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777 lines
22 KiB
Fortran
777 lines
22 KiB
Fortran
! Gradient v1
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subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
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implicit none
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BEGIN_DOC
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! Compute gradient for the Pipek-Mezey localization
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END_DOC
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integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
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double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
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double precision, allocatable :: m_grad(:,:), tmp_int(:,:)
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integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
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! Allocation
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allocate(m_grad(tmp_list_size, tmp_list_size), tmp_int(tmp_list_size, tmp_list_size))
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! Initialization
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m_grad = 0d0
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do a = 1, nucl_num ! loop over the nuclei
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tmp_int = 0d0 ! Initialization for each nuclei
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! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
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do tmp_j = 1, tmp_list_size
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j = tmp_list(tmp_j)
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do tmp_i = 1, tmp_list_size
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i = tmp_list(tmp_i)
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do rho = 1, ao_cart_num ! loop over all the AOs
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do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
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mu = nucl_aos(a,b) ! AO centered on atom a
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tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
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+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
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enddo
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enddo
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enddo
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enddo
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! Gradient
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
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enddo
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enddo
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enddo
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! 2D -> 1D
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do tmp_k = 1, tmp_n
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call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
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v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
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enddo
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! Maximum element in the gradient
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max_elem = 0d0
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do tmp_k = 1, tmp_n
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if (ABS(v_grad(tmp_k)) > max_elem) then
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max_elem = ABS(v_grad(tmp_k))
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endif
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enddo
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! Norm of the gradient
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norm_grad = 0d0
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do tmp_k = 1, tmp_n
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norm_grad = norm_grad + v_grad(tmp_k)**2
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enddo
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norm_grad = dsqrt(norm_grad)
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print*, 'Maximal element in the gradient:', max_elem
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print*, 'Norm of the gradient:', norm_grad
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! Deallocation
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deallocate(m_grad,tmp_int)
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end subroutine grad_pipek
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! Gradient
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! The gradient is
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! \begin{align*}
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! \left. \frac{\partial \mathcal{P} (\theta)}{\partial \theta} \right|_{\theta=0}= \gamma^{PM}
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! \end{align*}
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! with
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! \begin{align*}
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! \gamma_{st}^{PM} = \sum_{A=1}^N <s|P_A|t> \left[ <s| P_A |s> - <t|P_A|t> \right]
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! \end{align*}
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! \begin{align*}
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! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
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! \end{align*}
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! $\sum_{\rho}$ -> sum over all the AOs
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! $\sum_{\mu \in A}$ -> sum over the AOs which belongs to atom A
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! $c^t$ -> expansion coefficient of orbital |t>
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! Input:
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! | tmp_n | integer | Number of parameters in the MO subspace |
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! | tmp_list_size | integer | Number of MOs in the mo_class we want to localize |
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! | tmp_list(tmp_list_size) | integer | MOs in the mo_class |
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! Output:
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! | v_grad(tmp_n) | double precision | Gradient in the subspace |
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! | max_elem | double precision | Maximal element in the gradient |
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! | norm_grad | double precision | Norm of the gradient |
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! Internal:
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! | m_grad(tmp_list_size,tmp_list_size) | double precision | Gradient in a 2D array |
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! | tmp_int(tmp_list_size,tmp_list_size) | | Temporary array to store the integrals |
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! | tmp_accu(tmp_list_size,tmp_list_size) | | Temporary array to store a matrix |
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! | | | product and compute tmp_int |
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! | CS(tmp_list_size,ao_cart_num) | | Array to store the result of mo_cart_coef * ao_cart_overlap |
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! | tmp_mo_cart_coef(ao_cart_num,tmp_list_size) | | Array to store just the useful MO coefficients |
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! | | | depending of the mo_class |
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! | tmp_mo_cart_coef2(nucl_n_aos(a),tmp_list_size) | | Array to store just the useful MO coefficients |
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! | | | depending of the nuclei |
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! | tmp_CS(tmp_list_size,nucl_n_aos(a)) | | Array to store just the useful mo_cart_coef * ao_cart_overlap |
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! | | | values depending of the nuclei |
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! | a | | index to loop over the nuclei |
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! | b | | index to loop over the AOs which belongs to the nuclei a |
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! | mu | | index to refer to an AO which belongs to the nuclei a |
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! | rho | | index to loop over all the AOs |
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subroutine gradient_PM(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
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implicit none
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BEGIN_DOC
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! Compute gradient for the Pipek-Mezey localization
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END_DOC
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integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
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double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
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double precision, allocatable :: m_grad(:,:), tmp_int(:,:), CS(:,:), tmp_mo_cart_coef(:,:), tmp_mo_cart_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
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integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
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double precision :: t1,t2,t3
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print*,''
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print*,'---gradient_PM---'
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call wall_time(t1)
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! Allocation
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allocate(m_grad(tmp_list_size, tmp_list_size), tmp_int(tmp_list_size, tmp_list_size),tmp_accu(tmp_list_size, tmp_list_size))
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allocate(CS(tmp_list_size,ao_cart_num),tmp_mo_cart_coef(ao_cart_num,tmp_list_size))
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! submatrix of the mo_cart_coef
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do tmp_i = 1, tmp_list_size
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i = tmp_list(tmp_i)
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do j = 1, ao_cart_num
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tmp_mo_cart_coef(j,tmp_i) = mo_cart_coef(j,i)
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enddo
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enddo
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call dgemm('T','N',tmp_list_size,ao_cart_num,ao_cart_num,1d0,tmp_mo_cart_coef,size(tmp_mo_cart_coef,1),ao_cart_overlap,size(ao_cart_overlap,1),0d0,CS,size(CS,1))
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m_grad = 0d0
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do a = 1, nucl_num ! loop over the nuclei
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tmp_int = 0d0
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!do tmp_j = 1, tmp_list_size
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! do tmp_i = 1, tmp_list_size
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! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
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! mu = nucl_aos(a,b)
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! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_cart_coef(mu,tmp_j) + tmp_mo_cart_coef(mu,tmp_i) * CS(tmp_j,mu))
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! ! (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
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! !+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
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! enddo
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! enddo
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!enddo
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allocate(tmp_mo_cart_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
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do tmp_i = 1, tmp_list_size
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do b = 1, nucl_n_aos(a)
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mu = nucl_aos(a,b)
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tmp_mo_cart_coef2(b,tmp_i) = tmp_mo_cart_coef(mu,tmp_i)
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enddo
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enddo
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do b = 1, nucl_n_aos(a)
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mu = nucl_aos(a,b)
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do tmp_i = 1, tmp_list_size
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tmp_CS(tmp_i,b) = CS(tmp_i,mu)
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enddo
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enddo
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call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_cart_coef2,size(tmp_mo_cart_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
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enddo
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enddo
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deallocate(tmp_mo_cart_coef2,tmp_CS)
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
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enddo
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enddo
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enddo
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! 2D -> 1D
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do tmp_k = 1, tmp_n
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call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
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v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
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enddo
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! Maximum element in the gradient
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max_elem = 0d0
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do tmp_k = 1, tmp_n
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if (ABS(v_grad(tmp_k)) > max_elem) then
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max_elem = ABS(v_grad(tmp_k))
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endif
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enddo
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! Norm of the gradient
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norm_grad = 0d0
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do tmp_k = 1, tmp_n
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norm_grad = norm_grad + v_grad(tmp_k)**2
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enddo
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norm_grad = dsqrt(norm_grad)
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print*, 'Maximal element in the gradient:', max_elem
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print*, 'Norm of the gradient:', norm_grad
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! Deallocation
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deallocate(m_grad,tmp_int,CS,tmp_mo_cart_coef)
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call wall_time(t2)
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t3 = t2 - t1
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print*,'Time in gradient_PM:', t3
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print*,'---End gradient_PM---'
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end
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! Hessian v1
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subroutine hess_pipek(tmp_n, tmp_list_size, tmp_list, H)
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implicit none
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BEGIN_DOC
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! Compute diagonal hessian for the Pipek-Mezey localization
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END_DOC
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integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
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double precision, intent(out) :: H(tmp_n)
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double precision, allocatable :: beta(:,:),tmp_int(:,:)
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integer :: i,j,tmp_k,tmp_i, tmp_j, a,b,rho,mu
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double precision :: max_elem
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! Allocation
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allocate(beta(tmp_list_size,tmp_list_size),tmp_int(tmp_list_size,tmp_list_size))
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beta = 0d0
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do a = 1, nucl_num
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tmp_int = 0d0
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do tmp_j = 1, tmp_list_size
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j = tmp_list(tmp_j)
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do tmp_i = 1, tmp_list_size
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i = tmp_list(tmp_i)
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do rho = 1, ao_cart_num
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do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
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mu = nucl_aos(a,b)
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tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
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+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
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enddo
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enddo
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enddo
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enddo
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! Calculation
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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beta(tmp_i,tmp_j) = beta(tmp_i, tmp_j) + (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))**2 - 4d0 * tmp_int(tmp_i,tmp_j)**2
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enddo
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enddo
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enddo
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H = 0d0
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do tmp_k = 1, tmp_n
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call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
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H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
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enddo
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! Deallocation
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deallocate(beta,tmp_int)
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end
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! Hessian
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! The hessian is
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! \begin{align*}
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! \left. \frac{\partial^2 \mathcal{P} (\theta)}{\partial \theta^2}\right|_{\theta=0} = 4 \beta^{PM}
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! \end{align*}
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! \begin{align*}
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! \beta_{st}^{PM} = \sum_{A=1}^N \left( <s|P_A|t>^2 - \frac{1}{4} \left[<s|P_A|s> - <t|P_A|t> \right]^2 \right)
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! \end{align*}
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! with
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! \begin{align*}
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! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
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! \end{align*}
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! $\sum_{\rho}$ -> sum over all the AOs
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! $\sum_{\mu \in A}$ -> sum over the AOs which belongs to atom A
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! $c^t$ -> expansion coefficient of orbital |t>
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subroutine hessian_PM(tmp_n, tmp_list_size, tmp_list, H)
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implicit none
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BEGIN_DOC
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! Compute diagonal hessian for the Pipek-Mezey localization
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END_DOC
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integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
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double precision, intent(out) :: H(tmp_n)
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double precision, allocatable :: beta(:,:),tmp_int(:,:),CS(:,:),tmp_mo_cart_coef(:,:),tmp_mo_cart_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
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integer :: i,j,tmp_k,tmp_i, tmp_j, a,b,rho,mu
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double precision :: max_elem, t1,t2,t3
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print*,''
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print*,'---hessian_PM---'
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call wall_time(t1)
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! Allocation
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allocate(beta(tmp_list_size,tmp_list_size),tmp_int(tmp_list_size,tmp_list_size),tmp_accu(tmp_list_size,tmp_list_size))
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allocate(CS(tmp_list_size,ao_cart_num),tmp_mo_cart_coef(ao_cart_num,tmp_list_size))
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beta = 0d0
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do tmp_i = 1, tmp_list_size
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i = tmp_list(tmp_i)
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do j = 1, ao_cart_num
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tmp_mo_cart_coef(j,tmp_i) = mo_cart_coef(j,i)
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enddo
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enddo
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call dgemm('T','N',tmp_list_size,ao_cart_num,ao_cart_num,1d0,tmp_mo_cart_coef,size(tmp_mo_cart_coef,1),ao_cart_overlap,size(ao_cart_overlap,1),0d0,CS,size(CS,1))
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do a = 1, nucl_num ! loop over the nuclei
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tmp_int = 0d0
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!do tmp_j = 1, tmp_list_size
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! do tmp_i = 1, tmp_list_size
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! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
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! mu = nucl_aos(a,b)
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! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_cart_coef(mu,tmp_j) + tmp_mo_cart_coef(mu,tmp_i) * CS(tmp_j,mu))
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! ! (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
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! !+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
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! enddo
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! enddo
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!enddo
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allocate(tmp_mo_cart_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
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do tmp_i = 1, tmp_list_size
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do b = 1, nucl_n_aos(a)
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mu = nucl_aos(a,b)
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tmp_mo_cart_coef2(b,tmp_i) = tmp_mo_cart_coef(mu,tmp_i)
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enddo
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enddo
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do b = 1, nucl_n_aos(a)
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mu = nucl_aos(a,b)
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do tmp_i = 1, tmp_list_size
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tmp_CS(tmp_i,b) = CS(tmp_i,mu)
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enddo
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enddo
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call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_cart_coef2,size(tmp_mo_cart_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
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enddo
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enddo
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deallocate(tmp_mo_cart_coef2,tmp_CS)
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! Calculation
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do tmp_j = 1, tmp_list_size
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do tmp_i = 1, tmp_list_size
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|
|
|
beta(tmp_i,tmp_j) = beta(tmp_i, tmp_j) + (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))**2 - 4d0 * tmp_int(tmp_i,tmp_j)**2
|
|
|
|
enddo
|
|
enddo
|
|
|
|
enddo
|
|
|
|
H = 0d0
|
|
do tmp_k = 1, tmp_n
|
|
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
|
|
H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
|
|
enddo
|
|
|
|
! Deallocation
|
|
deallocate(beta,tmp_int)
|
|
|
|
call wall_time(t2)
|
|
t3 = t2 - t1
|
|
print*,'Time in hessian_PM:', t3
|
|
|
|
print*,'---End hessian_PM---'
|
|
|
|
end
|
|
|
|
! Criterion PM (old)
|
|
|
|
subroutine compute_crit_pipek(criterion)
|
|
|
|
implicit none
|
|
|
|
BEGIN_DOC
|
|
! Compute the Pipek-Mezey localization criterion
|
|
END_DOC
|
|
|
|
double precision, intent(out) :: criterion
|
|
double precision, allocatable :: tmp_int(:,:)
|
|
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
|
|
|
|
! Allocation
|
|
allocate(tmp_int(mo_num, mo_num))
|
|
|
|
criterion = 0d0
|
|
|
|
do a = 1, nucl_num ! loop over the nuclei
|
|
tmp_int = 0d0
|
|
|
|
do i = 1, mo_num
|
|
do rho = 1, ao_cart_num ! loop over all the AOs
|
|
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
|
|
mu = nucl_aos(a,b)
|
|
|
|
tmp_int(i,i) = tmp_int(i,i) + 0.5d0 * (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,i) &
|
|
+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,i))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do i = 1, mo_num
|
|
criterion = criterion + tmp_int(i,i)**2
|
|
enddo
|
|
|
|
enddo
|
|
|
|
criterion = - criterion
|
|
|
|
deallocate(tmp_int)
|
|
|
|
end
|
|
|
|
! Criterion PM
|
|
|
|
! The criterion is computed as
|
|
! \begin{align*}
|
|
! \mathcal{P} = \sum_{i=1}^n \sum_{A=1}^N \left[ <i|P_A|i> \right]^2
|
|
! \end{align*}
|
|
! with
|
|
! \begin{align*}
|
|
! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
|
|
! \end{align*}
|
|
|
|
|
|
subroutine criterion_PM(tmp_list_size,tmp_list,criterion)
|
|
|
|
implicit none
|
|
|
|
BEGIN_DOC
|
|
! Compute the Pipek-Mezey localization criterion
|
|
END_DOC
|
|
|
|
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
|
|
double precision, intent(out) :: criterion
|
|
double precision, allocatable :: tmp_int(:,:),CS(:,:)
|
|
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
|
|
|
|
print*,''
|
|
print*,'---criterion_PM---'
|
|
|
|
! Allocation
|
|
allocate(tmp_int(tmp_list_size, tmp_list_size),CS(mo_num,ao_cart_num))
|
|
|
|
! Initialization
|
|
criterion = 0d0
|
|
|
|
call dgemm('T','N',mo_num,ao_cart_num,ao_cart_num,1d0,mo_cart_coef,size(mo_cart_coef,1),ao_cart_overlap,size(ao_cart_overlap,1),0d0,CS,size(CS,1))
|
|
|
|
do a = 1, nucl_num ! loop over the nuclei
|
|
tmp_int = 0d0
|
|
|
|
do tmp_i = 1, tmp_list_size
|
|
i = tmp_list(tmp_i)
|
|
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
|
|
mu = nucl_aos(a,b)
|
|
|
|
tmp_int(tmp_i,tmp_i) = tmp_int(tmp_i,tmp_i) + 0.5d0 * (CS(i,mu) * mo_cart_coef(mu,i) + mo_cart_coef(mu,i) * CS(i,mu))
|
|
|
|
! (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
|
|
!+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
|
|
|
|
enddo
|
|
enddo
|
|
|
|
do tmp_i = 1, tmp_list_size
|
|
criterion = criterion + tmp_int(tmp_i,tmp_i)**2
|
|
enddo
|
|
|
|
enddo
|
|
|
|
criterion = - criterion
|
|
|
|
deallocate(tmp_int,CS)
|
|
|
|
print*,'---End criterion_PM---'
|
|
|
|
end
|
|
|
|
! Criterion PM v3
|
|
|
|
subroutine criterion_PM_v3(tmp_list_size,tmp_list,criterion)
|
|
|
|
implicit none
|
|
|
|
BEGIN_DOC
|
|
! Compute the Pipek-Mezey localization criterion
|
|
END_DOC
|
|
|
|
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
|
|
double precision, intent(out) :: criterion
|
|
double precision, allocatable :: tmp_int(:,:), CS(:,:), tmp_mo_cart_coef(:,:), tmp_mo_cart_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
|
|
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho,nu,c
|
|
double precision :: t1,t2,t3
|
|
|
|
print*,''
|
|
print*,'---criterion_PM_v3---'
|
|
|
|
call wall_time(t1)
|
|
|
|
! Allocation
|
|
allocate(tmp_int(tmp_list_size, tmp_list_size),tmp_accu(tmp_list_size, tmp_list_size))
|
|
allocate(CS(tmp_list_size,ao_cart_num),tmp_mo_cart_coef(ao_cart_num,tmp_list_size))
|
|
|
|
criterion = 0d0
|
|
|
|
! submatrix of the mo_cart_coef
|
|
do tmp_i = 1, tmp_list_size
|
|
i = tmp_list(tmp_i)
|
|
do j = 1, ao_cart_num
|
|
|
|
tmp_mo_cart_coef(j,tmp_i) = mo_cart_coef(j,i)
|
|
|
|
enddo
|
|
enddo
|
|
|
|
! ao_cart_overlap(ao_cart_num,ao_cart_num)
|
|
! mo_cart_coef(ao_cart_num,mo_num)
|
|
call dgemm('T','N',tmp_list_size,ao_cart_num,ao_cart_num,1d0,tmp_mo_cart_coef,size(tmp_mo_cart_coef,1),ao_cart_overlap,size(ao_cart_overlap,1),0d0,CS,size(CS,1))
|
|
|
|
do a = 1, nucl_num ! loop over the nuclei
|
|
|
|
do j = 1, tmp_list_size
|
|
do i = 1, tmp_list_size
|
|
tmp_int(i,j) = 0d0
|
|
enddo
|
|
enddo
|
|
|
|
!do tmp_j = 1, tmp_list_size
|
|
! do tmp_i = 1, tmp_list_size
|
|
! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
|
|
! mu = nucl_aos(a,b)
|
|
|
|
! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_cart_coef(mu,tmp_j) + tmp_mo_cart_coef(mu,tmp_i) * CS(tmp_j,mu))
|
|
|
|
! ! (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
|
|
! !+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
|
|
|
|
! enddo
|
|
! enddo
|
|
!enddo
|
|
|
|
allocate(tmp_mo_cart_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
|
|
|
|
do tmp_i = 1, tmp_list_size
|
|
do b = 1, nucl_n_aos(a)
|
|
mu = nucl_aos(a,b)
|
|
|
|
tmp_mo_cart_coef2(b,tmp_i) = tmp_mo_cart_coef(mu,tmp_i)
|
|
|
|
enddo
|
|
enddo
|
|
|
|
do b = 1, nucl_n_aos(a)
|
|
mu = nucl_aos(a,b)
|
|
do tmp_i = 1, tmp_list_size
|
|
|
|
tmp_CS(tmp_i,b) = CS(tmp_i,mu)
|
|
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_cart_coef2,size(tmp_mo_cart_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
|
|
|
|
! Integrals
|
|
do tmp_j = 1, tmp_list_size
|
|
do tmp_i = 1, tmp_list_size
|
|
|
|
tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
|
|
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(tmp_mo_cart_coef2,tmp_CS)
|
|
|
|
! Criterion
|
|
do tmp_i = 1, tmp_list_size
|
|
criterion = criterion + tmp_int(tmp_i,tmp_i)**2
|
|
enddo
|
|
|
|
enddo
|
|
|
|
criterion = - criterion
|
|
|
|
deallocate(tmp_int,CS,tmp_accu,tmp_mo_cart_coef)
|
|
|
|
call wall_time(t2)
|
|
t3 = t2 - t1
|
|
print*,'Time in criterion_PM_v3:', t3
|
|
|
|
print*,'---End criterion_PM_v3---'
|
|
|
|
end
|
|
|
|
subroutine theta_PM(l, n, m_x, max_elem)
|
|
|
|
include 'pi.h'
|
|
|
|
BEGIN_DOC
|
|
! Compute the angles to minimize the Pipek-Mezey criterion by using pairwise rotations of the MOs
|
|
! Warning: you must give - the angles to build the rotation matrix...
|
|
END_DOC
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: n, l(n)
|
|
double precision, intent(out) :: m_x(n,n), max_elem
|
|
|
|
integer :: a,b,i,j,tmp_i,tmp_j,rho,mu,nu,idx_i,idx_j
|
|
double precision, allocatable :: Aij(:,:), Bij(:,:), Pa(:,:)
|
|
|
|
allocate(Aij(n,n), Bij(n,n), Pa(n,n))
|
|
|
|
do a = 1, nucl_num ! loop over the nuclei
|
|
Pa = 0d0 ! Initialization for each nuclei
|
|
|
|
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
|
|
do tmp_j = 1, n
|
|
j = l(tmp_j)
|
|
do tmp_i = 1, n
|
|
i = l(tmp_i)
|
|
do rho = 1, ao_cart_num ! loop over all the AOs
|
|
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
|
|
mu = nucl_aos(a,b) ! AO centered on atom a
|
|
|
|
Pa(tmp_i,tmp_j) = Pa(tmp_i,tmp_j) + 0.5d0 * (mo_cart_coef(rho,i) * ao_cart_overlap(rho,mu) * mo_cart_coef(mu,j) &
|
|
+ mo_cart_coef(mu,i) * ao_cart_overlap(mu,rho) * mo_cart_coef(rho,j))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
! A
|
|
do j = 1, n
|
|
do i = 1, n
|
|
Aij(i,j) = Aij(i,j) + Pa(i,j)**2 - 0.25d0 * (Pa(i,i) - Pa(j,j))**2
|
|
enddo
|
|
enddo
|
|
|
|
! B
|
|
do j = 1, n
|
|
do i = 1, n
|
|
Bij(i,j) = Bij(i,j) + Pa(i,j) * (Pa(i,i) - Pa(j,j))
|
|
enddo
|
|
enddo
|
|
|
|
enddo
|
|
|
|
! Theta
|
|
do j = 1, n
|
|
do i = 1, n
|
|
m_x(i,j) = 0.25d0 * atan2(Bij(i,j), -Aij(i,j))
|
|
enddo
|
|
enddo
|
|
|
|
! Enforce a perfect antisymmetry
|
|
do j = 1, n-1
|
|
do i = j+1, n
|
|
m_x(j,i) = - m_x(i,j)
|
|
enddo
|
|
enddo
|
|
do i = 1, n
|
|
m_x(i,i) = 0d0
|
|
enddo
|
|
|
|
! Max
|
|
max_elem = 0d0
|
|
do j = 1, n-1
|
|
do i = j+1, n
|
|
if (dabs(m_x(i,j)) > dabs(max_elem)) then
|
|
max_elem = m_x(i,j)
|
|
idx_i = i
|
|
idx_j = j
|
|
endif
|
|
enddo
|
|
enddo
|
|
|
|
! Debug
|
|
!do i = 1, n
|
|
! write(*,'(100F10.4)') m_x(i,:)
|
|
!enddo
|
|
!print*,'Max',idx_i,idx_j,max_elem
|
|
|
|
max_elem = dabs(max_elem)
|
|
|
|
deallocate(Aij,Bij,Pa)
|
|
|
|
end
|
|
|