 0
exx_fraction = 1.0_DP
ishybrid = ( exx_fraction /= 0.0_DP )
write (stdout,'(/,5x,a)') "XC functional enforced to be EXXRPA"
call write_dft_name
write (stdout,'(5x,a)') "!!! Any further DFT definition will be discarded"
write (stdout,'(5x,a/)') "!!! Please, verify this is what you really want !"
return
end subroutine enforce_dft_exxrpa
!-----------------------------------------------------------------------
subroutine init_dft_exxrpa ( )
!
implicit none
!
exx_fraction = 1.0_DP
ishybrid = ( exx_fraction /= 0.0_DP )
write (stdout,'(/,5x,a)') "Only exx_fraction is set to 1.d0"
write (stdout,'(5x,a)') "XC functional still not changed"
call write_dft_name
return
end subroutine init_dft_exxrpa
!-----------------------------------------------------------------------
subroutine start_exx
if (.not. ishybrid) &
call errore('start_exx','dft is not hybrid, wrong call',1)
exx_started = .true.
end subroutine start_exx
!-----------------------------------------------------------------------
subroutine stop_exx
if (.not. ishybrid) &
call errore('stop_exx','dft is not hybrid, wrong call',1)
exx_started = .false.
end subroutine stop_exx
!-----------------------------------------------------------------------
function exx_is_active ()
logical exx_is_active
exx_is_active = exx_started
end function exx_is_active
!-----------------------------------------------------------------------
subroutine set_exx_fraction (exxf_)
implicit none
real(DP):: exxf_
exx_fraction = exxf_
write (stdout,'(5x,a,f6.2)') 'EXX fraction changed: ',exx_fraction
end subroutine set_exx_fraction
!---------------------------------------------------------------------
subroutine set_screening_parameter (scrparm_)
implicit none
real(DP):: scrparm_
screening_parameter = scrparm_
write (stdout,'(5x,a,f12.7)') 'EXX Screening parameter changed: ', &
& screening_parameter
end subroutine set_screening_parameter
!----------------------------------------------------------------------
function get_screening_parameter ()
real(DP):: get_screening_parameter
get_screening_parameter = screening_parameter
return
end function get_screening_parameter
!---------------------------------------------------------------------
subroutine set_gau_parameter (gauparm_)
implicit none
real(DP):: gauparm_
gau_parameter = gauparm_
write (stdout,'(5x,a,f12.7)') 'EXX Gau parameter changed: ', &
& gau_parameter
end subroutine set_gau_parameter
!----------------------------------------------------------------------
function get_gau_parameter ()
real(DP):: get_gau_parameter
get_gau_parameter = gau_parameter
return
end function get_gau_parameter
!-----------------------------------------------------------------------
function get_iexch ()
integer get_iexch
get_iexch = iexch
return
end function get_iexch
!-----------------------------------------------------------------------
function get_icorr ()
integer get_icorr
get_icorr = icorr
return
end function get_icorr
!-----------------------------------------------------------------------
function get_igcx ()
integer get_igcx
get_igcx = igcx
return
end function get_igcx
!-----------------------------------------------------------------------
function get_igcc ()
integer get_igcc
get_igcc = igcc
return
end function get_igcc
!-----------------------------------------------------------------------
function get_meta ()
integer get_meta
get_meta = imeta
return
end function get_meta
!-----------------------------------------------------------------------
function get_inlc ()
integer get_inlc
get_inlc = inlc
return
end function get_inlc
!-----------------------------------------------------------------------
function dft_is_nonlocc ()
logical :: dft_is_nonlocc
dft_is_nonlocc = isnonlocc
return
end function dft_is_nonlocc
!-----------------------------------------------------------------------
function get_exx_fraction ()
real(DP):: get_exx_fraction
get_exx_fraction = exx_fraction
return
end function get_exx_fraction
!-----------------------------------------------------------------------
function get_dft_name ()
character (len=25) :: get_dft_name
get_dft_name = dft
return
end function get_dft_name
!-----------------------------------------------------------------------
function dft_is_gradient ()
logical :: dft_is_gradient
dft_is_gradient = isgradient
return
end function dft_is_gradient
!-----------------------------------------------------------------------
function dft_is_meta ()
logical :: dft_is_meta
dft_is_meta = ismeta
return
end function dft_is_meta
!-----------------------------------------------------------------------
function dft_is_hybrid ()
logical :: dft_is_hybrid
dft_is_hybrid = ishybrid
return
end function dft_is_hybrid
!-----------------------------------------------------------------------
function igcc_is_lyp ()
logical :: igcc_is_lyp
igcc_is_lyp = (get_igcc() == 3 .or. get_igcc() == 7)
return
end function igcc_is_lyp
!-----------------------------------------------------------------------
function dft_has_finite_size_correction ()
logical :: dft_has_finite_size_correction
dft_has_finite_size_correction = has_finite_size_correction
return
end function dft_has_finite_size_correction
!-----------------------------------------------------------------------
subroutine set_finite_size_volume(volume)
real, intent (IN) :: volume
if (.not. has_finite_size_correction) &
call errore('set_finite_size_volume', &
'dft w/o finite_size_correction, wrong call',1)
if (volume <= 0.d0) &
call errore('set_finite_size_volume', &
'volume is not positive, check omega and/or nk1,nk2,nk3',1)
finite_size_cell_volume = volume
finite_size_cell_volume_set = .TRUE.
end subroutine set_finite_size_volume
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
subroutine set_dft_from_indices(iexch_,icorr_,igcx_,igcc_, inlc_)
integer :: iexch_, icorr_, igcx_, igcc_, inlc_
if ( discard_input_dft ) return
if (iexch == notset) iexch = iexch_
if (iexch /= iexch_) then
write (stdout,*) iexch, iexch_
call errore('set_dft',' conflicting values for iexch',1)
end if
if (icorr == notset) icorr = icorr_
if (icorr /= icorr_) then
write (stdout,*) icorr, icorr_
call errore('set_dft',' conflicting values for icorr',1)
end if
if (igcx == notset) igcx = igcx_
if (igcx /= igcx_) then
write (stdout,*) igcx, igcx_
call errore('set_dft',' conflicting values for igcx',1)
end if
if (igcc == notset) igcc = igcc_
if (igcc /= igcc_) then
write (stdout,*) igcc, igcc_
call errore('set_dft',' conflicting values for igcc',1)
end if
if (inlc == notset) inlc = inlc_
if (inlc /= inlc_) then
write (stdout,*) inlc, inlc_
call errore('set_dft',' conflicting values for inlc',1)
end if
dft = exc (iexch) //'-'//corr (icorr) //'-'//gradx (igcx) //'-' &
&//gradc (igcc)//'-'//nonlocc (inlc)
! WRITE( stdout,'(a)') dft
call set_auxiliary_flags
return
end subroutine set_dft_from_indices
!---------------------------------------------------------------------
subroutine dft_name(iexch_, icorr_, igcx_, igcc_, inlc_, imeta_, &
longname_, shortname_)
!---------------------------------------------------------------------
! convert the four indices iexch, icorr, igcx, igcc
! into user-readable strings
!
implicit none
integer iexch_, icorr_, igcx_, igcc_, imeta_, inlc_
! AF: the following variable is actually not used
character (len=20):: shortname_
character (len=25):: longname_
!
shortname_ = ' '
if (iexch_==1.and.igcx_==0.and.igcc_==0) then
shortname_ = corr(icorr_)
else if (iexch_==1.and.icorr_==3.and.igcx_==1.and.igcc_==3) then
shortname_ = 'BLYP'
else if (iexch_==1.and.icorr_==1.and.igcx_==1.and.igcc_==0) then
shortname_ = 'B88'
else if (iexch_==1.and.icorr_==1.and.igcx_==1.and.igcc_==1) then
shortname_ = 'BP'
else if (iexch_==1.and.icorr_==4.and.igcx_==2.and.igcc_==2) then
shortname_ = 'PW91'
else if (iexch_==1.and.icorr_==4.and.igcx_==3.and.igcc_==4) then
shortname_ = 'PBE'
else if (iexch_==6.and.icorr_==4.and.igcx_==8.and.igcc_==4) then
shortname_ = 'PBE0'
else if (iexch_==1.and.icorr_==4.and.igcx_==4.and.igcc_==4) then
shortname_ = 'revPBE'
else if (iexch_==1.and.icorr_==4.and.igcx_==10.and.igcc_==8) then
shortname_ = 'PBESOL'
else if (iexch_==1.and.icorr_==4.and.igcx_==19.and.igcc_==12) then
shortname_ = 'Q2D'
else if (iexch_==1.and.icorr_==4.and.igcx_==12.and.igcc_==4) then
shortname_ = 'HSE'
else if (iexch_==1.and.icorr_==4.and.igcx_==20.and.igcc_==4) then
shortname_ = 'GAUPBE'
else if (iexch_==1.and.icorr_==4.and.igcx_==11.and.igcc_==4) then
shortname_ = 'WC'
else if (iexch_==7.and.icorr_==12.and.igcx_==9.and. igcc_==7) then
shortname_ = 'B3LYP'
else if (iexch_==7.and.icorr_==13.and.igcx_==9.and. igcc_==7) then
shortname_ = 'B3LYP-V1R'
else if (iexch_==9.and.icorr_==14.and.igcx_==28.and. igcc_==13) then
shortname_ = 'X3LYP'
else if (iexch_==0.and.icorr_==3.and.igcx_==6.and.igcc_==3) then
shortname_ = 'OLYP'
else if (iexch_==1.and.icorr_==4.and.igcx_==17.and.igcc_==4) then
shortname_ = 'SOGGA'
else if (iexch_==1.and.icorr_==4.and.igcx_==25.and.igcc_==0) then
shortname_ = 'EV93'
end if
if (imeta_ == 1 ) then
shortname_ = 'TPSS'
else if (imeta_ == 2) then
shortname_ = 'M06L'
else if (imeta_ == 3) then
shortname_ = 'TB09'
end if
if ( inlc_==1 ) then
if (iexch_==1.and.icorr_==4.and.igcx_==4.and.igcc_==0) then
shortname_ = 'VDW-DF'
else if (iexch_==1.and.icorr_==4.and.igcx_==27.and.igcc_==0) then
shortname_ = 'VDW-DF-CX'
else if (iexch_==1.and.icorr_==4.and.igcx_==16.and.igcc_==0) then
shortname_ = 'VDW-DF-C09'
else if (iexch_==1.and.icorr_==4.and.igcx_==24.and.igcc_==0) then
shortname_ = 'VDW-DF-OB86'
else if (iexch_==1.and.icorr_==4.and.igcx_==23.and.igcc_==0) then
shortname_ = 'VDW-DF-OBK8'
end if
else if ( inlc_==2 ) then
if (iexch_==1.and.icorr_==4.and.igcx_==13.and.igcc_==0) then
shortname_ = 'VDW-DF2'
else if (iexch_==1.and.icorr_==4.and.igcx_==16.and.igcc_==0) then
shortname_ = 'VDW-DF2-C09'
else if (iexch_==1.and.icorr_==4.and.igcx_==26.and.igcc_==0) then
shortname_ = 'VDW-DF2-B86R'
else if ( inlc_==3) then
shortname_ = 'RVV10'
end if
end if
write(longname_,'(4a5)') exc(iexch_),corr(icorr_),gradx(igcx_),gradc(igcc_)
if ( imeta > 0 ) then
longname_=longname_(1:20)//trim(meta(imeta_))
else if ( inlc_ > 0 ) then
longname_=longname_(1:20)//trim(nonlocc(inlc_))
end if
return
end subroutine dft_name
!-----------------------------------------------------------------------
subroutine write_dft_name
!-----------------------------------------------------------------------
WRITE( stdout, '(5X,"Exchange-correlation = ",A, &
& " (",I2,3I3,2I2,")")') TRIM( dft ), iexch,icorr,igcx,igcc,inlc,imeta
IF ( get_exx_fraction() > 0.0_dp ) WRITE( stdout, &
'(5X,"EXX-fraction =",F12.2)') get_exx_fraction()
return
end subroutine write_dft_name
!
!-----------------------------------------------------------------------
!------- LDA DRIVERS --------------------------------------------------
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine xc (rho, ex, ec, vx, vc)
!-----------------------------------------------------------------------
! lda exchange and correlation functionals - Hartree a.u.
!
! exchange : Slater, relativistic Slater
! correlation: Ceperley-Alder (Perdew-Zunger parameters)
! Vosko-Wilk-Nusair
! Lee-Yang-Parr
! Perdew-Wang
! Wigner
! Hedin-Lundqvist
! Ortiz-Ballone (Perdew-Zunger formula)
! Ortiz-Ballone (Perdew-Wang formula)
! Gunnarsson-Lundqvist
!
! input : rho=rho(r)
! definitions: E_x = \int E_x(rho) dr, E_x(rho) = rho\epsilon_c(rho)
! same for correlation
! output: ex = \epsilon_x(rho) ( NOT E_x(rho) )
! vx = dE_x(rho)/drho ( NOT d\epsilon_x(rho)/drho )
! ec, vc as above for correlation
!
implicit none
real(DP) :: rho, ec, vc, ex, vx
real(DP) :: ec__, vc__
!
real(DP), parameter :: small = 1.E-10_DP, third = 1.0_DP / 3.0_DP, &
pi34 = 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
real(DP) :: rs
!
if (rho <= small) then
ec = 0.0_DP
vc = 0.0_DP
ex = 0.0_DP
vx = 0.0_DP
return
else
rs = pi34 / rho**third
! rs as in the theory of metals: rs=(3/(4pi rho))^(1/3)
endif
!..exchange
if (iexch == 1) THEN ! 'sla'
call slater (rs, ex, vx)
ELSEIF (iexch == 2) THEN ! 'sl1'
call slater1(rs, ex, vx)
ELSEIF (iexch == 3) THEN ! 'rxc'
CALL slater_rxc(rs, ex, vx)
ELSEIF ((iexch == 4).or.(iexch==5)) THEN ! 'oep','hf'
IF (exx_started) then
ex = 0.0_DP
vx = 0.0_DP
else
call slater (rs, ex, vx)
endif
ELSEIF (iexch == 6) THEN ! 'pb0x'
CALL slater(rs, ex, vx)
if (exx_started) then
ex = (1.0_DP - exx_fraction) * ex
vx = (1.0_DP - exx_fraction) * vx
end if
ELSEIF (iexch == 7) THEN ! 'B3LYP'
CALL slater(rs, ex, vx)
if (exx_started) then
ex = 0.8_DP * ex
vx = 0.8_DP * vx
end if
ELSEIF (iexch == 8) THEN ! 'sla+kzk'
if (.NOT. finite_size_cell_volume_set) call errore ('XC',&
'finite size corrected exchange used w/o initialization',1)
call slaterKZK (rs, ex, vx, finite_size_cell_volume)
!
ELSEIF (iexch == 9) THEN ! 'X3LYP'
CALL slater(rs, ex, vx)
if (exx_started) then
ex = 0.782_DP * ex
vx = 0.782_DP * vx
end if
else
ex = 0.0_DP
vx = 0.0_DP
endif
!..correlation
if (icorr == 1) then
call pz (rs, 1, ec, vc)
elseif (icorr == 2) then
call vwn (rs, ec, vc)
elseif (icorr == 3) then
call lyp (rs, ec, vc)
elseif (icorr == 4) then
call pw (rs, 1, ec, vc)
elseif (icorr == 5) then
call wigner (rs, ec, vc)
elseif (icorr == 6) then
call hl (rs, ec, vc)
elseif (icorr == 7) then
call pz (rs, 2, ec, vc)
elseif (icorr == 8) then
call pw (rs, 2, ec, vc)
elseif (icorr == 9) then
call gl (rs, ec, vc)
elseif (icorr ==10) then
if (.NOT. finite_size_cell_volume_set) call errore ('XC',&
'finite size corrected correlation used w/o initialization',1)
call pzKZK (rs, ec, vc, finite_size_cell_volume)
elseif (icorr ==11) then
call vwn1_rpa (rs, ec, vc)
elseif (icorr ==12) then ! 'B3LYP'
call vwn (rs, ec, vc)
ec = 0.19_DP * ec
vc = 0.19_DP * vc
call lyp( rs, ec__, vc__ )
ec = ec + 0.81_DP * ec__
vc = vc + 0.81_DP * vc__
elseif (icorr ==13) then ! 'B3LYP-V1R'
call vwn1_rpa (rs, ec, vc)
ec = 0.19_DP * ec
vc = 0.19_DP * vc
call lyp( rs, ec__, vc__ )
ec = ec + 0.81_DP * ec__
vc = vc + 0.81_DP * vc__
elseif (icorr ==14) then ! 'X3LYP'
call vwn1_rpa (rs, ec, vc)
ec = 0.129_DP * ec
vc = 0.129_DP * vc
call lyp( rs, ec__, vc__ )
ec = ec + 0.871_DP * ec__
vc = vc + 0.871_DP * vc__
else
ec = 0.0_DP
vc = 0.0_DP
endif
!
return
end subroutine xc
!!!!!!!!!!!!!!SPIN
!-----------------------------------------------------------------------
subroutine xc_spin (rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw)
!-----------------------------------------------------------------------
! lsd exchange and correlation functionals - Hartree a.u.
!
! exchange : Slater (alpha=2/3)
! correlation: Ceperley & Alder (Perdew-Zunger parameters)
! Perdew & Wang
!
! input : rho = rhoup(r)+rhodw(r)
! zeta=(rhoup(r)-rhodw(r))/rho
!
implicit none
real(DP) :: rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw
real(DP) :: ec__, vcup__, vcdw__
!
real(DP), parameter :: small= 1.E-10_DP, third = 1.0_DP/3.0_DP, &
pi34= 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
real(DP) :: rs
!
if (rho <= small) then
ec = 0.0_DP
vcup = 0.0_DP
vcdw = 0.0_DP
ex = 0.0_DP
vxup = 0.0_DP
vxdw = 0.0_DP
return
else
rs = pi34 / rho**third
endif
!..exchange
IF (iexch == 1) THEN ! 'sla'
call slater_spin (rho, zeta, ex, vxup, vxdw)
ELSEIF (iexch == 2) THEN ! 'sl1'
call slater1_spin (rho, zeta, ex, vxup, vxdw)
ELSEIF (iexch == 3) THEN ! 'rxc'
call slater_rxc_spin ( rho, zeta, ex, vxup, vxdw )
ELSEIF ((iexch == 4).or.(iexch==5)) THEN ! 'oep','hf'
IF (exx_started) then
ex = 0.0_DP
vxup = 0.0_DP
vxdw = 0.0_DP
else
call slater_spin (rho, zeta, ex, vxup, vxdw)
endif
ELSEIF (iexch == 6) THEN ! 'pb0x'
call slater_spin (rho, zeta, ex, vxup, vxdw)
if (exx_started) then
ex = (1.0_DP - exx_fraction) * ex
vxup = (1.0_DP - exx_fraction) * vxup
vxdw = (1.0_DP - exx_fraction) * vxdw
end if
ELSEIF (iexch == 7) THEN ! 'B3LYP'
call slater_spin (rho, zeta, ex, vxup, vxdw)
if (exx_started) then
ex = 0.8_DP * ex
vxup = 0.8_DP * vxup
vxdw = 0.8_DP * vxdw
end if
ELSE
ex = 0.0_DP
vxup = 0.0_DP
vxdw = 0.0_DP
ENDIF
!..correlation
if (icorr == 0) then
ec = 0.0_DP
vcup = 0.0_DP
vcdw = 0.0_DP
elseif (icorr == 1) then
call pz_spin (rs, zeta, ec, vcup, vcdw)
elseif (icorr == 2) then
call vwn_spin (rs, zeta, ec, vcup, vcdw)
elseif (icorr == 3) then
call lsd_lyp (rho, zeta, ec, vcup, vcdw) ! from CP/FPMD (more_functionals)
elseif (icorr == 4) then
call pw_spin (rs, zeta, ec, vcup, vcdw)
elseif (icorr == 12) then ! 'B3LYP'
call vwn_spin (rs, zeta, ec, vcup, vcdw)
ec = 0.19_DP * ec
vcup = 0.19_DP * vcup
vcdw = 0.19_DP * vcdw
call lsd_lyp (rho, zeta, ec__, vcup__, vcdw__) ! from CP/FPMD (more_functionals)
ec = ec + 0.81_DP * ec__
vcup = vcup + 0.81_DP * vcup__
vcdw = vcdw + 0.81_DP * vcdw__
elseif (icorr == 13) then ! 'B3LYP-V1R'
call vwn1_rpa_spin (rs, zeta, ec, vcup, vcdw)
ec = 0.19_DP * ec
vcup = 0.19_DP * vcup
vcdw = 0.19_DP * vcdw
call lsd_lyp (rho, zeta, ec__, vcup__, vcdw__) ! from CP/FPMD (more_functionals)
ec = ec + 0.81_DP * ec__
vcup = vcup + 0.81_DP * vcup__
vcdw = vcdw + 0.81_DP * vcdw__
else
call errore ('lsda_functional (xc_spin)', 'not implemented', icorr)
endif
!
return
end subroutine xc_spin
!
!-----------------------------------------------------------------------
subroutine xc_spin_vec (rho, zeta, length, evx, evc)
!-----------------------------------------------------------------------
! lsd exchange and correlation functionals - Hartree a.u.
!
! exchange : Slater (alpha=2/3)
! correlation: Ceperley & Alder (Perdew-Zunger parameters)
! Perdew & Wang
!
! input : rho = rhoup(r)+rhodw(r)
! zeta=(rhoup(r)-rhodw(r))/rho
!
implicit none
integer, intent(in) :: length
real(DP), intent(in) :: rho(length), zeta(length)
real(DP), intent(out) :: evx(length,3), evc(length,3)
!
real(DP), parameter :: small= 1.E-10_DP, third = 1.0_DP/3.0_DP, &
pi34= 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
!
integer :: i
logical :: comp_energy_loc
real(DP) :: rs(length)
!
!..exchange
select case (iexch)
case(1) ! 'sla'
call slater_spin_vec (rho, zeta, evx, length)
case(2) ! 'sl1'
do i=1,length
call slater1_spin (rho(i), zeta(i), evx(i,3), evx(i,1), evx(i,2))
end do
case(3) ! 'rxc'
do i=1,length
call slater_rxc_spin (rho(i), zeta(i), evx(i,3), evx(i,1), evx(i,2))
end do
case(4,5) ! 'oep','hf'
if (exx_started) then
evx = 0.0_DP
else
call slater_spin_vec (rho, zeta, evx, length)
endif
case(6) ! 'pb0x'
call slater_spin_vec (rho, zeta, evx, length)
if (exx_started) then
evx = (1.0_DP - exx_fraction) * evx
end if
case(7) ! 'B3LYP'
call slater_spin_vec (rho, zeta, evx, length)
if (exx_started) then
evx = 0.8_DP * evx
end if
case default
evx = 0.0_DP
end select
!..correlation
where (rho.gt.small)
rs = pi34 / rho**third
elsewhere
rs = 1.0_DP ! just a sane default, results are discarded anyway
end where
select case(icorr)
case (0)
evc = 0.0_DP
case (1)
do i=1,length
call pz_spin (rs(i), zeta(i), evc(i,3), evc(i,1), evc(i,2))
end do
case (2)
do i=1,length
call vwn_spin (rs(i), zeta(i), evc(i,3), evc(i,1), evc(i,2))
end do
case(3)
do i=1,length
call lsd_lyp (rho(i), zeta(i), evc(i,3), evc(i,1), evc(i,2)) ! from CP/FPMD (more_functionals)
end do
case(4)
call pw_spin_vec (rs, zeta, evc, length)
case default
call errore ('lsda_functional (xc_spin_vec)', 'not implemented', icorr)
end select
!
where (rho.le.small)
evx(:,1) = 0.0_DP
evc(:,1) = 0.0_DP
evx(:,2) = 0.0_DP
evc(:,2) = 0.0_DP
evx(:,3) = 0.0_DP
evc(:,3) = 0.0_DP
end where
!
end subroutine xc_spin_vec
!
!-----------------------------------------------------------------------
!------- GRADIENT CORRECTIONS DRIVERS ----------------------------------
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine gcxc (rho, grho, sx, sc, v1x, v2x, v1c, v2c)
!-----------------------------------------------------------------------
! gradient corrections for exchange and correlation - Hartree a.u.
! See comments at the beginning of module for implemented cases
!
! input: rho, grho=|\nabla rho|^2
! definition: E_x = \int E_x(rho,grho) dr
! output: sx = E_x(rho,grho)
! v1x= D(E_x)/D(rho)
! v2x= D(E_x)/D( D rho/D r_alpha ) / |\nabla rho|
! sc, v1c, v2c as above for correlation
!
implicit none
real(DP) :: rho, grho, sx, sc, v1x, v2x, v1c, v2c
real(DP) :: sx__,v1x__, v2x__
real(DP) :: sxsr, v1xsr, v2xsr
real(DP), parameter:: small = 1.E-10_DP
! exchange
if (rho <= small) then
sx = 0.0_DP
v1x = 0.0_DP
v2x = 0.0_DP
elseif (igcx == 1) then
call becke88 (rho, grho, sx, v1x, v2x)
elseif (igcx == 2) then
call ggax (rho, grho, sx, v1x, v2x)
elseif (igcx == 3) then
call pbex (rho, grho, 1, sx, v1x, v2x)
elseif (igcx == 4) then
call pbex (rho, grho, 2, sx, v1x, v2x)
elseif (igcx == 5 .and. igcc == 5) then
call hcth(rho, grho, sx, v1x, v2x)
elseif (igcx == 6) then
call optx (rho, grho, sx, v1x, v2x)
! case igcx == 7 (meta-GGA) must be treated in a separate call to another
! routine: needs kinetic energy density in addition to rho and grad rho
elseif (igcx == 8) then ! 'PBE0'
call pbex (rho, grho, 1, sx, v1x, v2x)
if (exx_started) then
sx = (1.0_DP - exx_fraction) * sx
v1x = (1.0_DP - exx_fraction) * v1x
v2x = (1.0_DP - exx_fraction) * v2x
end if
elseif (igcx == 9) then ! 'B3LYP'
call becke88 (rho, grho, sx, v1x, v2x)
if (exx_started) then
sx = 0.72_DP * sx
v1x = 0.72_DP * v1x
v2x = 0.72_DP * v2x
end if
elseif (igcx ==10) then ! 'pbesol'
call pbex (rho, grho, 3, sx, v1x, v2x)
elseif (igcx ==11) then ! 'wc'
call wcx (rho, grho, sx, v1x, v2x)
elseif (igcx ==12) then ! 'pbexsr'
call pbex (rho, grho, 1, sx, v1x, v2x)
if(exx_started) then
call pbexsr (rho, grho, sxsr, v1xsr, v2xsr, screening_parameter)
sx = sx - exx_fraction * sxsr
v1x = v1x - exx_fraction * v1xsr
v2x = v2x - exx_fraction * v2xsr
endif
elseif (igcx ==13) then ! 'rPW86'
call rPW86 (rho, grho, sx, v1x, v2x)
elseif (igcx ==16) then ! 'C09x'
call c09x (rho, grho, sx, v1x, v2x)
elseif (igcx ==17) then ! 'sogga'
call sogga(rho, grho, sx, v1x, v2x)
elseif (igcx ==19) then ! 'pbeq2d'
call pbex (rho, grho, 4, sx, v1x, v2x)
elseif (igcx ==20) then ! 'gau-pbe'
call pbex (rho, grho, 1, sx, v1x, v2x)
if(exx_started) then
call pbexgau (rho, grho, sxsr, v1xsr, v2xsr, gau_parameter)
sx = sx - exx_fraction * sxsr
v1x = v1x - exx_fraction * v1xsr
v2x = v2x - exx_fraction * v2xsr
endif
elseif (igcx == 21) then ! 'pw86'
call pw86 (rho, grho, sx, v1x, v2x)
elseif (igcx == 22) then ! 'b86b'
call becke86b (rho, grho, sx, v1x, v2x)
! call b86b (rho, grho, 1, sx, v1x, v2x)
elseif (igcx == 23) then ! 'optB88'
call pbex (rho, grho, 5, sx, v1x, v2x)
elseif (igcx == 24) then ! 'optB86b'
call pbex (rho, grho, 6, sx, v1x, v2x)
! call b86b (rho, grho, 2, sx, v1x, v2x)
elseif (igcx == 25) then ! 'ev93'
call pbex (rho, grho, 7, sx, v1x, v2x)
elseif (igcx == 26) then ! 'b86r'
call b86b (rho, grho, 3, sx, v1x, v2x)
elseif (igcx == 27) then ! 'cx13'
call cx13 (rho, grho, sx, v1x, v2x)
elseif (igcx == 28) then ! 'X3LYP'
call becke88 (rho, grho, sx, v1x, v2x)
call pbex (rho, grho, 1, sx__, v1x__, v2x__)
if (exx_started) then
sx = real(0.765*0.709,DP) * sx
v1x = real(0.765*0.709,DP) * v1x
v2x = real(0.765*0.709,DP) * v2x
sx = sx + real(0.235*0.709) * sx__
v1x = v1x + real(0.235*0.709) * v1x__
v2x = v2x + real(0.235*0.709) * v2x__
end if
else
sx = 0.0_DP
v1x = 0.0_DP
v2x = 0.0_DP
endif
! correlation
if (rho.le.small) then
sc = 0.0_DP
v1c = 0.0_DP
v2c = 0.0_DP
elseif (igcc == 1) then
call perdew86 (rho, grho, sc, v1c, v2c)
elseif (igcc == 2) then
call ggac (rho, grho, sc, v1c, v2c)
elseif (igcc == 3) then
call glyp (rho, grho, sc, v1c, v2c)
elseif (igcc == 4) then
call pbec (rho, grho, 1, sc, v1c, v2c)
! igcc == 5 (HCTH) is calculated together with case igcx=5
! igcc == 6 (meta-GGA) is treated in a different routine
elseif (igcc == 7) then !'B3LYP'
call glyp (rho, grho, sc, v1c, v2c)
if (exx_started) then
sc = 0.81_DP * sc
v1c = 0.81_DP * v1c
v2c = 0.81_DP * v2c
end if
elseif (igcc == 8) then ! 'PBEsol'
call pbec (rho, grho, 2, sc, v1c, v2c)
! igcc == 9 set to 5, back-compatibility
! igcc ==10 set to 6, back-compatibility
! igcc ==11 M06L calculated in another routine
else if (igcc == 12) then ! 'Q2D'
call pbec (rho, grho, 3, sc, v1c, v2c)
elseif (igcc == 13) then !'X3LYP'
call glyp (rho, grho, sc, v1c, v2c)
if (exx_started) then
sc = 0.871_DP * sc
v1c = 0.871_DP * v1c
v2c = 0.871_DP * v2c
end if
else
sc = 0.0_DP
v1c = 0.0_DP
v2c = 0.0_DP
endif
!
return
end subroutine gcxc
!
!!!!!!!!!!!!!!SPIN
!-----------------------------------------------------------------------
subroutine gcx_spin (rhoup, rhodw, grhoup2, grhodw2, &
sx, v1xup, v1xdw, v2xup, v2xdw)
!-----------------------------------------------------------------------
! gradient corrections for exchange - Hartree a.u.
!
implicit none
!
! dummy arguments
!
real(DP) :: rhoup, rhodw, grhoup2, grhodw2, sx, v1xup, v1xdw, &
v2xup, v2xdw
! up and down charge
! up and down gradient of the charge
! exchange and correlation energies
! derivatives of exchange wr. rho
! derivatives of exchange wr. grho
!
real(DP) :: sxsr, v1xupsr, v2xupsr, v1xdwsr, v2xdwsr
real(DP), parameter :: small = 1.E-10_DP
real(DP) :: rho, sxup, sxdw
integer :: iflag
!
!
! exchange
rho = rhoup + rhodw
if (rho <= small .or. igcx == 0) then
sx = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
elseif (igcx == 1) then
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call becke88_spin (rhoup, grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call becke88_spin (rhodw, grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = sxup + sxdw
elseif (igcx == 2) then
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call ggax (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call ggax (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 3 .or. igcx == 4 .or. igcx == 8 .or. &
igcx == 10 .or. igcx == 12 .or. igcx == 20 .or. igcx == 25) then
! igcx=3: PBE, igcx=4: revised PBE, igcx=8: PBE0, igcx=10: PBEsol
! igcx=12: HSE, igcx=20: gau-pbe, igcx=25: ev93
if (igcx == 4) then
iflag = 2
elseif (igcx == 10) then
iflag = 3
elseif (igcx == 25) then
iflag = 7
else
iflag = 1
endif
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call pbex (2.0_DP * rhoup, 4.0_DP * grhoup2, iflag, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call pbex (2.0_DP * rhodw, 4.0_DP * grhodw2, iflag, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
if (igcx == 8 .and. exx_started ) then
sx = (1.0_DP - exx_fraction) * sx
v1xup = (1.0_DP - exx_fraction) * v1xup
v1xdw = (1.0_DP - exx_fraction) * v1xdw
v2xup = (1.0_DP - exx_fraction) * v2xup
v2xdw = (1.0_DP - exx_fraction) * v2xdw
end if
if (igcx == 12 .and. exx_started ) then
call pbexsr_lsd (rhoup, rhodw, grhoup2, grhodw2, sxsr, &
v1xupsr, v2xupsr, v1xdwsr, v2xdwsr, &
screening_parameter)
sx = sx - exx_fraction*sxsr
v1xup = v1xup - exx_fraction*v1xupsr
v2xup = v2xup - exx_fraction*v2xupsr
v1xdw = v1xdw - exx_fraction*v1xdwsr
v2xdw = v2xdw - exx_fraction*v2xdwsr
end if
if (igcx == 20 .and. exx_started ) then
! gau-pbe
call pbexgau_lsd (rhoup, rhodw, grhoup2, grhodw2, sxsr, &
v1xupsr, v2xupsr, v1xdwsr, v2xdwsr, &
gau_parameter)
sx = sx - exx_fraction*sxsr
v1xup = v1xup - exx_fraction*v1xupsr
v2xup = v2xup - exx_fraction*v2xupsr
v1xdw = v1xdw - exx_fraction*v1xdwsr
v2xdw = v2xdw - exx_fraction*v2xdwsr
end if
elseif (igcx == 9) then
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call becke88_spin (rhoup, grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call becke88_spin (rhodw, grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = sxup + sxdw
if (exx_started ) then
sx = 0.72_DP * sx
v1xup = 0.72_DP * v1xup
v1xdw = 0.72_DP * v1xdw
v2xup = 0.72_DP * v2xup
v2xdw = 0.72_DP * v2xdw
end if
elseif (igcx == 11) then ! 'Wu-Cohen'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call wcx (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call wcx (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 13) then ! 'revised PW86 for vdw-df2'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call rPW86 (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call rPW86 (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 16) then ! 'c09x for vdw-df-c09.'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call c09x (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call c09x (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 21) then ! 'PW86'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call pw86 (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call pw86 (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 22) then ! 'B86B'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call becke86b (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call becke86b (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 26) then ! 'B86R for rev-vdW-DF2'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call b86b (2.0_DP * rhoup, 4.0_DP * grhoup2, 3, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call b86b (2.0_DP * rhodw, 4.0_DP * grhodw2, 3, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
elseif (igcx == 27) then ! 'cx13 for vdw-df-cx'
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
call cx13 (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
else
sxup = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
endif
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
call cx13 (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
else
sxdw = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
endif
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
! case igcx == 5 (HCTH) and 6 (OPTX) not implemented
! case igcx == 7 (meta-GGA) must be treated in a separate call to another
! routine: needs kinetic energy density in addition to rho and grad rho
else
call errore ('gcx_spin', 'not implemented', igcx)
endif
!
return
end subroutine gcx_spin
!
!-----------------------------------------------------------------------
subroutine gcx_spin_vec(rhoup, rhodw, grhoup2, grhodw2, &
sx, v1xup, v1xdw, v2xup, v2xdw, length)
!-----------------------------------------------------------------------
! gradient corrections for exchange - Hartree a.u.
!
implicit none
!
! dummy arguments
!
integer, intent(in) :: length
real(DP),intent(in) :: rhoup(length), rhodw(length)
real(DP),intent(in) :: grhoup2(length), grhodw2(length)
real(DP),intent(out) :: sx(length)
real(DP),intent(out) :: v1xup(length), v1xdw(length)
real(DP),intent(out) :: v2xup(length), v2xdw(length)
! up and down charge
! up and down gradient of the charge
! exchange and correlation energies
! derivatives of exchange wr. rho
! derivatives of exchange wr. grho
!
real(DP), parameter :: small = 1.E-10_DP
real(DP) :: rho(length), sxup(length), sxdw(length)
integer :: iflag
integer :: i
! only used for HSE (igcx == 12):
real(DP) :: sxsr, v1xupsr, v2xupsr, v1xdwsr, v2xdwsr
!
!
! exchange
rho = rhoup + rhodw
select case(igcx)
case(0)
sx = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
case(1)
do i=1,length
if (rhoup(i) > small .and. sqrt (abs (grhoup2(i)) ) > small) then
call becke88_spin (rhoup(i), grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt (abs (grhodw2(i)) ) > small) then
call becke88_spin (rhodw(i), grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = sxup + sxdw
case(2)
do i=1,length
if (rhoup(i) > small .and. sqrt (abs (grhoup2(i)) ) > small) then
call ggax (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt (abs (grhodw2(i)) ) > small) then
call ggax (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(3,4,8,10,12,25)
! igcx=3: PBE, igcx=4: revised PBE, igcx=8 PBE0, igcx=10: PBEsol,
! igcx=25: EV93
if (igcx == 4) then
iflag = 2
elseif (igcx == 10) then
iflag = 3
elseif (igcx == 25) then
iflag = 7
else
iflag = 1
endif
call pbex_vec (2.0_DP * rhoup, 4.0_DP * grhoup2, iflag, sxup, v1xup, v2xup, length, small)
call pbex_vec (2.0_DP * rhodw, 4.0_DP * grhodw2, iflag, sxdw, v1xdw, v2xdw, length, small)
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
if (igcx == 8 .and. exx_started ) then
sx = (1.0_DP - exx_fraction) * sx
v1xup = (1.0_DP - exx_fraction) * v1xup
v1xdw = (1.0_DP - exx_fraction) * v1xdw
v2xup = (1.0_DP - exx_fraction) * v2xup
v2xdw = (1.0_DP - exx_fraction) * v2xdw
end if
if (igcx == 12 .and. exx_started ) then
! in this case the subroutine is not really "vector"
DO i = 1, length
call pbexsr_lsd (rhoup(i), rhodw(i), grhoup2(i), grhodw2(i), sxsr, &
v1xupsr, v2xupsr, v1xdwsr, v2xdwsr, &
screening_parameter)
sx(i) = sx(i) - exx_fraction*sxsr
v1xup(i) = v1xup(i) - exx_fraction*v1xupsr
v2xup(i) = v2xup(i) - exx_fraction*v2xupsr
v1xdw(i) = v1xdw(i) - exx_fraction*v1xdwsr
v2xdw(i) = v2xdw(i) - exx_fraction*v2xdwsr
ENDDO
end if
case(9)
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i)) ) > small) then
call becke88_spin (rhoup(i), grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call becke88_spin (rhodw(i), grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = sxup + sxdw
if (exx_started ) then
sx = 0.72_DP * sx
v1xup = 0.72_DP * v1xup
v1xdw = 0.72_DP * v1xdw
v2xup = 0.72_DP * v2xup
v2xdw = 0.72_DP * v2xdw
end if
case(11) ! 'Wu-Cohen'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call wcx (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call wcx (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(13) ! 'rPW86 for vdw-df2'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call rPW86 (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call rPW86 (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(16) ! 'c09x for vdw-df-c09'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call c09x (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call c09x (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(21) ! 'pw86'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call pw86 (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call pw86 (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(22) ! 'b86b'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call becke86b (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call becke86b (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(26) ! 'B86R for rev-vdW-DF2'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call b86b (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), 3, sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call b86b (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), 3, sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case(27) ! 'cx13 for vdw-df-cx'
do i=1,length
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
call cx13 (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
else
sxup(i) = 0.0_DP
v1xup(i) = 0.0_DP
v2xup(i) = 0.0_DP
endif
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
call cx13 (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
else
sxdw(i) = 0.0_DP
v1xdw(i) = 0.0_DP
v2xdw(i) = 0.0_DP
endif
end do
sx = 0.5_DP * (sxup + sxdw)
v2xup = 2.0_DP * v2xup
v2xdw = 2.0_DP * v2xdw
case default
call errore ('gcx_spin_vec', 'not implemented', igcx)
end select
!
if (igcx.ne.0) then
where (rho.le.small)
sx = 0.0_DP
v1xup = 0.0_DP
v2xup = 0.0_DP
v1xdw = 0.0_DP
v2xdw = 0.0_DP
end where
end if
!
end subroutine gcx_spin_vec
!
!-----------------------------------------------------------------------
subroutine gcc_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
!-----------------------------------------------------------------------
! gradient corrections for correlations - Hartree a.u.
! Implemented: Perdew86, GGA (PW91), PBE
!
implicit none
!
! dummy arguments
!
real(DP) :: rho, zeta, grho, sc, v1cup, v1cdw, v2c
! the total charge
! the magnetization
! the gradient of the charge squared
! exchange and correlation energies
! derivatives of correlation wr. rho
! derivatives of correlation wr. grho
real(DP), parameter :: small = 1.E-10_DP, epsr=1.E-6_DP
!
if ( abs(zeta) > 1.0_DP ) then
sc = 0.0_DP
v1cup = 0.0_DP
v1cdw = 0.0_DP
v2c = 0.0_DP
return
else
!
! ... ( - 1.0 + epsr ) < zeta < ( 1.0 - epsr )
zeta = SIGN( MIN( ABS( zeta ), ( 1.0_DP - epsr ) ) , zeta )
endif
if (igcc == 0 .or. rho <= small .or. sqrt(abs(grho)) <= small) then
sc = 0.0_DP
v1cup = 0.0_DP
v1cdw = 0.0_DP
v2c = 0.0_DP
elseif (igcc == 1) then
call perdew86_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
elseif (igcc == 2) then
call ggac_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
elseif (igcc == 4) then
call pbec_spin (rho, zeta, grho, 1, sc, v1cup, v1cdw, v2c)
elseif (igcc == 8) then
call pbec_spin (rho, zeta, grho, 2, sc, v1cup, v1cdw, v2c)
else
call errore ('lsda_functionals (gcc_spin)', 'not implemented', igcc)
endif
!
return
end subroutine gcc_spin
!
! ==================================================================
SUBROUTINE gcc_spin_more( RHOA, RHOB, GRHOAA, GRHOBB, GRHOAB, &
SC, V1CA, V1CB, V2CA, V2CB, V2CAB )
! ==--------------------------------------------------------------==
! == GRADIENT CORRECTIONS FOR EXCHANGE AND CORRELATION ==
! == ==
! == EXCHANGE : BECKE88 ==
! == GGAX ==
! == CORRELATION : PERDEW86 ==
! == LEE, YANG & PARR ==
! == GGAC ==
! ==--------------------------------------------------------------==
IMPLICIT NONE
REAL(DP) :: RHOA,RHOB,GRHOAA,GRHOBB,GRHOAB
REAL(DP) :: SC,V1CA,V2CA,V1CB,V2CB,V2CAB
! ... Gradient Correction for correlation
REAL(DP) :: SMALL, RHO
PARAMETER(SMALL=1.E-20_DP)
SC=0.0_DP
V1CA=0.0_DP
V2CA=0.0_DP
V1CB=0.0_DP
V2CB=0.0_DP
V2CAB=0.0_DP
IF( igcc == 3 .or. igcc == 7) THEN
RHO=RHOA+RHOB
IF(RHO.GT.SMALL) then
CALL LSD_GLYP(RHOA,RHOB,GRHOAA,GRHOAB,GRHOBB,SC,&
V1CA,V2CA,V1CB,V2CB,V2CAB)
if (igcc == 7 .and. exx_started) then
SC = 0.81d0*SC
V1CA = 0.81d0*V1CA
V2CA = 0.81d0*V2CA
V1CB = 0.81d0*V1CB
V2CB = 0.81d0*V2CB
V2CAB = 0.81d0*V2CAB
endif
endif
ELSE
CALL errore( " gcc_spin_more ", " gradiet correction not implemented ", 1 )
ENDIF
! ==--------------------------------------------------------------==
RETURN
END SUBROUTINE gcc_spin_more
!
!
!-----------------------------------------------------------------------
!------- NONLOCAL CORRECTIONS DRIVERS ----------------------------------
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine nlc (rho_valence, rho_core, nspin, enl, vnl, v)
!-----------------------------------------------------------------------
! non local correction for the correlation
!
! input: rho_valence, rho_core
! definition: E_nl = \int E_nl(rho',grho',rho'',grho'',|r'-r''|) dr
! output: enl = E_nl
! vnl= D(E_x)/D(rho)
! v = Correction to the potential
!
USE vdW_DF, ONLY: xc_vdW_DF, xc_vdW_DF_spin, vdw_type
USE rVV10, ONLY: xc_rVV10
implicit none
REAL(DP), INTENT(IN) :: rho_valence(:,:), rho_core(:)
INTEGER, INTENT(IN) :: nspin
REAL(DP), INTENT(INOUT) :: v(:,:)
REAL(DP), INTENT(INOUT) :: enl, vnl
if ( inlc == 1 .or. inlc == 2 .or. inlc == 4 .or. inlc == 5 .or. inlc == 6 ) then
vdw_type = inlc
if( nspin == 1 ) then
call xc_vdW_DF (rho_valence, rho_core, enl, vnl, v)
else if( nspin == 2 ) then
call xc_vdW_DF_spin (rho_valence, rho_core, enl, vnl, v)
else
call errore ('nlc','vdW-DF not available for noncollinear spin case',1)
end if
elseif (inlc == 3) then
call xc_rVV10 (rho_valence, rho_core, nspin, enl, vnl, v)
else
enl = 0.0_DP
vnl = 0.0_DP
v = 0.0_DP
endif
!
return
end subroutine nlc
!
!-----------------------------------------------------------------------
!------- META CORRECTIONS DRIVERS ----------------------------------
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
subroutine tau_xc (rho, grho, tau, ex, ec, v1x, v2x, v3x, v1c, v2c, v3c)
!-----------------------------------------------------------------------
! gradient corrections for exchange and correlation - Hartree a.u.
! See comments at the beginning of module for implemented cases
!
! input: rho, grho=|\nabla rho|^2
!
! definition: E_x = \int e_x(rho,grho) dr
!
! output: sx = e_x(rho,grho) = grad corr
! v1x= D(E_x)/D(rho)
! v2x= D(E_x)/D( D rho/D r_alpha ) / |\nabla rho|
! v3x= D(E_x)/D(tau)
!
! sc, v1c, v2c as above for correlation
!
implicit none
real(DP) :: rho, grho, tau, ex, ec, v1x, v2x, v3x, v1c, v2c, v3c
!_________________________________________________________________________
if (imeta == 1) then
call tpsscxc (rho, grho, tau, ex, ec, v1x, v2x, v3x, v1c, v2c, v3c)
elseif (imeta == 2) then
call m06lxc (rho, grho, tau, ex, ec, v1x, v2x, v3x, v1c, v2c, v3c)
elseif (imeta == 3) then
call tb09cxc (rho, grho, tau, ex, ec, v1x, v2x, v3x, v1c, v2c, v3c)
else
call errore('v_xc_meta','wrong igcx and/or igcc',1)
end if
return
end subroutine tau_xc
!
!
!-----------------------------------------------------------------------
subroutine tau_xc_spin (rhoup, rhodw, grhoup, grhodw, tauup, taudw, ex, ec, &
& v1xup, v1xdw, v2xup, v2xdw, v3xup, v3xdw, v1cup, v1cdw,&
& v2cup, v2cdw, v3cup, v3cdw)
!-----------------------------------------------------------------------
!
!
implicit none
real(dp), intent(in) :: rhoup, rhodw, tauup, taudw
real(dp), dimension (3), intent(in) :: grhoup, grhodw
real(dp), intent(out) :: ex, ec, v1xup, v1xdw, v2xup, v2xdw, v3xup, v3xdw, &
& v1cup, v1cdw, v3cup, v3cdw
real(dp), dimension(3), intent(out) :: v2cup, v2cdw
!
! Local variables
!
integer :: ipol
real(dp) :: rh, zeta, atau, grhoup2, grhodw2
real(dp), parameter :: epsr=1.0d-08, zero=0._dp
!
!_____________________________
grhoup2 = zero
grhodw2 = zero
v2cup = zero
v2cdw = zero
do ipol=1,3
grhoup2 = grhoup2 + grhoup(ipol)**2
grhodw2 = grhodw2 + grhodw(ipol)**2
end do
if (imeta == 1) then
call tpsscx_spin(rhoup, rhodw, grhoup2, grhodw2, tauup, &
& taudw, ex, v1xup,v1xdw,v2xup,v2xdw,v3xup,v3xdw)
rh = rhoup + rhodw
zeta = (rhoup - rhodw) / rh
atau = tauup + taudw ! KE-density in Hartree
call tpsscc_spin(rh,zeta,grhoup,grhodw, atau,ec, &
& v1cup,v1cdw,v2cup,v2cdw,v3cup, v3cdw)
elseif (imeta == 2) then
call m06lxc_spin (rhoup, rhodw, grhoup2, grhodw2, tauup, taudw, &
& ex, ec, v1xup, v1xdw, v2xup, v2xdw, v3xup, v3xdw, &
& v1cup, v1cdw, v2cup(1), v2cdw(1), v3cup, v3cdw)
else
call errore('v_xc_meta','wrong igcx and/or igcc',1)
end if
end subroutine tau_xc_spin
!-----------------------------------------------------------------------
!------- DRIVERS FOR DERIVATIVES OF XC POTENTIAL -----------------------
!-----------------------------------------------------------------------
!
!-----------------------------------------------------------------------
function dmxc (rho)
!-----------------------------------------------------------------------
!
! derivative of the xc potential with respect to the local density
!
!
implicit none
!
real(DP), intent(in) :: rho
! input: the charge density ( positive )
real(DP) :: dmxc
! output: the derivative of the xc potential
!
! local variables
!
real(DP) :: dr, vxp, vcp, vxm, vcm, vx, ex, ec, rs
real(DP), external :: dpz
integer :: iflg
!
real(DP), parameter :: small = 1.E-30_DP, e2 = 2.0_DP, &
pi34 = 0.75_DP / 3.141592653589793_DP, third = 1.0_DP /3.0_DP
!
dmxc = 0.0_DP
if (rho < small) then
return
endif
!
! first case: analytical derivatives available
!
if (get_iexch() == 1 .and. get_icorr() == 1) then
rs = (pi34 / rho) **third
!..exchange
call slater (rs, ex, vx)
dmxc = vx / (3.0_DP * rho)
!..correlation
iflg = 2
if (rs < 1.0_DP) iflg = 1
dmxc = dmxc + dpz (rs, iflg)
else
!
! second case: numerical derivatives
!
dr = min (1.E-6_DP, 1.E-4_DP * rho)
call xc (rho + dr, ex, ec, vxp, vcp)
call xc (rho - dr, ex, ec, vxm, vcm)
dmxc = (vxp + vcp - vxm - vcm) / (2.0_DP * dr)
endif
!
! bring to rydberg units
!
dmxc = e2 * dmxc
return
!
end function dmxc
!
!-----------------------------------------------------------------------
subroutine dmxc_spin (rhoup, rhodw, dmuxc_uu, dmuxc_ud, dmuxc_du, &
dmuxc_dd)
!-----------------------------------------------------------------------
! derivative of the xc potential with respect to the local density
! spin-polarized case
!
implicit none
!
real(DP), intent(in) :: rhoup, rhodw
! input: spin-up and spin-down charge density
real(DP), intent(out) :: dmuxc_uu, dmuxc_ud, dmuxc_du, dmuxc_dd
! output: up-up, up-down, down-up, down-down derivatives of the
! XC functional
!
! local variables
!
real(DP) :: rhotot, rs, zeta, fz, fz1, fz2, ex, vx, ecu, ecp, vcu, &
vcp, dmcu, dmcp, aa, bb, cc, dr, dz, ec, vxupm, vxdwm, vcupm, &
vcdwm, rho, vxupp, vxdwp, vcupp, vcdwp, zeta_eff
real(DP), external :: dpz, dpz_polarized
integer :: iflg
!
real(DP), parameter :: small = 1.E-30_DP, e2 = 2.0_DP, &
pi34 = 0.75_DP / 3.141592653589793_DP, third = 1.0_DP/3.0_DP, &
p43 = 4.0_DP / 3.0_DP, p49 = 4.0_DP / 9.0_DP, m23 = -2.0_DP / 3.0_DP
!
dmuxc_uu = 0.0_DP
dmuxc_du = 0.0_DP
dmuxc_ud = 0.0_DP
dmuxc_dd = 0.0_DP
!
rhotot = rhoup + rhodw
if (rhotot <= small) return
zeta = (rhoup - rhodw) / rhotot
if (abs (zeta) > 1.0_DP) return
if (get_iexch() == 1 .and. get_icorr() == 1) then
!
! first case: analytical derivative available
!
!..exchange
rs = (pi34 / (2.0_DP * rhoup) ) **third
call slater (rs, ex, vx)
dmuxc_uu = vx / (3.0_DP * rhoup)
rs = (pi34 / (2.0_DP * rhodw) ) **third
call slater (rs, ex, vx)
dmuxc_dd = vx / (3.0_DP * rhodw)
!..correlation
rs = (pi34 / rhotot) **third
iflg = 2
if (rs < 1.0_DP) iflg = 1
dmcu = dpz (rs, iflg)
dmcp = dpz_polarized (rs, iflg)
call pz (rs, 1, ecu, vcu)
call pz_polarized (rs, ecp, vcp)
fz = ( (1.0_DP + zeta) **p43 + (1.0_DP - zeta) **p43 - 2.0_DP) &
/ (2.0_DP**p43 - 2.0_DP)
fz1 = p43 * ( (1.0_DP + zeta) **third- (1.0_DP - zeta) **third) &
/ (2.0_DP**p43 - 2.0_DP)
fz2 = p49 * ( (1.0_DP + zeta) **m23 + (1.0_DP - zeta) **m23) &
/ (2.0_DP**p43 - 2.0_DP)
aa = dmcu + fz * (dmcp - dmcu)
bb = 2.0_DP * fz1 * (vcp - vcu - (ecp - ecu) ) / rhotot
cc = fz2 * (ecp - ecu) / rhotot
dmuxc_uu = dmuxc_uu + aa + (1.0_DP - zeta) * bb + (1.0_DP - zeta)**2 * cc
dmuxc_du = dmuxc_du + aa + ( - zeta) * bb + (zeta**2 - 1.0_DP) * cc
dmuxc_ud = dmuxc_du
dmuxc_dd = dmuxc_dd+aa - (1.0_DP + zeta) * bb + (1.0_DP + zeta)**2 * cc
else
rho = rhoup + rhodw
dr = min (1.E-6_DP, 1.E-4_DP * rho)
call xc_spin (rho - dr, zeta, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
call xc_spin (rho + dr, zeta, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
dmuxc_uu = (vxupp + vcupp - vxupm - vcupm) / (2.0_DP * dr)
dmuxc_ud = dmuxc_uu
dmuxc_dd = (vxdwp + vcdwp - vxdwm - vcdwm) / (2.0_DP * dr)
dmuxc_du = dmuxc_dd
! dz = min (1.d-6, 1.d-4 * abs (zeta) )
dz = 1.E-6_DP
!
! If zeta is too close to +-1, the derivative is computed at a slightly
! smaller zeta
!
zeta_eff = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dz ) ) , zeta )
call xc_spin (rho, zeta_eff - dz, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
call xc_spin (rho, zeta_eff + dz, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
dmuxc_uu = dmuxc_uu + (vxupp + vcupp - vxupm - vcupm) * &
(1.0_DP - zeta) / rho / (2.0_DP * dz)
dmuxc_ud = dmuxc_ud- (vxupp + vcupp - vxupm - vcupm) * &
(1.0_DP + zeta) / rho / (2.0_DP * dz)
dmuxc_du = dmuxc_du + (vxdwp + vcdwp - vxdwm - vcdwm) * &
(1.0_DP - zeta) / rho / (2.0_DP * dz)
dmuxc_dd = dmuxc_dd- (vxdwp + vcdwp - vxdwm - vcdwm) * &
(1.0_DP + zeta) / rho / (2.0_DP * dz)
endif
!
! bring to rydberg units
!
dmuxc_uu = e2 * dmuxc_uu
dmuxc_du = e2 * dmuxc_du
dmuxc_ud = e2 * dmuxc_ud
dmuxc_dd = e2 * dmuxc_dd
!
return
end subroutine dmxc_spin
!-----------------------------------------------------------------------
subroutine dmxc_nc (rho, mx, my, mz, dmuxc)
!-----------------------------------------------------------------------
! derivative of the xc potential with respect to the local density
! and magnetization
! non colinear case
!
implicit none
!
real(DP), intent(in) :: rho, mx, my, mz
! input: charge density and magnetization
real(DP), intent(out) :: dmuxc(4,4)
! output: derivative of XC functional
!
! local variables
!
REAL(DP) :: zeta, ex, ec, dr, dz, vxupm, vxdwm, vcupm, &
vcdwm, vxupp, vxdwp, vcupp, vcdwp, vxup, vxdw, vcup, vcdw
REAL(DP) :: amag, vs, dvxc_rho, dvxc_mx, dvxc_my, dvxc_mz, &
dbx_rho, dbx_mx, dbx_my, dbx_mz, dby_rho, dby_mx, &
dby_my, dby_mz, dbz_rho, dbz_mx, dbz_my, dbz_mz, zeta_eff
REAL(DP), PARAMETER :: small = 1.E-30_DP, e2 = 2.0_DP
!
!
dmuxc = 0.0_DP
!
IF (rho <= small) RETURN
amag = sqrt(mx**2+my**2+mz**2)
zeta = amag / rho
IF (abs (zeta) > 1.0_DP) RETURN
CALL xc_spin (rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw)
vs=0.5_DP*(vxup+vcup-vxdw-vcdw)
dr = min (1.E-6_DP, 1.E-4_DP * rho)
CALL xc_spin (rho - dr, zeta, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
CALL xc_spin (rho + dr, zeta, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
dvxc_rho = ((vxupp + vcupp - vxupm - vcupm)+ &
(vxdwp + vcdwp - vxdwm - vcdwm)) / (4.0_DP * dr)
IF (amag > 1.E-10_DP) THEN
dbx_rho = ((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))* mx / (4.0_DP*dr*amag)
dby_rho = ((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))* my / (4.0_DP*dr*amag)
dbz_rho = ((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))* mz / (4.0_DP*dr*amag)
! dz = min (1.d-6, 1.d-4 * abs (zeta) )
dz = 1.0E-6_DP
!
! If zeta is too close to +-1, the derivative is computed at a slightly
! smaller zeta
!
zeta_eff = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dz ) ) , zeta )
CALL xc_spin (rho, zeta_eff - dz, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
CALL xc_spin (rho, zeta_eff + dz, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
! The variables are rho and m, so zeta depends on rho
!
dvxc_rho=dvxc_rho- ((vxupp + vcupp - vxupm - vcupm)+ &
(vxdwp + vcdwp - vxdwm - vcdwm))*zeta/rho/(4.0_DP * dz)
dbx_rho = dbx_rho-((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*zeta/rho/(4.0_DP*dz*amag)
dby_rho = dby_rho-((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))*my*zeta/rho/(4.0_DP*dz*amag)
dbz_rho = dbz_rho-((vxupp + vcupp - vxupm - vcupm)- &
(vxdwp + vcdwp - vxdwm - vcdwm))*mz*zeta/rho/(4.0_DP*dz*amag)
!
! here the derivatives with respect to m
!
dvxc_mx = ((vxupp + vcupp - vxupm - vcupm) + &
(vxdwp + vcdwp - vxdwm - vcdwm))*mx/rho/(4.0_DP*dz*amag)
dvxc_my = ((vxupp + vcupp - vxupm - vcupm) + &
(vxdwp + vcdwp - vxdwm - vcdwm))*my/rho/(4.0_DP*dz*amag)
dvxc_mz = ((vxupp + vcupp - vxupm - vcupm) + &
(vxdwp + vcdwp - vxdwm - vcdwm))*mz/rho/(4.0_DP*dz*amag)
dbx_mx = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*mx**2*amag/rho/ &
(4.0_DP*dz) + vs*(my**2+mz**2))/amag**3
dbx_my = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*my*amag/rho/ &
(4.0_DP*dz) - vs*(mx*my))/amag**3
dbx_mz = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*mz*amag/rho/ &
(4.0_DP*dz) - vs*(mx*mz))/amag**3
dby_mx = dbx_my
dby_my = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*my**2*amag/rho/ &
(4.0_DP*dz) + vs*(mx**2+mz**2))/amag**3
dby_mz = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*my*mz*amag/rho/ &
(4.0_DP*dz) - vs*(my*mz))/amag**3
dbz_mx = dbx_mz
dbz_my = dby_mz
dbz_mz = (((vxupp + vcupp - vxupm - vcupm) - &
(vxdwp + vcdwp - vxdwm - vcdwm))*mz**2*amag/rho/ &
(4.0_DP*dz) + vs*(mx**2+my**2))/amag**3
dmuxc(1,1)=dvxc_rho
dmuxc(1,2)=dvxc_mx
dmuxc(1,3)=dvxc_my
dmuxc(1,4)=dvxc_mz
dmuxc(2,1)=dbx_rho
dmuxc(2,2)=dbx_mx
dmuxc(2,3)=dbx_my
dmuxc(2,4)=dbx_mz
dmuxc(3,1)=dby_rho
dmuxc(3,2)=dby_mx
dmuxc(3,3)=dby_my
dmuxc(3,4)=dby_mz
dmuxc(4,1)=dbz_rho
dmuxc(4,2)=dbz_mx
dmuxc(4,3)=dbz_my
dmuxc(4,4)=dbz_mz
ELSE
dmuxc(1,1)=dvxc_rho
ENDIF
!
! bring to rydberg units
!
dmuxc = e2 * dmuxc
!
RETURN
end subroutine dmxc_nc
!
!-----------------------------------------------------------------------
subroutine dgcxc (r, s2, vrrx, vsrx, vssx, vrrc, vsrc, vssc)
!-----------------------------------------------------------------------
USE kinds, only : DP
implicit none
real(DP) :: r, s2, vrrx, vsrx, vssx, vrrc, vsrc, vssc
real(DP) :: dr, s, ds
real(DP) :: sx, sc, v1xp, v2xp, v1cp, v2cp, v1xm, v2xm, v1cm, &
v2cm
s = sqrt (s2)
dr = min (1.d-4, 1.d-2 * r)
ds = min (1.d-4, 1.d-2 * s)
call gcxc (r + dr, s2, sx, sc, v1xp, v2xp, v1cp, v2cp)
call gcxc (r - dr, s2, sx, sc, v1xm, v2xm, v1cm, v2cm)
vrrx = 0.5d0 * (v1xp - v1xm) / dr
vrrc = 0.5d0 * (v1cp - v1cm) / dr
vsrx = 0.25d0 * (v2xp - v2xm) / dr
vsrc = 0.25d0 * (v2cp - v2cm) / dr
call gcxc (r, (s + ds) **2, sx, sc, v1xp, v2xp, v1cp, v2cp)
call gcxc (r, (s - ds) **2, sx, sc, v1xm, v2xm, v1cm, v2cm)
vsrx = vsrx + 0.25d0 * (v1xp - v1xm) / ds / s
vsrc = vsrc + 0.25d0 * (v1cp - v1cm) / ds / s
vssx = 0.5d0 * (v2xp - v2xm) / ds / s
vssc = 0.5d0 * (v2cp - v2cm) / ds / s
return
end subroutine dgcxc
!
!-----------------------------------------------------------------------
subroutine dgcxc_spin (rup, rdw, gup, gdw, vrrxup, vrrxdw, vrsxup, &
vrsxdw, vssxup, vssxdw, vrrcup, vrrcdw, vrscup, vrscdw, vssc, &
vrzcup, vrzcdw)
!-----------------------------------------------------------------------
!
! This routine computes the derivative of the exchange and correlatio
! potentials with respect to the density, the gradient and zeta
!
USE kinds, only : DP
implicit none
real(DP), intent(in) :: rup, rdw, gup (3), gdw (3)
! input: the charges and the gradient
real(DP), intent(out):: vrrxup, vrrxdw, vrsxup, vrsxdw, vssxup, &
vssxdw, vrrcup, vrrcdw, vrscup, vrscdw, vssc, vrzcup, vrzcdw
! output: derivatives of the exchange and of the correlation
!
! local variables
!
real(DP) :: r, zeta, sup2, sdw2, s2, s, sup, sdw, dr, dzeta, ds, &
drup, drdw, dsup, dsdw, sx, sc, v1xupp, v1xdwp, v2xupp, v2xdwp, &
v1xupm, v1xdwm, v2xupm, v2xdwm, v1cupp, v1cdwp, v2cp, v1cupm, &
v1cdwm, v2cm
! charge densities and square gradients
! delta charge densities and gra
! delta gradients
! energies
! exchange potentials
! exchange potentials
! coorelation potentials
! coorelation potentials
real(DP), parameter :: eps = 1.d-6
!
r = rup + rdw
if (r.gt.eps) then
zeta = (rup - rdw) / r
else
zeta = 2.d0
endif
sup2 = gup (1) **2 + gup (2) **2 + gup (3) **2
sdw2 = gdw (1) **2 + gdw (2) **2 + gdw (3) **2
s2 = (gup (1) + gdw (1) ) **2 + (gup (2) + gdw (2) ) **2 + &
(gup (3) + gdw (3) ) **2
sup = sqrt (sup2)
sdw = sqrt (sdw2)
s = sqrt (s2)
!
! up part of exchange
!
if (rup.gt.eps.and.sup.gt.eps) then
drup = min (1.d-4, 1.d-2 * rup)
dsup = min (1.d-4, 1.d-2 * sdw)
!
! derivatives of exchange: up part
!
call gcx_spin (rup + drup, rdw, sup2, sdw2, sx, v1xupp, v1xdwp, &
v2xupp, v2xdwp)
call gcx_spin (rup - drup, rdw, sup2, sdw2, sx, v1xupm, v1xdwm, &
v2xupm, v2xdwm)
vrrxup = 0.5d0 * (v1xupp - v1xupm) / drup
vrsxup = 0.25d0 * (v2xupp - v2xupm) / drup
call gcx_spin (rup, rdw, (sup + dsup) **2, sdw2, sx, v1xupp, &
v1xdwp, v2xupp, v2xdwp)
call gcx_spin (rup, rdw, (sup - dsup) **2, sdw2, sx, v1xupm, &
v1xdwm, v2xupm, v2xdwm)
vrsxup = vrsxup + 0.25d0 * (v1xupp - v1xupm) / dsup / sup
vssxup = 0.5d0 * (v2xupp - v2xupm) / dsup / sup
else
vrrxup = 0.d0
vrsxup = 0.d0
vssxup = 0.d0
endif
if (rdw.gt.eps.and.sdw.gt.eps) then
drdw = min (1.d-4, 1.d-2 * rdw)
dsdw = min (1.d-4, 1.d-2 * sdw)
!
! derivatives of exchange: down part
!
call gcx_spin (rup, rdw + drdw, sup2, sdw2, sx, v1xupp, v1xdwp, &
v2xupp, v2xdwp)
call gcx_spin (rup, rdw - drdw, sup2, sdw2, sx, v1xupm, v1xdwm, &
v2xupm, v2xdwm)
vrrxdw = 0.5d0 * (v1xdwp - v1xdwm) / drdw
vrsxdw = 0.25d0 * (v2xdwp - v2xdwm) / drdw
call gcx_spin (rup, rdw, sup2, (sdw + dsdw) **2, sx, v1xupp, &
v1xdwp, v2xupp, v2xdwp)
call gcx_spin (rup, rdw, sup2, (sdw - dsdw) **2, sx, v1xupm, &
v1xdwm, v2xupm, v2xdwm)
vrsxdw = vrsxdw + 0.25d0 * (v1xdwp - v1xdwm) / dsdw / sdw
vssxdw = 0.5d0 * (v2xdwp - v2xdwm) / dsdw / sdw
else
vrrxdw = 0.d0
vrsxdw = 0.d0
vssxdw = 0.d0
endif
!
! derivatives of correlation
!
if (r.gt.eps.and.abs (zeta) .le.1.d0.and.s.gt.eps) then
dr = min (1.d-4, 1.d-2 * r)
call gcc_spin (r + dr, zeta, s2, sc, v1cupp, v1cdwp, v2cp)
call gcc_spin (r - dr, zeta, s2, sc, v1cupm, v1cdwm, v2cm)
vrrcup = 0.5d0 * (v1cupp - v1cupm) / dr
vrrcdw = 0.5d0 * (v1cdwp - v1cdwm) / dr
ds = min (1.d-4, 1.d-2 * s)
call gcc_spin (r, zeta, (s + ds) **2, sc, v1cupp, v1cdwp, v2cp)
call gcc_spin (r, zeta, (s - ds) **2, sc, v1cupm, v1cdwm, v2cm)
vrscup = 0.5d0 * (v1cupp - v1cupm) / ds / s
vrscdw = 0.5d0 * (v1cdwp - v1cdwm) / ds / s
vssc = 0.5d0 * (v2cp - v2cm) / ds / s
! dzeta = min (1.d-4, 1.d-2 * abs (zeta) )
dzeta = 1.d-6
!
! If zeta is too close to +-1 the derivative is evaluated at a slightly
! smaller value
!
zeta = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dzeta ) ) , zeta )
call gcc_spin (r, zeta + dzeta, s2, sc, v1cupp, v1cdwp, v2cp)
call gcc_spin (r, zeta - dzeta, s2, sc, v1cupm, v1cdwm, v2cm)
vrzcup = 0.5d0 * (v1cupp - v1cupm) / dzeta
vrzcdw = 0.5d0 * (v1cdwp - v1cdwm) / dzeta
else
vrrcup = 0.d0
vrrcdw = 0.d0
vrscup = 0.d0
vrscdw = 0.d0
vssc = 0.d0
vrzcup = 0.d0
vrzcdw = 0.d0
endif
return
end subroutine dgcxc_spin
!
!-----------------------------------------------------------------------
!------- VECTOR AND GENERAL XC DRIVERS -------------------------------
!-----------------------------------------------------------------------
!
subroutine evxc_t_vec(rho,rhoc,lsd,length,vxc,exc)
!---------------------------------------------------------------
!
! this function returns the XC potential in LDA or LSDA approximation
!
integer, intent(in) :: lsd, length
real(DP), intent(in) :: rho(length,2), rhoc(length)
real(DP), intent(out), optional :: vxc(length,2)
real(DP), intent(out), optional :: exc(length)
!
real(DP) :: arho
real(DP) :: arhoV(length), zetaV(length)
real(DP) :: evx(length,3), evc(length,3)
real(DP) :: ex, ec, vx, vc
!
integer :: i
real(DP), parameter :: e2 = 2.0_dp, eps = 1.e-30_dp
if (lsd.eq.0) then
!
! LDA case
!
do i=1,length
arho = abs(rho(i,1)+rhoc(i))
if (arho.gt.eps) then
call xc(arho,ex,ec,vx,vc)
else
ex = 0.0_dp
ec = 0.0_dp
vx = 0.0_dp
vc = 0.0_dp
end if
if (present(vxc)) vxc(i,1) = e2*(vx+vc)
if (present(exc)) exc(i) = e2*(ex+ec)
end do
else
!
! LSDA case
!
arhoV = abs(rho(:,1)+rho(:,2)+rhoc(:))
where (arhoV.gt.eps)
zetaV = (rho(:,1)-rho(:,2)) / arhoV
elsewhere
zetaV = 0.0_DP ! just a sane default, results are discarded anyway
end where
! zeta has to stay between -1 and 1, but can get a little
! out of bound during the first iterations.
zetaV = min( 1.0_DP, zetaV)
zetaV = max(-1.0_DP, zetaV)
call xc_spin_vec(arhoV, zetaV, length, evx, evc)
if (present(vxc)) then
vxc(:,1) = e2*(evx(:,1) + evc(:,1))
vxc(:,2) = e2*(evx(:,2) + evc(:,2))
end if
if (present(exc)) exc = e2*(evx(:,3)+evc(:,3))
end if
end subroutine evxc_t_vec
end module funct