richmol.rot package

`Molecule`()	Describes rigid molecule
`solve`(mol[, Jmin, Jmax, verbose, filter])	Solves rotational eigenvalue problem
`Solution`([val])	Represents rotational solutions for different values of J and symmetry
`mol_tensor`(val)	Declares new molecular-frame Cartesian tensor which is dynamically rotated to a chosen molecular frame `Molecule.frame()` whenever the latter is changed
`LabTensor`(arg, basis[, thresh])	Represents rotational matrix elements of laboratory-frame Cartesian tensor operator

Rigid molecule description

class richmol.rot.Molecule

Describes rigid molecule

XYZ()

Cartesian coordinates and masses of atoms

Parameters:

arg –

Atomic labels, Cartesian coordinates of atoms, and units in a tuple, for example,

water.XYZ = ("bohr",
             "O",  0.00000000,   0.00000000,   0.12395915,
             "H",  0.00000000,  -1.43102686,  -0.98366080,
             "H",  0.00000000,   1.43102686,  -0.98366080)

To define a non-standard isotoplogue, add the corresponding number next to the atom label, e.g., “O18”, “H2”. Cartesian coordinates can also be read from an XYZ file, in this case arg should contain the name of XYZ file.

Returns:

structured numpy array: XYZ[‘xyz’] - Cartesian coordinates of atoms in Angstrom, XYZ[‘mass’] - atomic masses, XYZ[‘label’] - atomic labels

frame()

Molecular frame embedding

Parameters:

arg –

String defining molecular frame

water.frame = "diag(inertia)" # rotates to a frame where the inertia tensor
                              # becomes diagonal
water.frame = "zxy" # permutes the x, y, and z axes
water.pol = [[9.1369, 0, 0], [0, 9.8701, 0], [0, 0, 9.4486]]
water.frame = "pol" # rotates frame with water.pol matrix
water.frame = "diag(pol)" # rotates to a frame where water.pol tensor
                          # becomes diagonal
water.frame = "None" # or None, resets frame to the one defined
                     # by the input  molecular geometry

Returns:

array (3,3): Frame rotation matrix

B()

Molecular rotational constants

Parameters:: arg – Tuple with Bx, By, and Bz user-defined rotational constants (in \(cm^{-1}\)).
Returns:: Tuple with Bx, By, and Bz user-defined rotational constants. If constants were not defined, returns constants computed from the input molecular geometry.

B_geom(): Returns Bx, By, and Bz rotational constants (in units of \(cm^{-1}\)), calculated from molecular geometry input

sym()

Molecular point symmetry group

Parameters:: arg – str Molecular symmetry label, e.g., “C1”, “D2”, “C2v”
Returns:: richmol.rot.symmetry.SymtopSymmetry class.

store_xyz(file_name, comment='')

Stores Cartesian coordinates of atoms into XYZ file

Parameters:

file_name – str Name of XYZ file
comment – str Optional comment line

imom(): Computes inertia tensor

gmat(): Computes rotational kinetic energy matrix (in units of \(cm^{-1}\))

linear(): Returns True/False if molecule is linear/non-linear

kappa(): Returns rotational asymmetry parameter kappa = (2*B-A-C)/(A-C)

store(filename, name=None, comment=None, replace=False)

Stores object in HDF5 file

Parameters:

filename – str Name of HDF5 file
name – str Name of the data group, by default name of the variable is used
comment – str User comment
replace – bool If True, the existing data set will be replaced

read(filename, name=None)

Reads object from HDF5 file

Parameters:

filename – str Name of HDF5 file
name – str Name of the data group, if None, first group with matching “__class_name__” attribute will be loaded

richmol.rot.mol_tensor(val)

Declares new molecular-frame Cartesian tensor which is dynamically rotated to a chosen molecular frame Molecule.frame() whenever the latter is changed

Parameters:: val – array Cartesian tensor
Returns:: object, needs to be assigned to an attribute of class Molecule

Rotational solutions

richmol.rot.solve(mol, Jmin=0, Jmax=10, verbose=False, filter=<function <lambda>>)

Solves rotational eigenvalue problem

Parameters:

mol – Molecule Molecular parameters.
Jmin – int Min value of J quantum number.
Jmax – int Max value of J quantum number.
verbose – bool If True, some log will be printed.
filter –
function(**kw) State filter, takes as arguments state quantum numbers J and m and symmetry sym, and returns True or False depending if the corresponding state needs to be included (True) or excluded (False) form the basis. By default, all states spanned by J=Jmin..Jmax will be included. The following keyword arguments are passed into the filter function:

Jint
J quantum number

symstr
Symmetry

mint
m quantum number

Returns:

Solution: Nested dictionary containing rotational wave functions richmol.rot.SymtopBasis for different values of J=Jmin..Jmax and different symmetries

class richmol.rot.Solution(val=None)

Represents rotational solutions for different values of J and symmetry

This is a subclass of collections.UserDict class.

Parameters:: val – dict Nested dictionary containing rotational wave functions richmol.rot.SymtopBasis for different values of J=Jmin..Jmax and different symmetries

store(filename, name=None, comment=None, replace=False)

Stores object into HDF5 file

Parameters:

filename – str Name of HDF5 file
name – str Name of the data group, by default name of the variable is used
comment – str User comment
replace – bool If True, the existing data set will be replaced

read(filename, name=None)

Reads object from HDF5 file

Parameters:

filename – str Name of HDF5 file
name – str Name of the data group, if None, first group with matching “__class_name__” attribute will be loaded

Matrix elements

class richmol.rot.LabTensor(arg, basis, thresh=None, **kwargs)

Represents rotational matrix elements of laboratory-frame Cartesian tensor operator

This is a subclass of richmol.field.CarTens class.

Attrs:

Usnumpy.complex128 2D array: Cartesian-to-spherical tensor transformation matrix.
Uxnumpy.complex128 2D array: Spherical-to-Cartesian tensor transformation matrix, Ux = np.conj(Us.T)
tens_flat1D array: Flattened molecular-frame Cartesian tensor.
moleculerichmol.rot.Molecule: Molecular parameters.

Parameters:

arg – numpy.ndarray, list or tuple, richmol.rot.Molecule, function, or str Depending on the type of argument, initializes lab-frame molecular tensor operator (arg is numpy.ndarray, list, or tuple), field-free Hamiltonian operator (arg is richmol.rot.Molecule), arbitrary function of spherical coordinates theta and phi (arg is function(theta, phi)), or matrix elements of some named operators (arg is str). Named operators: “cos2theta” for cos²(theta), “costheta” for cos(theta).
basis – richmol.rot.Solution Rotational wave functions.
thresh – float Threshold for neglecting matrix elements.

Kwargs:

bra, ketfunction(**kw)

State filters for bra and ket basis sets, take as arguments state quantum numbers, symmetry, and energy, i.e., J, m, k, sym, and enr, and return True or False depending if the corresponding state needs to be included (True) or excluded (False) form the basis. By default, all states spanned by basis are included. The following keyword arguments are passed into the bra and ket functions:

Jfloat (round to first decimal)
Value of J (or F) quantum number

symstr
State symmetry

enrfloat
State energy

mstr
State assignment in the M subspace, usually just a value of the m quantum number

kstr
State assignment in the K subspace, which are state’s rotational or ro-vibrational quanta and energy combined in a string

wig_jmaxint

Maximal value of J quantum number used in the expansion of input user-defined function of spherical coordinates in terms of Wigner D-functions (used when arg is function).

leb_degint (deprecated, use leb_ind)

Degree of angular Lebedev quadrature used for computing the Wigner expansion coefficients (used when arg is function)

leb_indint

Index (0..32) of the angular Lebedev quadrature used for computing the Wigner expansion coefficients (used when arg is a function)