BEGIN_PROVIDER [integer, n_points_radial_grid] &BEGIN_PROVIDER [integer, n_points_integration_angular] implicit none 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 if(.not.my_grid_becke)then 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 END_PROVIDER BEGIN_PROVIDER [integer, n_points_grid_per_atom] implicit none BEGIN_DOC ! Number of grid points per atom END_DOC n_points_grid_per_atom = n_points_integration_angular * n_points_radial_grid END_PROVIDER BEGIN_PROVIDER [double precision, angular_quadrature_points, (n_points_integration_angular,3) ] &BEGIN_PROVIDER [double precision, weights_angular_points, (n_points_integration_angular)] implicit none BEGIN_DOC ! weights and grid points for the integration on the angular variables on ! the unit sphere centered on (0,0,0) ! According to the LEBEDEV scheme END_DOC include 'constants.include.F' integer :: i double precision :: accu double precision :: degre_rad double precision :: x(n_points_integration_angular) double precision :: y(n_points_integration_angular) double precision :: z(n_points_integration_angular) double precision :: w(n_points_integration_angular) degre_rad = pi/180.d0 accu = 0.d0 select case (n_points_integration_angular) case (5810) call LD5810(X,Y,Z,W,n_points_integration_angular) case (2030) call LD2030(X,Y,Z,W,n_points_integration_angular) case (1202) call LD1202(X,Y,Z,W,n_points_integration_angular) case (0590) call LD0590(X,Y,Z,W,n_points_integration_angular) case (302) call LD0302(X,Y,Z,W,n_points_integration_angular) case (266) call LD0266(X,Y,Z,W,n_points_integration_angular) case (194) call LD0194(X,Y,Z,W,n_points_integration_angular) case (170) call LD0170(X,Y,Z,W,n_points_integration_angular) case (74) call LD0074(X,Y,Z,W,n_points_integration_angular) case (50) call LD0050(X,Y,Z,W,n_points_integration_angular) case default print *, irp_here//': wrong n_points_integration_angular. Expected:' print *, '[ 50 | 74 | 170 | 194 | 266 | 302 | 590 | 1202 | 2030 | 5810 ]' stop -1 end select do i = 1, n_points_integration_angular angular_quadrature_points(i,1) = x(i) angular_quadrature_points(i,2) = y(i) angular_quadrature_points(i,3) = z(i) weights_angular_points(i) = w(i) * 4.d0 * pi accu += w(i) enddo END_PROVIDER BEGIN_PROVIDER [integer , m_knowles] implicit none BEGIN_DOC ! value of the "m" parameter in the equation (7) of the paper of Knowles (JCP, 104, 1996) END_DOC m_knowles = 3 END_PROVIDER BEGIN_PROVIDER [double precision, grid_points_radial, (n_points_radial_grid)] &BEGIN_PROVIDER [double precision, dr_radial_integral] implicit none BEGIN_DOC ! points in [0,1] to map the radial integral [0,\infty] END_DOC dr_radial_integral = 1.d0/dble(n_points_radial_grid-1) integer :: i do i = 1, n_points_radial_grid grid_points_radial(i) = dble(i-1) * dr_radial_integral enddo END_PROVIDER BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular,n_points_radial_grid,nucl_num)] BEGIN_DOC ! x,y,z coordinates of grid points used for integration in 3d space END_DOC implicit none integer :: i,j,k double precision :: dr,x_ref,y_ref,z_ref double precision :: knowles_function 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 double precision :: x,r ! 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 enddo enddo END_PROVIDER BEGIN_PROVIDER [double precision, weight_at_r, (n_points_integration_angular,n_points_radial_grid,nucl_num) ] 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 implicit none integer :: i,j,k,l,m double precision :: r(3) double precision :: accu,cell_function_becke double precision :: tmp_array(nucl_num) ! 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) 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 tmp_array(i) = cell_function_becke(r,i) ! P_n(r) ! 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 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 stop endif enddo enddo enddo END_PROVIDER BEGIN_PROVIDER [double precision, final_weight_at_r, (n_points_integration_angular,n_points_radial_grid,nucl_num) ] BEGIN_DOC ! Total weight on each grid point which takes into account all Lebedev, Voronoi and radial weights. END_DOC implicit none integer :: i,j,k,l,m double precision :: r(3) double precision :: accu,cell_function_becke double precision :: tmp_array(nucl_num) double precision :: contrib_integration,x double precision :: derivative_knowles_function,knowles_function ! 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 , dr_radial_integral stop endif enddo enddo enddo END_PROVIDER