# get_lmat_el_ua Function

## public pure function get_lmat_el_ua(a, b, c, i, j, k) result(matel)

### Arguments

Type IntentOptional Attributes Name
integer, value :: a
integer, value :: b
integer, value :: c
integer, intent(in) :: i
integer, intent(in) :: j
integer, intent(in) :: k

## Source Code

    pure function get_lmat_el_ua(a, b, c, i, j, k) result(matel)
use SystemData, only: G1
use UMatCache, only: gtID
! Gets an entry of the 3-body tensor L:
! L_{abc}^{ijk} - triple excitation from abc to ijk
integer, value :: a, b, c
integer :: a2, b2, c2
integer, intent(in) :: i, j, k
HElement_t(dp) :: matel

! convert to spatial orbs if required

matel = 0

if (G1(a)%ms == G1(b)%ms .and. G1(a)%ms /= G1(c)%ms) then
a2 = a
b2 = b
c2 = c
else if (G1(a)%ms == G1(c)%ms .and. G1(a)%ms /= G1(b)%ms) then
a2 = c
b2 = a
c2 = b
else if (G1(b)%ms == G1(c)%ms .and. G1(a)%ms /= G1(b)%ms) then
a2 = b
b2 = c
c2 = a
else
return
end if

! only add the contribution if the spins match
call addMatelContribution_ua(i, j, k, 1, matel)
call addMatelContribution_ua(j, k, i, 1, matel)
call addMatelContribution_ua(k, i, j, 1, matel)
call addMatelContribution_ua(j, i, k, -1, matel)
call addMatelContribution_ua(i, k, j, -1, matel)
call addMatelContribution_ua(k, j, i, -1, matel)
contains

pure subroutine addMatelContribution_ua(p, q, r, sgn, matel)
integer, value :: p, q, r
integer, intent(in) :: sgn
HElement_t(dp), intent(inout) :: matel

if (G1(p)%ms == G1(a2)%ms .and. G1(q)%ms == G1(b2)%ms .and. G1(r)%ms == G1(c2)%ms) then
matel = matel + 2.d0 * sgn * get_lmat_ua(a2, b2, c2, p, q, r)
end if