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@ -2065,7 +2065,9 @@ assert(fabs(asymp_jasb[1]-0.31567342786262853) < 1.e-12);
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component and the electron-electron rescaled distances ~ee_distance_rescaled~.
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\[
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f_\text{ee} = \sum_{i,j<i} \left[ \frac{\delta_{ij}^{\uparrow\downarrow} B_0\, C_{ij}}{1 - B_1\, C_{ij}} + \sum^{n_\text{ord}}_{k} B_k\, C_{ij}^k - {J_{\text{ee}}^{\infty}}_{ij} \right]
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f_\text{ee} = \sum_{i,j<i} \left[
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\frac{\delta_{ij}^{\uparrow\downarrow} B_0\, C_{ij}}{1 - B_1\,
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C_{ij}} + \sum_{k=2}^{n_\text{ord}} B_k\, C_{ij}^k - {J_{\text{ee}}^{\infty}}_{ij} \right]
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\]
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$\delta$ is the spin factor, $B$ is the vector of $b$ parameters,
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@ -2521,13 +2523,17 @@ assert(fabs(factor_ee[0]+4.282760865958113) < 1.e-12);
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** Electron-electron component derivative \(f'_{ee}\)
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Calculate the derivative of the ~factor_ee~ using the ~ee_distance_rescaled~ and
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The derivative of ~factor_ee~ is computed using the ~ee_distance_rescaled~ and
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the electron-electron rescaled distances derivatives ~ee_distance_rescaled_deriv_e~.
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There are four components, the gradient which has 3 components in the \(x, y, z\)
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directions and the laplacian as the last component.
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# TODO: Add equation
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\[ \nabla_i f_\text{ee} = \frac{1}{2}\sum_{j}
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\left[\frac{\delta_{ij}^{\uparrow\downarrow} B_0\, \nabla_i
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C_{ij}}{(1 - B_1\, C_{ij})^2} + \sum^{n_\text{ord}}_{k=2}
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B_k\, k\, C_{ij}^{k-1} \nabla C_{ij} \right] \]
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# TODO Laplacian
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*** Get
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#+begin_src c :comments org :tangle (eval h_func) :noweb yes
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qmckl_exit_code
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@ -2740,8 +2746,8 @@ integer function qmckl_compute_factor_ee_deriv_e_doc_f( &
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dx(3) = ee_distance_rescaled_deriv_e(3, i, j, nw)
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dx(4) = ee_distance_rescaled_deriv_e(4, i, j, nw)
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if((i .LE. up_num .AND. j .LE. up_num ) .OR. &
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(i .GT. up_num .AND. j .GT. up_num)) then
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if((i <= up_num && j <= up_num ) .OR. &
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(i > up_num && j > up_num)) then
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spin_fact = 0.5d0
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endif
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@ -2761,8 +2767,8 @@ integer function qmckl_compute_factor_ee_deriv_e_doc_f( &
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lap3 = lap3 - 2.0d0 * b_vector(2) * dx(ii) * dx(ii)
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factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) + spin_fact * b_vector(1) * &
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dx(ii) * invden2 + pow_ser_g(ii)
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factor_ee_deriv_e( j, ii, nw) = factor_ee_deriv_e( j, ii, nw) &
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+ spin_fact * b_vector(1) * dx(ii) * invden2 + pow_ser_g(ii)
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end do
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ii = 4
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