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|
! This file is part of xtb.
!
! Copyright (C) 2017-2020 Stefan Grimme
!
! xtb is free software: you can redistribute it and/or modify it under
! the terms of the GNU Lesser General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! xtb is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU Lesser General Public License for more details.
!
! You should have received a copy of the GNU Lesser General Public License
! along with xtb. If not, see <https://www.gnu.org/licenses/>.
module xtb_axis
use xtb_mctc_accuracy, only : wp
contains
subroutine axis(numat,nat,xyz,aa,bb,cc)
use xtb_splitparam
implicit double precision (a-h,o-z)
dimension xyz(3,numat)
integer nat(numat)
PARAMETER (BOHR=0.52917726)
dimension t(6), rot(3), xyzmom(3), eig(3), evec(3,3)
dimension x(numat),y(numat),z(numat),coord(3,numat)
data t /6*0.d0/
!************************************************************************
!* const1 = 10**40/(n*a*a)
!* n = avergadro's number
!* a = cm in an angstrom
!* 10**40 is to allow units to be 10**(-40)gram-cm**2
!*
!************************************************************************
const1 = 1.66053d0
!************************************************************************
!*
!* const2 = conversion factor from angstrom-amu to cm**(-1)
!*
!* = (planck's constant*n*10**16)/(8*pi*pi*c)
!* = 6.62618*10**(-27)[erg-sec]*6.02205*10**23*10**16/
!* (8*(3.1415926535)**2*2.997925*10**10[cm/sec])
!*
!***********************************************************************
const2=16.8576522d0
sumw=1.d-20
sumwx=0.d0
sumwy=0.d0
sumwz=0.d0
coord(1:3,1:numat)=xyz(1:3,1:numat)*bohr
do i=1,numat
sumw=sumw+atmass(i)
sumwx=sumwx+atmass(i)*coord(1,i)
sumwy=sumwy+atmass(i)*coord(2,i)
sumwz=sumwz+atmass(i)*coord(3,i)
enddo
sumwx=sumwx/sumw
sumwy=sumwy/sumw
sumwz=sumwz/sumw
f=1.0d0/bohr
do i=1,numat
x(i)=coord(1,i)-sumwx
y(i)=coord(2,i)-sumwy
z(i)=coord(3,i)-sumwz
enddo
!************************************************************************
!* matrix for moments of inertia is of form
!*
!* | y**2+z**2 |
!* | -y*x z**2+x**2 | -i =0
!* | -z*x -z*y x**2+y**2 |
!*
!************************************************************************
do i=1,6
t(i)=dble(i)*1.0d-10
enddo
do i=1,numat
t(1)=t(1)+atmass(i)*(y(i)**2+z(i)**2)
t(2)=t(2)-atmass(i)*x(i)*y(i)
t(3)=t(3)+atmass(i)*(z(i)**2+x(i)**2)
t(4)=t(4)-atmass(i)*z(i)*x(i)
t(5)=t(5)-atmass(i)*y(i)*z(i)
t(6)=t(6)+atmass(i)*(x(i)**2+y(i)**2)
enddo
call rsp(t,3,3,eig,evec)
! xsum=evec(1,1)*(evec(2,2)*evec(3,3)-evec(3,2)*evec(2,3)) +
! 1 evec(1,2)*(evec(2,3)*evec(3,1)-evec(2,1)*evec(3,3)) +
! 2 evec(1,3)*(evec(2,1)*evec(3,2)-evec(2,2)*evec(3,1))
do i=1,3
if(eig(i).lt.3.d-4) then
eig(i)=0.d0
rot(i)=0.d0
else
rot(i)=2.9979245d+4*const2/eig(i)
endif
xyzmom(i)=eig(i)*const1
enddo
aa=rot(3)/2.9979245d+4
bb=rot(2)/2.9979245d+4
cc=rot(1)/2.9979245d+4
avmom=1.d-47*(xyzmom(1)+xyzmom(2)+xyzmom(3))/3.
return
end subroutine axis
subroutine axis2(n,xyz,aa,bb,cc,avmom,sumw)
use xtb_splitparam, only : atmass
use xtb_mctc_convert, only : autoaa
implicit double precision (a-h,o-z)
!> number of atoms
integer, intent(in) :: n
!> cartesian coordinates
real(wp), intent(in) :: xyz(:,:)
!> rotational constants
real(wp), intent(out) :: aa,bb,cc
!> average moment of inertia
real(wp), intent(out) :: avmom
!> sum of atomic masses
real(wp), intent(out) :: sumw
!> const1 = 10**40/(n*a*a)
!> n = avergadro's number
!> a = cm in an angstrom
!> 10**40 is to allow units to be 10**(-40)gram-cm**2
real(wp), parameter :: const1 = 1.66053_wp
!> const2 = conversion factor from angstrom-amu to cm**(-1)
!> = (planck's constant*n*10**16)/(8*pi*pi*c)
!> = 6.62618*10**(-27)[erg-sec]*6.02205*10**23*10**16/
!> (8*(3.1415926535)**2*2.997925*10**10[cm/sec])
real(wp), parameter :: const2 = 16.8576522_wp
!> temporary variables
real(wp) :: xsum,eps,ams
!> weighted sum of coordinates
real(wp) :: sumwx,sumwy,sumwz
!> loop variables
integer :: i
!> temporary arrays
real(wp) :: t(6), rot(3), xyzmom(3), eig(3), evec(3,3)
real(wp) :: x(n),y(n),z(n)
!> Cartesian coordinates in Bohr
real(wp) :: coord(3,n)
t(:) = 0.0_wp
sumw = 0.0_wp
sumwx = 0.0_wp
sumwy = 0.0_wp
sumwz = 0.0_wp
! convert Bohr to Angstrom !
coord(:,:) = xyz(:,:) * autoaa
! cma !
do i=1,n
sumw=sumw+atmass(i)
sumwx=sumwx+atmass(i)*coord(1,i)
sumwy=sumwy+atmass(i)*coord(2,i)
sumwz=sumwz+atmass(i)*coord(3,i)
enddo
sumwx=sumwx/sumw
sumwy=sumwy/sumw
sumwz=sumwz/sumw
do i=1,n
x(i)=coord(1,i)-sumwx
y(i)=coord(2,i)-sumwy
z(i)=coord(3,i)-sumwz
enddo
!************************************************************************
!* matrix for moments of inertia is of form
!*
!* | y**2+z**2 |
!* | -y*x z**2+x**2 | -i =0
!* | -z*x -z*y x**2+y**2 |
!*
!************************************************************************
do i=1,6
t(i)=dble(i)*1.0d-10
enddo
do i=1,n
t(1)=t(1)+atmass(i)*(y(i)**2+z(i)**2)
t(2)=t(2)-atmass(i)*x(i)*y(i)
t(3)=t(3)+atmass(i)*(z(i)**2+x(i)**2)
t(4)=t(4)-atmass(i)*z(i)*x(i)
t(5)=t(5)-atmass(i)*y(i)*z(i)
t(6)=t(6)+atmass(i)*(x(i)**2+y(i)**2)
enddo
call rsp(t,3,3,eig,evec)
do i=1,3
if(eig(i).lt.3.d-4) then
eig(i)=0.d0
rot(i)=0.d0
else
rot(i)=2.9979245d+4*const2/eig(i)
endif
xyzmom(i)=eig(i)*const1
enddo
aa=rot(3)/2.9979245d+4
bb=rot(2)/2.9979245d+4
cc=rot(1)/2.9979245d+4
avmom=1.d-47*(xyzmom(1)+xyzmom(2)+xyzmom(3))/3.
end subroutine axis2
subroutine axisvec(numat,nat,xyz,aa,bb,cc,evec)
use xtb_splitparam
implicit double precision (a-h,o-z)
dimension xyz(3,numat)
integer nat(numat)
PARAMETER (BOHR=0.52917726)
dimension t(6), rot(3), xyzmom(3), eig(3), evec(3,3)
dimension x(numat),y(numat),z(numat),coord(3,numat)
data t /6*0.d0/
!************************************************************************
!* const1 = 10**40/(n*a*a)
!* n = avergadro's number
!* a = cm in an angstrom
!* 10**40 is to allow units to be 10**(-40)gram-cm**2
!*
!************************************************************************
const1 = 1.66053d0
!************************************************************************
!*
!* const2 = conversion factor from angstrom-amu to cm**(-1)
!*
!* = (planck's constant*n*10**16)/(8*pi*pi*c)
!* = 6.62618*10**(-27)[erg-sec]*6.02205*10**23*10**16/
!* (8*(3.1415926535)**2*2.997925*10**10[cm/sec])
!*
!************************************************************************
const2=16.8576522d0
sumw=1.d-20
sumwx=0.d0
sumwy=0.d0
sumwz=0.d0
coord(1:3,1:numat)=xyz(1:3,1:numat)*bohr
do i=1,numat
sumw=sumw+atmass(i)
sumwx=sumwx+atmass(i)*coord(1,i)
sumwy=sumwy+atmass(i)*coord(2,i)
sumwz=sumwz+atmass(i)*coord(3,i)
enddo
sumwx=sumwx/sumw
sumwy=sumwy/sumw
sumwz=sumwz/sumw
f=1.0d0/bohr
do i=1,numat
x(i)=coord(1,i)-sumwx
y(i)=coord(2,i)-sumwy
z(i)=coord(3,i)-sumwz
enddo
!************************************************************************
!* matrix for moments of inertia is of form
!*
!* | y**2+z**2 |
!* | -y*x z**2+x**2 | -i =0
!* | -z*x -z*y x**2+y**2 |
!*
!************************************************************************
do i=1,6
t(i)=dble(i)*1.0d-10
enddo
do i=1,numat
t(1)=t(1)+atmass(i)*(y(i)**2+z(i)**2)
t(2)=t(2)-atmass(i)*x(i)*y(i)
t(3)=t(3)+atmass(i)*(z(i)**2+x(i)**2)
t(4)=t(4)-atmass(i)*z(i)*x(i)
t(5)=t(5)-atmass(i)*y(i)*z(i)
t(6)=t(6)+atmass(i)*(x(i)**2+y(i)**2)
enddo
call rsp(t,3,3,eig,evec)
! xsum=evec(1,1)*(evec(2,2)*evec(3,3)-evec(3,2)*evec(2,3)) +
! 1 evec(1,2)*(evec(2,3)*evec(3,1)-evec(2,1)*evec(3,3)) +
! 2 evec(1,3)*(evec(2,1)*evec(3,2)-evec(2,2)*evec(3,1))
do i=1,3
if(eig(i).lt.3.d-4) then
eig(i)=0.d0
rot(i)=0.d0
else
rot(i)=2.9979245d+4*const2/eig(i)
endif
xyzmom(i)=eig(i)*const1
enddo
aa=rot(3)/2.9979245d+4
bb=rot(2)/2.9979245d+4
cc=rot(1)/2.9979245d+4
avmom=1.d-47*(xyzmom(1)+xyzmom(2)+xyzmom(3))/3.
return
end subroutine axisvec
!*****************************************************************
! transform to CMA for output on trj xyz file
! input coords remain unchanged
!*****************************************************************
subroutine axis3(mode,numat,nat,coord,coordout,eig)
use xtb_splitparam
implicit none
integer, intent(in) :: numat,nat(numat),mode
real(wp),intent(in) :: coord(3,numat)
real(wp),intent(out) :: coordout(3,numat),eig(3)
real(wp) :: sumw,sumwx,sumwy,sumwz,xsum,eps,ams
real(wp) :: t(6), evec(3,3)
real(wp) :: x(numat),y(numat),z(numat),coordtmp(3,numat)
real(wp) :: coord1(3,numat)
integer :: i,j,k
t = (/(0.0_wp,i=1,6)/)
sumw=1.e-20_wp
sumwx=0.0_wp
sumwy=0.0_wp
sumwz=0.0_wp
do i=1,numat
if(mode.eq.0)then
ams = atmass(i)
else
ams = 1._wp/atmass(i)
endif
sumw=sumw+ams
sumwx=sumwx+ams*coord(1,i)
sumwy=sumwy+ams*coord(2,i)
sumwz=sumwz+ams*coord(3,i)
enddo
eps=1.e-3_wp
sumwx=sumwx/sumw
sumwy=sumwy/sumw
sumwz=sumwz/sumw
do i=1,numat
x(i)=coord(1,i)-sumwx
y(i)=coord(2,i)-sumwy
z(i)=coord(3,i)-sumwz
coordtmp(1,i)=x(i)
coordtmp(2,i)=y(i)
coordtmp(3,i)=z(i)
enddo
do i=1,6
t(i)=real(i,wp)*1.0e-10_wp
enddo
do i=1,numat
t(1)=t(1)+atmass(i)*(y(i)**2+z(i)**2)+eps
t(2)=t(2)-atmass(i)*x(i)*y(i)
t(3)=t(3)+atmass(i)*(z(i)**2+x(i)**2)+eps
t(4)=t(4)-atmass(i)*z(i)*x(i)
t(5)=t(5)-atmass(i)*y(i)*z(i)
t(6)=t(6)+atmass(i)*(x(i)**2+y(i)**2)+eps
enddo
call rsp(t,3,3,eig,evec)
! now to orient the molecule so the chirality is preserved
xsum=evec(1,1)*(evec(2,2)*evec(3,3)-evec(3,2)*evec(2,3)) + &
& evec(1,2)*(evec(2,3)*evec(3,1)-evec(2,1)*evec(3,3)) + &
& evec(1,3)*(evec(2,1)*evec(3,2)-evec(2,2)*evec(3,1))
if( xsum .lt. 0) then
do j=1,3
80 evec(j,1)=-evec(j,1)
enddo
endif
! call prmat(6,evec,3,3,'Rmat')
do i=1,numat
do j=1,3
xsum=0.d0
do k=1,3
xsum=xsum+coordtmp(k,i)*evec(k,j)
enddo
coord1(j,i)=xsum
enddo
enddo
do i=1,numat
coordout(1,i)=coord1(1,i)
coordout(2,i)=coord1(2,i)
coordout(3,i)=coord1(3,i)
enddo
return
end subroutine axis3
end module xtb_axis
|
