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Added doc for the three energies. #41

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v1j4y 2021-10-11 18:48:48 +02:00
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41
org/qmckl_local_energy.org
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@ -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