Expanding examples

examples/.gitignore

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 *.pdf
-*.ply
+*.ply
+*.pickle

examples/example_ch4_orthonormalization.py

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+# -*- coding: utf-8 -*-
+
+# 
+# This file is part of the PyPWDFT distribution 
+# Copyright (c) 2024 Ivo Filot
+# 
+# This program is free software: you can redistribute it and/or modify  
+# it under the terms of the GNU General Public License as published by  
+# the Free Software Foundation, version 3.
+#
+# This program is distributed in the hope that it will be useful, but 
+# WITHOUT ANY WARRANTY; without even the implied warranty of 
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
+# General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License 
+# along with this program. If not, see <http://www.gnu.org/licenses/>.
+#
+
+# PURPOSE
+# =======
+#
+# Perform an electronic structure calculation of CO and visualize its valence 
+# orbitals. This script builds the isosurfaces
+#
+
+import os
+import numpy as np
+from pytessel import PyTessel
+from pypwdft import PyPWDFT, SystemBuilder
+import pickle
+
+def main():
+    # create cubic periodic system with lattice size of 10 Bohr units
+    npts = 32       # number of grid points
+    sz = 10
+
+    if os.path.exists('ch4.pickle'):
+        with open('ch4.pickle', 'rb') as f:
+            res = pickle.load(f)
+    else:
+        # construct CO molecule system via SystemBuilder
+        s = SystemBuilder().from_name('CH4', sz=sz, npts=npts)
+
+        # construct calculator object
+        calculator = PyPWDFT(s)
+
+        # perform self-consistent field procedure and store results in res object
+        res = calculator.scf(tol=1e-5, verbose=True)
+
+        # print molecular orbital energies
+        print(res['orbe'])
+
+        # create cached result
+        with open('ch4.pickle', 'wb') as f:
+            pickle.dump(res, f, pickle.HIGHEST_PROTOCOL)
+
+    # generate PyTessel object
+    pytessel = PyTessel()
+
+    S = calculate_overlap_matrix(res['orbc_rs'], sz, npts)
+    print(S)
+
+    for i in range(5):
+        res['orbc_rs'][i] = np.sign(res['orbc_rs'][i].real)*np.abs(res['orbc_rs'][i])
+
+    S = calculate_overlap_matrix(res['orbc_rs'], sz, npts)
+    print(S)
+
+    for i in range(5):
+        print('Building isosurfaces: %02i' % (i+1))
+        scalarfield = upsample_grid(res['orbc_rs'][i], sz, npts, 4)
+        #scalarfield = res['orbc_rs'][i]
+        unitcell = np.identity(3) * sz
+
+        # build positive real isosurface
+        vertices, normals, indices = pytessel.marching_cubes(scalarfield.flatten().real, scalarfield.shape, unitcell.flatten(), 0.03)
+        pytessel.write_ply('MO_PR_%02i.ply' % (i+1), vertices, normals, indices)
+
+        # build negative real isosurface
+        vertices, normals, indices = pytessel.marching_cubes(scalarfield.flatten().real, scalarfield.shape, unitcell.flatten(), -0.03)
+        pytessel.write_ply('MO_NR_%02i.ply' % (i+1), vertices, normals, indices)
+
+def upsample_grid(scalarfield, sz, npts, upsample=4):
+    """
+    Upsample the grid
+    """
+    ct = np.sqrt(sz**3) / npts**3
+    scalarfield_fft = np.fft.fftn(scalarfield) * ct
+
+    Nx, Ny, Nz = scalarfield_fft.shape
+    Nx_up = Nx * upsample
+    Ny_up = Nx * upsample
+    Nz_up = Nx * upsample
+
+    # shift the frequencies
+    fft = np.fft.fftshift(scalarfield_fft)
+
+    # perform padding
+    fft_upsampled = np.pad(fft, [((Nz_up-Nz)//2,),
+                                ((Ny_up-Ny)//2,),
+                                ((Nx_up-Nx)//2,)], 'constant')
+
+    # shift back
+    ct = np.sqrt(sz**3) / np.prod([Nx_up, Ny_up, Nz_up])
+    fft_hires = np.fft.ifftshift(fft_upsampled) / ct
+
+    return np.fft.ifftn(fft_hires)
+
+def calculate_overlap_matrix(orbc, sz, npts):
+    """
+    Calculate the overlap matrix in real-space
+    """
+    N = len(orbc)
+    S = np.zeros((N,N))
+    dV = (sz / npts)**3
+    for i in range(N):
+        for j in range(N):
+            S[i,j] = (np.sum(orbc[i].conjugate() * orbc[j]) * dV).real
+
+    return S
+
+if __name__ == '__main__':
+    main()