TREX/qmckl
1
0
Fork 0
mirror of https://github.com/TREX-CoE/qmckl.git synced 2024-12-22 20:36:01 +01:00
Code Issues Projects Releases Wiki Activity

Documentation of Jastrow

Browse Source
This commit is contained in:
Anthony Scemama 2022-02-09 14:37:38 +01:00
parent 3488455110
commit 484c0a7d5c
2 changed files with 110 additions and 62 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
org/qmckl_distance.org
View File

@ -872,7 +872,7 @@ end function test_qmckl_dist
pairs of points in two sets, one point within each set:
\[
C_{ij} = \left( 1 - \exp{-\kappa C_{ij}}\right)/\kappa
C_{ij} = \left( 1 - \exp \left(-\kappa C_{ij} \right) \right)/\kappa
\]
If the input array is normal (~'N'~), the xyz coordinates are in

170
org/qmckl_jastrow.org
View File

@ -3,10 +3,61 @@
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
Functions for the calculation of the Jastrow factor \(f_{ee}, f_{en}, f_{een}\).
These are stored in the ~factor_ee~, ~factor_en~, and ~factor_een~ variables.
The ~jastrow~ structure contains all the information required to build
these factors along with their derivatives.
* Introduction
The Jastrow factor depends on the electronic ($\mathbf{r}$) and
nuclear ($\mathbf{R}$) coordinates. Its defined as $\exp(J(\mathbf{r},\mathbf{R}))$, where
\[
J(\mathbf{r},\mathbf{R}) = J_{\text{eN}}(\mathbf{r},\mathbf{R}) + J_{\text{ee}}(\mathbf{r}) + J_{\text{eeN}}(\mathbf{r},\mathbf{R})
\]
In the following, we us the notations $r_{ij} = |\mathbf{r}_i - \mathbf{r}_j|$ and
$R_{i\alpha} = |\mathbf{r}_i - \mathbf{R}_\alpha|$.
$J_{\text{eN}}$ contains electron-nucleus terms:
\[
J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{i=1}^{N_\text{elec}} \sum_{\alpha=1}^{N_\text{nucl}}
\frac{a_1\, f(R_{i\alpha})}{1+a_2\, f(R_{i\alpha})} +
\sum_{p=2}^{N_\text{ord}^a} a_{p+1}\, [f(R_{i\alpha})]^p - J_{eN}^\infty
\]
$J_{\text{ee}}$ contains electron-electron terms:
\[
J_{\text{ee}}(\mathbf{r}) =
\sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1}
\frac{b_1\, f(r_{ij})}{1+b_2\, f(r_{ij})} +
\sum_{p=2}^{N_\text{ord}^b} a_{p+1}\, [f(r_{ij})]^p - J_{ee}^\infty
\]
and $J_{\text{eeN}}$ contains electron-electron-Nucleus terms:
\[
J_{\text{eeN}}(\mathbf{r},\mathbf{R}) =
\sum_{\alpha=1}^{N_{\text{nucl}}}
\sum_{i=1}^{N_{\text{elec}}}
\sum_{j=1}^{i-1}
\sum_{p=2}^{N_{\text{ord}}}
\sum_{k=0}^{p-1}
\sum_{l=0}^{p-k-2\delta_{k,0}}
c_{lkp\alpha} \left[ g({r}_{ij}) \right]^k
\left[ \left[ g({R}_{i\alpha}) \right]^l + \left[ g({R}_{j\alpha}) \right]^l \right]
\left[ g({R}_{i\,\alpha}) \, g({R}_{j\alpha}) \right]^{(p-k-l)/2}
\]
$c_{lkp\alpha}$ are non-zero only when $p-k-l$ is even.
$f$ and $g$ are scaling function defined as
\[
f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and }
g(r) = e^{-\kappa\, r}.
\]
The terms $J_{\text{ee}}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that
$J_{\text{ee}}$ and $J_{\text{eN}}$ have an asymptotic value of zero.
* Headers :noexport:
#+begin_src elisp :noexport :results none
@ -80,7 +131,7 @@ int main() {
#+NAME: qmckl_jastrow_args
| Variable | Type | In/Out | Description |
|---------------------------+---------------------------------------+--------+-------------------------------------------------------------------|
| ~uninitialized~ | ~int32_t~ | in | Keeps bit set for uninitialized data |
| ~uninitialized~ | ~int32_t~ | in | Keeps bits set for uninitialized data |
| ~aord_num~ | ~int64_t~ | in | The number of a coeffecients |
| ~bord_num~ | ~int64_t~ | in | The number of b coeffecients |
| ~cord_num~ | ~int64_t~ | in | The number of c coeffecients |
@ -124,12 +175,11 @@ int main() {
| ~een_rescaled_n_deriv_e~ | ~double[walk_num][elec_num][4][nucl_num][0:cord_num]~ | The electron-electron rescaled distances raised to the powers defined by cord derivatives wrt electrons | |
| ~een_rescaled_n_deriv_e_date~ | ~uint64_t~ | Keep track of the date of creation | |
For H2O we have the following data:
#+NAME: jastrow_data
#+BEGIN_SRC python :results output
#+BEGIN_SRC python :results none :exports none
import numpy as np
# For H2O we have the following data:
elec_num = 10
nucl_num = 2
up_num = 5
@ -150,46 +200,46 @@ elec_coord = [[[-0.250655104764153 , 0.503070975550133 , -0.16655
[ 0.397978144318712 , -0.254277292595981 , 2.54553335476344]]];
ee_distance_rescaled = [
[ 0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.550227800352402 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.919155060185168 ,0.937695909123175 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.893325429242815 ,0.851181978173561 ,0.978501685226877 ,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.982457268305353 ,0.976125002619471 ,0.994349933143149 ,
0.844077311588328 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.482407528408731 ,0.414816073699124 ,0.894716035479343 ,
0.876540187084407 ,0.978921170036895 ,0.000000000000000E+000,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.459541909660400 ,0.545007215761510 ,0.883752955884551 ,
0.918958134888791 ,0.986386936267237 ,0.362209822236419 ,
0.000000000000000E+000 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.763732576854455 ,0.817282762358449 ,0.801802919535959 ,
0.900089095449775 ,0.975704636491453 ,0.707836537586060 ,
0.755705808346586 ,0.000000000000000E+000 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.904249454052971 ,0.871097965261373 ,0.982717262706270 ,
0.239901207363622 ,0.836519456769083 ,0.896135326270534 ,
0.930694340243023 ,0.917708540815567 ,0.000000000000000E+000,
0.000000000000000E+000],
[ 0.944400908070716 ,0.922589018494961 ,0.984615718580670 ,
0.514328661540623 ,0.692362267147064 ,0.931894098453677 ,
0.956034127544344 ,0.931221472309472 ,0.540903688625053 ,
0.000000000000000E+000]]
[ 0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.550227800352402, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.919155060185168, 0.937695909123175, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.893325429242815, 0.851181978173561, 0.978501685226877,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.982457268305353, 0.976125002619471, 0.994349933143149,
0.844077311588328, 0.000000000000000, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.482407528408731, 0.414816073699124, 0.894716035479343,
0.876540187084407, 0.978921170036895, 0.000000000000000,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.459541909660400, 0.545007215761510, 0.883752955884551,
0.918958134888791, 0.986386936267237, 0.362209822236419,
0.000000000000000, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.763732576854455, 0.817282762358449, 0.801802919535959,
0.900089095449775, 0.975704636491453, 0.707836537586060,
0.755705808346586, 0.000000000000000, 0.000000000000000,
0.000000000000000 ],
[ 0.904249454052971, 0.871097965261373, 0.982717262706270,
0.239901207363622, 0.836519456769083, 0.896135326270534,
0.930694340243023, 0.917708540815567, 0.000000000000000,
0.000000000000000 ],
[ 0.944400908070716, 0.922589018494961, 0.984615718580670,
0.514328661540623, 0.692362267147064, 0.931894098453677,
0.956034127544344, 0.931221472309472, 0.540903688625053,
0.000000000000000 ]]
en_distance_rescaled = np.transpose(np.array([
[ 0.443570948411811 , 0.467602196999105 , 0.893870160799932 ,
@ -276,8 +326,6 @@ kappa = 1.0
kappa_inv = 1.0/kappa
#+END_SRC
#+RESULTS: jastrow_data
** Data structure
#+begin_src c :comments org :tangle (eval h_private_type)
@ -922,7 +970,7 @@ qmckl_exit_code qmckl_set_jastrow_cord_vector(qmckl_context context, double cons
When the required information is completely entered, other data structures are
computed to accelerate the calculations. The intermediates factors
are precontracted using BLAS LEVEL 3 operations for an optimal FLOP count.
are precontracted using BLAS LEVEL 3 operations for an optimal flop count.
#+begin_src c :comments org :tangle (eval h_private_func) :noweb yes :exports none
qmckl_exit_code qmckl_finalize_jastrow(qmckl_context context);
@ -1151,14 +1199,14 @@ assert(qmckl_nucleus_provided(context));
compute. If it is the case, then the data is recomputed and the
current date is stored.
** Asymptotic component for \(f_{ee}\)
** Asymptotic component for \(J_{ee}\)
Calculate the asymptotic component ~asymp_jasb~ to be substracted from the final
electron-electron jastrow factor \(f_{ee}\). The asymptotic componenet is calculated
electron-electron jastrow factor \(J_{\text{ee}}\). The asymptotic component is calculated
via the ~bord_vector~ and the electron-electron rescale factor ~rescale_factor_kappa~.
\[
J_{asymp} = \frac{b_1 \kappa^-1}{1 + b_2 \kappa^-1}
J_{\text{ee}}^{\infty} = \frac{b_1 \kappa^{-1}}{1 + b_2 \kappa^{-1}}
\]
*** Get
@ -1255,13 +1303,13 @@ qmckl_exit_code qmckl_provide_asymp_jasb(qmckl_context context)
:END:
#+NAME: qmckl_asymp_jasb_args
| Variable | Type | In/Out | Description |
|---------------------------+----------------------+--------+-----------------------------|
| ~context~ | ~qmckl_context~ | in | Global state |
| ~bord_num~ | ~int64_t~ | in | Number of electrons |
| ~bord_vector~ | ~double[bord_num+1]~ | in | Number of walkers |
| ~rescale_factor_kappa_ee~ | ~double~ | in | Electron coordinates |
| ~asymp_jasb~ | ~double[2]~ | out | Electron-electron distances |
| Variable | Type | In/Out | Description |
|---------------------------+----------------------+--------+-------------------------|
| ~context~ | ~qmckl_context~ | in | Global state |
| ~bord_num~ | ~int64_t~ | in | Order of the polynomial |
| ~bord_vector~ | ~double[bord_num+1]~ | in | Values of b |
| ~rescale_factor_kappa_ee~ | ~double~ | in | Electron coordinates |
| ~asymp_jasb~ | ~double[2]~ | out | Asymptotic value |
#+begin_src f90 :comments org :tangle (eval f) :noweb yes
integer function qmckl_compute_asymp_jasb_f(context, bord_num, bord_vector, rescale_factor_kappa_ee, asymp_jasb) &