Theoretical innovation and computational experiments in Quantum Monte Carlo / Inovações teoricas e experimentos computacionais em Monte Carlo Quantico

AUTOR(ES)
DATA DE PUBLICAÇÃO

2005

RESUMO

The Hartree-Fock method (HF) is the principal strategy used in theoretical chemistry for electronic structure calculations. Although valuable results can be obtain with HF, this method has deficiencies in the treatment of some systems, which are related mainly with electronic correlation. Several methods were developed, known as "post-Hartree-Fock", in arder to expand the present limit of HF. The techniques developed keep some characteristics of HF because they also use the self-consistent-field (SCF). Recently, it was proposed a new strategy, based on statistical mechanics, that alIows to access the exact wave function of the system, by principIe, known as Quantum Monte Carlo (QMC). Among methods that belong to QMC, the Variational Monte Carlo (VMC) and the Diffusion Monte Carlo (DMC) are especialIy important. However, to implement these methods, a particular constraint is used which is not completely compatible with the principIe of anti-symmetry of Pauli. The main goal of this work is to propose and verify the use of density matrix theory in the formalism of VMC and DMC to promote the development of these methods and to render them totalIy compatible with the Quantum Chemistry Postulates. First of alI, it was investigated the present limits of the traditional VMC strategy that use a wave function created as a product of two Slater determinants, one for a electrons and another for b electrons. This wave function is not anti-symmetric for electrons of opposite spins. The influence of this characteristic in electronic distribution and energy of atomic systems were also studied. Theoretical formalism has been developed for Variational Monte Carlo in order to describe the systems through density matrix and, this way, restore the formalism completeness within the method. Some algorithms were created and some programs were written to implement this new methodology in the VMC. Many different systems in different states (fundamental and excited one) were studied with the strategy developed. Moreover, various basis functions were tested with this new VMC. With these studies, we verified the viability and the reliability of the developed method and of the written program and the differences on the properties results caused by this changes in the description of the systems. The correlation effect on Variational Monte Carlo was also studied. First of alI, it was verified the inclusion of the correlation function of Boys and Handy that is commonly used in VMC calculations, in the new method based on density matrix. Next, it was proposed the use of Rayleigh-Schrödinger perturbation method to include the correlation effect on VMC with matrix density theory, an alternative never tried before in Quantum Monte Carlo methods. Next, the Diffusion Monte Carlo was studied. The most used strategy of this method also takes the wave function as a product of two Slater determinants. This way, the methodology has the same limitation of VMC (incompatibility with the anti-symmetry postulate of Pauli). The concept of density matrix was used once again to recover the compatibility of the method and the quantum formalism. So, alI theoretical development to include the matrix density in Diffusion Monte Carlo was done and a new program for this method was written as welI. Computational experiments were performed with systems previously studied in order to ascertain the viability of this method, to certify the quality and to compare the differences of the results obtained by DMC based on density matrix and the traditional one.

ASSUNTO(S)

monte carlo variacional variational monte carlo electronic structure estrutura eletronica diffusion monte carlo density matrix monte carlo de difusão matriz de densidade

ACESSO AO ARTIGO

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