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Update the keys

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jean paul nshuti 2025-10-08 15:03:35 +02:00
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!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! % SUBROUTINE CTRANS(...)
! %
! % M. Vossel 21.03.2023
! %
! % Routine to transform symmetryinput coordinates to symmetrized
! % coordinates. Distances Are discribet by Morse coordinates or
! % TMC depending on Set Parameters in the Genetic Input.
! %
! % input variables
! % q:
! % q(1): H1x
! % q(2): y
! % q(3): z
! % q(4): H2x
! % q(5): y
! % q(6): z
! % q(7): H3x
! % q(8): y
! % q(9): z
!
!
!
! % Internal variables:
! % t: primitive coordinates (double[qn])
! % t(1):
! % t(2):
! % t(3):
! % t(4):
! % t(5):
! % t(6):
! % t(7):
! % t(8):
! % t(9):
! % t: dummy (double[qn])
! % p: parameter vector
! % npar: length of parameter vector
! %
! % Output variables
! % s: symmetrized coordinates (double[qn])
! % s(1): CH-symetric streatch
! % s(2): CH-asymetric streatch-ex
! % s(3): CH-asymetric streatch-ey
! % s(4): CH-bend-ex
! % s(5): CH-bend-ey
! % s(6): CH-umbrella
! % s(7): CH-umbrella**2
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
module ctrans_mod
use accuracy_constants, only: dp, idp
implicit none
! precalculate pi, 2*pi and angle to radian conversion
real(dp), parameter :: pi = 4.0_dp*datan(1.0_dp)
real(dp), parameter :: pi2 = 2.0_dp*pi
real(dp), parameter :: ang2rad = pi/180.0_dp
! precalculate roots
real(dp), parameter:: sq2 = 1.0_dp/dsqrt(2.0_dp)
real(dp), parameter:: sq3 = 1.0_dp/dsqrt(3.0_dp)
real(dp), parameter:: sq6 = 1.0_dp/dsqrt(6.0_dp)
! change distances for equilibrium
!real(dp), parameter :: dchequi = 1.02289024_dp
real(dp), parameter :: dchequi = 2.344419_dp ! NO3
!real(dp), parameter :: dchequi = 2.34451900_dp
! see changes
contains
subroutine ctrans(q, x1,x2, invariants)
use dim_parameter, only: qn
integer(idp) k !running indices
real(dp), intent(in) :: q(qn) !given coordinates
real(dp), intent(out) :: x1(qn) !output coordinates symmetry adapted and scaled
real(dp), intent(out) :: x2(qn) !output coordinates symmetry adapted but not scaled
! ANN Variables
real(dp), optional, intent(out) :: invariants(:)
real(dp) :: s(qn),t(qn)
! kartesian coordianates copy from MeF+ so substitute c by n and removed f
real(dp) ch1(3), ch2(3), ch3(3), c_atom(3)
real(dp) nh1(3), nh2(3), nh3(3)
real(dp) zaxis(3), xaxis(3), yaxis(3)
real(dp) ph1(3), ph2(3), ph3(3)
! primitive coordinates
real(dp) dch1, dch2, dch3 !nh-distances
real(dp) umb !Umbrella Angle from xy-plane
! Symmetry coordinates
real(dp) aR !a1-modes H-Dist.,
real(dp) exR, exAng !ex components H-Dist., H-Ang.
real(dp) eyR, eyAng !ey components H-Dist., H-Ang.
! debugging
logical, parameter :: dbg = .false.
! initialize coordinate vectors
s = 0.0_dp
t = 0.0_dp
! write kartesian coords for readability
c_atom(1:3) = q(1:3)
do k = 1, 3
ch1(k) = q(k + 3)
ch2(k) = q(k + 6)
ch3(k) = q(k + 9)
end do
! construct z-axis
nh1 = normalized(ch1)
nh2 = normalized(ch2)
nh3 = normalized(ch3)
zaxis = create_plane(nh1, nh2, nh3)
! calculate bonding distance
dch1 = norm(ch1)
dch2 = norm(ch2)
dch3 = norm(ch3)
! construct symmertic and antisymmetric strech
aR = symmetrize(dch1 - dchequi, dch2 - dchequi, dch3 - dchequi, 'a')
exR = symmetrize(dch1, dch2, dch3, 'x')
eyR = symmetrize(dch1, dch2, dch3, 'y')
! construc x-axis and y axis
ph1 = normalized(project_point_into_plane(nh1, zaxis, c_atom))
xaxis = normalized(ph1)
yaxis = xproduct(zaxis, xaxis) ! right hand side koordinates
! project H atoms into C plane
ph2 = normalized(project_point_into_plane(nh2, zaxis, c_atom))
ph3 = normalized(project_point_into_plane(nh3, zaxis, c_atom))
call construct_HBend(exAng, eyAng, ph1, ph2, ph3, xaxis, yaxis)
umb = construct_umbrella(nh1, nh2, nh3, zaxis)
! set symmetry coordinates and even powers of umbrella
!s(1) = dch1- dchequi !aR
!s(2) = dch2 - dchequi !exR
!s(3) = dch3 - dchequi !eyR
s(1) = aR
s(2) = exR
s(3) = eyR
s(4) = exAng
s(5) = eyAng
s(6) = umb
s(7) = umb**2
s(8) = 0
s(9) = 0
! pairwise distances as second coordinate set
t = 0._dp
call pair_distance(q, t(1:6))
if (dbg) write (6, '("sym coords s=",9f16.8)') s(1:qn)
if (dbg) write (6, '("sym coords t=",9f16.8)') t(1:qn)
if (present(invariants)) then
call get_invariants(s, invariants)
end if
! transform s and t to x1 and x2
x1(1:qn)=s(1:qn)
x1(5)=x1(5)
! set other x coordinate to zero other than strech
!X1(4:qn)=0.0d0
x2(1:qn)=t(1:qn)
end subroutine ctrans
subroutine pair_distance(q, r)
real(dp), intent(in) :: q(9)
real(dp), intent(out) :: r(6)
real(dp) :: atom(3, 4)
integer :: n, k, count
!atom order: H1 H2 H3 N
atom(:, 1:3) = reshape(q, [3, 3])
atom(:, 4) = (/0.0_dp, 0.0_dp, 0.0_dp/)
! disntace order 12 13 14 23 24 34
count = 0
do n = 1, size(atom, 2)
do k = n + 1, size(atom, 2)
count = count + 1
r(count) = sqrt(sum((atom(:, k) - atom(:, n))**2))
end do
end do
end subroutine pair_distance
function morse_and_symmetrize(x,p,pst) result(s)
real(dp), intent(in),dimension(3) :: x
real(dp), intent(in),dimension(11) :: p
integer, intent(in),dimension(2) :: pst
integer :: k
real(dp), dimension(3) :: s
real(dp), dimension(3) :: t
! Morse transform
do k=1,3
t(k) = morse_transform(x(k), p, pst)
end do
s(1) = symmetrize(t(1), t(2), t(3), 'a')
s(2) = symmetrize(t(1), t(2), t(3), 'x')
s(3) = symmetrize(t(1), t(2), t(3), 'y')
end function morse_and_symmetrize
subroutine get_invariants(s, inv_out)
use dim_parameter, only: qn
use select_monom_mod, only: v_e_monom, v_ee_monom
real(dp), intent(in) :: s(qn)
real(dp), intent(out) :: inv_out(:)
! real(dp), parameter :: ck = 1.0_dp, dk = 1.0_dp/ck ! scaling for higher order invariants
real(dp) inv(24)
integer, parameter :: inv_order(12) = & ! the order in which the invariants are selected
& [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
real(dp) Rch, umb, xR, yR, xAng, yAng
! for readability
Rch = s(1)
xR = s(2)
yR = s(3)
xAng = s(4)
yAng = s(5)
umb = s(6)**2
! invarianten
! a moden
inv(1) = Rch
inv(2) = umb
! invariante e pairs
inv(3) = v_e_monom(xR, yR, 1)
inv(4) = v_e_monom(xAng, yAng, 1)
! third order e pairs
inv(5) = v_e_monom(xR, yR, 2)
inv(6) = v_e_monom(xAng, yAng, 2)
! invariant ee coupling
inv(7) = v_ee_monom(xR, yR, xAng, yAng, 1)
! mode combinations
inv(8) = Rch*umb
inv(9) = Rch*v_e_monom(xR, yR, 1)
inv(10) = umb*v_e_monom(xR, yR, 1)
inv(11) = Rch*v_e_monom(xAng, yAng, 1)
inv(12) = umb*v_e_monom(xAng, yAng, 1)
! damp coordinates because of second order and higher invariants
inv(3) = sign(sqrt(abs(inv(3))), inv(3))
inv(4) = sign(sqrt(abs(inv(4))), inv(4))
inv(5) = sign((abs(inv(5))**(1./3.)), inv(5))
inv(6) = sign((abs(inv(6))**(1./3.)), inv(6))
inv(7) = sign((abs(inv(7))**(1./3.)), inv(7))
inv(8) = sign(sqrt(abs(inv(8))), inv(8))
inv(9) = sign((abs(inv(9))**(1./3.)), inv(9))
inv(10) = sign((abs(inv(10))**(1./3.)), inv(10))
inv(11) = sign((abs(inv(11))**(1./3.)), inv(11))
inv(12) = sign((abs(inv(12))**(1./3.)), inv(12))
inv_out(:) = inv(inv_order(1:size(inv_out, 1)))
end subroutine get_invariants
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! % real part of spherical harmonics
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Ylm shifted to 0 for theta=0
real(dp) function ylm(theta, phi, l, m)
implicit none
real(dp) theta, phi
integer(idp) l, m
ylm = plm2(dcos(theta), l, m)*cos(m*phi) - plm2(1.0_dp, l, m)
end function ylm
!----------------------------------------------------------
real(dp) function plm2(x, l, n)
implicit none
real(dp) x
integer(idp) l, m, n
real(dp) pmm, p_mp1m, pllm
integer(idp) ll
! negative m und bereich von x abfangen
if ((l .lt. 0)&
&.or. (abs(n) .gt. abs(l))&
&.or. (abs(x) .gt. 1.)) then
write (6, '(''bad arguments in legendre'')')
stop
end if
! fix sign of m to compute the positiv m
m = abs(n)
pmm = (-1)**m*dsqrt(fac(2*m))*1./((2**m)*fac(m))& !compute P(m,m) not P(l,l)
&*(dsqrt(1.-x**2))**m
if (l .eq. m) then
plm2 = pmm !P(l,m)=P(m,m)
else
p_mp1m = x*dsqrt(dble(2*m + 1))*pmm !compute P(m+1,m)
if (l .eq. m + 1) then
plm2 = p_mp1m !P(l,m)=P(m+1,m)
else
do ll = m + 2, l
pllm = x*(2*l - 1)/dsqrt(dble(l**2 - m**2))*p_mp1m& ! compute P(m+2,m) up to P(l,m) recursively
&- dsqrt(dble((l - 1)**2 - m**2))&
&/dsqrt(dble(l**2 - m**2))*pmm
! schreibe m+2 und m+1 jeweils fuer die naechste iteration
pmm = p_mp1m !P(m,m) = P(m+1,m)
p_mp1m = pllm !P(m+1,m) = P(m+2,m)
end do
plm2 = pllm !P(l,m)=P(m+k,m), k element N
end if
end if
! sets the phase of -m term right (ignored to gurantee Ylm=(Yl-m)* for JT terms
! if(n.lt.0) then
! plm2 = (-1)**m * plm2 !* fac(l-m)/fac(l+m)
! endif
end function
!----------------------------------------------------------------------------------------------------
real(dp) function fac(i)
integer(idp) i
select case (i)
case (0)
fac = 1.0_dp
case (1)
fac = 1.0_dp
case (2)
fac = 2.0_dp
case (3)
fac = 6.0_dp
case (4)
fac = 24.0_dp
case (5)
fac = 120.0_dp
case (6)
fac = 720.0_dp
case (7)
fac = 5040.0_dp
case (8)
fac = 40320.0_dp
case (9)
fac = 362880.0_dp
case (10)
fac = 3628800.0_dp
case (11)
fac = 39916800.0_dp
case (12)
fac = 479001600.0_dp
case default
write (*, *) 'ERROR: no case for given faculty, Max is 12!'
stop
end select
end function fac
! Does the simplest morse transform possible
! one skaling factor + shift
function morse_transform(x, p, pst) result(t)
real(dp), intent(in) :: x
real(dp), intent(in) :: p(11)
integer, intent(in) :: pst(2)
real(dp) :: t
if (pst(2) == 11) then
t = 1.0_dp - exp(-abs(p(2))*(x - p(1)))
else
error stop 'in morse_transform key required or wrong number of parameters'
end if
end function morse_transform
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! % FUNCTION F(...) ! MAIK DEPRICATING OVER THE TOP MORSE FUNCTION FOR MYSELF
! %
! % Returns exponent of tunable Morse coordinate
! % exponent is polynomial * gaussian (skewed)
! % ilabel = 1 or 2 selects the parameters a and sfac to be used
! %
! % Background: better representation of the prefector in the
! % exponend of the morse function.
! % Formular: f(r) = lest no3 paper
! %
! % Variables:
! % x: distance of atoms (double)
! % p: parameter vector (double[20])
! % ii: 1 for CCl and 2 for CCH (int)
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pure function f(x, p, ii)
integer(idp), intent(in) :: ii !1 for CCL and 2 for CCH
real(dp), intent(in) :: x !coordinate
real(dp), intent(in) :: p(11) !parameter-vector
integer(idp) i !running index
real(dp) r !equilibrium distance
real(dp) gaus !gaus part of f
real(dp) poly !polynom part of f
real(dp) skew !tanh part of f
real(dp) f !prefactor of exponent and returned value
integer(idp) npoly(2) !order of polynom
! Maximum polynom order
npoly(1) = 5
npoly(2) = 5
! p(1): position of equilibrium
! p(2): constant of exponent
! p(3): constant for skewing the gaussian
! p(4): tuning for skewing the gaussian
! p(5): Gaussian exponent
! p(6): Shift of Gaussian maximum
! p(7)...: polynomial coefficients
! p(8+n)...: coefficients of Morse Power series
! 1-exp{[p(2)+exp{-p(5)[x-p(6)]^2}[Taylor{p(7+n)}(x-p(6))]][x-p(1)]}
! Tunable Morse function
! Power series in Tunable Morse coordinates of order m
! exponent is polynomial of order npoly * gaussian + switching function
! set r r-r_e
r = x
r = r - p(1)
! set up skewing function:
skew = 0.5_dp*p(3)*(dtanh(dabs(p(4))*(r - p(6))) + 1.0_dp)
! set up gaussian function:
gaus = dexp(-dabs(p(5))*(r - p(6))**2)
! set up power series:
poly = 0.0_dp
do i = 0, npoly(ii) - 1
poly = poly + p(7 + i)*(r - p(6))**i
end do
! set up full exponent function:
f = dabs(p(2)) + skew + gaus*poly
end function
!----------------------------------------------------------------------------------------------------
pure function xproduct(a, b) result(axb)
real(dp), intent(in) :: a(3), b(3)
real(dp) :: axb(3) !crossproduct a x b
axb(1) = a(2)*b(3) - a(3)*b(2)
axb(2) = a(3)*b(1) - a(1)*b(3)
axb(3) = a(1)*b(2) - a(2)*b(1)
end function xproduct
pure function normalized(v) result(r)
real(dp), intent(in) :: v(:)
real(dp) :: r(size(v))
r = v/norm(v)
end function normalized
pure function norm(v) result(n)
real(dp), intent(in) :: v(:)
real(dp) n
n = dsqrt(sum(v(:)**2))
end function norm
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! % FUNCTION Project_Point_Into_Plane(x,n,r0) result(p)
! % return the to n orthogonal part of a vector x-r0
! % p: projected point in plane
! % x: point being projected
! % n: normalvector of plane
! % r0: Point in plane
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pure function project_point_into_plane(x, n, r0) result(p)
real(dp), intent(in) :: x(:), n(:), r0(:)
real(dp) :: p(size(x)), xs(size(x))
xs = x - r0
p = xs - plane_to_point(x, n, r0)
end function project_point_into_plane
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! % Function Plane_To_Point(x,n,r0) result(p)
! % p: part of n in x
! % x: point being projected
! % n: normalvector of plane
! % r0: Point in plane
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
pure function plane_to_point(x, n, r0) result(p)
real(dp), intent(in) :: x(:), n(:), r0(:)
real(dp) p(size(x)), xs(size(x)), nn(size(n))
nn = normalized(n)
xs = x - r0
p = dot_product(nn, xs)*nn
end function plane_to_point
subroutine check_coordinates(q)
! check for faulty kartesain coordinates
real(dp), intent(in) :: q(:)
integer(idp) :: i
if (all(abs(q) <= epsilon(0.0_dp))) then
stop 'Error (ctrans): all kartesian coordinates are<=1d-8'
end if
do i = 1, 9, 3
if (all(abs(q(i:i + 2)) <= epsilon(0.0_dp))) then
write (*, *) q
stop 'Error(ctrans):kartesian coordinates zero for one atom'
end if
end do
end subroutine
pure function rotor_a_to_z(a, z) result(r)
real(dp), intent(in) :: a(3), z(3)
real(dp) :: r(3, 3)
real(dp) :: alpha
real(dp) :: s1(3), s(3, 3), rotor(3, 3)
s1 = xproduct(normalized(a), normalized(z))
alpha = asin(norm(s1))
s(:, 1) = normalized(s1)
s(:, 2) = normalized(z)
s(:, 3) = xproduct(s1, z)
rotor = init_rotor(alpha, 0.0_dp, 0.0_dp)
r = matmul(s, matmul(rotor, transpose(s)))
end function
! function returning Rz(gamma) * Ry(beta) * Rx(alpha) for basis order xyz
pure function init_rotor(alpha, beta, gamma) result(rotor)
real(dp), intent(in) :: alpha, beta, gamma
real(dp) :: rotor(3, 3)
rotor = 0.0_dp
rotor(1, 1) = dcos(beta)*dcos(gamma)
rotor(1, 2) = dsin(alpha)*dsin(beta)*dcos(gamma)&
&- dcos(alpha)*dsin(gamma)
rotor(1, 3) = dcos(alpha)*dsin(beta)*dcos(gamma)&
&+ dsin(alpha)*dsin(gamma)
rotor(2, 1) = dcos(beta)*dsin(gamma)
rotor(2, 2) = dsin(alpha)*dsin(beta)*dsin(gamma)&
&+ dcos(alpha)*dcos(gamma)
rotor(2, 3) = dcos(alpha)*dsin(beta)*dsin(gamma)&
&- dsin(alpha)*dcos(gamma)
rotor(3, 1) = -dsin(beta)
rotor(3, 2) = dsin(alpha)*dcos(beta)
rotor(3, 3) = dcos(alpha)*dcos(beta)
end function init_rotor
pure function create_plane(a, b, c) result(n)
real(dp), intent(in) :: a(3), b(3), c(3)
real(dp) :: n(3)
real(dp) :: axb(3), bxc(3), cxa(3)
axb = xproduct(a, b)
bxc = xproduct(b, c)
cxa = xproduct(c, a)
n = normalized(axb + bxc + cxa)
end function create_plane
function symmetrize(q1, q2, q3, sym) result(s)
real(dp), intent(in) :: q1, q2, q3
character, intent(in) :: sym
real(dp) :: s
select case (sym)
case ('a')
s = (q1 + q2 + q3)*sq3
case ('x')
s = sq6*(2.0_dp*q1 - q2 - q3)
case ('y')
s = sq2*(q2 - q3)
case default
write (*, *) 'ERROR: no rule for symmetrize with sym=', sym
stop
end select
end function symmetrize
subroutine construct_HBend(ex, ey, ph1, ph2, ph3, x_axis, y_axis)
real(dp), intent(in) :: ph1(3), ph2(3), ph3(3)
real(dp), intent(in) :: x_axis(3), y_axis(3)
real(dp), intent(out) :: ex, ey
real(dp) :: x1, y1, alpha1
real(dp) :: x2, y2, alpha2
real(dp) :: x3, y3, alpha3
! get x and y components of projected points
x1 = dot_product(ph1, x_axis)
y1 = dot_product(ph1, y_axis)
x2 = dot_product(ph2, x_axis)
y2 = dot_product(ph2, y_axis)
x3 = dot_product(ph3, x_axis)
y3 = dot_product(ph3, y_axis)
! -> calculate H deformation angles
alpha3 = datan2(y2, x2)
alpha2 = -datan2(y3, x3) !-120*ang2rad
! write(*,*)' atan2'
! write(*,*) 'alpha2:' , alpha2/ang2rad
! write(*,*) 'alpha3:' , alpha3/ang2rad
if (alpha2 .lt. 0) alpha2 = alpha2 + pi2
if (alpha3 .lt. 0) alpha3 = alpha3 + pi2
alpha1 = (pi2 - alpha2 - alpha3)
! write(*,*)' fixed break line'
! write(*,*) 'alpha1:' , alpha1/ang2rad
! write(*,*) 'alpha2:' , alpha2/ang2rad
! write(*,*) 'alpha3:' , alpha3/ang2rad
alpha1 = alpha1 !- 120.0_dp*ang2rad
alpha2 = alpha2 !- 120.0_dp*ang2rad
alpha3 = alpha3 !- 120.0_dp*ang2rad
! write(*,*)' delta alpha'
! write(*,*) 'alpha1:' , alpha1/ang2rad
! write(*,*) 'alpha2:' , alpha2/ang2rad
! write(*,*) 'alpha3:' , alpha3/ang2rad
! write(*,*)
! construct symmetric and antisymmetric H angles
ex = symmetrize(alpha1, alpha2, alpha3, 'x')
ey = symmetrize(alpha1, alpha2, alpha3, 'y')
end subroutine construct_HBend
pure function construct_umbrella(nh1, nh2, nh3, n)&
&result(umb)
real(dp), intent(in) :: nh1(3), nh2(3), nh3(3)
real(dp), intent(in) :: n(3)
real(dp) :: umb
real(dp) :: theta(3)
! calculate projections for umberella angle
theta(1) = dacos(dot_product(n, nh1))
theta(2) = dacos(dot_product(n, nh2))
theta(3) = dacos(dot_product(n, nh3))
! construct umberella angle
umb = sum(theta(1:3))/3.0_dp - 90.0_dp*ang2rad
end function construct_umbrella
pure subroutine construct_sphericals&
&(theta, phi, cf, xaxis, yaxis, zaxis)
real(dp), intent(in) :: cf(3), xaxis(3), yaxis(3), zaxis(3)
real(dp), intent(out) :: theta, phi
real(dp) :: x, y, z, v(3)
v = normalized(cf)
x = dot_product(v, normalized(xaxis))
y = dot_product(v, normalized(yaxis))
z = dot_product(v, normalized(zaxis))
theta = dacos(z)
phi = -datan2(y, x)
end subroutine construct_sphericals
subroutine int2kart(internal, kart)
real(dp), intent(in) :: internal(6)
real(dp), intent(out) :: kart(9)
real(dp) :: h1x, h1y, h1z
real(dp) :: h2x, h2y, h2z
real(dp) :: h3x, h3y, h3z
real(dp) :: dch0, dch1, dch2, dch3
real(dp) :: a1, a2, a3, wci
kart = 0.0_dp
dch1 = dchequi + sq3*internal(1) + 2*sq6*internal(2)
dch2 = dchequi + sq3*internal(1) - sq6*internal(2) + sq2*internal(3)
dch3 = dchequi + sq3*internal(1) - sq6*internal(2) - sq2*internal(3)
a1 = 2*sq6*internal(4)
a2 = -sq6*internal(4) + sq2*internal(5)
a3 = -sq6*internal(4) - sq2*internal(5)
wci = internal(6)
! Berechnung kartesische Koordinaten
! -----------------------
h1x = dch1*cos(wci*ang2rad)
h1y = 0.0
h1z = -dch1*sin(wci*ang2rad)
h3x = dch2*cos((a2 + 120)*ang2rad)*cos(wci*ang2rad)
h3y = dch2*sin((a2 + 120)*ang2rad)*cos(wci*ang2rad)
h3z = -dch2*sin(wci*ang2rad)
h2x = dch3*cos((-a3 - 120)*ang2rad)*cos(wci*ang2rad)
h2y = dch3*sin((-a3 - 120)*ang2rad)*cos(wci*ang2rad)
h2z = -dch3*sin(wci*ang2rad)
kart(1) = h1x
kart(2) = h1y
kart(3) = h1z
kart(4) = h2x
kart(5) = h2y
kart(6) = h2z
kart(7) = h3x
kart(8) = h3y
kart(9) = h3z
end subroutine int2kart
end module ctrans_mod

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src/model/Maik_chngs/select_monom_mod.f90
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src/model/Maik_chngs/sphericalharmonics_mod.f90
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! Module contains the spherical harmonics up to l=5 m=-l,..,0,..,l listed on https://en.wikipedia.org/wiki/Table_of_spherical_harmonics from 19.07.2022
! the functions are implementde by calling switch case function for given m or l value and return the corresdpondig value for given theta and phi
! the functions are split for diffrent l values and are named by P_lm.
! example for l=1 and m=-1 the realpart of the spherical harmonic for given theta and phi
! is returned by calling Re_Y_lm(1,-1,theta,phi) which itself calls the corresponding function P_1m(m,theta) and multilpies it by cos(m*phi) to account for the real part of exp(m*phi*i)
! Attention the legendre polynoms are shifted to account for the missing zero order term in spherical harmonic expansions
module sphericalharmonics_mod
use accuracy_constants, only: dp, idp
implicit none
real(kind=dp), parameter :: PI = 4.0_dp * atan( 1.0_dp )
contains
!----------------------------------------------------------------------------------------------------
function Y_lm( l , m , theta , phi ) result( y )
integer(kind=idp), intent( in ) :: l , m
real(kind=dp), intent( in ) :: theta , phi
real(kind=dp) y
character(len=70) :: errmesg
select case ( l )
case (1)
y = Y_1m( m , theta , phi )
case (2)
y = Y_2m( m , theta , phi )
case (3)
y = Y_3m( m , theta , phi )
case (4)
y = Y_4m( m , theta , phi )
case (5)
y = Y_5m( m , theta , phi )
case default
write(errmesg,'(A,i0)')&
&'order of spherical harmonics not implemented', l
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_lm
!----------------------------------------------------------------------------------------------------
function Re_Y_lm( l , m , theta , phi ) result( y )
integer(kind=idp), intent( in ) :: l , m
real(kind=dp), intent( in ) :: theta , phi
real(kind=dp) y
character(len=70) :: errmesg
select case ( l )
case (1)
y = P_1m( m , theta ) * cos(m*phi)
case (2)
y = P_2m( m , theta ) * cos(m*phi)
case (3)
y = P_3m( m , theta ) * cos(m*phi)
case (4)
y = P_4m( m , theta ) * cos(m*phi)
case (5)
y = P_5m( m , theta ) * cos(m*phi)
case (6)
y = P_6m( m , theta ) * cos(m*phi)
case default
write(errmesg,'(A,i0)')&
&'order of spherical harmonics not implemented', l
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Re_Y_lm
!----------------------------------------------------------------------------------------------------
function Im_Y_lm( l , m , theta , phi ) result( y )
integer(kind=idp), intent( in ) :: l , m
real(kind=dp), intent( in ) :: theta , phi
real(kind=dp) y
character(len=70) :: errmesg
select case ( l )
case (1)
y = P_1m( m , theta ) * sin(m*phi)
case (2)
y = P_2m( m , theta ) * sin(m*phi)
case (3)
y = P_3m( m , theta ) * sin(m*phi)
case (4)
y = P_4m( m , theta ) * sin(m*phi)
case (5)
y = P_5m( m , theta ) * sin(m*phi)
case (6)
y = P_6m( m , theta ) * sin(m*phi)
case default
write(errmesg,'(a,i0)')&
&'order of spherical harmonics not implemented',l
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Im_Y_lm
!----------------------------------------------------------------------------------------------------
!----------------------------------------------------------------------------------------------------
function Y_1m( m , theta , phi ) result( y )
integer(kind=idp),intent( in ):: m
real(kind=dp),intent( in ):: theta , phi
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-1)
y = 0.5_dp*sqrt(3.0_dp/(PI*2.0_dp))*sin(theta)*cos(phi)
case (0)
y = 0.5_dp*sqrt(3.0_dp/PI)*cos(theta)
case (1)
y = -0.5_dp*sqrt(3.0_dp/(PI*2.0_dp))*sin(theta)*cos(phi)
case default
write(errmesg,'(a,i0)') 'in y_1m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_1m
!----------------------------------------------------------------------------------------------------
function Y_2m(m,theta,phi) result(y)
integer(kind=idp),intent(in):: m
real(kind=dp),intent(in):: theta,phi
real(kind=dp) y
character(len=70) :: errmesg
select case (m)
case (-2)
y=0.25_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(2.0_dp*phi)
case (-1)
y=0.5_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)*cos(theta)*cos(phi)
case (0)
y=0.25_dp*sqrt(5.0_dp/PI)&
&*(3.0_dp*cos(theta)**2-1.0_dp)
case (1)
y=-0.5_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)*cos(theta)*cos(phi)
case (2)
y=0.25_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(2.0_dp*phi)
case default
write(errmesg,'(A,i0)')'in y_2m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_2m
!----------------------------------------------------------------------------------------------------
function Y_3m(m,theta,phi) result(y)
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta,phi
real(kind=dp) y
character(len=70) :: errmesg
select case (m)
case (-3)
y=0.125_dp*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(3.0_dp*phi)
case (-2)
y=0.25_dp*sqrt(105.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(theta)*cos(2.0_dp*phi)
case (-1)
y=0.125_dp*sqrt(21.0_dp/(PI))&
&*sin(theta)*(5.0_dp*cos(theta)**2-1.0_dp)*cos(phi)
case (0)
y=0.25_dp*sqrt(7.0_dp/PI)&
&*(5.0_dp*cos(theta)**3-3.0_dp*cos(theta))
case (1)
y=-0.125_dp*sqrt(21.0_dp/(PI))&
&*sin(theta)*(5.0_dp*cos(theta)**2-1.0_dp)*cos(phi)
case (2)
y=0.25_dp*sqrt(105.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(theta)*cos(2.0_dp*phi)
case (3)
y=-0.125_dp*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(3.0_dp*phi)
case default
write(errmesg,'(A,i0)')'in y_3m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_3m
!----------------------------------------------------------------------------------------------------
function Y_4m(m,theta,phi) result(y)
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta,phi
real(kind=dp) y
character(len=70) :: errmesg
select case (m)
case (-4)
y=(3.0_dp/16.0_dp)*sqrt(35.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(4.0_dp*phi)
case (-3)
y=0.375_dp*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(theta)*cos(3.0_dp*phi)
case (-2)
y=0.375_dp*sqrt(5.0_dp/(PI*2.0_dp))&
&*sin(theta)**2&
&*(7.0_dp*cos(theta)**2-1)*cos(2.0_dp*phi)
case (-1)
y=0.375_dp*sqrt(5.0_dp/(PI))&
&*sin(theta)*(7.0_dp*cos(theta)**3&
&-3.0_dp*cos(theta))*cos(phi)
case (0)
y=(3.0_dp/16.0_dp)/sqrt(PI)&
&*(35.0_dp*cos(theta)**4&
&-30.0_dp*cos(theta)**2+3.0_dp)
case (1)
y=-0.375_dp*sqrt(5.0_dp/(PI))&
&*sin(theta)*(7.0_dp*cos(theta)**3&
&-3.0_dp*cos(theta))*cos(phi)
case (2)
y=0.375_dp*sqrt(5.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(7.0_dp*cos(theta)**2-1.0_dp)&
&*cos(2*phi)
case (3)
y=-0.375_dp*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(theta)*cos(3.0_dp*phi)
case (4)
y=(3.0_dp/16.0_dp)*sqrt(35.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(4.0_dp*phi)
case default
write(errmesg,'(a,i0)')'in y_4m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_4m
!----------------------------------------------------------------------------------------------------
function Y_5m(m,theta,phi) result(y)
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta,phi
real(kind=dp) y
character(len=70) :: errmesg
select case (m)
case (-5)
y=(3.0_dp/32.0_dp)*sqrt(77.0_dp/PI)&
&*sin(theta)**5*cos(5*phi)
case (-4)
y=(3.0_dp/16.0_dp)*sqrt(385.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(theta)*cos(4*phi)
case (-3)
y=(1.0_dp/32.0_dp)*sqrt(385.0_dp/PI)&
&*sin(theta)**3*(9*cos(theta)**2-1.0_dp)*cos(3*phi)
case (-2)
y=0.125*sqrt(1155.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(3*cos(theta)**3-cos(theta))*cos(2*phi)
case (-1)
y=(1.0_dp/16.0_dp)*sqrt(165.0_dp/(2.0_dp*PI))&
&*sin(theta)*(21.0_dp*cos(theta)**4&
&-14.0_dp*cos(theta)**2+1.0_dp)*cos(phi)
case (0)
y=(1.0_dp/16.0_dp)/sqrt(11.0_dp/PI)&
&*(63.0_dp*cos(theta)**5-70.0_dp*cos(theta)**3&
&+15.0_dp*cos(theta))
case (1)
y=(-1.0_dp/16.0_dp)*sqrt(165.0_dp/(2.0_dp*PI))&
&*sin(theta)*(21.0_dp*cos(theta)**4&
&-14.0_dp*cos(theta)**2+1.0_dp)*cos(phi)
case (2)
y=0.125*sqrt(1155.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(3*cos(theta)**3-cos(theta))*cos(2*phi)
case (3)
y=(-1.0_dp/32.0_dp)*sqrt(385.0_dp/PI)&
&*sin(theta)**3*(9.0_dp*cos(theta)**2-1.0_dp)&
&*cos(3.0_dp*phi)
case (4)
y=(3.0_dp/16.0_dp)*sqrt(385.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(theta)*cos(4.0_dp*phi)
case (5)
y=(-3.0_dp/32.0_dp)*sqrt(77.0_dp/PI)&
&*sin(theta)**5*cos(5.0_dp*phi)
case default
write(errmesg,'(A,i0)')'in y_5m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function Y_5m
!----------------------------------------------------------------------------------------------------
function P_1m( m , theta ) result( y )
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=1 and given m and theta
integer(kind=idp),intent( in ):: m
real(kind=dp),intent( in ):: theta
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-1)
y = 0.5_dp*sqrt(3.0_dp/(PI*2.0_dp))*sin(theta)
case (0)
y = 0.5_dp*sqrt(3.0_dp/PI)*(cos(theta)-1.0_dp) ! -1 is subtracted to shift so that for theta=0 y=0
case (1)
y = -0.5_dp*sqrt(3.0_dp/(PI*2.0_dp))*sin(theta)
case default
write(errmesg,'(A,i0)')'in p_1m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_1m
!----------------------------------------------------------------------------------------------------
function P_2m( m , theta ) result( y )
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=2 and given m and theta
integer(kind=idp),intent(in):: m
real(kind=dp),intent(in):: theta
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-2)
y=0.25_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)**2
case (-1)
y=0.5_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)*cos(theta)
case (0)
y = (3.0_dp*cos(theta)**2-1.0_dp)
y = y - 2.0_dp !2.0 is subtracted to shift so that for theta=0 y=0
y = y * 0.25_dp*sqrt(5.0_dp/PI) ! normalize
case (1)
y = -0.5_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)*cos(theta)
case (2)
y = 0.25_dp*sqrt(15.0_dp/(PI*2.0_dp))&
&*sin(theta)**2
case default
write(errmesg,'(A,i0)')'in p_2m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_2m
!----------------------------------------------------------------------------------------------------
function P_3m( m , theta ) result( y )
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=3 and given m and theta
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-3)
y=0.125_dp*sqrt(35.0_dp/PI)&
&*sin(theta)**3
case (-2)
y=0.25_dp*sqrt(105.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(theta)
case (-1)
y=0.125_dp*sqrt(21.0_dp/(PI))&
&*sin(theta)*(5*cos(theta)**2-1.0_dp)
case (0)
y=(5.0_dp*cos(theta)**3-3*cos(theta))
y=y-2.0_dp ! 2.0 is subtracted to shift so that for theta=0 y=0
y=y*0.25_dp*sqrt(7.0_dp/PI) ! normalize
case (1)
y=-0.125_dp*sqrt(21.0_dp/(PI))&
&*sin(theta)*(5.0_dp*cos(theta)**2-1.0_dp)
case (2)
y=0.25*sqrt(105.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*cos(theta)
case (3)
y=-0.125*sqrt(35.0_dp/PI)&
&*sin(theta)**3
case default
write(errmesg,'(A,i0)')'in p_3m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_3m
!----------------------------------------------------------------------------------------------------
function P_4m(m,theta) result(y)
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=4 and given m and theta
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-4)
y=(3.0_dp/16.0_dp)*sqrt(35.0_dp/2.0_dp*PI)&
&*sin(theta)**4
case (-3)
y=0.375*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(theta)
case (-2)
y=0.375*sqrt(5.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(7*cos(theta)**2-1)
case (-1)
y=0.375*sqrt(5.0_dp/(PI))&
&*sin(theta)*(7*cos(theta)**3-3*cos(theta))
case (0)
y=(35*cos(theta)**4-30*cos(theta)**2+3)
y = y - 8.0_dp !8.0 is subtracted to shift so that for theta=0 y=0
y = y * (3.0_dp/16.0_dp)/sqrt(PI)
case (1)
y=-0.375*sqrt(5.0_dp/(PI))&
&*sin(theta)*(7*cos(theta)**3-3*cos(theta))
case (2)
y=0.375*sqrt(5.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(7*cos(theta)**2-1)
case (3)
y=-0.375*sqrt(35.0_dp/PI)&
&*sin(theta)**3*cos(theta)
case (4)
y=(3.0_dp/16.0_dp)*sqrt(35.0_dp/2.0_dp*PI)&
&*sin(theta)**4
case default
write(errmesg,'(A,i0)')'in p_4m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_4m
!----------------------------------------------------------------------------------------------------
function P_5m(m,theta) result(y)
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=5 and given m and theta
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta
real(kind=dp) y
character(len=70) :: errmesg
select case ( m )
case (-5)
y=(3.0_dp/32.0_dp)*sqrt(77.0_dp/PI)&
&*sin(theta)**5
case (-4)
y=(3.0_dp/16.0_dp)*sqrt(385.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(theta)
case (-3)
y=(1.0_dp/32.0_dp)*sqrt(385.0_dp/PI)&
&*sin(theta)**3*(9*cos(theta)**2-1.0_dp)
case (-2)
y=0.125*sqrt(1155.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(3*cos(theta)**3-cos(theta))
case (-1)
y=(1.0_dp/16.0_dp)*sqrt(165.0_dp/(2.0_dp*PI))&
&*sin(theta)*(21*cos(theta)**4-14*cos(theta)**2+1)
case (0)
y = (63*cos(theta)**5-70*cos(theta)**3+15*cos(theta))
y = y - 8.0_dp !8.0 is subtracted to shift so that for theta=0 y=0
y = y * (1.0_dp/16.0_dp)/sqrt(11.0_dp/PI)
case (1)
y=(-1.0_dp/16.0_dp)*sqrt(165.0_dp/(2.0_dp*PI))&
&*sin(theta)*(21*cos(theta)**4-14*cos(theta)**2+1)
case (2)
y=0.125*sqrt(1155.0_dp/(PI*2.0_dp))&
&*sin(theta)**2*(3*cos(theta)**3-cos(theta))
case (3)
y=(-1.0_dp/32.0_dp)*sqrt(385.0_dp/PI)&
&*sin(theta)**3*(9*cos(theta)**2-1.0_dp)
case (4)
y=(3.0_dp/16.0_dp)*sqrt(385.0_dp/2.0_dp*PI)&
&*sin(theta)**4*cos(theta)
case (5)
y=(-3.0_dp/32.0_dp)*sqrt(77.0_dp/PI)&
&*sin(theta)**5
case default
write(errmesg,'(A,i0)')'in p_5m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_5m
!----------------------------------------------------------------------------------------------------
function P_6m(m,theta) result(y)
! >Function returns the value of the corresponding normalized Associated legendre polynom for l=6 and given m and theta
integer(kind=idp), intent(in) :: m
real(kind=dp), intent(in) :: theta
real(kind=dp):: y
character(len=70) :: errmesg
select case ( m )
case (-6)
y = (1.0_dp/64.0_dp)*sqrt(3003.0_dp/PI)&
&* sin(theta)**6
case (-5)
y = (3.0_dp/32.0_dp)*sqrt(1001.0_dp/PI)&
&* sin(theta)**5&
&* cos(theta)
case (-4)
y= (3.0_dp/32.0_dp)*sqrt(91.0_dp/(2.0_dp*PI))&
&* sin(theta)**4&
&* (11*cos(theta)**2 - 1 )
case (-3)
y= (1.0_dp/32.0_dp)*sqrt(1365.0_dp/PI)&
&* sin(theta)**3&
&* (11*cos(theta)**3 - 3*cos(theta) )
case (-2)
y= (1.0_dp/64.0_dp)*sqrt(1365.0_dp/PI)&
&* sin(theta)**2&
&* (33*cos(theta)**4 - 18*cos(theta)**2 + 1 )
case (-1)
y= (1.0_dp/16.0_dp)*sqrt(273.0_dp/(2.0_dp*PI))&
&* sin(theta)&
&* (33*cos(theta)**5 - 30*cos(theta)**3 + 5*cos(theta) )
case (0)
y = 231*cos(theta)**6 - 315*cos(theta)**4 + 105*cos(theta)**2-5
y = y - 16.0_dp !16.0 is subtracted to shift so that for theta=0 y=0
y = y * (1.0_dp/32.0_dp)*sqrt(13.0_dp/PI)
case (1)
y= -(1.0_dp/16.0_dp)*sqrt(273.0_dp/(2.0_dp*PI))&
&* sin(theta)&
&* (33*cos(theta)**5 - 30*cos(theta)**3 + 5*cos(theta) )
case (2)
y= (1.0_dp/64.0_dp)*sqrt(1365.0_dp/PI)&
&* sin(theta)**2&
&* (33*cos(theta)**4 - 18*cos(theta)**2 + 1 )
case (3)
y= -(1.0_dp/32.0_dp)*sqrt(1365.0_dp/PI)&
&* sin(theta)**3&
&* (11*cos(theta)**3 - 3*cos(theta) )
case (4)
y= (3.0_dp/32.0_dp)*sqrt(91.0_dp/(2.0_dp*PI))&
&* sin(theta)**4&
&* (11*cos(theta)**2 - 1 )
case (5)
y= -(3.0_dp/32.0_dp)*sqrt(1001.0_dp/PI)&
&* sin(theta)**5 * cos(theta)
case (6)
y = (1.0_dp/64.0_dp)*sqrt(3003.0_dp/PI)&
&* sin(theta)**6
case default
write(errmesg,'(A,i0)')'in p_6m given m not logic, ', m
error stop 'error in spherical harmonics' !error stop errmesg
end select
end function P_6m
!----------------------------------------------------------------------------------------------------
end module

4
src/model/adia.f90
View File

@ -66,9 +66,9 @@
! init eigenvector matrix
TYPES = int(p(pst(1,32)))
TYPES = int(p(pst(1,33)))
BLK = int(p(pst(1,32)+1)) ! BLOCK IF TYPE IS 3
BLK = int(p(pst(1,33)+1)) ! BLOCK IF TYPE IS 3
u = 0.d0
vx=0.0d0
skip=.false.

10
src/model/data_transform.f90
View File

@ -32,14 +32,14 @@
if (pst(2,32) .ne. 2) then
if (pst(2,33) .ne. 2) then
write(*,*) "Error in Paramater Keys, TYPE_CAL should be 2 parameter", pst(2,32)
write(*,*) "Error in Paramater Keys, TYPE_CAL should be 2 parameter", pst(2,33)
stop
end if
TYPES = int(p(pst(1,32)))! TYPE OF THE CALCULATION
BLK= int(p(pst(1,32)+1))! BLOCK IF TYPE IS 3
TYPES = int(p(pst(1,33)))! TYPE OF THE CALCULATION
BLK= int(p(pst(1,33)+1))! BLOCK IF TYPE IS 3
write(*,*) "TYPE of calculation:",TYPES
pt=1
@ -109,7 +109,7 @@
call one_dia_upper(mat_z,y(1:ntot,pt))
else
write(*,*) "Error in TYPE of calculationss",TYPES
write(*,*) "the value:,", p(pst(1,32))
write(*,*) "the value:,", p(pst(1,33))
stop
end if
pt=pt+1

7
src/model/keys.f90
View File

@ -10,7 +10,7 @@ contains
character(len=1) prefix(4)
parameter (prefix=['N','P','A','S'])
!character (len=20) key(4,25)
integer,parameter:: np=32
integer,parameter:: np=33
character(len=16) parname(np)
integer i,j
! Defining keys for potential
@ -63,11 +63,12 @@ contains
parname(27)='LZPE1E2O1'
parname(28)='LZPE1E2O2'
parname(29)='LZPA2E1O1'
parname(30)='LZPA2E2O2'
parname(30)='LZPA2E1O2'
parname(31)='LZPA2E2O1'
parname(32)='LZPA2E2O2'
parname(32)='TYPE_CAL'! TYPE OF THE CALCULATION WHETHER IT IS THE TRACE OR SOMETHING ELSE
parname(33)='TYPE_CAL'! TYPE OF THE CALCULATION WHETHER IT IS THE TRACE OR SOMETHING ELSE
do i=1,np
do j=1,4

6
src/model/matrix_form.f90
View File

@ -12,7 +12,7 @@
y=0.0d0
!y(1)=mx(4,4)+mx(5,5)
do i=2,3
do i=1,ndiab
y(1)=y(1)+mx(i,i)
y(2)=y(2)+my(i,i)
enddo
@ -298,8 +298,8 @@
double precision, intent(in) :: p(:)
integer, intent(in) :: id_write
integer :: type_calc, blk
type_calc = int(p(pst(1,32)))
blk = int(p(pst(1,32)+1))
type_calc = int(p(pst(1,33)))
blk = int(p(pst(1,33)+1))
if (type_calc ==1) then
write(id_write,*) "Type of calculation: TRACE"

26
src/model/model.f90
View File

@ -64,7 +64,8 @@ module diab_mod
id=id+1 ! 4
! order 2
e(1,1)=e(1,1)+p(pst(1,id))*(xs**2-ys**2)+p(pst(1,id)+1)*(xb**2-yb**2) & ! 5 p
e(1,1)=e(1,1)+p(pst(1,id))*(xs**2-ys**2)+p(pst(1,id)+1)*(xb**2-yb**2) & ! 3 p
+p(pst(1,id)+2)*(xs*xb-ys*yb)
id =id+1 ! 5
e(2,2)=e(2,2)+p(pst(1,id))*(xs**2-ys**2)+p(pst(1,id)+1)*(xb**2-yb**2) &
@ -388,13 +389,13 @@ module diab_mod
! w and z of E''
! order 1
id = id
id = id ! 22
e(2,2) = e(2,2) + p(pst(1,id))*ys + p(pst(1,id)+1)*yb
e(3,3) = e(3,3) - p(pst(1,id))*ys - p(pst(1,id)+1)*yb
e(2,3) = e(2,3) - p(pst(1,id))*xs -p(pst(1,id)+1)*xb
! order 2
id = id +1
id = id +1 ! 23
do i =1,3
e(2,2) = e(2,2) + p(pst(1,id)+(i-1))*v2(i+3)
e(3,3) = e(3,3) - p(pst(1,id)+(i-1))*v2(i+3)
@ -404,13 +405,13 @@ module diab_mod
! W and Z of E'
! order 1
id = id +1
id = id +1 ! 24
e(4,4) = e(4,4) + p(pst(1,id))*ys + p(pst(1,id)+1)*yb
e(5,5) = e(5,5) - p(pst(1,id))*ys - p(pst(1,id)+1)*yb
e(4,5) = e(4,5) - p(pst(1,id))*xs -p(pst(1,id)+1)*xb
! order 2
id = id +1
id = id +1 ! 25
do i =1,3
e(4,4) = e(4,4) + p(pst(1,id)+(i-1))*v2(i+3)
e(5,5) = e(5,5) - p(pst(1,id)+(i-1))*v2(i+3)
@ -420,7 +421,7 @@ module diab_mod
! Pseudo of E' and E''
! it must have odd power of b
id = id +1
id = id +1 !26
! order 0
e(2,4) = e(2,4)
e(3,5) = e(3,5)
@ -428,13 +429,13 @@ module diab_mod
e(3,4) = e(3,4) - b*(p(pst(1,id)))
! order 1
id = id +1
id = id +1 !27
e(2,4) = e(2,4) + b*(p(pst(1,id))*ys + p(pst(1,id)+1)*yb)
e(3,5) = e(3,5) + b*(p(pst(1,id))*ys + p(pst(1,id)+1)*yb)
e(2,5) = e(2,5) - b*(p(pst(1,id))*xs + p(pst(1,id)+1)*xb)
e(3,4) = e(3,4) + b*(p(pst(1,id))*xs + p(pst(1,id)+1)*xb)
! order 2
id = id +1
id = id +1 !28
do i=1,3
e(2,4) = e(2,4) + b*(p(pst(1,id)+(i-1)))*v2(i+3)
e(3,5) = e(3,5) + b*(p(pst(1,id)+(i-1)))*v2(i+3)
@ -445,11 +446,12 @@ module diab_mod
! the coupling between A2' and E''
! order 1
id = id +1
id = id +1 !29
e(1,2) = e(1,2) + b*(p(pst(1,id))*xs + p(pst(1,id)*xb))
e(1,3) = e(1,3) - b*(p(pst(1,id))*ys + p(pst(1,id)*yb))
id = id +1
id = id +1 !30
! order 2
do i=1,3
e(1,2) = e(1,2) + b*(p(pst(1,id)+(i-1)))*v2(i)
@ -459,11 +461,11 @@ module diab_mod
! the coupling of A2' and E'
! order 1
id = id +1
id = id +1 !31
e(1,2) = e(1,2) + (p(pst(1,id))*xs + p(pst(1,id)*xb))
e(1,3) = e(1,3) - (p(pst(1,id))*ys + p(pst(1,id)*yb))
id = id +1
id = id +1 ! 32
! order 2
do i=1,3
e(1,2) = e(1,2) + (p(pst(1,id)+(i-1)))*v2(i)

38
src/model/trans/JTmod.incl
View File

@ -1,38 +0,0 @@
!*** Relevant parameters for the analytic model
!*** offsets:
!*** offsets(1): morse equilibrium (N-H, Angström)
!*** offsets(2): reference angle (H-N-H)
!*** offsets(3): --
!*** pat_index: vector giving the position of the
!*** various coordinates (see below)
!*** ppars: polynomial parameters for tmcs
!*** vcfs: coefficients for V expressions.
!*** wzcfs: coefficients for W & Z expressions.
!*** ifc: inverse factorials.
integer matdim
parameter (matdim=5) ! matrix is (matdim)x(matdim)
real*8 offsets(2)
integer pat_index(maxnin)
! NH3 params
parameter (offsets=[1.0228710942d0,120.d0])
!##########################################################################
! coordinate order; the first #I number of coords are given to the
! ANN, where #I is the number of input neurons. The position i in
! pat_index corresponds to a coordinate, the value of pat_index(i)
! signifies its position.
!
! The vector is ordered as follows:
! a,xs,ys,xb,yb,b,rs**2,rb**2,b**2,
! es*eb, es**3, eb**3,es**2*eb, es*eb**2
! ri**2 := xi**2+yi**2 = ei**2; ei := (xi,yi), i = s,b
!
! parts not supposed to be read by ANN are marked by ';' for your
! convenience.
!##########################################################################
! a,rs**2,rb**2,es*eb,es**3,eb**3,es**2*eb,es*eb**2,b**2 #I=9 (6D)
parameter (pat_index=[1,2,3,4,5,6,7,8,9,10,11,12,13,14])
!**************************************************************************

260
src/model/trans/cart2int.f
View File

@ -1,260 +0,0 @@
subroutine cart2int(cart,qint)
implicit none
! This version merges both coordinate transformation routines into
! one. JTmod's sscales(2:3) are ignored.
! This is the first version to be compatible with one of my proper 6D fits
! Time-stamp: <2024-10-22 13:52:59 dwilliams>
! Input (cartesian, in Angström)
! cart(:,1): N
! cart(:,1+i): Hi
! Output
! qint(i): order defined in JTmod.
! Internal Variables
! no(1:3): NO distances 1-3
! pat_in: temporary coordinates
! axis: main axis of NO3
include 'nnparams.incl'
include 'JTmod.incl'
real*8 cart(3,4),qint(maxnin)
real*8 no(3), r1, r2, r3
real*8 v1(3), v2(3), v3(3)
real*8 n1(3), n2(3), n3(3), tr(3)
real*8 ortho(3)
real*8 pat_in(maxnin)
logical ignore_umbrella,dbg_umbrella
logical dbg_distances
!.. Debugging parameters
!.. set umbrella to 0
parameter (ignore_umbrella=.false.)
! parameter (ignore_umbrella=.true.)
!.. break if umbrella is not 0
parameter (dbg_umbrella=.false.)
! parameter (dbg_umbrella=.true.)
!.. break for tiny distances
parameter (dbg_distances=.false.)
! parameter (dbg_distances=.true.)
integer k
!.. get N-O vectors and distances:
do k=1,3
v1(k)=cart(k,2)-cart(k,1)
v2(k)=cart(k,3)-cart(k,1)
v3(k)=cart(k,4)-cart(k,1)
enddo
no(1)=norm(v1,3)
no(2)=norm(v2,3)
no(3)=norm(v3,3)
!.. temporarily store displacements
do k=1,3
pat_in(k)=no(k)-offsets(1)
enddo
do k=1,3
v1(k)=v1(k)/no(1)
v2(k)=v2(k)/no(2)
v3(k)=v3(k)/no(3)
enddo
!.. compute three normal vectors for the ONO planes:
call xprod(n1,v1,v2)
call xprod(n2,v2,v3)
call xprod(n3,v3,v1)
do k=1,3
tr(k)=(n1(k)+n2(k)+n3(k))/3.d0
enddo
r1=norm(tr,3)
do k=1,3
tr(k)=tr(k)/r1
enddo
! rotate trisector
call rot_trisec(tr,v1,v2,v3)
!.. determine trisector angle:
if (ignore_umbrella) then
pat_in(7)=0.0d0
else
pat_in(7)=pi/2.0d0 - acos(scalar(v1,tr,3))
pat_in(7)=sign(pat_in(7),cart(1,2))
endif
!.. molecule now lies in yz plane, compute projected ONO angles:
v1(1)=0.d0
v2(1)=0.d0
v3(1)=0.d0
r1=norm(v1,3)
r2=norm(v2,3)
r3=norm(v3,3)
do k=2,3
v1(k)=v1(k)/r1
v2(k)=v2(k)/r2
v3(k)=v3(k)/r3
enddo
! make orthogonal vector to v3
ortho(1)=0.0d0
ortho(2)=v3(3)
ortho(3)=-v3(2)
!.. projected ONO angles in radians
pat_in(4)=get_ang(v2,v3,ortho)
pat_in(5)=get_ang(v1,v3,ortho)
pat_in(6)=dabs(pat_in(5)-pat_in(4))
!.. account for rotational order of atoms
if (pat_in(4).le.pat_in(5)) then
pat_in(5)=2*pi-pat_in(4)-pat_in(6)
else
pat_in(4)=2*pi-pat_in(5)-pat_in(6)
endif
pat_in(4)=rad2deg*pat_in(4)-offsets(2)
pat_in(5)=rad2deg*pat_in(5)-offsets(2)
pat_in(6)=rad2deg*pat_in(6)-offsets(2)
pat_in(7)=rad2deg*pat_in(7)
call genANN_ctrans(pat_in)
qint(:)=pat_in(:)
contains
!-------------------------------------------------------------------
! compute vector product n1 of vectors v1 x v2
subroutine xprod(n1,v1,v2)
implicit none
real*8 n1(3), v1(3), v2(3)
n1(1) = v1(2)*v2(3) - v1(3)*v2(2)
n1(2) = v1(3)*v2(1) - v1(1)*v2(3)
n1(3) = v1(1)*v2(2) - v1(2)*v2(1)
end subroutine
!-------------------------------------------------------------------
! compute scalar product of vectors v1 and v2:
real*8 function scalar(v1,v2,n)
implicit none
integer i, n
real*8 v1(*), v2(*)
scalar=0.d0
do i=1,n
scalar=scalar+v1(i)*v2(i)
enddo
end function
!-------------------------------------------------------------------
! compute norm of vector:
real*8 function norm(x,n)
implicit none
integer i, n
real*8 x(*)
norm=0.d0
do i=1,n
norm=norm+x(i)**2
enddo
norm=sqrt(norm)
end function
!-------------------------------------------------------------------
subroutine rot_trisec(tr,v1,v2,v3)
implicit none
real*8 tr(3),v1(3),v2(3),v3(3)
real*8 vrot(3)
real*8 rot_ax(3)
real*8 cos_phi,sin_phi
! evaluate cos(-phi) and sin(-phi), where phi is the angle between
! tr and (1,0,0)
cos_phi=tr(1)
sin_phi=dsqrt(tr(2)**2+tr(3)**2)
if (sin_phi.lt.1.0d-12) then
return
endif
! determine rotational axis
rot_ax(1) = 0.0d0
rot_ax(2) = tr(3)
rot_ax(3) = -tr(2)
! normalize
rot_ax=rot_ax/sin_phi
! now the rotation can be done using Rodrigues' rotation formula
! v'=v*cos(p) + (k x v)sin(p) + k (k*v) (1-cos(p))
! for v=tr k*v vanishes by construction:
! check that the rotation does what it should
call rodrigues(vrot,tr,rot_ax,cos_phi,sin_phi)
if (dsqrt(vrot(2)**2+vrot(3)**2).gt.1.0d-12) then
write(6,*) "ERROR: BROKEN TRISECTOR"
stop
endif
tr=vrot
call rodrigues(vrot,v1,rot_ax,cos_phi,sin_phi)
v1=vrot
call rodrigues(vrot,v2,rot_ax,cos_phi,sin_phi)
v2=vrot
call rodrigues(vrot,v3,rot_ax,cos_phi,sin_phi)
v3=vrot
end subroutine
!-------------------------------------------------------------------
subroutine rodrigues(vrot,v,axis,cos_phi,sin_phi)
implicit none
real*8 vrot(3),v(3),axis(3)
real*8 cos_phi,sin_phi
real*8 ortho(3)
call xprod(ortho,axis,v)
vrot = v*cos_phi + ortho*sin_phi
> + axis*scalar(axis,v,3)*(1-cos_phi)
end subroutine
!-------------------------------------------------------------------
real*8 function get_ang(v,xaxis,yaxis)
implicit none
! get normalized [0:2pi) angle from vectors in the yz plane
real*8 v(3),xaxis(3),yaxis(3)
real*8 phi
real*8 pi
parameter (pi=3.141592653589793d0)
phi=atan2(scalar(yaxis,v,3),scalar(xaxis,v,3))
if (phi.lt.0.0d0) then
phi=2*pi+phi
endif
get_ang=phi
end function
end subroutine cart2int

88
src/model/trans/ctrans.f
View File

@ -1,88 +0,0 @@
!-------------------------------------------------------------------
! Time-stamp: "2024-10-09 13:33:50 dwilliams"
subroutine genANN_ctrans(pat_in)
implicit none
include 'nnparams.incl'
include 'JTmod.incl'
real*8 pat_in(maxnin)
real*8 raw_in(maxnin),off_in(maxnin),ptrans_in(7)
real*8 r0
real*8 a,b,xs,ys,xb,yb
integer k
off_in(1:7)=pat_in(1:7)
r0=offsets(1)
! transform primitives
! recover raw distances from offset coords
do k=1,3
raw_in(k)=off_in(k)+offsets(1)
enddo
do k=1,3
ptrans_in(k)=off_in(k)
enddo
! rescale ONO angles
ptrans_in(4)=deg2rad*off_in(4)
ptrans_in(5)=deg2rad*off_in(5)
ptrans_in(6)=deg2rad*off_in(6)
! rescale umbrella
ptrans_in(7)=off_in(7)*deg2rad
! compute symmetry coordinates
! A (breathing)
a=(ptrans_in(1)+ptrans_in(2)+ptrans_in(3))/dsqrt(3.0d0)
! ES
call prim2emode(ptrans_in(1:3),xs,ys)
! EB
call prim2emode(ptrans_in(4:6),xb,yb)
! B (umbrella)
b=ptrans_in(7)
! overwrite input with output
pat_in(pat_index(1))=a ! 1
pat_in(pat_index(2))=xs
pat_in(pat_index(3))=ys
pat_in(pat_index(4))=xb
pat_in(pat_index(5))=yb
pat_in(pat_index(6))=b
! totally symmetric monomials
pat_in(pat_index(7))=xs**2 + ys**2 ! 2
pat_in(pat_index(8))=xb**2 + yb**2 ! 3
pat_in(pat_index(9))=b**2 ! 9
pat_in(pat_index(10))=xs*xb+ys*yb ! 4
! S^3, B^3
pat_in(pat_index(11))=xs*(xs**2-3*ys**2) ! 5
pat_in(pat_index(12))=xb*(xb**2-3*yb**2) ! 6
! S^2 B, S B^2
pat_in(pat_index(13))=xb*(xs**2-ys**2) - 2*yb*xs*ys ! 7
pat_in(pat_index(14))=xs*(xb**2-yb**2) - 2*ys*xb*yb ! 8
do k=11,14
pat_in(pat_index(k))=tanh(0.1d0*pat_in(pat_index(k)))*10.0d0
enddo
contains
subroutine prim2emode(prim,ex,ey)
implicit none
! Takes a 2D-vector prim and returns the degenerate modes x and y
! following our standard conventions.
real*8 prim(3),ex,ey
ex=(2.0d0*prim(1)-prim(2)-prim(3))/dsqrt(6.0d0)
ey=(prim(2)-prim(3))/dsqrt(2.0d0)
end
end subroutine

43
src/model/trans/nnparams.incl
View File

@ -1,43 +0,0 @@
!**** Declarations
real*8 pi
real*8 hart2eV, eV2hart
real*8 hart2icm, icm2hart
real*8 eV2icm, icm2eV
real*8 deg2rad, rad2deg
integer maxnin,maxnout
!**********************************************************
!**** Parameters
!*** maxnin: max. number of neurons in input layer
!*** maxnout: max. number of neurons in output layer
parameter (maxnin=14,maxnout=15)
!**********************************************************
!**** Numerical Parameters
!*** infty: largest possible double precision real value.
!*** iinfty: largest possible integer value.
! 3.14159265358979323846264338327950...
parameter (pi=3.1415926536D0)
!**********************************************************
!**** Unit Conversion Parameters
!*** X2Y: convert from X to Y.
!***
!*** hart: hartree
!*** eV: electron volt
!*** icm: inverse centimeters (h*c/cm)
!****
!*** deg: degree
!*** rad: radians
parameter (hart2icm=219474.69d0)
parameter (hart2eV=27.211385d0)
parameter (eV2icm=hart2icm/hart2eV)
parameter (icm2hart=1.0d0/hart2icm)
parameter (eV2hart=1.0d0/hart2eV)
parameter (icm2eV=1.0d0/eV2icm)
parameter (deg2rad=pi/180.0d0)
parameter (rad2deg=1.0d0/deg2rad)

8
src/model/write.f
View File

@ -400,10 +400,10 @@
call print_plotheader(id_plot,coord,npt,set)
do i=1,npt
write(id_plot,"(ES16.8,*(3(ES16.8),:))")
> x(coord,i), ymod(:,i),y(:,i),(wt(:,i))
! write(id_plot,"(2ES16.8,*(3(ES16.8),:))")
! > x(coord,i), x(coord+1,i),y(:,i)
! write(id_plot,"(ES16.8,*(3(ES16.8),:))")
! > x(coord,i), ymod(:,i),y(:,i),(wt(:,i))
write(id_plot,"(2ES16.8,*(3(ES16.8),:))")
> x(coord,i), x(coord+1,i),y(:,i)
enddo
end subroutine