110 lines
3.6 KiB
Fortran
110 lines
3.6 KiB
Fortran
BEGIN_PROVIDER [ double precision, integral_density_alpha_knowles_becke_per_atom, (nucl_num)]
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&BEGIN_PROVIDER [ double precision, integral_density_beta_knowles_becke_per_atom, (nucl_num)]
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implicit none
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double precision :: accu
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integer :: i,j,k,l
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double precision :: x
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double precision :: integrand(n_points_angular_grid), weights(n_points_angular_grid)
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double precision :: f_average_angular_alpha,f_average_angular_beta
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double precision :: derivative_knowles_function,knowles_function
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! Run over all nuclei in order to perform the Voronoi partition
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! according ot equation (6) of the paper of Becke (JCP, (88), 1988)
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! Here the m index is referred to the w_m(r) weight functions of equation (22)
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! Run over all points of integrations : there are
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! n_points_radial_grid (i) * n_points_angular_grid (k)
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do j = 1, nucl_num
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integral_density_alpha_knowles_becke_per_atom(j) = 0.d0
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integral_density_beta_knowles_becke_per_atom(j) = 0.d0
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do i = 1, n_points_radial_grid-1
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! Angular integration over the solid angle Omega for a FIXED angular coordinate "r"
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f_average_angular_alpha = 0.d0
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f_average_angular_beta = 0.d0
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do k = 1, n_points_angular_grid
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f_average_angular_alpha += weights_angular_points(k) * one_body_dm_mo_alpha_at_grid_points(k,i,j) * weight_functions_at_grid_points(k,i,j)
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f_average_angular_beta += weights_angular_points(k) * one_body_dm_mo_beta_at_grid_points(k,i,j) * weight_functions_at_grid_points(k,i,j)
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enddo
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!
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x = grid_points_radial(i) ! x value for the mapping of the [0, +\infty] to [0,1]
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double precision :: contrib_integration
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! print*,m_knowles
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contrib_integration = derivative_knowles_function(alpha_knowles(int(nucl_charge(j))),m_knowles,x) &
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*knowles_function(alpha_knowles(int(nucl_charge(j))),m_knowles,x)**2
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integral_density_alpha_knowles_becke_per_atom(j) += contrib_integration *f_average_angular_alpha
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integral_density_beta_knowles_becke_per_atom(j) += contrib_integration *f_average_angular_beta
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enddo
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integral_density_alpha_knowles_becke_per_atom(j) *= dr_radial_integral
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integral_density_beta_knowles_becke_per_atom(j) *= dr_radial_integral
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enddo
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END_PROVIDER
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double precision function knowles_function(alpha,m,x)
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implicit none
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BEGIN_DOC
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! function proposed by Knowles (JCP, 104, 1996) for distributing the radial points :
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! the Log "m" function ( equation (7) in the paper )
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END_DOC
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double precision, intent(in) :: alpha,x
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integer, intent(in) :: m
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knowles_function = -alpha * dlog(1.d0-x**m)
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end
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double precision function derivative_knowles_function(alpha,m,x)
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implicit none
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BEGIN_DOC
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! derivative of the function proposed by Knowles (JCP, 104, 1996) for distributing the radial points
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END_DOC
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double precision, intent(in) :: alpha,x
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integer, intent(in) :: m
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derivative_knowles_function = alpha * dble(m) * x**(m-1) / (1.d0 - x**m)
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end
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BEGIN_PROVIDER [double precision, alpha_knowles, (100)]
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implicit none
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integer :: i
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BEGIN_DOC
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! recommended values for the alpha parameters according to the paper of Knowles (JCP, 104, 1996)
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! as a function of the nuclear charge
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END_DOC
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! H-He
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alpha_knowles(1) = 5.d0
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alpha_knowles(2) = 5.d0
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! Li-Be
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alpha_knowles(3) = 7.d0
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alpha_knowles(4) = 7.d0
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! B-Ne
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do i = 5, 10
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alpha_knowles(i) = 5.d0
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enddo
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! Na-Mg
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do i = 11, 12
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alpha_knowles(i) = 7.d0
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enddo
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! Al-Ar
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do i = 13, 18
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alpha_knowles(i) = 5.d0
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enddo
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! K-Ca
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do i = 19, 20
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alpha_knowles(i) = 7.d0
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enddo
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! Sc-Zn
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do i = 21, 30
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alpha_knowles(i) = 5.d0
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enddo
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! Ga-Kr
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do i = 31, 36
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alpha_knowles(i) = 7.d0
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enddo
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END_PROVIDER
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