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example_LJ_model.F90
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! publically accessible things required for interface to pymatnest
!
! subroutine ll_init_model(N_params, params)
! integer :: N_params ! number of parameters
! double precision :: params(N_params) ! list of parameters
!
! initializes potential
!
! subroutine ll_init_config(N, Z, pos, cell, Emax)
! integer :: N ! number of atoms
! integer :: Z(N) ! atomic numbers of atoms
! double precision :: pos(3,N), cell(3,3) ! positions, cell vectors
! double precision :: Emax ! maximum energy for config acceptance
!
! initializes a configuration with energy < Emax
! config will be tested for failure after return
!
! double precision function ll_eval_energy(N, Z, pos, n_extra_data, extra_data, cell)
! integer :: N ! number of atoms
! double precision :: pos(3,N), cell(3,3) ! positions, cell vectors
! integer :: n_extra_data ! width of extra data array
! double precision :: extra_data(n_extra_data, N) ! extra data on output
!
! evaluates energy of a config, sets extra_data, returns energy
!
! integer function ll_move_atom_1(N, pos, n_extra_data, extra_data, cell, d_i, d_pos, dEmax, dE)
! integer :: N ! number of atoms
! double precision :: pos(3,N), cell(3,3) ! positions, cell vectors, on output updated (pos only) to be consistent with acceptance/rejection
! integer :: n_extra_data ! width of extra data array
! double precision :: extra_data(n_extra_data, N) ! extra data on input, on output updated to be consistent with acceptance/rejection
! integer :: d_i ! index of atom to be perturbed, 1-based (called from fortran_MC())
! double precision :: d_pos(3) ! displacement of perturbed atom
! double precision :: dEmax ! maximum change in energy for move acceptance
! double precision :: dE ! on output actual change in energy, 0.0 if move is rejected
!
! moves an atom if dE < dEmax
! if move is accepted, updates pos, extra_data, sets dE
! if move is rejected, nothing is updated, dE set to 0.0
! returns 1 for accept, 0 for reject
!
! double precision function ll_eval_forces(N, pos, n_extra_data, extra_data, cell, forces)
! integer :: N ! number of atoms
! double precision :: pos(3,N), cell(3,3), forces(3,N) ! positions, cell vectors, forces
! integer :: n_extra_data ! width of extra data array
! double precision :: extra_data(n_extra_data, N) ! extra data on output
!
! evaluates forces, sets extra_data
! returns energy
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine ll_init_model(N_params, params)
use example_LJ_params_mod
implicit none
integer :: N_params
double precision :: params(N_params)
if (N_params==1) then
write(*,*) "No LJ parameters were found, the default will be used:"
epsilon(1,1) = 4.0
epsilon(2,2) = 4.0
epsilon(1,2) = 6.0
epsilon(2,1) = epsilon(1,2)
sigma(1,1) = 1.0
sigma(2,2) = 1.0
sigma(1,2) = (sigma(1,1)+sigma(2,2))/2.0
sigma(2,1) = sigma(1,2)
cutoff = 3.0*sigma
cutoff_sq = cutoff*cutoff
else if (N_params == 7) then
epsilon(1,1) = 4.0*params(1)
epsilon(2,2) = 4.0*params(2)
epsilon(1,2) = 4.0*params(3)
epsilon(2,1) = epsilon(1,2)
sigma(1,1) = params(4)
sigma(2,2) = params(5)
sigma(1,2) = params(6)
sigma(2,1) = sigma(1,2)
cutoff = params(7)*sigma
cutoff_sq = cutoff*cutoff
write(*,*) "User defined LJ parameters:"
write(*,*) "(1)-(1)Epsilon=",params(1),"(2)-(2)Epsilon=",params(2), &
&"(1)-(2)Epsilon=",params(3)
write(*,*) "(1)-(1)Sigma=", params(4),"(2)-(2)Sigma=",params(5), &
&"(1)-(2)Sigma=",params(6)
write(*,*) "Mixed term LJ parameters are set using", &
&" user defined values."
write(*,*) "sigma(1,1), sigma(2,2), sigma(1,2) and sigma(2,1) are set to:"
write(*,*) sigma(1,1), sigma(2,2), sigma(1,2), sigma(2,1)
write(*,*) "LJ cutoff(1,1), LJ cutoff(2,2), LJ cutoff(1,2) and LJ cutoff(2,1) are set to:"
write(*,*) cutoff(1,1), cutoff(2,2), cutoff(1,2), cutoff(2,1)
else
epsilon(1,1) = 4.0*params(1) ! The usual 4 factor in the LJ equation is
! included here!
epsilon(2,2) = 4.0*params(2)
epsilon(1,2) = sqrt(epsilon(1,1)*epsilon(2,2))
epsilon(2,1) = epsilon(1,2)
sigma(1,1) = params(3)
sigma(2,2) = params(4)
sigma(1,2) = (sigma(1,1)+sigma(2,2))/2.0
sigma(2,1) = sigma(1,2)
cutoff = params(5)*sigma
cutoff_sq = cutoff*cutoff
write(*,*) "User defined LJ parameters:"
write(*,*) "(1)-(1)Epsilon=",params(1),"(2)-(2)Epsilon=",params(2)
write(*,*) "(1)-(1)Sigma=", params(3),"(2)-(2)Sigma=",params(4)
write(*,*) "Mixed term LJ parameters are calculated using the", &
&" Lorenz-Berthelot rule."
write(*,*) "LJ cutoff=",cutoff
endif
E_offset = (sigma/cutoff)**12 - (sigma/cutoff)**6
write(*,*) "LJ offset=",E_offset
end subroutine ll_init_model
subroutine ll_init_config(N, Z, pos, cell, Emax)
implicit none
integer :: N
integer :: Z(N)
double precision :: pos(3,N), cell(3,3)
double precision :: Emax
return
end subroutine ll_init_config
double precision function ll_eval_energy(N, Z, pos, n_extra_data, extra_data, cell)
use example_mat_mod
use example_LJ_params_mod
implicit none
integer :: N
integer :: Z(N)
double precision :: pos(3,N), cell(3,3)
integer :: n_extra_data
double precision :: extra_data(n_extra_data, N)
integer :: i, j, Z_i, Z_j
double precision :: dr(3), dr_mag, dr_mag_sq, dr_l(3), dr_l0(3), pos_l(3,N)
double precision :: cell_inv(3,3), E_term
integer :: dj1, dj2, dj3
integer :: n_images
double precision cell_height(3), v_norm_hat(3)
call matrix3x3_inverse(cell, cell_inv)
! into lattice coodinates
pos_l = matmul(cell_inv, pos)
if (n_extra_data == 1) extra_data = 0.0
do i=1, 3
v_norm_hat = cell(:,mod(i,3)+1) .cross. cell(:,mod(i+1,3)+1)
v_norm_hat = v_norm_hat / sqrt(sum(v_norm_hat**2))
cell_height(i) = abs(sum(v_norm_hat*cell(:,i)))
end do
n_images = ceiling(maxval(cutoff)/minval(cell_height))
ll_eval_energy = 0.0
do i=1, N
Z_i = Z(i)
do j=i, N
Z_j = Z(j)
dr_l0 = pos_l(:,i)-pos_l(:,j)
dr_l0 = dr_l0 - floor(dr_l0+0.5)
do dj1=-n_images,n_images
dr_l(1) = dr_l0(1) + real(dj1, 8)
do dj2=-n_images,n_images
dr_l(2) = dr_l0(2) + real(dj2, 8)
do dj3=-n_images,n_images
dr_l(3) = dr_l0(3) + real(dj3, 8)
if (i == j .and. dj1 == 0 .and. dj2 == 0 .and. dj3 == 0) cycle
dr(1) = sum(cell(1,:)*dr_l)
dr(2) = sum(cell(2,:)*dr_l)
dr(3) = sum(cell(3,:)*dr_l)
dr_mag_sq = sum(dr*dr)
if (dr_mag_sq < cutoff_sq(Z_i,Z_j)) then
dr_mag = sqrt(dr_mag_sq)
E_term = epsilon(Z_i,Z_j)*(((sigma(Z_i,Z_j)/dr_mag)**12 - (sigma(Z_i,Z_j)/dr_mag)**6) - E_offset(Z_i,Z_j))
if (i == j) E_term = E_term * 0.5
ll_eval_energy = ll_eval_energy + E_term
if (n_extra_data == 1) then
extra_data(1,i) = extra_data(1,i) + 0.5*E_term
extra_data(1,j) = extra_data(1,j) + 0.5*E_term
endif
endif
end do
end do
end do
end do
end do
end function ll_eval_energy
integer function ll_move_atom_1(N, Z, pos, n_extra_data, extra_data, cell, d_i, d_pos, dEmax, dE)
use example_mat_mod
use example_LJ_params_mod
implicit none
integer :: N
integer :: Z(N)
double precision :: pos(3,N), cell(3,3)
integer :: n_extra_data
double precision :: extra_data(n_extra_data, N)
integer :: d_i
double precision :: d_pos(3)
double precision :: dEmax, dE
integer :: i, j, Z_i, Z_j
double precision :: dr(3), drp(3), dr_l(3), drp_l(3), dr_l0(3), drp_l0(3), dr_mag, drp_mag, &
dr_mag_sq, drp_mag_sq, pos_l(3,N), d_pos_l(3)
double precision :: cell_inv(3,3)
integer :: dj1, dj2, dj3
double precision, allocatable, save :: new_extra_data(:,:)
integer n_images
double precision cell_height(3), v_norm_hat(3)
do i=1, 3
v_norm_hat = cell(:,mod(i,3)+1) .cross. cell(:,mod(i+1,3)+1)
v_norm_hat = v_norm_hat / sqrt(sum(v_norm_hat**2))
cell_height(i) = abs(sum(v_norm_hat*cell(:,i)))
end do
n_images = ceiling(maxval(cutoff)/minval(cell_height))
call matrix3x3_inverse(cell, cell_inv)
! into lattice coodinates
do i=1, N
pos_l(1,i) = sum(cell_inv(1,:)*pos(:,i))
pos_l(2,i) = sum(cell_inv(2,:)*pos(:,i))
pos_l(3,i) = sum(cell_inv(3,:)*pos(:,i))
end do
d_pos_l(1) = sum(cell_inv(1,:)*d_pos(:))
d_pos_l(2) = sum(cell_inv(2,:)*d_pos(:))
d_pos_l(3) = sum(cell_inv(3,:)*d_pos(:))
if (n_extra_data == 1 .and. allocated(new_extra_data)) then
if (any(shape(new_extra_data) /= shape(extra_data))) then
deallocate(new_extra_data)
endif
endif
if (n_extra_data == 1 .and. .not. allocated(new_extra_data)) then
allocate(new_extra_data(n_extra_data, N))
endif
if (n_extra_data == 1) new_extra_data = extra_data
dE = 0.0
i=d_i
Z_i = Z(i)
do j=1,N
if (j == i) cycle
Z_j = Z(j)
dr_l0 = pos_l(:,i) - pos_l(:,j)
dr_l0 = dr_l0 - floor(dr_l0+0.5)
drp_l0 = pos_l(:,i)+d_pos_l(:) - pos_l(:,j)
drp_l0 = drp_l0 - floor(drp_l0+0.5)
do dj1=-n_images,n_images
dr_l(1) = dr_l0(1) + real(dj1, 8)
drp_l(1) = drp_l0(1) + real(dj1, 8)
do dj2=-n_images,n_images
dr_l(2) = dr_l0(2) + real(dj2, 8)
drp_l(2) = drp_l0(2) + real(dj2, 8)
do dj3=-n_images,n_images
dr_l(3) = dr_l0(3) + real(dj3, 8)
drp_l(3) = drp_l0(3) + real(dj3, 8)
dr(1) = sum(cell(1,:)*dr_l)
dr(2) = sum(cell(2,:)*dr_l)
dr(3) = sum(cell(3,:)*dr_l)
drp(1) = sum(cell(1,:)*drp_l)
drp(2) = sum(cell(2,:)*drp_l)
drp(3) = sum(cell(3,:)*drp_l)
dr_mag_sq = sum(dr*dr)
drp_mag_sq = sum(drp*drp)
if (dr_mag_sq < cutoff_sq(Z_i,Z_j)) then
dr_mag = sqrt(dr_mag_sq)
dE = dE - epsilon(Z_i,Z_j)*(((sigma(Z_i,Z_j)/dr_mag)**12 - (sigma(Z_i,Z_j)/dr_mag)**6) - E_offset(Z_i,Z_j))
if (n_extra_data == 1) then
new_extra_data(1,i) = new_extra_data(1,i) - 0.5*((sigma(Z_i,Z_j)/dr_mag)**12 - &
(sigma(Z_i,Z_j)/dr_mag)**6 - E_offset(Z_i,Z_j))
new_extra_data(1,j) = new_extra_data(1,j) - 0.5*((sigma(Z_i,Z_j)/dr_mag)**12 - &
(sigma(Z_i,Z_j)/dr_mag)**6 - E_offset(Z_i,Z_j))
endif
endif
if (drp_mag_sq < cutoff_sq(Z_i,Z_j)) then
drp_mag = sqrt(drp_mag_sq)
dE = dE + epsilon(Z_i,Z_j)*(((sigma(Z_i,Z_j)/drp_mag)**12 - (sigma(Z_i,Z_j)/drp_mag)**6) - E_offset(Z_i,Z_j))
if (n_extra_data == 1) then
new_extra_data(1,i) = new_extra_data(1,i) + 0.5*epsilon(Z_i,Z_j)*(((sigma(Z_i,Z_j)/drp_mag)**12 - &
(sigma(Z_i,Z_j)/drp_mag)**6) - E_offset(Z_i,Z_j))
new_extra_data(1,j) = new_extra_data(1,j) + 0.5*epsilon(Z_i,Z_j)*(((sigma(Z_i,Z_j)/drp_mag)**12 - &
(sigma(Z_i,Z_j)/drp_mag)**6) - E_offset(Z_i,Z_j))
endif
endif
end do
end do
end do
end do
if (dE < dEmax) then ! accept
pos(:,i) = pos(:,i) + d_pos(:)
if (n_extra_data == 1) extra_data = new_extra_data
ll_move_atom_1 = 1
else ! reject
dE = 0.0
ll_move_atom_1 = 0
endif
end function ll_move_atom_1
function ll_eval_forces(N, Z, pos, n_extra_data, extra_data, cell, forces) result(energy)
use example_mat_mod
use example_LJ_params_mod
implicit none
integer :: N
integer :: Z(N)
double precision :: pos(3,N), cell(3,3), forces(3,N)
integer :: n_extra_data
double precision :: extra_data(n_extra_data, N)
double precision :: energy ! result
integer :: i, j, Z_i, Z_j
double precision :: dr(3), dr_mag, dr_mag_sq, dr_l(3), dr_l0(3), pos_l(3,N)
double precision :: cell_inv(3,3), E_term
integer :: dj1, dj2, dj3
integer n_images
double precision cell_height(3), v_norm_hat(3)
do i=1, 3
v_norm_hat = cell(:,mod(i,3)+1) .cross. cell(:,mod(i+1,3)+1)
v_norm_hat = v_norm_hat / sqrt(sum(v_norm_hat**2))
cell_height(i) = abs(sum(v_norm_hat*cell(:,i)))
end do
n_images = ceiling(maxval(cutoff)/minval(cell_height))
call matrix3x3_inverse(cell, cell_inv)
do i=1, N
pos_l(1,i) = sum(cell_inv(1,:)*pos(:,i))
pos_l(2,i) = sum(cell_inv(2,:)*pos(:,i))
pos_l(3,i) = sum(cell_inv(3,:)*pos(:,i))
end do
if (n_extra_data == 1) extra_data = 0.0
energy = 0.0
forces = 0.0
do i=1, N
Z_i = Z(i)
do j=i, N
Z_j = Z(j)
dr_l0 = pos_l(:,i) - pos_l(:,j)
dr_l0 = dr_l0 - floor(dr_l0+0.5)
do dj1=-n_images,n_images
dr_l(1) = dr_l0(1) + real(dj1, 8)
do dj2=-n_images,n_images
dr_l(2) = dr_l0(2) + real(dj2, 8)
do dj3=-n_images,n_images
dr_l(3) = dr_l0(3) + real(dj3, 8)
if (i == j .and. dj1 == 0 .and. dj2 == 0 .and. dj3 == 0) cycle
dr(1) = sum(cell(1,:)*dr_l)
dr(2) = sum(cell(2,:)*dr_l)
dr(3) = sum(cell(3,:)*dr_l)
dr_mag_sq = sum(dr*dr)
if (dr_mag_sq < cutoff_sq(Z_i,Z_j)) then
dr_mag = sqrt(dr_mag_sq)
E_term = epsilon(Z_i,Z_j)*((sigma(Z_i,Z_j)/dr_mag)**12 - (sigma(Z_i,Z_j)/dr_mag)**6 - E_offset(Z_i,Z_j))
if (i == j) E_term = E_term * 0.5
energy = energy + E_term
if (n_extra_data == 1) then
extra_data(1,i) = extra_data(1,i) + 0.5*E_term
extra_data(1,j) = extra_data(1,j) + 0.5*E_term
endif
if (i /= j) then
forces(:,i) = forces(:,i) - epsilon(Z_i,Z_j)*(-12.0*sigma(Z_i,Z_j)**12/dr_mag**13 + &
6.0*sigma(Z_i,Z_j)**6/dr_mag**7)*(dr/dr_mag)
forces(:,j) = forces(:,j) + epsilon(Z_i,Z_j)*(-12.0*sigma(Z_i,Z_j)**12/dr_mag**13 + &
6.0*sigma(Z_i,Z_j)**6/dr_mag**7)*(dr/dr_mag)
endif
endif
end do
end do
end do
end do
end do
end function ll_eval_forces