BEGIN_PROVIDER [ double precision, ao_ortho_canonical_coef, (ao_num_align,ao_num)]
&BEGIN_PROVIDER [ integer, ao_ortho_canonical_num ]
  implicit none
  BEGIN_DOC
! 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(:,:) = 0.d0
  do i=1,ao_num
    ao_ortho_canonical_coef(i,i) = 1.d0
  enddo
  call ortho_canonical(ao_overlap,ao_num_align,ao_num,ao_ortho_canonical_coef,ao_num_align,ao_ortho_canonical_num)
END_PROVIDER

BEGIN_PROVIDER [double precision, ao_ortho_canonical_overlap, (ao_ortho_canonical_num,ao_ortho_canonical_num)]
  implicit none
  BEGIN_DOC
! overlap matrix of the ao_ortho_canonical
! supposed to be the Identity
  END_DOC
  integer                        :: i,j,k,l
  double precision               :: c
  do j=1, ao_ortho_canonical_num
    do i=1, ao_ortho_canonical_num
      ao_ortho_canonical_overlap(i,j) = 0.d0
    enddo
  enddo
  do j=1, ao_ortho_canonical_num
    do k=1, ao_num
      c = 0.d0
      do l=1, ao_num
        c +=  ao_ortho_canonical_coef(l,j) * ao_overlap(l,k)
      enddo
      do i=1, ao_ortho_canonical_num
        ao_ortho_canonical_overlap(i,j) += ao_ortho_canonical_coef(k,i) * c
      enddo
    enddo
  enddo
END_PROVIDER