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mol_xy2.f90
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mol_xy2.f90
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!
! This unit defines all specific routines for a triatomic molecule of XY2 type
!
module mol_xy2
use accuracy
use moltype
use symmetry,only : sym
implicit none
public ML_b0_XY2,ML_coordinate_transform_XY2,ML_symmetry_transformation_XY2,ML_rotsymmetry_XY2
!
private
!
integer(ik), parameter :: verbose = 4 ! Verbosity level
!
contains
!
!
! Here we define the coordinate transformation from the local coordinates (r,alpha) to
! the internal coordinates chi used in the jacobian transformation and thereafter in the
! as conjugate momenta coordinates
!
function ML_coordinate_transform_XY2(src,ndst,direct) result (dst)
!
real(ark),intent(in) :: src(:)
integer(ik),intent(in) :: ndst
logical,intent(in):: direct
!
real(ark),dimension(ndst) :: dst
real(ark) :: c_t(3,3),dsrc(size(src)),r_e1(2),r_e2(2),radau_e1(2),radau_e2(2),radau_e(2)
real(ark) :: m1,m2,m3,a0,r_t1(2),r_t2(2),radau_t1(2),radau_t2(2),cosalpha,rho,alpha,sinalpha
real(ark) :: r1,r2,r3,R,r12,r12e,r13e,alpha1,alpha2,theta,sintheta,q0,q,q1,q2,alpha0
!
!
integer(ik) :: nsrc
!
if (verbose>=5) write(out,"('ML_coordinate_transform_XY2/start')")
!
if (direct) then
!
dsrc(:) = src(:) - molec%local_eq(:)
!
else
!
dsrc(:) = src(:)
!
endif
!
nsrc = size(src)
!
select case(trim(molec%coords_transform))
case default
write (out,"('ML_coordinate_transform_XY2: coord. type ',a,' unknown')") trim(molec%coords_transform)
stop 'ML_coordinate_transform_XY2 - bad coord. type'
!
case('C2V-SYMMETRY')
!
c_t = reshape( &
(/1.0_ark/sqrt2, 1.0_ark/sqrt2 , 0.0_ark , & ! 1
1.0_ark/sqrt2,-1.0_ark/sqrt2 , 0.0_ark , & ! 3
0.0_ark , 0.0_ark , 1.0_ark/) , & ! 2
(/3,3/))
!
if (direct) then
dst = matmul(c_t,dsrc)
else
dst = matmul(transpose(c_t),dsrc)
dst(:) = dst(:) + molec%local_eq(:)
endif
!
case('R-RHO','R-RHO-Z','R-RHO-Z-ECKART')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = pi-src(3)
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = pi-src(3)
endif
!
case('R-RHO-HALF')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = (pi-src(3))*0.5_ark
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = pi-src(3)*2.0_ark
endif
!
case('R-PHI-RHO','R-PHI-RHO-Z')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = src(4)
dst(4) = src(3)
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = src(4)
dst(4) = src(3)
endif
!
case('R1-R2-Y+X')
!
if (direct) then
!
dst(1:2) = dsrc(1:2)
!
dst(3) =-src(4)-molec%local_eq(3)
dst(4) = src(3)-molec%local_eq(4)
!
else
!
dst(1:2) = src(1:2)+molec%local_eq(1:2)
!
dst(3) = src(4)+molec%local_eq(4)
dst(4) =-src(3)-molec%local_eq(3)
!
endif
!
case('R-PHI1-PHI2','R-PHI1-PHI2-Z','R1-R2-PHI1-PHI2-Z')
!
if (direct) then
dst(1:4) = dsrc(1:4)
else
dst(1:4) = src(1:4)+molec%local_eq(1:4)
endif
!
case('R-ALPHA-THETA-Z')
!
alpha0 = pi-asin( sqrt( sin(molec%taueq(1))**2+sin(molec%taueq(2))**2 ))
q0 = sqrt(molec%taueq(1)**2+molec%taueq(2)**2 )
!
if (direct) then
dst(1:2) = dsrc(1:2)
q1 = src(3)
q2 = src(4)
dst(3) = sqrt(q1**2+q2**2) - q0
dst(4) = atan2(q2,q1)
!
else
q = src(3)+q0
theta = src(4)
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = q*cos(theta)
dst(4) = q*sin(theta)
endif
!
case('R-S1-S2','R-S1-S2-Z')
!
if (direct) then
dst(1:2) = dsrc(1:2)
!
dst(3) = (dsrc(3)-dsrc(4))/sqrt(2.0_ark)
dst(4) = (dsrc(3)+dsrc(4))/sqrt(2.0_ark)
!
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
!
dst(3) = (src(3)+src(4))/sqrt(2.0_ark)+molec%local_eq(3)
dst(4) = (src(4)-src(3))/sqrt(2.0_ark)+molec%local_eq(4)
!
endif
!
case('R-PHI1','R-PHI1-Z')
!
if (direct) then
dst(1:3) = dsrc(1:3)
else
dst(1:3) = src(1:3)+molec%local_eq(1:3)
endif
!
case('R12-R')
!
if (direct) then
!
r1 = src(1) ; r2 = src(2) ; alpha = src(3)
!
r12 = sqrt(r1**2+r2**2-2.0_ark*r1*r2*cos(alpha))
!
!sinalpha = r1/r12*sin(alpha)
!alpha1 = 0
!if (sinalpha>small_) alpha1 = asin(sinalpha)
!!
!sinalpha = r2/r12*sin(alpha)
!alpha2 = 0
!if (sinalpha>small_) alpha2 = asin(sinalpha)
!
R = 0.5_ark*sqrt(r1**2+r2**2+2.0_ark*r1*r2*cos(alpha))
!
!sintheta = r1/R*sin(alpha2)
!theta = 0
!
!if ( abs(sintheta)>1.0_ark+sqrt(small_) ) then
! !
! write (out,"('MLpoten_xy2_R_R12_theta: sintheta>1: ',f18.8)") sintheta
! stop 'MLpoten_xy2_R_R12_theta - bad sintheta'
! !
!elseif ( sintheta>=1.0_ark) then
! theta = 0.5_ark*pi
!else
! theta = asin(sintheta)
!endif
!
r12e = ML_MEP_xy2_R12_R(R)
!
!r12e = sqrt(2.0_ark*molec%local_eq(1)**2-2.0_ark*molec%local_eq(1)**2*cos(molec%local_eq(3)))
!
dst(1) = r12 -r12e
dst(2) = (r1-r2)*0.5_ark
dst(3) = R
!
else
!
R = src(3)
!
r12e = ML_MEP_xy2_R12_R(R)
!
!r12e = sqrt(2.0_ark*molec%local_eq(1)**2-2.0_ark*molec%local_eq(1)**2*cos(molec%local_eq(3)))
!
!theta = src(2) + pi*0.5_ark
!
r12 = src(1) + r12e
!
r1 = sqrt(R**2-src(2)**2+0.25_ark*r12**2)+src(2)
r2 = sqrt(R**2-src(2)**2+0.25_ark*r12**2)-src(2)
!
!r1 = sqrt(R**2+0.25_ark*r12**2-R*r12*cos(theta))
!r2 = sqrt(R**2+0.25_ark*r12**2+R*r12*cos(theta))
!
cosalpha = (r1**2+r2**2-r12**2)/(2.0_ark*r1*r2)
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
alpha = 0
else
alpha = acos(cosalpha)
endif
!
dst(1) = r1
dst(2) = r2
dst(3) = alpha
!
endif
!
case('R-R-R')
!
if (direct) then
!
r1 = src(1) ; r2 = src(2) ; alpha = src(3)
!
r3 = sqrt(r1**2+r2**2-2.0_ark*r1*r2*cos(alpha))
!
dst(1) = r1-molec%local_eq(1)
dst(2) = r2-molec%local_eq(1)
dst(3) = r3-molec%local_eq(1)
!
else
!
r1 = src(1)+molec%local_eq(1)
r2 = src(2)+molec%local_eq(1)
r3 = src(3)+molec%local_eq(1)
!R = src(3)+molec%local_eq(1)
!
cosalpha = (r1**2+r2**2-r3**2)/(2.0_ark*r1*r2)
!
dst(1) = r1
dst(2) = r2
dst(3) = acos(cosalpha)
!
endif
!
case('R12-RHO')
!
if (direct) then
!
r1 = src(1) ; r2 = src(2) ; alpha = src(3)
!
r12e = ML_MEP_xy2_R12_ALPHA(alpha)
!
dst(1) = r1-r12e
dst(2) = r2-r12e
dst(3) = pi-alpha
!
else
!
alpha = pi-src(3)
!
r12e = ML_MEP_xy2_R12_ALPHA(alpha)
!
r1 = src(1) + r12e
r2 = src(2) + r12e
!
dst(1) = r1
dst(2) = r2
dst(3) = alpha
!
endif
!
case('R13-RHO')
!
if (direct) then
!
r1 = src(1) ; r2 = src(2) ; alpha = src(3)
!
r13e = ML_MEP_xy2_R13_ALPHA(alpha)
r12e = 0.5_ark*r13e/sin(alpha*0.5_ark)
!
dst(1) = r1-r12e
dst(2) = r2-r12e
dst(3) = pi-alpha
!
else
!
alpha = pi-src(3)
!
r13e = ML_MEP_xy2_R13_ALPHA(alpha)
r12e = 0.5_ark*r13e/sin(alpha*0.5_ark)
!
r1 = src(1) + r12e
r2 = src(2) + r12e
!
dst(1) = r1
dst(2) = r2
dst(3) = alpha
!
endif
!
case('R12-R-LIN')
!
if (direct) then
!
r1 = src(1) ; r2 = src(2) ; alpha = src(3)
!
r12 = sqrt(r1**2+r2**2-2.0_ark*r1*r2*cos(alpha))
!
R = 0.5_ark*sqrt(r1**2+r2**2+2.0_ark*r1*r2*cos(alpha))
!
!r1x = 0.5_ark*r1*r2*sin(alpha)/R
!r1y = 0.5_ark*r1*(r1+r2*cos(alpha))/R
!r2x =-0.5_ark*r1*r2*sin(alpha)/R
!r2y = 0.5_ark*r2*(r2+r1*cos(alpha))/R
!
r12e = ML_MEP_xy2_R12_R(R)
!
!r12e = sqrt(2.0_ark*molec%local_eq(1)**2-2.0_ark*molec%local_eq(1)**2*cos(molec%local_eq(3)))
!
!dst(1) = r1x-0.5_ark*r12e-(r2x+0.5_ark*r12e)
dst(2) = (r1-r2)*0.5_ark
dst(3) = R
!
else
!
R = src(3)
!
r12e = ML_MEP_xy2_R12_R(R)
!
!r12e = sqrt(2.0_ark*molec%local_eq(1)**2-2.0_ark*molec%local_eq(1)**2*cos(molec%local_eq(3)))
!
!theta = src(2) + pi*0.5_ark
!
r12 = src(1) + r12e
!
r1 = sqrt(R**2-src(2)**2+0.25_ark*r12**2)+src(2)
r2 = sqrt(R**2-src(2)**2+0.25_ark*r12**2)-src(2)
!
!r1 = sqrt(R**2+0.25_ark*r12**2-R*r12*cos(theta))
!r2 = sqrt(R**2+0.25_ark*r12**2+R*r12*cos(theta))
!
cosalpha = (r1**2+r2**2-r12**2)/(2.0_ark*r1*r2)
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
alpha = 0
else
alpha = acos(cosalpha)
endif
!
dst(1) = r1
dst(2) = r2
dst(3) = alpha
!
endif
!
case('R-EXPRHO')
!
if (direct) then
!
dst(1:2) = dsrc(1:2)
!
rho = max(pi-src(3),small_)
!
dst(3) = log(rho)
!
!dst(3) = (1.0_ark+rho**2)/rho
!
else
!
dst(1:2) = src(1:2)+molec%local_eq(1:2)
!
rho = exp(src(3))
!
!rho = (src(3))**(0.1)
!
!rho = 0.5_ark*(src(3)-sqrt( src(3)**2-4.0_ark ))
!
dst(3) = pi-rho
!
endif
!
case('RADAU-R-ALPHA-Z')
!
m1 = molec%AtomMasses(2) ; m2 = molec%AtomMasses(3) ; m3 = molec%AtomMasses(1)
!
a0=sqrt(m3/(m1+m2+m3))
!
r_e1(1) = molec%local_eq(1)
r_e1(2) = 0
!
r_e2(1) = molec%local_eq(2)*cos(molec%local_eq(3))
r_e2(2) = molec%local_eq(2)*sin(molec%local_eq(3))
!
radau_e1(:) = ( 1.0_ark+(a0-1.0_ark)*m1/(m1+m2) )*r_e1(:)+(a0-1.0_ark)*m2/(m1+m2)*r_e2(:)
radau_e2(:) = ( 1.0_ark+(a0-1.0_ark)*m2/(m1+m2) )*r_e2(:)+(a0-1.0_ark)*m1/(m1+m2)*r_e1(:)
!
radau_e(1) = sqrt( sum( radau_e1(:)**2 ) )
radau_e(2) = sqrt( sum( radau_e2(:)**2 ) )
!
if (direct) then
!
alpha1 = src(3)
!
r_t1(1) = src(1)
r_t1(2) = 0
!
r_t2(1) = src(2)*cos(alpha1)
r_t2(2) = src(2)*sin(alpha1)
!
radau_t1(:) = ( 1.0_ark+(a0-1.0_ark)*m1/(m1+m2) )*r_t1(:)+(a0-1.0_ark)*m2/(m1+m2)*r_t2(:)
radau_t2(:) = ( 1.0_ark+(a0-1.0_ark)*m2/(m1+m2) )*r_t2(:)+(a0-1.0_ark)*m1/(m1+m2)*r_t1(:)
!
dst(1) = sqrt( sum( radau_t1(:)**2 ) )
dst(2) = sqrt( sum( radau_t2(:)**2 ) )
cosalpha = sum(radau_t1(:)*radau_t2(:) )/( dst(1)*dst(2) )
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
dst(3) = pi
else
dst(3) = pi-acos(cosalpha)
endif
!
dst(1) = dst(1)-radau_e(1)
dst(2) = dst(2)-radau_e(2)
!
!dst(3) = 1.0_ark+cosalpha
!
else
!
!alpha1 = acos(src(3)-1.0_ark)
alpha1 = pi-src(3)
!
dsrc(1:2) = src(1:2) + radau_e(1:2)
!
radau_t1(1) = dsrc(1)
radau_t1(2) = 0
!
radau_t2(1) = dsrc(2)*cos(alpha1)
radau_t2(2) = dsrc(2)*sin(alpha1)
!
r_t1(:) = ( 1.0_ark+(1.0_ark/a0-1.0_ark)*m1/(m1+m2) )*radau_t1(:)+(1.0_ark/a0-1.0_ark)*m2/(m1+m2)*radau_t2(:)
r_t2(:) = ( 1.0_ark+(1.0_ark/a0-1.0_ark)*m2/(m1+m2) )*radau_t2(:)+(1.0_ark/a0-1.0_ark)*m1/(m1+m2)*radau_t1(:)
!
dst(1) = sqrt( sum( r_t1(:)**2 ) )
dst(2) = sqrt( sum( r_t2(:)**2 ) )
cosalpha = sum(r_t1(:)*r_t2(:) )/( dst(1)*dst(2) )
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
dst(3) = 0.0_ark
else
dst(3) = acos(cosalpha)
endif
!
endif
!
case('RADAU')
!
m1 = molec%AtomMasses(2) ; m2 = molec%AtomMasses(3) ; m3 = molec%AtomMasses(1)
!
a0=sqrt(m3/(m1+m2+m3))
!
r_e1(1) = molec%local_eq(1)
r_e1(2) = 0
!
r_e2(1) = molec%local_eq(2)*cos(molec%local_eq(3))
r_e2(2) = molec%local_eq(2)*sin(molec%local_eq(3))
!
radau_e1(:) = ( 1.0_ark+(a0-1.0_ark)*m1/(m1+m2) )*r_e1(:)+(a0-1.0_ark)*m2/(m1+m2)*r_e2(:)
radau_e2(:) = ( 1.0_ark+(a0-1.0_ark)*m2/(m1+m2) )*r_e2(:)+(a0-1.0_ark)*m1/(m1+m2)*r_e1(:)
!
radau_e(1) = sqrt( sum( radau_e1(:)**2 ) )
radau_e(2) = sqrt( sum( radau_e2(:)**2 ) )
!
if (direct) then
!
alpha1 = src(3)
!
r_t1(1) = src(1)
r_t1(2) = 0
!
r_t2(1) = src(2)*cos(alpha1)
r_t2(2) = src(2)*sin(alpha1)
!
radau_t1(:) = ( 1.0_ark+(a0-1.0_ark)*m1/(m1+m2) )*r_t1(:)+(a0-1.0_ark)*m2/(m1+m2)*r_t2(:)
radau_t2(:) = ( 1.0_ark+(a0-1.0_ark)*m2/(m1+m2) )*r_t2(:)+(a0-1.0_ark)*m1/(m1+m2)*r_t1(:)
!
dst(1) = sqrt( sum( radau_t1(:)**2 ) )
dst(2) = sqrt( sum( radau_t2(:)**2 ) )
cosalpha = sum(radau_t1(:)*radau_t2(:) )/( dst(1)*dst(2) )
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
dst(3) = pi
else
dst(3) = pi-acos(cosalpha)
endif
!
dst(1) = dst(1)-radau_e(1)
dst(2) = dst(2)-radau_e(2)
!
!dst(3) = 1.0_ark+cosalpha
!
else
!
!alpha1 = acos(src(3)-1.0_ark)
alpha1 = pi-src(3)
!
dsrc(1:2) = src(1:2) + radau_e(1:2)
!
radau_t1(1) = dsrc(1)
radau_t1(2) = 0
!
radau_t2(1) = dsrc(2)*cos(alpha1)
radau_t2(1) = dsrc(2)*sin(alpha1)
!
r_t1(:) = ( 1.0_ark+(1.0_ark/a0-1.0_ark)*m1/(m1+m2) )*radau_t1(:)+(1.0_ark/a0-1.0_ark)*m2/(m1+m2)*radau_t2(:)
r_t2(:) = ( 1.0_ark+(1.0_ark/a0-1.0_ark)*m2/(m1+m2) )*radau_t2(:)+(1.0_ark/a0-1.0_ark)*m1/(m1+m2)*radau_t1(:)
!
dst(1) = sqrt( sum( r_t1(:)**2 ) )
dst(2) = sqrt( sum( r_t2(:)**2 ) )
cosalpha = sum(r_t1(:)*r_t2(:) )/( dst(1)*dst(2) )
!
if ( abs(cosalpha)>1.0_ark+sqrt(small_) ) then
!
write (out,"('ML_coordinate_transform_XY2: cosalpha>1: ',f18.8)") cosalpha
stop 'ML_coordinate_transform_XY2 - bad cosalpha'
!
elseif ( cosalpha>=1.0_ark) then
dst(3) = 0.0_ark
else
dst(3) = acos(cosalpha)
endif
!
endif
!
case('R-LINRHO')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = pi-src(3)-molec%local_eq(3)
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = pi-(src(3)+molec%local_eq(3))
endif
!
case('R1-Z-R2-RHO','R1-Z-R2-RHO-ECKART')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = pi-src(3)
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = pi-src(3)
endif
!
case('R1-Z-R2-ALPHA')
!
if (direct) then
dst(1:2) = dsrc(1:2)
dst(3) = dsrc(3)
else
dst(1:2) = src(1:2)+molec%local_eq(1:2)
dst(3) = src(3)+molec%local_eq(3)
endif
!
end select
!
!
if (verbose>=5) write(out,"('ML_coordinate_transform_XY2/end')")
!
!
end function ML_coordinate_transform_XY2
! Here we define structural parameters for an XY2 molecule,
! a0/b0
! which determine the reference geometry
!
subroutine ML_b0_XY2(Npoints,Natoms,b0,rho_i,rho_ref,rho_borders)
!
integer(ik),intent(in) :: Npoints,Natoms
!
real(ark), intent(out) :: b0(molec%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) :: re13,m1,m2,m3,rho,m,rho0,re23,u2,u3,u23,e,r12,alphaR,R0
real(ark) :: alpha,alphae_h,a02,cosa,a,b,g1,g2,rot(3,3),alphaeq
real(ark) :: rho_ark,alpha_ark,transform(3,3),CM_shift,a_t,a0(molec%Natoms,3),phi
real(ark) :: tmat(3,3),transform0(3,3),transform1(3,3),sinrho,hx,hy,unit(3),tanphi,Inert(3),tau
integer(ik) :: i,Nbonds,ix,jx
integer(ik) :: ijk(3,2),ioper,Nangles,iatom
character(cl) :: method
!
!
if (verbose>=4) write(out,"('ML_b0_XY2/start')")
!
if (natoms/=molec%Natoms) stop 'Illegal number of atoms'
!
Nbonds = molec%Nbonds
Nangles = molec%Nangles
!
if (Nbonds/=2) then
write(out,"('ML_b0_XY2: Nbonds must be 2 in this routine, not ',i9)") Nbonds
stop 'ML_a0_XY2: wrong Nbonds '
endif
!
if (Natoms/=3) then
write(out,"('ML_b0_XY2: Natoms must be 3 in this routine, not ',i9)") Natoms
stop 'ML_a0_XY2: wrong Natoms '
endif
!if (molec%req(1)/=molec%req(2)) then
! write(out,"('ML_b0_XY2: req-s must be equal: ',3f14.6)") molec%req(1:2)
! stop 'ML_a0_XY2: req-s must be equal: '
!endif
!
re13 = molec%req(1)
re23 = molec%req(2)
!
if (Nangles>0) then
alphaeq = molec%alphaeq(1)
elseif (molec%Ndihedrals>1) then
!alphaeq = pi-(molec%taueq(1)**2+molec%taueq(2)**2) !asin(sin(molec%taueq(1))*sqrt(2.0_ark))
!
alphaeq = pi-asin(sqrt(molec%taueq(1)**2+molec%taueq(2)**2))
!
else
alphaeq = pi-molec%taueq(1)
endif
alphae_h = alphaeq*0.5_ark
!
m1 = molec%AtomMasses(1) ; m2 = molec%AtomMasses(2) ; m3 = molec%AtomMasses(3)
!
m = m1+m2+m3
!
u3 =m3*(m2+m1)*re13**2
u2 =m2*(m1+m3)*re23**2
u23=m3*m2*re13*re23
!
b0(1,1,0) = 0.0_ark
b0(1,2,0) = 0.0_ark
b0(1,3,0) = 2.0_ark*m3/m*re13*cos(alphae_h)
!
b0(2,1,0) =-re13*sin(alphae_h)
b0(2,2,0) = 0.0_ark
b0(2,3,0) =-m1/m*re13*cos(alphae_h)
!
b0(3,1,0) = re13*sin(alphae_h)
b0(3,2,0) = 0.0_ark
b0(3,3,0) =-m1/m*re13*cos(alphae_h)
!
rho = pi - alphaeq
!
! Sayvetz :
!
!e = rho*0.5_ark+(u3-u2)/sqrt((u3+u2)**2-4.0_ark*u23**2)*atan(sqrt((u3+u2-2.0_ark*u23)/(u3+u2+2*u23))*tan(rho*0.5_ark))
!
!b0(3,2,0) = 0
!b0(1,2,0) = 0
!b0(2,2,0) = 0
!
!b0(3,3,0) = (m2+m1)/m*re13*sin(rho-e)-m2/m*re23*sin(e)
!b0(1,3,0) = -m3/m*re13*sin(rho-e)-m2/m*re23*sin(e)
!b0(2,3,0) = (m1+m3)/m*re23*sin(e)-m3/m*re13*sin(rho-e)
!
!b0(3,1,0) =-(m2+m1)/m*re13*cos(rho-e)-m2/m*re23*cos(e)
!b0(1,1,0) = m3/m*re13*cos(rho-e)-m2/m*re23*cos(e)
!b0(2,1,0) = (m1+m3)/m*re23*cos(e)+m3/m*re13*cos(rho-e)
select case(trim(molec%coords_transform))
case default
!
case('R-RHO-Z','R-PHI-RHO-Z','R-RHO-Z-ECKART','R-RHO-HALF')
!
if (Nangles>0) then
alphaeq = molec%alphaeq(1)
elseif (molec%Ndihedrals>1) then
alphaeq = pi+(-molec%taueq(1)+molec%taueq(2)) !asin(sin(molec%taueq(1))*sqrt(2.0_ark))
else
alphaeq = pi-molec%taueq(1)
endif
alphae_h = alphaeq*0.5_ark
!
b0(1,3,0) = 0.0_ark
b0(1,2,0) = 0.0_ark
b0(1,1,0) = 2.0_ark*m3/m*re13*cos(alphae_h)
!
b0(2,3,0) =-re13*sin(alphae_h)
b0(2,2,0) = 0.0_ark
b0(2,1,0) =-m1/m*re13*cos(alphae_h)
!
b0(3,3,0) = re13*sin(alphae_h)
b0(3,2,0) = 0.0_ark
b0(3,1,0) =-m1/m*re13*cos(alphae_h)
!
case('RADAU-R-ALPHA-Z')
!
if (Nangles>0) then
alphaeq = molec%alphaeq(1)
elseif (molec%Ndihedrals>1) then
alphaeq = pi+(-molec%taueq(1)+molec%taueq(2))
else
alphaeq = pi-molec%taueq(1)
endif
!
alphaR = acos((cos(alphaeq)*m1-m2)/(m1+m2))
!
alphae_h = alphaR*0.5_ark
!
R0 = re13*sqrt(m1/(m2*cos(alphaR)+m2+m1))
!
b0(1,3,0) = 0.0_ark
b0(1,2,0) = 0.0_ark
b0(1,1,0) = R0*cos(alphae_h)*( sqrt(M/m1)-1.0_ark )
!
b0(2,3,0) = R0*sin(alphae_h)
b0(2,2,0) = 0.0_ark
b0(2,1,0) =-R0*cos(alphae_h)
!
b0(3,3,0) =-R0*sin(alphae_h)
b0(3,2,0) = 0.0_ark
b0(3,1,0) =-R0*cos(alphae_h)
!
do i = 1,3
CM_shift = sum(b0(:,i,0)*molec%AtomMasses(:))/sum(molec%AtomMasses(:))
b0(:,i,0) = b0(:,i,0) - CM_shift
enddo
!
case('R1-R2-Y+X')
!
if (Nangles>0) then
alphaeq = molec%alphaeq(1)
elseif (molec%Ndihedrals>1) then
alphaeq = pi-asin(sqrt(molec%taueq(1)**2+molec%taueq(2)**2))
else
alphaeq = pi-molec%taueq(1)
endif
!
tau = pi*0.25_ark
alphae_h = alphaeq*0.5_ark
!
b0(1,3,0) = 0.0_ark
b0(1,2,0) = 2.0_ark*m3/m*re13*cos(alphae_h)*sin(tau)
b0(1,1,0) = 2.0_ark*m3/m*re13*cos(alphae_h)*cos(tau)
!
b0(2,3,0) =-re13*sin(alphae_h)
b0(2,2,0) =-m1/m*re13*cos(alphae_h)*sin(tau)
b0(2,1,0) =-m1/m*re13*cos(alphae_h)*cos(tau)
!
b0(3,3,0) = re13*sin(alphae_h)
b0(3,2,0) =-m1/m*re13*cos(alphae_h)*sin(tau)
b0(3,1,0) =-m1/m*re13*cos(alphae_h)*cos(tau)
!
case('R-PHI1-PHI2-Z','R-PHI1-Z','R-S1-S2-Z','R-ALPHA-THETA-Z')
!
if (Nangles>0) then
alphaeq = molec%alphaeq(1)
elseif (molec%Ndihedrals>1) then
!alphaeq = pi-(molec%taueq(1)+molec%taueq(2)) !asin(sin(molec%taueq(1))*sqrt(2.0_ark))
alphaeq = pi-asin( sqrt( sin(molec%taueq(1))**2+sin(molec%taueq(2))**2 ))
else
alphaeq = pi-molec%taueq(1)
endif
alphae_h = alphaeq*0.5_ark
!
b0(1,3,0) = 0.0_ark
b0(1,2,0) = 0.0_ark
b0(1,1,0) = 2.0_ark*m3/m*re13*cos(alphae_h)
!
b0(2,3,0) =-re13*sin(alphae_h)
b0(2,2,0) = 0.0_ark
b0(2,1,0) =-m1/m*re13*cos(alphae_h)
!
b0(3,3,0) = re13*sin(alphae_h)
b0(3,2,0) = 0.0_ark
b0(3,1,0) =-m1/m*re13*cos(alphae_h)
!
!a0(:,:) = b0(:,:,0)
!
!b0(:,1,0) = sqrt(0.5_ark)*( a0(:,1)+a0(:,2) )
!b0(:,2,0) = sqrt(0.5_ark)*( a0(:,1)-a0(:,2) )
!
case('R1-Z-R2-ALPHA','R1-Z-R2-RHO','R1-Z-R2-RHO-ECKART','R1-R2-PHI1-PHI2-Z')
!
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) = re13
!
b0(3,1,0) = re23*sin(alphaeq)
b0(3,2,0) = 0.0_ark
b0(3,3,0) = re23*cos(alphaeq)
!
do i = 1,3
CM_shift = sum(b0(:,i,0)*molec%AtomMasses(:))/sum(molec%AtomMasses(:))
b0(:,i,0) = b0(:,i,0) - CM_shift
enddo
!
case('R1-R2-ALPHA-Z')
!
if (all(molec%AtomMasses(2:3)==m2).and.re13==re23) then
stop 'R1-R2-ALPHA-Z is not meant for symmeitric XY2 molecules'
endif
!
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) = re13
!
b0(3,1,0) = re23*sin(alphaeq)
b0(3,2,0) = 0.0_ark
b0(3,3,0) = re23*cos(alphaeq)
!
do i = 1,3
CM_shift = sum(b0(:,i,0)*molec%AtomMasses(:))/sum(molec%AtomMasses(:))
b0(:,i,0) = b0(:,i,0) - CM_shift
enddo
!
call MLorienting_a0(molec%Natoms,molec%AtomMasses,b0(:,:,0),transform)
!
Inert(1) = sum(molec%AtomMasses(:)*( b0(:,2,0)**2+ b0(:,3,0)**2) )
Inert(2) = sum(molec%AtomMasses(:)*( b0(:,1,0)**2+ b0(:,3,0)**2) )
Inert(3) = sum(molec%AtomMasses(:)*( b0(:,1,0)**2+ b0(:,2,0)**2) )
!
! Second Eckart equation
!
do ix = 1,3
do jx = 1,3
if (ix/=jx) then
!
a_t = sum(molec%AtomMasses(:)*b0(:,ix,0)*b0(:,jx,0) )
!
if (abs(a_t)>100.0_rk*small_) then
write(out,"('ML_b0_XY3: b0 is not a solution of Eckart 2 for ix,jx =',2i4,d18.8)") ix,jx,a_t
stop 'ML_b0_XY3: b0 is not solution of Eckart2'
endif
endif
enddo
!
enddo
!
end select
!
!
! define the rho-type coordinate
!
! We can also simulate the reference structure at each point of rho, if npoints presented
!
if (Npoints/=0) then
!
!if (.not.present(rho_borders).or..not.present(rho_ref)) then
! write(out,"('ML_b0_XY2: rho_borders and rho_ref must be presented if Npoints ne 0 ')")
! stop 'ML_b0_XY2: rho_borders or rho_ref not specified '
!endif
!
select case(trim(molec%coords_transform))
case default
write (out,"('ML_b0_XY2: coord. type ',a,' unknown')") trim(molec%coords_transform)
stop 'ML_b0_XY2 - bad coord. type'
!
case('LINEAR')
!
rho_ref = alphaeq
rho0 = rho_ref
a02 = (m1/m)
!
case('DX-RHO')
!
rho_ref = alphaeq
rho0 = 0.0
a02 = (m1/m)
!
case('R-RHO','R-EXPRHO','R-RHO-Z','R12-R','R12-RHO','R13-RHO','R-PHI-RHO','R-PHI-RHO-Z','R-PHI1-PHI2-Z','R-PHI1-Z',&
'R-S1-S2-Z','R-ALPHA-THETA-Z','R-RHO-Z-ECKART')
!
rho_ref = 0.0_ark
rho0 = 0.0_ark
a02 = (m1/m)
!
case('R-RHO-HALF')
!
rho_ref = 0.0_ark
rho0 = 0.0_ark
a02 = (m1/m)
!
case('RADAU','RADAU-R-ALPHA-Z')
!
rho_ref = 0.0_ark
rho0 = 0.0_ark
a02 = (m1/m)
!
a = sqrt(m3 / m)
b = m2 / (m1+m2)
g1 = 1.0_ark - a / (a+b-a*b)
g2 = 1.0_ark - a / (1.0_ark-b+a*b)
!
case('R1-Z-R2-RHO','R1-Z-R2-ALPHA','R1-Z-R2-RHO-ECKART','R1-R2-PHI1-PHI2-Z')
!
rho_ref = 0.0_ark
rho0 = 0.0_ark
!
end select
!
if ( rho0+rho_borders(1)<0.0.or.rho0+rho_borders(2)>pi) then
write(out,"('ML_b0_XY2: rho_borders exceed the [0,pi] interval: ',2f12.4)") (rho0+rho_borders(1:2))*rad
!stop 'ML_b0_XY2: rho_borders exceed 0..pi '
endif
do i = 0,npoints
!
rho = rho0+rho_i(i)
!
alpha = rho
!
select case(trim(molec%coords_transform))
case ('R-RHO','R12-RHO','R13-RHO','R-RHO-Z','R-PHI-RHO','R-PHI-RHO-Z',&
'R1-Z-R2-RHO','R-RHO-Z-ECKART','R1-Z-R2-RHO-ECKART','RADAU-R-ALPHA-Z')
alpha = pi-rho
case('R-RHO-HALF')
alpha = pi-rho*2.0_ark
end select
!
if(trim(molec%coords_transform)=='R-EXPRHO') alpha = pi-exp(rho)
!
!if(trim(molec%coords_transform)=='R-EXPRHO') alpha = pi-log(rho)
!
!if(trim(molec%coords_transform)=='R-EXPRHO') alpha = pi-(1.0_ark+rho**2)/(max(rho,small_))
!
if(trim(molec%coords_transform)=='RADAU') then
!
!
!f1= 1.0_ark/g1
!f2= 1.0_ark/g2
!f12= 1.0_ark - f1*f2