2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_PROVIDER [integer, n_points_radial_grid]
|
|
|
|
|
&BEGIN_PROVIDER [integer, n_points_integration_angular]
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
BEGIN_DOC
|
|
|
|
|
! n_points_radial_grid = number of radial grid points per atom
|
|
|
|
|
!
|
|
|
|
|
! n_points_integration_angular = number of angular grid points per atom
|
|
|
|
|
!
|
|
|
|
|
! These numbers are automatically set by setting the grid_type_sgn parameter
|
|
|
|
|
END_DOC
|
|
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
|
2023-09-05 11:52:08 +02:00
|
|
|
if(.not. my_grid_becke) then
|
2023-05-15 00:31:28 +02:00
|
|
|
select case (grid_type_sgn)
|
|
|
|
|
case(0)
|
|
|
|
|
n_points_radial_grid = 23
|
|
|
|
|
n_points_integration_angular = 170
|
|
|
|
|
case(1)
|
|
|
|
|
n_points_radial_grid = 50
|
|
|
|
|
n_points_integration_angular = 194
|
|
|
|
|
case(2)
|
|
|
|
|
n_points_radial_grid = 75
|
|
|
|
|
n_points_integration_angular = 302
|
|
|
|
|
case(3)
|
|
|
|
|
n_points_radial_grid = 99
|
|
|
|
|
n_points_integration_angular = 590
|
|
|
|
|
case default
|
|
|
|
|
write(*,*) '!!! Quadrature grid not available !!!'
|
|
|
|
|
stop
|
|
|
|
|
end select
|
|
|
|
|
else
|
|
|
|
|
n_points_radial_grid = my_n_pt_r_grid
|
|
|
|
|
n_points_integration_angular = my_n_pt_a_grid
|
|
|
|
|
endif
|
|
|
|
|
|
2023-09-06 19:21:14 +02:00
|
|
|
print*, " n_points_radial_grid = ", n_points_radial_grid
|
|
|
|
|
print*, " n_points_integration_angular = ", n_points_integration_angular
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_PROVIDER [integer, n_points_grid_per_atom]
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_DOC
|
|
|
|
|
! Number of grid points per atom
|
|
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
n_points_grid_per_atom = n_points_integration_angular * n_points_radial_grid
|
|
|
|
|
|
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
BEGIN_PROVIDER [integer, m_knowles]
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_DOC
|
|
|
|
|
! value of the "m" parameter in the equation (7) of the paper of Knowles (JCP, 104, 1996)
|
|
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
m_knowles = 3
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
BEGIN_PROVIDER [double precision, R_gill]
|
|
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
|
|
|
|
|
R_gill = 3.d0
|
|
|
|
|
|
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
|
|
|
|
! ---
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_PROVIDER [double precision, grid_points_radial, (n_points_radial_grid)]
|
|
|
|
|
&BEGIN_PROVIDER [double precision, dr_radial_integral]
|
|
|
|
|
|
|
|
|
|
BEGIN_DOC
|
|
|
|
|
! points in [0,1] to map the radial integral [0,\infty]
|
|
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
|
integer :: i
|
|
|
|
|
|
|
|
|
|
dr_radial_integral = 1.d0 / dble(n_points_radial_grid-1)
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
do i = 1, n_points_radial_grid
|
|
|
|
|
grid_points_radial(i) = dble(i-1) * dr_radial_integral
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular,n_points_radial_grid,nucl_num)]
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_DOC
|
|
|
|
|
! x,y,z coordinates of grid points used for integration in 3d space
|
|
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
implicit none
|
2023-05-15 00:31:28 +02:00
|
|
|
integer :: i, j, k
|
|
|
|
|
double precision :: dr, x_ref, y_ref, z_ref
|
|
|
|
|
double precision :: x, r, tmp
|
|
|
|
|
double precision, external :: knowles_function
|
|
|
|
|
|
|
|
|
|
grid_points_per_atom = 0.d0
|
|
|
|
|
|
|
|
|
|
PROVIDE rad_grid_type
|
|
|
|
|
if(rad_grid_type .eq. "KNOWLES") then
|
|
|
|
|
|
|
|
|
|
do i = 1, nucl_num
|
|
|
|
|
x_ref = nucl_coord(i,1)
|
|
|
|
|
y_ref = nucl_coord(i,2)
|
|
|
|
|
z_ref = nucl_coord(i,3)
|
|
|
|
|
do j = 1, n_points_radial_grid-1
|
|
|
|
|
|
|
|
|
|
! x value for the mapping of the [0, +\infty] to [0,1]
|
|
|
|
|
x = grid_points_radial(j)
|
|
|
|
|
! value of the radial coordinate for the integration
|
|
|
|
|
r = knowles_function(alpha_knowles(grid_atomic_number(i)), m_knowles, x)
|
|
|
|
|
|
|
|
|
|
! explicit values of the grid points centered around each atom
|
|
|
|
|
do k = 1, n_points_integration_angular
|
|
|
|
|
grid_points_per_atom(1,k,j,i) = x_ref + angular_quadrature_points(k,1) * r
|
|
|
|
|
grid_points_per_atom(2,k,j,i) = y_ref + angular_quadrature_points(k,2) * r
|
|
|
|
|
grid_points_per_atom(3,k,j,i) = z_ref + angular_quadrature_points(k,3) * r
|
|
|
|
|
enddo
|
2019-01-25 11:39:31 +01:00
|
|
|
enddo
|
|
|
|
|
enddo
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
elseif(rad_grid_type .eq. "GILL") then
|
|
|
|
|
! GILL & CHIEN, 2002
|
|
|
|
|
|
|
|
|
|
do i = 1, nucl_num
|
|
|
|
|
x_ref = nucl_coord(i,1)
|
|
|
|
|
y_ref = nucl_coord(i,2)
|
|
|
|
|
z_ref = nucl_coord(i,3)
|
|
|
|
|
do j = 1, n_points_radial_grid-1
|
|
|
|
|
|
|
|
|
|
r = R_gill * dble(j-1)**2 / dble(n_points_radial_grid-j+1)**2
|
|
|
|
|
|
|
|
|
|
! explicit values of the grid points centered around each atom
|
|
|
|
|
do k = 1, n_points_integration_angular
|
|
|
|
|
grid_points_per_atom(1,k,j,i) = x_ref + angular_quadrature_points(k,1) * r
|
|
|
|
|
grid_points_per_atom(2,k,j,i) = y_ref + angular_quadrature_points(k,2) * r
|
|
|
|
|
grid_points_per_atom(3,k,j,i) = z_ref + angular_quadrature_points(k,3) * r
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
else
|
|
|
|
|
|
|
|
|
|
print*, " rad_grid_type = ", rad_grid_type, ' is not implemented'
|
|
|
|
|
stop
|
|
|
|
|
|
|
|
|
|
endif
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
BEGIN_PROVIDER [double precision, weight_at_r, (n_points_integration_angular,n_points_radial_grid,nucl_num)]
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
BEGIN_DOC
|
|
|
|
|
! Weight function at grid points : w_n(r) according to the equation (22)
|
|
|
|
|
! of Becke original paper (JCP, 88, 1988)
|
|
|
|
|
!
|
|
|
|
|
! The "n" discrete variable represents the nucleis which in this array is
|
|
|
|
|
! represented by the last dimension and the points are labelled by the
|
|
|
|
|
! other dimensions.
|
|
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
implicit none
|
2023-05-15 00:31:28 +02:00
|
|
|
integer :: i, j, k, l, m
|
|
|
|
|
double precision :: r(3), accu
|
|
|
|
|
double precision :: tmp_array(nucl_num)
|
|
|
|
|
double precision, external :: cell_function_becke
|
|
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
! run over all points in space
|
|
|
|
|
! that are referred to each atom
|
|
|
|
|
do j = 1, nucl_num
|
|
|
|
|
!for each radial grid attached to the "jth" atom
|
|
|
|
|
do k = 1, n_points_radial_grid -1
|
|
|
|
|
! for each angular point attached to the "jth" atom
|
|
|
|
|
do l = 1, n_points_integration_angular
|
|
|
|
|
r(1) = grid_points_per_atom(1,l,k,j)
|
|
|
|
|
r(2) = grid_points_per_atom(2,l,k,j)
|
|
|
|
|
r(3) = grid_points_per_atom(3,l,k,j)
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
accu = 0.d0
|
|
|
|
|
! For each of these points in space, ou need to evaluate the P_n(r)
|
|
|
|
|
do i = 1, nucl_num
|
|
|
|
|
! function defined for each atom "i" by equation (13) and (21) with k == 3
|
2023-05-15 00:31:28 +02:00
|
|
|
tmp_array(i) = cell_function_becke(r, i) ! P_n(r)
|
2019-01-25 11:39:31 +01:00
|
|
|
! Then you compute the summ the P_n(r) function for each of the "r" points
|
|
|
|
|
accu += tmp_array(i)
|
|
|
|
|
enddo
|
|
|
|
|
accu = 1.d0/accu
|
|
|
|
|
weight_at_r(l,k,j) = tmp_array(j) * accu
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
if(isnan(weight_at_r(l,k,j))) then
|
|
|
|
|
print*,'isnan(weight_at_r(l,k,j))'
|
|
|
|
|
print*,l,k,j
|
|
|
|
|
accu = 0.d0
|
|
|
|
|
do i = 1, nucl_num
|
|
|
|
|
! function defined for each atom "i" by equation (13) and (21) with k == 3
|
|
|
|
|
tmp_array(i) = cell_function_becke(r,i) ! P_n(r)
|
|
|
|
|
print*,i,tmp_array(i)
|
|
|
|
|
! Then you compute the summ the P_n(r) function for each of the "r" points
|
|
|
|
|
accu += tmp_array(i)
|
|
|
|
|
enddo
|
|
|
|
|
write(*,'(100(F16.10,X))')tmp_array(j) , accu
|
2019-03-27 12:56:32 +01:00
|
|
|
stop
|
|
|
|
|
endif
|
2019-01-25 11:39:31 +01:00
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
|
|
END_PROVIDER
|
|
|
|
|
|
2023-05-15 00:31:28 +02:00
|
|
|
! ---
|
|
|
|
|
|
|
|
|
|
BEGIN_PROVIDER [double precision, final_weight_at_r, (n_points_integration_angular,n_points_radial_grid,nucl_num)]
|
2019-01-25 11:39:31 +01:00
|
|
|
|
|
|
|
|
BEGIN_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
! Total weight on each grid point which takes into account all Lebedev, Voronoi and radial weights.
|
2019-01-25 11:39:31 +01:00
|
|
|
END_DOC
|
2023-05-15 00:31:28 +02:00
|
|
|
|
2019-01-25 11:39:31 +01:00
|
|
|
implicit none
|
2023-05-15 00:31:28 +02:00
|
|
|
integer :: i, j, k, l, m
|
|
|
|
|
double precision :: r(3)
|
|
|
|
|
double precision :: tmp_array(nucl_num)
|
|
|
|
|
double precision :: contrib_integration, x, tmp
|
|
|
|
|
double precision, external :: derivative_knowles_function, knowles_function
|
|
|
|
|
|
|
|
|
|
final_weight_at_r = 0.d0
|
|
|
|
|
|
|
|
|
|
PROVIDE rad_grid_type
|
|
|
|
|
if(rad_grid_type .eq. "KNOWLES") then
|
|
|
|
|
|
|
|
|
|
! run over all points in space
|
|
|
|
|
do j = 1, nucl_num ! that are referred to each atom
|
|
|
|
|
do i = 1, n_points_radial_grid -1 !for each radial grid attached to the "jth" atom
|
|
|
|
|
x = grid_points_radial(i) ! x value for the mapping of the [0, +\infty] to [0,1]
|
|
|
|
|
|
|
|
|
|
do k = 1, n_points_integration_angular ! for each angular point attached to the "jth" atom
|
|
|
|
|
contrib_integration = derivative_knowles_function(alpha_knowles(grid_atomic_number(j)), m_knowles, x) &
|
|
|
|
|
* knowles_function(alpha_knowles(grid_atomic_number(j)), m_knowles, x)**2
|
|
|
|
|
|
|
|
|
|
final_weight_at_r(k,i,j) = weights_angular_points(k) * weight_at_r(k,i,j) * contrib_integration * dr_radial_integral
|
|
|
|
|
|
|
|
|
|
if(isnan(final_weight_at_r(k,i,j))) then
|
|
|
|
|
print*,'isnan(final_weight_at_r(k,i,j))'
|
|
|
|
|
print*,k,i,j
|
|
|
|
|
write(*,'(100(F16.10,X))') weights_angular_points(k), weight_at_r(k,i,j), contrib_integration
|
|
|
|
|
stop
|
|
|
|
|
endif
|
|
|
|
|
enddo
|
2019-01-25 11:39:31 +01:00
|
|
|
enddo
|
|
|
|
|
enddo
|
2023-05-15 00:31:28 +02:00
|
|
|
|
|
|
|
|
elseif(rad_grid_type .eq. "GILL") then
|
|
|
|
|
! GILL & CHIEN, 2002
|
|
|
|
|
|
|
|
|
|
tmp = 2.d0 * R_gill * R_gill * R_gill * dble(n_points_radial_grid)
|
|
|
|
|
|
|
|
|
|
! run over all points in space
|
|
|
|
|
do j = 1, nucl_num ! that are referred to each atom
|
|
|
|
|
do i = 1, n_points_radial_grid - 1 !for each radial grid attached to the "jth" atom
|
|
|
|
|
contrib_integration = tmp * dble(i-1)**5 / dble(n_points_radial_grid-i+1)**7
|
|
|
|
|
do k = 1, n_points_integration_angular ! for each angular point attached to the "jth" atom
|
|
|
|
|
final_weight_at_r(k,i,j) = weights_angular_points(k) * weight_at_r(k,i,j) * contrib_integration
|
|
|
|
|
|
|
|
|
|
if(isnan(final_weight_at_r(k,i,j))) then
|
|
|
|
|
print*,'isnan(final_weight_at_r(k,i,j))'
|
|
|
|
|
print*,k,i,j
|
|
|
|
|
write(*,'(100(F16.10,X))') weights_angular_points(k), weight_at_r(k,i,j), contrib_integration, dr_radial_integral
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stop
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endif
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enddo
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enddo
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enddo
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else
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print*, " rad_grid_type = ", rad_grid_type, ' is not implemented'
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stop
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endif
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2019-01-25 11:39:31 +01:00
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END_PROVIDER
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2023-05-15 00:31:28 +02:00
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|
