chemtools.utils.molecule.BaseMolecule¶

class chemtools.utils.molecule.BaseMolecule(coordinates, numbers)[source]¶

Molecule Class.

This class serves as a template for the internal datatype used in ChemTools. Each of the methods are required to run different parts of ChemTools. If these methods are not defined, then a NotImplementedError will be raised to indicate that this method is not compatible with the given Molecule instance/class.

Initialize class.

Parameters:	coordinates (ndarray) – The 2d-array containing the cartesian coordinates of atomic centers. It has a shape of (M, 3) where M is the number of atoms. numbers (ndarray) – The 1d-array containing the atomic number of atoms. It has a shape of (M,) where M is the number of atoms.

classmethod from_file(filename)[source]¶

Initialize class given a file.

Parameters:	filename (str) – Path to molecule’s files.

coordinates¶: Cartesian coordinates of atomic centers.

numbers¶: Aomic number of atomic centers.

natom¶: Number of atoms.

nbasis¶: Number of basis functions.

nelectrons¶: Number of alpha and beta electrons.

homo_index¶: Index of alpha and beta HOMO orbital.

lumo_index¶: Index of alpha and beta LUMO orbital.

homo_energy¶: Energy of alpha and beta HOMO orbital.

lumo_energy¶: Energy of alpha and beta LUMO orbital.

orbital_occupation¶: Orbital occupation of alpha and beta electrons.

orbital_energy¶: Orbital energy of alpha and beta electrons.

orbital_coefficient¶

Orbital coefficient of alpha and beta electrons.

The alpha and beta orbital coefficients are each storied in a 2d-array in which the columns represent the basis coefficients of each molecular orbital.

compute_density_matrix_array(spin='ab')[source]¶

Return the density matrix array for the specified spin orbitals.

Parameters:	spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons

compute_density(points, spin='ab', orbital_index=None, output=None)[source]¶

Return electron density evaluated on the given points for the spin orbitals.

Parameters:

points (ndarray) – The 2d-array containing the cartesian coordinates of points on which density is evaluated. It has a shape (n, 3) where n is the number of points.
spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons
orbital_index (sequence) – Sequence of integers representing the index of spin orbitals. Alpha and beta spin orbitals are each indexed from 1 to nbasis. If None, all occupied spin orbtails are included.
output (np.ndarray) – Array with shape (n,) to store the output, where n in the number of points. When None the array is allocated.

compute_gradient(points, spin='ab', orbital_index=None, output=None)[source]¶

Return gradient of electron density evaluated on the given points for the spin orbitals.

Parameters:

points (ndarray) – The 2d-array containing the cartesian coordinates of points on which density is evaluated. It has a shape (n, 3) where n is the number of points.
spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons
orbital_index (sequence) – Sequence of integers representing the index of spin orbitals. Alpha and beta spin orbitals are each indexed from 1 to nbasis. If None, all occupied spin orbtails are included.
output (np.ndarray) – Array with shape (n, 3) to store the output, where n in the number of points. When None the array is allocated.

compute_hessian(points, spin='ab', orbital_index=None, output=None)[source]¶

Return hessian of electron density evaluated on the given points for the spin orbitals.

Parameters:

points (ndarray) – The 2d-array containing the cartesian coordinates of points on which density is evaluated. It has a shape (n, 3) where n is the number of points.
spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons
orbital_index (sequence) – Sequence of integers representing the index of spin orbitals. Alpha and beta spin orbitals are each indexed from 1 to nbasis. If None, all occupied spin orbtails are included.
output (np.ndarray) – Array with shape (n, 6) to store the output, where n in the number of points. When None the array is allocated.

compute_esp(points, spin='ab', orbital_index=None, output=None)[source]¶

Return the molecular electrostatic potential on the given points for the specified spin.

Parameters:

points (ndarray) – The 2d-array containing the cartesian coordinates of points on which density is evaluated. It has a shape (n, 3) where n is the number of points.
spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons
orbital_index (sequence) – Sequence of integers representing the index of spin orbitals. Alpha and beta spin orbitals are each indexed from 1 to nbasis. If None, all occupied spin orbtails are included.
output (np.ndarray) – Array with shape (n,) to store the output, where n in the number of points. When None the array is allocated.

compute_kinetic_energy_density(points, spin='ab', orbital_index=None, output=None)[source]¶

Return positive definite kinetic energy density on the given points for the specified spin.

Positive definite kinetic energy density is defined as,

\[\tau \left(\mathbf{r}\right) = \sum_i^N n_i \frac{1}{2} \rvert \nabla \phi_i \left(\mathbf{r}\right) \lvert^2\]

Parameters:

points (ndarray) – The 2d-array containing the cartesian coordinates of points on which density is evaluated. It has a shape (n, 3) where n is the number of points.
spin (str) – The type of occupied spin orbitals. By default, the alpha and beta electrons (i.e. alpha and beta occupied spin orbitals) are used for computing the electron density. - ‘a’ or ‘alpha’: consider alpha electrons - ‘b’ or ‘beta’: consider beta electrons - ‘ab’: consider alpha and beta electrons
orbital_index (sequence) – Sequence of integers representing the index of spin orbitals. Alpha and beta spin orbitals are each indexed from 1 to nbasis. If None, all occupied spin orbtails are included.
output (np.ndarray) – Array with shape (n,) to store the output, where n in the number of points. When None the array is allocated.