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functions.f90
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functions.f90
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module functions
!
use accuracy
use timer
!
implicit none
!
! Different 1D functions (potential, spin-orbit etc)
!
integer(ik),parameter :: verbose=5
!
public analytical_fieldT
!
!
abstract interface
!
function analytical_fieldT(r,parameters)
use accuracy
!
real(rk) :: analytical_fieldT !NB: NAG Fortran 6.0 doesn't like in-line declaration
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
!
end function analytical_fieldT
!
end interface
!
!
contains
!
!
subroutine define_analytical_field(ftype,fanalytical_field)
!
character(len=cl),intent(in) :: ftype
! NB: NAG Fortran 6.0 doesn't like intent(in) and initial nullification
procedure(analytical_fieldT),pointer :: fanalytical_field !=> null()
!
select case(ftype)
!
case("MORSE")
!
fanalytical_field => poten_morse
!
case("MORSE_DAMP")
!
fanalytical_field => poten_morse_damp
!
case("MODIFIED-MORSE","MODIFIED_MORSE","MMORSE")
!
fanalytical_field => poten_morse_modified
!
case("EMO") ! "Expanded MorseOscillator"
!
fanalytical_field => poten_EMO
!
case("MLR") ! "Morse/Long-Range"
!
fanalytical_field => poten_MLR
!
case("MLR_DS") ! "Morse/Long-Range with Douketis-damping"
!
fanalytical_field => poten_MLR_Douketis
!
case("MLR_DS_DARBY") ! "Morse/Long-Range with Douketis-damping"
!
fanalytical_field => poten_MLR_Douketis_Darby
!
case("MARQUARDT") ! "Marquardt"
!
fanalytical_field => poten_Marquardt
!
case("COSH-POLY") ! "Diabatic coupling as a polynom/cosh"
!
fanalytical_field => poten_cosh_polynom
!
case("BOBLEROY","BOB","SURKUS") ! "BOB expansion"
!
fanalytical_field => poten_BOBLeRoy
!
case("BOBNA") ! "BOB-NA expansion"
!
fanalytical_field => poten_BOBna
!
case("BOBLEROY_DAMP","BOB_DAMP","SURKUS_DAMP") ! "BOB expansion with damping to zero at r=0"
!
fanalytical_field => poten_BOBLeRoy_damp
!
case("DUNHAM")
!
fanalytical_field => poten_dunham
!
case("SPF")
!
fanalytical_field => poten_spf
!
case("SPF_1")
!
fanalytical_field => poten_spf_1
!
case("SPF_H2")
!
fanalytical_field => poten_spf_h2
!
case("HH","HULBERT-HIRSCHFELDER")
!
fanalytical_field => poten_Hulbert_Hirschfelder
!
case("CHEBYSHEV")
!
fanalytical_field => poten_cheb
!
case("POLYNOM", "POLYNOMIAL")
!
fanalytical_field => poten_polynom
!
case("EXPONENTIAL")
!
fanalytical_field => poten_exponential
!
case("LAURA_SO","ATAN_SO")
!
fanalytical_field => SO_arctan
!
case("POTEN_FERMI_T")
!
fanalytical_field => poten_fermi_t
!
case("M-S")
!
fanalytical_field => poten_Murrell_Sorbie
!
case("PADE_GOODISMAN2","PADE2")
!
fanalytical_field => poten_Pade_Goodisman_2
!
case("POLYNOM_DECAY")
!
fanalytical_field => dipole_polynom_exp
!
case("POLYNOM_DECAY_DAMP")
!
fanalytical_field => dipole_polynom_exp_damp
!
case("POLYNOM_DECAY_24")
!
fanalytical_field => dipole_polynom_exp24
!
case("DOUBLEEXP2")
!
fanalytical_field => dipole_doubleexp
!
case("DIABATIC_MU_DIAG","AVOIDEDCROSSING_DIAG_MU")
!
fanalytical_field => dipole_avoidedcrossing_diag_mu
!
case("TWO_COUPLED_EMOS")
!
fanalytical_field => poten_two_coupled_EMOs
!
case("NONE")
!
write(out,'("Analytical: Some fields are not properly defined and produce function type ",a)') trim(ftype)
stop "Analytical: Unknown function type "
!
case default
!
write(out,'("Analytical: Unknown function type ",a)') trim(ftype)
stop "Analytical: Unknown field type "
!
end select
!
end subroutine define_analytical_field
!
!
function poten_morse(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,a0,f,de
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
a0 = parameters(3)
!
y = 1.0_rk-exp(-a0*(r-r0))
! Note that the De is relative the absolute minimum of the ground state
!
f = v0
!
de = parameters(4)-v0
!
f = f + de*y**2
!
do k=5,N
f = f + parameters(k)*y**(k-2)
enddo
!
end function poten_morse
!
function poten_morse_damp(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,a0,f,de,vdamp,vshort,vlong,damp,dr,z
integer(ik) :: k,N,Npot,Nstruct
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
de = parameters(3)-v0
a0 = parameters(4)
damp = parameters(5)
!
! number of structural parameters
!
Nstruct = 5
!
Npot = N-Nstruct
!
dr = (r-r0)
!
y = 1.0_rk-exp(-a0*dr)
!
! Note that the De is relative the absolute minimum of the ground state
!
vlong = de*y**2
!
vdamp = exp(-damp*dr**4)
!
vshort = 0
!
z = (r-r0)/(r+r0)
!
do k=1,Npot
vshort = vshort + parameters(Nstruct+k)*y**(k+2)
enddo
!
f = v0+vdamp*vshort+vlong
!
end function poten_morse_damp
!
function poten_morse_modified(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,f0,f1,beta,beta_inf,z,y_inf
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
!
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
z = (r-r0)/(r+r0)
!
f0 = 0
f1 = 0
do k=4,N
f0 = f0 + parameters(k)*z**(k-4)
f1 = f1 + parameters(k) ! *(1.0_rk)**(k-4)
enddo
!
beta = z*f0
beta_inf = f1
!
y = 1.0_rk-exp(-beta)
y_inf = 1.0_rk-exp(-beta_inf)
!
f = de*y**2/y_inf**2+v0
!
end function poten_morse_modified
!
function poten_cosh_polynom(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,r0,f,f0,beta,z,v0
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
!
beta = parameters(2)
r0 = parameters(3)
!
z = (r-r0)
!
f0 = 0
do k=4,N
f0 = f0 + parameters(k)*z**(k-4)
enddo
!
y = cosh(beta*z)
!
f = v0+f0/y
!
end function poten_cosh_polynom
!
function poten_EMO(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,rref,z,phi
integer(ik) :: k,N,p
!
v0 = parameters(1)
r0 = parameters(2)
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
rref = parameters(4)
!
if (rref<=0.0_rk) rref = r0
!
if (r<=rref) then
p = nint(parameters(5))
N = parameters(7)
else
p = nint(parameters(6))
N = parameters(8)
endif
!
if (size(parameters)/=8+max(parameters(7),parameters(8))+1) then
write(out,"('poten_EMO: Illegal number of parameters in EMO, check NS and NL, must be max(NS,NL)+9')")
print*,parameters(:)
stop 'poten_EMO: Illegal number of parameters, check NS and NL'
endif
!
z = (r**p-rref**p)/(r**p+rref**p)
!
phi = 0
do k=0,N
phi = phi + parameters(k+9)*z**k
enddo
!
y = 1.0_rk-exp(-phi*(r-r0))
!
f = de*y**2+v0
!
end function poten_EMO
!
! Morse/Long-Range, see Le Roy manuals
!
function poten_MLR(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,rref,z,phi,phiinf,uLR,uLR0
integer(ik) :: k,N,p,M,Nstruc,Ntot,Npot
!
v0 = parameters(1)
r0 = parameters(2)
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
rref = parameters(4)
!
if (rref<=0.0_rk) rref = r0
!
p = nint(parameters(5))
!
if (r<=rref) then
N = parameters(6)
else
N = parameters(7)
endif
!
! Number of structural parameters
!
Nstruc = 7
!
! total number of parameters
!
Ntot = size(parameters(:),dim=1)
!
! Number of pot-parameters
!
Npot = max(parameters(6),parameters(7))+1
!
! number of long range parameters
!
M = Ntot-Npot-Nstruc
!
!if (size(parameters)/=8+max(parameters(7),parameters(8))+1) then
! write(out,"('poten_EMO: Illegal number of parameters in EMO, check NS and NL, must be max(NS,NL)+9')")
! stop 'poten_EMO: Illegal number of parameters, check NS and NL'
!endif
!
z = (r**p-rref**p)/(r**p+rref**p)
!
phi = 0
do k=0,N
phi = phi + parameters(k+Nstruc+1)*z**k
enddo
!
! double check uLR parameters
!
uLR = sum(parameters(1+Npot+Nstruc:M+Npot+Nstruc)**2)
!
if (uLR<small_) then
write(out,"('poten_MLR: At least one uLR should be non-zero')")
stop 'poten_MLR: At least one uLR should be non-zer'
endif
!
! long-range part
!
uLR = 0
do k=1,M
uLR = uLR + parameters(k+Npot+Nstruc)/r**k
enddo
!
! at R=Re
uLR0 = 0
do k=1,M
uLR0 = uLR0 + parameters(k+Npot+Nstruc)/r0**k
enddo
!
phiinf = log(2.0_rk*de/uLR0)
!
phi = (1.0_rk-z)*phi+z*phiinf
!
phi = uLR/uLR0*exp(-phi*z)
!
y = 1.0_rk-phi
!
f = de*y**2+v0
!
end function poten_MLR
! Morse/Long-Range with Douketis damping, see Le Roy manuals
!
function poten_MLR_Douketis(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,rref,z,beta,betainf,betaN,yq,yp,uLR,uLR0,rho,b,c,s,damp
integer(ik) :: k,N,p,M,Nstruc,Ntot,Npot,q
!
v0 = parameters(1)
r0 = parameters(2)
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
rref = parameters(4)
!
if (rref<=0.0_rk) rref = r0
!
p = nint(parameters(5))
q = nint(parameters(6))
N = parameters(7)
rho = parameters(8)
!
! Number of structural parameters
!
Nstruc = 8
!
! total number of parameters
!
Ntot = size(parameters(:),dim=1)
!
! Number of pot-parameters
!
Npot = N+1
!
! number of long range parameters
!
M = Ntot-Npot-Nstruc
!
!if (size(parameters)/=8+max(parameters(7),parameters(8))+1) then
! write(out,"('poten_EMO: Illegal number of parameters in EMO, check NS and NL, must be max(NS,NL)+9')")
! stop 'poten_EMO: Illegal number of parameters, check NS and NL'
!endif
!
z = (r**p-r0**p)/(r**p+r0**p)
yp = (r**p-rref**p)/(r**p+rref**p)
yq = (r**q-rref**q)/(r**q+rref**q)
!
! double check uLR parameters
!
uLR = sum(parameters(1+Npot+Nstruc:M+Npot+Nstruc)**2)
!
if (uLR<small_) then
write(out,"('poten_MLR: At least one uLR should be non-zero')")
stop 'poten_MLR: At least one uLR should be non-zer'
endif
!
! For the Damping part
! the values of s, b,c are as suggested by LeRoy 2011 (MLR paper)
!
s = -1.0_rk
b = 3.3_rk
c = 0.423_rk
!s = -2.0_rk
!b = 2.50_rk
!c = 0.468_rk
!
! long-range part
!
uLR = 0
do k=1,M
!
! Douketis damping function
Damp = ( 1.0_rk-exp( -b*rho*r/real(k,rk)-c*(rho*r)**2/sqrt(real(k,rk)) ) )**(real(k,rk)+s)
!
uLR = uLR + Damp*parameters(k+Npot+Nstruc)/r**k
!
enddo
!
!
! at R=Re
uLR0 = 0
do k=1,M
! Douketis damping function
Damp = ( 1.0_rk-exp( -b*rho*r0/real(k,rk)-c*(rho*r0)**2/sqrt(real(k,rk)) ) )**(real(k)+s)
!
uLR0 = uLR0 + Damp*parameters(k+Npot+Nstruc)/r0**k
!
enddo
!
betaN = 0
do k=0,N
betaN = betaN + parameters(k+Nstruc+1)*yq**k
enddo
!
betainf = log(2.0_rk*de/uLR0)
!
beta = (1.0_rk-yp)*betaN+yp*betainf
!
y = 1.0_rk-uLR/uLR0*exp(-beta*z)
!
f = de*y**2+v0
!
end function poten_MLR_Douketis
function poten_MLR_Douketis_Darby(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,rref,z,beta,betainf,betaN,yq,yp,uLR,uLR0,rho,b,c,s,damp,u,uinf,ma,mb
integer(ik) :: k,N,p,M,Nstruc,Ntot,Npot,q,NUa,NUb
!
v0 = parameters(1)
r0 = parameters(2)
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
rref = parameters(4)
!
if (rref<=0.0_rk) rref = r0
!
p = nint(parameters(5))
q = nint(parameters(6))
N = parameters(7)
rho = parameters(8)
!
! Number of structural parameters
!
Nstruc = 8
!
! total number of parameters
!
! Number of pot-parameters
!
Npot = N+1
!
! number of long range parameters
!
M = parameters(Nstruc+Npot+1)
!
!if (size(parameters)/=8+max(parameters(7),parameters(8))+1) then
! write(out,"('poten_EMO: Illegal number of parameters in EMO, check NS and NL, must be max(NS,NL)+9')")
! stop 'poten_EMO: Illegal number of parameters, check NS and NL'
!endif
!
z = (r**p-r0**p)/(r**p+r0**p)
yp = (r**p-rref**p)/(r**p+rref**p)
yq = (r**q-rref**q)/(r**q+rref**q)
!
! double check uLR parameters
!
uLR = sum(parameters(2+Npot+Nstruc:M+Npot+Nstruc)**2)
!
if (uLR<small_) then
write(out,"('poten_MLR: At least one uLR should be non-zero')")
stop 'poten_MLR: At least one uLR should be non-zer'
endif
!
! For the Damping part
! the values of s, b,c are as suggested by LeRoy 2011 (MLR paper)
!
s = -1.0_rk
b = 3.3_rk
c = 0.423_rk
!s = -2.0_rk
!b = 2.50_rk
!c = 0.468_rk
!
! long-range part
!
uLR = 0
do k=1,M
!
! Douketis damping function
Damp = ( 1.0_rk-exp( -b*rho*r/real(k,rk)-c*(rho*r)**2/sqrt(real(k,rk)) ) )**(real(k,rk)+s)
!
uLR = uLR + Damp*parameters(1+k+Npot+Nstruc)/r**k
!
enddo
!
!
! at R=Re
uLR0 = 0
do k=1,M
! Douketis damping function
Damp = ( 1.0_rk-exp( -b*rho*r0/real(k,rk)-c*(rho*r0)**2/sqrt(real(k,rk)) ) )**(real(k)+s)
!
uLR0 = uLR0 + Damp*parameters(1+k+Npot+Nstruc)/r0**k
!
enddo
!
betaN = 0
do k=0,N
betaN = betaN + parameters(k+Nstruc+1)*yq**k
enddo
!
betainf = log(2.0_rk*de/uLR0)
!
beta = (1.0_rk-yp)*betaN+yp*betainf
!
y = 1.0_rk-uLR/uLR0*exp(-beta*z)
!
!
ma = 1.0_rk - parameters(2+M+Npot+Nstruc)/parameters(3+M+Npot+Nstruc)
mb = 1.0_rk - parameters(4+M+Npot+Nstruc)/parameters(5+M+Npot+Nstruc)
!
! write(out,*) parameters(2+M+Npot+Nstruc), parameters(3+M+Npot+Nstruc)
! write(out,*) parameters(4+M+Npot+Nstruc), parameters(5+M+Npot+Nstruc)
p = nint(parameters(6+M+Npot+Nstruc))
q = nint(parameters(7+M+Npot+Nstruc))
!
NUa = nint(parameters(8+M+Npot+Nstruc))
!
NUb = nint(parameters(9+M+Npot+Nstruc))
!
yp = (r**p-r0**p)/(r**p+r0**p)
yq = (r**q-r0**q)/(r**q+r0**q)
!
u = 0
do k=0,NUa
u = u + ma*parameters(k+10+M+Npot+Nstruc)*yq**k
enddo
do k=0,NUb
u = u + mb*parameters(k+12+NUa+M+Npot+Nstruc)*yq**k
enddo
!
uinf = parameters(11+NUa+M+Npot+Nstruc)*ma + parameters(13+NUa+NUb+M+Npot+Nstruc)*mb
f = de*y**2+v0 + ( (1.0_rk-yp)*u + uinf*yp )
!
end function poten_MLR_Douketis_Darby
!
function poten_Marquardt(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,de,f,rref,z,phi,eps6,eps8,rs,damp
integer(ik) :: k,N,p
!
v0 = parameters(1)
r0 = parameters(2)
! Note that the De is relative the absolute minimum of the ground state
De = parameters(3)-v0
!
rref = parameters(4)
!
if (rref<=0.0_rk) rref = r0
!
if (r<=rref) then
p = nint(parameters(5))
N = parameters(7)
else
p = nint(parameters(6))
N = parameters(8)
endif
!
eps6 = parameters(9)
eps8 = parameters(10)
rs = parameters(11)
!
z = (r**p-rref**p)/(r**p+rref**p)
!
phi = 0
do k=0,N
phi = phi + parameters(k+12)*z**k
enddo
!
y = 1.0_rk-exp(-phi*(r-r0))
!
damp = ( 1.0_rk+eps6*(-(rs/r)**6) )*( 1.0_rk+eps8*(-(rs/r)**8) )
y = y*damp
!
f = de*y**2+v0
!
end function poten_Marquardt
!
function poten_BOBLeRoy(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: r0,f,rref,z,t,tinf
integer(ik) :: k,N,p
!
r0 = parameters(1)
!
rref = parameters(2)
!
p = nint(parameters(3))
N = size(parameters)-4-2
!
!if (size(parameters)/=4+N+2) then
! write(out,"('poten_BOBLeRoy: Illegal number of parameters, check N')")
! stop 'poten_BOBLeRoy: Illegal number of parameters, check N'
!endif
!
z = (r**p-r0**p)/(r**p+r0**p)
!
t = 0
do k=0,N
t = t + parameters(k+5)*z**k
enddo
!
tinf = parameters(N+6)
!
f = (1.0_rk-z)*t+z*tinf
!
end function poten_BOBLeRoy
!
function poten_BOBLeRoy_damp(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: r0,f,rref,z,t,tinf,f_damp,a_d,r_d,t_0
integer(ik) :: k,N,p
!
r0 = parameters(1)
!
rref = parameters(2)
!
p = nint(parameters(3))
N = size(parameters)-4-2-3
!
!if (size(parameters)/=4+N+2) then
! write(out,"('poten_BOBLeRoy: Illegal number of parameters, check N')")
! stop 'poten_BOBLeRoy: Illegal number of parameters, check N'
!endif
!
z = (r**p-r0**p)/(r**p+r0**p)
!
t = 0
do k=0,N
t = t + parameters(k+4)*z**k
enddo
!
tinf = parameters(N+6)
!
t_0 = parameters(N+7)
r_d = parameters(N+8)
a_d = parameters(N+9)
!
!f = (1.0_rk-z)*t+z*tinf
!
f_damp = ( 1.0_rk+tanh(a_d*(r-r_d)) )*0.5_rk
!
f = ( (1.0_rk-z)*t+z*tinf )*f_damp+t_0*(1.0_rk-f_damp)
!
end function poten_BOBLeRoy_damp
!
function poten_BOBna(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: r0,f,yq,t,tinf,ma,mb,q
integer(ik) :: k,NTa,NTb
!
r0 = parameters(1)
!
ma = parameters(2)/parameters(3)
mb = parameters(4)/parameters(5)
! write(out,*) r, ma, parameters(2), parameters(3), mb, parameters(4), parameters(5)
!
q = parameters(6)
!
NTa = nint(parameters(7))
!
NTb = nint(parameters(8))
!
yq = (r**q-r0**q)/(r**q+r0**q)
!
t = 0
do k=0,NTa
t = t + ma*parameters(k+9)*yq**k
enddo
do k=0,NTb
t = t + mb*parameters(k+11+NTa)*yq**k
enddo
!
tinf = parameters(10+NTa)*ma + parameters(12+NTa+NTb)*mb
!
! write(out,*) r, ( (1.0_rk-yq)*t + tinf*yq ),( (1.0_rk-yq)*t + tinf*yq )+1.0_rk
f = ( (1.0_rk-yq)*t + tinf*yq )
!
end function poten_BOBna
!
!
function poten_dunham(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,a0,f
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
a0 = parameters(3)
!
y = (r-r0)/r0
!
f = 1.0_rk
do k=4,N
f = f + parameters(k)*y**(k-3)
enddo
!
f = f*a0*y**2 + v0
!
end function poten_dunham
!
function poten_spf(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,b0,f
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
b0 = parameters(3)
!
y = (r-r0)/r
!
f = 1.0_rk
do k=4,N
f = f + parameters(k)*y**(k-3)
enddo
!
f = f*b0*y**2 + v0
!
end function poten_spf
!
function poten_spf_1(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0, f !, b0
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
!
y = (r-r0)/r
!
f = 0.0_rk
do k=3,N
f = f + parameters(k)*y**(k-2)
enddo
!
f = f + v0
!
end function poten_spf_1
!
function poten_spf_h2(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,b0,f,vh2
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
b0 = parameters(3)
!
y = (r-r0)/r
!
f = 1.0_rk
do k=4,N-4
f = f + parameters(k)*y**(k-3)
enddo
!
f = f*b0*y**2 + v0
!
vh2 = 0
!
do k=1,4
vh2 = vh2+parameters(N-4+k)*y**k
enddo
!
f = f + vh2
!
end function poten_spf_h2
!
!
! SO functional form
!
function poten_Hulbert_Hirschfelder(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: x,De,Aatom,re,a,b,c,f,UHH
!
if (size(parameters)/=6) stop 'Illegal number of parameters in poten_Hulbert_Hirschfelder (must be 6)'
!
! Aatom is the atomic limit
! De is ASO(eq)-A(atom)
! re is the "equilibrium"
! a,b,c are the expansion parameters
!
De = parameters(1)
Aatom = parameters(2)
re = parameters(3)
a = parameters(4)
b = parameters(5)
c = parameters(6)
!
x = a*(r/re-1.0_rk)
!
! Note that the De is difference between SO at equilibrium and SO(atomic limit)
!
UHH = De*( ( 1.0_rk-exp(-x) )**2+c*exp( -2.0_rk*x )*x**3*( 1.0_rk+b*x ) )
!
f = Aatom-De+UHH
!
end function poten_Hulbert_Hirschfelder
!
function poten_Murrell_Sorbie(r,parameters) result(f)
!
real(rk),intent(in) :: r ! geometry (Ang)
real(rk),intent(in) :: parameters(:) ! potential parameters
real(rk) :: y,v0,r0,a0,f,de,f_t,f_exp
integer(ik) :: k,N
!
N = size(parameters)
!
v0 = parameters(1)
r0 = parameters(2)
a0 = parameters(4)
!
y = (r-r0)
! Note that the De is relative the absolute minimum of the ground state
!
de = parameters(3)-v0
!
f_exp = exp(-a0*y)