posym module
Project description
PoSym
A simple point symmetry analysis tool written in python.
This tool is mainly designed for theoretical chemistry but
can be used in general for other objects by defining subclasses
of the SymmetryBase
class. At this point SymmetryModes
and
SymmetryFunction
subclasses are defined for the analysis of
vibrational normal modes and molecular orbitals respectively.
Features
- Use as simple calculator for irreducible representations supporting direct sum and product
- Handles pseudosymmetry
- Determine point symmetry from normal modes
- Determine point symmetry functions defined in gaussian basis
- Compatibility with PyQchem (http://www.github.com/abelcarreras/pyqchem)
Requisites
- numpy
- scipy
- pandas
- yaml
Use as a simple symmetry calculation
posym allows to create symmetry python objects that can be operated using usual operators
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
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 in 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']
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['alpha']):
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 compute the wave function symmetry 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 compute a multi-reference wave function (defined as a liner combination of Slater determinants) symmetry 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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BLAKE2b-256 | 106ad0ed6cc5f7eadb4ad694b18246e9cfa2be2ebd0eb44e40f7a5f28fbf87ca |
Hashes for posym-0.2.5-cp37-cp37m-win32.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 070ca6e2c110a63b77ef2612b206532ba79ebb38add8a2a0a08b6225abd90acf |
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MD5 | d5d77d85beafeb1a2625cfd374edb8c6 |
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BLAKE2b-256 | 1e0f0d8d59cb1b3cc41f7d34abae67e97107c46c49f4f895eed3165a5dfc2b9e |
Hashes for posym-0.2.5-cp37-cp37m-musllinux_1_1_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | b2ae9df97000064599d886f47536c3b3ca82625fe2b64c27a3c3adcf060dbcad |
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MD5 | bd60192c437db08d560a2fe0dafbaef8 |
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BLAKE2b-256 | 19624be3c193fbb857ec84dae1fc45a2b7ffc739dd206d53663543ccad91883d |
Hashes for posym-0.2.5-cp37-cp37m-musllinux_1_1_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | f3d4819af667c3f7d530c80749d947e16786fefc1bc4c44ce918fbcc99bb2830 |
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MD5 | 4cd0be30b70c2c668eb3e3e38780d369 |
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BLAKE2b-256 | f05e643f8e77bb0f6d055b97ecf0ed79d8fe055b2dffdae47e0f802818d495f3 |
Hashes for posym-0.2.5-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 1e8d0b0a1947a2c30e0b153fe24899fbaf2ff5907ddf36e243252e29d72b0a4b |
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MD5 | 33d878621332a237bc4e74a5e8214225 |
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BLAKE2b-256 | 17adfae2cd48412464a4ffd1e4ba2106523ab311850f4f4fb41a5dab70508032 |
Hashes for posym-0.2.5-cp37-cp37m-manylinux_2_17_i686.manylinux2014_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 47a3c9f378f4992d77b49c3370cd8ec35ff0cead52f56e371f030a85a24e0444 |
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MD5 | 6e0041e34296dbd14db73e278b128fc2 |
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BLAKE2b-256 | 286587bf3fbed249758286356ccba51c2938645c4a8df71ee4c0db2a58394b3e |
Hashes for posym-0.2.5-cp37-cp37m-macosx_10_9_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | a36e0b6f72d942e16ca5042c07cc2de21b193e5afbf34a3f0f22be8dff38d12d |
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MD5 | be134bbc1cc066eb8e2d8fbc22287ec7 |
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BLAKE2b-256 | a7a5f4cbaf4171f827085d534793580a0b5f7ce10f380760831a3b5b694a7e18 |
Hashes for posym-0.2.5-cp36-cp36m-win_amd64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | e7391184710f4658e98bb59e7326e05dc54f82ca51f42f503f9087430e256ed9 |
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MD5 | 7541b49b40d7f546ce4d1742dcdf056e |
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BLAKE2b-256 | 2d73be2cca5382667b8db77354d9b606d7199958c28084ddf042327f67cd9f6d |
Hashes for posym-0.2.5-cp36-cp36m-win32.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | cf4e149e270454105bbc458d9e01224bfe39ee1f0868da35c778e9e9f3f29000 |
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MD5 | 46c26e8f946195c8583195566b42e13c |
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BLAKE2b-256 | 4ff1cc0327eaaf47bf3daa7ec8dd47f065e9a4c1b3f3c8367e57c29718b89638 |
Hashes for posym-0.2.5-cp36-cp36m-musllinux_1_1_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | a43826fa1ef5b8b8409a6a52420d380405f5bac2c95d3e54d053be6ae6fae64d |
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MD5 | bb5e09c57286114e850c2148f2f3773f |
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BLAKE2b-256 | 7a3732ae321a11578654fe40886918fd0c7ddebfeacb04ad2ca39a0dd420126c |
Hashes for posym-0.2.5-cp36-cp36m-musllinux_1_1_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | 6f523c686592848fe5a9d5ab55e6832851d4781ef0b16a4c1ae30732a37b9a15 |
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MD5 | d8e34dff4d4dabfc5216d4f86548bd7d |
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BLAKE2b-256 | d6a2b76ac89181cce579576b33783f459e4bf70717ccded7cfa5ebcb9683d10d |
Hashes for posym-0.2.5-cp36-cp36m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | d74004b0805c0a60de41b562f18e8a2025ec0c4fe8028b2fb98ff282c316e111 |
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MD5 | 1683dd5309e99d2270dd28ed5977be1b |
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BLAKE2b-256 | 617d8b2b084e3bc587916ae021a99f756ed4a313c602bcf0bd093f1614eb0800 |
Hashes for posym-0.2.5-cp36-cp36m-manylinux_2_17_i686.manylinux2014_i686.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | f7d308f66fe409d8ed2959e97765b846ef9d55b8acfa11f5dd2ba1855ec94051 |
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MD5 | 76d3e81c86ca588331563cc0819e53c3 |
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BLAKE2b-256 | fa8ec0c3928cc59b5820831a9b7709781dcb509abc17f5f444d82120fba95a71 |
Hashes for posym-0.2.5-cp36-cp36m-macosx_10_9_x86_64.whl
Algorithm | Hash digest | |
---|---|---|
SHA256 | fc02b89da955156603cb454318b919cd2d965de11338fb88b462b3dba62c220a |
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MD5 | de7652dd512c33bab333586122f40695 |
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BLAKE2b-256 | 28ae229480b4e05fa95993b9445f124fa970525abd8330e5ee995ac7f4a58769 |