Determine the prefactor for a diagonal contribution (i.e. three pairs of frozen orbitals) @param[in] indices orbital indices of the frozen entry - need to belong to a contribution @param[out] prefactor prefactor with which this LMat entry enters the matrix element
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer(kind=int64), | intent(in) | :: | indices(num_inds) | |||
| real(kind=dp), | intent(out) | :: | prefactor |
pure subroutine frozen_diagonal_entry(indices, prefactor)
integer(int64), intent(in) :: indices(num_inds)
real(dp), intent(out) :: prefactor
integer :: ct, directs
logical :: t_quad
! Only one info is needed here, that is the parity and number of contributing spin
! configs.
! If there are five or more repeated indices, the LMat entry does not contribute
! (it would require three same-spin electrons
t_quad = .false.
do ct = 1, 3
if(count(indices(ct) == indices) > 4) then
prefactor = 0.0_dp
return
end if
if(count(indices(ct) == indices) > 3) t_quad = .true.
end do
! Both relate to the number of different direct excits, so count these
directs = 0
do ct = 1, step
if(is_repeated_pair(indices, ct)) directs = directs + 1
end do
! If there is a quadruple index, the spin of it is fixed (both have to be occupied), then,
! the prefactor is always +/- 2, depending on if there is more than one direct pair
if(t_quad) then
! The only options with a quadruple index are
! a) one direct excitation => -2
! b) three direct exctiations => +2
prefactor = merge(-2.0_dp, 2.0_dp, directs == 1)
else
! In the other case, there are three relevant cases:
! a) All excitations are direct => prefactor 8 = 2**3 (all spins are free)
! b) One excitation is direct => prefactor -4 (from the spin freedom of the direct orb + overall spin)
! c) No excitation is direct => prefactor 4
! the factor of 4 comes from two sources: a factor of 2 from the overall spin
! and another factor of two from permutational symmetry: both indirect terms
! are identical in this case, so this entry has to be counted as both
if(directs == 0) then
prefactor = 4.0_dp
elseif(directs == 1) then
prefactor = -4.0_dp
else ! directs == 3
prefactor = 8.0_dp
endif
endif
end subroutine frozen_diagonal_entry