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876 lines
26 KiB
Org Mode
876 lines
26 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 provide hands-on examples to demonstrate the capabilities
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of the QMCkl library. We furnish code samples in C, Fortran, and Python,
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serving as exhaustive tutorials for effectively leveraging QMCkl.
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For simplicity, we assume that the wave function parameters are stored in a
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[[https://github.com/TREX-CoE/trexio][TREXIO]] file.
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* Overlap matrix in the MO basis
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The focal point of this example is the numerical evaluation of the overlap
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matrix in the MO basis. Utilizing QMCkl, we approximate the MOs at
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discrete grid points to compute the overlap matrix \( S_{ij} \) as follows:
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\[
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S_{ij} = \int \phi_i(\mathbf{r})\, \phi_j(\mathbf{r}) \text{d}\mathbf{r} \approx
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\sum_k \phi_i(\mathbf{r}_k)\, \phi_j(\mathbf{r}_k) \delta\mathbf{r}
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\]
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The code starts by reading a wave function from a TREXIO file. This is
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accomplished using the ~qmckl_trexio_read~ function, which populates a
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~qmckl_context~ with the necessary wave function parameters. The context
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serves as the primary interface for interacting with the QMCkl library,
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encapsulating the state and configurations of the system.
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Subsequently, the code retrieves various attributes such as the number of
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nuclei ~nucl_num~ and coordinates ~nucl_coord~.
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These attributes are essential for setting up the integration grid.
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The core of the example lies in the numerical computation of the overlap
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matrix. To achieve this, the code employs a regular grid in three-dimensional
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space, and the grid points are then populated into the ~qmckl_context~ using
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the ~qmckl_set_point~ function.
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The MO values at these grid points are computed using the
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~qmckl_get_mo_basis_mo_value~ function. These values are then used to
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calculate the overlap matrix through a matrix multiplication operation
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facilitated by the ~qmckl_dgemm~ function.
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The code is also instrumented to measure the execution time for the MO
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value computation, providing an empirical assessment of the computational
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efficiency. Error handling is robustly implemented at each stage to ensure the
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reliability of the simulation.
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In summary, this example serves as a holistic guide for leveraging the QMCkl
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library, demonstrating its ease of use. It provides a concrete starting point
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for researchers and developers interested in integrating QMCkl into their QMC
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code.
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** Python
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:PROPERTIES:
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:header-args: :tangle mo_ortho.py
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:END:
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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) ).T # Transpose to get mo_num x point_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 : 5.577778577804565 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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$M.M^\dagger$.
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#+begin_src python :exports code
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overlap = mo_value @ mo_value.T * 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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In this example, electron-nucleus cusp fitting is added.
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:PROPERTIES:
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:header-args: :tangle mo_ortho.c
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:END:
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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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#include <string.h>
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#include <sys/time.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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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 c :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]), nucl_num);
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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_cusp[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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r_cusp[i] = 0.5;
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break;
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case 8:
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r_cusp[i] = 0.1;
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break;
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}
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}
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rc = qmckl_set_mo_basis_r_cusp(context, &(r_cusp[0]), nucl_num);
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error setting r_cusp:\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 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 c :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",
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(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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}
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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 c :exports code
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size_t nx[3] = { 120, 120, 120 };
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double shift[3] = {5.,5.,5.};
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int64_t point_num = nx[0] * nx[1] * nx[2];
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double rmin[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
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double rmax[3] = { nucl_coord[0][0], nucl_coord[0][1], nucl_coord[0][2] } ;
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for (size_t i=0 ; i<nucl_num ; ++i) {
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for (int j=0 ; j<3 ; ++j) {
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rmin[j] = nucl_coord[i][j] < rmin[j] ? nucl_coord[i][j] : rmin[j];
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rmax[j] = nucl_coord[i][j] > rmax[j] ? nucl_coord[i][j] : rmax[j];
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}
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}
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rmin[0] -= shift[0]; rmin[1] -= shift[1]; rmin[2] -= shift[2];
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rmax[0] += shift[0]; rmax[1] += shift[1]; rmax[2] += shift[2];
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double step[3];
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double* linspace[3];
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for (int i=0 ; i<3 ; ++i) {
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linspace[i] = (double*) calloc( sizeof(double), nx[i] );
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if (linspace[i] == NULL) {
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fprintf(stderr, "Allocation failed (linspace)\n");
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exit(1);
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}
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step[i] = (rmax[i] - rmin[i]) / ((double) (nx[i]-1));
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for (size_t j=0 ; j<nx[i] ; ++j) {
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linspace[i][j] = rmin[i] + j*step[i];
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}
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}
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double dr = step[0] * step[1] * step[2];
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#+end_src
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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 c :exports code
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double* point = (double*) calloc(sizeof(double), 3*point_num);
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if (point == NULL) {
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fprintf(stderr, "Allocation failed (point)\n");
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exit(1);
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}
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size_t m = 0;
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for (size_t i=0 ; i<nx[0] ; ++i) {
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for (size_t j=0 ; j<nx[1] ; ++j) {
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for (size_t k=0 ; k<nx[2] ; ++k) {
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point[m] = linspace[0][i];
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m++;
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point[m] = linspace[1][j];
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m++;
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point[m] = linspace[2][k];
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m++;
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}
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}
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}
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rc = qmckl_set_point(context, 'N', point_num, point, (point_num*3));
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error setting points:\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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#+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 $M_{ki} = \langle \mathbf{r}_k | \phi_i
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\rangle = \phi_i(\mathbf{r}_k)$.
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#+begin_src c :exports code
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int64_t mo_num;
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rc = qmckl_get_mo_basis_mo_num(context, &mo_num);
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long before, after;
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struct timeval timecheck;
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double* mo_value = (double*) calloc(sizeof(double), point_num*mo_num);
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if (mo_value == NULL) {
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fprintf(stderr, "Allocation failed (mo_value)\n");
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exit(1);
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}
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gettimeofday(&timecheck, NULL);
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before = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
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rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num*mo_num);
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if (rc != QMCKL_SUCCESS) {
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fprintf(stderr, "Error getting mo_value)\n");
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exit(1);
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}
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gettimeofday(&timecheck, NULL);
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after = (long)timecheck.tv_sec * 1000 + (long)timecheck.tv_usec / 1000;
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printf("Number of MOs: %ld\n", (long) mo_num);
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printf("Number of grid points: %ld\n", (long) point_num);
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printf("Execution time : %f seconds\n", (after - before)*1.e-3);
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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 : 5.608000 seconds
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#+end_example
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and finally we compute the overlap between all the MOs as
|
|
$M.M^\dagger$.
|
|
|
|
#+begin_src c :exports code
|
|
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");
|
|
}
|
|
|
|
// Clean-up and exit
|
|
free(mo_value);
|
|
free(overlap);
|
|
|
|
rc = qmckl_context_destroy(context);
|
|
if (rc != QMCKL_SUCCESS) {
|
|
fprintf(stderr, "Error destroying context)\n");
|
|
exit(1);
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
#+end_src
|
|
|
|
#+begin_example
|
|
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
|
|
#+end_example
|
|
|
|
|
|
** Fortran
|
|
Here is the same piece of code translated in Fortran
|
|
#+begin_src f90
|
|
#include <qmckl_f.F90>
|
|
|
|
program main
|
|
use iso_c_binding
|
|
use qmckl
|
|
implicit none
|
|
|
|
! Declare variables
|
|
integer :: argc
|
|
character(128) :: trexio_filename, err_msg
|
|
integer(qmckl_exit_code) :: rc
|
|
integer(qmckl_context) :: context
|
|
integer*8 :: nucl_num, mo_num, point_num
|
|
double precision, allocatable :: nucl_coord(:,:)
|
|
integer*8 :: nx(3)
|
|
double precision, dimension(3) :: shift, step, rmin, rmax
|
|
double precision, allocatable :: mo_value(:,:), overlap(:,:), point(:), linspace(:,:)
|
|
double precision :: before, after, dr
|
|
integer*8 :: i,j,k,m
|
|
|
|
! Initialize variables
|
|
err_msg = ' '
|
|
argc = command_argument_count()
|
|
if (argc /= 1) then
|
|
print *, "Usage: ./program <TREXIO filename>"
|
|
stop -1
|
|
end if
|
|
call get_command_argument(1, trexio_filename)
|
|
rc = QMCKL_SUCCESS
|
|
|
|
! Create a QMCkl context
|
|
context = qmckl_context_create()
|
|
|
|
! Read the TREXIO file into the context
|
|
rc = qmckl_trexio_read(context, trim(trexio_filename), len(trexio_filename)*1_8)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error reading TREXIO file:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
! Retrieve the number of nuclei
|
|
rc = qmckl_get_nucleus_num(context, nucl_num)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error getting nucl_num:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
! Retrieve the nuclear coordinates
|
|
allocate(nucl_coord(3, nucl_num))
|
|
rc = qmckl_get_nucleus_coord(context, 'N', nucl_coord, nucl_num * 3_8)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error getting nucl_coord:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
! Retrieve the number of MOs
|
|
rc = qmckl_get_mo_basis_mo_num(context, mo_num)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error getting mo_num:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
! Initialize grid points for the calculation
|
|
nx = (/ 120, 120, 120 /)
|
|
shift = (/ 5.d0, 5.d0, 5.d0 /)
|
|
point_num = nx(1) * nx(2) * nx(3)
|
|
|
|
! Initialize rmin and rmax
|
|
rmin = nucl_coord(:,1)
|
|
rmax = nucl_coord(:,1)
|
|
|
|
! Update rmin and rmax based on nucl_coord
|
|
do i = 1, 3
|
|
do j = 1, nucl_num
|
|
rmin(i) = min(nucl_coord(i,j), rmin(i))
|
|
rmax(i) = max(nucl_coord(i,j), rmax(i))
|
|
end do
|
|
end do
|
|
|
|
! Apply shift
|
|
rmin = rmin - shift
|
|
rmax = rmax + shift
|
|
|
|
! Initialize linspace and step
|
|
allocate(linspace(3, maxval(nx)))
|
|
|
|
do i = 1, 3
|
|
step(i) = (rmax(i) - rmin(i)) / real(nx(i) - 1, 8)
|
|
do j = 1, nx(i)
|
|
linspace(i, j) = rmin(i) + (j - 1) * step(i)
|
|
end do
|
|
end do
|
|
|
|
! Initialize point array
|
|
allocate(point(3 * point_num))
|
|
m = 1
|
|
do i = 1, nx(1)
|
|
do j = 1, nx(2)
|
|
do k = 1, nx(3)
|
|
point(m) = linspace(1, i); m = m + 1
|
|
point(m) = linspace(2, j); m = m + 1
|
|
point(m) = linspace(3, k); m = m + 1
|
|
end do
|
|
end do
|
|
end do
|
|
|
|
deallocate(linspace)
|
|
|
|
|
|
! Set points in QMCKL context
|
|
rc = qmckl_set_point(context, 'N', point_num, point, point_num * 3)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error setting point:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
|
|
|
|
|
|
! Perform the actual calculation and measure the time taken
|
|
call cpu_time(before)
|
|
allocate(mo_value(point_num, mo_num))
|
|
rc = qmckl_get_mo_basis_mo_value(context, mo_value, point_num * mo_num)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error getting mo_value:", err_msg
|
|
stop
|
|
end if
|
|
call cpu_time(after)
|
|
|
|
write(*,*) "Number of MOs:", mo_num
|
|
write(*,*) "Number of grid points:", point_num
|
|
write(*,*) "Execution time:", (after - before), "seconds"
|
|
|
|
! Compute the overlap matrix
|
|
dr = step(1) * step(2) * step(3)
|
|
|
|
allocate(overlap(mo_num, mo_num))
|
|
rc = qmckl_dgemm(context, 'N', 'T', mo_num, mo_num, point_num, dr, &
|
|
mo_value, mo_num, mo_value, mo_num, 0.d0, overlap, mo_num)
|
|
|
|
! Print the overlap matrix
|
|
do i = 1, mo_num
|
|
write(*,'(i4)', advance='no') i
|
|
do j = 1, mo_num
|
|
write(*,'(f8.4)', advance='no') overlap(i, j)
|
|
end do
|
|
write(*,*)
|
|
end do
|
|
|
|
! Clean-up and exit
|
|
deallocate(mo_value, overlap)
|
|
rc = qmckl_context_destroy(context)
|
|
if (rc /= QMCKL_SUCCESS) then
|
|
call qmckl_string_of_error(rc, err_msg)
|
|
write(*,*) "Error destroying context:", err_msg
|
|
stop -1
|
|
end if
|
|
|
|
end program main
|
|
#+end_src
|
|
* 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.
|
|
|
|
#+NAME: qmckl_check_error
|
|
#+begin_src f90
|
|
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_error
|
|
#+end_src
|
|
|
|
** Computing an atomic orbital on a grid
|
|
:PROPERTIES:
|
|
:header-args: :tangle ao_grid.f90
|
|
:END:
|
|
|
|
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
|
|
|
|
#+begin_src bash :tangle no :exports code
|
|
$ ao_grid <trexio_file> <AO_id> <point_num>
|
|
#+end_src
|
|
|
|
|
|
#+begin_src f90 :noweb yes
|
|
<<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(:,:,:)
|
|
#+end_src
|
|
|
|
Start by fetching the command-line arguments:
|
|
|
|
#+begin_src f90
|
|
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 if
|
|
#+end_src
|
|
|
|
Create the QMCkl context and initialize it with the wave function
|
|
present in the TREXIO file:
|
|
|
|
#+begin_src f90
|
|
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')
|
|
#+end_src
|
|
|
|
We need to check that ~ao_id~ is in the range, so we get the total
|
|
number of AOs from QMCkl:
|
|
|
|
#+begin_src f90
|
|
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 if
|
|
#+end_src
|
|
|
|
Now 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.
|
|
|
|
#+begin_src f90
|
|
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')
|
|
#+end_src
|
|
|
|
We now compute the coordinates of opposite points of the box, and
|
|
the distance between points along the 3 directions:
|
|
|
|
#+begin_src f90
|
|
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)
|
|
#+end_src
|
|
|
|
We now produce the list of point coordinates where the AO will be
|
|
evaluated:
|
|
|
|
#+begin_src f90
|
|
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 do
|
|
#+end_src
|
|
|
|
We give the points to QMCkl:
|
|
|
|
#+begin_src f90
|
|
rc = qmckl_set_point(qmckl_ctx, 'T', point_num, points, size(points)*1_8 )
|
|
call qmckl_check_error(rc, 'Setting points')
|
|
#+end_src
|
|
|
|
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.
|
|
|
|
#+begin_src f90
|
|
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')
|
|
#+end_src
|
|
|
|
We finally print the value and Laplacian of the AO:
|
|
|
|
#+begin_src f90
|
|
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 do
|
|
#+end_src
|
|
|
|
#+begin_src f90
|
|
deallocate( nucl_coord, points, ao_vgl )
|
|
end program ao_grid
|
|
#+end_src
|
|
|