Avaliando polinômios como novas funções de base para cálculo químico-quânticos moleculares

Abstract

The Schrödinger equation, although theoretically capable of calculating electronic quantum states in chemical systems, faces limitations when dealing with systems with more than one electron. The Hartree-Fock-Roothaan (HFR) theory offers an approximate approach to overcome these limitations by transforming the problem of solving the coupled Schrödinger equation for N electrons into N independent problems for 1 electron subject to the nonlinear Coulomb nuclear potential and a mean field due to electronic interactions, with the solutions being adapted to the Pauli exclusion principle. The implementation of the HFR theory requires the use of basis functions, such as Gaussian Type Orbitals (GTOs). The analytical form of GTOs requires the calculation of exponentials, making the evaluation of parameters such as electron density computationally expensive. This work proposes an innovation by replacing GTOs with Polynomial Type Orbitals (PTOs), aiming to significantly accelerate quantum chemical calculations. The comparison between the energies obtained with PTOs and GTOs in the Helium atom and in the H2 molecule was performed following the variational theorem, which guides the search for a solution closer to the true one. The objective was to contribute to the effectiveness and efficiency of calculations in quantum chemistry and, potentially, positively influence several computational applications in this field. Three PTOs were tested, and one of them obtained through a Computational Fluid Dynamics (CFD) study presented excellent results both in computational efficiency and in energy calculation.