From edc6e0a4f603f53928d645823862731e1d2866eb Mon Sep 17 00:00:00 2001
From: v1j4y <vijay.gopal.c@gmail.com>
Date: Mon, 11 Oct 2021 18:48:48 +0200
Subject: [PATCH] Added doc for the three energies. #41

---
 org/qmckl_local_energy.org | 41 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/org/qmckl_local_energy.org b/org/qmckl_local_energy.org
index 9040693..afd5cac 100644
--- a/org/qmckl_local_energy.org
+++ b/org/qmckl_local_energy.org
@@ -185,6 +185,19 @@ typedef struct qmckl_local_energy_struct {
    :FRetType: qmckl_exit_code
    :END:
 
+Where the kinetic energy is given as:
+
+\[
+KE = -\frac{1}{2}\frac{\bigtriangleup \Psi}{\Psi} 
+\]
+
+The laplacian of the wavefunction in the single-determinant
+case is given as follows:
+
+\[
+\frac{\bigtriangleup \Psi(r)}{\Psi(r)} = \sum_{j=1}^{N_e} \bigtriangleup \Phi_j(r_i) D_{ji}^{-1}(r)
+\]
+
 *** Get
     
     #+begin_src c :comments org :tangle (eval h_func) :noweb yes
@@ -513,6 +526,27 @@ end function qmckl_compute_kinetic_energy_f
    :FRetType: qmckl_exit_code
    :END:
 
+The potential energy is the sum of all the following terms
+
+\[
+PE = \mathcal{V}_{ee} + \mathcal{V}_{en} + \mathcal{V}_{nn}
+\]
+
+The potential for is calculated as the sum of single electron
+contributions.
+
+\[
+\mathcal{V}_{ee} = \sum_{i=1}^{N_e}\sum_{j<i} \frac{1}{r_{ij}}
+\]
+
+\[
+\mathcal{V}_{en} = - \sum_{i=1}^{N_e}\sum_{A=1}^{N_n}\frac{Z_A}{r_{iA}}
+\]
+
+\[
+\mathcal{V}_{nn} = \sum_{A=1}^{N_n}\sum_{B<A}\frac{Z_A Z_B}{r_{AB}}
+\]
+
 *** Get
     
     #+begin_src c :comments org :tangle (eval h_func) :noweb yes
@@ -756,6 +790,13 @@ end function qmckl_compute_potential_energy_f
    :FRetType: qmckl_exit_code
    :END:
 
+The local energy is the sum of kinetic and potential energies.
+
+\[
+E_L = KE + PE
+\]
+
+
 *** Get
     
     #+begin_src c :comments org :tangle (eval h_func) :noweb yes