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Initial commit benzene example
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@ifilot
ifilot committed Jul 8, 2023
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112 changes: 112 additions & 0 deletions examples/benzene.py
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# -*- coding: utf-8 -*-

import sys
import os
import numpy as np

# add a reference to load the Sphecerix library
sys.path.append(os.path.join(os.path.dirname(__file__), '..'))

from sphecerix import Molecule, BasisFunction, SymmetryOperations,\
visualize_matrices, CharacterTable, ProjectionOperator

def main():
mol = Molecule()
mol.add_atom('C', 0.0000000015, -1.3868467444, 0.0000000000, unit='angstrom')
mol.add_atom('C', 1.2010445126, -0.6934233709, 0.0000000000, unit='angstrom')
mol.add_atom('C', 1.2010445111, 0.6934233735, 0.0000000000, unit='angstrom')
mol.add_atom('C', -0.0000000015, 1.3868467444, 0.0000000000, unit='angstrom')
mol.add_atom('C', -1.2010445126, 0.6934233709, 0.0000000000, unit='angstrom')
mol.add_atom('C', -1.2010445111, -0.6934233735, 0.0000000000, unit='angstrom')
mol.add_atom('H', 0.0000000027, -2.4694205285, 0.0000000000, unit='angstrom')
mol.add_atom('H', 2.1385809117, -1.2347102619, 0.0000000000, unit='angstrom')
mol.add_atom('H', 2.1385809090, 1.2347102666, 0.0000000000, unit='angstrom')
mol.add_atom('H', -0.0000000027, 2.4694205285, 0.0000000000, unit='angstrom')
mol.add_atom('H', -2.1385809117, 1.2347102619, 0.0000000000, unit='angstrom')
mol.add_atom('H', -2.1385809090, -1.2347102666, 0.0000000000, unit='angstrom')

molset = {
'C': [BasisFunction(2,0,0)],
'H': []
}
mol.build_basis(molset)

symops = SymmetryOperations(mol)

# E
symops.add('identity')

# 2C6
symops.add('rotation', '6+', np.array([0,0,1]), 2.0 * np.pi / 6)
symops.add('rotation', '6-', np.array([0,0,1]), -2.0 * np.pi / 6)

# 2C3
symops.add('rotation', '3+', np.array([0,0,1]), 2.0 * np.pi / 3)
symops.add('rotation', '3-', np.array([0,0,1]), -2.0 * np.pi / 3)

# C2
symops.add('rotation', '2', np.array([0,0,1]), np.pi)

# 3C2'
for i in range(0,3):
symops.add('rotation', '2,%i' % i, np.array([np.sin(i * 2.0 * np.pi / 3),
np.cos(i * 2.0 * np.pi / 3),
0.0]), np.pi)

# 3C2''
for i in range(0,3):
symops.add('rotation', '2,%i' % i, np.array([np.sin(i * 2.0 * np.pi * (1./3 + 1./6)),
np.cos(i * 2.0 * np.pi * (1./3 + 1./6)),
0.0]), np.pi)


# inversion
symops.add('inversion')

# 2S3
symops.add('improper', '3+', np.array([0,0,1]), 2.0 * np.pi / 3)
symops.add('improper', '3-', np.array([0,0,1]), -2.0 * np.pi / 3)

# 2S6
symops.add('improper', '6+', np.array([0,0,1]), 2.0 * np.pi / 6)
symops.add('improper', '6-', np.array([0,0,1]), -2.0 * np.pi / 6)

# sigma_h
symops.add('mirror', 'h(xy)', np.array([0,0,1]))

# sigma_d
for i in range(0,3):
symops.add('mirror', 'd,%i' % i, np.array([np.sin(i * 2.0 * np.pi * (1./3 + 1./6)),
np.cos(i * 2.0 * np.pi * (1./3 + 1./6)),
0.0]))

# sigma_v
for i in range(0,3):
symops.add('mirror', 'v,%i' % i, np.array([np.cos(i * 2.0 * np.pi / 3),
np.sin(i * 2.0 * np.pi / 3),
0.0]))

symops.run()

visualize_matrices(symops.operation_matrices,
[op.name for op in symops.operations],
[bf.name for bf in symops.mol.basis],
xlabelrot=90, figsize=(24,32), numcols=4)

# print result LOT
ct = CharacterTable('d6h')
print(ct.lot(np.trace(symops.operation_matrices, axis1=1, axis2=2)))

# apply projection operator
po = ProjectionOperator(ct, symops)

mos = po.build_mos(verbose=True)
newmats = [mos @ m @ mos.transpose() for m in symops.operation_matrices]

visualize_matrices(newmats,
[op.name for op in symops.operations],
['$\phi_{%i}$' % (i+1) for i in range(len(symops.mol.basis))],
figsize=(24,32), numcols=4)

if __name__ == '__main__':
main()
103 changes: 103 additions & 0 deletions sphecerix/charactertables/d6h.json
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{
"name":"d6h",
"classes": [
{
"symbol": "E",
"multiplicity": 1
},
{
"symbol": "C6(z)",
"multiplicity": 2
},
{
"symbol": "C3",
"multiplicity": 2
},
{
"symbol": "C2",
"multiplicity": 1
},
{
"symbol": "C2'",
"multiplicity": 3
},
{
"symbol": "C2''",
"multiplicity": 3
},
{
"symbol": "i",
"multiplicity": 1
},
{
"symbol": "S3",
"multiplicity": 2
},
{
"symbol": "S6",
"multiplicity": 2
},
{
"symbol": "sigma(h)",
"multiplicity": 1
},
{
"symbol": "sigma(d)",
"multiplicity": 3
},
{
"symbol": "sigma(v)",
"multiplicity": 3
}
],
"symmetry_groups": [
{
"symbol": "A1g",
"characters": [1,1,1,1,1,1,1,1,1,1,1,1]
},
{
"symbol": "A2g",
"characters": [1,1,1,1,-1,-1,1,1,1,1,-1,-1]
},
{
"symbol": "B1g",
"characters": [1,-1,1,-1,1,-1,1,-1,1,-1,1,-1]
},
{
"symbol": "B2g",
"characters": [1,-1,1,-1,-1,1,1,-1,1,-1,-1,1]
},
{
"symbol": "E1g",
"characters": [2,1,-1,-2,0,0,2,1,-1,-2,0,0]
},
{
"symbol": "E2g",
"characters": [2,-1,-1,2,0,0,2,-1,-1,2,0,0]
},
{
"symbol": "A1u",
"characters": [1,1,1,1,1,1,-1,-1,-1,-1,-1,-1]
},
{
"symbol": "A2u",
"characters": [1,1,1,1,-1,-1,-1,-1,-1,-1,1,1]
},
{
"symbol": "B1u",
"characters": [1,-1,1,-1,1,-1,-1,1,-1,1,-1,1]
},
{
"symbol": "B2u",
"characters": [1,-1,1,-1,-1,1,-1,1,-1,1,1,-1]
},
{
"symbol": "E1u",
"characters": [2,1,-1,-2,0,0,-2,-1,1,2,0,0]
},
{
"symbol": "E2u",
"characters": [2,-1,-1,2,0,0,-2,1,1,-2,0,0]
}
]
}

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