An analytical procedure to evaluate electronic integrals for molecular quantum mechanical calculations

The main contribution of this paper is to provide an alternative strategy to reduce the number of bi-electronic integrals in ab initio quantum mechanics calculations. An analytical procedure to evaluate the energy of a molecule as well as two-electron integrals is proposed. This approach is based on the generalized exponential function (q-exponential) and is particularly advantageous because it reduces substantially the CPU time in quantum mechanical calculations. Some examples of the effectiveness of this methodology are presented. It is important to point out that the new methodology is applicable to any kind of molecular system including relatively large molecular systems in the context of the Hartree–Fock (HF) and density functional theories (DFT).