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Optimized polynomials
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@ -39,7 +39,23 @@ MunitResult test_qmckl_ao() {
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* Polynomials
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\[ P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c \]
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\[
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P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c
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\]
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\begin{eqnarray*}
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\frac{\partial }{\partial x} P_l\left(\mathbf{r},\mathbf{R}_i \right) & = & a (x-X_i)^{a-1} (y-Y_i)^b (z-Z_i)^c \\
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\frac{\partial }{\partial y} P_l\left(\mathbf{r},\mathbf{R}_i \right) & = & b (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c \\
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\frac{\partial }{\partial z} P_l\left(\mathbf{r},\mathbf{R}_i \right) & = & c (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1} \\
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\end{eqnarray*}
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\begin{eqnarray*}
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\left( \frac{\partial }{\partial x^2} +
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\frac{\partial }{\partial y^2} +
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\frac{\partial }{\partial z^2} \right) P_l
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\left(\mathbf{r},\mathbf{R}_i \right) & = &
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a(a-1) (x-X_i)^{a-2} (y-Y_i)^b (z-Z_i)^c + \\
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&& b(b-1) (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c + \\
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&& c(c-1) (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1}
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\end{eqnarray*}
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** =qmckl_ao_powers=
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@ -244,6 +260,7 @@ integer function qmckl_ao_polynomial_vgl_f(context, X, R, lmax, n, L, ldl, VGL,
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integer :: lmax_array(3)
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real*8 :: pows(-2:lmax,3)
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integer, external :: qmckl_ao_powers_f
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double precision :: xy, yz, xz
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info = 0
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@ -293,16 +310,24 @@ integer function qmckl_ao_polynomial_vgl_f(context, X, R, lmax, n, L, ldl, VGL,
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l(2,n) = b
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l(3,n) = c
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vgl(1,n) = pows(a,1) * pows(b,2) * pows(c,3)
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xy = pows(a,1) * pows(b,2)
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yz = pows(b,2) * pows(c,3)
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xz = pows(a,1) * pows(c,3)
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vgl(2,n) = dble(a) * pows(a-1,1) * pows(b ,2) * pows(c ,3)
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vgl(3,n) = dble(b) * pows(a ,1) * pows(b-1,2) * pows(c ,3)
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vgl(4,n) = dble(c) * pows(a ,1) * pows(b ,2) * pows(c-1,3)
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vgl(1,n) = xy * pows(c,3)
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xy = dble(c) * xy
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xz = dble(b) * xz
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yz = dble(a) * yz
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vgl(2,n) = pows(a-1,1) * yz
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vgl(3,n) = pows(b-1,2) * xz
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vgl(4,n) = pows(c-1,3) * xy
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vgl(5,n) = &
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dble(a) * dble(a-1) * pows(a-2,1) * pows(b ,2) * pows(c ,3) + &
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dble(b) * dble(b-1) * pows(a ,1) * pows(b-2,2) * pows(c ,3) + &
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dble(c) * dble(c-1) * pows(a ,1) * pows(b ,2) * pows(c-2,3)
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dble(a-1) * pows(a-2,1) * yz + &
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dble(b-1) * pows(b-2,2) * xz + &
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dble(c-1) * pows(c-2,3) * xy
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exit
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end if
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end do
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