posym module
Project description
PoSym
A point symmetry analysis tool written in python designed for theoretical chemistry.
This tool makes use of continuous symmetry ideas to provide a robust implementation
to compute the symmetry of different objects. This library is designed to be easily
extendable to other objects by subclassing the SymmetryBase
class.
Features
- Use as simple calculator for irreducible representations supporting direct sum and product
- Determine symmetry of:
- normal modes
- functions defined in gaussian basis (molecular orbitals, electronic densities, operators)
- wave functions defined as a slater determinant
- wave functions defined as linear combination of slater determinants (Multi-reference/CI)
- Compatibility with PyQchem (http://www.github.com/abelcarreras/pyqchem)
Requisites
- numpy
- scipy
- pandas
- yaml
Use as a simple symmetry calculation
Posym allows to create basic continuous symmetry python objects that can be operated using direct sum (+) and direct product (*).
from posym import PointGroup, SymmetryBase
pg = PointGroup(group='Td')
print(pg)
a1 = SymmetryBase(group='Td', rep='A1')
a2 = SymmetryBase(group='Td', rep='A2')
e = SymmetryBase(group='Td', rep='E')
t1 = SymmetryBase(group='Td', rep='T1')
print('e*e + a1:', e * (e + a1))
Determine the symmetry of normal modes
Symmetry objects can be obtained from normal modes using SymmetryModes
.
from posym import SymmetryModes
coordinates = [[ 0.00000, 0.0000000, -0.0808819],
[-1.43262, 0.0000000, -1.2823700],
[ 1.43262, 0.0000000, -1.2823700]]
symbols = ['O', 'H', 'H']
normal_modes = [[[ 0., 0., -0.075],
[-0.381, -0., 0.593],
[ 0.381, -0., 0.593]], # mode 1
[[-0. , -0., 0.044],
[-0.613, -0., -0.35 ],
[ 0.613, 0., -0.35 ]], # mode 2
[[-0.073, -0., -0. ],
[ 0.583, 0., 0.397],
[ 0.583, 0., -0.397]]] # mode 3
frequencies = [1737.01, 3988.5, 4145.43]
sym_modes_gs = SymmetryModes(group='c2v', coordinates=coordinates, modes=normal_modes, symbols=symbols)
for i in range(len(normal_modes)):
print('Mode {:2}: {:8.3f} :'.format(i + 1, frequencies[i]), sym_modes_gs.get_state_mode(i))
print('Total symmetry: ', sym_modes_gs)
Define basis set functions in gaussian basis
Define basis function as linear combination of gaussian that act as normal python functions
from posym.basis import PrimitiveGaussian, BasisFunction
# Oxigen atom
sa = PrimitiveGaussian(alpha=130.70932)
sb = PrimitiveGaussian(alpha=23.808861)
sc = PrimitiveGaussian(alpha=6.4436083)
s_O = BasisFunction([sa, sb, sc],
[0.154328969, 0.535328136, 0.444634536],
center=[0.0000000000, 0.000000000, -0.0808819]) # Bohr
sa = PrimitiveGaussian(alpha=5.03315132)
sb = PrimitiveGaussian(alpha=1.1695961)
sc = PrimitiveGaussian(alpha=0.3803890)
s2_O = BasisFunction([sa, sb, sc],
[-0.099967228, 0.399512825, 0.700115461],
center=[0.0000000000, 0.000000000, -0.0808819])
pxa = PrimitiveGaussian(alpha=5.0331513, l=[1, 0, 0])
pxb = PrimitiveGaussian(alpha=1.1695961, l=[1, 0, 0])
pxc = PrimitiveGaussian(alpha=0.3803890, l=[1, 0, 0])
pya = PrimitiveGaussian(alpha=5.0331513, l=[0, 1, 0])
pyb = PrimitiveGaussian(alpha=1.1695961, l=[0, 1, 0])
pyc = PrimitiveGaussian(alpha=0.3803890, l=[0, 1, 0])
pza = PrimitiveGaussian(alpha=5.0331513, l=[0, 0, 1])
pzb = PrimitiveGaussian(alpha=1.1695961, l=[0, 0, 1])
pzc = PrimitiveGaussian(alpha=0.3803890, l=[0, 0, 1])
px_O = BasisFunction([pxa, pxb, pxc],
[0.155916268, 0.6076837186, 0.3919573931],
center=[0.0000000000, 0.000000000, -0.0808819])
py_O = BasisFunction([pya, pyb, pyc],
[0.155916268, 0.6076837186, 0.3919573931],
center=[0.0000000000, 0.000000000, -0.0808819])
pz_O = BasisFunction([pza, pzb, pzc],
[0.155916268, 0.6076837186, 0.3919573931],
center=[0.0000000000, 0.000000000, -0.0808819])
# Hydrogen atoms
sa = PrimitiveGaussian(alpha=3.42525091)
sb = PrimitiveGaussian(alpha=0.62391373)
sc = PrimitiveGaussian(alpha=0.1688554)
s_H = BasisFunction([sa, sb, sc],
[0.154328971, 0.535328142, 0.444634542],
center=[-1.43262, 0.000000000, -1.28237])
s2_H = BasisFunction([sa, sb, sc],
[0.154328971, 0.535328142, 0.444634542],
center=[1.43262, 0.000000000, -1.28237])
basis_set = [s_O, s2_O, px_O, py_O, pz_O, s_H, s2_H]
# Operate with basis functions in analytic form
px_O2 = px_O * px_O
print('integral from -inf to inf:', px_O2.integrate)
# plot functions
from matplotlib import pyplot as plt
import numpy as np
xrange = np.linspace(-5, 5, 100)
plt.plot(xrange, [s_O(x, 0, 0) for x in xrange] , label='s_O')
plt.plot(xrange, [px_O(x, 0, 0) for x in xrange] , label='px_O')
plt.legend()
Create molecular orbitals from basis set
Define molecular orbitals straightforwardly from molecular orbitals coefficients using usual operators
# Orbital 1
o1 = s_O * 0.994216442 + s2_O * 0.025846814 + px_O * 0.0 + py_O * 0.0 + pz_O * -0.004164076 + s_H * -0.005583712 + s2_H * -0.005583712
# Orbital 2
o2 = s_O * 0.23376666 + s2_O * -0.844456594 + px_O * 0.0 + py_O * 0.0 + pz_O * 0.122829781 + s_H * -0.155593214 + s2_H * -0.155593214
# Orbital 3
o3 = s_O * 0.0 + s2_O * 0.0 + px_O * 0.612692349 + py_O * 0.0 + pz_O * 0.0 + s_H * -0.44922168 + s2_H * 0.449221684
# Orbital 4
o4 = s_O * -0.104033343 + s2_O * 0.538153649 + px_O * 0.0 + py_O * 0.0 + pz_O * 0.755880259 + s_H * -0.295107107 + s2_H * -0.2951071074
# Orbital 5
o5 = s_O * 0.0 + s2_O * 0.0 + px_O * 0.0 + py_O * -1.0 + pz_O * 0.0 + s_H * 0.0 + s2_H * 0.0
# Orbital 6
o6 = s_O * -0.125818566 + s2_O * 0.820120983 + px_O * 0.0 + py_O * 0.0 + pz_O * -0.763538862 + s_H * -0.769155124 + s2_H * -0.769155124
# Check orthogonality
print('<o1|o1>: ', (o1*o1).integrate)
print('<o2|o2>: ', (o2*o2).integrate)
print('<o1|o2>: ', (o1*o2).integrate)
Analyze symmetry of molecular orbitals
Get symmetry of molecular orbitals defined as PrimitiveGaussian/BasisFunction
type objects
from posym import SymmetryFunction
sym_o1 = SymmetryFunction('c2v', o1)
sym_o2 = SymmetryFunction('c2v', o2)
sym_o3 = SymmetryFunction('c2v', o3)
sym_o4 = SymmetryFunction('c2v', o4)
sym_o5 = SymmetryFunction('c2v', o5)
sym_o6 = SymmetryFunction('c2v', o6)
print('Symmetry O1: ', sym_o1)
print('Symmetry O2: ', sym_o2)
print('Symmetry O3: ', sym_o3)
print('Symmetry O4: ', sym_o4)
print('Symmetry O5: ', sym_o5)
print('Symmetry O6: ', sym_o6)
# Operate molecular orbitals symmetries to get the symmetry of non-degenerate wave functions
# restricted close shell
sym_wf_gs = sym_o1*sym_o1 * sym_o2*sym_o2 * sym_o3*sym_o3 * sym_o4*sym_o4 * sym_o5*sym_o5
print('Symmetry WF (ground state): ', sym_wf_gs)
# restricted open shell
sym_wf_excited_1 = sym_o1*sym_o1 * sym_o2*sym_o2 * sym_o3*sym_o3 * sym_o4*sym_o4 * sym_o5*sym_o6
print('Symmetry WF (excited state 1): ', sym_wf_excited_1)
# restricted close shell
sym_wf_excited_2 = sym_o1*sym_o1 * sym_o2*sym_o2 * sym_o3*sym_o3 * sym_o4*sym_o4 * sym_o6*sym_o6
print('Symmetry WF (excited state 2): ', sym_wf_excited_2)
Combine with PyQchem to create useful automations
PyQchem (https://github.com/abelcarreras/PyQchem) is a Python interface for Q-Chem (https://www.q-chem.com). PyQchem can be used to obtain wave functions and normal modes as Python objects that can be directly used in Posym.
from pyqchem import get_output_from_qchem, QchemInput, Structure
from pyqchem.parsers.basic import basic_parser_qchem
from posym import SymmetryFunction
# convenient functions to connect pyqchem - posym
from posym.tools import get_basis_set, build_orbital
# define molecules
butadiene = Structure(coordinates=[[ -1.07076839, -2.13175980, 0.03234382],
[ -0.53741536, -3.05918866, 0.04995793],
[ -2.14073783, -2.12969357, 0.04016267],
[ -0.39112115, -0.95974916, 0.00012984],
[ 0.67884827, -0.96181542, -0.00769025],
[ -1.15875076, 0.37505495, -0.02522296],
[ -0.62213437, 1.30041753, -0.05065831],
[ -2.51391203, 0.37767199, -0.01531698],
[ -3.04726506, 1.30510083, -0.03293196],
[ -3.05052841, -0.54769055, 0.01011971]],
symbols=['C', 'H', 'H', 'C', 'H', 'C', 'H', 'C', 'H', 'H'])
# create qchem input
qc_input = QchemInput(butadiene,
jobtype='sp',
exchange='hf',
basis='sto-3g',
)
# calculate and parse qchem output
data, ee = get_output_from_qchem(qc_input,
read_fchk=True,
processors=4,
parser=basic_parser_qchem)
# extract required information from Q-Chem calculation
coordinates = ee['structure'].get_coordinates()
mo_coefficients = ee['coefficients']['alpha']
basis = ee['basis']
# print results
print('Molecular orbitals (alpha) symmetry')
basis_set = get_basis_set(coordinates, basis)
for i, orbital_coeff in enumerate(mo_coefficients):
orbital = build_orbital(basis_set, orbital_coeff)
sym_orbital = SymmetryFunction('c2v', orbital)
print('Symmetry O{}: '.format(i+1), sym_orbital)
Compute the symmetry of wave functions defined as a Slater determinant
Use SymmetryWaveFunction
class to determine the symmetry of a wave function
from a set of occupied molecular orbitals defined as BasisFunction
objects
from posym import SymmetryWaveFunction
from posym.tools import build_orbital
# get orbitals from basis set and MO coefficients
orbital1 = build_orbital(basis_set, coefficients['alpha'][0]) # A1
orbital2 = build_orbital(basis_set, coefficients['alpha'][1]) # A1
orbital3 = build_orbital(basis_set, coefficients['alpha'][2]) # T1
orbital4 = build_orbital(basis_set, coefficients['alpha'][3]) # T1
orbital5 = build_orbital(basis_set, coefficients['alpha'][4]) # T1
wf_sym = SymmetryWaveFunction('Td',
alpha_orbitals=[orbital1, orbital2, orbital5],
beta_orbitals=[orbital1, orbital2, orbital4],
center=[0, 0, 0])
print('Configuration 1: ', wf_sym) # T1 + T2
wf_sym = SymmetryWaveFunction('Td',
alpha_orbitals=[orbital1, orbital2, orbital3],
beta_orbitals=[orbital1, orbital2, orbital3],
center=[0, 0, 0])
print('Configuration 2: ', wf_sym) # A1 + E
Compute the symmetry of multi-reference wave functions
Use SymmetryWaveFunctionCI
class to determine the symmetry of multi-reference wave function
(defined as a liner combination of Slater determinants) from a set of
occupied molecular orbitals defined as BasisFunction
objects and a configurations dictionary.
from posym import SymmetryWaveFunctionCI
configurations = [{'amplitude': -0.03216, 'occupations': {'alpha': [1, 1, 0, 0, 1], 'beta': [1, 1, 1, 0, 0]}},
{'amplitude': 0.70637, 'occupations': {'alpha': [1, 1, 0, 1, 0], 'beta': [1, 1, 1, 0, 0]}},
{'amplitude': 0.03216, 'occupations': {'alpha': [1, 1, 1, 0, 0], 'beta': [1, 1, 0, 0, 1]}},
{'amplitude': -0.70637, 'occupations': {'alpha': [1, 1, 1, 0, 0], 'beta': [1, 1, 0, 1, 0]}}]
wf_sym = SymmetryWaveFunctionCI('Td',
orbitals=[orbital1, orbital2, orbital3, orbital4, orbital5],
configurations=configurations,
center=[0, 0, 0])
print('State 1: ', wf_sym) # T1
Try an interactive example in Google Colab
Contact info
Abel Carreras
abelcarreras83@gmail.com
Donostia International Physics Center (DIPC)
Donostia-San Sebastian (Spain)
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MD5 | b28eeefad0cf608b76d0e72e12e40963 |
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BLAKE2b-256 | de55624345de53d223798e02133131aca9b4549f5bd194324022adfe2e05cc35 |
Hashes for posym-0.2.6-cp37-cp37m-win32.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | e2b1208f3083fa658d4f1bf99e12be9c433ae246d3aa475bc82b31a20f46d472 |
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MD5 | 4c7585b4207ad7f9a19609dd31a35897 |
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BLAKE2b-256 | 5e2f638c078d26a470d5565a15fd78fa062db7cec74fe1a1c9009fa620f8f7b8 |
Hashes for posym-0.2.6-cp37-cp37m-musllinux_1_1_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 32cffed0f6e0a41612ff97e1746d29ad6d84f06d4edcb901d5ca59a03af884b0 |
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MD5 | d4ec6d2392e4ce39ef9997692e16d49f |
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BLAKE2b-256 | b6200395de4171008935730234267991553a47a5b08488182dcc23824a41be6a |
Hashes for posym-0.2.6-cp37-cp37m-musllinux_1_1_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 8a08a1ff050db5d3d9d371bdd50edf3519c8ae856573bea02e2a3c0a2d086161 |
|
MD5 | cbaf1ca7b2a912d9de882d6bf6531c35 |
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BLAKE2b-256 | fca36526604bc57118015fb3ba01193e4d8fab34692631d8db2e2236aaef6661 |
Hashes for posym-0.2.6-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 3532d02d5375eeaa653ec1912abe9169180dcae252a3947e576cd0a78846ccb5 |
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MD5 | cc19873cdda7d70ec854e96b08ab9614 |
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BLAKE2b-256 | 2617e0996332b8c1c0d468b1966d137b683cc7d7a284445f955b1581288cc8a3 |
Hashes for posym-0.2.6-cp37-cp37m-manylinux_2_17_i686.manylinux2014_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 8f9a36933c4949991da9972199887e56f6736619562de8983db68110c1be7294 |
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MD5 | 8edddf6862911ee36d49499fd5888dd4 |
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BLAKE2b-256 | 679e7d6300fe121207c360a74ea75ff54ab23505625c4face23fee88fd2eae2a |
Hashes for posym-0.2.6-cp37-cp37m-macosx_10_9_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | b498ba1fffe7ce3d0d25f56d489a123291c226044daacf9a8722df81ff8f7833 |
|
MD5 | cbd08bb215453c3d1353a644eed36364 |
|
BLAKE2b-256 | 5f577f3b8ef50fc090e33c1774d76c1c8e421c124e4542318a5a6c2a9178f1a4 |
Hashes for posym-0.2.6-cp36-cp36m-win_amd64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 2619493c475b9f15e1e4bade3d0ed63858395b608580ad72948a375f04f4113c |
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MD5 | c3693491fdc7029679c046d348384279 |
|
BLAKE2b-256 | 5d9d7befb9c7bcaf7076cea309c6a83d14e611d4a0ea90422af3c399c2a82923 |
Hashes for posym-0.2.6-cp36-cp36m-win32.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 6e6b0712254600aecd1026c70e57259bda79447bc34bb2446d36d7edbc703327 |
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MD5 | b34a4cd817b9ce1582c22a3fba3d3402 |
|
BLAKE2b-256 | 5dadbb5f0a39bbc6003b99069c0370fb3d2ddf0a43122f8c6be05ff441eb80d7 |
Hashes for posym-0.2.6-cp36-cp36m-musllinux_1_1_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 584e449a4b02082b4d91cf4abb9bf867d634d5538a5345b6eb27c7c1f4dfb691 |
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MD5 | 3a228f29faa934cf7664511d2c3cf5ca |
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BLAKE2b-256 | eb12a5c6fe3751ba7db1e097498d536eb85632e263de1bc5d9e75a139bc2ca5c |
Hashes for posym-0.2.6-cp36-cp36m-musllinux_1_1_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 97d3feebac41062c473a22d3b4abe916f768ffd5647960147908e575d3be36f3 |
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MD5 | cf75db0cfec825a66cb9e1e1a9f87988 |
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BLAKE2b-256 | 451d2d547aef7baea480a007b949eba935dc00e8ddd3638e2b5e583ee6ecb223 |
Hashes for posym-0.2.6-cp36-cp36m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | c3166a52c18d369eb0cfc9278032b1f1908721fbff6d5d561c018aaa4b18eda0 |
|
MD5 | 1edcbb96c88fa579b86caa3fc1f42d0f |
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BLAKE2b-256 | cbbc0ccb931a953f68123d18e8d68b3b4b32ce7d3fe0f66a3de9727548a58439 |
Hashes for posym-0.2.6-cp36-cp36m-manylinux_2_17_i686.manylinux2014_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 7cdfe9b1de610830907e1f84727e7240bfd5a6431c9b55cd9c2c318104580a13 |
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MD5 | bd567fb619e2f8bc790216a1b30a4977 |
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BLAKE2b-256 | ce332476cf76279f72738d9672a33007d2dcece96d25ff6abfdeaa70d188bb7d |
Hashes for posym-0.2.6-cp36-cp36m-macosx_10_9_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 8f1041ee89bc00317de6b081968ffa152fd5a9acbba652b2dfce9d1f5a89d2b0 |
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MD5 | e7f31453c2ad4e753b8f78a0380bb48d |
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BLAKE2b-256 | 282322d1adafea00a2143bca8eb96ae433a9086af7330941b4c561b150409222 |