Abstract: The Guass-Legendre numerical quadrature method was introduced into the calculation of STO two-centre overlap integrals. The result shows that this method is efficient and accurate, and it can be applicable to the integer power and non-integer power of r, and to the sufficiently wide range of values of orbital parameters and internuclear distances as well.

Key words: Molecules integrals, Overlap integrals, Gauss quadrature method