196 lines
8.4 KiB
Fortran
196 lines
8.4 KiB
Fortran
double precision function NAI_pol_mult_erf_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
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BEGIN_DOC
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! Computes the following integral R^3 :
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!
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! .. math::
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!
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! \int dr (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
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! \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$ exp(-delta (r - D)^2 ).
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!
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END_DOC
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implicit none
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include 'constants.include.F'
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double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
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double precision, intent(in) :: C_center(3),mu ! coulomb center "C" and "mu" in the erf(mu*x)/x function
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double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
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integer, intent(in) :: power_A(3),power_B(3)
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double precision :: NAI_pol_mult_erf
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! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
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double precision :: A_new(0:max_dim,3)! new polynom
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double precision :: A_center_new(3) ! new center
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integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
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double precision :: alpha_new ! new exponent
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double precision :: fact_a_new ! constant factor
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double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
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integer :: d(3),i,lx,ly,lz,iorder_tmp(3)
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thr = 1.d-10
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d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
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! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
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call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
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delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
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! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
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accu = 0.d0
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do lx = 0, iorder_a_new(1)
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coefx = A_new(lx,1)
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if(dabs(coefx).lt.thr)cycle
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iorder_tmp(1) = lx
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do ly = 0, iorder_a_new(2)
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coefy = A_new(ly,2)
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coefxy = coefx * coefy
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if(dabs(coefxy).lt.thr)cycle
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iorder_tmp(2) = ly
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do lz = 0, iorder_a_new(3)
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coefz = A_new(lz,3)
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coefxyz = coefxy * coefz
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if(dabs(coefxyz).lt.thr)cycle
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iorder_tmp(3) = lz
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accu += coefxyz * NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,C_center,n_pt_max_integrals,mu)
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enddo
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enddo
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enddo
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NAI_pol_mult_erf_gauss_r12 = fact_a_new * accu
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end
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subroutine erfc_mu_gauss_xyz(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in,xyz_ints)
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BEGIN_DOC
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! Computes the following integral :
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!
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! .. math::
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!
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! \int dr exp(-delta (r - D)^2 ) x/y/z * (1 - erf(mu |r-r'|))/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
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!
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! xyz_ints(1) = x , xyz_ints(2) = y, xyz_ints(3) = z, xyz_ints(4) = x^0
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END_DOC
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implicit none
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include 'constants.include.F'
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double precision, intent(in) :: D_center(3), delta,mu ! pure gaussian "D" and mu parameter
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double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
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integer, intent(in) :: power_A(3),power_B(3),n_pt_in
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double precision, intent(out) :: xyz_ints(4)
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double precision :: NAI_pol_mult_erf
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! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
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double precision :: A_new(0:max_dim,3)! new polynom
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double precision :: A_center_new(3) ! new center
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integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
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double precision :: alpha_new ! new exponent
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double precision :: fact_a_new ! constant factor
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double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
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integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
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integer :: power_B_tmp(3)
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dim1=100
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mu_inf = 1.d+10
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thr = 1.d-10
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d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
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! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
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call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
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delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
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! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
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xyz_ints = 0.d0
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do lx = 0, iorder_a_new(1)
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coefx = A_new(lx,1)
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if(dabs(coefx).lt.thr)cycle
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iorder_tmp(1) = lx
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do ly = 0, iorder_a_new(2)
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coefy = A_new(ly,2)
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coefxy = coefx * coefy
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if(dabs(coefxy).lt.thr)cycle
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iorder_tmp(2) = ly
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do lz = 0, iorder_a_new(3)
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coefz = A_new(lz,3)
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coefxyz = coefxy * coefz
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if(dabs(coefxyz).lt.thr)cycle
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iorder_tmp(3) = lz
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power_B_tmp = power_B
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contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
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contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
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xyz_ints(4) += (contrib_inf - contrib) * coefxyz ! usual term with no x/y/z
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do mm = 1, 3
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! (x phi_i ) * phi_j
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! x * (x - B_x)^b_x = B_x (x - B_x)^b_x + 1 * (x - B_x)^{b_x+1}
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!
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! first contribution :: B_x (x - B_x)^b_x :: usual integral multiplied by B_x
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power_B_tmp = power_B
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contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
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contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
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xyz_ints(mm) += (contrib_inf - contrib) * B_center(mm) * coefxyz
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!
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! second contribution :: (x - B_x)^(b_x+1) :: integral with b_x=>b_x+1
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power_B_tmp(mm) += 1
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contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)
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contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)
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xyz_ints(mm) += (contrib_inf - contrib) * coefxyz
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enddo
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enddo
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enddo
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enddo
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xyz_ints *= fact_a_new
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end
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double precision function erf_mu_gauss(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in)
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BEGIN_DOC
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! Computes the following integral :
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!
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! .. math::
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!
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! \int dr exp(-delta (r - D)^2 ) erf(mu*|r-r'|)/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
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!
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END_DOC
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implicit none
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include 'constants.include.F'
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double precision, intent(in) :: D_center(3), delta,mu ! pure gaussian "D" and mu parameter
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double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
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integer, intent(in) :: power_A(3),power_B(3),n_pt_in
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double precision :: NAI_pol_mult_erf
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! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
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double precision :: A_new(0:max_dim,3)! new polynom
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double precision :: A_center_new(3) ! new center
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integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
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double precision :: alpha_new ! new exponent
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double precision :: fact_a_new ! constant factor
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double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
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integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
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dim1=100
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mu_inf = 1.d+10
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thr = 1.d-10
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d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
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! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
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call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
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delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
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! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
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erf_mu_gauss = 0.d0
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do lx = 0, iorder_a_new(1)
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coefx = A_new(lx,1)
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if(dabs(coefx).lt.thr)cycle
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iorder_tmp(1) = lx
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do ly = 0, iorder_a_new(2)
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coefy = A_new(ly,2)
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coefxy = coefx * coefy
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if(dabs(coefxy).lt.thr)cycle
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iorder_tmp(2) = ly
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do lz = 0, iorder_a_new(3)
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coefz = A_new(lz,3)
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coefxyz = coefxy * coefz
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if(dabs(coefxyz).lt.thr)cycle
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iorder_tmp(3) = lz
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contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,D_center,n_pt_in,mu)
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erf_mu_gauss += contrib * coefxyz
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enddo
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enddo
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enddo
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erf_mu_gauss *= fact_a_new
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end
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