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mat_element_pol.f90
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module mat_element_pol
use globals
use intindex_module
contains
function mat_el_1h1p (i, a, j, b) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{i}^{a} | H | ^{1}\Psi_{j}^{b} >
! -----------------
integer :: i, j
integer :: a, b
double precision :: mat_el
double precision :: dij, dab
dij = s_mat(i, j)
dab = s_mat(a, b)
mat_el = dij * dab * (emo(b) - emo(j))&
+ 2.0d0 * int2e(intindex(a, i, j, b))&
- int2e(intindex(a, b, j, i))
end function mat_el_1h1p
! -----------------
! 2h2p type 1
! -----------------
function mat_el_2h2p_11 (i, a, b, k, c, d) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{ii}^{ab} | H | ^{1}\Psi_{kk}^{cb} >
! -----------------
integer :: i, k
integer :: a, b, c, d
double precision :: mat_el
double precision :: dad, dbd, dbc, dac, dik
dbc = s_mat(b, c)
dac = s_mat(a, c)
dbd = s_mat(b, d)
dad = s_mat(a, d)
dik = s_mat(i, k)
mat_el = (dik * dac * dbd + dik * dbc * dad)*( - emo(k) + emo(d) - emo(k) + emo(c)) &
+ dik * int2e(intindex(c, a, d, b)) + dik * int2e(intindex(c, b, d, a)) &
+ dbc * dad * int2e(intindex(i, k, i, k)) + dac * dbd * int2e(intindex(i, k, i, k)) &
-2.0d0 * dac * dik * int2e(intindex(d, b, i, k)) + dac * dik * int2e(intindex(d, k, i, b)) &
-2.0d0 * dbc * dik * int2e(intindex(d, a, i, k)) + dbc * dik * int2e(intindex(d, k, i, a)) &
-2.0d0 * dad * dik * int2e(intindex(c, b, i, k)) + dad * dik * int2e(intindex(c, k, i, b)) &
-2.0d0 * dbd * dik * int2e(intindex(c, a, i, k)) + dbd * dik * int2e(intindex(c, k, i, a))
end function mat_el_2h2p_11
function mat_el_test(i, a, b) result (mat_el)
integer :: i, a, b
double precision :: mat_el
mat_el = emo(a) + emo(b) - 2*emo(i) + &
+ int2e(intindex(b, i, i, b))&
- 2.0d0* int2e(intindex(b, b, i, i))&
+ int2e(intindex(a, i, i, a))&
- 2.0d0* int2e(intindex(a, a, i, i))&
+ int2e(intindex(a, a, b, b))&
+ int2e(intindex(a, b, b, a))&
+ int2e(intindex(i, i, i, i))
end function mat_el_test
function mat_el_2h2p_a_test(i, j, a, b) result (mat_el)
integer :: i, j,a, b
double precision :: mat_el
mat_el = emo(a) + emo(b) - emo(j) - emo(i) + &
+ int2e(intindex(a, a, b, b))&
- int2e(intindex(a, b, b, a))&
+ int2e(intindex(i, i, j, j))&
- int2e(intindex(i, j, j, i))&
+ 1.5d0* int2e(intindex(a, i, i, a))&
- int2e(intindex(a, a, i, i))&
+ 1.5d0* int2e(intindex(b, i, i, b))&
- int2e(intindex(b, b, i, i))&
+ 1.5d0* int2e(intindex(a, j, j, a))&
- int2e(intindex(a, a, j, j))&
+ 1.5d0* int2e(intindex(b, j, j, b))&
- int2e(intindex(b, b, j, j))
end function mat_el_2h2p_a_test
! -----------------
! 2h2p type A
! -----------------
function mat_el_2h2p_AA (i, j, a, b, k, l, c) result (mat_el)
! -----------------
! computes < ^{A}\Psi_{ij}^{ab} | H | ^{A}\Psi_{kl}^{cb} >
! -----------------
integer :: i, j, k, l
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dbc, dil, dik, djl, djk
dab = s_mat(a, b)
dbc = s_mat(b, c)
dac = s_mat(a, c)
djl = s_mat(j, l)
djk = s_mat(j, k)
dil = s_mat(i, l)
dik = s_mat(i, k)
mat_el = (dik * djl * dac - djk * dil * dac) * (emo(b) + emo(c) - emo(k) - emo(l))&
+ dbc * dab * int2e(intindex(i, l, j, k)) - dbc * dab * int2e(intindex(i, k, j, l))&
+ dik * djl * int2e(intindex(c, a, b, b)) - dik * djl * int2e(intindex(c, b, b, a))&
+ djk * dil * int2e(intindex(c, b, b, a)) - djk * dil * int2e(intindex(c, a, b, b))&
- dab * dil * int2e(intindex(c, b, j, k)) + 1.5d0 * dab * dil * int2e(intindex(c, k, j, b))&
- dab * djk * int2e(intindex(c, b, i, l)) + 1.5d0 * dab * djk * int2e(intindex(c, l, i, b))&
+ dab * djl * int2e(intindex(c, b, i, k)) - 1.5d0 * dab * djl * int2e(intindex(c, k, i, b))&
+ dab * dik * int2e(intindex(c, b, j, l)) - 1.5d0 * dab * dik * int2e(intindex(c, l, j, b))&
+ dac * dil * int2e(intindex(b, b, j, k)) - 1.5d0 * dac * dil * int2e(intindex(b, k, j, b))&
+ dac * djk * int2e(intindex(b, b, i, l)) - 1.5d0 * dac * djk * int2e(intindex(b, l, i, b))&
- dac * dik * int2e(intindex(b, b, j, l)) + 1.5d0 * dac * dik * int2e(intindex(b, l, j, b))&
- dac * djl * int2e(intindex(b, b, i, k)) + 1.5d0 * dac * djl * int2e(intindex(b, k, i, b))&
+ dbc * djl * int2e(intindex(b, a, i, k)) - 1.5d0 * dbc * djl * int2e(intindex(b, k, i, a))&
- dbc * djk * int2e(intindex(b, a, i, l)) + 1.5d0 * dbc * djk * int2e(intindex(b, l, i, a))&
- dbc * dil * int2e(intindex(b, a, j, k)) + 1.5d0 * dbc * dil * int2e(intindex(b, k, j, a))&
+ dbc * dik * int2e(intindex(b, a, j, l)) - 1.5d0 * dbc * dik * int2e(intindex(b, l, j, a))&
- dik * int2e(intindex(c, a, j, l)) + 1.5d0 * dik * int2e(intindex(c, l, j, a))&
+ dil * int2e(intindex(c, a, j, k)) - 1.5d0 * dil * int2e(intindex(c, k, j, a))&
+ djk * int2e(intindex(c, a, i, l)) - 1.5d0 * djk * int2e(intindex(c, l, i, a))&
- djl * int2e(intindex(c, a, i, k)) + 1.5d0 * djl * int2e(intindex(c, k, i, a))&
- dac * int2e(intindex(i, l, j, k)) + dac * int2e(intindex(i, k, j, l))
end function mat_el_2h2p_AA
! -----------------
! 2h2p type B
! -----------------
function mat_el_2h2p_BB (i, j, a, b, k, l, c) result (mat_el)
! -----------------
! computes < ^{B}\Psi_{ij}^{ab} | H | ^{B}\Psi_{kl}^{cb} >
! -----------------
integer :: i, j, k, l
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dbc, dil, dik, djl, djk
dab = s_mat(a, b)
dbc = s_mat(b, c)
dac = s_mat(a, c)
djl = s_mat(j, l)
djk = s_mat(j, k)
dil = s_mat(i, l)
dik = s_mat(i, k)
mat_el = (djk * dil * dac + dik * djl * dac) * (emo(b) + emo(c) - emo(k) - emo(l))&
+ dac * int2e(intindex(i, l, j, k)) + dac * int2e(intindex(i, k, j, l))&
+ dbc * dab * int2e(intindex(i, l, j, k)) + dbc * dab * int2e(intindex(i, k, j, l))&
+ djk * dil * int2e(intindex(c, a, b, b)) + dik * djl * int2e(intindex(c, a, b, b))&
+ dik * djl * int2e(intindex(c, b, b, a)) + djk * dil * int2e(intindex(c, b, b, a))&
+ 0.5d0 * dab * djk * int2e(intindex(c, l, i, b)) - dab * djk * int2e(intindex(c, b, i, l))&
+ 0.5d0 * dab * djl * int2e(intindex(c, k, i, b)) - dab * djl * int2e(intindex(c, b, i, k))&
+ 0.5d0 * dab * dik * int2e(intindex(c, l, j, b)) - dab * dik * int2e(intindex(c, b, j, l))&
+ 0.5d0 * dab * dil * int2e(intindex(c, k, j, b)) - dab * dil * int2e(intindex(c, b, j, k))&
+ 0.5d0 * dac * dik * int2e(intindex(b, l, j, b)) - dac * dik * int2e(intindex(b, b, j, l))&
+ 0.5d0 * dac * dil * int2e(intindex(b, k, j, b)) - dac * dil * int2e(intindex(b, b, j, k))&
+ 0.5d0 * dac * djk * int2e(intindex(b, l, i, b)) - dac * djk * int2e(intindex(b, b, i, l))&
+ 0.5d0 * dac * djl * int2e(intindex(b, k, i, b)) - dac * djl * int2e(intindex(b, b, i, k))&
+ 0.5d0 * dbc * djk * int2e(intindex(b, l, i, a)) - dbc * djk * int2e(intindex(b, a, i, l))&
+ 0.5d0 * dbc * dil * int2e(intindex(b, k, j, a)) - dbc * dil * int2e(intindex(b, a, j, k))&
+ 0.5d0 * dbc * djl * int2e(intindex(b, k, i, a)) - dbc * djl * int2e(intindex(b, a, i, k))&
+ 0.5d0 * dbc * dik * int2e(intindex(b, l, j, a)) - dbc * dik * int2e(intindex(b, a, j, l))&
+ 0.5d0 * dik * int2e(intindex(c, l, j, a)) - dik * int2e(intindex(c, a, j, l))&
+ 0.5d0 * dil * int2e(intindex(c, k, j, a)) - dil * int2e(intindex(c, a, j, k))&
+ 0.5d0 * djk * int2e(intindex(c, l, i, a)) - djk * int2e(intindex(c, a, i, l))&
+ 0.5d0 * djl * int2e(intindex(c, k, i, a)) - djl * int2e(intindex(c, a, i, k))
end function mat_el_2h2p_BB
! =====================
! COUPLING BLOCKS
! =====================
! ----------------------------
! 2h2p type 1 / 2h2p type A
! ----------------------------
function mat_el_2h2p_1A (i, a, b, k, l, c) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{ii}^{ab} | H | ^{A}\Psi_{kl}^{cb} >
! -----------------
integer :: i, k, l
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dbc, dac, dil, dik
dab = s_mat(a, b)
dbc = s_mat(b, c)
dac = s_mat(a, c)
dil = s_mat(i, l)
dik = s_mat(i, k)
mat_el = sqrt(1.5d0) * (dab * dil * int2e(intindex(c, k, i, b)) - dab * dik * int2e(intindex(c, l, i, b))&
+ dac * dik * int2e(intindex(b, l, i, b)) - dac * dil * int2e(intindex(b, k, i, b))&
+ dbc * dik * int2e(intindex(b, l, i, a)) - dbc * dil * int2e(intindex(b, k, i, a))&
- dik * int2e(intindex(c, l, i, a)) + dil * int2e(intindex(c, k, i, a)))
end function mat_el_2h2p_1A
! ----------------------------
! 2h2p type 1 / 2h2p type B
! ----------------------------
function mat_el_2h2p_1B (i, a, b, k, l, c) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{ii}^{ab} | H | ^{B}\Psi_{kl}^{cb} >
! -----------------
integer :: i, k, l
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dbc, dac, dil, dik
dab = s_mat(a, b)
dbc = s_mat(b, c)
dac = s_mat(a, c)
dil = s_mat(i, l)
dik = s_mat(i, k)
! October 15, 2016
! a minus sign added due to the difference btw definitions of |ij ab, B>
mat_el = -sqrt(0.5d0) * &
(dbc * dab * int2e(intindex(i, l, i, k)) + dbc * dab * int2e(intindex(i, k, i, l))&
+ 2.0d0 * dik * dil * int2e(intindex(c, a, b, b)) + 2.0d0 * dik * dil * int2e(intindex(c, b, b, a))&
- 2.0d0 * dab * dik * int2e(intindex(c, b, i, l)) + dab * dik * int2e(intindex(c, l, i, b))&
- 2.0d0 * dab * dil * int2e(intindex(c, b, i, k)) + dab * dil * int2e(intindex(c, k, i, b))&
- 2.0d0 * dac * dik * int2e(intindex(b, b, i, l)) + dac * dik * int2e(intindex(b, l, i, b))&
- 2.0d0 * dac * dil * int2e(intindex(b, b, i, k)) + dac * dil * int2e(intindex(b, k, i, b))&
- 2.0d0 * dbc * dik * int2e(intindex(b, a, i, l)) + dbc * dik * int2e(intindex(b, l, i, a))&
- 2.0d0 * dbc * dil * int2e(intindex(b, a, i, k)) + dbc * dil * int2e(intindex(b, k, i, a))&
+ dac * int2e(intindex(i, k, i, l)) + dac * int2e(intindex(i, l, i, k))&
- 2.0d0 * dil * int2e(intindex(c, a, i, k)) + dil * int2e(intindex(c, k, i, a))&
- 2.0d0 * dik * int2e(intindex(c, a, i, l)) + dik * int2e(intindex(c, l, i, a)))
end function mat_el_2h2p_1B
! ----------------------------
! 2h2p type A / 2h2p type B
! ----------------------------
function mat_el_2h2p_AB (i, j, a, b, k, l, c) result (mat_el)
! -----------------
! computes < ^{A}\Psi_{ij}^{ab} | H | ^{B}\Psi_{kl}^{cb} >
! -----------------
integer :: i, j, k, l
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dbc, dil, dik, djl, djk
dab = s_mat(a, b)
dbc = s_mat(b, c)
dac = s_mat(a, c)
djl = s_mat(j, l)
djk = s_mat(j, k)
dil = s_mat(i, l)
dik = s_mat(i, k)
! October 15, 2016
! a minus sign added due to the difference btw definitions of |ij ab, B>
mat_el = -sqrt(3.0d0) * 0.5d0 * (&
+ dab * dik * int2e(intindex(c, l, j, b))&
+ dab * dil * int2e(intindex(c, k, j, b))&
- dab * djk * int2e(intindex(c, l, i, b))&
- dab * djl * int2e(intindex(c, k, i, b))&
+ dac * dik * int2e(intindex(b, l, j, b))&
+ dac * dil * int2e(intindex(b, k, j, b))&
- dac * djk * int2e(intindex(b, l, i, b))&
- dac * djl * int2e(intindex(b, k, i, b))&
- dbc * dik * int2e(intindex(b, l, j, a))&
- dbc * dil * int2e(intindex(b, k, j, a))&
+ dbc * djk * int2e(intindex(b, l, i, a))&
+ dbc * djl * int2e(intindex(b, k, i, a))&
- dik * int2e(intindex(c, l, j, a))&
- dil * int2e(intindex(c, k, j, a))&
+ djk * int2e(intindex(c, l, i, a))&
+ djl * int2e(intindex(c, k, i, a)))
end function mat_el_2h2p_AB
! ----------------------------
! 1h1p / 2h2p type 1
! ----------------------------
function mat_el_1h1p_2h2p_1 (i, a, j, b, c) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{i}^{a} | H | ^{1}\Psi_{jj}^{bc} >
! -----------------
integer :: i, j
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dij
dab = s_mat(a, b)
dac = s_mat(a, c)
dij = s_mat(i, j)
mat_el = 0.5d0 * (-2.0d0 * dij * int2e(intindex(a, c, j, b)) -2.0d0 * dij * int2e(intindex(a, b, j, c)) &
+ dac * int2e(intindex(j, b, j, i)) + dac * int2e(intindex(j, i, j, b))&
+ dab * int2e(intindex(j, i, j, c)) + dab * int2e(intindex(j, c, j, i)))
end function mat_el_1h1p_2h2p_1
! ----------------------------
! 1h1p / 2h2p type A
! ----------------------------
function mat_el_1h1p_2h2p_A (i, a, j, k, b, c) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{i}^{a} | H | ^{A}\Psi_{jk}^{bc} >
! -----------------
integer :: i, j, k
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dij, dik
dab = s_mat(a, b)
dac = s_mat(a, c)
dij = s_mat(i, j)
dik = s_mat(i, k)
mat_el = sqrt(1.5d0) *&
( dac * int2e(intindex(k, i, j, b)) - dac * int2e(intindex(k, b, j, i))&
+ dik * int2e(intindex(a, b, j, c)) - dik * int2e(intindex(a, c, j, b))&
+ dij * int2e(intindex(a, c, k, b)) - dij * int2e(intindex(a, b, k, c))&
+ dab * int2e(intindex(k, c, j, i)) - dab * int2e(intindex(k, i, j, c)))
end function mat_el_1h1p_2h2p_A
! ----------------------------
! 1h1p / 2h2p type B
! ----------------------------
function mat_el_1h1p_2h2p_B (i, a, j, k, b, c) result (mat_el)
! -----------------
! computes < ^{1}\Psi_{i}^{a} | H | ^{B}\Psi_{jk}^{bc} >
! -----------------
integer :: i, j, k
integer :: a, b, c
double precision :: mat_el
double precision :: dab, dac, dij, dik
dab = s_mat(a, b)
dac = s_mat(a, c)
dij = s_mat(i, j)
dik = s_mat(i, k)
! October 15, 2016
! a minus sign added due to the difference btw definitions of |ij ab, B>
mat_el = -sqrt(0.5d0) * (dac * int2e(intindex(k, i, j, b)) + dac * int2e(intindex(k, b, j, i))&
+ dab * int2e(intindex(k, c, j, i)) + dab * int2e(intindex(k, i, j, c))&
- dik * int2e(intindex(a, c, j, b)) - dik * int2e(intindex(a, b, j, c))&
- dij * int2e(intindex(a, b, k, c)) - dij * int2e(intindex(a, c, k, b)))
end function mat_el_1h1p_2h2p_B
end module mat_element_pol