الفهرس 
Chapter 1 Introduction to quantum Monte CarloOnly 14 pages are availabe for public view
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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.