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254 KiB
254 KiB
Atomic Orbitals
Introduction
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 primitive functions that can be of type Slater ($p=1$) or Gaussian ($p=2$):
\[ R_s(\mathbf{r}) = \mathcal{N}_s |\mathbf{r}-\mathbf{R}_A|^{n_s} \sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks} \exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right). \]
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 (integrate) to unity. Usually, basis sets are given a combination of normalized primitives, so the normalization coefficients of the primitives, $f_{ks}$, need also to be provided.
Atomic orbitals (AOs) are defined as
\[ \chi_i (\mathbf{r}) = \mathcal{M}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r}) \]
where $\theta(i)$ returns the shell on which the AO is expanded, and $\eta(i)$ denotes which angular function is chosen and $P$ are the generating functions of the given angular momentum $\eta(i)$. Here, the parameter $\mathcal{M}_i$ is an extra parameter which allows the normalization of the different functions of the same shell to be different, as in GAMESS for example.
In this section we describe first how the basis set is stored in the context, and then we present the kernels used to compute the values, gradients and Laplacian of the atomic basis functions.
Context
Constant data
The following arrays are stored in the context, and need to be set when initializing the library:
| Variable | Type | Description |
type |
char |
Gaussian ('G') or Slater ('S') |
shell_num |
int64_t |
Number of shells |
prim_num |
int64_t |
Total number of primitives |
nucleus_index |
int64_t[nucl_num] |
Index of the first shell of each nucleus |
nucleus_shell_num |
int64_t[nucl_num] |
Number of shells per nucleus |
shell_ang_mom |
int32_t[shell_num] |
Angular momentum of each shell |
shell_prim_num |
int64_t[shell_num] |
Number of primitives in each shell |
shell_prim_index |
int64_t[shell_num] |
Address of the first primitive of each shell in the EXPONENT array |
shell_factor |
double[shell_num] |
Normalization factor for each shell |
exponent |
double[prim_num] |
Array of exponents |
coefficient |
double[prim_num] |
Array of coefficients |
prim_factor |
double[prim_num] |
Normalization factors of the primtives |
ao_num |
int64_t |
Number of AOs |
ao_cartesian |
bool |
If true, use polynomials. Otherwise, use spherical harmonics |
ao_factor |
double[ao_num] |
Normalization factor of the AO |
The following data is computed when the basis is finalized:
| Variable | Type | Description |
nucleus_prim_index |
int64_t[nucl_num+1] |
Index of the first primitive of each nucleus |
nucleus_max_ang_mom |
int32_t[nucl_num] |
Maximum angular momentum of each nucleus |
coefficient_normalized~ |
double[prim_num] |
Normalized array of coefficients |
ao_ang_mom |
int32_t[ao_num] |
Angular momentum of the shell to which the AO belongs |
ao_nucl |
int64_t[ao_num] |
Nucleus on which the AO is centered |
nucleus_range |
double[nucl_num] |
Used to compute the distance beyond which all Gaussian AOs are zero, depending on the precision |
For H_2 with the following basis set,
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
we have:
type = 'G' shell_num = 12 prim_num = 20 ao_num = 30 nucleus_index = [0 , 6] shell_ang_mom = [0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2] 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 = [0 , 5 , 6 , 7 , 8 , 9 , 10, 15, 16, 17, 18, 19] 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] prim_factor = [ 1.0006253235944540e+01, 2.4169531573445120e+00, 7.9610924849766440e-01 3.0734305383061117e-01, 1.2929684417481876e-01, 3.0734305383061117e-01, 1.2929684417481876e-01, 2.1842769845268308e+00, 4.3649547399719840e-01, 1.8135965626177861e+00, 1.0006253235944540e+01, 2.4169531573445120e+00, 7.9610924849766440e-01, 3.0734305383061117e-01, 1.2929684417481876e-01, 3.0734305383061117e-01, 1.2929684417481876e-01, 2.1842769845268308e+00, 4.3649547399719840e-01, 1.8135965626177861e+00 ]
A scalar variable $V$ present in this table can be set or get by
calling the functions:
qmckl_exit_code qmckl_set_ao_basis_$V$ ( qmckl_context context,
const $type_of_V$ $V$);
qmckl_exit_code qmckl_get_ao_basis_$V$ ( const qmckl_context context,
$type_of_V$ const $V$);interface
integer(c_int32_t) function qmckl_set_ao_basis_$V$ (context, $V$) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
$f_type_of_V$ , intent(in) , value :: $V$
end function qmckl_set_ao_basis_$V$
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_$V$ (context, $V$) &
bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
$f_type_of_V$ , intent(out) :: $V$
end function qmckl_get_ao_basis_$V$
end interfaceFor array variables, use the rule:
qmckl_exit_code qmckl_set_ao_basis_$V$ ( qmckl_context context,
const $type_of_V$ $V$,
const int64_t size_max);
qmckl_exit_code qmckl_get_ao_basis_$V$ ( const qmckl_context context,
$type_of_V$ const $V$,
const int64_t size_max);interface
integer(c_int32_t) function qmckl_set_ao_basis_$V$ (context, &
$V$, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
$f_type_of_V$ , intent(in) , value :: $V$
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_$V$
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_$V$ (context, &
$V$, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
$f_type_of_V$ , intent(out) :: $V$
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_$V$
end interfaceInitialization functions
size_max is the dimension of the input array, which should be
equal of larger than the value given in the table of section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Context.
C interface
#+NAME:pre2
#+NAME:post2
To set the basis set, all the following functions need to be called.
qmckl_exit_code
qmckl_set_ao_basis_type (qmckl_context context,
const char basis_type);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_nucleus_shell_num (qmckl_context context,
const int64_t* nucleus_shell_num,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_nucleus_index (qmckl_context context,
const int64_t* nucleus_index,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_shell_ang_mom (qmckl_context context,
const int32_t* shell_ang_mom,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_shell_prim_num (qmckl_context context,
const int64_t* shell_prim_num,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_shell_prim_index (qmckl_context context,
const int64_t* shell_prim_index,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_shell_factor (qmckl_context context,
const double* shell_factor,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_exponent (qmckl_context context,
const double* exponent,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_coefficient (qmckl_context context,
const double* coefficient,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_prim_factor (qmckl_context context,
const double* prim_factor,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_ao_num (qmckl_context context,
const int64_t ao_num);qmckl_exit_code
qmckl_set_ao_basis_ao_factor (qmckl_context context,
const double* ao_factor,
const int64_t size_max);qmckl_exit_code
qmckl_set_ao_basis_cartesian (qmckl_context context,
const bool cartesian);Fortran interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_type (context, &
basis_type) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
character(c_char) , intent(in) , value :: basis_type
end function qmckl_set_ao_basis_type
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_shell_num(context, &
num) 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 :: num
end function qmckl_set_ao_basis_shell_num
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_prim_num(context, &
num) 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 :: num
end function qmckl_set_ao_basis_prim_num
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_nucleus_index(context, &
idx, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) :: idx(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_nucleus_index
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_nucleus_shell_num(context, &
shell_num, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) :: shell_num(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_nucleus_shell_num
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_shell_ang_mom(context, &
shell_ang_mom, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int32_t) , intent(in) :: shell_ang_mom(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_shell_ang_mom
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_shell_prim_num(context, &
shell_prim_num, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) :: shell_prim_num(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_shell_prim_num
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_shell_prim_index(context, &
shell_prim_index, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(in) :: shell_prim_index(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_shell_prim_index
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_shell_factor(context, &
shell_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: shell_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_shell_factor
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_exponent(context, &
exponent, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: exponent(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_exponent
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_coefficient(context, &
coefficient, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: coefficient(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_coefficient
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_prim_factor(context, &
prim_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: prim_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_prim_factor
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_ao_num(context, &
num) 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 :: num
end function qmckl_set_ao_basis_ao_num
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_cartesian(context, &
cartesian) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
logical (c_bool) , intent(in) , value :: cartesian
end function qmckl_set_ao_basis_cartesian
end interface
interface
integer(c_int32_t) function qmckl_set_ao_basis_ao_factor(context, &
ao_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(in) :: ao_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_set_ao_basis_ao_factor
end interfaceAccess functions
size_max is the dimension of the input array, which should be
equal of larger than the value given in the table of section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Context.
C interface
qmckl_exit_code
qmckl_get_ao_basis_type (const qmckl_context context,
char* const basis_type);qmckl_exit_code
qmckl_get_ao_basis_shell_num (const qmckl_context context,
int64_t* const shell_num);qmckl_exit_code
qmckl_get_ao_basis_prim_num (const qmckl_context context,
int64_t* const prim_num);qmckl_exit_code
qmckl_get_ao_basis_nucleus_shell_num (const qmckl_context context,
int64_t* const nucleus_shell_num,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_nucleus_index (const qmckl_context context,
int64_t* const nucleus_index,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_shell_ang_mom (const qmckl_context context,
int32_t* const shell_ang_mom,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_shell_prim_num (const qmckl_context context,
int64_t* const shell_prim_num,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_shell_prim_index (const qmckl_context context,
int64_t* const shell_prim_index,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_shell_factor (const qmckl_context context,
double* const shell_factor,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_exponent (const qmckl_context context,
double* const exponent,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_coefficient (const qmckl_context context,
double* const coefficient,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_prim_factor (const qmckl_context context,
double* const prim_factor,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_ao_num (const qmckl_context context,
int64_t* const ao_num);qmckl_exit_code
qmckl_get_ao_basis_ao_factor (const qmckl_context context,
double* const ao_factor,
const int64_t size_max);
When all the data for the AOs have been provided, the following
function returns true.
bool qmckl_ao_basis_provided (const qmckl_context context);Fortran interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_type (context, &
basis_type) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
character(c_char) , intent(out) :: basis_type
end function qmckl_get_ao_basis_type
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_shell_num(context, &
num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: num
end function qmckl_get_ao_basis_shell_num
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_prim_num(context, &
num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: num
end function qmckl_get_ao_basis_prim_num
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_nucleus_shell_num(context, &
shell_num, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: shell_num(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_nucleus_shell_num
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_nucleus_index(context, &
idx, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: idx(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_nucleus_index
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_shell_ang_mom(context, &
shell_ang_mom, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int32_t) , intent(out) :: shell_ang_mom(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_shell_ang_mom
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_shell_prim_num(context, &
shell_prim_num, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: shell_prim_num(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_shell_prim_num
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_shell_prim_index(context, &
shell_prim_index, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: shell_prim_index(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_shell_prim_index
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_shell_factor(context, &
shell_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(out) :: shell_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_shell_factor
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_exponent(context, &
exponent, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(out) :: exponent(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_exponent
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_coefficient(context, &
coefficient, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(out) :: coefficient(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_coefficient
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_prim_factor(context, &
prim_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(out) :: prim_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_prim_factor
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_ao_num(context, &
num) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
integer (c_int64_t) , intent(out) :: num
end function qmckl_get_ao_basis_ao_num
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_cartesian(context, &
cartesian) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
logical (c_bool) , intent(out) :: cartesian
end function qmckl_get_ao_basis_cartesian
end interface
interface
integer(c_int32_t) function qmckl_get_ao_basis_ao_factor(context, &
ao_factor, size_max) bind(C)
use, intrinsic :: iso_c_binding
import
implicit none
integer (c_int64_t) , intent(in) , value :: context
real (c_double) , intent(out) :: ao_factor(*)
integer (c_int64_t) , intent(in) , value :: size_max
end function qmckl_get_ao_basis_ao_factor
end interfaceComputed data
The following data is computed as described in the next sections:
| Variable | Type | Description |
primitive_vgl |
double[point_num][5][prim_num] |
Value, gradients, Laplacian of the primitives at current positions |
primitive_vgl_date |
uint64_t |
Last modification date of Value, gradients, Laplacian of the primitives at current positions |
shell_vgl |
double[point_num][5][shell_num] |
Value, gradients, Laplacian of the primitives at current positions |
shell_vgl_date |
uint64_t |
Last modification date of Value, gradients, Laplacian of the AOs at current positions |
ao_vgl |
double[point_num][5][ao_num] |
Value, gradients, Laplacian of the AOs at current positions |
ao_vgl_date |
uint64_t |
Last modification date of Value, gradients, Laplacian of the AOs at current positions |
ao_value |
double[point_num][ao_num] |
Values of the the AOs at current positions |
ao_value_date |
uint64_t |
Last modification date of the values of the AOs at current positions |
After initialization
When the basis set is completely entered, extra data structures may be computed to accelerate the calculations. The primitives within each contraction are sorted in ascending order of their exponents, such that as soon as a primitive is zero all the following functions vanish. Also, it is possible to compute a nuclear radius beyond which all the primitives are zero up to the numerical accuracy defined in the context.
TODO HPC-specific data structures
For faster access, we provide extra arrays for the shell information as:
- $C_{psa}$ =
coef_per_nucleus[inucl][ishell][iprim] - $\gamma_{pa}$
expo_per_nucleus[inucl][iprim]
such that the computation of the radial parts can be vectorized.
Exponents are sorted in increasing order to exit loops quickly, and only unique exponents are kept. This also allows to pack the exponents to enable vectorization of exponentials.
The computation of the radial part is made as \[ R_{sa} = \sum_p C_{psa} \gamma_{pa} \] which is a matrix-vector product.
#+NAME:HPC_struct
Access functions
qmckl_exit_code
qmckl_get_ao_basis_primitive_vgl (qmckl_context context,
double* const primitive_vgl,
const int64_t size_max);Returns the array of values, gradients an Laplacian of primitive basis functions evaluated at the current coordinates. See section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Computation%20of%20primitives.
qmckl_exit_code
qmckl_get_ao_basis_shell_vgl (qmckl_context context,
double* const shell_vgl,
const int64_t size_max);Returns the array of values, gradients an Laplacian of contracted shells evaluated at the current coordinates. See section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Computation%20of%20shells.
qmckl_exit_code
qmckl_get_ao_basis_ao_vgl (qmckl_context context,
double* const ao_vgl,
const int64_t size_max);Returns the array of values, gradients an Laplacian of the atomic orbitals evaluated at the current coordinates. See section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Combining%20radial%20and%20polynomial%20parts.
Uses the given array to compute the VGL.
qmckl_exit_code
qmckl_get_ao_basis_ao_vgl_inplace (qmckl_context context,
double* const ao_vgl,
const int64_t size_max);qmckl_exit_code
qmckl_get_ao_basis_ao_value (qmckl_context context,
double* const ao_value,
const int64_t size_max);Returns the array of values of the atomic orbitals evaluated at the current coordinates. See section /TREX/qmckl/src/commit/be2a7199c2ab42a764459343ab21b1bd9aab926c/org/Combining%20radial%20and%20polynomial%20parts.
Uses the given array to compute the value.
qmckl_exit_code
qmckl_get_ao_basis_ao_value_inplace (qmckl_context context,
double* const ao_value,
const int64_t size_max);Radial part
General functions for 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:
\[ v_i = \exp(-a_i |X-R|^2) \] \[ \nabla_x v_i = -2 a_i (X_x - R_x) v_i \] \[ \nabla_y v_i = -2 a_i (X_y - R_y) v_i \] \[ \nabla_z v_i = -2 a_i (X_z - R_z) v_i \] \[ \Delta v_i = a_i (4 |X-R|^2 a_i - 6) v_i \]
| Variable | Type | Description |
context |
qmckl_context |
Global state |
X(3) |
double[3] |
Array containing the coordinates of the points |
R(3) |
double[3] |
Array containing the x,y,z coordinates of the center |
n |
int64_t |
Number of computed Gaussians |
A(n) |
double[n] |
Exponents of the Gaussians |
VGL(ldv,5) |
double[5][ldv] |
Value, gradients and Laplacian of the Gaussians |
ldv |
int64_t |
Leading dimension of array VGL |
Requirements:
context≠ 0n> 0ldv>= 5A(i)> 0 for alliXis allocated with at least $3 \times 8$ bytesRis allocated with at least $3 \times 8$ bytesAis allocated with at least $n \times 8$ bytesVGLis allocated with at least $n \times 5 \times 8$ bytes
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);function qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
implicit none
integer (qmckl_context) , 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 (qmckl_exit_code) :: info
integer*8 :: i,j
double precision :: 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_vglComputation of primitives
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
prim_num |
int64_t |
in | Number of primitives |
point_num |
int64_t |
in | Number of points considered |
nucl_num |
int64_t |
in | Number of nuclei |
nucleus_prim_index |
int64_t[nucl_num+1] |
in | Index of the 1st primitive of each nucleus |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
expo |
double[prim_num] |
in | Exponents of the primitives |
primitive_vgl |
double[point_num][5][prim_num] |
out | Value, gradients and Laplacian of the primitives |
qmckl_exit_code qmckl_compute_ao_basis_primitive_gaussian_vgl (
const qmckl_context context,
const int64_t prim_num,
const int64_t point_num,
const int64_t nucl_num,
const int64_t* nucleus_prim_index,
const double* coord,
const double* nucl_coord,
const double* expo,
double* const primitive_vgl );function qmckl_compute_ao_basis_primitive_gaussian_vgl &
(context, prim_num, point_num, nucl_num, nucleus_prim_index, coord, nucl_coord, expo, primitive_vgl) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
use qmckl, only: qmckl_get_numprec_precision
implicit none
integer (qmckl_context), intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: prim_num
integer (c_int64_t) , intent(in) , value :: point_num
integer (c_int64_t) , intent(in) , value :: nucl_num
integer (c_int64_t) , intent(in) :: nucleus_prim_index(nucl_num+1)
real (c_double ) , intent(in) :: coord(point_num,3)
real (c_double ) , intent(in) :: nucl_coord(nucl_num,3)
real (c_double ) , intent(in) :: expo(prim_num)
real (c_double ) , intent(out) :: primitive_vgl(prim_num,5,point_num)
integer(qmckl_exit_code) :: info
integer*8 :: inucl, iprim, ipoint
double precision :: x, y, z, two_a, ar2, r2, v, cutoff
info = QMCKL_SUCCESS
! Don't compute exponentials when the result will be almost zero.
<<fortran_cutoff>>
do inucl=1,nucl_num
! C is zero-based, so shift bounds by one
do iprim = nucleus_prim_index(inucl)+1, nucleus_prim_index(inucl+1)
do ipoint = 1, point_num
x = coord(ipoint,1) - nucl_coord(inucl,1)
y = coord(ipoint,2) - nucl_coord(inucl,2)
z = coord(ipoint,3) - nucl_coord(inucl,3)
r2 = x*x + y*y + z*z
ar2 = expo(iprim)*r2
if (ar2 > cutoff) cycle
v = dexp(-ar2)
two_a = -2.d0 * expo(iprim) * v
primitive_vgl(iprim, 1, ipoint) = v
primitive_vgl(iprim, 2, ipoint) = two_a * x
primitive_vgl(iprim, 3, ipoint) = two_a * y
primitive_vgl(iprim, 4, ipoint) = two_a * z
primitive_vgl(iprim, 5, ipoint) = two_a * (3.d0 - 2.d0*ar2)
end do
end do
end do
end function qmckl_compute_ao_basis_primitive_gaussian_vglComputation of shells
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
prim_num |
int64_t |
in | Number of primitives |
shell_num |
int64_t |
in | Number of shells |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
nucleus_shell_num |
int64_t[nucl_num] |
in | Number of shells for each nucleus |
nucleus_index |
int64_t[nucl_num] |
in | Index of the 1st shell of each nucleus |
nucleus_range |
double[nucl_num] |
in | Range of the nucleus |
shell_prim_index |
int64_t[shell_num] |
in | Index of the 1st primitive of each shell |
shell_prim_num |
int64_t[shell_num] |
in | Number of primitives per shell |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
expo |
double[prim_num] |
in | Exponents of the primitives |
coef_normalized |
double[prim_num] |
in | Coefficients of the primitives |
shell_vgl |
double[point_num][5][shell_num] |
out | Value, gradients and Laplacian of the shells |
qmckl_exit_code qmckl_compute_ao_basis_shell_gaussian_vgl (
const qmckl_context context,
const int64_t prim_num,
const int64_t shell_num,
const int64_t point_num,
const int64_t nucl_num,
const int64_t* nucleus_shell_num,
const int64_t* nucleus_index,
const double* nucleus_range,
const int64_t* shell_prim_index,
const int64_t* shell_prim_num,
const double* coord,
const double* nucl_coord,
const double* expo,
const double* coef_normalized,
double* const shell_vgl );function qmckl_compute_ao_basis_shell_gaussian_vgl( &
context, prim_num, shell_num, point_num, nucl_num, &
nucleus_shell_num, nucleus_index, nucleus_range, &
shell_prim_index, shell_prim_num, coord, nucl_coord, &
expo, coef_normalized, shell_vgl) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
use qmckl, only: qmckl_get_numprec_precision
implicit none
integer (qmckl_context), intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: prim_num
integer (c_int64_t) , intent(in) , value :: shell_num
integer (c_int64_t) , intent(in) , value :: point_num
integer (c_int64_t) , intent(in) , value :: nucl_num
integer (c_int64_t) , intent(in) :: nucleus_shell_num(nucl_num)
integer (c_int64_t) , intent(in) :: nucleus_index(nucl_num)
real (c_double ) , intent(in) :: nucleus_range(nucl_num)
integer (c_int64_t) , intent(in) :: shell_prim_index(shell_num)
integer (c_int64_t) , intent(in) :: shell_prim_num(shell_num)
real (c_double ) , intent(in) :: coord(point_num,3)
real (c_double ) , intent(in) :: nucl_coord(nucl_num,3)
real (c_double ) , intent(in) :: expo(prim_num)
real (c_double ) , intent(in) :: coef_normalized(prim_num)
real (c_double ) , intent(out) :: shell_vgl(shell_num,5,point_num)
integer(qmckl_exit_code) :: info
integer*8 :: inucl, iprim, ipoint, ishell
integer*8 :: ishell_start, ishell_end
integer*8 :: iprim_start , iprim_end
double precision :: x, y, z, two_a, ar2, r2, v, cutoff
info = QMCKL_SUCCESS
! Don't compute exponentials when the result will be almost zero.
<<fortran_cutoff>>
do ipoint = 1, point_num
do inucl=1,nucl_num
x = coord(ipoint,1) - nucl_coord(inucl,1)
y = coord(ipoint,2) - nucl_coord(inucl,2)
z = coord(ipoint,3) - nucl_coord(inucl,3)
r2 = x*x + y*y + z*z
if (r2 > cutoff*nucleus_range(inucl)) then
cycle
end if
! C is zero-based, so shift bounds by one
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell=ishell_start, ishell_end
shell_vgl(ishell, 1, ipoint) = 0.d0
shell_vgl(ishell, 2, ipoint) = 0.d0
shell_vgl(ishell, 3, ipoint) = 0.d0
shell_vgl(ishell, 4, ipoint) = 0.d0
shell_vgl(ishell, 5, ipoint) = 0.d0
iprim_start = shell_prim_index(ishell) + 1
iprim_end = shell_prim_index(ishell) + shell_prim_num(ishell)
do iprim = iprim_start, iprim_end
ar2 = expo(iprim)*r2
if (ar2 > cutoff) then
cycle
end if
v = coef_normalized(iprim) * dexp(-ar2)
two_a = -2.d0 * expo(iprim) * v
shell_vgl(ishell, 1, ipoint) = &
shell_vgl(ishell, 1, ipoint) + v
shell_vgl(ishell, 2, ipoint) = &
shell_vgl(ishell, 2, ipoint) + two_a * x
shell_vgl(ishell, 3, ipoint) = &
shell_vgl(ishell, 3, ipoint) + two_a * y
shell_vgl(ishell, 4, ipoint) = &
shell_vgl(ishell, 4, ipoint) + two_a * z
shell_vgl(ishell, 5, ipoint) = &
shell_vgl(ishell, 5, ipoint) + two_a * (3.d0 - 2.d0*ar2)
end do
end do
end do
end do
end function qmckl_compute_ao_basis_shell_gaussian_vglPolynomial part
Going from the atomic basis set to AOs implies a systematic construction of all the angular functions of each shell. We consider two cases for the angular functions: the real-valued spherical harmonics, and the polynomials in Cartesian coordinates. In the case of spherical harmonics, the AOs are ordered in increasing magnetic quantum number ($-l \le m \le l$), and in the case of polynomials we choose the canonical ordering, i.e
\begin{eqnarray} p & : & p_x, p_y, p_z \nonumber \\ d & : & d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz} \nonumber \\ f & : & f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}, f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, f_{zzz} \nonumber \\ {\rm etc.} \nonumber \end{eqnarray}General functions for Powers of $x-X_i$
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:
\[ P_{ik} = X_i^k \]
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
n |
int64_t | in | Number of values |
X |
double[n] | in | Array containing the input values |
LMAX |
int32_t[n] | in | Array containing the maximum power for each value |
P |
double[n][ldp] | out | Array containing all the powers of X |
ldp |
int64_t | in | Leading dimension of array P |
Requirements:
contextis notQMCKL_NULL_CONTEXTn> 0Xis allocated with at least $n \times 8$ bytesLMAXis allocated with at least $n \times 4$ bytesPis allocated with at least $n \times \max_i \text{LMAX}_i \times 8$ bytesLDP>= $\max_i$LMAX[i]
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 );function qmckl_ao_power(context, n, X, LMAX, P, ldp) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
implicit none
integer (qmckl_context), 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(qmckl_exit_code) :: info
integer(c_int64_t) :: 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_powerGeneral functions for Value, Gradient and Laplacian of a polynomial
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-2} (z-Z_i)^c + \\ && c(c-1) (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-2}. \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.
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
X |
double[3] |
in | Array containing the coordinates of the points |
R |
double[3] |
in | Array containing the x,y,z coordinates of the center |
lmax |
int32_t |
in | Maximum angular momentum |
n |
int64_t |
inout | Number of computed polynomials |
L |
int32_t[n][ldl] |
out | Contains a,b,c for all n results |
ldl |
int64_t |
in | Leading dimension of L |
VGL |
double[n][ldv] |
out | Value, gradients and Laplacian of the polynomials |
ldv |
int64_t |
in | Leading dimension of array VGL |
Requirements:
context≠QMCKL_NULL_CONTEXTn> 0lmax>= 0ldl>= 3ldv>= 5Xis allocated with at least $3 \times 8$ bytesRis allocated with at least $3 \times 8$ bytesn>=(lmax+1)(lmax+2)(lmax+3)/6Lis allocated with at least $3 \times n \times 4$ bytesVGLis allocated with at least $5 \times n \times 8$ bytes- On output,
nshould 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"
- Increasing values of
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 );qmckl_exit_code qmckl_ao_polynomial_vgl_doc (
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 );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 )
{
#ifdef HAVE_HPC
//return qmckl_ao_polynomial_vgl_hpc (context, X, R, lmax, n, L, ldl, VGL, ldv);
return qmckl_ao_polynomial_vgl_doc
#else
return qmckl_ao_polynomial_vgl_doc
#endif
(context, X, R, lmax, n, L, ldl, VGL, ldv);
}function qmckl_ao_polynomial_vgl_doc (context, &
X, R, lmax, n, L, ldl, VGL, ldv) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
implicit none
integer (qmckl_context), 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,(lmax+1)*(lmax+2)*(lmax+3)/6)
integer (c_int64_t) , intent(in) , value :: ldl
real (c_double ) , intent(out) :: VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)
integer (c_int64_t) , intent(in) , value :: ldv
integer(qmckl_exit_code) :: info
integer*8 :: i,j
integer :: a,b,c,d
double precision :: Y(3)
double precision :: pows(-2:lmax,3)
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
if (lmax == 0) then
VGL(1,1) = 1.d0
VGL(2,1) = 0.d0
VGL(3,1) = 0.d0
VGL(4,1) = 0.d0
VGL(5,1) = 0.d0
l(1,1) = 0
l(2,1) = 0
l(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
VGL(1,1) = 1.d0
VGL(1,2) = pows(1,1)
VGL(2,2) = 1.d0
VGL(1,3) = pows(1,2)
VGL(3,3) = 1.d0
VGL(1,4) = pows(1,3)
VGL(4,4) = 1.d0
l (1:3,1:4) = 0
l (1,2) = 1
l (2,3) = 1
l (3,4) = 1
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_docqmckl_exit_code qmckl_ao_polynomial_transp_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 );qmckl_exit_code qmckl_ao_polynomial_transp_vgl_doc (
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 );qmckl_exit_code qmckl_ao_polynomial_transp_vgl_hpc (
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 );qmckl_exit_code
qmckl_ao_polynomial_transp_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 )
{
#ifdef HAVE_HPC
return qmckl_ao_polynomial_transp_vgl_hpc
#else
return qmckl_ao_polynomial_transp_vgl_doc
#endif
(context, X, R, lmax, n, L, ldl, VGL, ldv);
}function qmckl_ao_polynomial_transp_vgl_doc (context, &
X, R, lmax, n, L, ldl, VGL, ldv) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
implicit none
integer (qmckl_context), 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,(lmax+1)*(lmax+2)*(lmax+3)/6)
integer (c_int64_t) , intent(in) , value :: ldl
real (c_double ) , intent(out) :: VGL(ldv,5)
integer (c_int64_t) , intent(in) , value :: ldv
integer(qmckl_exit_code) :: info
integer*8 :: i,j
integer :: a,b,c,d
real*8 :: Y(3)
real*8 :: pows(-2:21,3) ! lmax < 22
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 < (lmax+1)*(lmax+2)*(lmax+3)/6) then
info = QMCKL_INVALID_ARG_9
return
endif
if (lmax > 0) then
do i=1,3
Y(i) = X(i) - R(i)
end do
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
l (1:3,1:4) = 0
VGL(1:4,1:5) = 0.d0
VGL(1 ,1 ) = 1.d0
l (1,2) = 1
VGL(2,1) = Y(1)
VGL(2,2) = 1.d0
l (2,3) = 1
VGL(3,1) = Y(2)
VGL(3,3) = 1.d0
l (3,4) = 1
VGL(4,1) = Y(3)
VGL(4,4) = 1.d0
n=4
else
VGL(1,1) = 1.d0
VGL(1,2:5) = 0.d0
l(1:3,1) = 0
n=1
return
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
xy = pows(a,1) * pows(b,2)
yz = pows(b,2) * pows(c,3)
xz = pows(a,1) * pows(c,3)
l(1,n) = a
l(2,n) = b
l(3,n) = c
VGL(n,1) = xy * pows(c,3)
xy = dc * xy
xz = db * xz
yz = da * yz
VGL(n,2) = pows(a-1,1) * yz
VGL(n,3) = pows(b-1,2) * xz
VGL(n,4) = pows(c-1,3) * xy
VGL(n,5) = &
(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_transp_vgl_docstatic inline qmckl_exit_code
qmckl_ao_polynomial_transp_vgl_hpc_inline (const qmckl_context context,
const double* restrict X,
const double* restrict R,
const int32_t lmax,
int64_t* n,
int32_t* restrict const L,
const int64_t ldl,
double* restrict const VGL,
const int64_t ldv )
{
const qmckl_context_struct* ctx = (qmckl_context_struct*) context;
assert (ctx != NULL && X != NULL && R != NULL && n != NULL && L != NULL && VGL != NULL);
if (lmax < 0) return QMCKL_INVALID_ARG_4;
if (ldl < 3) return QMCKL_INVALID_ARG_7;
int32_t m;
switch (lmax) {
case 0:
{
if (ldv < 1) return QMCKL_INVALID_ARG_9;
L[0] = 0; L[1] = 0; L[2] = 0;
VGL[0 ] = 1.0;
VGL[ldv ] = 0.0;
VGL[ldv<<1 ] = 0.0;
VGL[(ldv<<1)+ldv] = 0.0;
VGL[ldv<<2 ] = 0.0;
m=1;
break;
}
case 1:
{
if (ldv < 4) return QMCKL_INVALID_ARG_9;
if (ldl == 3) {
const int32_t ltmp[12] = {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1};
for (int i=0 ; i<12 ; ++i)
L[i] = ltmp[i];
} else {
int32_t* restrict const l[4] = {L, L+ldl, L+(ldl<<1), L+ldl+(ldl<<1)};
l[0][0] = 0; l[0][1] = 0; l[0][2] = 0;
l[1][0] = 1; l[1][1] = 0; l[1][2] = 0;
l[2][0] = 0; l[2][1] = 1; l[2][2] = 0;
l[3][0] = 0; l[3][1] = 0; l[3][2] = 1;
}
if (ldv == 4) {
const double tmp[20] = {1.0, X[0]-R[0], X[1]-R[1], X[2]-R[2],
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 1.0,
0.0, 0.0, 0.0, 0.0};
for (int i=0 ; i<20 ; ++i)
VGL[i] = tmp[i];
} else {
double* restrict const vgl1 = VGL;
double* restrict const vgl2 = VGL + ldv;
double* restrict const vgl3 = VGL + (ldv << 1);
double* restrict const vgl4 = VGL + ldv + (ldv << 1);
double* restrict const vgl5 = VGL + (ldv << 2);
for (int32_t k=0 ; k<4 ; ++k) {
vgl2[k] = 0.0;
vgl3[k] = 0.0;
vgl4[k] = 0.0;
vgl5[k] = 0.0;
}
vgl1[0] = 1.0;
vgl1[1] = X[0]-R[0];
vgl1[2] = X[1]-R[1];
vgl1[3] = X[2]-R[2];
vgl2[1] = 1.0;
vgl3[2] = 1.0;
vgl4[3] = 1.0;
}
m=4;
break;
}
case 2:
{
if (ldv < 10) return QMCKL_INVALID_ARG_9;
if (ldl == 3) {
const int32_t ltmp[30] = {0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
2, 0, 0, 1, 1, 0, 1, 0, 1, 0, 2, 0,
0, 1, 1, 0, 0, 2};
for (int i=0 ; i<30 ; ++i)
L[i] = ltmp[i];
} else {
int32_t* restrict l[10];
for (int32_t i=0 ; i<10 ; ++i) {
l[i] = L + i*ldl;
}
l[0][0] = 0; l[0][1] = 0; l[0][2] = 0;
l[1][0] = 1; l[1][1] = 0; l[1][2] = 0;
l[2][0] = 0; l[2][1] = 1; l[2][2] = 0;
l[3][0] = 0; l[3][1] = 0; l[3][2] = 1;
l[4][0] = 2; l[4][1] = 0; l[4][2] = 0;
l[5][0] = 1; l[5][1] = 1; l[5][2] = 0;
l[6][0] = 1; l[6][1] = 0; l[6][2] = 1;
l[7][0] = 0; l[7][1] = 2; l[7][2] = 0;
l[8][0] = 0; l[8][1] = 1; l[8][2] = 1;
l[9][0] = 0; l[9][1] = 0; l[9][2] = 2;
}
const double Y[3] = { X[0]-R[0],
X[1]-R[1],
X[2]-R[2] };
if (ldv == 50) {
const double tmp[50] = {
1.0, Y[0], Y[1], Y[2], Y[0] * Y[0],
Y[0] * Y[1], Y[0] * Y[2], Y[1] * Y[1], Y[1] * Y[2], Y[2] * Y[2],
0.0, 1.0, 0.0, 0.0, Y[0] + Y[0],
Y[1], Y[2], 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0, 0.0,
Y[0], 0.0, Y[1] + Y[1], Y[2], 0.0,
0.0, 0.0, 0.0, 1.0, 0.0,
0.0, Y[0], 0.0, Y[1], Y[2] + Y[2],
0.0, 0.0, 0.0, 0.0, 2.0,
0.0, 0.0, 2.0, 0., 2.0 };
for (int i=0 ; i<50 ; ++i)
VGL[i] = tmp[i];
} else {
double* restrict const vgl1 = VGL;
double* restrict const vgl2 = VGL + ldv;
double* restrict const vgl3 = VGL + (ldv << 1);
double* restrict const vgl4 = VGL + 3*ldv;
double* restrict const vgl5 = VGL + (ldv << 2);
vgl1[0] = 1.0 ; vgl1[1] = Y[0] ; vgl1[2] = Y[1];
vgl1[3] = Y[2] ; vgl1[4] = Y[0]*Y[0]; vgl1[5] = Y[0]*Y[1];
vgl1[6] = Y[0]*Y[2]; vgl1[7] = Y[1]*Y[1]; vgl1[8] = Y[1]*Y[2];
vgl1[9] = Y[2]*Y[2];
vgl2[0] = 0.0 ; vgl2[1] = 1.0 ; vgl2[2] = 0.0 ;
vgl2[3] = 0.0 ; vgl2[4] = Y[0]+Y[0]; vgl2[5] = Y[1];
vgl2[6] = Y[2]; vgl2[7] = 0.0 ; vgl2[8] = 0.0 ;
vgl2[9] = 0.0 ;
vgl3[0] = 0.0; vgl3[1] = 0.0 ; vgl3[2] = 1.0 ;
vgl3[3] = 0.0; vgl3[4] = 0.0 ; vgl3[5] = Y[0];
vgl3[6] = 0.0; vgl3[7] = Y[1]+Y[1]; vgl3[8] = Y[2];
vgl3[9] = 0.0;
vgl4[0] = 0.0 ; vgl4[1] = 0.0; vgl4[2] = 0.0 ;
vgl4[3] = 1.0 ; vgl4[4] = 0.0; vgl4[5] = 0.0 ;
vgl4[6] = Y[0] ; vgl4[7] = 0.0; vgl4[8] = Y[1];
vgl4[9] = Y[2]+Y[2];
vgl5[0] = 0.0; vgl5[1] = 0.0; vgl5[2] = 0.0;
vgl5[3] = 0.0; vgl5[4] = 2.0; vgl5[5] = 0.0;
vgl5[6] = 0.0; vgl5[7] = 2.0; vgl5[8] = 0.0;
vgl5[9] = 2.0;
}
m=10;
break;
}
default:
{
const int32_t size_max = (lmax+1)*(lmax+2)*(lmax+3)/6;
if (ldv < size_max) return QMCKL_INVALID_ARG_9;
double* restrict const vgl1 = VGL;
double* restrict const vgl2 = VGL + ldv;
double* restrict const vgl3 = VGL + (ldv<<1);
double* restrict const vgl4 = VGL + ldv + (ldv<<1);
double* restrict const vgl5 = VGL + (ldv<<2);
const double Y[3] = { X[0]-R[0],
X[1]-R[1],
X[2]-R[2] };
assert(size_max > lmax+3);
double pows[3][size_max];
for (int32_t i=0 ; i<3 ; ++i) {
pows[0][i] = 1.0;
pows[1][i] = 1.0;
pows[2][i] = 1.0;
}
for (int32_t i=3 ; i<=lmax+2 ; ++i) {
pows[0][i] = pows[0][i-1] * Y[0];
pows[1][i] = pows[1][i-1] * Y[1];
pows[2][i] = pows[2][i-1] * Y[2];
}
int32_t* l[size_max];
for (int32_t i=0 ; i<size_max ; ++i) {
l[i] = &(L[i*ldl]);
}
for (int32_t i=0 ; i<4 ; ++i) {
l[i][0] = 0;
l[i][1] = 0;
l[i][2] = 0;
}
l[1][0] = 1;
l[2][1] = 1;
l[3][2] = 1;
for (int32_t k=0 ; k<4 ; ++k) {
vgl2[k] = 0.0;
vgl3[k] = 0.0;
vgl4[k] = 0.0;
vgl5[k] = 0.0;
}
vgl1[0] = 1.0;
vgl1[1] = Y[0];
vgl1[2] = Y[1];
vgl1[3] = Y[2];
vgl2[1] = 1.0;
vgl3[2] = 1.0;
vgl4[3] = 1.0;
m=4;
double dd = 2.0;
for (int32_t d=2 ; d<= lmax ; ++d) {
double da = dd;
for (int32_t a=d ; a>=0 ; --a) {
double db = dd-da;
for (int32_t b=d-a ; b>=0 ; --b) {
const int32_t c = d - a - b;
const double dc = dd - da - db;
double xy = pows[0][a+2] * pows[1][b+2];
double yz = pows[1][b+2] * pows[2][c+2];
double xz = pows[0][a+2] * pows[2][c+2];
l[m][0] = a;
l[m][1] = b;
l[m][2] = c;
vgl1[m] = xy * pows[2][c+2];
xy *= dc;
xz *= db;
yz *= da;
vgl2[m] = pows[0][a+1] * yz;
vgl3[m] = pows[1][b+1] * xz;
vgl4[m] = pows[2][c+1] * xy;
vgl5[m] = (da-1.) * pows[0][a] * yz +
(db-1.) * pows[1][b] * xz +
(dc-1.) * pows[2][c] * xy;
db -= 1.0;
++m;
}
da -= 1.0;
}
dd += 1.0;
}
}
}
,*n = m;
return QMCKL_SUCCESS;
}
qmckl_exit_code
qmckl_ao_polynomial_transp_vgl_hpc (const qmckl_context context,
const double* restrict X,
const double* restrict R,
const int32_t lmax,
int64_t* n,
int32_t* restrict const L,
const int64_t ldl,
double* restrict const VGL,
const int64_t ldv )
{
return qmckl_ao_polynomial_transp_vgl_hpc_inline (context,
X, R, lmax, n, L, ldl, VGL, ldv );
}Combining radial and polynomial parts
Determination of nucleus ranges
The range of a nucleus is defined as the distance beyond which all the AOs are zero, up to a given precision. For all possible numbers of bits of precision (1-53), a range is given.
qmckl_exit_code qmckl_compute_nucleus_range_gaussian(
const qmckl_context context,
const int64_t ao_num,
const int64_t shell_num,
const int64_t prim_num,
const int64_t nucl_num,
const double* nucl_coord,
const int64_t* nucleus_index,
const int64_t* nucleus_shell_num,
const int32_t* nucleus_max_ang_mom,
const int64_t* shell_prim_index,
const int64_t* shell_prim_num,
const int32_t* shell_ang_mom,
const double* ao_factor,
const double* ao_expo,
const double* coefficient_normalized,
double* const nucleus_range);function qmckl_compute_nucleus_range_gaussian(context, &
ao_num, shell_num, prim_num, nucl_num, &
nucl_coord, nucleus_index, nucleus_shell_num, &
nucleus_max_ang_mom, shell_prim_index, shell_prim_num, shell_ang_mom, &
ao_factor, expo, coef_normalized, nucleus_range) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
use qmckl, only: qmckl_ao_polynomial_vgl, qmckl_get_numprec_precision
implicit none
integer (qmckl_context), intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: ao_num
integer (c_int64_t) , intent(in) , value :: shell_num
integer (c_int64_t) , intent(in) , value :: prim_num
integer (c_int64_t) , intent(in) , value :: nucl_num
real (c_double ) , intent(in) :: nucl_coord(nucl_num,3)
integer (c_int64_t) , intent(in) :: nucleus_index(nucl_num)
integer (c_int64_t) , intent(in) :: nucleus_shell_num(nucl_num)
integer (c_int32_t) , intent(in) :: nucleus_max_ang_mom(nucl_num)
integer (c_int64_t) , intent(in) :: shell_prim_index(shell_num)
integer (c_int64_t) , intent(in) :: shell_prim_num(shell_num)
integer (c_int32_t) , intent(in) :: shell_ang_mom(shell_num)
real (c_double ) , intent(in) :: ao_factor(ao_num)
real (c_double ) , intent(in) :: expo(prim_num)
real (c_double ) , intent(in) :: coef_normalized(prim_num)
real (c_double ) , intent(out) :: nucleus_range(nucl_num,53)
integer(qmckl_exit_code) :: info
double precision :: e_coord(3), n_coord(3)
integer*8 :: n_poly, iprim, iprim_start, iprim_end
integer :: l, il, k, iprecision
integer*8 :: ipoint, inucl, ishell
integer*8 :: ishell_start, ishell_end
integer :: lstart(0:20)
double precision :: shell_vgl(3)
double precision :: x, y, z, r2, ar2, two_a
double precision :: vmax, cutoff, v
double precision, allocatable :: poly_vgl(:,:), ao_vgl(:,:)
integer , allocatable :: powers(:,:), ao_index(:)
allocate(poly_vgl(5,ao_num), powers(3,ao_num), ao_index(ao_num))
! Pre-computed data
do l=0,20
lstart(l) = l*(l+1)*(l+2)/6 +1
end do
k=1
do inucl=1,nucl_num
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
l = shell_ang_mom(ishell)
ao_index(ishell) = k
k = k + lstart(l+1) - lstart(l)
end do
end do
info = QMCKL_SUCCESS
n_coord(1) = 0.d0
n_coord(2) = 0.d0
n_coord(3) = 0.d0
e_coord(2) = 0.d0
e_coord(3) = 0.d0
nucleus_range = 50.d0
do inucl=1,nucl_num
x = 50.d0
do iprecision = 53,2,-1
cutoff = 1.d0 / ( 2.d0** (iprecision-2) )
vmax = 0.d0
do while ( (vmax < cutoff) .and. (x > 0.d0) )
x = x - .1d0
vmax = 0.d0
e_coord(1) = x
r2 = x*x
! Compute polynomials
info = qmckl_ao_polynomial_vgl(context, e_coord, n_coord, &
nucleus_max_ang_mom(inucl), n_poly, powers, 3_8, &
poly_vgl, 5_8)
! Loop over shells
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
shell_vgl(1) = 0.d0
shell_vgl(2) = 0.d0
shell_vgl(3) = 0.d0
iprim_start = shell_prim_index(ishell) + 1
iprim_end = shell_prim_index(ishell) + shell_prim_num(ishell)
do iprim = iprim_start, iprim_end
ar2 = expo(iprim)*r2
v = coef_normalized(iprim) * dexp(-ar2)
two_a = -2.d0 * expo(iprim) * v
shell_vgl(1) = shell_vgl(1) + v
shell_vgl(2) = shell_vgl(2) + two_a * x
shell_vgl(3) = shell_vgl(3) + two_a * (3.d0 - 2.d0*ar2)
end do
k = ao_index(ishell)
l = shell_ang_mom(ishell)
do il = lstart(l), lstart(l+1)-1
vmax = max(vmax, poly_vgl(1,il) * shell_vgl(1) * ao_factor(k))
vmax = max(vmax, ( poly_vgl(2,il) * shell_vgl(1) + poly_vgl(1,il) * shell_vgl(2) ) * ao_factor(k))
vmax = max(vmax, ( poly_vgl(5,il) * shell_vgl(3) + poly_vgl(1,il) * shell_vgl(3) + &
2.d0 * (poly_vgl(2,il) * shell_vgl(2) ) ) * ao_factor(k) )
k = k+1
end do
end do
end do
nucleus_range(inucl,iprecision) = x
end do
end do
deallocate(poly_vgl, powers)
end function qmckl_compute_nucleus_range_gaussianValues only
Unoptimized version
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
ao_num |
int64_t |
in | Number of AOs |
shell_num |
int64_t |
in | Number of shells |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
nucleus_index |
int64_t[nucl_num] |
in | Index of the 1st shell of each nucleus |
nucleus_shell_num |
int64_t[nucl_num] |
in | Number of shells per nucleus |
nucleus_range |
double[nucl_num] |
in | Range beyond which all is zero |
nucleus_max_ang_mom |
int32_t[nucl_num] |
in | Maximum angular momentum per nucleus |
shell_ang_mom |
int32_t[shell_num] |
in | Angular momentum of each shell |
ao_factor |
double[ao_num] |
in | Normalization factor of the AOs |
shell_vgl |
double[point_num][5][shell_num] |
in | Value, gradients and Laplacian of the shells |
ao_value |
double[point_num][ao_num] |
out | Values of the AOs |
function qmckl_compute_ao_value_doc(context, &
ao_num, shell_num, point_num, nucl_num, &
coord, nucl_coord, nucleus_index, nucleus_shell_num, &
nucleus_range, nucleus_max_ang_mom, shell_ang_mom, &
ao_factor, shell_vgl, ao_value) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
use qmckl, only: qmckl_ao_polynomial_vgl, qmckl_get_numprec_precision
implicit none
integer (qmckl_context), intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: ao_num
integer (c_int64_t) , intent(in) , value :: shell_num
integer (c_int64_t) , intent(in) , value :: point_num
integer (c_int64_t) , intent(in) , value :: nucl_num
real (c_double ) , intent(in) :: coord(point_num,3)
real (c_double ) , intent(in) :: nucl_coord(nucl_num,3)
integer (c_int64_t) , intent(in) :: nucleus_index(nucl_num)
integer (c_int64_t) , intent(in) :: nucleus_shell_num(nucl_num)
real (c_double ) , intent(in) :: nucleus_range(nucl_num)
integer (c_int32_t) , intent(in) :: nucleus_max_ang_mom(nucl_num)
integer (c_int32_t) , intent(in) :: shell_ang_mom(shell_num)
real (c_double ) , intent(in) :: ao_factor(ao_num)
real (c_double ) , intent(in) :: shell_vgl(shell_num,5,point_num)
real (c_double ) , intent(out) :: ao_value(ao_num,point_num)
integer(qmckl_exit_code) :: info
double precision :: e_coord(3), n_coord(3)
integer*8 :: n_poly
integer :: l, il, k
integer*8 :: ipoint, inucl, ishell
integer*8 :: ishell_start, ishell_end
integer :: lstart(0:20)
double precision :: x, y, z, r2
double precision :: cutoff
double precision, allocatable :: poly_vgl(:,:)
integer , allocatable :: powers(:,:), ao_index(:)
allocate(poly_vgl(5,ao_num), powers(3,ao_num), ao_index(ao_num))
! Pre-computed data
do l=0,20
lstart(l) = l*(l+1)*(l+2)/6 +1
end do
k=1
do inucl=1,nucl_num
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
l = shell_ang_mom(ishell)
ao_index(ishell) = k
k = k + lstart(l+1) - lstart(l)
end do
end do
info = QMCKL_SUCCESS
! Don't compute polynomials when the radial part is zero.
<<fortran_cutoff>>
do ipoint = 1, point_num
e_coord(1) = coord(ipoint,1)
e_coord(2) = coord(ipoint,2)
e_coord(3) = coord(ipoint,3)
ao_value(:,ipoint) = 0.d0
do inucl=1,nucl_num
n_coord(1) = nucl_coord(inucl,1)
n_coord(2) = nucl_coord(inucl,2)
n_coord(3) = nucl_coord(inucl,3)
! Test if the point is in the range of the nucleus
x = e_coord(1) - n_coord(1)
y = e_coord(2) - n_coord(2)
z = e_coord(3) - n_coord(3)
r2 = x*x + y*y + z*z
if (r2 > cutoff*nucleus_range(inucl)) then
cycle
end if
! Compute polynomials
info = qmckl_ao_polynomial_vgl(context, e_coord, n_coord, &
nucleus_max_ang_mom(inucl), n_poly, powers, 3_8, &
poly_vgl, 5_8)
! Loop over shells
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
k = ao_index(ishell)
l = shell_ang_mom(ishell)
do il = lstart(l), lstart(l+1)-1
! Value
ao_value(k,ipoint) = &
poly_vgl(1,il) * shell_vgl(ishell,1,ipoint) * ao_factor(k)
k = k+1
end do
end do
end do
end do
deallocate(poly_vgl, powers)
end function qmckl_compute_ao_value_docHPC version
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
ao_num |
int64_t |
in | Number of AOs |
shell_num |
int64_t |
in | Number of shells |
prim_num |
int64_t |
in | Number of primitives |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
nucleus_index |
int64_t[nucl_num] |
in | Index of the 1st shell of each nucleus |
nucleus_shell_num |
int64_t[nucl_num] |
in | Number of shells per nucleus |
nucleus_range |
double[nucl_num] |
in | Range beyond which all is zero |
nucleus_max_ang_mom |
int32_t[nucl_num] |
in | Maximum angular momentum per nucleus |
shell_ang_mom |
int32_t[shell_num] |
in | Angular momentum of each shell |
shell_prim_index |
int64_t[shell_num] |
in | Index of the 1st primitive of each shell |
shell_prim_num |
int64_t[shell_num] |
in | Number of primitives per shell |
ao_factor |
double[ao_num] |
in | Normalization factor of the AOs |
ao_expo |
double[prim_num] |
in | Value, gradients and Laplacian of the shells |
coef_normalized |
double[prim_num] |
in | Value, gradients and Laplacian of the shells |
ao_value |
double[point_num][ao_num] |
out | Values of the AOs |
#+NAME:ao_value_constants
Interfaces
qmckl_exit_code qmckl_compute_ao_value_doc (
const qmckl_context context,
const int64_t ao_num,
const int64_t shell_num,
const int64_t point_num,
const int64_t nucl_num,
const double* coord,
const double* nucl_coord,
const int64_t* nucleus_index,
const int64_t* nucleus_shell_num,
const double* nucleus_range,
const int32_t* nucleus_max_ang_mom,
const int32_t* shell_ang_mom,
const double* ao_factor,
const double* shell_vgl,
double* const ao_value );#ifdef HAVE_HPC
qmckl_exit_code qmckl_compute_ao_value_hpc_gaussian (
const qmckl_context context,
const int64_t ao_num,
const int64_t shell_num,
const int32_t* prim_num_per_nucleus,
const int64_t point_num,
const int64_t nucl_num,
const double* coord,
const double* nucl_coord,
const int64_t* nucleus_index,
const int64_t* nucleus_shell_num,
const double* nucleus_range,
const int32_t* nucleus_max_ang_mom,
const int32_t* shell_ang_mom,
const double* ao_factor,
const qmckl_matrix expo_per_nucleus,
const qmckl_tensor coef_per_nucleus,
double* const ao_value );
#endifValue, gradients, Laplacian
Reference version
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
ao_num |
int64_t |
in | Number of AOs |
shell_num |
int64_t |
in | Number of shells |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
nucleus_index |
int64_t[nucl_num] |
in | Index of the 1st shell of each nucleus |
nucleus_shell_num |
int64_t[nucl_num] |
in | Number of shells per nucleus |
nucleus_range |
double[nucl_num] |
in | Range beyond which all is zero |
nucleus_max_ang_mom |
int32_t[nucl_num] |
in | Maximum angular momentum per nucleus |
shell_ang_mom |
int32_t[shell_num] |
in | Angular momentum of each shell |
ao_factor |
double[ao_num] |
in | Normalization factor of the AOs |
shell_vgl |
double[point_num][5][shell_num] |
in | Value, gradients and Laplacian of the shells |
ao_vgl |
double[point_num][5][ao_num] |
out | Value, gradients and Laplacian of the AOs |
function qmckl_compute_ao_vgl_doc(context, &
ao_num, shell_num, point_num, nucl_num, &
coord, nucl_coord, nucleus_index, nucleus_shell_num, &
nucleus_range, nucleus_max_ang_mom, shell_ang_mom, &
ao_factor, shell_vgl, ao_vgl) &
bind(C) result(info)
use, intrinsic :: iso_c_binding
use qmckl_constants
use qmckl, only : qmckl_ao_polynomial_vgl, qmckl_get_numprec_precision
implicit none
integer (qmckl_context), intent(in) , value :: context
integer (c_int64_t) , intent(in) , value :: ao_num
integer (c_int64_t) , intent(in) , value :: shell_num
integer (c_int64_t) , intent(in) , value :: point_num
integer (c_int64_t) , intent(in) , value :: nucl_num
real (c_double ) , intent(in) :: coord(point_num,3)
real (c_double ) , intent(in) :: nucl_coord(nucl_num,3)
integer (c_int64_t) , intent(in) :: nucleus_index(nucl_num)
integer (c_int64_t) , intent(in) :: nucleus_shell_num(nucl_num)
real (c_double ) , intent(in) :: nucleus_range(nucl_num)
integer (c_int32_t) , intent(in) :: nucleus_max_ang_mom(nucl_num)
integer (c_int32_t) , intent(in) :: shell_ang_mom(shell_num)
real (c_double ) , intent(in) :: ao_factor(ao_num)
real (c_double ) , intent(in) :: shell_vgl(shell_num,5,point_num)
real (c_double ) , intent(out) :: ao_vgl(ao_num,5,point_num)
integer(qmckl_exit_code) :: info
double precision :: e_coord(3), n_coord(3)
integer*8 :: n_poly
integer :: l, il, k
integer*8 :: ipoint, inucl, ishell
integer*8 :: ishell_start, ishell_end
integer :: lstart(0:20)
double precision :: x, y, z, r2
double precision :: cutoff
double precision, allocatable :: poly_vgl(:,:)
integer , allocatable :: powers(:,:), ao_index(:)
allocate(poly_vgl(5,ao_num), powers(3,ao_num), ao_index(ao_num))
! Pre-computed data
do l=0,20
lstart(l) = l*(l+1)*(l+2)/6 +1
end do
k=1
do inucl=1,nucl_num
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
l = shell_ang_mom(ishell)
ao_index(ishell) = k
k = k + lstart(l+1) - lstart(l)
end do
end do
info = QMCKL_SUCCESS
! Don't compute polynomials when the radial part is zero.
<<fortran_cutoff>>
do ipoint = 1, point_num
e_coord(1) = coord(ipoint,1)
e_coord(2) = coord(ipoint,2)
e_coord(3) = coord(ipoint,3)
ao_vgl(:,:,ipoint) = 0.d0
do inucl=1,nucl_num
n_coord(1) = nucl_coord(inucl,1)
n_coord(2) = nucl_coord(inucl,2)
n_coord(3) = nucl_coord(inucl,3)
! Test if the point is in the range of the nucleus
x = e_coord(1) - n_coord(1)
y = e_coord(2) - n_coord(2)
z = e_coord(3) - n_coord(3)
r2 = x*x + y*y + z*z
if (r2 > cutoff*nucleus_range(inucl)) then
cycle
end if
! Compute polynomials
info = qmckl_ao_polynomial_vgl(context, e_coord, n_coord, &
nucleus_max_ang_mom(inucl), n_poly, powers, 3_8, &
poly_vgl, 5_8)
! Loop over shells
ishell_start = nucleus_index(inucl) + 1
ishell_end = nucleus_index(inucl) + nucleus_shell_num(inucl)
do ishell = ishell_start, ishell_end
k = ao_index(ishell)
l = shell_ang_mom(ishell)
do il = lstart(l), lstart(l+1)-1
! Value
ao_vgl(k,1,ipoint) = &
poly_vgl(1,il) * shell_vgl(ishell,1,ipoint) * ao_factor(k)
! Grad_x
ao_vgl(k,2,ipoint) = ( &
poly_vgl(2,il) * shell_vgl(ishell,1,ipoint) + &
poly_vgl(1,il) * shell_vgl(ishell,2,ipoint) &
) * ao_factor(k)
! Grad_y
ao_vgl(k,3,ipoint) = ( &
poly_vgl(3,il) * shell_vgl(ishell,1,ipoint) + &
poly_vgl(1,il) * shell_vgl(ishell,3,ipoint) &
) * ao_factor(k)
! Grad_z
ao_vgl(k,4,ipoint) = ( &
poly_vgl(4,il) * shell_vgl(ishell,1,ipoint) + &
poly_vgl(1,il) * shell_vgl(ishell,4,ipoint) &
) * ao_factor(k)
! Lapl_z
ao_vgl(k,5,ipoint) = ( &
poly_vgl(5,il) * shell_vgl(ishell,1,ipoint) + &
poly_vgl(1,il) * shell_vgl(ishell,5,ipoint) + &
2.d0 * ( &
poly_vgl(2,il) * shell_vgl(ishell,2,ipoint) + &
poly_vgl(3,il) * shell_vgl(ishell,3,ipoint) + &
poly_vgl(4,il) * shell_vgl(ishell,4,ipoint) ) &
) * ao_factor(k)
k = k+1
end do
end do
end do
end do
deallocate(poly_vgl, powers)
end function qmckl_compute_ao_vgl_docHPC version
| Variable | Type | In/Out | Description |
|---|---|---|---|
context |
qmckl_context |
in | Global state |
ao_num |
int64_t |
in | Number of AOs |
shell_num |
int64_t |
in | Number of shells |
prim_num |
int64_t |
in | Number of primitives |
point_num |
int64_t |
in | Number of points |
nucl_num |
int64_t |
in | Number of nuclei |
coord |
double[3][point_num] |
in | Coordinates |
nucl_coord |
double[3][nucl_num] |
in | Nuclear coordinates |
nucleus_index |
int64_t[nucl_num] |
in | Index of the 1st shell of each nucleus |
nucleus_shell_num |
int64_t[nucl_num] |
in | Number of shells per nucleus |
nucleus_range |
double[nucl_num] |
in | Range beyond which all is zero |
nucleus_max_ang_mom |
int32_t[nucl_num] |
in | Maximum angular momentum per nucleus |
shell_ang_mom |
int32_t[shell_num] |
in | Angular momentum of each shell |
shell_prim_index |
int64_t[shell_num] |
in | Index of the 1st primitive of each shell |
shell_prim_num |
int64_t[shell_num] |
in | Number of primitives per shell |
ao_factor |
double[ao_num] |
in | Normalization factor of the AOs |
ao_expo |
double[prim_num] |
in | Exponents of the primitives |
coef_normalized |
double[prim_num] |
in | Normalized coefficients of the primitives |
ao_vgl |
double[point_num][5][ao_num] |
out | Value, gradients and Laplacian of the AOs |
Interfaces
qmckl_exit_code qmckl_compute_ao_vgl_doc (
const qmckl_context context,
const int64_t ao_num,
const int64_t shell_num,
const int64_t point_num,
const int64_t nucl_num,
const double* coord,
const double* nucl_coord,
const int64_t* nucleus_index,
const int64_t* nucleus_shell_num,
const double* nucleus_range,
const int32_t* nucleus_max_ang_mom,
const int32_t* shell_ang_mom,
const double* ao_factor,
const double* shell_vgl,
double* const ao_vgl );#ifdef HAVE_HPC
qmckl_exit_code qmckl_compute_ao_vgl_hpc_gaussian (
const qmckl_context context,
const int64_t ao_num,
const int64_t shell_num,
const int32_t* prim_num_per_nucleus,
const int64_t point_num,
const int64_t nucl_num,
const double* coord,
const double* nucl_coord,
const int64_t* nucleus_index,
const int64_t* nucleus_shell_num,
const double* nucleus_range,
const int32_t* nucleus_max_ang_mom,
const int32_t* shell_ang_mom,
const double* ao_factor,
const qmckl_matrix expo_per_nucleus,
const qmckl_tensor coef_per_nucleus,
double* const ao_vgl );
#endif