Very Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functions

Persistent Link:
http://hdl.handle.net/10150/560835
Title:
Very Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functions
Author:
Sharkey, Keeper Layne
Issue Date:
2015
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.
Type:
text; Electronic Dissertation
Keywords:
Computation; Molecule; Quantum; Rydberg; Theory; Chemistry; Atom
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Chemistry
Degree Grantor:
University of Arizona
Advisor:
Adamowicz, Ludwik

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleVery Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functionsen_US
dc.creatorSharkey, Keeper Layneen
dc.contributor.authorSharkey, Keeper Layneen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractDue to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectComputationen
dc.subjectMoleculeen
dc.subjectQuantumen
dc.subjectRydbergen
dc.subjectTheoryen
dc.subjectChemistryen
dc.subjectAtomen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineChemistryen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorAdamowicz, Ludwiken
dc.contributor.committeememberLichtenberger, Dennisen
dc.contributor.committeememberBrown, Michael F.en
dc.contributor.committeememberAnderson, Brian P.en
dc.contributor.committeememberAdamowicz, Ludwiken
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