/
ISC-DSO-FINITE-TEMPERATURE.f90
397 lines (288 loc) · 12.8 KB
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ISC-DSO-FINITE-TEMPERATURE.f90
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PROGRAM ISC_DSO_CORRELATION_TEMP
IMPLICIT NONE
REAL*8,DIMENSION(30,30)::RJ,RJT,OMEGAS,OMEGAT,OMEGAS2, &
OMEGA2,OMEGA,ST,STI,BT,BTI,RJ1,RJ2,B1,B2,B3,B4,C1,C2,C3, &
C4,R,R1,OMEGAT2,P,P1,P2,A1,P5IIM,P5IR,BSR,BSIR,BSIM,BSIIM, &
SSIR,SSIIM,B5,B6,B7,C5,C6,E1,E2,P3,P4,X4,X5,X1,X2,X3,X3I
REAL*8,DIMENSION(30,1)::WS,WT,A3,A4,A5,A6,F4,F5,D,A2,F3
REAL*8,DIMENSION(1,1)::A7,F7,F6
REAL*8,DIMENSION(1,30)::DT
COMPLEX*16,DIMENSION(30,30)::RT,RTI,RT1,P5I,P5,E,BS,SS,BSI,SSI
REAL*8::TMIN,TMAX,H,CM_AU,S_AU,T,AMP,SQ_DET,K1,TEMP_AU, &
K2,DELE_AB,SOC,GEN_FUNC,KISC_DIR,AMU_AU,CONST,AU_HZ,KBT, &
ETA,U2,U1,GEN_FN,THETA,U,BETA,TEMP,SUM_Z,EV_AU,KB, &
SCAL,SCAL1
COMPLEX*16::DET
INTEGER::I,J,N,K,M,INFO
INTEGER,DIMENSION(30)::IPIV
COMPLEX*16,DIMENSION(30)::WORK
! THIS INPUT SECTION IS FOR INTERSYSTEM CROSSING RATE CALCULATION OF
! URACIL MOLECULE
OPEN(30,FILE='JMAT-URACIL-S1-T1.TXT')
OPEN(3,FILE='WS1-URACIL.TXT')
OPEN(2,FILE='WT1-URACIL.TXT')
OPEN(10,FILE='SHIFT-VECTOR-URACIL-S1-T1.TXT')
OPEN(34,FILE='GEN_FN.TXT')
! WRITE(*,*)'GIVE N,TMIN,TMAX,M,ETA,TEMP' !INPUT PARAMETER FOR NUMERICAL INTEGRATION
! READ(*,*)N,TMIN,TMAX,M,ETA,TEMP !TEMP=TEMPERATURE IN KELVIN
N=30
TMIN=1.0D0*(10.0D0**(-24.0D0))
TMAX=20.0D0*(10.0D0**(-12.0D0))
M=20000
ETA=2.0D0
TEMP=300.0D0
!READ THE DUSCHINSKY ROTATION MATRIX, FREQUENCIES AND SHIFT
!VECTOR
READ(30,*)((RJ(I,J),J=1,N),I=1,N) !RJ=DUSCHINSKY ROTATION MATRIX
READ(3,*)(WS(I,1),I=1,N) !WS=FREQUENCY VECTOR OF SINGLET STATE
READ(2,*)(WT(I,1),I=1,N) !WT=FREQUENCY VECTOR OF TRIPLET STATE
READ(10,*)(D(I,1),I=1,N) !D=DISPLACEMENT VECTOR
!TRANSFER THE DATA TO ATOMIC UNIT
AU_HZ=6.579D0*(10.0D0**15.0D0)
CM_AU=4.55634D0*(10.0D0**(-6.0D0))
S_AU=0.4134D0*(10.0D0**17.0D0)
AMU_AU=(1.82289D0*(10.0D0**3.0D0))
AMU_AU=((AMU_AU)**0.5D0)
EV_AU=0.036749844D0
DELE_AB=0.810D0 !ENERGY GAP BETWEEN S1 AND T1 IN EV
DELE_AB=DELE_AB*EV_AU
SOC=53.10D0 !SPIN-ORBIT COUPLING BETWEEN S1 AND T1 IN CM^(-1)
SOC=SOC*CM_AU
KB=1.3806452D0*(10.0D0**(-23.0D0))
KBT=KB*TEMP
KBT=KBT*(6.242D0*(10.0D0**(18.0D0))) !JOULE To EV
KBT=KBT*EV_AU !EV TO AU
BETA=(1.0D0/KBT)
DO I=1,N
WS(I,1)=WS(I,1)*CM_AU
WT(I,1)=WT(I,1)*CM_AU
ENDDO
TMAX=TMAX*S_AU
TMIN=TMIN*S_AU
ETA=ETA*CM_AU
!GENERATE THE DIAGONAL FREQUENCY MATRIX
DO I=1,N
DO J=1,N
IF(I.EQ.J)THEN
OMEGAS(I,J)=WS(I,1)
OMEGAT(I,J)=WT(I,1)
ELSE
OMEGAS(I,J)=0.0D0
OMEGAT(I,J)=0.0D0
ENDIF
ENDDO
ENDDO
!GENERATE THE TRANSPOSE OF RJ AND D
DO I=1,N
DO J=1,N
RJT(I,J)=RJ(J,I) !RJTRANSPOSE OF DUSCHINSKY ROTATION MATRIX RJ
ENDDO
ENDDO
!GENERATE THE TRANSPOSE OF THE DISPLACEMENT VECTOR
DO I=1,N
DT(1,I)=D(I,1) !DT=TRANSPOSE OF DISPLACEMENT VECTOR
ENDDO
!GENERATE THE SQUARE OF THE FREQUENCY OMEGAT AND OMEGAS MATRIX
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,OMEGAS,N,0.0D0,OMEGAS2,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAT,N,OMEGAT,N,0.0D0,OMEGAT2,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,OMEGAT,N,0.0D0,OMEGA2,N)
!CALCULATION OF THE CANONICAL PARTITION FUNCTION
SUM_Z=0.0D0
SCAL=1.0D0
DO I=1,N
DO J=1,N
IF(I.EQ.J)THEN
SUM_Z=SUM_Z+(EXP(-OMEGAS(I,J)*BETA)) !SUM_OMEGAS=SUMMATION OF DIAGONAL ELEMENT OF WS ELEMENT
SCAL=SCAL*(4.0D0*(((COSH(BETA*OMEGAS(I,J)/2.0D0))**2.0D0)-1))
ELSE
ENDIF
ENDDO
ENDDO
WRITE(*,*)SUM_Z,SCAL,SQRT(SCAL)
!........................................................................................................................................................\\
!GENERATE THE REQUIRED MATRIX AND MATRIX MULTIPLICATION WITHIN
!THE TIME LOOP FOR DETERMINANT CALCULATION
KISC_DIR=0.0D0
H=(TMAX-TMIN)/FLOAT(M)
DO K=1,M
T=TMIN+(H*(K-1))
DO I=1,N
DO J=1,N
IF(I.EQ.J)THEN
ST(I,J)=SIN(OMEGAT(I,J)*T) !FORM OF ST DIAGONAL MATRIX
STI(I,J)=(1.0D0)/ST(I,J) !INVERSE OF ST MATRIX
BT(I,J)=TAN((OMEGAT(I,J)*T)/2.0D0) !FORM OF DIAGONAL BT MATRIX
BTI(I,J)=(1.0D0)/(BT(I,J)) !INVERSE OF ST MATRIX
!FORM THE DIAGONAL SS AND BS MATRIX
X1(I,J)=(OMEGAS(I,J)*BETA)/2.0D0
X2(I,J)=(OMEGAS(I,J)*T)/2.0D0
X4(I,J)=(EXP(X1(I,J)*2.0D0)+EXP(-2.0D0*X1(I,J)))/2.0D0 !DEFINITION OF COSH(X)
X5(I,J)=(EXP(X1(I,J)*2.0D0)-EXP(-2.0D0*X1(I,J)))/2.0D0 !DEFINITION OF SINH(X)
X3(I,J)=X4(I,J)+COS(X2(I,J)*2.0D0)
X3I(I,J)=1.0D0/X3(I,J)
BS(I,J)=CMPLX((X5(I,J)*X3I(I,J)),((-SIN(X2(I,J)*2.0D0) &
*X3I(I,J)))) !FORM OF BS DIAGONAL MATRIX
BSI(I,J)=(1.0D0/(BS(I,J))) !INVERSE OF BS MATRIX IS BSI
SS(I,J)=CMPLX((X5(I,J)*COS(2.0D0*X2(I,J))),(-X4(I,J) &
*SIN(2.0D0*X2(I,J)))) !FORM OF SS DIAGONAL MATRIX
SSI(I,J)=(1.0D0/(SS(I,J))) !INVERSE OF SS MATRIX IS SSI
ELSE
ST(I,J)=0.0D0
STI(I,J)=0.0D0
BT(I,J)=0.0D0
BTI(I,J)=0.0D0
BS(I,J)=(0.0D0,0.0D0)
BSI(I,J)=(0.0D0,0.0D0)
SS(I,J)=(0.0D0,0.0D0)
SSI(I,J)=(0.0D0,0.0D0)
ENDIF
ENDDO
ENDDO
DO I=1,N
DO J=1,N
BSR(I,J)=REAL(BS(I,J)) !REAL PART OF BS COMPLEX MATRIX
BSIM(I,J)=AIMAG(BS(I,J)) !IMAGINARY PART OF BS COMPLEX MATRIX
BSIR(I,J)=REAL(BSI(I,J)) !REAL PART OF INVERSE OF BS MATRIX
BSIIM(I,J)=AIMAG(BSI(I,J)) !IMAGINARY PART OF INVERSE OF BS MATRIX
SSIR(I,J)=REAL(SSI(I,J)) !REAL PART OF INVERSE OF SS MATRIX
SSIIM(I,J)=AIMAG(SSI(I,J)) !IMAGINARY PART OF INVERSE OF SS MATRIX
ENDDO
ENDDO
!GENERATE THE MATRIX RJT*OMRGAT2*RJ
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAT2,N,RJ,N,0.0D0,RJ1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,RJT,N,RJ1,N,0.0D0,RJ2,N)
!GENERATE THE MATRIX OMEGAS*BSR*RJT*OMEGAT*BTI*RJ
CALL DGEMM('N','N',N,N,N,1.0D0,BTI,N,RJ,N,0.0D0,B1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAT,N,B1,N,0.0D0,B2,N)
CALL DGEMM('N','N',N,N,N,1.0D0,RJT,N,B2,N,0.0D0,B3,N)
CALL DGEMM('N','N',N,N,N,1.0D0,BSR,N,B3,N,0.0D0,B4,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,B4,N,0.0D0,B5,N)
!GENERATE THE TERM OMEGAS*BSIM*RJT*OMEGAT*BTI*RJ
CALL DGEMM('N','N',N,N,N,1.0D0,BSIM,N,B3,N,0.0D0,B6,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,B6,N,0.0D0,B7,N)
!GENERATE THE MATRIX RJT*OMEGAT*BT*RJ*OMEGAS
CALL DGEMM('N','N',N,N,N,1.0D0,RJ,N,OMEGAS,N,0.0D0,C1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,BT,N,C1,N,0.0D0,C2,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAT,N,C2,N,0.0D0,C3,N)
CALL DGEMM('N','N',N,N,N,1.0D0,RJT,N,C3,N,0.0D0,C4,N)
CALL DGEMM('N','N',N,N,N,1.0D0,C4,N,BSIR,N,0.0D0,C5,N)
CALL DGEMM('N','N',N,N,N,1.0D0,C4,N,BSIIM,N,0.0D0,C6,N)
DO I=1,N
DO J=1,N
R(I,J)=RJ2(I,J)+OMEGAS2(I,J)+B7(I,J)-C6(I,J)
R1(I,J)=C5(I,J)-B5(I,J)
RT(I,J)=CMPLX(R(I,J),R1(I,J))
ENDDO
ENDDO
!GENERATE THE INVERSE OF DENOMINATOR MATRIX RT RT=FORM OF
!DENOMINATOR MATRIX WITHIN SQUARE ROOT
DO I=1,N
DO J=1,N
RTI(I,J)=RT(I,J)
ENDDO
ENDDO
CALL ZGETRF(N,N,RTI,N,IPIV,INFO)
CALL ZGETRI(N,RTI,N,IPIV,WORK,N,INFO)
!GENERATE THE MATRIX SSI*STI*OMEGAT*OMEGAS !MATRIX FORM OF NUMERATOR WITHIN SQUARE ROOT
CALL DGEMM('N','N',N,N,N,1.0D0,STI,N,OMEGA2,N,0.0D0,OMEGA,N)
CALL DGEMM('N','N',N,N,N,1.0D0,SSIR,N,OMEGA,N,0.0D0,E1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,SSIIM,N,OMEGA,N,0.0D0,E2,N)
DO I=1,N
DO J=1,N
E(I,J)=CMPLX(-E2(I,J),E1(I,J))
ENDDO
ENDDO
!GENERATE THE TOTAL MATRIX FORM FOR DETERMINANT CALCULATION =OMEGAI*RTI
CALL ZGEMM('N','N',N,N,N,(1.0D0,0.0D0),E,N,RTI, &
N,(0.0D0,0.0D0),RT1,N)
!CALCULATE THE DETERMINANT OF THE MATRIX RT1
CALL DETERMINANT(N,RT1,DET) !RT1=COMPLETE DETERMINANT WITHIN SQUARE ROOT
U1=AIMAG(DET)
U2=REAL(DET)
AMP=ABS(DET) !AMP=AMPLITUDE OF DETERMINANT
THETA=(ATAN(U1/U2)) !THETA=PHASE FACTOR OF THE INDIVIDUAL DETERMINANT AT EACH TIME
THETA=THETA/2.0D0
SQ_DET=SQRT(AMP) !SQ_RT=SQUARE ROOT OF THE ABSLOUTE VALUE OF DETERMINANT
!........................................................................................................................................//
!GENERATE THE REAL EXPONENTIAL PART
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAT,N,BT,N,0.0D0,A1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,A1,N,RJ,N,0.0D0,P1,N)
CALL DGEMM('N','N',N,N,N,1.0D0,RJT,N,P1,N,0.0D0,P,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,BSR,N,0.0D0,P2,N)
CALL DGEMM('N','N',N,N,N,1.0D0,OMEGAS,N,BSIM,N,0.0D0,P3,N)
DO I=1,N
DO J=1,N
P4(I,J)=(P(I,J)+P3(I,J))
P5(I,J)=CMPLX(P2(I,J),P4(I,J))
ENDDO
ENDDO
DO I=1,N
DO J=1,N
P5I(I,J)=P5(I,J)
ENDDO
ENDDO
CALL ZGETRF(N,N,P5I,N,IPIV,INFO)
CALL ZGETRI(N,P5I,N,IPIV,WORK,N,INFO)
DO I=1,N
DO J=1,N
P5IR(I,J)=REAL(P5I(I,J))
P5IIM(I,J)=AIMAG(P5I(I,J))
ENDDO
ENDDO
CALL DGEMM('N','N',N,1,N,1.0D0,A1,N,D,N,0.0D0,A2,N)
CALL DGEMM('N','N',N,1,N,1.0D0,RJT,N,A2,N,0.0D0,A3,N)
CALL DGEMM('N','N',N,1,N,1.0D0,P5IR,N,A3,N,0.0D0,A4,N)
CALL DGEMM('N','N',N,1,N,1.0D0,RJ,N,A4,N,0.0D0,A5,N)
CALL DGEMM('N','N',N,1,N,1.0D0,A1,N,A5,N,0.0D0,A6,N)
CALL DGEMM('N','N',1,1,N,1.0D0,DT,1,A6,N,0.0D0,A7,1)
K1=-A7(1,1) !K1=TERM WITHIN THE EXPONENTIAL TERM
!..................................................................................................................................................//
!GENERATE THE TERM WITHIN COSINE
CALL DGEMM('N','N',N,1,N,1.0D0,P5IIM,N,A3,N,0.0D0,F3,N)
CALL DGEMM('N','N',N,1,N,1.0D0,RJ,N,F3,N,0.0D0,F4,N)
CALL DGEMM('N','N',N,1,N,1.0D0,A1,N,F4,N,0.0D0,F5,N)
CALL DGEMM('N','N',1,1,N,1.0D0,DT,1,F5,N,0.0D0,F6,1)
CALL DGEMM('N','N',1,1,N,1.0D0,DT,1,A2,N,0.0D0,F7,1)
K2=(-F6(1,1)-F7(1,1)+(T*DELE_AB)) !K2=TERM WITHIN THE COSINE TERM
!FINAL EXPRESSION OF THE REAL PART
CONST=(SOC**2.0D0)*(1.0D0/SUM_Z)*2.0D0
GEN_FUNC=SQ_DET*EXP(K1)*COS(K2+THETA) &
*EXP(-ETA*(T**2.0D0))
WRITE(34,*)T,GEN_FUNC
!......................................................................................................................................................//
!INTEGRATION USING SIMPSIN'S ONE-THIRD RULE WITHIN TIME DOMAIN
IF((K.EQ.1).OR.(K.EQ.(M)))THEN
KISC_DIR=KISC_DIR+GEN_FUNC
ELSE
IF(MOD(K,2).EQ.0.0D0)THEN
KISC_DIR=KISC_DIR+(GEN_FUNC*4.0D0)
ELSE
KISC_DIR=KISC_DIR+(2.0D0*GEN_FUNC)
ENDIF
ENDIF
ENDDO
KISC_DIR=(KISC_DIR*H*CONST)/3.0D0
KISC_DIR=KISC_DIR*AU_HZ
WRITE(*,*)'KISC_DIR IS',KISC_DIR,CONST
END PROGRAM ISC_DSO_CORRELATION_TEMP
!..................................................................................................................................................................\\
!SUBROUTINE FOR DETERMINANT CALCULATION USING LAPACK-BLAS LIBRARY
SUBROUTINE DETERMINANT(N,A,DET)
COMPLEX*16::A(N,N)
COMPLEX*16::DET,SGN
INTEGER::I,INFO,N
INTEGER::IPIV(N)
CALL ZGETRF(N, N, A, N, IPIV,INFO)
DET =(1.0D0,0.0D0)
DO I =1,N
DET = DET*A(I,I)
ENDDO
SGN =(1.0D0,0.0D0)
DO I = 1, N
IF(IPIV(I) /= I) THEN
SGN = -SGN
END IF
ENDDO
DET= SGN*DET
RETURN
END