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Version 0.4.1
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@ -35,7 +35,7 @@
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AC_PREREQ([2.69])
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AC_INIT([qmckl],[0.3.1],[https://github.com/TREX-CoE/qmckl/issues],[],[https://trex-coe.github.io/qmckl/index.html])
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AC_INIT([qmckl],[0.4.1],[https://github.com/TREX-CoE/qmckl/issues],[],[https://trex-coe.github.io/qmckl/index.html])
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AC_CONFIG_AUX_DIR([tools])
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AM_INIT_AUTOMAKE([subdir-objects color-tests parallel-tests silent-rules 1.11])
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@ -82,6 +82,223 @@ rmin = np.array( list([ np.min(nucl_coord[:,a]) for a in range(3) ]) )
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rmax = np.array( list([ np.max(nucl_coord[:,a]) for a in range(3) ]) )
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linspace = [ None for i in range(3) ]
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step = [ None for i in range(3) ]
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for a in range(3):
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linspace[a], step[a] = np.linspace(rmin[a]-shift[a],
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rmax[a]+shift[a],
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num=nx[a],
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retstep=True)
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dr = step[0] * step[1] * step[2]
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#+end_src
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#+RESULTS:
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Now the grid is ready, we can create the list of grid points
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$\mathbf{r}_k$ on which the MOs $\phi_i$ will be evaluated, and
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transfer them to the QMCkl context:
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#+begin_src python :exports code
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point = []
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for x in linspace[0]:
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for y in linspace[1]:
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for z in linspace[2]:
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point += [ [x, y, z] ]
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point = np.array(point)
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point_num = len(point)
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qmckl.set_point(context, 'N', point_num, np.reshape(point, (point_num*3)))
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#+end_src
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#+RESULTS:
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: None
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Then, we evaluate all the MOs at the grid points (and time the execution),
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and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle =
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\phi_i(\mathbf{r}_k)$.
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#+begin_src python :exports code
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import time
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mo_num = qmckl.get_mo_basis_mo_num(context)
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before = time.time()
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mo_value = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
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after = time.time()
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mo_value = np.reshape( mo_value, (point_num, mo_num) )
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print("Number of MOs: ", mo_num)
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print("Number of grid points: ", point_num)
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print("Execution time : ", (after - before), "seconds")
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#+end_src
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#+begin_example
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Number of MOs: 201
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Number of grid points: 1728000
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Execution time : 3.511528968811035 seconds
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#+end_example
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and finally we compute the overlap between all the MOs as
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$M^\dagger M$.
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#+begin_src python :exports code
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overlap = mo_value.T @ mo_value * dr
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print (overlap)
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#+end_src
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#+begin_example
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[[ 9.88693941e-01 2.34719693e-03 -1.50518232e-08 ... 3.12084178e-09
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-5.81064929e-10 3.70130091e-02]
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[ 2.34719693e-03 9.99509628e-01 3.18930040e-09 ... -2.46888958e-10
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-1.06064273e-09 -7.65567973e-03]
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[-1.50518232e-08 3.18930040e-09 9.99995073e-01 ... -5.84882580e-06
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-1.21598117e-06 4.59036468e-08]
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...
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[ 3.12084178e-09 -2.46888958e-10 -5.84882580e-06 ... 1.00019107e+00
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-2.03342837e-04 -1.36954855e-08]
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[-5.81064929e-10 -1.06064273e-09 -1.21598117e-06 ... -2.03342837e-04
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9.99262427e-01 1.18264754e-09]
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[ 3.70130091e-02 -7.65567973e-03 4.59036468e-08 ... -1.36954855e-08
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1.18264754e-09 8.97215950e-01]]
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#+end_example
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* C
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** Check numerically that MOs are orthonormal, with cusp fitting
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In this example, we will compute numerically the overlap
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between the molecular orbitals:
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\[
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S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
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\text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
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\phi_j(\mathbf{r}_k) \delta \mathbf{r}
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\]
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\[
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S_{ij} = \langle \phi_i | \phi_j \rangle
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\sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
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\langle \mathbf{r}_k | \phi_j \rangle
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\]
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We apply the cusp fitting procedure, so the MOs might deviate
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slightly from orthonormality.
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#+begin_src c :exports code
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#include <qmckl.h>
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#include <stdio.h>
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int main(int argc, char** argv)
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{
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const char* trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5";
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qmckl_exit_code rc = QMCKL_SUCCESS;
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#+end_src
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First, we create a context for the QMCkl calculation, and load the
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wave function stored in =h2o_5z.h5= inside it. It is a Hartree-Fock
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determinant for the water molecule in the cc-pV5Z basis set.
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#+begin_src c :exports code
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qmckl_context context = qmckl_context_create();
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if (context == NULL) {
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fprintf(stderr, "Error creating context\n");
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exit(1);
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}
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rc = qmckl_trexio_read(context, trexio_filename, strlen(trexio_filename));
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error reading TREXIO file:\n%s\n", qmckl_string_of_error(rc));
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exit(1);
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}
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#+end_src
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We impose the electron-nucleus cusp fitting to occur when the
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electrons are close to the nuclei. The critical distance
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is 0.5 atomic units for hydrogens and 0.1 for the oxygen.
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To identify which atom is an oxygen and which are hydrogens, we
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fetch the nuclear charges from the context.
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#+begin_src python :exports code
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int64_t nucl_num;
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rc = qmckl_get_nucleus_num(context, &nucl_num);
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error getting nucl_num:\n%s\n", qmckl_string_of_error(rc));
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exit(1);
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}
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double nucl_charge[nucl_num];
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rc = qmckl_get_nucleus_charge(context, &(nucl_charge[0]));
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error getting nucl_charge:\n%s\n", qmckl_string_of_error(rc));
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exit(1);
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}
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double r_c[nucl_num];
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for (size_t i=0 ; i<nucl_num ; ++i) {
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switch ((int) nucl_charge[i]) {
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case 1:
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nucl_charge[i] = 0.5;
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break;
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case 8:
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nucl_charge[i] = 0.1;
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break;
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}
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}
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#+end_src
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#+begin_src python :exports code
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double nucl_coord[nucl_num][3];
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rc = qmckl_get_nucleus_coord(context, 'N', &(nucl_coord[0][0]), nucl_num*3)
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error getting nucl_coord:\n%s\n", qmckl_string_of_error(rc));
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exit(1);
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}
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for (size_t i=0 ; i<nucl_num ; ++i) {
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printf("%d %+f %+f %+f\n", (int32_t) nucl_charge[i],
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nucl_coord[i][0],
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nucl_coord[i][1],
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nucl_coord[i][2]) );
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#+end_src
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#+begin_example
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8 +0.000000 +0.000000 +0.000000
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1 -1.430429 +0.000000 -1.107157
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1 +1.430429 +0.000000 -1.107157
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#+end_example
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We now define the grid points $\mathbf{r}_k$ as a regular grid around the
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molecule.
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We fetch the nuclear coordinates from the context,
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and compute the coordinates of the grid points:
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#+begin_src python :exports code
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nx = ( 120, 120, 120 )
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shift = np.array([5.,5.,5.])
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point_num = nx[0] * nx[1] * nx[2]
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rmin = np.array( list([ np.min(nucl_coord[:,a]) for a in range(3) ]) )
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rmax = np.array( list([ np.max(nucl_coord[:,a]) for a in range(3) ]) )
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linspace = [ None for i in range(3) ]
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step = [ None for i in range(3) ]
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for a in range(3):
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