3-body doc

org/qmckl_jastrow_champ_single.org

@@ -996,21 +996,80 @@ Here we calculate the single electron contributions to the electron-electron-nuc
 To start, we need to calculate the rescaled distances for the single electron electron-nucleus and electron-electron distances.
 These rescaled distances are calculates by
 \[
-\widetilde{R}_{\alpha} = e^{-\kappa R_{\alpha}} \quad \text{and} \quad \widetilde{r}_{i} = e^{-\kappa r_{i}}.
+\widetilde{R}_{\alpha} = e^{-\kappa l R_{\alpha}} \quad \text{and} \quad \widetilde{r}_{i} = e^{-\kappa l r_{i}}.
 \]
-
+Here, $\kappa$ is the rescaling factor and $l$ the power. The neccessery powers are stored in the same array. 
-With these, we can now calculate the single electron contribution to the $\delta P$ matrix, using the equation
+From these, we can calculate the $\delta \widetilde{R}$ and $\delta \widetilde{r}$ using
 \begin{eqnarray*}
-\delta P_{i,\alpha,k,l} &= P^{\text{new}}_{i,\alpha,k,l} - P^{\text{old}}_{i,\alpha,k,l}\\
+\delta \widetilde{R}_{\alpha} &=& \widetilde{R}_{\alpha}^\text{new} - \widetilde{R}_{\alpha}^\text{old} \quad \text{and}\\
-&= \sum_{j=1}^{N_\text{elec}} \left(\widetilde{r}_{i,j,k} \delta \widetilde{R}_{j,\alpha,l}\delta_{j,\text{num}} + 
+\delta \widetilde{r}_{i} &=& \widetilde{r}_{i}^\text{new} - \widetilde{r}_{i}^\text{old}.
-\delta \widetilde{r}_{i,j,k} \widetilde{R}_{j,\alpha,l} (\delta_{j,\text{num}} 
-+ \delta_{i,\text{num}}) + \delta \widetilde{r}_{i,j,k} \delta \widetilde{R}_{j,\alpha,l} \delta_{j,\text{num}}\right)\\
-&= \sum_{j=1}^{N_\text{elec}} \left( \delta \widetilde{r}_{\text{num},j,k} \widetilde{R}_{j,\alpha,l}  \right) 
-+ \widetilde{r}_{i,\text{num},k} \delta \widetilde{R}_{\text{num},\alpha,l} + \delta \widetilde{r}_{i,\text{num},k} \left( \widetilde{R}_{\text{num},\alpha,l}
-+ \delta \widetilde{R}_{\text{num},\alpha,l} \right)
 \end{eqnarray*}
 
 
+With these, we can now calculate the single electron contribution to the $\delta P$ matrix, using the equation
+\begin{eqnarray*}
+\delta P_{i,\alpha,k,l} &=& P^{\text{new}}_{i,\alpha,k,l} - P^{\text{old}}_{i,\alpha,k,l}\\
+&=& \sum_{j=1}^{N_\text{elec}} \left(\widetilde{r}_{i,j,k} \delta \widetilde{R}_{j,\alpha,l}\delta_{j,\text{num}} + 
+\delta \widetilde{r}_{i,j,k} \widetilde{R}_{j,\alpha,l} (\delta_{j,\text{num}} 
++ \delta_{i,\text{num}}) + \delta \widetilde{r}_{i,j,k} \delta \widetilde{R}_{j,\alpha,l} \delta_{j,\text{num}}\right)\\
+&=& \sum_{j=1}^{N_\text{elec}} \left( \delta \widetilde{r}_{\text{num},j,k} \widetilde{R}_{j,\alpha,l}  \right) 
++ \widetilde{r}_{i,\text{num},k} \delta \widetilde{R}_{\text{num},\alpha,l} + \delta \widetilde{r}_{i,\text{num},k} \left( \widetilde{R}_{\text{num},\alpha,l}
++ \delta \widetilde{R}_{\text{num},\alpha,l} \right).
+\end{eqnarray*}
+
+Then, the electron-electron-nucleus Jastrow value can be calculated by
+\begin{eqnarray*}
+J_{een} &=& J_{een}^{\text{new}} - J_{een}^{\text{old}}\\
+&=&\sum_{p=2}^{N_\text{nord}} \sum_{k=0}^{p-1} \sum_{l=0}^{p-k-2\delta_{k,0}}\sum_{\alpha=1}^{N_\text{nucl}} c_{l,k,p,\alpha}
+\sum_{i=1}^{N_\text{elec}} \left( \delta \widetilde{R}_{i,\alpha,(p-k-l)/2} P_{i,\alpha,k,(p-k+l)/2} \delta_{i,\text{num}}
++  \widetilde{R}_{i,\alpha,(p-k-l)/2} \delta P_{i,\alpha,k,(p-k+l)/2} 
++  \delta \widetilde{R}_{i,\alpha,(p-k-l)/2} \delta P_{i,\alpha,k,(p-k+l)/2} \delta_{i,\text{num}} \right)\\
+&=& \sum_{p=2}^{N_\text{nord}} \sum_{k=0}^{p-1} \sum_{l=0}^{p-k-2\delta_{k,0}}\sum_{\alpha=1}^{N_\text{nucl}} c_{l,k,p,\alpha} \left(
+\sum_{i=1}^{N_\text{elec}} \left( \widetilde{R}_{i,\alpha,(p-k-l)/2} \delta P_{i,\alpha,k,(p-k+l)/2} \right)
++ \delta \widetilde{R}_{\text{num},\alpha,(p-k-l)/2} \left(P_{\text{num},\alpha,k,(p-k+l)/2} + \delta P_{\text{num},\alpha,k,(p-k+l)/2}  \right)\right)
+\end{eqnarray*}
+
+
+To calculate the gradients and Laplacian of the electron-electron-nucleus Jastrow, 
+we first have to calculate the gradients and Laplacian of the rescaled distances,
+\[
+\partial_{i,m} \widetilde{R}_{\alpha} = -\kappa l e^{-\kappa l R_{\alpha}} \frac{x_m - X_{m,\alpha}}{R_\alpha} \quad \text{and} \quad
+\partial_{i,4} \widetilde{R}_{\alpha} = -\kappa l \left(\frac{2}{R_\alpha}- \kappa l \right) e^{-\kappa l R_{\alpha}},
+\]
+where $i$ is the electron of which we are taking the derivative and $m=1:3$ are the gradients and $m=4$ is the Laplacian. 
+The derivatives of the single electron rescaled electron-nucleus distances are only nonzero when $i=\text{num}$.
+Similarly for $r$ we get
+\[
+\partial_{i,m} \widetilde{r}_{i} = -\kappa l e^{-\kappa l r_{i}} \frac{x_m - X_{m,i}}{r_i} \quad \text{and} \quad
+\partial_{i,4} \widetilde{r}_{i} = -\kappa l \left(\frac{2}{r_i}- \kappa l \right) e^{-\kappa l r_{i}}.
+\]
+
+With these, we can now calculate the gradient and Laplacian of the $\delta P$ matrix, using the equation
+\begin{eqnarray*}
+\partial_{i,m} \delta P_{i,\alpha,k,l} &=& \partial_{i,m} P_{i,\alpha,k,l}^\text{new} - \partial_{i,m}  P_{i,\alpha,k,l}^\text{old}\\
+&=& \partial_{i,m}\delta \widetilde{r}_{\text{num},i,k} \left(\partial_{i,m}\delta \widetilde{R}_{\text{num},\alpha,l} + \partial_{i,m}\widetilde{R}_{\text{num},\alpha,l} \right) g_m
++ \partial_{i,m}\widetilde{r}_{\text{num},i,k} \delta \widetilde{R}_{\text{num},\alpha,l}
++ \delta_{i,\text{num}} \sum_{j=1}^{N_\text{elec}} \left( \partial_{j,m} \delta \widetilde{r}_{\text{num},j,k} \widetilde{R}_{j,\alpha,l} \right),
+\end{eqnarray*}
+where $g_m = \{-1,-1,-1,1\}$.
+
+Then, the gradient and Laplacian of the electron-electron-nucleus Jastrow value can be calculated by
+\begin{eqnarray*}
+\partial_{i,m} J_{een} &=& \partial_{i,m} J_{een}^{\text{new}} - \partial_{i,m} J_{een}^{\text{old}}\\
+&=&\sum_{p=2}^{N_\text{nord}} \sum_{k=0}^{p-1} \sum_{l=0}^{p-k-2\delta_{k,0}}\sum_{\alpha=1}^{N_\text{nucl}} c_{l,k,p,\alpha}
+\left( \widetilde{R}_{i,\alpha,(p-k-l)/2} \partial_{i,m} \delta P_{i,\alpha,k,(p-k+l)/2} 
++ \widetilde{R}_{i,\alpha,(p-k+l)/2} \partial_{i,m} \delta P_{i,\alpha,k,(p-k-l)/2}  \right. \\
+& &\ + \partial_{i,m}\widetilde{R}_{i,\alpha,(p-k-l)/2} \delta P_{i,\alpha,k,(p-k+l)/2}
++ \partial_{i,m}\widetilde{R}_{i,\alpha,(p-k+l)/2} \delta P_{i,\alpha,k,(p-k-l)/2} \\
+& &\ + \delta_{i,\text{num}} \left( \delta \widetilde{R}_{i,\alpha,(p-k-l)/2} \left ( \partial_{i,m} P_{i,\alpha,k,(p-k+l)/2} + \partial_{i,m} \delta P_{i,\alpha,k,(p-k+l)/2} \right) 
++ \delta \widetilde{R}_{i,\alpha,(p-k+l)/2} \left ( \partial_{i,m} P_{i,\alpha,k,(p-k-l)/2} + \partial_{i,m} \delta P_{i,\alpha,k,(p-k-l)/2} \right) \right. \\
+& &\ \left. + \partial_{i,m} \delta \widetilde{R}_{i,\alpha,(p-k-l)/2} \left ( P_{i,\alpha,k,(p-k+l)/2} + \delta P_{i,\alpha,k,(p-k+l)/2} \right) 
++ \partial_{i,m} \delta \widetilde{R}_{i,\alpha,(p-k+l)/2} \left ( P_{i,\alpha,k,(p-k-l)/2} + \delta P_{i,\alpha,k,(p-k-l)/2} \right) \right)\\
+& &\ + \delta_{m,4} \sum_{d=1}^3 \left( \partial_{i,d} \widetilde{R}_{i,\alpha,(p-k-l)/2}  \partial_{i,d} \delta P_{i,\alpha,k,(p-k+l)/2}
++ \partial_{i,d} \widetilde{R}_{i,\alpha,(p-k+l)/2} \partial_{i,d} \delta P_{i,\alpha,k,(p-k-l)/2} \right)\\
+& &\ \left. + \delta_{m,4}\delta_{i,\text{num}} \sum_{d=1}^3\left( \partial_{i,d}\delta \widetilde{R}_{i,\alpha,(p-k-l)/2} \left( \partial_{i,d} P_{i,\alpha,k,(p-k+l)/2} + \partial_{i,d}\delta P_{i,\alpha,k,(p-k+l)/2} \right)
++ \partial_{i,d}\delta \widetilde{R}_{i,\alpha,(p-k+l)/2} \left( \partial_{i,d} P_{i,\alpha,k,(p-k-l)/2} + \partial_{i,d} \delta P_{i,\alpha,k,(p-k-l)/2} \right) \right) \right)
+\end{eqnarray*}
 ** Electron-electron rescaled distances
 
 *** Get
@@ -2618,7 +2677,7 @@ for (int elec = 0; elec < elec_num; elec++){
 }
       #+end_src
 
-** Electorn-electron rescaled distances derivative
+** Electron-electron rescaled distances derivative
 
 *** Get
 
@@ -3200,7 +3259,8 @@ integer(qmckl_exit_code) function qmckl_compute_jastrow_champ_delta_p_gl_doc( &
            do k = 1, 4
               do a = 1, nucl_num
                  een_rescaled_delta_n = een_rescaled_single_n(a,l,nw) - een_rescaled_n(num, a, l, nw)
-                 tmp = fk(k) * (een_rescaled_n(num,a,l,nw) + een_rescaled_delta_n)
+                 !tmp = fk(k) * (een_rescaled_n(num,a,l,nw) + een_rescaled_delta_n)
+                 tmp = fk(k) * een_rescaled_single_n(a,l,nw)
                  do j = 1, elec_num
                     delta_p_gl(j,a,k,l,m,nw) =  delta_e_gl(j,k) * tmp  + &
                          een_rescaled_e_gl(j,k,num,m,nw) * een_rescaled_delta_n