Basis Set

Abstract

The most widely used quantum chemical methods are based on the idea of the expansion of atomic or molecular orbitals as a linear combination of basis functions

$$ {{\varphi }_{i}} = {{c}_{{i1}}}{{\chi }_{1}} + {{c}_{{i2}}}{{\chi }_{2}} + \cdots + {{c}_{{in}}}{{\chi }_{n}} $$

((2.2))

where ϕ_i is a molecular or atomic orbital and y are selected Slater--type, Gaussian or some other functions that are referred to as basis set. If ϕ_i is a molecular orbital (MO), the expansion (2.1) is called MO-LCAO (linear combination of atomic orbitals), though with ab initio calculations it has a broader meaning than implied by the abreviation. The expansion coefficients c_i1, c_i2, ..., c_in for i = 1, ..., n (n is the number of basis set functions) are variational pa-rameters and they are determined by the solution of the SCF problem (see Chapter 3). It is clear that in calculations on atoms the expansion (2,1) must contain at least one function for each occupied atomic orbital. Such a basis set is called minimum basis set. For example, for oxygen the minimum basis set is 1s, 2s, 2p_x, 2p_y and 2p_z.