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SUBROUTINE FFHPOL (HEAT0,ATPOL)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
CHARACTER*1 AXIS(3)
LOGICAL DEBUG
INCLUDE 'SIZES'
C***********************************************************************
C SUBROUTINE FOR THE FINITE FIELD CALCULATION OF ELECTRIC RESPONSE
C PROPERTIES (DIPOLE MOMENT, POLARIZABILITY, AND 1ST AND 2ND
C HYPERPOLARIZABILITY.
C
C HENRY A. KURTZ, DEPARTMENT OF CHEMISTRY
C MEMPHIS STATE UNIVERSITY
C MEMPHIS, TN 38152
C
C***********************************************************************
COMMON /CORE / CORE(107)
COMMON /GEOM / GEO(3,NUMATM), XCOORD(3,NUMATM)
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM),NORS,NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /COORD / COORD(3,NUMATM)
COMMON /KEYWRD/ KEYWRD
COMMON /FIELD / EFIELD(3)
COMMON /EULER / TVEC(3,3),IDTVEC
CHARACTER*241 KEYWRD
C
C
C DIPE4 AND DIPDP HOLD THE CALCULATED DIPOLE MOMENTS
C
C APOLE4 AND APOLDP HOLD THE POLARIZABILITY TENSOR AS
C A PACKED ARRAY XX,XY,YY,XZ,YZ,ZZ
C
C BETAE4 AND BETAEP HOLD THE FIRST HYPERPOLARIZABILITY
C 1. XXX
C 2. YYY 6. YXX
C 3. ZZZ 7. YZZ
C 4. XYY 8. ZXX
C 5. XZZ 9. ZYY
C
DIMENSION HEATE(3,2),
1 DIPE4(3),APOLE4(6),BETAE4(9),GAMME4(6),
2 DIPDP(3),APOLDP(6),BETADP(9),GAMMDP(6),
3 DIP1P(3),DIP1M(3),DIP2P(3),DIP2M(3)
DIMENSION IPTBD(6), GRAD(MAXPAR)
DATA IPTBD /5,7,4,9,6,8/
C Energy: a.u. to kcal/mole
AUTOKC = 23.061D+00*27.2107D+00
C Dipole: a.u. to debye
AUTODB = 2.541563D+00
C Electric Field: a.u. to volt/meter
AUTOVM = 51.4257D+00
NBDIP = 1
NBCNT = 4
NGCNT = 4
C
DATA AXIS/'X','Y','Z'/
DEBUG = (INDEX(KEYWRD,'DEBUG').NE.0)
C
C FIELD STRENGTH IN A.U.
C
EFVAL=0.001D0
IDIP=1
C modification for variable field strength
IF(INDEX(KEYWRD,'POLAR=').NE.0)
1EFVAL=READA(KEYWRD,INDEX(KEYWRD,'POLAR='))
WRITE (6,10) EFVAL
10 FORMAT (//' APPLIED ELECTRIC FIELD MAGNITUDE: ',F15.5)
SFE = 1.D00/EFVAL
WRITE (6,20) 6.74834D0*ATPOL
20 FORMAT (//' ATOMIC CONTRIBUTION TO THE POLARIZABILITY: ',F15.6,/,
1 ' (IT IS ONLY APPLIED TO THE E4 RESULT)')
C.......................................................................
C CALCULATE THE POLARIZABILITY AND HYPERPOLARIZABILITIES ALONG
C THE THREE PRINCIPLE AXES. (THESE AXES DEPEND ON YOUR ARBITRARY
C ORIENTATION AND MAY NOT BE THE TRUE PRINCIPLE AXES.)
C.......................................................................
DO 150 ID = 1,3
IF (DEBUG) THEN
WRITE (6,30) AXIS(ID)
30 FORMAT (//,' ****** FIELD IN ',A1,' DIRECTION *****',/)
ENDIF
C
C ZERO THE FIELD
C
DO 40 I = 1,3
EFIELD(I) = 0.0D00
40 CONTINUE
HNUC = 0.0D00
DO 50 I = 1,NUMAT
HNUC = HNUC + EFVAL*GEO(ID,I)*CORE(NAT(I))*AUTOVM
50 CONTINUE
HNUC = HNUC*23.061D00
C +E(ID)
EFIELD(ID) = EFVAL
CALL COMPFG(GEO,.TRUE.,HEAT1P,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1P)
DIIP = DIP1P(ID)
C -E(ID)
EFIELD(ID) = -EFVAL
CALL COMPFG(GEO,.TRUE.,HEAT1M,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1M)
DIIM = DIP1M(ID)
C +2E(ID)
EFIELD(ID) = 2.0D00*EFVAL
CALL COMPFG(GEO,.TRUE.,HEAT2P,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP2P)
C -2E(ID)
EFIELD(ID) = -2.0D00*EFVAL
CALL COMPFG(GEO,.TRUE.,HEAT2M,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP2M)
C
C CORRECT FOR ELECTRIC FIELD - NUCLEAR INTERACTIONS
C
HEAT1P = HEAT1P + HNUC
HEATE(ID,1) = HEAT1P
HEAT1M = HEAT1M - HNUC
HEATE(ID,2) = HEAT1M
HEAT2P = HEAT2P + HNUC*2.D00
HEAT2M = HEAT2M - HNUC*2.D00
C
IF (DEBUG) THEN
WRITE (6,60)
60 FORMAT (' FIELDS OF: ',5X,'F',21X,'2F')
WRITE (6,70) HEAT1P,HEAT2P,HEAT1M,HEAT2M,
1 DIP1P(ID),DIP2P(ID),DIP1M(ID),DIP2M(ID)
70 FORMAT (' ENERGY:'/,
1 ' + ',2(F20.10,3X),/,' - ',2(F20.10,3X),/,
2 ' DIPOLE:'/,
3 ' + ',2(F20.10,3X),/,' - ',2(F20.10,3X))
ENDIF
C
C DIPOLE
C
ETERM = (1.0D00/12.D00)*(HEAT2P - HEAT2M)
1 - (2.0D00/3.0D00)*(HEAT1P - HEAT1M)
DIPE4(ID) = ETERM*SFE/AUTOKC
C
C ALPHA
C
IVL = (ID*(ID+1))/2
ETERM = 2.5D00*HEAT0 - (4.D00/3.D00)*(HEAT1P + HEAT1M)
1 + (1.D00/12.0D00)*(HEAT2P + HEAT2M)
APOLE4(IVL) = ETERM*SFE*SFE/AUTOKC + ATPOL*6.74834D0
C
C BETA
C
ETERM = (HEAT1P - HEAT1M) - 0.5D00*(HEAT2P - HEAT2M)
BETAE4(ID) = ETERM*SFE*SFE*SFE/AUTOKC
C
C GAMMA
C
ETERM = 4.0D00*(HEAT1P + HEAT1M) - (HEAT2P + HEAT2M)
1 - 6.0D00*HEAT0
GAMME4(ID) = ETERM*SFE*SFE*SFE*SFE/AUTOKC
C
C DIPOLE CALCULATIONS
C
DMU = (2.0D00/3.0D00)*(DIP1P(ID) + DIP1M(ID))
1 - (1.D00/6.0D00)*(DIP2P(ID) + DIP2M(ID))
DIPDP(ID) = DMU/AUTODB
AE = (2.0D00/3.0D00)*(DIP1P(ID) - DIP1M(ID))
1 - (1.0D00/12.D00)*(DIP2P(ID) - DIP2M(ID))
APOLDP(IVL) = AE*SFE/AUTODB
BE = (1.D00/3.0D00)*(DIP2P(ID) + DIP2M(ID)
1 - DIP1P(ID) - DIP1M(ID))
BETADP(ID) = BE*SFE*SFE/AUTODB
GE = 0.5D00*(DIP2P(ID) - DIP2M(ID))
1 - (DIP1P(ID) - DIP1M(ID))
GAMMDP(ID) = GE*SFE*SFE*SFE/AUTODB
DO 80 KD = 1,3
IF (KD.LT.ID) THEN
KVL = (ID*(ID-1))/2 + KD
AKI = (2.0D00/3.0D00)*(DIP1P(KD) - DIP1M(KD))
1 - (1.0D00/12.0D00)*(DIP2P(KD) - DIP2M(KD))
APOLDP(KVL) = AKI*SFE/AUTODB
ENDIF
IF (KD.NE.ID) THEN
BKII = (1.0D00/3.0D00)*(DIP2P(KD) + DIP2M(KD)
1 - DIP1P(KD) - DIP1M(KD))
NBD = IPTBD(NBDIP)
BETADP(NBD) = BKII*SFE*SFE/AUTODB
NBDIP = NBDIP + 1
ENDIF
80 CONTINUE
C.......................................................................
C
C NOW CALCULATE THE OFF AXIS RESULTS.
C
C.......................................................................
IDM1 = ID - 1
DO 140 JD = 1,IDM1
HNUCJ = 0.0D00
DO 90 I = 1,NUMAT
HNUCJ = HNUCJ + EFVAL*GEO(JD,I)*CORE(NAT(I))*51.4257D0
90 CONTINUE
HNUCJ = HNUCJ*23.061D0
DO 100 I = 1,3
EFIELD(I) = 0.0D00
100 CONTINUE
C
C DIAGONAL FIELDS WITH COMPONENTS EQUAL TO EFVAL
C
EFIELD(ID) = EFVAL
EFIELD(JD) = EFVAL
CALL COMPFG(GEO,.TRUE.,HPP,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1P)
DPP = DIP1P(ID)
EFIELD(JD) = -EFVAL
CALL COMPFG(GEO,.TRUE.,HPM,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1P)
DPM = DIP1P(ID)
EFIELD(ID) = -EFVAL
CALL COMPFG(GEO,.TRUE.,HMM,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1P)
DMM = DIP1P(ID)
EFIELD(JD) = EFVAL
CALL COMPFG(GEO,.TRUE.,HMP,.TRUE.,GRAD,.FALSE.)
CALL DIPIND (DIP1P)
DMP = DIP1P(ID)
HPP = HPP + HNUC + HNUCJ
HPM = HPM + HNUC - HNUCJ
HMM = HMM - HNUC - HNUCJ
HMP = HMP - HNUC + HNUCJ
IF (DEBUG) THEN
WRITE (6,110)
110 FORMAT (/,' ',12X,'+,+',15X,'+,-',15X,'-,+',15X,'-,-')
WRITE (6,120) HPP,HPM,HMP,HMM
120 FORMAT (' E ',4F15.6)
ENDIF
C
C DIAGONAL FIELDS WITH COMPONENTS EQUAL TO 2*EFVAL
C
EFIELD(ID) = EFVAL*2.D00
EFIELD(JD) = EFVAL*2.D00
CALL COMPFG(GEO,.TRUE.,H2PP,.TRUE.,GRAD,.FALSE.)
EFIELD(JD) = -EFVAL*2.D00
CALL COMPFG(GEO,.TRUE.,H2PM,.TRUE.,GRAD,.FALSE.)
EFIELD(ID) = -EFVAL*2.D00
CALL COMPFG(GEO,.TRUE.,H2MM,.TRUE.,GRAD,.FALSE.)
EFIELD(JD) = EFVAL*2.D00
CALL COMPFG(GEO,.TRUE.,H2MP,.TRUE.,GRAD,.FALSE.)
H2PP = H2PP + 2.0D00*(HNUC + HNUCJ)
H2PM = H2PM + 2.0D00*(HNUC - HNUCJ)
H2MM = H2MM - 2.0D00*(HNUC + HNUCJ)
H2MP = H2MP - 2.0D00*(HNUC - HNUCJ)
IF (DEBUG) THEN
WRITE (6,130) H2PP,H2PM,H2MP,H2MM
130 FORMAT (' 2E ',4F15.6)
ENDIF
C
ATERM = (1.0D00/48.0D00)*(H2PP - H2PM - H2MP + H2MM)
1 - (1.0D00/3.0D00)*(HPP - HPM - HMP + HMM)
AIJ = ATERM*SFE*SFE/AUTOKC
IVL = (ID*(ID-1))/2 + JD
APOLE4(IVL) = AIJ
BTERM = 0.5D00*(HMM - HPP + HPM - HMP)
1 + HEATE(JD,1) - HEATE(JD,2)
BJII = BTERM*SFE*SFE*SFE/AUTOKC
BETAE4(NBCNT) = BJII
NBCNT = NBCNT + 1
BTERM = 0.5D00*(HMM - HPP + HMP - HPM)
1 + HEATE(ID,1) - HEATE(ID,2)
BIJJ = BTERM*SFE*SFE*SFE/AUTOKC
BETAE4(NBCNT) = BIJJ
NBCNT = NBCNT + 1
C
GTERM = -(HPP + HMM + HPM + HMP) - 4.0D00*HEAT0
1 + 2.0D00*(HEATE(ID,1) + HEATE(ID,2))
2 + 2.0D00*(HEATE(JD,1) + HEATE(JD,2))
GIIJJ = GTERM*SFE*SFE*SFE*SFE/AUTOKC
GAMME4(NGCNT) = GIIJJ
GDIP = 0.5D00*(DPP - DMP + DPM - DMM) - (DIIP - DIIM)
GAMMDP(NGCNT) = GDIP*SFE*SFE*SFE/AUTODB
NGCNT = NGCNT + 1
140 CONTINUE
C
150 CONTINUE
C-----------------------------------------------------------------------
C SUMMARIZE THE RESULTS
C-----------------------------------------------------------------------
WRITE (6,160)
160 FORMAT (//,' ',30('*'),' DIPOLE ',30('*'),//)
DIPE4T = SQRT(DIPE4(1)*DIPE4(1) + DIPE4(2)*DIPE4(2)
1 + DIPE4(3)*DIPE4(3))
DIPE4D = DIPE4T*AUTODB
DIPDPT = SQRT(DIPDP(1)*DIPDP(1) + DIPDP(2)*DIPDP(2)
1 + DIPDP(3)*DIPDP(3))
DIPDPD = DIPDPT*AUTODB
WRITE (6,170)
170 FORMAT (21X,'E4',13X,'DIP',/)
WRITE (6,180) 'X',DIPE4(1),DIPDP(1)
WRITE (6,180) 'Y',DIPE4(2),DIPDP(2)
WRITE (6,180) 'Z',DIPE4(3),DIPDP(3)
180 FORMAT (5X,A1,7X,2F15.6)
WRITE (6,190) DIPE4T,DIPDPT,
1 DIPE4D,DIPDPD
190 FORMAT (//' MAGNITUDE: ',2F15.6,' (A.U.)',/,
1 ' ',12X,2F15.6,' (DEBYE)')
C
C FIND EIGENVALUES AND EIGENVECTORS OF POLARIZATION MATRIX.
C
WRITE (6,200)
200 FORMAT (//,' ',22('*'),' POLARIZABILITY (ALPHA)',21('*'),//)
AVGPE4 = (APOLE4(1)+APOLE4(3)+APOLE4(6))/3.0D00
AVGA3 = AVGPE4*0.14818D00
AVGESU = AVGPE4*0.296352D-24
AVGPDP = (APOLDP(1)+APOLDP(3)+APOLDP(6))/3.0D00
AVGA3D = AVGPDP*0.14818D00
AVGESD = AVGPDP*0.296352D-24
WRITE (6,210)
210 FORMAT (' COMPONENT',12X,'E4',13X,'DIP',/)
WRITE (6,220) 'XX',APOLE4(1),APOLDP(1),
1 'YY',APOLE4(3),APOLDP(3),
2 'ZZ',APOLE4(6),APOLDP(6),
3 'XY',APOLE4(2),APOLDP(2),
4 'XZ',APOLE4(4),APOLDP(4),
5 'YZ',APOLE4(5),APOLDP(5)
220 FORMAT (' ',5X,A4,5X,2F15.6)
WRITE (6,230) AVGPE4,AVGPDP,AVGA3,AVGA3D,AVGESU,AVGESD
230 FORMAT (//,' AVERAGE POLARIZABILITY:',8X,'E4',13X,'DIP',/,
1 ' ',24X,2F15.6,' A.U.',/,
2 ' ',24X,2F15.6,' ANG.**3',/,
3 ' ',24X,2(1PD15.6),' ESU')
C
C CALCULATE "EXPERIMENTAL" HYPERPOLARIZABILITIES
C
C 8.65710D-33 is a.u. to e.s.u. conversion
WRITE (6,240)
240 FORMAT (//,' ',30('*'),' SECOND-ORDER (BETA)',25('*'),//)
BX4 = 0.6D00*(BETAE4(1) + BETAE4(4) + BETAE4(6))
BY4 = 0.6D00*(BETAE4(2) + BETAE4(5) + BETAE4(8))
BZ4 = 0.6D00*(BETAE4(3) + BETAE4(7) + BETAE4(9))
B4MU = (BX4*DIPE4(1) + BY4*DIPE4(2) + BZ4*DIPE4(3))/DIPE4T
B4ESU = B4MU*8.65710D-03
BXD = 0.6D00*(BETADP(1) + BETADP(4) + BETADP(6))
BYD = 0.6D00*(BETADP(2) + BETADP(5) + BETADP(8))
BZD = 0.6D00*(BETADP(3) + BETADP(7) + BETADP(9))
BDMU = (BXD*DIPDP(1) + BYD*DIPDP(2) + BZD*DIPDP(3))/DIPDPT
BDESU = BDMU*8.65710D-03
C
WRITE(6,'(29X,A2,25X,A6)')'1X','(1/2)X'
WRITE (6,250)
250 FORMAT (' COMPONENT',2(12X,'E4',10X,'DIP',2X),/)
WRITE (6,260) 'XXX',BETAE4(1),BETADP(1),BETAE4(1)/2,BETADP(1)/2
WRITE (6,260) 'XYY',BETAE4(4),BETADP(4),BETAE4(4)/2,BETADP(4)/2
WRITE (6,260) 'XZZ',BETAE4(6),BETADP(6),BETAE4(6)/2,BETADP(6)/2
WRITE (6,260) 'YYY',BETAE4(2),BETADP(2),BETAE4(2)/2,BETADP(2)/2
WRITE (6,260) 'YXX',BETAE4(5),BETADP(5),BETAE4(5)/2,BETADP(5)/2
WRITE (6,260) 'YZZ',BETAE4(8),BETADP(8),BETAE4(8)/2,BETADP(8)/2
WRITE (6,260) 'ZZZ',BETAE4(3),BETADP(3),BETAE4(3)/2,BETADP(3)/2
WRITE (6,260) 'ZXX',BETAE4(7),BETADP(7),BETAE4(7)/2,BETADP(7)/2
WRITE (6,260) 'ZYY',BETAE4(9),BETADP(9),BETAE4(9)/2,BETADP(9)/2
260 FORMAT (' ',5X,A4,2(5X,2F12.3))
WRITE (6,270)
270 FORMAT (//,' VECTOR COMPONENTS GIVEN BY:',/,
1 ' BI = (2/5)*(BI11+BI22+BI33)'/)
WRITE (6,280) 'BX',BX4,BXD,BX4/2,BXD/2
WRITE (6,280) 'BY',BY4,BYD,BY4/2,BYD/2
WRITE (6,280) 'BZ',BZ4,BZD,BZ4/2,BZD/2
280 FORMAT (' ',6X,A2,2(6X,2F12.3))
WRITE (6,290)
290 FORMAT (//' VALUE OF BETA ALONG THE DIPOLE MOMENT:'/)
WRITE (6,300) B4MU,BDMU,B4MU/2,BDMU/2,B4ESU,BDESU,B4ESU/2,BDESU/2
300 FORMAT (' ',4X,'B(AU)',2(5X,2F12.3,2X),/,
1 ' ',4X,'B(ESU)',4X,2F12.3,7X,2F12.3,' (X10-30)')
C
WRITE (6,310)
310 FORMAT (//' ',24('*'),' THIRD-ORDER (GAMMA)',24('*'),//)
GAMVAL = (GAMME4(1) + GAMME4(2) + GAMME4(3))
GAMVAL = GAMVAL + 2.0D00*(GAMME4(4) + GAMME4(5) + GAMME4(6))
GAMVAL = GAMVAL/5.0D00
C 5.05116D-40 is the a.u. to e.s.u. conversion
GAMESU = GAMVAL*5.05116D-04
GAMDIP = (GAMMDP(1) + GAMMDP(2) + GAMMDP(3))
GAMDIP = GAMDIP + 2.0D00*(GAMMDP(4) + GAMMDP(5) + GAMMDP(6))
GAMDIP = GAMDIP/5.0D00
GAMDES = GAMDIP*5.05116D-04
WRITE(6,'(23X,A2,25X,A6)')'1X','(1/6)X'
WRITE (6,320)
320 FORMAT (' ',17X,'E4',8X,'DIP',16X,'E4',8X,'DIP',/)
WRITE (6,330) 'XXXX',GAMME4(1),GAMMDP(1),GAMME4(1)/6,GAMMDP(1)/6
WRITE (6,330) 'YYYY',GAMME4(2),GAMMDP(2),GAMME4(2)/6,GAMMDP(2)/6
WRITE (6,330) 'ZZZZ',GAMME4(3),GAMMDP(3),GAMME4(3)/6,GAMMDP(3)/6
WRITE (6,330) 'XXYY',GAMME4(4),GAMMDP(4),GAMME4(4)/6,GAMMDP(4)/6
WRITE (6,330) 'XXZZ',GAMME4(5),GAMMDP(5),GAMME4(5)/6,GAMMDP(5)/6
WRITE (6,330) 'YYZZ',GAMME4(6),GAMMDP(6),GAMME4(6)/6,GAMMDP(6)/6
330 FORMAT (5X,A4,2F12.3,5X,2F12.3)
WRITE (6,340)
340 FORMAT (//' AVERAGE GAMMA GIVEN BY:',/,
1 ' (1/5)*[GXXX + GYYY + GZZZ + 2.0*(GXXYY + GXXZZ + GYYZZ)]')
WRITE(6,'(/,20X,A2,22X,A6)')'1X','(1/6)X'
WRITE (6,350) GAMVAL,GAMDIP,GAMVAL/6,GAMDIP/6,
1 GAMESU,GAMDES,GAMESU/6,GAMDES/6
350 FORMAT (/' <GAMMA> ',1PD12.5,1PD12.5,5X,1PD12.5,1PD12.5,' A.U.'/,
1 ' ',8X,1PD12.5,1PD12.5,5X,1PD12.5,1PD12.5,' ESU (X10-36)')
C
RETURN
END
|
