High-accuracy electronic structure quantum Monte Carlo for molecular systems
Torelli, Tommaso
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https://hdl.handle.net/2142/31342
Description
Title
High-accuracy electronic structure quantum Monte Carlo for molecular systems
Author(s)
Torelli, Tommaso
Issue Date
2001
Doctoral Committee Chair(s)
Ceperley, David M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Quantum Monte Carlo methods
quantum many-body problems
molecular systems
Language
en
Abstract
Quantum Monte Carlo (QMC) is one of the most promising methods for solving
quantum many-body problems. QMC combines known analytical properties of wave
functions, results from other methods, and stochastic techniques, into a powerful
tool for investigation of the electronic structure of real materials. Furthermore, the
method has a favorable scaling ( O[N3] in the number of electrons), perfect scalability
on parallel architectures, and can be applied to a wide range of systems.
Our work has focused both on expanding the capabilities of QMC for calculation
of quantities beyond energies, such as interatomic forces, and on application of the
method to challenging problems in nanostructure materials research. For the calculation
of interatomic forces we have implemented a finite difference correlated sampling
method. The correlated sampling enables us to avoid the problem of statistical noise
in evaluating the energy differences and allows us to obtain forces with an average
1% error. We have analyzed the effect of the method's main approximations on the
estimate of the forces, both by theoretical arguments and by performing a variety of
tests on small systems. Furthermore, we have used this newly developed method for
estimating equilibrium geometries in a problem where other methods have failed.
QMC enabled us to treat the electron correlation effects with high accuracy and
to provide accurate predictions in a number of interesting applications. In particular,
for carbon rings of C4N+2 stoichiometry we have resolved a long-standing problem
regarding the competition between the aromaticity and second order Jahn-Teller effects.
We have found that the dominant mechanism at small and intermediate sizes,
which stabilizes the bond angle and bond length alternated geometries, is the secondorder
Jahn-Teller effect while the aromatic isomer is always found to be a transition
state. These high accuracy calculations which have involved multi-reference wave
functions, extensive variational optimizations, and the use of massively parallel platforms
demonstrate clearly the unique capabilities of the QMC approach.
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