class BasisFunction(l, alpha, coeff, r)[source]

Bases: object

Create a basis function object.

A basis set is composed of a set of basis functions that are typically constructed as a linear combination of primitive Gaussian functions. For instance, a basis function in the STO-3G basis set is formed as

\[\psi = a_1 G_1 + a_2 G_2 + a_3 G_3,\]

where \(a\) denotes the contraction coefficients and \(G\) is a Gaussian function defined as

\[G = x^l y^m z^n e^{-\alpha r^2}.\]

Each Gaussian function is characterized by the angular momentum numbers \((l, m, n)\) that determine the type of the orbital, the exponent \(\alpha\) and the position vector \(r = (x, y, z)\). These parameters and the contraction coefficients \(a\) define atomic basis functions. Predefined values of the exponents and contraction coefficients for each atomic orbital of a given chemical element can be obtained from reference libraries such as the Basis Set Exchange library.

The basis function object created by the BasisFunction class stores all the basis set parameters including the angular momentum, exponents, positions and coefficients of the Gaussian functions.

The basis function object can be easily passed to the functions that compute various types of integrals over such functions, e.g., overlap integrals, which are essential for Hartree-Fock calculations.

  • l (tuple[int]) – angular momentum numbers of the basis function.

  • alpha (array(float)) – exponents of the primitive Gaussian functions

  • coeff (array(float)) – coefficients of the contracted Gaussian functions

  • r (array(float)) – positions of the Gaussian functions