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mol_ch3oh.f90
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mol_ch3oh.f90
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!
! This unit defines all specific routines for a fouratomic molecule of ch3oh type
!
module mol_ch3oh
use accuracy
use moltype
use lapack
use pot_ch3oh, only : ML_CH3OH_MEP_geometry
implicit none
public ML_b0_ch3oh,ML_coordinate_transform_ch3oh
!
private
integer(ik), parameter :: verbose = 5 ! Verbosity level
!
contains
!
! Procedures to define ch3oh
!
function ML_coordinate_transform_ch3oh(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) :: dsrc(size(src))
real(ark) :: tau,rref(12,0:4),r_eq(12),r_t(12),xi_eq(12)
integer(ik) :: i0,nsrc, k(0:4),n(0:4),icoord
real(ark) :: beta(3),alpha(3),cosa(3),phi1,phi2,phi3,chi1,chi2,chi3
real(ark) :: alpha0(3),cosa0(3),phi(3),chi(3),coschi(3)
!
if (verbose>=7) write(out,"('ML_coordinate_transform_ch3oh/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,"('MLcoordinate_transform_func: coord. type ',a,' unknown')") trim(molec%coords_transform)
stop 'MLcoordinate_transform_func - bad coord. type'
!
case('R-TAU-BOWMAN-REF')
!
if (direct) then
!
alpha(3) = src( 9)
alpha(2) = src(11)
!
beta(1) = src(7)
beta(2) = src(8)
beta(3) = src(10)
!
cosa(2) = ( cos(alpha(2))-cos(beta(3))*cos(beta(1)) )/( sin(beta(3))*sin(beta(1)) )
cosa(3) = ( cos(alpha(3))-cos(beta(2))*cos(beta(1)) )/( sin(beta(2))*sin(beta(1)) )
!
chi2 =-acos(cosa(2))
chi3 = acos(cosa(3))
!
chi1 = 2.0_ark*pi-(-chi2+chi3)
!
tau = src(12)+(chi2+chi3)/3.0_ark
!
else
!
tau = src(12)
!
endif
!
case('R-TAU-CHI')
!
if (direct) then
!
!
phi1 = src(10)
phi2 = src(11)
phi3 = src(12)
!
if (phi2>2.0_ark/3.0_ark*pi) phi2 = phi2-2.0_ark*pi
!
tau = 1.0_ark/3.0_ark*( phi1+phi2+phi3 )
!
else
!
tau = src(12)
!
endif
!
end select
!
call ML_CH3OH_MEP_geometry(tau,r_eq(1),r_eq(2),r_eq(6),r_eq(3),r_eq(4),r_eq(5),beta(1),beta(2),beta(3),&
alpha(1),alpha(2),alpha(3),phi(1),phi(2),phi(3),chi(1),chi(2),chi(3))
!
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-TAU-CHI')
!
xi_eq(1:2) = r_eq(1:2)
xi_eq( 3) = 1.0_ark/sqrt(3.0_ark)*( r_eq(3)+r_eq(4)+r_eq(5) )
xi_eq( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*r_eq(3)-r_eq(4)-r_eq(5) )
xi_eq( 5) = 1.0_ark/sqrt(2.0_ark)*( r_eq(4)-r_eq(5) )
!
xi_eq(6) = r_eq(6)
!
xi_eq( 7) = 1.0_ark/sqrt(3.0_ark)*( beta(1)+beta(2)+beta(3) )
xi_eq( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*beta(1)-beta(2)-beta(3) )
xi_eq( 9) = 1.0_ark/sqrt(2.0_ark)*( beta(2)-beta(3) )
!
xi_eq(10) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*chi(1)-chi(2)-chi(3) )
xi_eq(11) = 1.0_ark/sqrt(2.0_ark)*( chi(2)-chi(3) )
xi_eq(12) = tau
!
if (direct) then
!
dst(1:2) = src(1:2)
!
dst( 3) = 1.0_ark/sqrt(3.0_ark)*( src(3)+src(4)+src(5) )
dst( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(3)-src(4)-src(5) )
dst( 5) = 1.0_ark/sqrt(2.0_ark)*( src(4)-src(5) )
!
dst( 6) = src(6)
!
dst( 7) = 1.0_ark/sqrt(3.0_ark)*( src(7)+src(8)+src(9) )
dst( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(7)-src(8)-src(9) )
dst( 9) = 1.0_ark/sqrt(2.0_ark)*( src(8)-src(9) )
!
beta(1) = src(7)
beta(2) = src(8)
beta(3) = src(9)
!
cosa(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( phi2 - phi3 )
cosa(2) = cos( beta(3) )*cos( beta(1) ) + sin( beta(3) )*sin( beta(1) )*cos( phi3 - phi1 )
cosa(3) = cos( beta(1) )*cos( beta(2) ) + sin( beta(1) )*sin( beta(2) )*cos( phi1 - phi2 )
!
if ( any(abs(cosa(:))>1.0_ark+sqrt(small_))) then
!
write (out,"('ML_coordinate_transform_ch3oh: cosalpha>1: ',3f18.8)") cosa(1:3)
write (out,"('Consider change coordinate type ')")
stop 'MLcoordinate_transform_func - bad cos(alpha)'
endif
!
cosa(:) = max(-1.0_ark,cosa(:))
cosa(:) = min( 1.0_ark,cosa(:))
!
alpha(:) = acos(cosa(:))
!
coschi(1) = ( cos(alpha(1))-cos(beta(2))*cos(beta(3)) )/( sin(beta(2))*sin(beta(3)) )
coschi(2) = ( cos(alpha(2))-cos(beta(3))*cos(beta(1)) )/( sin(beta(3))*sin(beta(1)) )
coschi(3) = ( cos(alpha(3))-cos(beta(2))*cos(beta(1)) )/( sin(beta(2))*sin(beta(1)) )
!
chi(:) = acos(coschi(:))
!
dst(10) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*chi(1)-chi(2)-chi(3) )
dst(11) = 1.0_ark/sqrt(2.0_ark)*( chi(2)-chi(3) )
dst(12) = tau
!
dst(1:11) = dst(1:11)-xi_eq(1:11)
!
else ! not direct
!
r_t(12) = tau
!
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
r_t(1:11) = src(1:11)+xi_eq(1:11)
!
dst(1:2) = r_t(1:2)
!
dst(3) =(sqrt(2.0_ark)*r_t(3)+2.0_ark*r_t(4) )/sqrt(6.0_ark)
dst(4) =(sqrt(2.0_ark)*r_t(3)- r_t(4)+sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
dst(5) =(sqrt(2.0_ark)*r_t(3)- r_t(4)-sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
!
dst(6) = r_t(6)
!
dst( 7) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
dst( 8) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
dst( 9) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!
beta(1) = dst(7)
beta(2) = dst(8)
beta(3) = dst(9)
!
call find_phi_from_beta(beta(1:3),r_t(10:12),phi(1:3))
!
dst(10:12) = phi(1:3)
!
endif
!
case('R-ALPHA-S-TAU-REF')
!
rref( 1,0:4) = molec%force( 1: 5)
rref( 2,0:4) = molec%force( 6:10)
rref( 3,0:4) = molec%force(11:15)
rref( 4,0:4) = molec%force(16:20)
rref( 5,0:4) = molec%force(21:25)
!
rref( 6,0:4) = molec%force(26:30)/rad
rref( 7,0:4) = molec%force(31:35)/rad
rref( 8,0:4) = molec%force(36:40)/rad
rref( 9,0:4) = molec%force(41:45)/rad
!
rref(10,0:4) = molec%force(46:50)/rad
rref(11,0:4) = molec%force(51:55)/rad
rref(12,0:4) = molec%force(56:60)/rad
!
!
if (direct) then
!
dsrc(10) = src(10)
if (dsrc(10)>2.0_ark*pi-sqrt(small_)) dsrc(10) = dsrc(10)-2.0_ark*pi
if (dsrc(10)<-sqrt(small_)) dsrc(10) = dsrc(10)+2.0_ark*pi
!
dsrc(11) = src(11)
if (dsrc(11)-rref(11,1)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
if (dsrc(11)-rref(11,1)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
dsrc(12) = src(12)
if (dsrc(12)-rref(12,1)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
if (dsrc(12)-rref(12,1)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
tau = 1.0_ark/3.0_ark*( dsrc(10)+dsrc(11)+dsrc(12) )
!
!tau = tau - molec%local_eq(10)
!
!tau = src(10)
!
else ! not direct
!
tau = src(12)
!
endif
!
i0 = 0
!
do icoord = 1,9
!
n(0:4) = molec%pot_ind(11,i0+1:i0+5)
k(0:4) = molec%pot_ind(12,i0+1:i0+5)
!
if (all(n(:)==0)) then
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*cos(real(k(1:4),ark)*tau))
!
else
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*sin(real(n(1:4),ark)*tau))
!
endif
!
i0 = i0+5
!
enddo
!
xi_eq(10:11) = rref(10:11,0)
xi_eq(12) = rref(12,0) + tau
!
!xi_eq(1:6) = r_t(1:6)
!
!xi_eq(8) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
!xi_eq(9) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!xi_eq(7) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!
!xi_eq(10:11) = r_t(10:11) !tau+molec%local_eq(10)-molec%local_eq(11)
!xi_eq(12) = 0
!
!xi_eq(11) = tau+molec%local_eq(10)-molec%local_eq(12)
!
if (direct) then
!
dst(1:2) = src(1:2)
!
dst( 3) = 1.0_ark/sqrt(3.0_ark)*( src(3)+src(4)+src(5) )
dst( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(3)-src(4)-src(5) )
dst( 5) = 1.0_ark/sqrt(2.0_ark)*( src(4)-src(5) )
!
dst( 6) = src(6)
!
dst( 7) = 1.0_ark/sqrt(3.0_ark)*( src(7)+src(8)+src(9) )
dst( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(7)-src(8)-src(9) )
dst( 9) = 1.0_ark/sqrt(2.0_ark)*( src(8)-src(9) )
!
!dsrc(10) = src(10)
!
!dsrc(11) = src(11)
!if (dsrc(11)-molec%local_eq(11)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
!if (dsrc(11)-molec%local_eq(11)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
!dsrc(12) = src(12)
!if (dsrc(12)-molec%local_eq(12)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
!if (dsrc(12)-molec%local_eq(12)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
!dsrc(11) = mod(src(11),rref(11,0))+rref(11,0)
!dsrc(12) = mod(src(12),rref(12,0))+rref(12,0)
!
dst(10) = 1.0_ark/6.0_ark*( 2.0_ark*dsrc(10)-dsrc(11)-dsrc(12) )
if (dst(10)>pi) dst(10) = 2.0_ark*pi-dst(10)
dst(11) = 1.0_ark/2.0_ark*( dsrc(11)-dsrc(12) )
if (dst(11)>pi) dst(11) =-(2.0_ark*pi-dst(11))
dst(12) = tau
if (dst(12)>pi) dst(12) = 2.0_ark*pi-dst(12)
!
dst(1:11) = dst(1:11)-xi_eq(1:11)
!
!
else ! not direct
!
r_t(12) = tau
!
r_t(1:11) = src(1:11)+xi_eq(1:11)
!
dst(1:2) = r_t(1:2)
!
dst(3) =(sqrt(2.0_ark)*r_t(3)+2.0_ark*r_t(4) )/sqrt(6.0_ark)
dst(4) =(sqrt(2.0_ark)*r_t(3)- r_t(4)+sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
dst(5) =(sqrt(2.0_ark)*r_t(3)- r_t(4)-sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
!
dst(6) = r_t(6)
!
dst(7) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
dst(8) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
dst(9) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!
dst(10) =(r_t(12)+2.0_ark*r_t(10) )
dst(11) =(r_t(12)- r_t(10)+r_t(11))
dst(12) =(r_t(12)- r_t(10)-r_t(11))
!
if (dst(10)>2.0_ark*pi-sqrt(small_)) dst(10) = dst(10)-2.0_ark*pi
if (dst(10)<-sqrt(small_)) dst(10) = dst(10)+2.0_ark*pi
!if (dst(10)>pi) dst(10) = 2.0_ark*pi-dst(10)
!
if (dst(11)-molec%local_eq(11)>2.0_ark*pi-sqrt(small_)) dst(11) = dst(11)-2.0_ark*pi
if (dst(11)-molec%local_eq(11)<-sqrt(small_)) dst(11) = dst(11)+2.0_ark*pi
!if (dst(11)-molec%local_eq(11)>pi) dst(11) = 2.0_ark*pi-dst(11)
!
if (dst(12)-molec%local_eq(12)>2.0_ark*pi-sqrt(small_)) dst(12) = dst(12)-2.0_ark*pi
if (dst(12)-molec%local_eq(12)<-sqrt(small_)) dst(12) = dst(12)+2.0_ark*pi
!if (dst(12)-molec%local_eq(12)>pi) dst(12) = -(2.0_ark*pi-dst(12))
!
endif
!
case('R-TAU-BOWMAN-REF')
!
rref( 1,0:4) = molec%force( 1: 5)
rref( 2,0:4) = molec%force( 6:10)
rref( 3,0:4) = molec%force(11:15)
rref( 4,0:4) = molec%force(16:20)
rref( 5,0:4) = molec%force(21:25)
!
rref( 6,0:4) = molec%force(26:30)/rad
rref( 7,0:4) = molec%force(31:35)/rad
rref( 8,0:4) = molec%force(36:40)/rad
rref( 9,0:4) = molec%force(41:45)/rad
!
rref(10,0:4) = molec%force(46:50)/rad
rref(11,0:4) = molec%force(51:55)/rad
rref(12,0:4) = molec%force(56:60)/rad
!
if (direct) then
!
alpha(3) = src( 9)
alpha(2) = src(11)
!
beta(1) = src(7)
beta(2) = src(8)
beta(3) = src(10)
!
cosa(2) = ( cos(alpha(2))-cos(beta(3))*cos(beta(1)) )/( sin(beta(3))*sin(beta(1)) )
cosa(3) = ( cos(alpha(3))-cos(beta(2))*cos(beta(1)) )/( sin(beta(2))*sin(beta(1)) )
!
chi2 =-acos(cosa(2))
chi3 = acos(cosa(3))
!
chi1 = 2.0_ark*pi-(-chi2+chi3)
!
tau = src(12)+(chi2+chi3)/3.0_ark
!
else
!
tau = src(12)
!
endif
!
i0 = 0
!
do icoord = 1,9
!
n(0:4) = molec%pot_ind(11,i0+1:i0+5)
k(0:4) = molec%pot_ind(12,i0+1:i0+5)
!
if (all(n(:)==0)) then
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*cos(real(k(1:4),ark)*tau))
!
else
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*sin(real(n(1:4),ark)*tau))
!
endif
!
i0 = i0+5
!
enddo
!
xi_eq(10:11) = rref(10:11,0)
xi_eq(12) = rref(12,0) + tau
!
beta(1) = (sqrt(2.0_ark)*xi_eq(7)+2.0_ark*xi_eq(8) )/sqrt(6.0_ark)
beta(2) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)+sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
beta(3) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)-sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
!
phi1 = (xi_eq(12)+2.0_ark*xi_eq(10) )
phi2 = (xi_eq(12)- xi_eq(10)+xi_eq(11))
phi3 = (xi_eq(12)- xi_eq(10)-xi_eq(11))
!
cosa0(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( phi2 - phi3 )
cosa0(2) = cos( beta(3) )*cos( beta(1) ) + sin( beta(3) )*sin( beta(1) )*cos( phi3 - phi1 )
cosa0(3) = cos( beta(1) )*cos( beta(2) ) + sin( beta(1) )*sin( beta(2) )*cos( phi1 - phi2 )
!
if ( any(abs(cosa0(:))>1.0_ark+sqrt(small_))) then
!
write (out,"('ML_coordinate_transform_ch3oh: cosalpha0>1: ',3f18.8)") cosa0(1:3)
write (out,"('Consider change coordinate type ')")
stop 'MLcoordinate_transform_func - bad cos(alpha)'
endif
!
cosa0(:) = max(-1.0_ark,cosa0(:))
cosa0(:) = min( 1.0_ark,cosa0(:))
!
alpha0(:) = acos(cosa0(:))
!
!xi_eq(10) = (alpha0(2)+alpha0(3))/sqrt(2.0_ark)
!xi_eq(11) = (alpha0(2)-alpha0(3))/sqrt(2.0_ark)
!
xi_eq(10) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*alpha0(1)-alpha0(2)-alpha0(3) )
xi_eq(11) = 1.0_ark/sqrt(2.0_ark)*( alpha0(2)-alpha0(3) )
!
if (direct) then
!
dst(1:2) = src(1:2)
!
dst( 3) = 1.0_ark/sqrt(3.0_ark)*( src(3)+src(4)+src(5) )
dst( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(3)-src(4)-src(5) )
dst( 5) = 1.0_ark/sqrt(2.0_ark)*( src(4)-src(5) )
!
dst( 6) = src(6)
!
dst( 7) = 1.0_ark/sqrt(3.0_ark)*( src(7)+src(8)+src(10) )
dst( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(7)-src(8)-src(10) )
dst( 9) = 1.0_ark/sqrt(2.0_ark)*( src(8)-src(10) )
!
!dsrc(10) = src(10)
!
!dsrc(11) = src(11)
!if (dsrc(11)-molec%local_eq(11)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
!if (dsrc(11)-molec%local_eq(11)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
!dsrc(12) = src(12)
!if (dsrc(12)-molec%local_eq(12)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
!if (dsrc(12)-molec%local_eq(12)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
!dsrc(11) = mod(src(11),rref(11,0))+rref(11,0)
!dsrc(12) = mod(src(12),rref(12,0))+rref(12,0)
!
!dst(7) = dst(7) /sqrt(2.0_ark)-(alpha(1) +alpha(2) +alpha(3) )/sqrt(6.0_ark)
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
!dst(10) = (src( 9)+src(11))/sqrt(2.0_ark)
!dst(11) = (src( 9)-src(11))/sqrt(2.0_ark)
!
beta(1) = src(7)
beta(2) = src(8)
beta(3) = src(10)
!
cosa(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( chi1 )
!
alpha(1) = acos(cosa(1))
!
dst(10) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*alpha(1)-alpha(2)-alpha(3) )
dst(11) = 1.0_ark/sqrt(2.0_ark)*( alpha(2)-alpha(3) )
dst(12) = tau
!
dst(1:11) = dst(1:11)-xi_eq(1:11)
!
else ! not direct
!
r_t(12) = tau
!
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
r_t(1:11) = src(1:11)+xi_eq(1:11)
!
dst(1:2) = r_t(1:2)
!
dst(3) =(sqrt(2.0_ark)*r_t(3)+2.0_ark*r_t(4) )/sqrt(6.0_ark)
dst(4) =(sqrt(2.0_ark)*r_t(3)- r_t(4)+sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
dst(5) =(sqrt(2.0_ark)*r_t(3)- r_t(4)-sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
!
dst(6) = r_t(6)
!
dst( 7) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
dst( 8) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
dst(10) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!
beta(1) = dst(7)
beta(2) = dst(8)
beta(3) = dst(10)
!
call find_alpha_from_beta(beta(1:3),r_t(10:12),dst(11),dst(9),dst(12))
!
endif
!
case('R-1TAU-2BETA-REF')
!
rref( 1,0:4) = molec%force( 1: 5)
rref( 2,0:4) = molec%force( 6:10)
rref( 3,0:4) = molec%force(11:15)
rref( 4,0:4) = molec%force(16:20)
rref( 5,0:4) = molec%force(21:25)
!
rref( 6,0:4) = molec%force(26:30)/rad
rref( 7,0:4) = molec%force(31:35)/rad
rref( 8,0:4) = molec%force(36:40)/rad
rref( 9,0:4) = molec%force(41:45)/rad
!
rref(10,0:4) = molec%force(46:50)/rad
rref(11,0:4) = molec%force(51:55)/rad
rref(12,0:4) = molec%force(56:60)/rad
!
!
tau = src(12)
!
i0 = 0
!
do icoord = 1,9
!
n(0:4) = molec%pot_ind(11,i0+1:i0+5)
k(0:4) = molec%pot_ind(12,i0+1:i0+5)
!
if (all(n(:)==0)) then
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*cos(real(k(1:4),ark)*tau))
!
else
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*sin(real(n(1:4),ark)*tau))
!
endif
!
i0 = i0+5
!
enddo
!
xi_eq(10:11) = rref(10:11,0)
xi_eq(12) = rref(12,0) + tau
!
beta(1) = (sqrt(2.0_ark)*xi_eq(7)+2.0_ark*xi_eq(8) )/sqrt(6.0_ark)
beta(2) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)+sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
beta(3) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)-sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
!
phi1 = (xi_eq(12)+2.0_ark*xi_eq(10) )
phi2 = (xi_eq(12)- xi_eq(10)+xi_eq(11))
phi3 = (xi_eq(12)- xi_eq(10)-xi_eq(11))
!
cosa0(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( phi2 - phi3 )
cosa0(2) = cos( beta(3) )*cos( beta(1) ) + sin( beta(3) )*sin( beta(1) )*cos( phi3 - phi1 )
cosa0(3) = cos( beta(1) )*cos( beta(2) ) + sin( beta(1) )*sin( beta(2) )*cos( phi1 - phi2 )
!
if ( any(abs(cosa0(:))>1.0_ark+sqrt(small_))) then
!
write (out,"('ML_coordinate_transform_ch3oh: cosalpha0>1: ',3f18.8)") cosa0(1:3)
write (out,"('Consider change coordinate type ')")
stop 'MLcoordinate_transform_func - bad cos(alpha)'
endif
!
cosa0(:) = max(-1.0_ark,cosa0(:))
cosa0(:) = min( 1.0_ark,cosa0(:))
!
alpha0(:) = acos(cosa0(:))
!
!xi_eq(10) = (alpha0(2)+alpha0(3))/sqrt(2.0_ark)
!xi_eq(11) = (alpha0(2)-alpha0(3))/sqrt(2.0_ark)
!
xi_eq(10) = alpha0(3)
xi_eq(11) = alpha0(2)
!
if (direct) then
!
dst(1:2) = src(1:2)
!
dst( 3) = 1.0_ark/sqrt(3.0_ark)*( src(3)+src(4)+src(5) )
dst( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(3)-src(4)-src(5) )
dst( 5) = 1.0_ark/sqrt(2.0_ark)*( src(4)-src(5) )
!
dst( 6) = src(6)
!
dst( 7) = 1.0_ark/sqrt(3.0_ark)*( src(7)+src(8)+src(10) )
dst( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(7)-src(8)-src(10) )
dst( 9) = 1.0_ark/sqrt(2.0_ark)*( src(8)-src(10) )
!
!dsrc(10) = src(10)
!
!dsrc(11) = src(11)
!if (dsrc(11)-molec%local_eq(11)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
!if (dsrc(11)-molec%local_eq(11)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
!dsrc(12) = src(12)
!if (dsrc(12)-molec%local_eq(12)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
!if (dsrc(12)-molec%local_eq(12)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
!dsrc(11) = mod(src(11),rref(11,0))+rref(11,0)
!dsrc(12) = mod(src(12),rref(12,0))+rref(12,0)
!
!dst(7) = dst(7) /sqrt(2.0_ark)-(alpha(1) +alpha(2) +alpha(3) )/sqrt(6.0_ark)
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
!dst(10) = (src( 9)+src(11))/sqrt(2.0_ark)
!dst(11) = (src( 9)-src(11))/sqrt(2.0_ark)
!
dst(10) = src( 9)
dst(11) = src(11)
dst(12) = tau
!
dst(1:11) = dst(1:11)-xi_eq(1:11)
!
else ! not direct
!
r_t(12) = tau
!
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
r_t(1:11) = src(1:11)+xi_eq(1:11)
!
dst(1:2) = r_t(1:2)
!
dst(3) =(sqrt(2.0_ark)*r_t(3)+2.0_ark*r_t(4) )/sqrt(6.0_ark)
dst(4) =(sqrt(2.0_ark)*r_t(3)- r_t(4)+sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
dst(5) =(sqrt(2.0_ark)*r_t(3)- r_t(4)-sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
!
dst(6) = r_t(6)
!
dst( 7) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
dst( 8) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
dst(10) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!dst( 9) = (r_t(10)+r_t(11))/sqrt(2.0_ark)
!dst(11) = (r_t(10)-r_t(11))/sqrt(2.0_ark)
!
dst( 9) = r_t(10)
dst(11) = r_t(11)
dst(12) = tau
!
!call find_alpha_for_ch3oh(dst(7:9),r_t(10:12),dst(10:12))
!call find_alpha_for_ch3oh_II(r_t(7:12),dst(7:12))
!
!dst(10) =(r_t(12)+2.0_ark*r_t(10) )
!dst(11) =(r_t(12)- r_t(10)+r_t(11))
!dst(12) =(r_t(12)- r_t(10)-r_t(11))
!
!dst(10:12) = mod(dst(10:12)+2.0_ark*pi,2.0_ark*pi)+molec%local_eq(10:12)
!
endif
case('R-ALPHA-S-TAU-BETA-REF')
!
rref( 1,0:4) = molec%force( 1: 5)
rref( 2,0:4) = molec%force( 6:10)
rref( 3,0:4) = molec%force(11:15)
rref( 4,0:4) = molec%force(16:20)
rref( 5,0:4) = molec%force(21:25)
!
rref( 6,0:4) = molec%force(26:30)/rad
rref( 7,0:4) = molec%force(31:35)/rad
rref( 8,0:4) = molec%force(36:40)/rad
rref( 9,0:4) = molec%force(41:45)/rad
!
rref(10,0:4) = molec%force(46:50)/rad
rref(11,0:4) = molec%force(51:55)/rad
rref(12,0:4) = molec%force(56:60)/rad
!
!
if (direct) then
!
!dsrc(10) = src(10)
!if (dsrc(10)>2.0_ark*pi-sqrt(small_)) dsrc(10) = dsrc(10)-2.0_ark*pi
!if (dsrc(10)<-sqrt(small_)) dsrc(10) = dsrc(10)+2.0_ark*pi
!
!dsrc(11) = src(11)
!if (dsrc(11)-rref(11,1)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
!if (dsrc(11)-rref(11,1)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
!dsrc(12) = src(12)
!if (dsrc(12)-rref(12,1)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
!if (dsrc(12)-rref(12,1)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
tau = src(10) ! 1.0_ark/3.0_ark*( src(10)+src(11)+src(12) )
!
!tau = 1.0_ark/3.0_ark*( src(10)+src(11)+src(12) )
!
!tau = mod(tau+2.0_ark*pi,2.0_ark*pi/3.0_ark)
!
beta(1) = src(7)
beta(2) = src(8)
beta(3) = src(9)
!
phi1 = src(10)
phi2 = src(11)
phi3 = src(12)
!
cosa(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( phi2 - phi3 )
cosa(2) = cos( beta(3) )*cos( beta(1) ) + sin( beta(3) )*sin( beta(1) )*cos( phi3 - phi1 )
cosa(3) = cos( beta(1) )*cos( beta(2) ) + sin( beta(1) )*sin( beta(2) )*cos( phi1 - phi2 )
!
if ( any(abs(cosa(:))>1.0_ark+sqrt(small_))) then
!
write (out,"('ML_coordinate_transform_ch3oh: cosalpha>1: ',3f18.8)") cosa(1:3)
write (out,"('Consider change coordinate type ')")
stop 'MLcoordinate_transform_func - bad cos(alpha)'
endif
!
cosa(:) = max(-1.0_ark,cosa(:))
cosa(:) = min( 1.0_ark,cosa(:))
!
alpha(:) = acos(cosa(:))
!
else ! not direct
!
tau = src(12)
!
endif
!
i0 = 0
!
do icoord = 1,9
!
n(0:4) = molec%pot_ind(11,i0+1:i0+5)
k(0:4) = molec%pot_ind(12,i0+1:i0+5)
!
if (all(n(:)==0)) then
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*cos(real(k(1:4),ark)*tau))
!
else
!
xi_eq(icoord) = rref(icoord,0)+sum(rref(icoord,1:4)*sin(real(n(1:4),ark)*tau))
!
endif
!
i0 = i0+5
!
enddo
!
xi_eq(10:11) = rref(10:11,0)
xi_eq(12) = rref(12,0) + tau
!
beta(1) = (sqrt(2.0_ark)*xi_eq(7)+2.0_ark*xi_eq(8) )/sqrt(6.0_ark)
beta(2) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)+sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
beta(3) = (sqrt(2.0_ark)*xi_eq(7)- xi_eq(8)-sqrt(3.0_ark)*xi_eq(9))/sqrt(6.0_ark)
!
phi1 = (xi_eq(12)+2.0_ark*xi_eq(10) )
phi2 = (xi_eq(12)- xi_eq(10)+xi_eq(11))
phi3 = (xi_eq(12)- xi_eq(10)-xi_eq(11))
!
cosa0(1) = cos( beta(2) )*cos( beta(3) ) + sin( beta(2) )*sin( beta(3) )*cos( phi2 - phi3 )
cosa0(2) = cos( beta(3) )*cos( beta(1) ) + sin( beta(3) )*sin( beta(1) )*cos( phi3 - phi1 )
cosa0(3) = cos( beta(1) )*cos( beta(2) ) + sin( beta(1) )*sin( beta(2) )*cos( phi1 - phi2 )
!
if ( any(abs(cosa0(:))>1.0_ark+sqrt(small_))) then
!
write (out,"('ML_coordinate_transform_ch3oh: cosalpha0>1: ',3f18.8)") cosa0(1:3)
write (out,"('Consider change coordinate type ')")
stop 'MLcoordinate_transform_func - bad cos(alpha)'
endif
!
cosa0(:) = max(-1.0_ark,cosa0(:))
cosa0(:) = min( 1.0_ark,cosa0(:))
!
alpha0(:) = acos(cosa0(:))
!
xi_eq(10) = (2.0_ark*alpha0(1)-alpha0(2)-alpha0(3))/sqrt(6.0_ark)
xi_eq(11) = ( alpha0(2)-alpha0(3))/sqrt(2.0_ark)
!
if (direct) then
!
dst(1:2) = src(1:2)
!
dst( 3) = 1.0_ark/sqrt(3.0_ark)*( src(3)+src(4)+src(5) )
dst( 4) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(3)-src(4)-src(5) )
dst( 5) = 1.0_ark/sqrt(2.0_ark)*( src(4)-src(5) )
!
dst( 6) = src(6)
!
dst( 7) = 1.0_ark/sqrt(3.0_ark)*( src(7)+src(8)+src(9) )
dst( 8) = 1.0_ark/sqrt(6.0_ark)*( 2.0_ark*src(7)-src(8)-src(9) )
dst( 9) = 1.0_ark/sqrt(2.0_ark)*( src(8)-src(9) )
!
!dsrc(10) = src(10)
!
!dsrc(11) = src(11)
!if (dsrc(11)-molec%local_eq(11)>2.0_ark*pi-sqrt(small_)) dsrc(11) = dsrc(11)-2.0_ark*pi
!if (dsrc(11)-molec%local_eq(11)<-sqrt(small_)) dsrc(11) = dsrc(11)+2.0_ark*pi
!dsrc(12) = src(12)
!if (dsrc(12)-molec%local_eq(12)>2.0_ark*pi-sqrt(small_)) dsrc(12) = dsrc(12)-2.0_ark*pi
!if (dsrc(12)-molec%local_eq(12)<-sqrt(small_)) dsrc(12) = dsrc(12)+2.0_ark*pi
!
!dsrc(11) = mod(src(11),rref(11,0))+rref(11,0)
!dsrc(12) = mod(src(12),rref(12,0))+rref(12,0)
!
!dst(7) = dst(7) /sqrt(2.0_ark)-(alpha(1) +alpha(2) +alpha(3) )/sqrt(6.0_ark)
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
dst(10) = (2.0_ark*alpha(1)-alpha(2)-alpha(3))/sqrt(6.0_ark)
dst(11) = ( alpha(2)-alpha(3))/sqrt(2.0_ark)
dst(12) = tau
!
dst(1:11) = dst(1:11)-xi_eq(1:11)
!
else ! not direct
!
r_t(12) = tau
!
!xi_eq(7) = xi_eq(7)/sqrt(2.0_ark)-(alpha0(1)+alpha0(2)+alpha0(3))/sqrt(6.0_ark)
!
r_t(1:11) = src(1:11)+xi_eq(1:11)
!
dst(1:2) = r_t(1:2)
!
dst(3) =(sqrt(2.0_ark)*r_t(3)+2.0_ark*r_t(4) )/sqrt(6.0_ark)
dst(4) =(sqrt(2.0_ark)*r_t(3)- r_t(4)+sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
dst(5) =(sqrt(2.0_ark)*r_t(3)- r_t(4)-sqrt(3.0_ark)*r_t(5))/sqrt(6.0_ark)
!
dst(6) = r_t(6)
!
dst(7) =(sqrt(2.0_ark)*r_t(7)+2.0_ark*r_t(8) )/sqrt(6.0_ark)
dst(8) =(sqrt(2.0_ark)*r_t(7)- r_t(8)+sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
dst(9) =(sqrt(2.0_ark)*r_t(7)- r_t(8)-sqrt(3.0_ark)*r_t(9))/sqrt(6.0_ark)
!
call find_alpha_for_ch3oh(dst(7:9),r_t(10:12),dst(10:12))
!call find_alpha_for_ch3oh_II(r_t(7:12),dst(7:12))
!
!dst(10) =(r_t(12)+2.0_ark*r_t(10) )
!dst(11) =(r_t(12)- r_t(10)+r_t(11))
!dst(12) =(r_t(12)- r_t(10)-r_t(11))
!
!dst(10:12) = mod(dst(10:12)+2.0_ark*pi,2.0_ark*pi)+molec%local_eq(10:12)
!
endif
!
end select
!
!
if (verbose>=7) write(out,"('ML_coordinate_transform_ch3oh/end')")
!
!
end function ML_coordinate_transform_ch3oh
!
subroutine find_alpha_from_beta(beta,xi,alpha2,alpha3,tau)
! obtaining 3 angles phi from 3 beta_i, tau, s_a, and s_b
real(ark),intent(in) :: beta(3),xi(3)
real(ark),intent(out) :: alpha2,alpha3,tau
real(ark) :: eps(3)
real(ark) :: rjacob(3,3),dx(3),phi_l(3),phi_r(3),xi_t(3),phi(3)
real(ark) :: hstep
real(rk) :: stadev_old,stability,stadev,stadev_best,ssq,a(3,3),b(3,1)
!
integer(ik) :: iter,itmax,i1,irow,icolumn
!
rjacob = 0
iter = 0
stadev_old = 1.e10
stability = 1.e10
stadev = 1.e10
!
hstep = 1e-4
!
phi(1) = molec%local_eq( 9)
phi(2) = molec%local_eq(11)
phi(3) = molec%local_eq(12)
xi_t = xi
!xi_t(3) = mod(xi_t(3)+2.0_ark*pi,2.0_ark*pi)
!
stadev_best = sqrt(small_)*0.01_ark
itmax = 500
!
outer_loop: &
do while( iter<itmax .and. stadev>stadev_best )
!
iter = iter + 1
ssq=0
!
! Caclulate the function
!
eps(:) = calc_xi(beta,phi)-xi_t(:)
!
ssq=sqrt(sum(eps(:)**2))
!
! calculate derivatives with respect to parameters (RJACOB)
!
do i1 = 1,3
!
phi_r = phi ; phi_l = phi
phi_r(i1) = phi(i1) + hstep
phi_l(i1) = phi(i1) - hstep
!
rjacob(:,i1) = ( calc_xi(beta,phi_r)-calc_xi(beta,phi_l))/hstep*0.5_ark
!
enddo
!
if (itmax>=0) then
!
! form A matrix
do irow=1,3 !==== row-...... ====!
do icolumn=1,irow !==== column-....====!
a(irow,icolumn)=sum( rjacob(:,irow)*rjacob(:,icolumn))
a(icolumn,irow) = a(irow,icolumn)
enddo
enddo
! form B matrix
do irow=1,3 !==== row-...... ====!
b(irow,1)=sum(eps(:)*rjacob(:,irow))
enddo
!
call lapack_gelss(a(:,:),b(:,:))
!
dx(:) = b(:,1)
!
stadev=sqrt(ssq)
!
phi(1:3) = phi(1:3) - dx(1:3)
!
!phi(:) = mod(phi(:)+2.0_ark*pi,2.0_ark*pi)
!
stability=abs( (stadev-stadev_old)/stadev )
stadev_old=stadev
else ! Itmax = 0, so there is no fit
! only straightforward calculations
!
stadev_old=stadev
stadev=sqrt(ssq)
!
endif
!
enddo outer_loop ! --- iter
!
if (iter==itmax) then
write(out,"('find_alpha_from_beta: could not find solution after ',i8,' iterations')") iter
stop 'find_alpha_from_beta: could not find solution'
endif
!
alpha2 = phi(1)
alpha3 = phi(2)
tau = phi(3)
!
contains
function calc_xi(beta,x) result (xi)
real(ark),intent(in) :: beta(3),x(3)
real(ark) :: xi(3)
real(ark) :: cosa(3),phi(3),tau,alpha(3),chi1,chi2,chi3
alpha(2) = x(1)
alpha(3) = x(2)
tau = x(3)
!
cosa(2) = ( cos(alpha(2))-cos(beta(3))*cos(beta(1)) )/( sin(beta(3))*sin(beta(1)) )