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geom.F90
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! Copyright 2014-2021 Kazuya Ishimura
!
! Licensed under the Apache License, Version 2.0 (the "License");
! you may not use this file except in compliance with the License.
! You may obtain a copy of the License at
!
! http:https://www.apache.org/licenses/LICENSE-2.0
!
! Unless required by applicable law or agreed to in writing, software
! distributed under the License is distributed on an "AS IS" BASIS,
! WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
! See the License for the specific language governing permissions and
! limitations under the License.
!
!----------------------------------------------------
subroutine nucenergy(threshatom,datamol,datacomp)
!----------------------------------------------------
!
! Calculate nuclear replusion energy
!
use modtype, only : typemol, typecomp
implicit none
type(typemol),intent(inout) :: datamol
type(typecomp),intent(inout) :: datacomp
integer :: iatom, jatom
real(8),parameter :: zero=0.0D+00
real(8),intent(in) :: threshatom
real(8) :: xyz(3), rr, chrgij
!
datamol%enuc= zero
do iatom= 2,datamol%natom
do jatom= 1,iatom-1
xyz(1)= datamol%coord(1,iatom)-datamol%coord(1,jatom)
xyz(2)= datamol%coord(2,iatom)-datamol%coord(2,jatom)
xyz(3)= datamol%coord(3,iatom)-datamol%coord(3,jatom)
rr= sqrt(xyz(1)*xyz(1)+xyz(2)*xyz(2)+xyz(3)*xyz(3))
chrgij= datamol%znuc(iatom)*datamol%znuc(jatom)
if(rr /= zero) then
datamol%enuc= datamol%enuc+chrgij/rr
if((rr <= threshatom).and.datacomp%master) then
write(datacomp%iout, &
& '("Warning! Distance of Atoms",i4," and",i4," is short!")') iatom, jatom
datacomp%nwarn= datacomp%nwarn+1
endif
else
if((chrgij /= zero).and.datacomp%master) then
write(*,'("Error! Atoms",i4," and",i4," are the same position!")') iatom, jatom
call iabort
endif
endif
enddo
enddo
return
end
!-----------------------------------------------------
subroutine nucgradient(egrad,nproc,myrank,datamol)
!-----------------------------------------------------
!
! Calculate gradinet of nuclear replusion energy
!
use modtype, only : typemol
implicit none
type(typemol),intent(in) :: datamol
integer,intent(in) :: nproc, myrank
integer :: iatom, jatom, i
real(8),intent(inout) :: egrad(3,datamol%natom)
real(8) :: xyz(3), rr, chrgij
!
do iatom= 2+myrank,datamol%natom,nproc
do jatom= 1,iatom-1
xyz(1)= datamol%coord(1,iatom)-datamol%coord(1,jatom)
xyz(2)= datamol%coord(2,iatom)-datamol%coord(2,jatom)
xyz(3)= datamol%coord(3,iatom)-datamol%coord(3,jatom)
rr= xyz(1)*xyz(1)+xyz(2)*xyz(2)+xyz(3)*xyz(3)
rr= rr*sqrt(rr)
chrgij= datamol%znuc(iatom)*datamol%znuc(jatom)
do i= 1,3
egrad(i,iatom)= egrad(i,iatom)-xyz(i)*chrgij/rr
egrad(i,jatom)= egrad(i,jatom)+xyz(i)*chrgij/rr
enddo
enddo
enddo
return
end
!-------------------------------------------------------------------------------------
subroutine setredundantcoord(iredun,isizered,numbond,numangle,numtorsion,exceed, &
& datajob,datamol,datacomp)
!-------------------------------------------------------------------------------------
!
! Set redundant internal coordinate
! Covalent radii (H - Cn): P. Pyykko, M. Atsumi, Chem. Eur. J., 186 (2009) 15.
!
use modparam, only : tobohr
use modtype, only : typejob, typemol, typecomp
implicit none
type(typejob),intent(in) :: datajob
type(typemol),intent(in) :: datamol
type(typecomp),intent(in) :: datacomp
integer,parameter :: maxconnect=13
integer,intent(in) :: isizered
integer,intent(out) :: iredun(4,isizered/4), numbond, numangle, numtorsion
integer :: numredun, maxsize, ijpair(datamol%natom,maxconnect), iatom, jatom, katom, icount
integer :: ibond, kpair, iangle, jangle, numb, iblock(datamol%natom), ib, jb, ijatom(2)
real(8),parameter :: zero=0.0D+00
real(8) :: radii(112), rrij, thresh, rrijmin
logical,intent(out) :: exceed
data radii/ &
& 0.32D+00, 0.46D+00, 1.33D+00, 1.02D+00, 0.85D+00, 0.75D+00, 0.71D+00, 0.63D+00, 0.64D+00, &
& 0.67D+00, 1.55D+00, 1.39D+00, 1.26D+00, 1.16D+00, 1.11D+00, 1.03D+00, 0.99D+00, 0.96D+00, &
& 1.96D+00, 1.71D+00, 1.48D+00, 1.36D+00, 1.34D+00, 1.22D+00, 1.19D+00, 1.16D+00, 1.11D+00, &
& 1.10D+00, 1.12D+00, 1.18D+00, 1.24D+00, 1.21D+00, 1.21D+00, 1.16D+00, 1.14D+00, 1.17D+00, &
& 2.10D+00, 1.85D+00, 1.63D+00, 1.54D+00, 1.47D+00, 1.38D+00, 1.28D+00, 1.25D+00, 1.25D+00, &
& 1.20D+00, 1.28D+00, 1.36D+00, 1.42D+00, 1.40D+00, 1.40D+00, 1.36D+00, 1.33D+00, 1.31D+00, &
& 2.32D+00, 1.96D+00, 1.80D+00, 1.63D+00, 1.76D+00, 1.74D+00, 1.73D+00, 1.72D+00, 1.68D+00, &
& 1.69D+00, 1.68D+00, 1.67D+00, 1.66D+00, 1.65D+00, 1.64D+00, 1.70D+00, 1.62D+00, 1.52D+00, &
& 1.46D+00, 1.37D+00, 1.31D+00, 1.29D+00, 1.22D+00, 1.23D+00, 1.24D+00, 1.33D+00, 1.44D+00, &
& 1.44D+00, 1.51D+00, 1.45D+00, 1.47D+00, 1.42D+00, 2.23D+00, 2.01D+00, 1.86D+00, 1.75D+00, &
& 1.69D+00, 1.70D+00, 1.71D+00, 1.72D+00, 1.66D+00, 1.66D+00, 1.68D+00, 1.68D+00, 1.65D+00, &
& 1.67D+00, 1.73D+00, 1.76D+00, 1.61D+00, 1.57D+00, 1.49D+00, 1.43D+00, 1.41D+00, 1.34D+00, &
& 1.29D+00, 1.28D+00, 1.21D+00, 1.22D+00/
!
ijpair(:,:)= 0
numredun= 0
maxsize= isizered/4
exceed=.false.
!
! Set bond strech
!
numbond= 0
do iatom= 1,datamol%natom
if(datamol%numatomic(iatom) > 112) then
if(datacomp%master) &
& write(*,'(" Error! This program supports up to Cn in Subroutine setredundantcoord.")')
call iabort
elseif(datamol%numatomic(iatom) < 1) then
if(datacomp%master) &
& write(*,'(" Error! This program does not support dummy and ghost atoms ", &
& "in Subroutine setredundantcoord currently.")')
call iabort
endif
icount= 0
do jatom= 1,datamol%natom
if(jatom == iatom) cycle
thresh=(datajob%fbond*tobohr &
& *(radii(datamol%numatomic(iatom))+radii(datamol%numatomic(jatom))))**2
rrij= (datamol%coord(1,jatom)-datamol%coord(1,iatom))**2 &
& +(datamol%coord(2,jatom)-datamol%coord(2,iatom))**2 &
& +(datamol%coord(3,jatom)-datamol%coord(3,iatom))**2
if(rrij <= thresh) then
icount= icount+1
if(icount > maxconnect) then
if(datacomp%master) &
& write(*,'(" Error! There are too many atoms near Atom",i4,".")')iatom
call iabort
endif
ijpair(iatom,icount)= jatom
if(jatom > iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numbond= numbond+1
iredun(1,numbond)= iatom
iredun(2,numbond)= jatom
endif
endif
enddo
enddo
!
! Check the number of molecular fragments
!
numb= 0
iblock(:)= 0
mblock:do iatom= 1,datamol%natom
if(iblock(iatom) /= 0) cycle
numb= numb+1
iblock(iatom)= numb
call checkbond(iatom,numb,iblock,ijpair,datamol%natom,maxconnect)
do jatom= iatom+1,datamol%natom
if(iblock(jatom) == 0) cycle mblock
enddo
exit mblock
enddo mblock
!
if(datacomp%master.and.(numb /= 1)) then
write(datacomp%iout,'(" There are",i3," moleclar blocks in redundant coordinate.")') numb
endif
!
! Calculate length between molecular fragments
!
do ib= 1, numb
do jb= ib+1,numb
rrijmin= zero
do iatom= 1,datamol%natom
if(iblock(iatom) /= ib) cycle
do jatom= iatom+1,datamol%natom
if(iblock(jatom) /= jb) cycle
rrij= (datamol%coord(1,jatom)-datamol%coord(1,iatom))**2 &
& +(datamol%coord(2,jatom)-datamol%coord(2,iatom))**2 &
& +(datamol%coord(3,jatom)-datamol%coord(3,iatom))**2
if((rrijmin == zero).or.(rrij < rrijmin)) then
rrijmin= rrij
ijatom(1)= min(iatom,jatom)
ijatom(2)= max(iatom,jatom)
endif
enddo
enddo
do icount= 1,maxconnect
if(ijpair(ijatom(1),icount) == 0) then
ijpair(ijatom(1),icount)= ijatom(2)
exit
endif
if(icount == maxconnect) then
if(datacomp%master) &
& write(*,'(" Error! There are too many atoms near Atom",i4,".")')ijatom(1)
call iabort
endif
enddo
do icount= 1,maxconnect
if(ijpair(ijatom(2),icount) == 0) then
ijpair(ijatom(2),icount)= ijatom(1)
exit
endif
if(icount == maxconnect) then
if(datacomp%master) &
& write(*,'(" Error! There are too many atoms near Atom",i4,".")')ijatom(2)
call iabort
endif
enddo
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numbond= numbond+1
iredun(1,numbond)= ijatom(1)
iredun(2,numbond)= ijatom(2)
enddo
enddo
!
! Set bond angle
!
numangle= 0
do ibond= 1,numbond
iatom= iredun(1,ibond)
jatom= iredun(2,ibond)
do kpair= 1,maxconnect
katom= ijpair(jatom,kpair)
if(katom == 0) exit
if(katom > iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numangle= numangle+1
iredun(1,numbond+numangle)= iatom
iredun(2,numbond+numangle)= jatom
iredun(3,numbond+numangle)= katom
endif
enddo
iatom= iredun(2,ibond)
jatom= iredun(1,ibond)
do kpair= 1,maxconnect
katom= ijpair(jatom,kpair)
if(katom == 0) exit
if(katom > iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numangle= numangle+1
iredun(1,numbond+numangle)= iatom
iredun(2,numbond+numangle)= jatom
iredun(3,numbond+numangle)= katom
endif
enddo
enddo
!
!
! Set dihedral angle
!
numtorsion= 0
do iangle= numbond+1,numbond+numangle
iatom= iredun(1,iangle)
jatom= iredun(2,iangle)
katom= iredun(3,iangle)
do jangle= iangle+1,numbond+numangle
if(iredun(1,jangle) == jatom) then
if(iredun(2,jangle) == katom) then
if(iredun(3,jangle) /= iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numtorsion= numtorsion+1
iredun(1,numbond+numangle+numtorsion)= iatom
iredun(2,numbond+numangle+numtorsion)= jatom
iredun(3,numbond+numangle+numtorsion)= katom
iredun(4,numbond+numangle+numtorsion)= iredun(3,jangle)
endif
endif
endif
if(iredun(3,jangle) == jatom) then
if(iredun(2,jangle) == katom) then
if(iredun(1,jangle) /= iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numtorsion= numtorsion+1
iredun(1,numbond+numangle+numtorsion)= iatom
iredun(2,numbond+numangle+numtorsion)= jatom
iredun(3,numbond+numangle+numtorsion)= katom
iredun(4,numbond+numangle+numtorsion)= iredun(1,jangle)
endif
endif
endif
enddo
iatom= iredun(3,iangle)
jatom= iredun(2,iangle)
katom= iredun(1,iangle)
do jangle= iangle+1,numbond+numangle
if(iredun(1,jangle) == jatom) then
if(iredun(2,jangle) == katom) then
if(iredun(3,jangle) /= iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numtorsion= numtorsion+1
iredun(1,numbond+numangle+numtorsion)= iatom
iredun(2,numbond+numangle+numtorsion)= jatom
iredun(3,numbond+numangle+numtorsion)= katom
iredun(4,numbond+numangle+numtorsion)= iredun(3,jangle)
endif
endif
endif
if(iredun(3,jangle) == jatom) then
if(iredun(2,jangle) == katom) then
if(iredun(1,jangle) /= iatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numtorsion= numtorsion+1
iredun(1,numbond+numangle+numtorsion)= iatom
iredun(2,numbond+numangle+numtorsion)= jatom
iredun(3,numbond+numangle+numtorsion)= katom
iredun(4,numbond+numangle+numtorsion)= iredun(1,jangle)
endif
endif
endif
enddo
enddo
!
if((datamol%natom >= 4).and.(numtorsion == 0)) then
do iangle= numbond+1,numbond+numangle
iatom= iredun(1,iangle)
jatom= iredun(2,iangle)
katom= iredun(3,iangle)
do jangle= iangle+1,numbond+numangle
if(iredun(1,jangle) == katom) then
if(iredun(2,jangle) == jatom) then
numredun= numredun+1
if(numredun > maxsize) then
exceed=.true.
return
endif
numtorsion= numtorsion+1
iredun(1,numbond+numangle+numtorsion)= iatom
iredun(2,numbond+numangle+numtorsion)= jatom
iredun(3,numbond+numangle+numtorsion)= katom
iredun(4,numbond+numangle+numtorsion)= iredun(3,jangle)
endif
endif
enddo
enddo
endif
!
return
end
!----------------------------------------------------------------------------
recursive subroutine checkbond(iatom,numb,iblock,ijpair,natom,maxconnect)
!----------------------------------------------------------------------------
!
! Check the number of molecular fragments
!
implicit none
integer,intent(in) :: iatom, numb, natom, maxconnect, ijpair(natom,maxconnect)
integer,intent(inout) :: iblock(natom)
integer :: icount, jatom
!
do icount= 1,maxconnect
jatom= ijpair(iatom,icount)
if(jatom == 0) exit
if(iblock(jatom) /= 0) cycle
iblock(jatom)= numb
call checkbond(jatom,numb,iblock,ijpair,natom,maxconnect)
enddo
!
return
end
!------------------------------------------------------------------------------------
subroutine calcnewcoord(coord,coordold,egrad,egradold,ehess,displc,natom3,iopt, &
& datajob,datamol,datacomp)
!------------------------------------------------------------------------------------
!
! Calculate new Cartesian coordinate with gradient and hessian
!
use modparam, only : toang
use modtype, only : typejob, typemol, typecomp
implicit none
type(typejob),intent(in) :: datajob
type(typemol),intent(in) :: datamol
type(typecomp),intent(in) :: datacomp
integer,intent(in) :: natom3, iopt
integer :: i, j, ii
real(8),parameter :: zero=0.0D+00, one=1.0D+00, third=0.3333333333333333D+00
real(8),intent(inout) :: egrad(natom3), egradold(natom3), ehess(natom3*(natom3+1)/2)
real(8),intent(inout) :: coord(natom3), coordold(natom3), displc(natom3*3)
!
real(8) :: work(natom3,natom3),eigen(natom3),work2(natom3,natom3),work3(natom3,natom3)
!
character(len=3) :: table(-9:112)= &
& (/'Bq9','Bq8','Bq7','Bq6','Bq5','Bq4','Bq3','Bq2','Bq ','X ',&
& 'H ','He ','Li ','Be ','B ','C ','N ','O ','F ','Ne ','Na ','Mg ','Al ','Si ','P ',&
& 'S ','Cl ','Ar ','K ','Ca ','Sc ','Ti ','V ','Cr ','Mn ','Fe ','Co ','Ni ','Cu ','Zn ',&
& 'Ga ','Ge ','As ','Se ','Br ','Kr ','Rb ','Sr ','Y ','Zr ','Nb ','Mo ','Tc ','Ru ','Rh ',&
& 'Pd ','Ag ','Cd ','In ','Sn ','Sb ','Te ','I ','Xe ','Cs ','Ba ','La ','Ce ','Pr ','Nd ',&
& 'Pm ','Sm ','Eu ','Gd ','Tb ','Dy ','Ho ','Er ','Tm ','Yb ','Lu ','Hf ','Ta ','W ','Re ',&
& 'Os ','Ir ','Pt ','Au ','Hg ','Tl ','Pb ','Bi ','Po ','At ','Rn ','Fr ','Ra ','Ac ','Th ',&
& 'Pa ','U ','Np ','Pu ','Am ','Cm ','Bk ','Cf ','Es ','Fm ','Md ','No ','Lr ','Rf ','Db ',&
& 'Sg ','Bh ','Hs ','Mt ','Ds ','Rg ','Cn '/)
!
if(datacomp%master) then
write(datacomp%iout,'(" ====================================================")')
write(datacomp%iout,'(" New geometry calculation in Cartesian coordinate")')
write(datacomp%iout,'(" ====================================================")')
endif
!
if(iopt == 1) then
!
! Set initial hessian
!
ehess(:)= zero
do i= 1,natom3
ehess(i*(i+1)/2)= third
enddo
else
!
! Updata hessian matrix
!
call hessianbfgs(ehess,coord,coordold,egrad,egradold,displc,natom3)
endif
!
do i=1,natom3
ii= i*(i-1)/2
do j=1,i
work(j,i)=ehess(ii+j)
enddo
enddo
call diag('V','U',natom3,work,natom3,eigen,datacomp)
!
do i=1,natom3
eigen(i)= one/eigen(i)
enddo
do i=1,natom3
do j=1,natom3
work2(j,i)=work(j,i)*eigen(i)
enddo
enddo
call dgemm('N','T',natom3,natom3,natom3,one,work,natom3,work2,natom3,zero,work3,natom3)
!
! Copy old coordinate and gradient
!
coordold(:)= coord(:)
egradold(:)= egrad(:)
!
do i=1,natom3
do j=1,natom3
coord(i)=coord(i)-work3(i,j)*egrad(j)
enddo
enddo
!
! Print delta xyz
!
if(datacomp%master.and.(mod(datajob%iprint,10) >= 3)) then
write(datacomp%iout,'(" ----------------------------------------------------")')
write(datacomp%iout,'(" Delta xyz (Angstrom)")')
write(datacomp%iout,'(" Atom X Y Z")')
write(datacomp%iout,'(" ----------------------------------------------------")')
do i= 1,natom3/3
write(datacomp%iout,'(3x,a3,3x,3f14.7)')table(datamol%numatomic(i)), &
& ((coord((i-1)*3+j)-coordold((i-1)*3+j))*toang,j=1,3)
enddo
write(datacomp%iout,'(" ----------------------------------------------------",/)')
endif
!
return
end
!-----------------------------------------------------------------------------------
subroutine calcnewcoordred(coord,coordold,coordredun,egrad,egradredun,ehess, &
& work1,work2,work3,work4,workv,iopt,iredun,isizered, &
& maxredun,numbond,numangle,numtorsion,numredun, &
& datajob,datamol,datacomp)
!-----------------------------------------------------------------------------------
!
! Calculate new Cartesian coordinate with gradient, hessian and redundant coordinate
! using Rational Function Optimization (RFO) method
!
! Parameters for force constants (bond strech (up to 3rd period), angle bend, torsion):
! H. B. Schlegel, Theoret. Chim. Acta, 333 (1984) 66.
! Parameters for force constants (bond strech (4th - 6th period)):
! J. M. Wittbrodt, H. B. Schlegel, J. Mol. Strut., 398 (1997) 55.
! Covalent raddi (H - Kr): H. B. Schlegel, Theoret. Chim. Acta, 333 (1984) 66.
! Covalent radii (Rb- Cn): P. Pyykko, M. Atsumi, Chem. Eur. J., 186 (2009) 15.
!
use modparam, only : toang, tobohr
use modtype, only : typejob, typemol, typecomp
implicit none
type(typejob),intent(in) :: datajob
type(typemol),intent(in) :: datamol
type(typecomp),intent(inout) :: datacomp
integer,parameter :: maxiterdx=100, maxiterrfo=1000
integer,intent(in) :: iopt, isizered, maxredun, iredun(4,isizered/4)
integer,intent(in) :: numbond, numangle, numtorsion, numredun
integer :: irow(112)
integer :: natom3, ii, jj, ij, kk, iatom, jatom, katom, iterrfo, iterdx
integer :: numdim
real(8),parameter :: zero=0.0D+00, one=1.0D+00, convl=1.0D-08, convrms=1.0D-06
real(8),parameter :: rad2deg=5.729577951308232D+01
real(8),intent(inout) :: coord(datamol%natom*3), coordold(datamol%natom*3)
real(8),intent(inout) :: coordredun(numredun,2)
real(8),intent(inout) :: egrad(datamol%natom*3), egradredun(numredun,2)
real(8),intent(inout) :: ehess(numredun*(numredun+1)/2), work1(maxredun,maxredun)
real(8),intent(inout) :: work2(maxredun,maxredun), work3(maxredun,maxredun)
real(8),intent(inout) :: work4(maxredun,maxredun), workv(maxredun,3)
real(8) :: parambond(7,7), rij, paramb
real(8) :: rcov(112), rjk, suml, rlambda, rmsdx, rmsqx, ddot
character(len=33) :: paramred
character(len=5) :: chartmp(5)
character(len=3) :: table(112)= &
& (/'H ','He ','Li ','Be ','B ','C ','N ','O ','F ','Ne ','Na ','Mg ','Al ','Si ','P ',&
& 'S ','Cl ','Ar ','K ','Ca ','Sc ','Ti ','V ','Cr ','Mn ','Fe ','Co ','Ni ','Cu ','Zn ',&
& 'Ga ','Ge ','As ','Se ','Br ','Kr ','Rb ','Sr ','Y ','Zr ','Nb ','Mo ','Tc ','Ru ','Rh ',&
& 'Pd ','Ag ','Cd ','In ','Sn ','Sb ','Te ','I ','Xe ','Cs ','Ba ','La ','Ce ','Pr ','Nd ',&
& 'Pm ','Sm ','Eu ','Gd ','Tb ','Dy ','Ho ','Er ','Tm ','Yb ','Lu ','Hf ','Ta ','W ','Re ',&
& 'Os ','Ir ','Pt ','Au ','Hg ','Tl ','Pb ','Bi ','Po ','At ','Rn ','Fr ','Ra ','Ac ','Th ',&
& 'Pa ','U ','Np ','Pu ','Am ','Cm ','Bk ','Cf ','Es ','Fm ','Md ','No ','Lr ','Rf ','Db ',&
& 'Sg ','Bh ','Hs ','Mt ','Ds ','Rg ','Cn '/)
data irow/2*1, 8*2, 8*3, 18*4, 18*5, 32*6, 26*7/
data parambond/ &
& -0.2440D+00, 0.3520D+00, 0.6600D+00, 0.7126D+00, 0.8335D+00, 0.9491D+00, 1.0D+00, &
& 0.3520D+00, 1.0850D+00, 1.5220D+00, 1.4725D+00, 1.6549D+00, 1.7190D+00, 1.8D+00, &
& 0.6600D+00, 1.5220D+00, 2.0680D+00, 1.8238D+00, 2.1164D+00, 2.3185D+00, 2.5D+00, &
& 0.7126D+00, 1.4725D+00, 1.8238D+00, 2.0203D+00, 2.2137D+00, 2.5206D+00, 2.8D+00, &
& 0.8335D+00, 1.6549D+00, 2.1164D+00, 2.2137D+00, 2.3718D+00, 2.5110D+00, 2.7D+00, &
& 0.9491D+00, 1.7190D+00, 2.3185D+00, 2.5206D+00, 2.5110D+00, 2.5D+00, 2.5D+00, &
& 1.0D+00, 1.8D+00, 2.5D+00, 2.8D+00, 2.7D+00, 2.5D+00, 2.5D+00/
data rcov/ &
& 0.32D+00, 0.60D+00, 1.20D+00, 1.05D+00, 0.81D+00, 0.77D+00, 0.74D+00, 0.74D+00, 0.72D+00, &
& 0.72D+00, 1.50D+00, 1.40D+00, 1.30D+00, 1.17D+00, 1.10D+00, 1.04D+00, 0.99D+00, 0.99D+00, &
& 1.80D+00, 1.60D+00, 1.40D+00, 1.40D+00, 1.40D+00, 1.40D+00, 1.40D+00, 1.40D+00, 1.40D+00, &
& 1.40D+00, 1.40D+00, 1.40D+00, 1.40D+00, 1.30D+00, 1.20D+00, 1.20D+00, 1.10D+00, 1.10D+00, &
& 2.10D+00, 1.85D+00, 1.63D+00, 1.54D+00, 1.47D+00, 1.38D+00, 1.28D+00, 1.25D+00, 1.25D+00, &
& 1.20D+00, 1.28D+00, 1.36D+00, 1.42D+00, 1.40D+00, 1.40D+00, 1.36D+00, 1.33D+00, 1.31D+00, &
& 2.32D+00, 1.96D+00, 1.80D+00, 1.63D+00, 1.76D+00, 1.74D+00, 1.73D+00, 1.72D+00, 1.68D+00, &
& 1.69D+00, 1.68D+00, 1.67D+00, 1.66D+00, 1.65D+00, 1.64D+00, 1.70D+00, 1.62D+00, 1.52D+00, &
& 1.46D+00, 1.37D+00, 1.31D+00, 1.29D+00, 1.22D+00, 1.23D+00, 1.24D+00, 1.33D+00, 1.44D+00, &
& 1.44D+00, 1.51D+00, 1.45D+00, 1.47D+00, 1.42D+00, 2.23D+00, 2.01D+00, 1.86D+00, 1.75D+00, &
& 1.69D+00, 1.70D+00, 1.71D+00, 1.72D+00, 1.66D+00, 1.66D+00, 1.68D+00, 1.68D+00, 1.65D+00, &
& 1.67D+00, 1.73D+00, 1.76D+00, 1.61D+00, 1.57D+00, 1.49D+00, 1.43D+00, 1.41D+00, 1.34D+00, &
& 1.29D+00, 1.28D+00, 1.21D+00, 1.22D+00/
!
if(datacomp%master) then
write(datacomp%iout,'(" ====================================================")')
write(datacomp%iout,'(" New geometry calculation in redundant coordinate")')
write(datacomp%iout,'(" ====================================================")')
endif
!
natom3= datamol%natom*3
!
! Calculate B-matrix
!
call calcbmatrix(coordredun,coord,work1,iredun,numbond,numangle,numtorsion,datamol%natom)
!
! Calculate G=B*Bt
!
call dgemm('N','T',numredun,numredun,natom3,one,work1,numredun,work1,numredun, &
& zero,work2,maxredun)
!
! Calculate G-inverse and K-matrix
!
call diag('V','U',numredun,work2,maxredun,workv(1,3),datacomp)
numdim=0
do ii= 1,numredun
if(abs(workv(ii,3)) >= 1.0D-5) then
numdim= numdim+1
workv(ii,3)= one/workv(ii,3)
endif
enddo
!$OMP parallel do
do ii= numredun-numdim+1,numredun
do jj= 1,numredun
work3(jj,ii)= work2(jj,ii)*workv(ii,3)
enddo
enddo
!$OMP end parallel do
call dgemm('N','T',numredun,numredun,numdim,one,work2(1,numredun-numdim+1),maxredun, &
& work3(1,numredun-numdim+1),maxredun,zero,work4,maxredun)
!
! Calculate (G-inverse)*B
!
call dgemm('N','N',numredun,natom3,numredun,one,work4,maxredun,work1,numredun, &
& zero,work3,maxredun)
!
! Calculate Fred=(G-inverse)*B*Fcart
!
call dgemv('N',numredun,natom3,one,work3,maxredun,egrad,1,zero,egradredun,1)
!
if(iopt >= 2) then
!
! Update Hessian
!
call hessianbfgsred(ehess,coordredun,coordredun(1,2),egradredun,egradredun(1,2), &
& workv,numredun,numbond,numangle,numtorsion)
!
do ii= 1,numredun
ij= ii*(ii-1)/2
do jj= 1,ii
work4(jj,ii)=ehess(ij+jj)
enddo
enddo
else
!
! Set initial Hessian
!
do ii= 1,numbond
iatom= datamol%numatomic(iredun(1,ii))
jatom= datamol%numatomic(iredun(2,ii))
rij= coordredun(ii,1)
paramb= parambond(irow(iatom),irow(jatom))
work4(ii,ii)= 1.734D+00/((rij-paramb)*(rij-paramb)*(rij-paramb))
enddo
do ii= numbond+1,numbond+numangle
iatom= datamol%numatomic(iredun(1,ii))
katom= datamol%numatomic(iredun(3,ii))
if((iatom == 1).or.(katom == 1)) then
work4(ii,ii)= 0.16D+00
else
work4(ii,ii)= 0.25D+00
endif
enddo
do ii= numbond+numangle+1,numredun
jatom= datamol%numatomic(iredun(2,ii))
katom= datamol%numatomic(iredun(3,ii))
jj=(iredun(2,ii)-1)*3
kk=(iredun(3,ii)-1)*3
rjk=sqrt((coord(jj+1)-coord(kk+1))**2+(coord(jj+2)-coord(kk+2))**2 &
& +(coord(jj+3)-coord(kk+3))**2)-(rcov(jatom)+rcov(katom))*tobohr
if(rjk > zero) rjk= zero
work4(ii,ii)= 0.0023D+00-0.07D+00*rjk
enddo
!
do ii= 1,numredun
ij= ii*(ii-1)/2
do jj= 1,ii-1
work4(jj,ii)= zero
ehess(ij+jj)= zero
enddo
ehess(ij+ii)= work4(ii,ii)
enddo
endif
!
! Copy coordinates and gradients
!
do ii= 1,natom3
coordold(ii)= coord(ii)
enddo
do ii= 1,numredun
coordredun(ii,2)= coordredun(ii,1)
egradredun(ii,2)= egradredun(ii,1)
enddo
!
! Calculate Kt*FC*K and diagonalize, and then obtain eigenvalues and orthogonal basis
!
call dsymm('L','U',numredun,numdim,one,work4,maxredun,work2(1,numredun-numdim+1),maxredun, &
& zero,work1,maxredun)
call dgemm('T','N',numdim,numdim,numredun,one,work2(1,numredun-numdim+1),maxredun, &
& work1,maxredun,zero,work4,maxredun)
call diag('V','U',numdim,work4,maxredun,workv(1,3),datacomp)
!
! Calculate K*(orthogonal basis)
!
call dgemm('N','N',numredun,numdim,numdim,one,work2(1,numredun-numdim+1),maxredun, &
& work4,maxredun,zero,work1,maxredun)
!
! Calculate (K*(orthogonal basis))t*Fred
!
call dgemv('T',numredun,numdim,one,work1,maxredun,egradredun,1,zero,workv,1)
!
! Rational Function Optimization (RFO) step
!
rlambda= zero
do iterrfo= 1,maxiterrfo
suml= zero
do ii= 1,numdim
suml= suml+workv(ii,1)*workv(ii,1)/(rlambda-workv(ii,3))
enddo
if(datacomp%master.and.(mod(datajob%iprint,10) >= 5)) then
write(datacomp%iout, &
& '(" Lambda iteration of RFO",i3,3x,"Lambda=",1p,d15.8,4x,"Sum=",1p,d15.8)') &
& iterrfo,rlambda,suml
endif
if(abs(rlambda-suml) <= convl) exit
rlambda= suml
if(iterrfo == maxiterrfo) then
if(datacomp%master) then
write(*,'(" Lambda iteration of RFO",i3,3x,"Lambda=",1p,d15.8,4x,"Sum=",1p,d15.8)') &
& iterrfo,rlambda,suml
write(*,'(" Error! RFO step in calcnewcoordred did not converge.")')
write(*,'(" Try cartesian=.false. in opt section of input file.")')
endif
call iabort
endif
enddo
!
! Calculate displacement work(*,3) in coordinate where Hessian is diagonal
!
do ii=1,numdim
workv(ii,1)= workv(ii,1)/(rlambda-workv(ii,3))
enddo
!
! Calculate displacement work(*,2) in redundant coordinate
!
call dgemv('N',numredun,numdim,one,work1,maxredun,workv,1,zero,workv(1,2),1)
!
! Calculate displacement work(*,1) in Cartesian coordinate
!
call dgemv('T',numredun,natom3,one,work3,maxredun,workv(1,2),1,zero,workv,1)
!
! Calculate next Cartesian coordinate
!
do iterdx= 1,maxiterdx
!
! Update Catesian coordinate
!
do ii= 1,natom3
coord(ii)=coord(ii)+workv(ii,1)
enddo
!
! Check convergence of displacement in Cartesian coordinate
!
rmsdx= sqrt(ddot(natom3,workv,1,workv,1)/natom3)
rmsqx= sqrt(ddot(numredun,workv(1,2),1,workv(1,2),1)/numredun)
if(datacomp%master.and.(mod(datajob%iprint,10) >= 5)) then
write(datacomp%iout,'(" Displacement Iteration",i3,2x,"RMS(Cart)=",1p,d10.3,4x, &
& "RMS(Red)=",1p,d10.3)') iterdx, rmsdx, rmsqx
endif
if(rmsdx < convrms) exit
!
! Calculate B-matrix and new displacement in redundant coordinate
!
! delta-q workv(*,3)
!
call calcbmatrix(workv,coord,work1,iredun,numbond,numangle,numtorsion,datamol%natom)
do ii= 1,numredun
workv(ii,3)= workv(ii,1)-coordredun(ii,1)
enddo
call fixdtor(workv(1,3),numbond,numangle,numtorsion)
!
! delta(delta-q) workv(*,2)
!
do ii= 1,numredun
workv(ii,2)=workv(ii,2)-workv(ii,3)
enddo
call fixdtor(workv(1,2),numbond,numangle,numtorsion)
!
do ii= 1,numredun
coordredun(ii,1)= workv(ii,1)
enddo
!
! Calculate G=B*Bt
!
call dgemm('N','T',numredun,numredun,natom3,one,work1,numredun,work1,numredun, &
& zero,work2,maxredun)
!
! Calculate G-inverse
!
call diag('V','U',numredun,work2,maxredun,workv(1,1),datacomp)
numdim=0
do ii= 1,numredun
if(abs(workv(ii,1)) >= 1.0D-5) then
numdim= numdim+1
workv(ii,1)= one/workv(ii,1)
endif
enddo
do ii= numredun-numdim+1,numredun
do jj= 1,numredun
work3(jj,ii)= work2(jj,ii)*workv(ii,1)
enddo
enddo
call dgemm('N','T',numredun,numredun,numdim,one,work2(1,numredun-numdim+1),maxredun, &
& work3(1,numredun-numdim+1),maxredun,zero,work4,maxredun)
!
! Calculate Bt*(G-inverse)
!
call dgemm('T','N',natom3,numredun,numredun,one,work1,numredun,work4,maxredun, &
& zero,work3,maxredun)
!
! Calculate displacement work(*,1) in Cartesian coordinate
!
call dgemv('N',natom3,numredun,one,work3,maxredun,workv(1,2),1,zero,workv,1)
!
if(iterdx == maxiterdx) then
if(datacomp%master) then
write(*,'(" Displacement Iteration",i3,2x,"RMS(Cart)=",1p,d10.3,4x, &
& "RMS(Red)=",1p,d10.3)') iterdx, rmsdx, rmsqx
write(*,'(" Error! Transformation from redundant to Cartesian did not converge.")')
write(*,'(" Try cartesian=.false. in opt section of input file.")')
endif
call iabort
endif
enddo
if(datacomp%master) then
if(mod(datajob%iprint,10) >= 3) then
write(datacomp%iout,'(" ------------------------------------------------------------")')
write(datacomp%iout,'(" Redundant coordinate parameters (Angstrom and Degree)")')
write(datacomp%iout,'(" New Old")')
write(datacomp%iout,'(" ------------------------------------------------------------")')
do ii= 1,numbond
write(chartmp(1:3),'(i5)')ii,iredun(1:2,ii)
paramred= trim(trim("Bond"//adjustl(chartmp(1)) //" ("//adjustl(chartmp(2)))//"," &
& //adjustl(chartmp(3)))//")"
write(datacomp%iout,'(3x,a33,f9.4,5x,f9.4)')paramred,coordredun(ii,1)*toang, &
& coordredun(ii,2)*toang
enddo
do ii= numbond+1,numbond+numangle
write(chartmp(1:4),'(i5)')ii-numbond,iredun(1:3,ii)
paramred= trim(trim(trim("Angle"//adjustl(chartmp(1)) //" ("//adjustl(chartmp(2))) &
& //","//adjustl(chartmp(3)))//","//adjustl(chartmp(4)))//")"
write(datacomp%iout,'(3x,a33,f9.4,5x,f9.4)')paramred,coordredun(ii,1)*rad2deg, &
& coordredun(ii,2)*rad2deg
enddo
do ii= numbond+numangle+1,numbond+numangle+numtorsion
write(chartmp(1:5),'(i5)')ii-numbond-numangle,iredun(1:4,ii)
paramred= trim(trim(trim(trim("Torsion"//adjustl(chartmp(1)) //"("// &
& adjustl(chartmp(2)))//","//adjustl(chartmp(3)))//","// &
& adjustl(chartmp(4)))//","//adjustl(chartmp(5)))//")"
write(datacomp%iout,'(3x,a33,f9.4,5x,f9.4)')paramred,coordredun(ii,1)*rad2deg, &
& coordredun(ii,2)*rad2deg
enddo
write(datacomp%iout,'(" ------------------------------------------------------------")')
endif
endif
!
! Print delta xyz
!
if(datacomp%master.and.(mod(datajob%iprint,10) >= 3)) then
write(datacomp%iout,'(" ----------------------------------------------------")')
write(datacomp%iout,'(" Delta xyz (Angstrom)")')
write(datacomp%iout,'(" Atom X Y Z")')
write(datacomp%iout,'(" ----------------------------------------------------")')
do ii= 1,natom3/3
write(datacomp%iout,'(3x,a3,3x,3f14.7)') table(datamol%numatomic(ii)), &
& ((coord((ii-1)*3+jj)-coordold((ii-1)*3+jj))*toang,jj=1,3)
enddo
write(datacomp%iout,'(" ----------------------------------------------------",/)')
endif
!
return
end
!-----------------------------------------------------------------------------------------
subroutine calcbmatrix(coordredun,coord,bmat,iredun,numbond,numangle,numtorsion,natom)
!-----------------------------------------------------------------------------------------
!
! Calculate transformation matrix(B-matrix) from Cartesian to internal coordinate
!
implicit none
integer,intent(in) :: numbond, numangle, numtorsion
integer,intent(in) :: iredun(4,numbond+numangle+numtorsion), natom
integer :: iatom, jatom, katom, latom, ii, jj, kk, ll, mm, ibond, iangle, itorsion
real(8),parameter :: zero=0.0D+00, one=1.0D+00, two=2.0D+00, four=4.0D+00
real(8),intent(in) :: coord(3,natom)
real(8),intent(out) :: coordredun(numbond+numangle+numtorsion)
real(8),intent(out) :: bmat(numbond+numangle+numtorsion,natom*3)
real(8) :: rrij, rrji, rrjk, rji, rjk, rrkl, rij, rkl, pi, pi2
real(8) :: dotj, dotk, dotjk, dotjk3, cp1(3), cp2(3), cp3(3), sinj, sink, b1, b2, b3
real(8) :: xyzji(3), xyzjk(3), xyzij(3), xyzkl(3)
real(8) :: unitji(3), unitjk(3), unitij(3), unitkl(3)
!
pi= atan(one)*four
pi2=pi*two
bmat(:,:)= zero
!
! Bond strech
!
do ibond= 1,numbond
iatom= iredun(1,ibond)
jatom= iredun(2,ibond)
rrij= (coord(1,jatom)-coord(1,iatom))**2+(coord(2,jatom)-coord(2,iatom))**2 &
& +(coord(3,jatom)-coord(3,iatom))**2
rij= sqrt(rrij)
coordredun(ibond)= rij
!
ii=(iatom-1)*3
jj=(jatom-1)*3
do mm= 1,3
bmat(ibond,ii+mm)=-(coord(mm,jatom)-coord(mm,iatom))/rij
bmat(ibond,jj+mm)= (coord(mm,jatom)-coord(mm,iatom))/rij
enddo
enddo
!
! Bond angle
!
do iangle= numbond+1,numbond+numangle
iatom= iredun(1,iangle)
jatom= iredun(2,iangle)
katom= iredun(3,iangle)
rrji= zero
rrjk= zero
do mm= 1,3
xyzji(mm)= coord(mm,iatom)-coord(mm,jatom)
xyzjk(mm)= coord(mm,katom)-coord(mm,jatom)
rrji= rrji+xyzji(mm)*xyzji(mm)
rrjk= rrjk+xyzjk(mm)*xyzjk(mm)
enddo
rji= sqrt(rrji)
rjk= sqrt(rrjk)
dotj= zero
do mm= 1,3
unitji(mm)= xyzji(mm)/rji
unitjk(mm)= xyzjk(mm)/rjk
dotj= dotj+unitji(mm)*unitjk(mm)
enddo
if(abs(dotj) >= one) then
write(*,'(" Error! During calculation of bond angles in calcbmatrix.")')
write(*,'(" Use Cartesian coordinate. The input is")')
write(*,'(" opt cartesian=.true.",/)')
call iabort
endif
coordredun(iangle)= acos(dotj)
!
sinj= sqrt(one-dotj*dotj)
ii=(iatom-1)*3
jj=(jatom-1)*3
kk=(katom-1)*3
do mm= 1,3
b1=(dotj*unitji(mm)-unitjk(mm))/(rji*sinj)
b2=(dotj*unitjk(mm)-unitji(mm))/(rjk*sinj)
bmat(iangle,ii+mm)= b1
bmat(iangle,kk+mm)= b2
bmat(iangle,jj+mm)=-(b1+b2)
enddo
enddo
!
! Set dihedral angle
!
do itorsion= numbond+numangle+1,numbond+numangle+numtorsion
iatom= iredun(1,itorsion)
jatom= iredun(2,itorsion)
katom= iredun(3,itorsion)
latom= iredun(4,itorsion)
rrij= zero
rrjk= zero
rrkl= zero
do mm= 1,3
xyzij(mm)= coord(mm,jatom)-coord(mm,iatom)
xyzjk(mm)= coord(mm,katom)-coord(mm,jatom)
xyzkl(mm)= coord(mm,latom)-coord(mm,katom)
rrij= rrij+xyzij(mm)*xyzij(mm)
rrjk= rrjk+xyzjk(mm)*xyzjk(mm)
rrkl= rrkl+xyzkl(mm)*xyzkl(mm)
enddo
rij= sqrt(rrij)
rjk= sqrt(rrjk)
rkl= sqrt(rrkl)
dotj= zero