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AFdiag.f
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AFdiag.f
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c***********************************************************************
SUBROUTINE AFdiag(RDIST,NCMM,NCMMax,MMLR,PSEL,De,Cm,rhoAB,sVSR2,
1 IDSTT,ULR,dULRdCm,dULRdR,dULRdDe)
c***********************************************************************
c** Aubert-Frecon Potential Model for u_{LR}(r)
c***********************************************************************
c** Subroutine to generate, at the onee distance RDIST, an eigenvalue
c of the 2x2 or 3x3 long-range interaction matrix described by Eqs.1
c and 10, resp., of J.Mol.Spec.188, 182 (1998) (Aubert-Frecon et al)
c** and its derivatives w.r.t. the C_m long-range parameters.
c***********************************************************************
c==> Input: r= RDIST, NCMM, m=MMLR & Cm's, rhoAB, sVSR2, IDSTT
c==> Output: ULR, partial derivatives dULRdCm & radial derivative dULRdR
c-----------------------------------------------------------------------
c** Summer 2008 Original Version from Nike Dattani for 3x3 case
c** July 2014 incorporated 2x2 case, removed retardation terms and
c incorporate damping ... by Kai Slaughter
c-----------------------------------------------------------------------
INTEGER NCMMax
c-----------------------------------------------------------------------
REAL*8 RDIST,Cm(NCMMax),ULR,dULRdCm(NCMMax),dULRdR,R2,R3,R5,
1 R6,R8,R9,T1,T0,T2,T0P,T0P23,DDe1,DDe2,DDe3,DELTAE,Modulus,Z,
2 Dm(NCMMax),Dmp(NCMMax),De,DDe(3,3),Dmpp(NCMMax),rhoAB,A(3,3),
3 DR(3,3),Q(3,3),DMx(NCMMax,3,3),DMtemp(3,3),DEIGMx(NCMMax,1,1),
4 DEIGMtemp(1,1),DEIGR(1,1),DEIGdDe(1,1),EIGVEC(3,1),RESID(3,1),
5 W(3),RPOW(NCMMax), dULRdDe
INTEGER H,I,J,K,L,M,X,NCMM,MMLR(NCMMax),sVSR2,IDSTT,PSEL
c-----------------------------------------------------------------------
DELTAE=Cm(1)
R2= 1.d0/RDIST**2
R3= R2/RDIST
R5= R2*R3
R6= R3*R3
R8= R6*R2
c-----------------------------------------------------------------------
c....... for rhoAB.le.0.0 returns Dm(m)=1 & Dmp(m)=Dmpp(m)=0
CALL dampF(RDIST,rhoAB,NCMM,NCMMAX,MMLR,sVSR2,IDSTT,Dm,Dmp,Dmpp)
c-----------------------------------------------------------------------
IF(MMLR(1).GE.-1) THEN !! For the A (0) or b (-1) state
c***********************************************************************
c************* Aubert Frecon 2x2 case NCMM= 7 and ...
c*** Cm(1) = DELTAE
c*** Cm(2) = C3Sig
c*** Cm(3) = C3Pi
c*** Cm(4) = C6Sig
c*** Cm(5) = C6Pi
c*** Cm(6) = C8Sig
c*** Cm(7) = C8Pi
c***********************************************************************
T1= R3*(Dm(2)*(Cm(2)-Cm(3)) + R3*Dm(4)*(Cm(4)-Cm(5)) +
1 R5*Dm(6)*(Cm(6)-Cm(7)))/3.d0
T0= DSQRT((T1 - Cm(1))**2 + 8.d0*T1**2)
ULR= 0.5d0*(-Cm(1) + R3*(Dm(2)*(Cm(2)+Cm(3)) +
1 R3*Dm(4)*(Cm(4)+Cm(5)) + R5*Dm(6)*(Cm(6)+Cm(7))) + T0)
c-----------------------------------------------------------------------
IF(MMLR(1).EQ.0) THEN
ULR= ULR + Cm(8)*R3*R6 !! add C9{adj correction
ENDIF
c... adjustment for the b-state
IF(MMLR(1).EQ.-1) THEN
ULR=ULR-T0
ULR= ULR + Cm(9)*R3*R6 !! add C9{adj correction
ENDIF
c... now get derivatives
T0P= 0.5d0*(9.d0*T1 - Cm(1))/T0
T0P23= 0.5d0 + T0P/3.d0
c... another adjustment for the b-state
IF(MMLR(1).EQ.-1) T0P23=T0P23-2.d0*T0P/3.d0
dULRdCm(1)= 0.d0
dULRdCm(2)= R3*(T0P23)
dULRdCm(3)= R3*(1.d0-T0P23)
dULRdCm(4)= R6*(T0P23)
dULRdCm(5)= R6*(1.d0 - T0P23)
dULRdCm(6)= R8*T0P23
dULRdCm(7)= R8*(1.d0-T0P23)
T2 =-T0P*R3*((Dm(2)*(Cm(2)-Cm(3))+R3*(Dm(4)*2.d0*(Cm(4)
1 -Cm(5))+R2*Dm(6)*8.d0/3.d0*(Cm(6)-Cm(7))))/RDIST
2 +(Dmp(2)*(Cm(2)-Cm(3))+R3*Dmp(4)*(Cm(4)-Cm(5))+
3 R2*R3*Dmp(6)*(Cm(6)-Cm(7)))/3.d0)
dULRdR = -R3*((1.5d0*Dm(2)*(Cm(2)+Cm(3)) + R3*(Dm(4)*3.d0*
1 (Cm(4)+Cm(5))+4.d0*Dm(6)*R2*(Cm(6)+Cm(7))))/RDIST
2 + 0.5d0*(Dmp(2)*(Cm(2)+Cm(3)) + Dmp(4)*R3*(Cm(4)+
3 Cm(5)) + Dmp(6)*R3*R2*(Cm(6)+Cm(7)))) + T2
c... and a final adjustment for the b-state
IF(MMLR(1).EQ.-1) dULRdR= dULRdR- 2.d0*T2
c-----------------------------------------------------------------------
ELSE
c***********************************************************************
c********* Aubert Frecon 3x3 case NCMM= 10 and ...
c********* Cm(1) = DELTAE
c********* Cm(2) = C3Sig
c********* Cm(3) = C3Pi1
c********* Cm(4) = C3Pi3
c********* Cm(5) = C6Sig
c********* Cm(6) = C6Pi1
c********* Cm(7) = C6Pi3
c********* Cm(8) = C8Sig
c********* Cm(9) = C8Pi1
c********* Cm(10)= C8Pi3
c***********************************************************************
c... Initialize interaction matrix to 0.d0
DO I= 1,3
DO J= 1,3
A(I,J)=0.0D0
DR(I,J)=0.d0
DO K= 1,NCMMax
DMx(K,I,J)=0.d0
ENDDO
ENDDO
ENDDO
c... Prepare interaction matrix A
DO I= 2,NCMM,3
RPOW(I)= RDIST**MMLR(I)
A(1,1)=A(1,1)-Dm(I)*(Cm(I)+Cm(I+1)+Cm(I+2))/(3.d0*RPOW(I))
A(1,2)=A(1,2)-Dm(I)*(Cm(I+2)+Cm(I+1)-2.d0*Cm(I))/(RPOW(I))
A(1,3)=A(1,3)-Dm(I)*(Cm(I+2)-Cm(I+1))/(RPOW(I))
A(2,2)= A(2,2)-Dm(I)*(Cm(I+2)+Cm(I+1)+4.d0*Cm(I))
1 /(6.d0*RPOW(I))
A(3,3)= A(3,3) - Dm(I)*(Cm(I+2)+Cm(I+1))/(2.d0*RPOW(I))
ENDDO
A(1,2) = A(1,2)/(3.d0*DSQRT(2.d0))
A(2,1) = A(1,2)
A(2,2) = A(2,2) + DELTAE
A(2,3) = A(1,3)/(2.d0*DSQRT(3.d0))
A(1,3) = A(1,3)/(DSQRT(6.d0))
A(3,1) = A(1,3)
A(3,2) = A(2,3)
A(3,3) = A(3,3) + DELTAE
c... Prepare radial derivative of interaction matrix (? is it needed ?)
DO I= 2,NCMM,3
DR(1,1)= DR(1,1) + Dm(I)*MMLR(I)*(Cm(I)+Cm(I+1)+Cm(I+2))
1 /(3.d0*RPOW(I)*RDIST)
2 -Dmp(I)*(Cm(I)+Cm(I+1)+Cm(I+2))/(3.d0*RPOW(I))
DR(1,2)= DR(1,2) + Dm(I)*MMLR(I)*(Cm(I+2)+Cm(I+1)-2.d0*
1 Cm(I))/(RPOW(I)*RDIST)
2 -Dmp(I)*(Cm(I+2)+Cm(I+1)-2.d0*Cm(I))/(RPOW(I))
DR(1,3)= DR(1,3) + Dm(I)*MMLR(I)*(Cm(I+2)-Cm(I+1))
1 /(RPOW(I)*RDIST)
2 -Dmp(I)*(Cm(I+2)-Cm(I+1))/(RPOW(I))
DR(2,2)= DR(2,2) + Dm(I)*MMLR(I)*(Cm(I+2)+Cm(I+1)+
1 4.d0*Cm(I))/(6.d0*RPOW(I)*RDIST)
2 -Dmp(I)*(Cm(I+2)+Cm(I+1)+4.d0*Cm(I))
3 /(6.d0*RPOW(I))
DR(3,3)= DR(3,3) + Dm(I)*MMLR(I)*(Cm(I+2)+Cm(I+1))
1 /(2.d0*RPOW(I)*RDIST)
2 -Dmp(I)*(Cm(I+2)+Cm(I+1))/(2.d0*RPOW(I))
ENDDO
DR(1,2) = DR(1,2)/(3.d0*DSQRT(2.d0))
DR(2,1) = DR(1,2)
DR(2,3) = DR(1,3)/(2.d0*DSQRT(3.d0))
DR(1,3) = DR(1,3)/(DSQRT(6.d0))
DR(3,1) = DR(1,3)
DR(3,2) = DR(2,3)
c... Partial derivatives of interaction matrix A w.r.t. Cm's
DO I= 2,NCMM,3
DMx(I,1,1)= -Dm(I)/(3.d0*RPOW(I)) !! d{1,1}/dCm{Sig}
DMx(I+1,1,1)= DMx(I,1,1) !! d{1,1}/dCm{1Pi}
DMx(I+2,1,1)= DMx(I,1,1) !! d{1,1}/dCm{3Pi}
DMx(I,1,2)= 2.d0*Dm(I)/(3.d0*DSQRT(2.d0)*RPOW(I))
DMx(I+1,1,2)= -DMx(I,1,2)/2.d0 !! d{1,2}/dCm{1Pi}
DMx(I+2,1,2)= DMx(I+1,1,2) !! d{1,2}/dCm{3Pi}
DMx(I,2,1)= DMx(I,1,2)
DMx(I+1,2,1)= DMx(I+1,1,2)
DMx(I+2,2,1)= DMx(I+2,1,2)
DMx(I,1,3)= 0.d0 !! no C3{sig} in {1,3}
DMx(I,3,1)= 0.d0 !! no C3{sig} in {3,1}
DMx(I+1,1,3)= Dm(I)/(DSQRT(6.d0)*RPOW(I))
DMx(I+2,1,3)= -DMx(I+1,1,3)
DMx(I+1,3,1)= DMx(I+1,1,3)
DMx(I+2,3,1)= DMx(I+2,1,3)
DMx(I,2,2)= -2.d0*Dm(I)/(3.d0*RPOW(I))
DMx(I+1,2,2)= DMx(I,2,2)/4.d0
DMx(I+2,2,2)= DMx(I+1,2,2)
DMx(I,2,3)= 0.d0
DMx(I,3,2)= 0.d0
DMx(I+1,2,3)= Dm(I)/(2.d0*DSQRT(3.d0)*RPOW(I))
DMx(I+2,2,3)= -DMx(I+1,2,3)
DMx(I+1,3,2)= DMx(I+1,2,3) !! by symmetry
DMx(I+2,3,2)= DMx(I+2,2,3) !! by symmetry
DMx(I,3,3)= 0.d0
DMx(I+1,3,3)= -Dm(I)/(2.d0*RPOW(I))
DMx(I+2,3,3)= DMx(I+1,3,3)
IF((RPOW(I).EQ.6).AND.(PSEL.EQ.2)) THEN
c!! For an MLR PEF, adjust derivatives for d/dC3{C6^{adj}} term
DO J= I-3,I-1 !! for {1,1} terms
DMx(J,1,1)= DMx(J,1,1)*(1.d0 + Dm(J)*Cm(J)/
1 (2.d0*De*RPOW(J)))
DMx(J,2,2)= DMx(J,2,2)*(1.d0 + Dm(J)*Cm(J)/
1 (2.d0*De*RPOW(J)))
DMx(J,1,2)= DMx(J,1,2)*(1.d0 + Dm(J)*Cm(J)/
1 (2.d0*De*RPOW(J)))
DMx(J,2,1)= DMx(J,2,1)
DMx(J,1,3)= DMx(J,1,3)*(1.d0 + Dm(J)*Cm(J)/
1 (2.d0*De*RPOW(J)))
DMx(J,3,1)= DMx(J,3,1)
DMx(J,3,3)= DMx(J,3,3)*(1.d0 + Dm(J)*Cm(J)/
1 (2.d0*De*RPOW(J)))
ENDDO
c!! and finally ... derivatives w.r.t. De
DDE1= ((Dm(I-3)*Cm(I-3)/2.d0*De)**2/RPOW(I)
DDE2= ((Dm(I-2)*Cm(I-2)/2.d0*De)**2/RPOW(I)
DDE3= ((Dm(I-1)*Cm(I-1)/2.d0*De)**2/RPOW(I)
DDe(1,1)= (DDe1 + DDe2 + DDe3)/3.d0
DDe(1,2)= (-2.d0*DDe1 + DDe2 + DDe3)/(3.d0*SQRT(2.d0))
DDe(2,1)= DDe(1,2)
DDe(1,3)= (-DDe2 + Dde3)/SQRT(6.d0)
DDe(3,1)= DDe(1,3)
DDe(2,2)= (4.d0*DDe1 + DDe2 + DDe3)/6.d0
DDe(2,3)= DDe(1,3)/SQRT(2.d0)
DDe(3,2)- DDe(2,3)
DDe(3,3)= (DDe2 + DDe3)/2.d0
ENDIF
ENDDO
c... Call subroutine to prepare and invert interaction matrix A
CALL DSYEVJ3(A,Q,W)
L=1
c... Now - identify the lowest eigenvalue of A and label it L
DO J=2,3
IF (W(J) .LT. W(L)) THEN
L=J
ENDIF
ENDDO
c... Identifiy the highest eigenvalue of A and label it H
H=1
DO J=2,3
IF(W(J).GT.W(H)) THEN
H=J
ENDIF
ENDDO
c... Identify the middle eigenvalue of A and label it M
M=1
DO J=2,3
IF((J.NE.L).AND.(J.NE.H)) M= J
ENDDO
c... Select which eigenvalue to use based on user input
IF(MMLR(1).EQ.-2) THEN
X = L
ELSEIF(MMLR(1).EQ.-3) THEN
X = M
ELSE
X = H
ENDIF
c... determine ULR and eigenvectors
ULR= -W(X)
IF(MMLR(1).EQ.-2) ULR= ULR+ Cm(11)*R3*R6 !! C9adj term
IF((MMLR(1).EQ.-3).OR.(MMLR(1).EQ.-4)) ULR = ULR + DELTAE
IF(MMLR(1).EQ.-3) ULR= ULR+ Cm(12)*R3*R6 !! C9adj term
IF(MMLR(1).EQ.-4) ULR= ULR+ Cm(13)*R3*R6 !! C9adj term
!!!!! print for testing !! print for testing !! print for testing
cc WRITE(25,600) RDIST ,ULR, W(1),W(2),W(3) !! print for testing
cc600 FORMAT(F12.4,1P,D16.7,2x,3D15.7) !! print for testing
!!!!! print for testing !! print for testing !! print for testing
DO I=1,3
EIGVEC(I,1) = Q(I,X)
ENDDO
cc loop over values of m to determine partial derivatives w.r.t. each Cm
DO I=2,NCMM
DMtemp(1:3,1:3) = DMx(I,1:3,1:3)
DEIGMtemp= -MATMUL(TRANSPOSE(EIGVEC),MATMUL(DMtemp,EIGVEC))
dULRdCm(I)= DEIGMtemp(1,1)
ENDDO
DEIGR = -MATMUL(TRANSPOSE(EIGVEC),MATMUL(DR,EIGVEC))
dULRdR= DEIGR(1,1) !! radial derivative w.r.t. r (I think!)
DEIGDe = -MATMUL(TRANSPOSE(EIGVEC),MATMUL(DDe,EIGVEC))
dULRdDe= DEIGDe(1,1) !! derivatives w.r.t. De ???
c------------------------------------------------------------------------
ENDIF
c------------------------------------------------------------------------
RETURN
CONTAINS
c=======================================================================
SUBROUTINE DSYEVJ3(A, Q, W)
c ----------------------------------------------------------------------
c** Subroutine to setup and diagonalize the matrix A and return
c eigenvalues W and eigenvector matrix Q
INTEGER N, I, X, Y, R
PARAMETER (N=3)
REAL*8 A(3,3), Q(3,3), W(3)
REAL*8 SD, SO, S, C, T, G, H, Z, THETA, THRESH
c Initialize Q to the identitity matrix
c --- This loop can be omitted if only the eigenvalues are desired ---
DO X = 1, N
Q(X,X) = 1.0D0
DO Y = 1, X-1
Q(X, Y) = 0.0D0
Q(Y, X) = 0.0D0
ENDDO
ENDDO
c Initialize W to diag(A)
DO X = 1, N
W(X) = A(X, X)
ENDDO
c Calculate SQR(tr(A))
SD = 0.0D0
DO X = 1, N
SD = SD + ABS(W(X))
ENDDO
SD = SD**2
c Main iteration loop
DO 40 I = 1, 50
c Test for convergence
SO = 0.0D0
DO X = 1, N
DO Y = X+1, N
SO = SO + ABS(A(X, Y))
ENDDO
ENDDO
IF(SO .EQ. 0.0D0) RETURN
IF(I .LT. 4) THEN
THRESH = 0.2D0 * SO / N**2
ELSE
THRESH = 0.0D0
END IF
c Do sweep
DO 60 X = 1, N
DO 61 Y = X+1, N
G = 100.0D0 * ( ABS(A(X, Y)) )
IF ( I .GT. 4 .AND. ABS(W(X)) + G .EQ. ABS(W(X))
$ .AND. ABS(W(Y)) + G .EQ. ABS(W(Y))) THEN
A(X, Y) = 0.0D0
ELSE IF (ABS(A(X, Y)) .GT. THRESH) THEN
c Calculate Jacobi transformation
H = W(Y) - W(X)
IF ( ABS(H) + G .EQ. ABS(H) ) THEN
T = A(X, Y) / H
ELSE
THETA = 0.5D0 * H / A(X, Y)
IF (THETA .LT. 0.0D0) THEN
T= -1.0D0/(SQRT(1.0D0 + THETA**2)-THETA)
ELSE
T= 1.0D0/(SQRT(1.0D0 + THETA**2) + THETA)
END IF
END IF
C = 1.0D0 / SQRT( 1.0D0 + T**2 )
S = T * C
Z = T * A(X, Y)
c Apply Jacobi transformation
A(X, Y) = 0.0D0
W(X) = W(X) - Z
W(Y) = W(Y) + Z
DO R = 1, X-1
T = A(R, X)
A(R, X) = C * T - S * A(R, Y)
A(R, Y) = S * T + C * A(R, Y)
ENDDO
DO R = X+1, Y-1
T = A(X, R)
A(X, R) = C * T - S * A(R, Y)
A(R, Y) = S * T + C * A(R, Y)
ENDDO
DO R = Y+1, N
T = A(X, R)
A(X, R) = C * T - S * A(Y, R)
A(Y, R) = S * T + C * A(Y, R)
ENDDO
c Update eigenvectors
c --- This loop can be omitted if only the eigenvalues are desired ---
DO R = 1, N
T = Q(R, X)
Q(R, X) = C * T - S * Q(R, Y)
Q(R, Y) = S * T + C * Q(R, Y)
ENDDO
END IF
61 CONTINUE
60 CONTINUE
40 CONTINUE
WRITE(6,'("DSYEVJ3: No convergence.")')
END SUBROUTINE DSYEVJ3
END SUBROUTINE AFdiag
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