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#+TITLE: Atomic Orbitals
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org
The atomic basis set is defined as a list of shells. Each shell $s$ is
centered on a nucleus $A$, possesses a given angular momentum $l$ and a
radial function $R_s$. The radial function is a linear combination of
\emph{primitive} functions that can be of type Slater ($p=1$) or
Gaussian ($p=2$):
\[
R_s(\mathbf{r}) = \mathcal{N}_s |\mathbf{r}-\mathbf{R}_A|^{n_s}
\sum_{k=1}^{N_{\text{prim}}} a_{ks}
\exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right).
\]
In the case of Gaussian functions, $n_s$ is always zero.
The normalization factor $\mathcal{N}_s$ ensures that all the functions
of the shell are normalized to unity. As this normalization requires
the ability to compute overlap integrals, it should be written in the
file to ensure that the file is self-contained and does not require
the client program to have the ability to compute such integrals.
Atomic orbitals (AOs) are defined as
\[
\chi_i (\mathbf{r}) = P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
\]
where $\theta(i)$ returns the shell on which the AO is expanded,
and $\eta(i)$ denotes which angular function is chosen.
In this section we describe the kernels used to compute the values,
gradients and Laplacian of the atomic basis functions.
* Headers :noexport:
#+begin_src elisp :noexport :results none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src
#+begin_src c :tangle (eval h_private_type)
#ifndef QMCKL_AO_HPT
#define QMCKL_AO_HPT
#include <stdbool.h>
#+end_src
#+begin_src c :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "munit.h"
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
MunitResult test_<<filename()>>() {
qmckl_context context;
context = qmckl_context_create();
#+end_src
#+begin_src c :tangle (eval c)
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#ifdef HAVE_STDINT_H
#include <stdint.h>
#elif HAVE_INTTYPES_H
#include <inttypes.h>
#endif
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>
#include "qmckl_error_type.h"
#include "qmckl_context_type.h"
#include "qmckl_context_private_type.h"
#include "qmckl_memory_private_type.h"
#include "qmckl_error_func.h"
#include "qmckl_memory_private_func.h"
#include "qmckl_memory_func.h"
#include "qmckl_context_func.h"
#+end_src
* Context
The following arrays are stored in the context:
| ~type~ | | Gaussian (~'G'~) or Slater (~'S'~) |
| ~shell_num~ | | Number of shells |
| ~prim_num~ | | Total number of primitives |
| ~shell_center~ | ~[shell_num]~ | Id of the nucleus on which each shell is centered |
| ~shell_ang_mom~ | ~[shell_num]~ | Angular momentum of each shell |
| ~shell_prim_num~ | ~[shell_num]~ | Number of primitives in each shell |
| ~shell_prim_index~ | ~[shell_num]~ | Address of the first primitive of each shell in the ~EXPONENT~ array |
| ~shell_factor~ | ~[shell_num]~ | Normalization factor for each shell |
| ~exponent~ | ~[prim_num]~ | Array of exponents |
| ~coefficient~ | ~[prim_num]~ | Array of coefficients |
For H_2 with the following basis set,
#+BEGIN_EXAMPLE
HYDROGEN
S 5
1 3.387000E+01 6.068000E-03
2 5.095000E+00 4.530800E-02
3 1.159000E+00 2.028220E-01
4 3.258000E-01 5.039030E-01
5 1.027000E-01 3.834210E-01
S 1
1 3.258000E-01 1.000000E+00
S 1
1 1.027000E-01 1.000000E+00
P 1
1 1.407000E+00 1.000000E+00
P 1
1 3.880000E-01 1.000000E+00
D 1
1 1.057000E+00 1.0000000
#+END_EXAMPLE
we have:
#+BEGIN_EXAMPLE
type = 'G'
shell_num = 12
prim_num = 20
shell_center = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
shell_ang_mom = ['S', 'S', 'S', 'P', 'P', 'D', 'S', 'S', 'S', 'P', 'P', 'D']
shell_factor = [ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]
shell_prim_num = [5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1]
shell_prim_index = [1, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20]
exponent = [ 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027,
1.407, 0.388, 1.057, 33.87, 5.095, 1.159, 0.3258, 0.1027,
0.3258, 0.1027, 1.407, 0.388, 1.057]
coefficient = [ 0.006068, 0.045308, 0.202822, 0.503903, 0.383421,
1.0, 1.0, 1.0, 1.0, 1.0, 0.006068, 0.045308, 0.202822,
0.503903, 0.383421, 1.0, 1.0, 1.0, 1.0, 1.0]
#+END_EXAMPLE
** Data structure
#+begin_src c :comments org :tangle (eval h_private_type)
typedef struct qmckl_ao_basis_struct {
int32_t uninitialized;
int64_t shell_num;
int64_t prim_num;
int64_t * shell_center;
char * shell_ang_mom;
int64_t * shell_prim_num;
int64_t * shell_prim_index;
double * shell_factor;
double * exponent ;
double * coefficient ;
bool provided;
char type;
} qmckl_ao_basis_struct;
#+end_src
The ~uninitialized~ integer contains one bit set to one for each
initialization function which has not bee called. It becomes equal
to zero after all initialization functions have been called. The
struct is then initialized and ~provided == true~.
** Access functions
#+begin_src c :comments org :tangle (eval h_private_func) :exports none
char qmckl_get_ao_basis_type (const qmckl_context context);
int64_t qmckl_get_ao_basis_shell_num (const qmckl_context context);
int64_t qmckl_get_ao_basis_prim_num (const qmckl_context context);
int64_t* qmckl_get_ao_basis_shell_center (const qmckl_context context);
char* qmckl_get_ao_basis_shell_ang_mom (const qmckl_context context);
int64_t* qmckl_get_ao_basis_shell_prim_num (const qmckl_context context);
int64_t* qmckl_get_ao_basis_shell_prim_index (const qmckl_context context);
double* qmckl_get_ao_basis_shell_factor (const qmckl_context context);
double* qmckl_get_ao_basis_exponent (const qmckl_context context);
double* qmckl_get_ao_basis_coefficient (const qmckl_context context);
#+end_src
When all the data for the AOs have been provided, the following
function returns ~true~.
#+begin_src c :comments org :tangle (eval h_func)
bool qmckl_ao_basis_provided (const qmckl_context context);
#+end_src
#+NAME:post
#+begin_src c :exports none
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
char qmckl_get_ao_basis_type (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return (char) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return (char) 0;
}
assert (ctx->ao_basis.type != (char) 0);
return ctx->ao_basis.type;
}
int64_t qmckl_get_ao_basis_shell_num (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return (int64_t) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 1;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return (int64_t) 0;
}
assert (ctx->ao_basis.shell_num > (int64_t) 0);
return ctx->ao_basis.shell_num;
}
int64_t qmckl_get_ao_basis_prim_num (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return (int64_t) 0;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 2;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return (int64_t) 0;
}
assert (ctx->ao_basis.prim_num > (int64_t) 0);
return ctx->ao_basis.prim_num;
}
int64_t* qmckl_get_ao_basis_shell_center (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 3;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.shell_center != NULL);
return ctx->ao_basis.shell_center;
}
char* qmckl_get_ao_basis_shell_ang_mom (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 4;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.shell_ang_mom != NULL);
return ctx->ao_basis.shell_ang_mom;
}
int64_t* qmckl_get_ao_basis_shell_prim_num (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 5;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.shell_prim_num != NULL);
return ctx->ao_basis.shell_prim_num;
}
int64_t* qmckl_get_ao_basis_shell_prim_index (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 6;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.shell_prim_index != NULL);
return ctx->ao_basis.shell_prim_index;
}
double* qmckl_get_ao_basis_shell_factor (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 7;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.shell_factor != NULL);
return ctx->ao_basis.shell_factor;
}
double* qmckl_get_ao_basis_exponent (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 8;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.exponent != NULL);
return ctx->ao_basis.exponent;
}
double* qmckl_get_ao_basis_coefficient (const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return NULL;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
int32_t mask = 1 << 9;
if ( (ctx->ao_basis.uninitialized & mask) != 0) {
return NULL;
}
assert (ctx->ao_basis.coefficient != NULL);
return ctx->ao_basis.coefficient;
}
bool qmckl_ao_basis_provided(const qmckl_context context) {
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return false;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
assert (ctx != NULL);
return ctx->ao_basis.provided;
}
#+end_src
** Initialization functions
To set the basis set, all the following functions need to be
called. When
#+begin_src c :comments org :tangle (eval h_func)
qmckl_exit_code qmckl_set_ao_basis_type (qmckl_context context, const char t);
qmckl_exit_code qmckl_set_ao_basis_shell_num (qmckl_context context, const int64_t shell_num);
qmckl_exit_code qmckl_set_ao_basis_prim_num (qmckl_context context, const int64_t prim_num);
qmckl_exit_code qmckl_set_ao_basis_shell_prim_index (qmckl_context context, const int64_t * shell_prim_index);
qmckl_exit_code qmckl_set_ao_basis_shell_center (qmckl_context context, const int64_t * shell_center);
qmckl_exit_code qmckl_set_ao_basis_shell_ang_mom (qmckl_context context, const char * shell_ang_mom);
qmckl_exit_code qmckl_set_ao_basis_shell_prim_num (qmckl_context context, const int64_t * shell_prim_num);
qmckl_exit_code qmckl_set_ao_basis_shell_factor (qmckl_context context, const double * shell_factor);
qmckl_exit_code qmckl_set_ao_basis_exponent (qmckl_context context, const double * exponent);
qmckl_exit_code qmckl_set_ao_basis_coefficient (qmckl_context context, const double * coefficient);
#+end_src
#+NAME:pre2
#+begin_src c :exports none
if (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
return QMCKL_NULL_CONTEXT;
}
qmckl_context_struct* const ctx = (qmckl_context_struct* const) context;
#+end_src
#+NAME:post2
#+begin_src c :exports none
ctx->ao_basis.uninitialized &= ~mask;
ctx->ao_basis.provided = (ctx->ao_basis.uninitialized == 0);
return QMCKL_SUCCESS;
#+end_src
#+begin_src c :comments org :tangle (eval c) :noweb yes :exports none
qmckl_exit_code qmckl_set_ao_basis_type(qmckl_context context, const char t) {
<<pre2>>
if (t != 'G' && t != 'S') {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_ao_basis_type",
NULL);
}
int32_t mask = 1;
ctx->ao_basis.type = t;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_num(qmckl_context context, const int64_t shell_num) {
<<pre2>>
if (shell_num <= 0) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_ao_basis_shell_num",
"shell_num <= 0");
}
int64_t prim_num = qmckl_get_ao_basis_prim_num(context);
if (0L < prim_num && prim_num < shell_num) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_ao_basis_shell_num",
"shell_num > prim_num");
}
int32_t mask = 1 << 1;
ctx->ao_basis.shell_num = shell_num;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_prim_num(qmckl_context context, const int64_t prim_num) {
<<pre2>>
if (prim_num <= 0) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_ao_basis_shell_num",
"prim_num must be positive");
}
int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (prim_num < shell_num) {
return qmckl_failwith( context,
QMCKL_INVALID_ARG_2,
"qmckl_set_ao_basis_shell_num",
"prim_num < shell_num");
}
int32_t mask = 1 << 2;
ctx->ao_basis.prim_num = prim_num;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_center(qmckl_context context, const int64_t* shell_center) {
<<pre2>>
int32_t mask = 1 << 3;
const int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (shell_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_shell_center",
"shell_num is not set");
}
if (ctx->ao_basis.shell_center != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.shell_center);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_shell_center",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = shell_num * sizeof(int64_t);
int64_t* new_array = (int64_t*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_shell_center",
NULL);
}
memcpy(new_array, shell_center, mem_info.size);
ctx->ao_basis.shell_center = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_ang_mom(qmckl_context context, const char* shell_ang_mom) {
<<pre2>>
int32_t mask = 1 << 4;
const int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (shell_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_shell_ang_mom",
"shell_num is not set");
}
if (ctx->ao_basis.shell_ang_mom != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.shell_ang_mom);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_shell_ang_mom",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = shell_num * sizeof(char);
char* new_array = (char*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_shell_ang_mom",
NULL);
}
memcpy(new_array, shell_ang_mom, mem_info.size);
ctx->ao_basis.shell_ang_mom = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_prim_num(qmckl_context context, const int64_t* shell_prim_num) {
<<pre2>>
int32_t mask = 1 << 5;
const int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (shell_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_shell_prim_num",
"shell_num is not set");
}
if (ctx->ao_basis.shell_prim_num != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.shell_prim_num);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_shell_prim_num",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = shell_num * sizeof(int64_t);
int64_t* new_array = (int64_t*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_shell_prim_num",
NULL);
}
memcpy(new_array, shell_prim_num, mem_info.size);
ctx->ao_basis.shell_prim_num = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_prim_index(qmckl_context context, const int64_t* shell_prim_index) {
<<pre2>>
int32_t mask = 1 << 6;
const int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (shell_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_shell_prim_index",
"shell_num is not set");
}
if (ctx->ao_basis.shell_prim_index != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.shell_prim_index);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_shell_prim_index",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = shell_num * sizeof(int64_t);
int64_t* new_array = (int64_t*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_shell_prim_index",
NULL);
}
memcpy(new_array, shell_prim_index, mem_info.size);
ctx->ao_basis.shell_prim_index = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_shell_factor(qmckl_context context, const double* shell_factor) {
<<pre2>>
int32_t mask = 1 << 7;
const int64_t shell_num = qmckl_get_ao_basis_shell_num(context);
if (shell_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_shell_factor",
"shell_num is not set");
}
if (ctx->ao_basis.shell_factor != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.shell_factor);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_shell_factor",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = shell_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_shell_factor",
NULL);
}
memcpy(new_array, shell_factor, mem_info.size);
ctx->ao_basis.shell_factor = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_exponent(qmckl_context context, const double* exponent) {
<<pre2>>
int32_t mask = 1 << 8;
const int64_t prim_num = qmckl_get_ao_basis_prim_num(context);
if (prim_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_exponent",
"prim_num is not set");
}
if (ctx->ao_basis.exponent != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.exponent);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_exponent",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = prim_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_exponent",
NULL);
}
memcpy(new_array, exponent, mem_info.size);
ctx->ao_basis.exponent = new_array;
<<post2>>
}
qmckl_exit_code qmckl_set_ao_basis_coefficient(qmckl_context context, const double* coefficient) {
<<pre2>>
int32_t mask = 1 << 9;
const int64_t prim_num = qmckl_get_ao_basis_prim_num(context);
if (prim_num == 0L) {
return qmckl_failwith( context,
QMCKL_FAILURE,
"qmckl_set_ao_basis_coefficient",
"prim_num is not set");
}
if (ctx->ao_basis.coefficient != NULL) {
qmckl_exit_code rc = qmckl_free(context, ctx->ao_basis.coefficient);
if (rc != QMCKL_SUCCESS) {
return qmckl_failwith( context, rc,
"qmckl_set_ao_basis_coefficient",
NULL);
}
}
qmckl_memory_info_struct mem_info = qmckl_memory_info_struct_zero;
mem_info.size = prim_num * sizeof(double);
double* new_array = (double*) qmckl_malloc(context, mem_info);
if (new_array == NULL) {
return qmckl_failwith( context,
QMCKL_ALLOCATION_FAILED,
"qmckl_set_ao_basis_coefficient",
NULL);
}
memcpy(new_array, coefficient, mem_info.size);
ctx->ao_basis.coefficient = new_array;
<<post2>>
}
#+end_src
** TODO Fortran interfaces
** Test :noexport:
#+begin_src c :tangle (eval c_test) :exports none :exports none
/* Reference input data */
char typ = 'G';
#define shell_num ((int64_t) 12)
#define prim_num ((int64_t) 20)
int64_t shell_center [shell_num] =
{ 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2 };
char shell_ang_mom [shell_num] =
{ 'S', 'S', 'S', 'P', 'P', 'D', 'S', 'S', 'S', 'P', 'P', 'D' };
double shell_factor [shell_num] =
{ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1. };
int64_t shell_prim_num [shell_num] =
{5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1};
int64_t shell_prim_index [shell_num] =
{1, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20};
double exponent [prim_num] =
{ 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027,
1.407, 0.388, 1.057, 33.87, 5.095, 1.159, 0.3258, 0.1027,
0.3258, 0.1027, 1.407, 0.388, 1.057 };
double coefficient [prim_num] =
{ 0.006068, 0.045308, 0.202822, 0.503903, 0.383421,
1.0, 1.0, 1.0, 1.0, 1.0, 0.006068, 0.045308, 0.202822,
0.503903, 0.383421, 1.0, 1.0, 1.0, 1.0, 1.0 };
/* --- */
qmckl_exit_code rc;
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_type (context, typ);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_num (context, shell_num);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_prim_num (context, prim_num);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_center (context, shell_center);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_ang_mom (context, shell_ang_mom);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_factor (context, shell_factor);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_center (context, shell_prim_num);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_prim_num (context, shell_prim_num);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_shell_prim_index (context, shell_prim_index);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_exponent (context, exponent);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(!qmckl_ao_basis_provided(context));
rc = qmckl_set_ao_basis_coefficient (context, coefficient);
munit_assert_int64(rc, ==, QMCKL_SUCCESS);
munit_assert(qmckl_ao_basis_provided(context));
#+end_src
* Polynomial part
** Powers of $x-X_i$
:PROPERTIES:
:Name: qmckl_ao_power
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
The ~qmckl_ao_power~ function computes all the powers of the ~n~
input data up to the given maximum value given in input for each of
the $n$ points:
\[ P_{ik} = X_i^k \]
#+NAME: qmckl_ao_power_args
| qmckl_context | context | in | Global state |
| int64_t | n | in | Number of values |
| double | X[n] | in | Array containing the input values |
| int32_t | LMAX[n] | in | Array containing the maximum power for each value |
| double | P[n][ldp] | out | Array containing all the powers of ~X~ |
| int64_t | ldp | in | Leading dimension of array ~P~ |
*** Requirements
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~n~ > 0
- ~X~ is allocated with at least $n \times 8$ bytes
- ~LMAX~ is allocated with at least $n \times 4$ bytes
- ~P~ is allocated with at least $n \times \max_i \text{LMAX}_i \times 8$ bytes
- ~LDP~ >= $\max_i$ ~LMAX[i]~
*** C Header
#+CALL: generate_c_header(table=qmckl_ao_power_args,rettyp=get_value("CRetType"),fname="qmckl_ao_power")
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_ao_power (
const qmckl_context context,
const int64_t n,
const double* X,
const int32_t* LMAX,
double* const P,
const int64_t ldp );
#+end_src
*** Source
#+begin_src f90 :tangle (eval f)
integer function qmckl_ao_power_f(context, n, X, LMAX, P, ldp) result(info)
use qmckl
implicit none
integer*8 , intent(in) :: context
integer*8 , intent(in) :: n
real*8 , intent(in) :: X(n)
integer , intent(in) :: LMAX(n)
real*8 , intent(out) :: P(ldp,n)
integer*8 , intent(in) :: ldp
integer*8 :: i,k
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (n <= ldp) then
info = QMCKL_INVALID_ARG_2
return
endif
k = MAXVAL(LMAX)
if (LDP < k) then
info = QMCKL_INVALID_ARG_6
return
endif
if (k <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
do i=1,n
P(1,i) = X(i)
do k=2,LMAX(i)
P(k,i) = P(k-1,i) * X(i)
end do
end do
end function qmckl_ao_power_f
#+end_src
*** C interface
#+CALL: generate_c_interface(table=qmckl_ao_power_args,rettyp=get_value("CRetType"),fname="qmckl_ao_power")
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_ao_power &
(context, n, X, LMAX, P, ldp) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: n
real (c_double ) , intent(in) :: X(n)
integer (c_int32_t) , intent(in) :: LMAX(n)
real (c_double ) , intent(out) :: P(ldp,n)
integer (c_int64_t) , intent(in) , value :: ldp
integer(c_int32_t), external :: qmckl_ao_power_f
info = qmckl_ao_power_f &
(context, n, X, LMAX, P, ldp)
end function qmckl_ao_power
#+end_src
*** Fortran interface
#+CALL: generate_f_interface(table=qmckl_ao_power_args,rettyp=get_value("CRetType"),fname="qmckl_ao_power")
#+RESULTS:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_ao_power &
(context, n, X, LMAX, P, ldp) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: n
real (c_double ) , intent(in) :: X(n)
integer (c_int32_t) , intent(in) :: LMAX(n)
real (c_double ) , intent(out) :: P(ldp,n)
integer (c_int64_t) , intent(in) , value :: ldp
end function qmckl_ao_power
end interface
#+end_src
*** Test
#+begin_src f90 :tangle (eval f_test)
integer(c_int32_t) function test_qmckl_ao_power(context) bind(C)
use qmckl
implicit none
integer(qmckl_context), intent(in), value :: context
integer*8 :: n, LDP
integer, allocatable :: LMAX(:)
double precision, allocatable :: X(:), P(:,:)
integer*8 :: i,j
double precision :: epsilon
epsilon = qmckl_get_numprec_epsilon(context)
n = 100;
LDP = 10;
allocate(X(n), P(LDP,n), LMAX(n))
do j=1,n
X(j) = -5.d0 + 0.1d0 * dble(j)
LMAX(j) = 1 + int(mod(j, 5),4)
end do
test_qmckl_ao_power = qmckl_ao_power(context, n, X, LMAX, P, LDP)
if (test_qmckl_ao_power /= QMCKL_SUCCESS) return
test_qmckl_ao_power = QMCKL_FAILURE
do j=1,n
do i=1,LMAX(j)
if ( X(j)**i == 0.d0 ) then
if ( P(i,j) /= 0.d0) return
else
if ( dabs(1.d0 - P(i,j) / (X(j)**i)) > epsilon ) return
end if
end do
end do
test_qmckl_ao_power = QMCKL_SUCCESS
deallocate(X,P,LMAX)
end function test_qmckl_ao_power
#+end_src
#+begin_src c :tangle (eval c_test) :exports none
int test_qmckl_ao_power(qmckl_context context);
munit_assert_int(0, ==, test_qmckl_ao_power(context));
#+end_src
** Value, Gradient and Laplacian of a polynomial
:PROPERTIES:
:Name: qmckl_ao_polynomial_vgl
:CRetType: qmckl_exit_code
:FRetType: qmckl_exit_code
:END:
A polynomial is centered on a nucleus $\mathbf{R}_i$
\[
P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c
\]
The gradients with respect to electron coordinates are
\begin{eqnarray*}
\frac{\partial }{\partial x} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
= & a (x-X_i)^{a-1} (y-Y_i)^b (z-Z_i)^c \\
\frac{\partial }{\partial y} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
= & b (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c \\
\frac{\partial }{\partial z} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
= & c (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1} \\
\end{eqnarray*}
and the Laplacian is
\begin{eqnarray*}
\left( \frac{\partial }{\partial x^2} +
\frac{\partial }{\partial y^2} +
\frac{\partial }{\partial z^2} \right) P_l
\left(\mathbf{r},\mathbf{R}_i \right) & = &
a(a-1) (x-X_i)^{a-2} (y-Y_i)^b (z-Z_i)^c + \\
&& b(b-1) (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c + \\
&& c(c-1) (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1}.
\end{eqnarray*} ~qmckl_ao_polynomial_vgl~ computes the values, gradients and
Laplacians at a given point in space, of all polynomials with an
angular momentum up to ~lmax~.
#+NAME: qmckl_ao_polynomial_vgl_args
| qmckl_context | context | in | Global state |
| double | X[3] | in | Array containing the coordinates of the points |
| double | R[3] | in | Array containing the x,y,z coordinates of the center |
| int32_t | lmax | in | Maximum angular momentum |
| int64_t | n | inout | Number of computed polynomials |
| int32_t | L[n][ldl] | out | Contains a,b,c for all ~n~ results |
| int64_t | ldl | in | Leading dimension of ~L~ |
| double | VGL[n][ldv] | out | Value, gradients and Laplacian of the polynomials |
| int64_t | ldv | in | Leading dimension of array ~VGL~ |
*** Requirements
- ~context~ is not ~QMCKL_NULL_CONTEXT~
- ~n~ > 0
- ~lmax~ >= 0
- ~ldl~ >= 3
- ~ldv~ >= 5
- ~X~ is allocated with at least $3 \times 8$ bytes
- ~R~ is allocated with at least $3 \times 8$ bytes
- ~n~ >= ~(lmax+1)(lmax+2)(lmax+3)/6~
- ~L~ is allocated with at least $3 \times n \times 4$ bytes
- ~VGL~ is allocated with at least $5 \times n \times 8$ bytes
- On output, ~n~ should be equal to ~(lmax+1)(lmax+2)(lmax+3)/6~
- On output, the powers are given in the following order (l=a+b+c):
- Increasing values of ~l~
- Within a given value of ~l~, alphabetical order of the
string made by a*"x" + b*"y" + c*"z" (in Python notation).
For example, with a=0, b=2 and c=1 the string is "yyz"
*** C Header
#+CALL: generate_c_header(table=qmckl_ao_polynomial_vgl_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src c :tangle (eval h_func) :comments org
qmckl_exit_code qmckl_ao_polynomial_vgl (
const qmckl_context context,
const double* X,
const double* R,
const int32_t lmax,
int64_t* n,
int32_t* const L,
const int64_t ldl,
double* const VGL,
const int64_t ldv );
#+end_src
*** Source
#+begin_src f90 :tangle (eval f)
integer function qmckl_ao_polynomial_vgl_f(context, X, R, lmax, n, L, ldl, VGL, ldv) result(info)
use qmckl
implicit none
integer*8 , intent(in) :: context
real*8 , intent(in) :: X(3), R(3)
integer , intent(in) :: lmax
integer*8 , intent(out) :: n
integer , intent(out) :: L(ldl,(lmax+1)*(lmax+2)*(lmax+3)/6)
integer*8 , intent(in) :: ldl
real*8 , intent(out) :: VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)
integer*8 , intent(in) :: ldv
integer*8 :: i,j
integer :: a,b,c,d
real*8 :: Y(3)
integer :: lmax_array(3)
real*8 :: pows(-2:lmax,3)
integer, external :: qmckl_ao_power_f
double precision :: xy, yz, xz
double precision :: da, db, dc, dd
info = 0
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (lmax < 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (ldl < 3) then
info = QMCKL_INVALID_ARG_7
return
endif
if (ldv < 5) then
info = QMCKL_INVALID_ARG_9
return
endif
do i=1,3
Y(i) = X(i) - R(i)
end do
lmax_array(1:3) = lmax
if (lmax == 0) then
VGL(1,1) = 1.d0
vgL(2:5,1) = 0.d0
l(1:3,1) = 0
n=1
else if (lmax > 0) then
pows(-2:0,1:3) = 1.d0
do i=1,lmax
pows(i,1) = pows(i-1,1) * Y(1)
pows(i,2) = pows(i-1,2) * Y(2)
pows(i,3) = pows(i-1,3) * Y(3)
end do
VGL(1:5,1:4) = 0.d0
l (1:3,1:4) = 0
VGL(1 ,1 ) = 1.d0
vgl(1:5,2:4) = 0.d0
l (1,2) = 1
vgl(1,2) = pows(1,1)
vgL(2,2) = 1.d0
l (2,3) = 1
vgl(1,3) = pows(1,2)
vgL(3,3) = 1.d0
l (3,4) = 1
vgl(1,4) = pows(1,3)
vgL(4,4) = 1.d0
n=4
endif
! l>=2
dd = 2.d0
do d=2,lmax
da = dd
do a=d,0,-1
db = dd-da
do b=d-a,0,-1
c = d - a - b
dc = dd - da - db
n = n+1
l(1,n) = a
l(2,n) = b
l(3,n) = c
xy = pows(a,1) * pows(b,2)
yz = pows(b,2) * pows(c,3)
xz = pows(a,1) * pows(c,3)
vgl(1,n) = xy * pows(c,3)
xy = dc * xy
xz = db * xz
yz = da * yz
vgl(2,n) = pows(a-1,1) * yz
vgl(3,n) = pows(b-1,2) * xz
vgl(4,n) = pows(c-1,3) * xy
vgl(5,n) = &
(da-1.d0) * pows(a-2,1) * yz + &
(db-1.d0) * pows(b-2,2) * xz + &
(dc-1.d0) * pows(c-2,3) * xy
db = db - 1.d0
end do
da = da - 1.d0
end do
dd = dd + 1.d0
end do
info = QMCKL_SUCCESS
end function qmckl_ao_polynomial_vgl_f
#+end_src
*** C interface
#+CALL: generate_c_interface(table=qmckl_ao_polynomial_vgl_args,rettyp=get_value("CRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src f90 :tangle (eval f) :comments org :exports none
integer(c_int32_t) function qmckl_ao_polynomial_vgl &
(context, X, R, lmax, n, L, ldl, VGL, ldv) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double ) , intent(in) :: X(3)
real (c_double ) , intent(in) :: R(3)
integer (c_int32_t) , intent(in) , value :: lmax
integer (c_int64_t) , intent(inout) :: n
integer (c_int32_t) , intent(out) :: L(ldl,n)
integer (c_int64_t) , intent(in) , value :: ldl
real (c_double ) , intent(out) :: VGL(ldv,n)
integer (c_int64_t) , intent(in) , value :: ldv
integer(c_int32_t), external :: qmckl_ao_polynomial_vgl_f
info = qmckl_ao_polynomial_vgl_f &
(context, X, R, lmax, n, L, ldl, VGL, ldv)
end function qmckl_ao_polynomial_vgl
#+end_src
*** Fortran interface
#+CALL: generate_f_interface(table=qmckl_ao_polynomial_vgl_args,rettyp=get_value("FRetType"),fname=get_value("Name"))
#+RESULTS:
#+begin_src f90 :tangle (eval fh_func) :comments org :exports none
interface
integer(c_int32_t) function qmckl_ao_polynomial_vgl &
(context, X, R, lmax, n, L, ldl, VGL, ldv) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double ) , intent(in) :: X(3)
real (c_double ) , intent(in) :: R(3)
integer (c_int32_t) , intent(in) , value :: lmax
integer (c_int64_t) , intent(inout) :: n
integer (c_int32_t) , intent(out) :: L(ldl,n)
integer (c_int64_t) , intent(in) , value :: ldl
real (c_double ) , intent(out) :: VGL(ldv,n)
integer (c_int64_t) , intent(in) , value :: ldv
end function qmckl_ao_polynomial_vgl
end interface
#+end_src
*** Test
#+begin_src f90 :tangle (eval f_test)
integer(c_int32_t) function test_qmckl_ao_polynomial_vgl(context) bind(C)
use qmckl
implicit none
integer(c_int64_t), intent(in), value :: context
integer :: lmax, d, i
integer, allocatable :: L(:,:)
integer*8 :: n, ldl, ldv, j
double precision :: X(3), R(3), Y(3)
double precision, allocatable :: VGL(:,:)
double precision :: w
double precision :: epsilon
epsilon = qmckl_get_numprec_epsilon(context)
X = (/ 1.1 , 2.2 , 3.3 /)
R = (/ 0.1 , 1.2 , -2.3 /)
Y(:) = X(:) - R(:)
lmax = 4;
ldl = 3;
ldv = 100;
d = (lmax+1)*(lmax+2)*(lmax+3)/6
allocate (L(ldl,d), VGL(ldv,d))
test_qmckl_ao_polynomial_vgl = &
qmckl_ao_polynomial_vgl(context, X, R, lmax, n, L, ldl, VGL, ldv)
if (test_qmckl_ao_polynomial_vgl /= QMCKL_SUCCESS) return
if (n /= d) return
do j=1,n
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
do i=1,3
if (L(i,j) < 0) return
end do
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
if (dabs(1.d0 - VGL(1,j) / (&
Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**L(3,j) &
)) > epsilon ) return
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
if (L(1,j) < 1) then
if (VGL(2,j) /= 0.d0) return
else
if (dabs(1.d0 - VGL(2,j) / (&
L(1,j) * Y(1)**(L(1,j)-1) * Y(2)**L(2,j) * Y(3)**L(3,j) &
)) > epsilon ) return
end if
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
if (L(2,j) < 1) then
if (VGL(3,j) /= 0.d0) return
else
if (dabs(1.d0 - VGL(3,j) / (&
L(2,j) * Y(1)**L(1,j) * Y(2)**(L(2,j)-1) * Y(3)**L(3,j) &
)) > epsilon ) return
end if
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
if (L(3,j) < 1) then
if (VGL(4,j) /= 0.d0) return
else
if (dabs(1.d0 - VGL(4,j) / (&
L(3,j) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-1) &
)) > epsilon ) return
end if
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
w = 0.d0
if (L(1,j) > 1) then
w = w + L(1,j) * (L(1,j)-1) * Y(1)**(L(1,j)-2) * Y(2)**L(2,j) * Y(3)**L(3,j)
end if
if (L(2,j) > 1) then
w = w + L(2,j) * (L(2,j)-1) * Y(1)**L(1,j) * Y(2)**(L(2,j)-2) * Y(3)**L(3,j)
end if
if (L(3,j) > 1) then
w = w + L(3,j) * (L(3,j)-1) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-2)
end if
if (dabs(1.d0 - VGL(5,j) / w) > epsilon ) return
end do
test_qmckl_ao_polynomial_vgl = QMCKL_SUCCESS
deallocate(L,VGL)
end function test_qmckl_ao_polynomial_vgl
#+end_src
#+begin_src c :tangle (eval c_test)
int test_qmckl_ao_polynomial_vgl(qmckl_context context);
munit_assert_int(0, ==, test_qmckl_ao_polynomial_vgl(context));
#+end_src
* Radial part
** Gaussian basis functions ~qmckl_ao_gaussian_vgl~ computes the values, gradients and
Laplacians at a given point of ~n~ Gaussian functions centered at
the same point:
\[ v_i = \exp(-a_i |X-R|^2) \]
\[ \nabla_x v_i = -2 a_i (X_x - R_x) v_i \]
\[ \nabla_y v_i = -2 a_i (X_y - R_y) v_i \]
\[ \nabla_z v_i = -2 a_i (X_z - R_z) v_i \]
\[ \Delta v_i = a_i (4 |X-R|^2 a_i - 6) v_i \]
| ~context~ | input | Global state |
| ~X(3)~ | input | Array containing the coordinates of the points |
| ~R(3)~ | input | Array containing the x,y,z coordinates of the center |
| ~n~ | input | Number of computed Gaussians |
| ~A(n)~ | input | Exponents of the Gaussians |
| ~VGL(ldv,5)~ | output | Value, gradients and Laplacian of the Gaussians |
| ~ldv~ | input | Leading dimension of array ~VGL~ |
Requirements
- ~context~ is not 0
- ~n~ > 0
- ~ldv~ >= 5
- ~A(i)~ > 0 for all ~i~
- ~X~ is allocated with at least $3 \times 8$ bytes
- ~R~ is allocated with at least $3 \times 8$ bytes
- ~A~ is allocated with at least $n \times 8$ bytes
- ~VGL~ is allocated with at least $n \times 5 \times 8$ bytes
#+begin_src c :tangle (eval h_func)
qmckl_exit_code
qmckl_ao_gaussian_vgl(const qmckl_context context,
const double *X,
const double *R,
const int64_t *n,
const int64_t *A,
const double *VGL,
const int64_t ldv);
#+end_src
#+begin_src f90 :tangle (eval f)
integer function qmckl_ao_gaussian_vgl_f(context, X, R, n, A, VGL, ldv) result(info)
use qmckl
implicit none
integer*8 , intent(in) :: context
real*8 , intent(in) :: X(3), R(3)
integer*8 , intent(in) :: n
real*8 , intent(in) :: A(n)
real*8 , intent(out) :: VGL(ldv,5)
integer*8 , intent(in) :: ldv
integer*8 :: i,j
real*8 :: Y(3), r2, t, u, v
info = QMCKL_SUCCESS
if (context == QMCKL_NULL_CONTEXT) then
info = QMCKL_INVALID_CONTEXT
return
endif
if (n <= 0) then
info = QMCKL_INVALID_ARG_4
return
endif
if (ldv < n) then
info = QMCKL_INVALID_ARG_7
return
endif
do i=1,3
Y(i) = X(i) - R(i)
end do
r2 = Y(1)*Y(1) + Y(2)*Y(2) + Y(3)*Y(3)
do i=1,n
VGL(i,1) = dexp(-A(i) * r2)
end do
do i=1,n
VGL(i,5) = A(i) * VGL(i,1)
end do
t = -2.d0 * ( X(1) - R(1) )
u = -2.d0 * ( X(2) - R(2) )
v = -2.d0 * ( X(3) - R(3) )
do i=1,n
VGL(i,2) = t * VGL(i,5)
VGL(i,3) = u * VGL(i,5)
VGL(i,4) = v * VGL(i,5)
end do
t = 4.d0 * r2
do i=1,n
VGL(i,5) = (t * A(i) - 6.d0) * VGL(i,5)
end do
end function qmckl_ao_gaussian_vgl_f
#+end_src
#+begin_src f90 :tangle (eval f) :exports none
integer(c_int32_t) function qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: X(3), R(3)
integer (c_int64_t) , intent(in) , value :: n
real (c_double) , intent(in) :: A(n)
real (c_double) , intent(out) :: VGL(ldv,5)
integer (c_int64_t) , intent(in) , value :: ldv
integer, external :: qmckl_ao_gaussian_vgl_f
info = qmckl_ao_gaussian_vgl_f(context, X, R, n, A, VGL, ldv)
end function qmckl_ao_gaussian_vgl
#+end_src
#+begin_src f90 :tangle (eval fh_func) :exports none
interface
integer(c_int32_t) function qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv) &
bind(C)
use, intrinsic :: iso_c_binding
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: ldv
integer (c_int64_t) , intent(in) , value :: n
real (c_double) , intent(in) :: X(3), R(3), A(n)
real (c_double) , intent(out) :: VGL(ldv,5)
end function qmckl_ao_gaussian_vgl
end interface
#+end_src
# Test
#+begin_src f90 :tangle (eval f_test)
integer(c_int32_t) function test_qmckl_ao_gaussian_vgl(context) bind(C)
use qmckl
implicit none
integer(c_int64_t), intent(in), value :: context
integer*8 :: n, ldv, j, i
double precision :: X(3), R(3), Y(3), r2
double precision, allocatable :: VGL(:,:), A(:)
double precision :: epsilon
epsilon = qmckl_get_numprec_epsilon(context)
X = (/ 1.1 , 2.2 , 3.3 /)
R = (/ 0.1 , 1.2 , -2.3 /)
Y(:) = X(:) - R(:)
r2 = Y(1)**2 + Y(2)**2 + Y(3)**2
n = 10;
ldv = 100;
allocate (A(n), VGL(ldv,5))
do i=1,n
A(i) = 0.0013 * dble(ishft(1,i))
end do
test_qmckl_ao_gaussian_vgl = &
qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv)
if (test_qmckl_ao_gaussian_vgl /= 0) return
test_qmckl_ao_gaussian_vgl = -1
do i=1,n
test_qmckl_ao_gaussian_vgl = -11
if (dabs(1.d0 - VGL(i,1) / (&
dexp(-A(i) * r2) &
)) > epsilon ) return
test_qmckl_ao_gaussian_vgl = -12
if (dabs(1.d0 - VGL(i,2) / (&
-2.d0 * A(i) * Y(1) * dexp(-A(i) * r2) &
)) > epsilon ) return
test_qmckl_ao_gaussian_vgl = -13
if (dabs(1.d0 - VGL(i,3) / (&
-2.d0 * A(i) * Y(2) * dexp(-A(i) * r2) &
)) > epsilon ) return
test_qmckl_ao_gaussian_vgl = -14
if (dabs(1.d0 - VGL(i,4) / (&
-2.d0 * A(i) * Y(3) * dexp(-A(i) * r2) &
)) > epsilon ) return
test_qmckl_ao_gaussian_vgl = -15
if (dabs(1.d0 - VGL(i,5) / (&
A(i) * (4.d0*r2*A(i) - 6.d0) * dexp(-A(i) * r2) &
)) > epsilon ) return
end do
test_qmckl_ao_gaussian_vgl = 0
deallocate(VGL)
end function test_qmckl_ao_gaussian_vgl
#+end_src
#+begin_src c :tangle (eval c_test) :exports none
int test_qmckl_ao_gaussian_vgl(qmckl_context context);
munit_assert_int(0, ==, test_qmckl_ao_gaussian_vgl(context));
#+end_src
** TODO Slater basis functions
** TODO Radial functions on a grid
* Combining radial and polynomial parts
* End of files :noexport:
#+begin_src c :tangle (eval h_private_type)
#endif
#+end_src
*** Test
#+begin_src c :tangle (eval c_test)
if (qmckl_context_destroy(context) != QMCKL_SUCCESS)
return QMCKL_FAILURE;
return MUNIT_OK;
}
#+end_src
**✸ Compute file names
#+begin_src emacs-lisp
; The following is required to compute the file names
(setq pwd (file-name-directory buffer-file-name))
(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
(setq f (concat pwd name "_f.f90"))
(setq fh (concat pwd name "_fh.f90"))
(setq c (concat pwd name ".c"))
(setq h (concat name ".h"))
(setq h_private (concat name "_private.h"))
(setq c_test (concat pwd "test_" name ".c"))
(setq f_test (concat pwd "test_" name "_f.f90"))
; Minted
(require 'ox-latex)
(setq org-latex-listings 'minted)
(add-to-list 'org-latex-packages-alist '("" "listings"))
(add-to-list 'org-latex-packages-alist '("" "color"))
#+end_src
#+RESULTS:
| | color |
| | listings |
# -*- mode: org -*-
# vim: syntax=c
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