الفهرس | Only 14 pages are availabe for public view |
Abstract Quantum Monte Carlo (QMC) methods are a class of stochastic techniques that employ random numbers for solving the Schrödinger equation and for evaluation of expectation values. The key advantage of QMC is its capability to deal with very complicated wavefunctions that incorporate correlation between the electrons. Additionally QMC has O(N3) scaling versus exponential scaling for methods such as configuration interaction method. In the main part of the thesis, we introduce- in detail (description, mathematical derivation, usage, algorithms, and flowcharts if possible) - different methods of quantum Monte Carlo like Blankenbecler-Scalapino- Sugar (BSS), Hirsch-Fye (HF) algorithms in addition the variational Monte Carlo (VMC) and the diffusion Monte Carlo (DMC) methods, as our main tools used in all our calculations. We introduce the application of Monte Carlo and quantum Monte Carlo methods throughout the thesis, e.g., in chapter one, we introduce the estimation of the value of p using Monte Carlo method, in chapter two we introduce two computed examples on BSS and HF algorithms and in chapter three the application of the VMC and DMC methods to estimate the ground state energy of some 3d transition elements, lanthanides, actinides and their corresponding cations. While very accurate QMC calculations have been reported for light atoms and molecules by a large number of researchers, for our knowledge this is the first time that QMC has been applied to lanthanides and actinides. Further, within the framework of the DMC method, the ionization potentials for the studied elements have been calculated and the obtained results for the transition elements and lanthanides are in good agreement with the available experimental data. But the situation is significantly worse for actinides; the results are still biased from the iii ABSTRACT experimental data. In addition, we have calculated the valence correlation energy for the transition elements, lanthanides and actinides and the relation between the difference in energies between the VMC and DMC and the atomic number Z have been discussed. Finally, we have studied the dependence of the DMC energies on the size of the time step; which is the most important error in practical DMC simulation. |