added complex ao_ortho_canonical

src/ao_one_e_ints/ao_ortho_canonical_complex.irp.f

@@ -0,0 +1,121 @@
+
+BEGIN_PROVIDER [ complex*16, ao_cart_to_sphe_coef_complex, (ao_num,ao_cart_to_sphe_num) ]
+ implicit none
+ BEGIN_DOC
+ ! complex version of ao_cart_to_sphe_coef
+ END_DOC
+ call zlacp2('A',ao_num,ao_cart_to_sphe_num, &
+        ao_cart_to_sphe_coef,size(ao_cart_to_sphe_coef,1), &
+        ao_cart_to_sphe_coef_complex,size(ao_cart_to_sphe_coef_complex,1))
+END_PROVIDER
+
+BEGIN_PROVIDER [ complex*16, ao_cart_to_sphe_overlap_complex, (ao_cart_to_sphe_num,ao_cart_to_sphe_num) ]
+ implicit none
+ BEGIN_DOC
+ ! AO overlap matrix in the spherical basis set
+ END_DOC
+ complex*16, allocatable :: S(:,:)
+ allocate (S(ao_cart_to_sphe_num,ao_num))
+
+ call zgemm('T','N',ao_cart_to_sphe_num,ao_num,ao_num, (1.d0,0.d0), &
+   ao_cart_to_sphe_coef_complex,size(ao_cart_to_sphe_coef_complex,1), &
+   ao_overlap_complex,size(ao_overlap_complex,1), (0.d0,0.d0), &
+   S, size(S,1))
+
+ call zgemm('N','N',ao_cart_to_sphe_num,ao_cart_to_sphe_num,ao_num, (1.d0,0.d0), &
+   S, size(S,1), &
+   ao_cart_to_sphe_coef_complex,size(ao_cart_to_sphe_coef_complex,1), (0.d0,0.d0), &
+   ao_cart_to_sphe_overlap_complex,size(ao_cart_to_sphe_overlap_complex,1))
+
+ deallocate(S)
+
+END_PROVIDER
+
+
+
+
+BEGIN_PROVIDER [ complex*16, ao_ortho_canonical_coef_inv_complex, (ao_num,ao_num)]
+ implicit none
+ BEGIN_DOC
+! ao_ortho_canonical_coef_complex^(-1)
+ END_DOC
+ call get_inverse_complex(ao_ortho_canonical_coef_complex,size(ao_ortho_canonical_coef_complex,1),&
+     ao_num, ao_ortho_canonical_coef_inv_complex, size(ao_ortho_canonical_coef_inv_complex,1))
+END_PROVIDER
+
+ BEGIN_PROVIDER [ complex*16, ao_ortho_canonical_coef_complex, (ao_num,ao_num)]
+&BEGIN_PROVIDER [ integer, ao_ortho_canonical_num_complex ]
+  implicit none
+  BEGIN_DOC
+! TODO: ao_ortho_canonical_num_complex should be the same as the real version
+!       maybe if the providers weren't linked we could avoid making a complex one?
+! matrix of the coefficients of the mos generated by the
+! orthonormalization by the S^{-1/2} canonical transformation of the aos
+! ao_ortho_canonical_coef(i,j) = coefficient of the ith ao on the jth ao_ortho_canonical orbital
+  END_DOC
+  integer :: i
+  ao_ortho_canonical_coef_complex = (0.d0,0.d0)
+  do i=1,ao_num
+    ao_ortho_canonical_coef_complex(i,i) = (1.d0,0.d0)
+  enddo
+
+!call ortho_lowdin(ao_overlap,size(ao_overlap,1),ao_num,ao_ortho_canonical_coef,size(ao_ortho_canonical_coef,1),ao_num)
+!ao_ortho_canonical_num=ao_num
+!return
+
+  if (ao_cartesian) then
+
+    ao_ortho_canonical_num_complex = ao_num
+    call ortho_canonical_complex(ao_overlap,size(ao_overlap,1), &
+      ao_num,ao_ortho_canonical_coef_complex,size(ao_ortho_canonical_coef_complex,1), &
+      ao_ortho_canonical_num_complex)
+
+
+  else
+
+    complex*16, allocatable :: S(:,:)
+
+    allocate(S(ao_cart_to_sphe_num,ao_cart_to_sphe_num))
+    S = (0.d0,0.d0)
+    do i=1,ao_cart_to_sphe_num
+      S(i,i) = (1.d0,0.d0)
+    enddo
+
+    ao_ortho_canonical_num_complex = ao_cart_to_sphe_num
+    call ortho_canonical_complex(ao_cart_to_sphe_overlap_complex, size(ao_cart_to_sphe_overlap_complex,1), &
+      ao_cart_to_sphe_num, S, size(S,1), ao_ortho_canonical_num_complex)
+
+    call zgemm('N','N', ao_num, ao_ortho_canonical_num_complex, ao_cart_to_sphe_num, (1.d0,0.d0), &
+      ao_cart_to_sphe_coef_complex, size(ao_cart_to_sphe_coef_complex,1), &
+      S, size(S,1), &
+      (0.d0,0.d0), ao_ortho_canonical_coef_complex, size(ao_ortho_canonical_coef_complex,1))
+
+    deallocate(S)
+  endif
+END_PROVIDER
+
+BEGIN_PROVIDER [complex*16, ao_ortho_canonical_overlap_complex, (ao_ortho_canonical_num_complex,ao_ortho_canonical_num_complex)]
+  implicit none
+  BEGIN_DOC
+! overlap matrix of the ao_ortho_canonical.
+! Expected to be the Identity
+  END_DOC
+  integer                        :: i,j,k,l
+  complex*16               :: c
+  do j=1, ao_ortho_canonical_num_complex
+    do i=1, ao_ortho_canonical_num_complex
+      ao_ortho_canonical_overlap_complex(i,j) = (0.d0,0.d0)
+    enddo
+  enddo
+  do j=1, ao_ortho_canonical_num_complex
+    do k=1, ao_num
+      c = (0.d0,0.d0)
+      do l=1, ao_num
+        c +=  conjg(ao_ortho_canonical_coef_complex(l,j)) * ao_overlap_complex(l,k)
+      enddo
+      do i=1, ao_ortho_canonical_num_complex
+        ao_ortho_canonical_overlap_complex(i,j) += ao_ortho_canonical_coef_complex(k,i) * c
+      enddo
+    enddo
+  enddo
+END_PROVIDER