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361 lines
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Org Mode
361 lines
10 KiB
Org Mode
#+TITLE: Code examples
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#+SETUPFILE: ../tools/theme.setup
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#+INCLUDE: ../tools/lib.org
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In this section, we present examples of usage of QMCkl.
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For simplicity, we assume that the wave function parameters are stored
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in a [[https://github.com/TREX-CoE/trexio][TREXIO]] file.
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* Python
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** Check numerically that MOs are orthonormal
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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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#+begin_src python :exports code
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import numpy as np
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import qmckl
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#+end_src
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#+RESULTS:
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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 python :exports code
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trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5"
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context = qmckl.context_create()
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qmckl.trexio_read(context, trexio_filename)
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#+end_src
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#+RESULTS:
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: None
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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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#+begin_src python :exports code
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nucl_num = qmckl.get_nucleus_num(context)
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nucl_charge = qmckl.get_nucleus_charge(context, nucl_num)
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nucl_coord = qmckl.get_nucleus_coord(context, 'N', nucl_num*3)
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nucl_coord = np.reshape(nucl_coord, (3, nucl_num))
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for i in range(nucl_num):
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print("%d %+f %+f %+f"%(int(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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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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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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* Fortran
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** Checking errors
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All QMCkl functions return an error code. A convenient way to handle
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errors is to write an error-checking function that displays the
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error in text format and exits the program.
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#+NAME: qmckl_check_error
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#+begin_src f90
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subroutine qmckl_check_error(rc, message)
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use qmckl
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implicit none
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integer(qmckl_exit_code), intent(in) :: rc
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character(len=*) , intent(in) :: message
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character(len=128) :: str_buffer
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if (rc /= QMCKL_SUCCESS) then
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print *, message
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call qmckl_string_of_error(rc, str_buffer)
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print *, str_buffer
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call exit(rc)
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end if
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end subroutine qmckl_check_error
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#+end_src
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** Computing an atomic orbital on a grid
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:PROPERTIES:
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:header-args: :tangle ao_grid.f90
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:END:
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The following program, in Fortran, computes the values of an atomic
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orbital on a regular 3-dimensional grid. The 100^3 grid points are
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automatically defined, such that the molecule fits in a box with 5
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atomic units in the borders.
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This program uses the ~qmckl_check_error~ function defined above.
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To use this program, run
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#+begin_src bash :tangle no :exports code
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$ ao_grid <trexio_file> <AO_id> <point_num>
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#+end_src
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#+begin_src f90 :noweb yes
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<<qmckl_check_error>>
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program ao_grid
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use qmckl
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implicit none
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integer(qmckl_context) :: qmckl_ctx ! QMCkl context
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integer(qmckl_exit_code) :: rc ! Exit code of QMCkl functions
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character(len=128) :: trexio_filename
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character(len=128) :: str_buffer
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integer :: ao_id
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integer :: point_num_x
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integer(c_int64_t) :: nucl_num
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double precision, allocatable :: nucl_coord(:,:)
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integer(c_int64_t) :: point_num
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integer(c_int64_t) :: ao_num
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integer(c_int64_t) :: ipoint, i, j, k
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double precision :: x, y, z, dr(3)
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double precision :: rmin(3), rmax(3)
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double precision, allocatable :: points(:,:)
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double precision, allocatable :: ao_vgl(:,:,:)
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#+end_src
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Start by fetching the command-line arguments:
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#+begin_src f90
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if (iargc() /= 3) then
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print *, 'Syntax: ao_grid <trexio_file> <AO_id> <point_num>'
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call exit(-1)
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end if
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call getarg(1, trexio_filename)
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call getarg(2, str_buffer)
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read(str_buffer, *) ao_id
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call getarg(3, str_buffer)
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read(str_buffer, *) point_num_x
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if (point_num_x < 0 .or. point_num_x > 300) then
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print *, 'Error: 0 < point_num < 300'
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call exit(-1)
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end if
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#+end_src
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Create the QMCkl context and initialize it with the wave function
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present in the TREXIO file:
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#+begin_src f90
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qmckl_ctx = qmckl_context_create()
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rc = qmckl_trexio_read(qmckl_ctx, trexio_filename, 1_8*len(trim(trexio_filename)))
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call qmckl_check_error(rc, 'Read TREXIO')
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#+end_src
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We need to check that ~ao_id~ is in the range, so we get the total
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number of AOs from QMCkl:
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#+begin_src f90
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rc = qmckl_get_ao_basis_ao_num(qmckl_ctx, ao_num)
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call qmckl_check_error(rc, 'Getting ao_num')
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if (ao_id < 0 .or. ao_id > ao_num) then
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print *, 'Error: 0 < ao_id < ', ao_num
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call exit(-1)
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end if
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#+end_src
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Now we will compute the limits of the box in which the molecule fits.
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For that, we first need to ask QMCkl the coordinates of nuclei.
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#+begin_src f90
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rc = qmckl_get_nucleus_num(qmckl_ctx, nucl_num)
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call qmckl_check_error(rc, 'Get nucleus num')
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allocate( nucl_coord(3, nucl_num) )
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rc = qmckl_get_nucleus_coord(qmckl_ctx, 'N', nucl_coord, 3_8*nucl_num)
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call qmckl_check_error(rc, 'Get nucleus coord')
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#+end_src
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We now compute the coordinates of opposite points of the box, and
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the distance between points along the 3 directions:
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#+begin_src f90
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rmin(1) = minval( nucl_coord(1,:) ) - 5.d0
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rmin(2) = minval( nucl_coord(2,:) ) - 5.d0
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rmin(3) = minval( nucl_coord(3,:) ) - 5.d0
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rmax(1) = maxval( nucl_coord(1,:) ) + 5.d0
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rmax(2) = maxval( nucl_coord(2,:) ) + 5.d0
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rmax(3) = maxval( nucl_coord(3,:) ) + 5.d0
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dr(1:3) = (rmax(1:3) - rmin(1:3)) / dble(point_num_x-1)
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#+end_src
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We now produce the list of point coordinates where the AO will be
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evaluated:
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#+begin_src f90
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point_num = point_num_x**3
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allocate( points(point_num, 3) )
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ipoint=0
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z = rmin(3)
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do k=1,point_num_x
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y = rmin(2)
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do j=1,point_num_x
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x = rmin(1)
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do i=1,point_num_x
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ipoint = ipoint+1
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points(ipoint,1) = x
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points(ipoint,2) = y
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points(ipoint,3) = z
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x = x + dr(1)
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end do
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y = y + dr(2)
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end do
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z = z + dr(3)
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end do
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#+end_src
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We give the points to QMCkl:
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#+begin_src f90
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rc = qmckl_set_point(qmckl_ctx, 'T', point_num, points, size(points)*1_8 )
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call qmckl_check_error(rc, 'Setting points')
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#+end_src
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We allocate the space required to retrieve the values, gradients and
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Laplacian of all AOs, and ask to retrieve the values of the
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AOs computed at the point positions.
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#+begin_src f90
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allocate( ao_vgl(ao_num, 5, point_num) )
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rc = qmckl_get_ao_basis_ao_vgl(qmckl_ctx, ao_vgl, ao_num*5_8*point_num)
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call qmckl_check_error(rc, 'Setting points')
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#+end_src
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We finally print the value and Laplacian of the AO:
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#+begin_src f90
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do ipoint=1, point_num
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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)
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end do
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#+end_src
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#+begin_src f90
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deallocate( nucl_coord, points, ao_vgl )
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end program ao_grid
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#+end_src
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