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mol_zxy3.f90
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mol_zxy3.f90
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!
! This unit defines all specific routines for a fouratomic molecule of ch3oh type
!
module mol_zxy3
use accuracy
use moltype
use lapack
implicit none
public ML_b0_zxy3,ML_coordinate_transform_zxy3,ML_rotsymmetry_ZXY3,ML_symmetry_transformation_ZXY3
!
private
integer(ik), parameter :: verbose = 5 ! Verbosity level
!
contains
!
! Procedures to define ch3oh
!
function ML_coordinate_transform_zxy3(src,ndst,direct) result (dst)
!
implicit none
!
real(ark),intent(in) :: src(:)
integer(ik),intent(in) :: ndst
logical,intent(in):: direct
!
real(ark),dimension(ndst) :: dst
real(ark) :: dsrc(size(src))
real(ark) :: tau1,tau2,tau3,x,y,z,phi1,phi2,phi3,alpha12,alpha13,alpha14,alpha23,alpha24,alpha34
real(ark) :: cosbeta,beta312,beta412,beta413,cosa34
character(len=cl) :: txt
!
if (verbose>=7) write(out,"('ML_coordinate_transform_zxy3/start')")
!
if (direct) then
!
dsrc(:) = src(:) - molec%local_eq(:)
!
else
!
dsrc(:) = src(:)
!
endif
!
select case(trim(molec%coords_transform))
case default
write (out,"('MLcoordinate_transform_func: coord. type ',a,' unknown')") trim(molec%coords_transform)
stop 'MLcoordinate_transform_func - bad coord. type'
!
case('R-BETA-TAU')
!
if (direct) then
!
tau2 = src( 8)
tau3 = src( 9)
phi1 = tau2-tau3
phi2 = 2.0_ark*pi-tau2
phi3 = tau3
!
phi1 = tau2-tau3
phi2 = 2.0_ark*pi-tau2
phi3 = tau3
!
dst(1:7) = dsrc(1:7)
dst(8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*phi1-phi2-phi3 )
dst(9) = 1.0_ark/sqrt(2.0_ark)*( phi2-phi3 )
!
else
!
x = 2.0_ark*pi/sqrt(3.0_ark)
y = src(8)
z = src(9)
!
phi1 =(sqrt(2.0_ark)*x+2.0_ark*y )/sqrt(6.0_ark)
phi2 =(sqrt(2.0_ark)*x- y+sqrt(3.0_ark)*z)/sqrt(6.0_ark)
phi3 =(sqrt(2.0_ark)*x- y-sqrt(3.0_ark)*z)/sqrt(6.0_ark)
!
tau3 = phi3
tau2 = 2.0_ark*pi-phi2
!
dst(8) = tau2
dst(9) = tau3
!
endif
!
case('R-BETA-SYM')
!
if (direct) then
!
alpha12 = src(5)
alpha13 = src(6)
alpha23 = src(7)
alpha14 = src(8)
alpha24 = src(9)
!
if (size(src)==10) then
!
alpha34 = src(10)
!
cosbeta = (cos(alpha23)-cos(alpha12)*cos(alpha13) )/(sin(alpha12)*sin(alpha13))
beta312 = aacos(cosbeta,txt)
!
cosbeta = (cos(alpha24)-cos(alpha12)*cos(alpha14) )/(sin(alpha12)*sin(alpha14))
beta412 = aacos(cosbeta,txt)
!
cosbeta = (cos(alpha34)-cos(alpha13)*cos(alpha14) )/(sin(alpha13)*sin(alpha14))
beta413 = aacos(cosbeta,txt)
!
else
!
!alpha34 = calc_alpha34(alpha12,alpha13,alpha14,alpha23,alpha24)
!
cosbeta = (cos(alpha23)-cos(alpha12)*cos(alpha13) )/(sin(alpha12)*sin(alpha13))
beta312 = aacos(cosbeta,txt)
!
cosbeta = (cos(alpha24)-cos(alpha12)*cos(alpha14) )/(sin(alpha12)*sin(alpha14))
beta412 = aacos(cosbeta,txt)
!
cosa34 = cos(alpha13)*cos(alpha14)+cos(beta312+beta412)*sin(alpha13)*sin(alpha14)
alpha34 = aacos(cosa34,txt)
!
endif
!
dst(1)=dsrc(1)
dst(2)=dsrc(2)
dst(3)=dsrc(3)
dst(4)=dsrc(4)
dst(5)=dsrc(5)
dst(6)=dsrc(6)
dst(7)=dsrc(8)
!
phi1 = beta413 !2.0_ark*pi-(beta312+beta412)
phi3 = beta312
phi2 = beta412
!
dst(8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*phi1-phi2-phi3 )
dst(9) = 1.0_ark/sqrt(2.0_ark)*( phi2-phi3 )
!
else
!
! write(out,*) dsrc
!
dst(1:4)=dsrc(1:4) + molec%local_eq(1:4)
!
call from_sym2alpha(src(5:9),dst(5:9),alpha34)
!
alpha12 = dst(5)
alpha13 = dst(6)
alpha23 = dst(7)
alpha14 = dst(8)
alpha24 = dst(9)
!
dst(5) = alpha12
dst(6) = alpha13
dst(7) = alpha23
dst(8) = alpha14
dst(9) = alpha24
!
if (size(dst)==10) then
!
dst(10) = alpha34
!
endif
!
!
endif
!
end select
!
if (verbose>=7) write(out,"('ML_coordinate_transform_zxy3/end')")
!
!
end function ML_coordinate_transform_zxy3
! Here we define structural parameters a0 for ABCD molecule,
!
subroutine ML_b0_zxy3(Npoints,Natoms,b0,rho_i,rho_ref,rho_borders)
!
implicit none
!
integer(ik), intent(in) :: Npoints,Natoms
real(ark), intent(out) :: b0(Natoms,3,0:Npoints)
real(ark), intent(in) ,optional :: rho_i(0:Npoints)
real(ark), intent(out),optional :: rho_ref
real(ark), intent(in),optional :: rho_borders(2) ! rhomim, rhomax - borders
!
real(ark) :: CM_shift,reYX
real(ark) :: mZ,mY,mX1,mX2,mX3,Mtotal,rho
integer(ik) :: i,i0,ix
if (verbose>=4) write(out,"('ML_b0_zxy3/start')")
!
if (size(molec%req)/=4) then
write(out,"('ML_b0_zxy3: Nbonds must be 4 in this routine, not ',i9)") size(molec%req)
stop 'ML_b0_zxy3: wrong Nbonds '
endif
!
if (molec%Natoms/=5) then
write(out,"('ML_b0_zxy3: Natoms must be 5 in this routine, not ',i9)") molec%Natoms
stop 'ML_b0_zxy3: wrong Natoms '
endif
!
mZ = molec%AtomMasses(1)
my = molec%AtomMasses(2)
!
mX1 = molec%AtomMasses(3)
mX2 = molec%AtomMasses(4)
mX3 = molec%AtomMasses(5)
!
Mtotal = mX1+mX2+mX3
!
reYX = molec%req(2)
rho = molec%alphaeq(1)
!
!rho = pi-asin(2.0_ark/sqrt(3.0_ark)*sin(alpha/2.0_ark))
!
b0(1,1,0) = 0
b0(1,2,0) = 0
b0(1,3,0) = 0
b0(2,1,0) = 0
b0(2,2,0) = 0
b0(2,3,0) = molec%req(1)
b0(3,1,0) = reYX*sin(rho)
b0(3,2,0) = 0
b0(3,3,0) = reYX*cos(rho)
b0(4,1,0) = -reYX*sin(rho)/2.0_ark
b0(4,2,0) = sqrt(3.0_ark)*reYX*sin(rho)/2.0_ark
b0(4,3,0) = reYX*cos(rho)
b0(5,1,0) = -reYX*sin(rho)/2.0_ark
b0(5,2,0) = -sqrt(3.0_ark)*reYX*sin(rho)/2.0_ark
b0(5,3,0) = reYX*cos(rho)
!
do i = 1,3
CM_shift = sum(b0(:,i,0)*molec%AtomMasses(:))/sum(molec%AtomMasses(:))
b0(:,i,0) = b0(:,i,0) - CM_shift
enddo
!
! We can also simulate the reference structure at each point of rho, if npoints presented
!
if (Npoints/=0) then
!
rho_ref = rho
!
if (.not.present(rho_borders).or..not.present(rho_ref)) then
write(out,"('ML_b0_zxy3: rho_borders and rho_ref must be presented if Npoints ne 0 ')")
stop 'ML_b0_zxy3: rho_borders or rho_ref not specified '
endif
!
do i = 0,npoints
!
rho = rho_i(i)
!
b0(1,1,i) = 0
b0(1,2,i) = 0
b0(1,3,i) = molec%req(1)
b0(2,1,i) = 0
b0(2,2,i) = 0
b0(2,3,i) = 0
b0(3,1,i) = reYX*sin(rho)
b0(3,2,i) = 0
b0(3,3,i) = reYX*cos(rho)
b0(4,1,i) = -reYX*sin(rho)/2.0_ark
b0(4,2,i) = sqrt(3.0_ark)*reYX*sin(rho)/2.0_ark
b0(4,3,i) = reYX*cos(rho)
b0(5,1,i) = -reYX*sin(rho)/2.0_ark
b0(5,2,i) = -sqrt(3.0_ark)*reYX*sin(rho)/2.0_ark
b0(5,3,i) = reYX*cos(rho)
!
do ix = 1,3
CM_shift = sum(b0(:,ix,0)*molec%AtomMasses(:))/sum(molec%AtomMasses(:))
b0(:,ix,i) = b0(:,ix,i) - CM_shift
enddo
!
if (verbose>=5) then
write(out,"(i6)") molec%natoms
!
write(out,"(/'C',3x,3f14.8)") b0(1,:,i)
write(out,"( 'O',3x,3f14.8)") b0(2,:,i)
write(out,"( 'H',3x,3f14.8)") b0(3,:,i)
write(out,"( 'H',3x,3f14.8)") b0(4,:,i)
write(out,"( 'H',3x,3f14.8)") b0(5,:,i)
write(out,"( 'H',3x,3f14.8)") b0(6,:,i)
endif
!
enddo
!
!
endif
!
!
if (verbose>=5) then
!
do i = 0,npoints
!
write(out,"(i6)") molec%natoms
!
write(out,"(/'C ',3x,3f14.8)") b0(1,:,i)
write(out,"( 'Cl',3x,3f14.8)") b0(2,:,i)
write(out,"( 'H ',3x,3f14.8)") b0(3,:,i)
write(out,"( 'H ',3x,3f14.8)") b0(4,:,i)
write(out,"( 'H ',3x,3f14.8)") b0(5,:,i)
!
enddo
!
endif
!
if (verbose>=4) write(out,"('ML_b0_zxy3/end')")
!
end subroutine ML_b0_zxy3
! Here we define the symmetry transformation of the Nmodes coordinates according the symmetry operations
!
subroutine ML_symmetry_transformation_ZXY3(ioper,natoms,src,dst)
!
integer(ik),intent(in) :: ioper ! group operation
integer(ik),intent(in) :: natoms
real(ark),intent(in) :: src(natoms)
real(ark),intent(out) :: dst(natoms)
real(ark) :: repres(12,2,2),a,b,e,o
!
integer(ik) :: nsrc
!
if (verbose>=6) write(out,"('ML_symmetry_transformation_ZXY3/start')")
!
nsrc = size(src)
!
select case(trim(molec%coords_transform))
!
case default
write (out,"('ML_coordinate_transform_ZXY2: coord. type ',a,' unknown')") trim(molec%coords_transform)
stop 'ML_coordinate_transform_ZXY2 - bad coord. type'
!
case('R-BETA-SYM')
!
select case(trim(molec%symmetry))
case default
write (out,"('ML_symmetry_transformation_ZXY3: symmetry ',a,' unknown')") trim(molec%symmetry)
stop 'ML_symmetry_transformation_ZXY3 - bad symm. type'
!
case('C3V','C3V(M)')
!
select case(ioper)
!
case (1) ! identity
!
dst = src
!
case (3) ! (123)
!
dst(2) = src(3)
dst(3) = src(4)
dst(4) = src(2)
!
dst(5) = src(6)
dst(6) = src(7)
dst(7) = src(5)
!
case (2) ! (321)
!
dst(2) = src(4)
dst(3) = src(2)
dst(4) = src(3)
!
dst(5) = src(7)
dst(6) = src(5)
dst(7) = src(6)
!
case (6) ! (12)
!
dst(2) = src(3)
dst(3) = src(2)
dst(4) = src(4)
!
dst(5) = src(6)
dst(6) = src(5)
dst(7) = src(7)
!
case (5) ! (13)
!
dst(2) = src(4)
dst(3) = src(3)
dst(4) = src(2)
!
dst(5) = src(7)
dst(6) = src(6)
dst(7) = src(5)
!
case (4) ! (23)
!
dst(2) = src(2)
dst(3) = src(4)
dst(4) = src(3)
!
dst(5) = src(5)
dst(6) = src(7)
dst(7) = src(6)
!
case default
!
write (out,"('symmetry_transformation_local: operation ',i8,' unknown')") ioper
stop 'symmetry_transformation_local - bad operation. type'
!
end select
!
a = 0.5_ark ; b = 0.5_ark*sqrt(3.0_ark) ; e = 1.0_ark ; o = 0.0_ark
!
repres ( 1,:,:)= reshape((/ e, o, &
o, e/),(/2,2/))
!
repres ( 3,:,:)= reshape((/-a,-b, &
b,-a/),(/2,2/))
!
repres ( 2,:,:)= reshape((/-a, b, &
-b,-a/),(/2,2/))
!
repres ( 4,:,:)= reshape((/ e, o, &
o,-e/),(/2,2/))
!
repres ( 6,:,:)= reshape((/-a, b, &
b, a/),(/2,2/))
!
repres ( 5,:,:)= reshape((/-a,-b, &
-b, a/),(/2,2/))
!
dst(8) = repres(ioper,1,1)*src(8)+repres(ioper,1,2)*src(9)
dst(9) = repres(ioper,2,1)*src(8)+repres(ioper,2,2)*src(9)
!
end select
!
end select
!
if (verbose>=6) write(out,"('ML_symmetry_transformation_ZXY3/end')")
!
end subroutine ML_symmetry_transformation_ZXY3
! Here we find the rotational symmetry from J,K
!
subroutine ML_rotsymmetry_ZXY3(J,K,tau,gamma,ideg)
!
integer(ik),intent(in) :: J,K,tau ! rot. quanta
integer(ik),intent(out) :: gamma,ideg
!
if (verbose>=5) write(out,"('ML_rotsymmetry_ZXY3/start')")
!
!
select case(trim(molec%symmetry))
case default
write (out,"('ML_rotsymmetry_ZXY3: symmetry ',a,' unknown')") trim(molec%symmetry)
stop 'ML_rotsymmetry_ZXY3 - bad symm. type'
!
case('C3V','C3V(M)')
!
gamma = 0
ideg = 1
!
if (mod(K+3,3)==0.and.tau==0) gamma = 1 !; return
if (mod(K+3,3)==0.and.tau==1) gamma = 2 !; return
!
if (mod(K+3,3)/=0.and.tau==0) then
gamma = 3 ; ideg = 1
endif
if (mod(K+3,3)/=0.and.tau==1) then
gamma = 3 ; ideg = 2
endif
!
end select
!
!
if (verbose>=5) write(out,"('ML_rotsymmetry_ZXY3/end')")
!
!
end subroutine ML_rotsymmetry_ZXY3
subroutine from_sym2alpha(s,local,alpha34)
!
! obtaining 5 angles from 5 internal sym. coordinates
!
real(ark),intent(in) :: s(5)
real(ark),intent(out) :: local(5),alpha34
!
real(ark) :: s_t(5),eps(5)
real(ark) :: rjacob(5,5),s_l(5),s_r(5)
real(ark) :: am(5,5),bm(5),cm(5),alpha34_
!
real(rk) :: a(5,5),b(5,1)
real(ark) :: stadev_old,stadev,ssq,stadev_best,h
!
integer(ik) :: iter,itmax,k,irow,icolumn,ierror
!
local(:) = molec%local_eq(5:)
!
iter = 0
stadev_old = 1.e10
stadev = 1.e10
!
stadev_best = sqrt(small_)*0.001_ark
itmax = 500
!
! Initial value for alpha10
!
outer_loop: &
do while( iter<itmax .and. stadev>stadev_best )
!
iter = iter + 1
ssq=0
!
! Caclulate the function
!
call calc_sym_from_alpha(local,s_r,alpha34)
!
eps(:) = s(:)-s_r(:)
!
do k = 1,5
!
h = 1.e-3*abs(local(k)) ; if (h<1e-12) h = 1e-7
!
local(k) = local(k) + h
!
call calc_sym_from_alpha(local,s_r,alpha34_)
!
local(k) = local(k) - h - h
!
call calc_sym_from_alpha(local,s_l,alpha34_)
!
rjacob(:,k) = ( s_r(:)-s_l(:))/h*0.5_ark
!
local(k) = local(k) + h
!
enddo
!
ssq=sqrt(sum(eps(:)**2))
!
! We constract a set of linear equations A x = B
!
! form A matrix
!
do irow=1,5 !==== row-...... ====!
do icolumn=1,irow !==== column-....====!
am(irow,icolumn)=sum(rjacob(:,icolumn)*rjacob(:,irow))
am(icolumn,irow)=am(irow,icolumn)
enddo
enddo
!
! form B matrix
!
do irow=1,5 !==== row-...... ====!
bm(irow)=sum(eps(:)*rjacob(:,irow))
enddo
!
! Solve the set of linear equations
!
call MLlinurark(5,am,bm(:),cm,ierror)
!
if (ierror>0) then
!
a = am ; b(:,1) = bm(:)
!
call lapack_gelss(a(:,:),b(:,:))
!
cm(:) = b(:,1)
!
endif
!
local(:)=local(:)+cm(:)
!
stadev=ssq/sqrt(5.0_ark)
!
stadev_old=stadev
!
enddo outer_loop ! --- iter
!
if (iter==itmax) then
write(out,"('from_sym2alpha: could not find solution after ',i8,' iterations')") iter
stop 'from_sym2alphaII: could not find solution'
endif
!
contains
subroutine calc_sym_from_alpha(src,dst,alpha34)
real(ark),intent(in) :: src(5)
real(ark),intent(out) :: dst(5),alpha34
real(ark) :: alpha12,alpha13,alpha23,alpha14,alpha24,cosbeta,beta312,beta412,beta413,cosa34,phi1,phi2,phi3
character(len=cl) :: txt
!
txt = 'calc_sym_from_alpha'
!
alpha12 = src(1)
alpha13 = src(2)
alpha23 = src(3)
alpha14 = src(4)
alpha24 = src(5)
!
!alpha34 = calc_alpha34(alpha12,alpha13,alpha14,alpha23,alpha24)
!
cosbeta = (cos(alpha23)-cos(alpha12)*cos(alpha13) )/(sin(alpha12)*sin(alpha13))
beta312 = aacos(cosbeta,txt)
!
cosbeta = (cos(alpha24)-cos(alpha12)*cos(alpha14) )/(sin(alpha12)*sin(alpha14))
beta412 = aacos(cosbeta,txt)
!
cosa34 = cos(alpha13)*cos(alpha14)+cos(beta312+beta412)*sin(alpha13)*sin(alpha14)
alpha34 = aacos(cosa34,txt)
!
cosbeta = (cos(alpha34)-cos(alpha13)*cos(alpha14) )/(sin(alpha13)*sin(alpha14))
beta413 = aacos(cosbeta,txt)
!
dst(1)=alpha12-molec%local_eq(5)
dst(2)=alpha13-molec%local_eq(6)
dst(3)=alpha14-molec%local_eq(8)
!
phi1 = beta413 ! 2.0_ark*pi-(beta312+beta412)
phi3 = beta312
phi2 = beta412
!
dst(4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*phi1-phi2-phi3 )
dst(5) = 1.0_ark/sqrt(2.0_ark)*( phi2-phi3 )
!
end subroutine calc_sym_from_alpha
!
end subroutine from_sym2alpha
end module mol_zxy3