New applications of density matrix theory in Quantum Monte Carlo Method for the improvement of the electron correlation effect

Author(s)

Wagner Fernando Delfino Angelotti

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Química
• Defense date: 2009-05-02

Examining board members

Rogério Custodio; Milan Trsic; Aguinaldo Robinson de Souza; Adalberto Bono Maurizio Sacchi Bassi; Nelson Henrique Morgon

• Advisor: Rogério Custodio

Abstract

This thesis explored different goals involving the quantum Monte Carlo method, of which stand out: assessment of the conventional method in electronic properties; formalization of relations between the density matrix theory and the variational and diffusion quantum Monte Carlo methods; study of the electronic correlation with different correlated functions and also through mixed method involving the perturbation theory and variational quantum Monte Carlo; applications to atoms of the first and second period of the periodic table and diatomic molecules. Computational experiments with the quantum Monte Carlo method and separation of spins were achieved producing excellent results for calculations of successive ionization potentials for atoms, single ionization of atoms and simple molecules and calculation of potential curves for simple molecules. Two analytical formulations were obtained that describes exactly the formal link between the density matrix and quantum Monte Carlo. This association has provided excellent results for variational and diffusion methods, presenting similarities and significant differences when compared to conventional treatment with respect to the nodal structure for each electronic state studied. Furthermore, the density matrix together with correlated wave functions is able to recover part of the electronic correlation and makes possible the correction of the wave functions within the association of quantum Monte Carlo and perturbation theory. (AU)