mirror of
https://github.com/TREX-CoE/qmckl.git
synced 2024-07-03 09:56:10 +02:00
361 lines
10 KiB
Org Mode
361 lines
10 KiB
Org Mode
#+TITLE: Code examples
|
|
#+SETUPFILE: ../tools/theme.setup
|
|
#+INCLUDE: ../tools/lib.org
|
|
|
|
In this section, we present examples of usage of QMCkl.
|
|
For simplicity, we assume that the wave function parameters are stored
|
|
in a [[https://github.com/TREX-CoE/trexio][TREXIO]] file.
|
|
|
|
* Python
|
|
** Check numerically that MOs are orthonormal
|
|
|
|
In this example, we will compute numerically the overlap
|
|
between the molecular orbitals:
|
|
|
|
\[
|
|
S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
|
|
\text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
|
|
\phi_j(\mathbf{r}_k) \delta \mathbf{r}
|
|
\]
|
|
\[
|
|
S_{ij} = \langle \phi_i | \phi_j \rangle
|
|
\sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
|
|
\langle \mathbf{r}_k | \phi_j \rangle
|
|
\]
|
|
|
|
|
|
#+begin_src python :exports code
|
|
import numpy as np
|
|
import qmckl
|
|
#+end_src
|
|
|
|
#+RESULTS:
|
|
|
|
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.
|
|
|
|
#+begin_src python :exports code
|
|
trexio_filename = "..//share/qmckl/test_data/h2o_5z.h5"
|
|
|
|
context = qmckl.context_create()
|
|
qmckl.trexio_read(context, trexio_filename)
|
|
#+end_src
|
|
|
|
#+RESULTS:
|
|
: None
|
|
|
|
We now define the grid points $\mathbf{r}_k$ as a regular grid around the
|
|
molecule.
|
|
|
|
We fetch the nuclear coordinates from the context,
|
|
|
|
#+begin_src python :exports code
|
|
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]) )
|
|
#+end_src
|
|
|
|
#+begin_example
|
|
8 +0.000000 +0.000000 +0.000000
|
|
1 -1.430429 +0.000000 -1.107157
|
|
1 +1.430429 +0.000000 -1.107157
|
|
#+end_example
|
|
|
|
and compute the coordinates of the grid points:
|
|
|
|
#+begin_src python :exports code
|
|
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]
|
|
#+end_src
|
|
|
|
#+RESULTS:
|
|
|
|
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:
|
|
|
|
#+begin_src python :exports code
|
|
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)))
|
|
#+end_src
|
|
|
|
#+RESULTS:
|
|
: None
|
|
|
|
Then, we evaluate all the MOs at the grid points (and time the execution),
|
|
and thus obtain the matrix $M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle =
|
|
\phi_i(\mathbf{r}_k)$.
|
|
|
|
#+begin_src python :exports code
|
|
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) )
|
|
|
|
print("Number of MOs: ", mo_num)
|
|
print("Number of grid points: ", point_num)
|
|
print("Execution time : ", (after - before), "seconds")
|
|
|
|
#+end_src
|
|
|
|
#+begin_example
|
|
Number of MOs: 201
|
|
Number of grid points: 1728000
|
|
Execution time : 3.511528968811035 seconds
|
|
#+end_example
|
|
|
|
and finally we compute the overlap between all the MOs as
|
|
$M^\dagger M$.
|
|
|
|
#+begin_src python :exports code
|
|
overlap = mo_value.T @ mo_value * dr
|
|
print (overlap)
|
|
#+end_src
|
|
|
|
#+begin_example
|
|
[[ 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]]
|
|
#+end_example
|
|
|
|
* 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
|
|
|