20 KiB
Code examples
In this section, we present examples of usage of QMCkl. For simplicity, we assume that the wave function parameters are stored in a TREXIO file.
Python
Check numerically that MOs are orthonormal
In this example, we will compute numerically the overlap between the molecular orbitals:
\[ S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r}) \text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k) \phi_j(\mathbf{r}_k) \delta \mathbf{r} \] \[ S_{ij} = \langle \phi_i | \phi_j \rangle \sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle \langle \mathbf{r}_k | \phi_j \rangle \]
import numpy as np
import qmckltrexio_filename = "..//share/qmckl/test_data/h2o_5z.h5"
context = qmckl.context_create()
qmckl.trexio_read(context, trexio_filename)We now define the grid points $\mathbf{r}_k$ as a regular grid around the molecule.
We fetch the nuclear coordinates from the context,
nucl_num = qmckl.get_nucleus_num(context)
nucl_charge = qmckl.get_nucleus_charge(context, nucl_num)
nucl_coord = qmckl.get_nucleus_coord(context, 'N', nucl_num*3)
nucl_coord = np.reshape(nucl_coord, (3, nucl_num))
for i in range(nucl_num):
print("%d %+f %+f %+f"%(int(nucl_charge[i]),
nucl_coord[i,0],
nucl_coord[i,1],
nucl_coord[i,2]) )8 +0.000000 +0.000000 +0.000000 1 -1.430429 +0.000000 -1.107157 1 +1.430429 +0.000000 -1.107157
and compute the coordinates of the grid points:
nx = ( 120, 120, 120 )
shift = np.array([5.,5.,5.])
point_num = nx[0] * nx[1] * nx[2]
rmin = np.array( list([ np.min(nucl_coord[:,a]) for a in range(3) ]) )
rmax = np.array( list([ np.max(nucl_coord[:,a]) for a in range(3) ]) )
linspace = [ None for i in range(3) ]
step = [ None for i in range(3) ]
for a in range(3):
linspace[a], step[a] = np.linspace(rmin[a]-shift[a],
rmax[a]+shift[a],
num=nx[a],
retstep=True)
dr = step[0] * step[1] * step[2]point = []
for x in linspace[0]:
for y in linspace[1]:
for z in linspace[2]:
point += [ [x, y, z] ]
point = np.array(point)
point_num = len(point)
qmckl.set_point(context, 'N', point_num, np.reshape(point, (point_num*3)))Then, we evaluate all the MOs at the grid points (and time the execution), and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle = \phi_i(\mathbf{r}_k)$.
import time
mo_num = qmckl.get_mo_basis_mo_num(context)
before = time.time()
mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
after = time.time()
mo_value = np.reshape( mo_value, (point_num, mo_num) ).T # Transpose to get mo_num x point_num
print("Number of MOs: ", mo_num)
print("Number of grid points: ", point_num)
print("Execution time : ", (after - before), "seconds")Number of MOs: 201 Number of grid points: 1728000 Execution time : 5.577778577804565 seconds
and finally we compute the overlap between all the MOs as $M.M^\dagger$.
overlap = mo_value @ mo_value.T * dr
print (overlap)[[ 9.88693941e-01 2.34719693e-03 -1.50518232e-08 ... 3.12084178e-09 -5.81064929e-10 3.70130091e-02] [ 2.34719693e-03 9.99509628e-01 3.18930040e-09 ... -2.46888958e-10 -1.06064273e-09 -7.65567973e-03] [-1.50518232e-08 3.18930040e-09 9.99995073e-01 ... -5.84882580e-06 -1.21598117e-06 4.59036468e-08] ... [ 3.12084178e-09 -2.46888958e-10 -5.84882580e-06 ... 1.00019107e+00 -2.03342837e-04 -1.36954855e-08] [-5.81064929e-10 -1.06064273e-09 -1.21598117e-06 ... -2.03342837e-04 9.99262427e-01 1.18264754e-09] [ 3.70130091e-02 -7.65567973e-03 4.59036468e-08 ... -1.36954855e-08 1.18264754e-09 8.97215950e-01]]
C
Check numerically that MOs are orthonormal, with cusp fitting
In this example, we will compute numerically the overlap between the molecular orbitals:
\[ S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r}) \text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k) \phi_j(\mathbf{r}_k) \delta \mathbf{r} \] \[ S_{ij} = \langle \phi_i | \phi_j \rangle \sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle \langle \mathbf{r}_k | \phi_j \rangle \]
We apply the cusp fitting procedure, so the MOs might deviate slightly from orthonormality.
#include <qmckl.h>
#include <stdio.h>
#include <string.h>
//#include <time.h>
#include <sys/time.h>
int main(int argc, char** argv)
{
const char* trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5";
qmckl_exit_code rc = QMCKL_SUCCESS;
First, we create a context for the QMCkl calculation, and load the
wave function stored in h2o_5z.h5 inside it. It is a Hartree-Fock
determinant for the water molecule in the cc-pV5Z basis set.
qmckl_context context = qmckl_context_create();
rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename));
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error reading TREXIO file:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}We impose the electron-nucleus cusp fitting to occur when the electrons are close to the nuclei. The critical distance is 0.5 atomic units for hydrogens and 0.1 for the oxygen. To identify which atom is an oxygen and which are hydrogens, we fetch the nuclear charges from the context.
int64_t nucl_num;
rc = qmckl_get_nucleus_num(context, &nucl_num);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting nucl_num:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}
double nucl_charge[nucl_num];
rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0]), nucl_num);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting nucl_charge:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}
double r_cusp[nucl_num];
for (size_t i=0 ; i<nucl_num ; ++i) {
switch ((int) nucl_charge[i]) {
case 1:
r_cusp[i] = 0.5;
break;
case 8:
r_cusp[i] = 0.1;
break;
}
}
rc = qmckl_set_mo_basis_r_cusp(context, &(r_cusp[0]), nucl_num);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error setting r_cusp:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}We now define the grid points $\mathbf{r}_k$ as a regular grid around the molecule. We fetch the nuclear coordinates from the context,
double nucl_coord[nucl_num][3];
rc = qmckl_get_nucleus_coord(context, 'N', &(nucl_coord[0][0]), nucl_num*3);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting nucl_coord:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}
for (size_t i=0 ; i<nucl_num ; ++i) {
printf("%d %+f %+f %+f\n",
(int32_t) nucl_charge[i],
nucl_coord[i][0],
nucl_coord[i][1],
nucl_coord[i][2]);
}8 +0.000000 +0.000000 +0.000000 1 -1.430429 +0.000000 -1.107157 1 +1.430429 +0.000000 -1.107157
and compute the coordinates of the grid points:
size_t nx[3] = { 120, 120, 120 };
double shift[3] = {5.,5.,5.};
int64_t point_num = nx[0] * nx[1] * nx[2];
double rmin[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
double rmax[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
for (size_t i=0 ; i<nucl_num ; ++i) {
for (int j=0 ; j<3 ; ++j) {
rmin[j] = nucl_coord[i][j] < rmin[j] ? nucl_coord[i][j] : rmin[j];
rmax[j] = nucl_coord[i][j] > rmax[j] ? nucl_coord[i][j] : rmax[j];
}
}
rmin[0] -= shift[0]; rmin[1] -= shift[1]; rmin[2] -= shift[2];
rmax[0] += shift[0]; rmax[1] += shift[1]; rmax[2] += shift[2];
double step[3];
double* linspace[3];
for (int i=0 ; i<3 ; ++i) {
linspace[i] = (double*) calloc( sizeof(double), nx[i] );
if (linspace[i] == NULL) {
fprintf(stderr, "Allocation failed (linspace)\n");
exit(1);
}
step[i] = (rmax[i] - rmin[i]) / ((double) (nx[i]-1));
for (size_t j=0 ; j<nx[i] ; ++j) {
linspace[i][j] = rmin[i] + j*step[i];
}
}
double dr = step[0] * step[1] * step[2];Now the grid is ready, we can create the list of grid points $\mathbf{r}_k$ on which the MOs $\phi_i$ will be evaluated, and transfer them to the QMCkl context:
double* point = (double*) calloc(sizeof(double), 3*point_num);
if (point == NULL) {
fprintf(stderr, "Allocation failed (point)\n");
exit(1);
}
size_t m = 0;
for (size_t i=0 ; i<nx[0] ; ++i) {
for (size_t j=0 ; j<nx[1] ; ++j) {
for (size_t k=0 ; k<nx[2] ; ++k) {
point[m] = linspace[0][i];
m++;
point[m] = linspace[1][j];
m++;
point[m] = linspace[2][k];
m++;
}
}
}
rc = qmckl_set_point(context, 'N', point_num, point, (point_num*3));
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error setting points:\n%s\n", qmckl_string_of_error(rc));
exit(1);
}Then, we evaluate all the MOs at the grid points (and time the execution), and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle = \phi_i(\mathbf{r}_k)$.
int64_t mo_num;
rc = qmckl_get_mo_basis_mo_num(context, &mo_num);
long before, after;
struct timeval timecheck;
double* mo_value = (double*) calloc(sizeof(double), point_num*mo_num);
if (mo_value == NULL) {
fprintf(stderr, "Allocation failed (mo_value)\n");
exit(1);
}
gettimeofday(&timecheck, NULL);
before = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num*mo_num);
if (rc != QMCKL_SUCCESS) {
fprintf(stderr, "Error getting mo_value)\n");
exit(1);
}
gettimeofday(&timecheck, NULL);
after = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
printf("Number of MOs: %ld\n", mo_num);
printf("Number of grid points: %ld\n", point_num);
printf("Execution time : %f seconds\n", (after - before)*1.e-3);Number of MOs: 201 Number of grid points: 1728000 Execution time : 5.608000 seconds
and finally we compute the overlap between all the MOs as $M.M^\dagger$.
double* overlap = (double*) malloc (mo_num*mo_num*sizeof(double));
rc = qmckl_dgemm(context, 'N', 'T', mo_num, mo_num, point_num, dr,
mo_value, mo_num, mo_value, mo_num, 0.0,
overlap, mo_num);
for (size_t i=0 ; i<mo_num ; ++i) {
printf("%4ld", i);
for (size_t j=0 ; j<mo_num ; ++j) {
printf(" %f", overlap[i*mo_num+j]);
}
printf("\n");
}
}0 0.988765 0.002336 0.000000 -0.000734 0.000000 0.000530 0.000000 0.000446 0.000000 -0.000000 -0.000511 -0.000000 -0.000267 0.000000 0.000000 0.001007 0.000000 0.000168 -0.000000 -0.000000 -0.000670 -0.000000 0.000000 -0.000251 -0.000261 -0.000000 -0.000000 -0.000000 -0.000397 -0.000000 -0.000810 0.000000 0.000231 -0.000000 -0.000000 0.000000 -0.000000 ... 200 0.039017 -0.013066 -0.000000 -0.001935 -0.000000 -0.003829 -0.000000 0.000996 -0.000000 0.000000 -0.003733 0.000000 0.000065 -0.000000 -0.000000 -0.002220 -0.000000 -0.001961 0.000000 0.000000 -0.004182 0.000000 -0.000000 -0.000165 -0.002445 0.000000 -0.000000 0.000000 0.001985 0.000000 0.001685 -0.000000 -0.002899 0.000000 0.000000 0.000000 -0.000000 0.002591 0.000000 -0.000000 0.000000 0.002385 0.000000 -0.011086 0.000000 -0.003885 0.000000 -0.000000 0.003602 -0.000000 0.000000 -0.003241 0.000000 0.000000 0.002613 -0.007344 -0.000000 -0.000000 0.000000 0.000017 0.000000 0.000000 0.000000 -0.008719 0.000000 -0.001358 -0.003233 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.003778 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.001190 0.000000 0.000000 -0.000000 0.005578 -0.000000 -0.001502 0.003899 -0.000000 -0.000000 0.000000 -0.003291 -0.001775 -0.000000 -0.002374 0.000000 -0.000000 -0.000000 -0.000000 -0.001290 -0.000000 0.002178 0.000000 0.000000 0.000000 -0.001252 0.000000 -0.000000 -0.000926 0.000000 -0.000000 -0.013130 -0.000000 0.012124 0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.025194 0.000343 -0.000000 0.000000 -0.000000 -0.004421 0.000000 0.000000 -0.000599 -0.000000 0.005289 0.000000 -0.000000 0.012826 -0.000000 0.000000 0.006190 0.000000 0.000000 -0.000000 0.000000 -0.000321 0.000000 -0.000000 -0.000000 0.000000 -0.000000 0.001499 -0.006629 0.000000 0.000000 0.000000 -0.000000 0.008737 -0.000000 0.006880 0.000000 -0.001851 -0.000000 -0.000000 0.000000 -0.007464 0.000000 0.010298 -0.000000 -0.000000 -0.000000 -0.000000 -0.000000 0.000000 0.000540 0.000000 -0.006616 -0.000000 0.000000 -0.002927 -0.000000 0.000000 0.010352 0.000000 -0.003103 -0.000000 -0.007640 -0.000000 -0.000000 0.005302 0.000000 0.000000 -0.000000 -0.000000 -0.010181 0.000000 -0.001108 0.000000 0.000000 -0.000000 0.000000 0.000000 -0.000998 -0.009754 0.013562 0.000000 -0.000000 0.887510
Fortran
Checking errors
All QMCkl functions return an error code. A convenient way to handle errors is to write an error-checking function that displays the error in text format and exits the program.
subroutine qmckl_check_error(rc, message)
use qmckl
implicit none
integer(qmckl_exit_code), intent(in) :: rc
character(len=*) , intent(in) :: message
character(len=128) :: str_buffer
if (rc /= QMCKL_SUCCESS) then
print *, message
call qmckl_string_of_error(rc, str_buffer)
print *, str_buffer
call exit(rc)
end if
end subroutine qmckl_check_errorComputing an atomic orbital on a grid
The following program, in Fortran, computes the values of an atomic orbital on a regular 3-dimensional grid. The 100^3 grid points are automatically defined, such that the molecule fits in a box with 5 atomic units in the borders.
This program uses the qmckl_check_error function defined above.
To use this program, run
$ ao_grid <trexio_file> <AO_id> <point_num><<qmckl_check_error>>
program ao_grid
use qmckl
implicit none
integer(qmckl_context) :: qmckl_ctx ! QMCkl context
integer(qmckl_exit_code) :: rc ! Exit code of QMCkl functions
character(len=128) :: trexio_filename
character(len=128) :: str_buffer
integer :: ao_id
integer :: point_num_x
integer(c_int64_t) :: nucl_num
double precision, allocatable :: nucl_coord(:,:)
integer(c_int64_t) :: point_num
integer(c_int64_t) :: ao_num
integer(c_int64_t) :: ipoint, i, j, k
double precision :: x, y, z, dr(3)
double precision :: rmin(3), rmax(3)
double precision, allocatable :: points(:,:)
double precision, allocatable :: ao_vgl(:,:,:)Start by fetching the command-line arguments:
if (iargc() /= 3) then
print *, 'Syntax: ao_grid <trexio_file> <AO_id> <point_num>'
call exit(-1)
end if
call getarg(1, trexio_filename)
call getarg(2, str_buffer)
read(str_buffer, *) ao_id
call getarg(3, str_buffer)
read(str_buffer, *) point_num_x
if (point_num_x < 0 .or. point_num_x > 300) then
print *, 'Error: 0 < point_num < 300'
call exit(-1)
end ifCreate the QMCkl context and initialize it with the wave function present in the TREXIO file:
qmckl_ctx = qmckl_context_create()
rc = qmckl_trexio_read(qmckl_ctx, trexio_filename, 1_8*len(trim(trexio_filename)))
call qmckl_check_error(rc, 'Read TREXIO')
We need to check that ao_id is in the range, so we get the total
number of AOs from QMCkl:
rc = qmckl_get_ao_basis_ao_num(qmckl_ctx, ao_num)
call qmckl_check_error(rc, 'Getting ao_num')
if (ao_id < 0 .or. ao_id > ao_num) then
print *, 'Error: 0 < ao_id < ', ao_num
call exit(-1)
end ifNow we will compute the limits of the box in which the molecule fits. For that, we first need to ask QMCkl the coordinates of nuclei.
rc = qmckl_get_nucleus_num(qmckl_ctx, nucl_num)
call qmckl_check_error(rc, 'Get nucleus num')
allocate( nucl_coord(3, nucl_num) )
rc = qmckl_get_nucleus_coord(qmckl_ctx, 'N', nucl_coord, 3_8*nucl_num)
call qmckl_check_error(rc, 'Get nucleus coord')We now compute the coordinates of opposite points of the box, and the distance between points along the 3 directions:
rmin(1) = minval( nucl_coord(1,:) ) - 5.d0
rmin(2) = minval( nucl_coord(2,:) ) - 5.d0
rmin(3) = minval( nucl_coord(3,:) ) - 5.d0
rmax(1) = maxval( nucl_coord(1,:) ) + 5.d0
rmax(2) = maxval( nucl_coord(2,:) ) + 5.d0
rmax(3) = maxval( nucl_coord(3,:) ) + 5.d0
dr(1:3) = (rmax(1:3) - rmin(1:3)) / dble(point_num_x-1)We now produce the list of point coordinates where the AO will be evaluated:
point_num = point_num_x**3
allocate( points(point_num, 3) )
ipoint=0
z = rmin(3)
do k=1,point_num_x
y = rmin(2)
do j=1,point_num_x
x = rmin(1)
do i=1,point_num_x
ipoint = ipoint+1
points(ipoint,1) = x
points(ipoint,2) = y
points(ipoint,3) = z
x = x + dr(1)
end do
y = y + dr(2)
end do
z = z + dr(3)
end doWe give the points to QMCkl:
rc = qmckl_set_point(qmckl_ctx, 'T', point_num, points, size(points)*1_8 )
call qmckl_check_error(rc, 'Setting points')We allocate the space required to retrieve the values, gradients and Laplacian of all AOs, and ask to retrieve the values of the AOs computed at the point positions.
allocate( ao_vgl(ao_num, 5, point_num) )
rc = qmckl_get_ao_basis_ao_vgl(qmckl_ctx, ao_vgl, ao_num*5_8*point_num)
call qmckl_check_error(rc, 'Setting points')We finally print the value and Laplacian of the AO:
do ipoint=1, point_num
print '(3(F10.6,X),2(E20.10,X))', points(ipoint, 1:3), ao_vgl(ao_id,1,ipoint), ao_vgl(ao_id,5,ipoint)
end dodeallocate( nucl_coord, points, ao_vgl )
end program ao_grid