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108 lines
3.5 KiB
Org Mode
108 lines
3.5 KiB
Org Mode
#+TITLE: Slater Determinant
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#+SETUPFILE: ../tools/theme.setup
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#+INCLUDE: ../tools/lib.org
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The slater deteminant is required for the calculation of the
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wavefunction, gradient, and derivatives. These quantities will be used
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to calculate the local Energy (\[E_L\]).
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ψ(x) = det|ϕ₁(x₁)...ϕᵢ(yᵢ)...ϕₙ(xₙ)|
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Concerning the gradient and laplacian, in fact what is actually
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calculated is the ratio of the gradient/laplacian and the determinant
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of the slater matrix:
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∇ψ(x)/ψ(x)
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and
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∇²ψ(x)/ψ(x)
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This avoids the unnecessary multiplication and division of by the
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determinant ψ(x).
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* Headers :noexport:
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#+begin_src elisp :noexport :results none
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(org-babel-lob-ingest "../tools/lib.org")
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#+end_src
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#+begin_src c :tangle (eval h_private_type)
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#ifndef QMCKL_MO_HPT
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#define QMCKL_MO_HPT
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#include <stdbool.h>
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#+end_src
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#+begin_src c :tangle (eval c_test) :noweb yes
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#include "qmckl.h"
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#include "assert.h"
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#include <stdio.h>
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#include <math.h>
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#include "chbrclf.h"
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#include "qmckl_ao_private_func.h"
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#include "qmckl_mo_private_func.h"
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#include "qmckl_slater_determinant_private_func.h"
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int main() {
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qmckl_context context;
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context = qmckl_context_create();
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qmckl_exit_code rc;
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#+end_src
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#+begin_src c :tangle (eval c)
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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#ifdef HAVE_STDINT_H
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#include <stdint.h>
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#elif HAVE_INTTYPES_H
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#include <inttypes.h>
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#endif
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#include <stdlib.h>
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#include <string.h>
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#include <stdbool.h>
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#include <assert.h>
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#include "qmckl.h"
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#include "qmckl_context_private_type.h"
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#include "qmckl_memory_private_type.h"
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#include "qmckl_memory_private_func.h"
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#include "qmckl_ao_private_type.h"
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#include "qmckl_ao_private_func.h"
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#include "qmckl_mo_private_type.h"
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#include "qmckl_mo_private_func.h"
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#include "qmckl_slater_determinant_private_type.h"
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#include "qmckl_slater_determinant_private_func.h"
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#+end_src
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* Context
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The following arrays are stored in the context:
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|-----------------+-------------------------------+------------------------------------|
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| ~type~ | ~char~ | α (~'A'~) or β (~'B'~) determinant |
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| ~walk_num~ | ~uint64_t~ | Number of walkers |
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| ~det_num~ | ~uint64_t~ | Number of determinants per walker |
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| ~fermi_num~ | ~uint64_t~ | Number of number of fermions |
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| ~mo_index_list~ | ~mo_index[walk_num][det_num]~ | Index of MOs for each walker |
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Computed data:
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|-------------------+------------------------------------------+----------------------------------------------------------------------------------------|
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| ~det_matrix_list~ | ~[walk_num][det_num][mo_num][fermi_num]~ | The slater matrix for each determinant of each walker. |
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|-------------------+------------------------------------------+----------------------------------------------------------------------------------------|
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| ~det_vgl~ | ~[5][walk_num][det_num]~ | Value, gradients, Laplacian of the MOs at electron positions |
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| ~det_vgl_date~ | ~uint64_t~ | Late modification date of Value, gradients, Laplacian of the MOs at electron positions |
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|-------------------+------------------------------------------+----------------------------------------------------------------------------------------|
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