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egrad_geh4oh.f
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egrad_geh4oh.f
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! CARACAL - Ring polymer molecular dynamics and rate constant calculations
! on black-box generated potential energy surfaces
!
! Copyright (c) 2023 by Julien Steffen ([email protected])
! Stefan Grimme ([email protected]) (QMDFF code)
!
! Permission is hereby granted, free of charge, to any person obtaining a
! copy of this software and associated documentation files (the "Software"),
! to deal in the Software without restriction, including without limitation
! the rights to use, copy, modify, merge, publish, distribute, sublicense,
! and/or sell copies of the Software, and to permit persons to whom the
! Software is furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in
! all copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
! THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
! FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
! DEALINGS IN THE SOFTWARE.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Potential energy routine taken from the POTLIB library:
! R. J. Duchovic, Y. L. Volobuev, G. C. Lynch, A. W. Jasper, D. G. Truhlar, T. C. Allison,
! A. F. Wagner, B. C. Garrett, J. Espinosa-García, and J. C. Corchado, POTLIB,
! https://comp.chem.umn.edu/potlib.
c
c driver routine
c
subroutine egrad_geh4oh(q,Natoms,Nbeads,V,dVdq,info)
integer, intent(in) :: Natoms
integer, intent(in) :: Nbeads
double precision, intent(in) :: q(3,Natoms,Nbeads)
double precision, intent(out) :: V(Nbeads)
double precision, intent(out) :: dVdq(3,Natoms,Nbeads)
double precision :: R(21), DEGSDR(21),ENGYGS
integer::i,j
c
c convert input structure
c
do i=1,natoms
do j=1,3
R((i-1)*3+j)=q(j,i,1)
end do
end do
c write(*,*) R
call pot_geh4oh(R,ENGYGS,DEGSDR)
c
c convert output gradient
c
V(1)=ENGYGS
do i=1,natoms
do j=1,3
dVdq(j,i,1)=DEGSDR((i-1)*3+j)
end do
end do
c stop "Jjgfdf"
return
end subroutine
c**************************************************************************
C System: GeH4OH
C Number of electronic surfaces: 1
C Number of derivatives: 0
C Number of bodies: 7
C Interface: potlib2001
C Common name: GeH4OH
C Notes:
C
C References: J. Espinosa-Garcia, C. Rangel and J.C. Corchado
C Phys. Chem. Chem. Phys. 18, 16941 (2016)
C
C Calling conventions: POLYRATE interface
SUBROUTINE pot_geh4oh(R_out,ENGYGS_out,DEGSDR_out)
C
C This potential is written such that:
C
C X(1) - X(3) : X, Y, Z for H1
C X(4) - X(6) : X, Y, Z for Ge
C X(7) - X(9) : X, Y, Z for H3
C X(10) - X(12) : X, Y, Z for H4
C X(13) - X(15) : X, Y, Z for H2
C X(16) - X(18) : X, Y, Z for O
C X(19) - X(21) : X, Y, Z for H(O)
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
real(kind=8)::R_out(21),ENGYGS_out,DEGSDR_out(21)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
C DIMENSION COORD(N3TM),DX(N3TM)
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
CALL CARTOU_geh4oh
CALL CARTTOR_geh4oh
C
C Changing units from angstrom to bohr and initialize
C
R(1:21)=R_OUT
DO 10 I = 1, 21
q(I) = R(I)*0.52918d0
pdot(I)=0.D0
10 CONTINUE
c
c calculate relative coordinates and bond lengths
c
en=0.0d0
call coorden_geh4oh
c
c calculate switching functions
c
call switchf_geh4oh
c
c calculate reference angles and their derivatives
c
call refangles_geh4oh
c
c calculate stretching potential
c
call stretch_geh4oh(vstr)
c
c calculate out of plane bending potential
c
call opbend_geh4oh(vop)
c
c calculate in plane bending potential
c
call ipbend_geh4oh(vip)
c
c total potential energy is vstr+vop+vip
c
en=vstr+vop+vip
c
c 0.03812 conversion factor from 10(5) j/mol to hartrees
c
en = en*0.03812D0
ENGYGS = en
c
CALL EUNITZERO_geh4oh
IF(NDER.NE.0) THEN
c
c 0.0201723 conversion factor from 10(5)j/mol/A to hartrees/bohr
c
do i=1,21
DEGSDR(i)=pdot(i)*0.0201723d0
enddo
CALL RTOCART_geh4oh
CALL DEDCOU_geh4oh
ENDIF
ENGYGS_OUT=ENGYGS
DEGSDR_OUT=DEGSDR(1:21)
C
return
end
c
c******************************************************
c
subroutine coorden_geh4oh
c
c calculates relative coordinates and bond lengths
c
implicit double precision (a-h,o-z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM_geh4oh/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
c calculate relative coordinates
c
do ind=1,3
tcb(ind)=q(nc(ind))-q(nhb(ind))
tno(ind)=q(no(ind))-q(nhb(ind))
do i=1,4
tch(i,ind)=q(nc(ind))-q(nh(i,ind))
tbh(i,ind)=q(nhb(ind))-q(nh(i,ind))
enddo
enddo
c
c calculate bond lengths
c
rcb=sqrt(tcb(1)*tcb(1)+tcb(2)*tcb(2)+tcb(3)*tcb(3))
rno=sqrt(tno(1)*tno(1)+tno(2)*tno(2)+tno(3)*tno(3))
do i=1,4
rch(i)=sqrt(tch(i,1)*tch(i,1)+tch(i,2)*tch(i,2)+
* tch(i,3)*tch(i,3))
rbh(i)=sqrt(tbh(i,1)*tbh(i,1)+tbh(i,2)*tbh(i,2)+
* tbh(i,3)*tbh(i,3))
enddo
return
end
c
c******************************************************
c
c
subroutine refangles_geh4oh
c
c subroutine calculates reference angles for the "in-plane" potential
c
implicit double precision (a-h,o-z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM_geh4oh/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
tau=acos(-1.0d0/3.0d0)
C pi=4.0d0*atan(1.0d0)
halfpi=0.5d0*pi
twopi=2.0d0*pi
taugeh=0.678d0*pi
c
c JEG, junio 2015, GeH3=piramidal, como en GeH4+H, 1999
c set diagonal elements to zero
c
do i=1,4
theta0(i,i)=0.0d0
do k=1,4
dtheta0(i,i,k)=0.0d0
enddo
enddo
c
c calculate reference angles
c
theta0(1,2)=tau+(tau-taugeh)*(sphi(1)*sphi(2)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(3)*stheta(4)-1.0d0)
theta0(1,3)=tau+(tau-taugeh)*(sphi(1)*sphi(3)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(2)*stheta(4)-1.0d0)
theta0(1,4)=tau+(tau-taugeh)*(sphi(1)*sphi(4)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(2)*stheta(3)-1.0d0)
theta0(2,3)=tau+(tau-taugeh)*(sphi(2)*sphi(3)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(1)*stheta(4)-1.0d0)
theta0(2,4)=tau+(tau-taugeh)*(sphi(2)*sphi(4)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(1)*stheta(3)-1.0d0)
theta0(3,4)=tau+(tau-taugeh)*(sphi(3)*sphi(4)-1.0d0)
* +(tau-twopi/3.0d0)*(stheta(1)*stheta(2)-1.0d0)
c
c calculate the derivatives of theta0(i,j) in terms of rch(k)
c quantity calulated is dtheta0(i,j,k)
c
c derivatives wrt rch(1)
c
dtheta0(1,2,1)=(tau-taugeh)*dsphi(1)*sphi(2)
dtheta0(1,3,1)=(tau-taugeh)*dsphi(1)*sphi(3)
dtheta0(1,4,1)=(tau-taugeh)*dsphi(1)*sphi(4)
dtheta0(2,3,1)=(tau-twopi/3.0d0)*dstheta(1)*stheta(4)
dtheta0(2,4,1)=(tau-twopi/3.0d0)*dstheta(1)*stheta(3)
dtheta0(3,4,1)=(tau-twopi/3.0d0)*dstheta(1)*stheta(2)
c
c derivatives wrt rch(2)
c
dtheta0(1,2,2)=(tau-taugeh)*sphi(1)*dsphi(2)
dtheta0(1,3,2)=(tau-twopi/3.0d0)*dstheta(2)*stheta(4)
dtheta0(1,4,2)=(tau-twopi/3.0d0)*dstheta(2)*stheta(3)
dtheta0(2,3,2)=(tau-taugeh)*dsphi(2)*sphi(3)
dtheta0(2,4,2)=(tau-taugeh)*dsphi(2)*sphi(4)
dtheta0(3,4,2)=(tau-twopi/3.0d0)*stheta(1)*dstheta(2)
c
c derivatives wrt rch(3)
c
dtheta0(1,2,3)=(tau-twopi/3.0d0)*dstheta(3)*stheta(4)
dtheta0(1,3,3)=(tau-taugeh)*sphi(1)*dsphi(3)
dtheta0(1,4,3)=(tau-twopi/3.0d0)*stheta(2)*dstheta(3)
dtheta0(2,3,3)=(tau-taugeh)*sphi(2)*dsphi(3)
dtheta0(2,4,3)=(tau-twopi/3.0d0)*stheta(1)*dstheta(3)
dtheta0(3,4,3)=(tau-taugeh)*dsphi(3)*sphi(4)
c
c derivatives wrt rch(4)
c
dtheta0(1,2,4)=(tau-twopi/3.0d0)*stheta(3)*dstheta(4)
dtheta0(1,3,4)=(tau-twopi/3.0d0)*stheta(2)*dstheta(4)
dtheta0(1,4,4)=(tau-taugeh)*sphi(1)*dsphi(4)
dtheta0(2,3,4)=(tau-twopi/3.0d0)*stheta(1)*dstheta(4)
dtheta0(2,4,4)=(tau-taugeh)*sphi(2)*dsphi(4)
dtheta0(3,4,4)=(tau-taugeh)*sphi(3)*dsphi(4)
c
c fill in the other half of the matrix
c
do i=1,3
do j=i+1,4
theta0(j,i)=theta0(i,j)
do k=1,4
dtheta0(j,i,k)=dtheta0(i,j,k)
enddo
enddo
enddo
return
end
c
c******************************************************
c
c
subroutine stretch_geh4oh(vstr)
c
c subroutine to calculate leps-type stretching potential and its
c derivatives
c
implicit double precision (a-h,o-z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM_geh4oh/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
dimension vqch(4),vjch(4),vqbh(4),vjbh(4),vq(4),vj(4),
* achdc(3),achdh(4,3)
c
c calculate avergage bond length for the methane moiety
c
rav=(rch(1)+rch(2)+rch(3)+rch(4))/4.0d0
c
c initialise:
c
vstr=0.0d0
c
c calculate d3cb and dd3cb
c
texp = exp(-(4.d0*(rav-rcbsp)/b3cb)**4.d0)
d3cb = (d3cbi-a3cb) + a3cb * texp
dd3cb = -4.d0*a3cb*texp*(rav-rcbsp)**3.d0*(4.d0/b3cb)**4.d0
c
c ach:
c
c in double precision tanh(19.0d0)=1.0d0 and we put the if statement
c in to avoid overflow/underflow errors
c
arga=c1ch*(rav-r0ch)
if(arga.lt.19.0d0)then
ach=a1ch+b1ch*(tanh(arga)+1.0d0)*0.5d0
dumach=b1ch*c1ch/(2.0d0*cosh(arga)**2)
else
ach=a1ch+b1ch
dumach=0.0d0
endif
c
c calculate singlet: e1, triplet: e3 energies and vq and vj
c terms for each bond
c
e1=d1cb*(exp(-2.0d0*acb*(rcb-r0cb))-2.0d0*exp(-acb*(rcb-r0cb)))
e3=d3cb*(exp(-2.0d0*acb*(rcb-r0cb))+2.0d0*exp(-acb*(rcb-r0cb)))
vqcb=(e1+e3)*0.5d0
vjcb=(e1-e3)*0.5d0
c
c O-H term (simple morse term)
c
dt=(rno-r0hh)
expterm=exp(-ahh*dt)
vno=d1hh*(1.d0-expterm)**2.d0
c
do i=1,4
e1=d1ch*(exp(-2.0d0*ach*(rch(i)-r0ch))
* -2.0d0*exp(-ach*(rch(i)-r0ch)))
e3=d3ch*(exp(-2.0d0*ach*(rch(i)-r0ch))
* +2.0d0*exp(-ach*(rch(i)-r0ch)))
vqch(i)=(e1+e3)*0.5d0
vjch(i)=(e1-e3)*0.5d0
e1=d1hh*(exp(-2.0d0*ahh*(rbh(i)-r0hh))
* -2.0d0*exp(-ahh*(rbh(i)-r0hh)))
e3=d3hh*(exp(-2.0d0*ahh*(rbh(i)-r0hh))
* +2.0d0*exp(-ahh*(rbh(i)-r0hh)))
vqbh(i)=(e1+e3)*0.5d0
vjbh(i)=(e1-e3)*0.5d0
c
c calculate 3 body potential
c
vq(i)=vqch(i)+vqcb+vqbh(i)
vj(i)=-sqrt(((vjch(i)-vjcb)**2+(vjcb-vjbh(i))**2
* +(vjbh(i)-vjch(i))**2)*0.5d0)
vstr=vstr+vq(i)+vj(i)
enddo
c
c add OH contribution
c
vstr=vstr+vno
c
c partial derivatives
c
c derivative of OH morse term with respect to dt:
c
deddt = 2.0d0 * ahh * d1hh * (1.0d0-expterm) *
* expterm
c
c chain rule: derivatives with respect to cartesian coordinates.
c
de = deddt / rno
do i=1,3
ded(i) = de * tno(i)
enddo
c
c now we need the derivative of ach:
c
do ind=1,3
achdc(ind)=dumach*(tch(1,ind)/rch(1)+tch(2,ind)/rch(2)
* +tch(3,ind)/rch(3)+tch(4,ind)/rch(4))/4.0d0
do i=1,4
achdh(i,ind)=-dumach*tch(i,ind)/rch(i)/4.0d0
enddo
enddo
dumqcb=-acb*((d1cb+d3cb)*exp(-2.0d0*acb*(rcb-r0cb))-
* (d1cb-d3cb)*exp(-acb*(rcb-r0cb)))/rcb
c
c calculate cartesian derivatives:
c looping over ch(i) and bh(i)
c
do i=1,4
dumqbh=-ahh*((d1hh+d3hh)*exp(-2.0d0*ahh*(rbh(i)-r0hh))-
* (d1hh-d3hh)*exp(-ahh*(rbh(i)-r0hh)))/rbh(i)
c
c adding the derv of D3cb wrt r
c
addd3 = dd3cb*(exp(-2.0d0*acb*(rcb-r0cb))+
* 2.0d0*exp(-acb*(rcb-r0cb)))
addd3 = addd3/4.d0 * 0.5d0 / rcb
dumqbh = dumqbh + addd3
c
factj=0.5d0/vj(i)
dumjcb=-acb*((d1cb-d3cb)*exp(-2.0d0*acb*(rcb-r0cb))
* -(d1cb+d3cb)*exp(-acb*(rcb-r0cb)))*factj/rcb
dumjbh=-ahh*((d1hh-d3hh)*exp(-2.0d0*ahh*(rbh(i)-r0hh))
* -(d1hh+d3hh)*exp(-ahh*(rbh(i)-r0hh)))*factj/rbh(i)
c
c adding derv of D3cb wrt r
c
addd3 = dd3cb*(exp(-2.0d0*acb*(rcb-r0cb))+
* 2.0d0*exp(-acb*(rcb-r0cb)))
addd3 = addd3/4.d0 * 0.5d0 * factj / rcb
dumjbh = dumjbh - addd3
c
do ind=1,3
c
c deriv wrt hb:
c
pdot(nhb(ind))=pdot(nhb(ind))
* -tcb(ind)*dumqcb+tbh(i,ind)*dumqbh
* +(vjch(i)-vjcb)*(dumjcb*tcb(ind))
* +(vjcb-vjbh(i))*(-dumjcb*tcb(ind)-dumjbh*tbh(i,ind))
* +(vjbh(i)-vjch(i))*dumjbh*tbh(i,ind)
c
c dvqch(i)/dc
c
dumqch=-(ach*tch(i,ind)/rch(i)+achdc(ind)*(rch(i)-r0ch))
* *((d1ch+d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch-d3ch)*exp(-ach*(rch(i)-r0ch)))
pdot(nc(ind))=pdot(nc(ind))+dumqch+tcb(ind)*dumqcb
c
c dvqch(i)/dh(i)
c
dumqhi=(ach*tch(i,ind)/rch(i)-achdh(i,ind)*(rch(i)-r0ch))
* *((d1ch+d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch-d3ch)*exp(-ach*(rch(i)-r0ch)))
pdot(nh(i,ind))=pdot(nh(i,ind))+dumqhi-tbh(i,ind)*dumqbh
c
c dvjch(i)/dc
c
dumjch=-(ach*tch(i,ind)/rch(i)+achdc(ind)*(rch(i)-r0ch))
* *((d1ch-d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch+d3ch)*exp(-ach*(rch(i)-r0ch)))*factj
c
c dvj(i)/dnc(ind)
c
pdot(nc(ind))=pdot(nc(ind))
* +(vjch(i)-vjcb)*(dumjch-dumjcb*tcb(ind))
* +(vjcb-vjbh(i))*dumjcb*tcb(ind)
* -(vjbh(i)-vjch(i))*dumjch
c
c dvjch(i)/dh(i)
c
dumjhi=(ach*tch(i,ind)/rch(i)-achdh(i,ind)*(rch(i)-r0ch))
* *((d1ch-d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch+d3ch)*exp(-ach*(rch(i)-r0ch)))*factj
c
c dvj(i)/dnh(i,ind)
c
pdot(nh(i,ind))=pdot(nh(i,ind))
* +(vjch(i)-vjcb)*dumjhi
* +(vjcb-vjbh(i))*dumjbh*tbh(i,ind)
* +(vjbh(i)-vjch(i))*(-dumjbh*tbh(i,ind)-dumjhi)
c
c dv(i)/dh(j)
c
do k=1,3
j=i+k
if(j.gt.4)j=j-4
dumqhj=-achdh(j,ind)*(rch(i)-r0ch)
* *((d1ch+d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch-d3ch)*exp(-ach*(rch(i)-r0ch)))
dumjhj=-achdh(j,ind)*(rch(i)-r0ch)
* *((d1ch-d3ch)*exp(-2.0d0*ach*(rch(i)-r0ch))
* -(d1ch+d3ch)*exp(-ach*(rch(i)-r0ch)))*factj
pdot(nh(j,ind))=pdot(nh(j,ind))+dumqhj
* +(vjch(i)-vjcb)*dumjhj
* -(vjbh(i)-vjch(i))*dumjhj
enddo
enddo
enddo
c
c add derivatives of OH morse term
c
do ind=1,3
pdot(nhb(ind))=pdot(nhb(ind)) - ded(ind)
pdot(no(ind))=pdot(no(ind)) + ded(ind)
enddo
c
return
end
c
c******************************************************
c
c
subroutine opbend_geh4oh(vop)
c
c subroutine calculates symmetrized vop potential and derivatives
c
implicit double precision (a-h,o-z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM_geh4oh/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
double precision norma
dimension sumd2(4),sumd4(4)
dimension in(3),a(3),b(3),axb(3),c(4,3),argd(4)
c
c
vop=0.0d0
c
c calculate force constants and their derivatives
c
call opforce_geh4oh
c
c calculate out-of-plane angle and derivatives
c
do i=1,4
j=i+1
if(j.gt.4)j=j-4
k=j+1
if(k.gt.4)k=k-4
l=k+1
if(l.gt.4)l=l-4
c
c modification to ensure that the set of methane CH bond vector
c (rj,rk,rl) is a right-handed set
c
in(1)=j
in(2)=k
in(3)=l
c
c vector a is rk-rj, vector b is rl-rj
c
do ind=1,3
a(ind)=q(nh(k,ind))-q(nh(j,ind))
b(ind)=q(nh(l,ind))-q(nh(j,ind))
enddo
c
c axb is vector a cross b
c
axb(1)=a(2)*b(3)-a(3)*b(2)
axb(2)=a(3)*b(1)-a(1)*b(3)
axb(3)=a(1)*b(2)-a(2)*b(1)
norma=axb(1)*axb(1)+axb(2)*axb(2)+axb(3)*axb(3)
norma=sqrt(norma)
c
c c is position vector of h(ii): calculate c(j),c(k),c(l)
c
do ii=1,3
do ind=1,3
c(in(ii),ind)=-tch(in(ii),ind)/rch(in(ii))
enddo
enddo
c
c argd is the dot product axb dot c
c
do ii=1,3
argd(in(ii))=axb(1)*c(in(ii),1)+axb(2)*c(in(ii),2)
* +axb(3)*c(in(ii),3)
argd(in(ii))=argd(in(ii))/norma
c
c if argd > 0 we need to switch vectors k and l around
c
if (argd(in(ii)).gt.0.d0) then
itemp=k
k=l
l=itemp
endif
enddo
c
c subroutine performs sum over j, k, l
c sum2 = sum delta**2
c sum4 = sum delta**4
c
call calcdelta_geh4oh(i,j,k,l,sum2,sum4)
sumd2(i)=sum2
sumd4(i)=sum4
vop=vop+fdelta(i)*sumd2(i)+hdelta(i)*sumd4(i)
enddo
do i=1,4
do j=1,4
c
c overall derivatives of force constants i wrt the bond-length rch(j)
c
ddr=dfdelta(i,j)*sumd2(i)+dhdelta(i,j)*sumd4(i)
c
c calculate derivatives in terms of cartesian coordinates:
c
do ind=1,3
pdot(nh(j,ind))=pdot(nh(j,ind))-tch(j,ind)*ddr/rch(j)
pdot(nc(ind))=pdot(nc(ind))+tch(j,ind)*ddr/rch(j)
enddo
enddo
enddo
return
end
c
c******************************************************
c
c
subroutine ipbend_geh4oh(vip)
c
c subroutine calculates symmetrised in plane bend term
c and its derivatives
c
implicit double precision (a-h,o-z)
C
CHARACTER*75 REF(5)
C
PARAMETER(N3ATOM = 75)
PARAMETER (ISURF = 5)
PARAMETER (JSURF = ISURF*(ISURF+1)/2)
C
PARAMETER (PI = 3.141592653589793D0)
PARAMETER (NATOM = 25)
C
COMMON/PT1CM_geh4oh/ R(N3ATOM), ENGYGS, DEGSDR(N3ATOM)
COMMON/PT3CM_geh4oh/ EZERO(ISURF+1)
COMMON/PT4CM_geh4oh/ ENGYES(ISURF), DEESDR(N3ATOM,ISURF)
COMMON/PT5CM_geh4oh/ ENGYIJ(JSURF), DEIJDR(N3ATOM,JSURF)
C
COMMON/INFOCM_geh4oh/ CARTNU(NATOM,3),INDEXES(NATOM),
+ IRCTNT,NATOMS,ICARTR,MDER,MSURF,REF
C
COMMON/USROCM_geh4oh/ PENGYGS,PENGYES(ISURF),
+ PENGYIJ(JSURF),
+ DGSCART(NATOM,3),DESCART(NATOM,3,ISURF),
+ DIJCART(NATOM,3,JSURF)
C
COMMON/USRICM_geh4oh/ CART(NATOM,3),ANUZERO,
+ NULBL(NATOM),NFLAG(20),
+ NASURF(ISURF+1,ISURF+1),NDER
C
COMMON /POTCM_geh4oh/ nnc,nnb,nnh(5),nno,
+ r0ch,d1ch,d3ch,
+ a1ch,b1ch,c1ch,
+ r0hh,d1hh,d3hh,ahh,
+ r0cb,d1cb,d3cbi,acb,
+ a3s,b3s,aphi,bphi,cphi,
+ atheta,btheta,ctheta,
+ fch3,hch3,
+ fkinf,ak,bk,aa1,aa2,aa3,aa4,
+ fkh2oeq,alph2o,anh2oeq,
+ a3cb,b3cb,rcbsp
C
common /angles/ theta0(4,4),dtheta0(4,4,4)
common /bonds/ rcb,rno,rch(4),rbh(4)
common /coords/ tcb(3),tno(3),tch(4,3),tbh(4,3)
common /delta1/ fdelta(4),hdelta(4)
common /delta2/ dfdelta(4,4),dhdelta(4,4)
common /force1/ fk0(4,4),f1(4),dfdc(4,4,4),dfdh(4,4,4)
common /fsw1/ a1s,b1s,a2s,b2s
common /ip1/ s1(4),ds1(4),s2(4),ds2(4)
common /ndx/ nc(3),nhb(3),nh(4,3),no(3)
common /op1/ s3(4),ds3(4)
common /qpdot_pl/ q(150),pdot(150)
common /switch1/ sphi(4),dsphi(4),stheta(4),dstheta(4)
common /addh2o/ded(3),angh2o(4),fkh2o(4),
+ dkdr(4),dkdx(4,3),dedo(3),dedhi(3),dedho(3)
C
dimension costh(4,4),theta(4,4),dth(4,4)
c
c initialise
c
vip=0.0d0
c
c calculate force constants: fk0(i,j), f1(i)
c and derivatives wrt rch(k) and rbh(k): dfdc(i,j,k), dfdh(i,j,k)
c
call ipforce_geh4oh
c
c calculate theta(i,j) and in plane bend potential
c
do i=1,3
do j=i+1,4
costh(i,j)=tch(i,1)*tch(j,1)+tch(i,2)*tch(j,2)
* +tch(i,3)*tch(j,3)
costh(i,j)=costh(i,j)/rch(i)/rch(j)
theta(i,j)=acos(costh(i,j))
dth(i,j)=theta(i,j)-theta0(i,j)
vip=vip+0.5d0*fk0(i,j)*f1(i)*f1(j)*dth(i,j)**2
c
c calculate partial derivatives wrt cartesian coordinates
c
c calculate pdots wrt theta:
c
termth=-1.0d0/sqrt(1.0d0-costh(i,j)*costh(i,j))
do ind=1,3
dthi=-tch(j,ind)/rch(i)/rch(j)
* +costh(i,j)*tch(i,ind)/rch(i)/rch(i)
dthi=dthi*termth
dthj=-tch(i,ind)/rch(i)/rch(j)
* +costh(i,j)*tch(j,ind)/rch(j)/rch(j)
dthj=dthj*termth
dthc=-(dthi+dthj)
pdot(nh(i,ind))=pdot(nh(i,ind))
* +fk0(i,j)*f1(i)*f1(j)*dthi*dth(i,j)
pdot(nh(j,ind))=pdot(nh(j,ind))
* +fk0(i,j)*f1(i)*f1(j)*dthj*dth(i,j)
pdot(nc(ind))=pdot(nc(ind))
* +fk0(i,j)*f1(i)*f1(j)*dthc*dth(i,j)
do k=1,4
c
c calculate pdots wrt force constants and wrt theta0
c
dth0k=-dtheta0(i,j,k)*tch(k,ind)/rch(k)
dth0c=-dth0k
pdot(nh(k,ind))=pdot(nh(k,ind))
* -0.5d0*tch(k,ind)*dfdc(i,j,k)*dth(i,j)**2/rch(k)
* -0.5d0*tbh(k,ind)*dfdh(i,j,k)*dth(i,j)**2/rbh(k)
* -fk0(i,j)*f1(i)*f1(j)*dth0k*dth(i,j)
pdot(nc(ind))=pdot(nc(ind))
* +0.5d0*tch(k,ind)*dfdc(i,j,k)*dth(i,j)**2/rch(k)
* -fk0(i,j)*f1(i)*f1(j)*dth0c*dth(i,j)
pdot(nhb(ind))=pdot(nhb(ind))
* +0.5d0*tbh(k,ind)*dfdh(i,j,k)*dth(i,j)**2/rbh(k)
enddo
enddo
enddo
enddo
c
c Now, calculate h2o bending energies.
c
c First, calculate the angles:
c
do i = 1,4
dot = 0.d0
do j = 1,3
dot = dot - tno(j)*tbh(i,j)
enddo