A Methodology for Modeling the Complexity of the Hartree-Fock Procedure

Abstract

The maximum number of two electrons integrals (2e-integrals) calculated in the Hartree-Fock (HF) method is given by N 4 , where N is the number of basis functions involved in the calculation. However, in real situations, this amount of integrals can be reduced to the range ~N 3.5 to ~N 2 , depending on factors such as: the molecular structure and the basis set used in the calculation. The methodology presented in this work allows for anticipating the real amount of 2e-integrals calculated in a HF procedure to different molecular structures. The proposal is based on the average of the inertia moments that represent the geometry of the executed molecule. The molecules have been divided in 3 groups of molecular geometry: 3D, planar and linear. The experiments considered molecules with regular and irregular geometries, in the STO-3G, 6-31G and 6-311G basis set. Calculations have been carried out using the GAMESS package. Results demonstrate a consistent behavior for the methodology proposed, as for molecules with regular geometry and for molecules with more irregular geometric structure. The results presented in this paper will allow one to estimate the demand for hard disk and CPU generated in the execution of a molecule with the HF procedure.