There has been recent interest in the nature of the interaction between atoms in molecules, atomic and molecular clusters, and the nature of the forces that leads to the crystalline structures such as that found in bulk calcium carbonate. With an understanding of the physics behind atomic interactions we can better understand how crystal structures grow, how materials are formed, how to predict the electrical properties of the materials, and how to create new materials that can be used in science.
The development of new, high performance, computer systems that fit on desktops, has led to an evolution in the development of new computational methods and algorithms in the field of quantum chemistry. Over the last 10 years new methods and algorithms have been developed to take advantage of the increase in computer speed and storage capabilities. The evolution of computer systems has led to new computational methods that allow us to better predict chemical, electrical, and thermodynamic properties in systems of atoms and molecules, to better predict chemical reaction and transition states, to better describe the formation of geometric structures and 3D modeling, and to better define the processes involved in the formation of bulk material from clusters of atoms and molecules.
The latest addition to
the family of supercomputers is called the ASCI White, which was developed by
IBM last year. It has the equivalent
power of roughly 50,000 desktop computers. It has the capability of storing 300
million books, or six Libraries of Congress.
According to Tomas Dias de le Rubia, a material program leader at
Livermore, the computer is capable of creating three-dimensional models that
can track the behavior of 1 billion atoms at once. This high-end supercomputer opens up new avenues in the field of
material sciences that will allow us to predict, and quantify, the
behavior of billions of atoms and molecules, and may one day lead to a better understanding in to the field of material sciences.
In
this thesis, I investigated the growth of calcium clusters and clusters of CaCO3
within the Density Functional Theory (DFT) framework and the General Gradient
Approximation (GGA). I determined the
structure, binding energies, and harmonic vibrational frequencies for several
isomers at each cluster size up to Ca13. Thermodynamic properties of the calcium clusters were found in
the harmonic approximation using the calculated values for the vibrational
frequencies. The lowest energy structure
for Ca6 and Ca10 through Ca13 had not been
reported before as global minimum energy structures. I found that the metallic character of calcium is far from
attained at Ca13 because the difference between the Highest Occupied
Molecular Orbital (HOMO) and the Lowest Occupied Molecular Orbital (LUMO) was
still high at 0.8 eV. Several reaction
paths that connected different isomers via a transition structure were
investigated. The investigation went from calcium clusters to calcium carbonate
clusters where the lowest energy structures for CaCO3 were found for
up to four molecules. This was about
the limit of computational ability. The
energy and structures were than fitted to parameters of the Rigid Ion Model
(RIM) potential in an effort to investigate clusters containing more than four
molecules.
There is a special
interest and need in the study of hazardous chemicals and nerve agents. These are chemicals that are difficult to
handle and very difficult to study due to the hazards associated with these
chemicals. An alternative to
experiments, and to allow the prediction of chemical properties of substances
like sarin, an analysis was performed on the degradation of sarin with water
and the hydroxyl radical. Using Hartree-Fock methods, I identified the lowest energy path
of the reaction of sarin with (OH)* that would result in the formation of a
less toxic substance.
This thesis is
organized as follows: In Chapter 2, I
discuss the general theory, ab-initio methods used in the study, and
computational methods used in the analysis.
In Chapter 3, I present the results of ab-initio calculations on calcium
clusters. In Chapter 4, I present
quantum mechanical calculations performed in the analysis and hydrolysis of GB
with OH. Chapter 5 contains the
investigation of clusters of Calcium Carbonate molecules, where the GGA was
used to optimize the parameters of the Rigid Ion Model Potential. The new parameters can then be used to
extend the semi-empirical equations to larger clusters. Chapter 6 contains a
summary of the results of the thesis and the computer programs used in the
analysis which includes the method used in locating transition structures and
reaction paths, discussion of the Nudged Elastic Band (NEB) method, non-linear
least square fitting, and geometric optimization from semi-empirical equations
using the conjugant gradient method.