Tesi sul tema "Gaussian quantum mechanics"

Thermal (canonical) condensed-phase systems are of considerable interest in computational science, and include for example reactions in solution. Time-independent properties of these systems include free energies and thermally averaged geometries - time-dependent properties include correlation functions and thermal reaction rates. Accounting for quantum effects in such simulations remains a considerable challenge, especially for large systems, due to the quantum nature and high dimensionality of the phase space. Additionally time-dependent properties require treatment of quantum dynamics. Most current methods rely on semi-classical trajectories, path integrals or imaginary-time propagation of wave packets. Trajectory based approaches use continuous phase-space trajectories, similar to classical molecular dynamics, but lack a direct link to a wave packet and so the time-dependent schrodinger equation. Imaginary time propagation methods retain the wave packet, however the imaginary-time trajectory cannot be used as an approximation for real-time dynamics. We present a new approach that combines aspects of both. Using a generalisation of the coherent-state basis allows for mapping of the quantum canonical statistical average onto a phase-space average of the centre and width of thawed Gaussian wave packets. An approximate phase-space density that is exact in the low-temperature harmonic limit, and is a direct function of the phase space is proposed, defining the Gaussian statistical average. A novel Nose-Hoover looped chain thermostat is developed to generate the Gaussian statistical average via the ergodic principle, in conjunction with variational thawed Gaussian wave-packet dynamics. Numerical tests are performed on simple model systems, including quartic bond stretching modes and a double well potential. The Gaussian statistical average is found to be accurate to around 10% for geometric properties at room temperature, but gives energies two to three times too large. An approach to correct the Gaussian statistical average and ensure classical statistics is retrieved at high temperature is then derived, called the switched statistical average. This involves transitioning the potential surface upon which the Gaussian wave packet propagates, and the system property being averaged. Switching functions designed to perform these tasks are derived and tested on model systems. Bond lengths and their uncertainties calculated using the switched statistical average were found to be accurate to within 1% relative to exact results, and similarly for energies. The switched statistical average, calculated with Nose- Hoover looped chain thermostatted Gaussian dynamics, forms a new platform for evaluating statistical properties of quantum condensed-phase systems using an explicit real-time wave packet, whilst retaining appealing features of trajectory based approaches.

This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

Employing correlation consistent basis sets coupled with electronic structure methods has enabled accurate predictions of chemical properties for second- and third-row main group and transition metal molecular species. For third-row (Ga-Kr) molecules, the performance of the correlation consistent basis sets (cc-pVnZ, n=D, T, Q, 5) for computing energetic (e.g., atomization energies, ionization energies, electron and proton affinities) and structural properties using the ab initio coupled cluster method including single, double, and quasiperturbative triple excitations [CCSD(T)] and the B3LYP density functional method was examined. The impact of relativistic corrections on these molecular properties was determined utilizing the Douglas-Kroll (cc-pVnZ-DK) and pseudopotential (cc-pVnZ-PP) forms of the correlation consistent basis sets. This work was extended to the characterization of molecular properties of novel chemically bonded krypton species, including HKrCl, FKrCF3, FKrSiF3, FKrGeF3, FKrCCF, and FKrCCKrF, and provided the first evidence of krypton bonding to germanium and the first di-krypton system. For second-row (Al-Ar) species, the construction of the core-valence correlation consistent basis sets, cc-pCVnZ was reexamined, and a revised series, cc-pCV(n+d)Z, was developed as a complement to the augmented tight-d valence series, cc-pV(n+d)Z. Benchmark calculations were performed to show the utility of these new sets for second-row species. Finally, the correlation consistent basis sets were used to study the structural and spectroscopic properties of Au(CO)Cl, providing conclusive evidence that luminescence in the solid-state can be attributed to oligomeric species rather than to the monomer.

L'informatique quantique est basée sur des phénomènes de physique quantique, tels que superposition et intrication et elle promet de révolutionner le monde de l'informatique. La photonique est une plateforme de premier plan pour réaliser l'informatique quantique tolérante aux erreurs. Elle possède plusieurs qualités : fonctionnement à température ambiante, fabricabilité à grande échelle à l'aide des fonderies existantes pour les puces de silicium et compatibilité avec les communications optique pour interconnecter différents ordinateurs quantiques.Notre objectif principal est d'automatiser la conception de circuits quantiques photoniques et de leurs interconnexions. Avant de pouvoir fabriquer un véritable ordinateur quantique photonique, il est essentiel de simuler numériquement et d'optimiser les circuits correspondants, qui sont en pratique construits à partir de composants gaussiens tels que des squeezers, des séparateurs de faisceaux, des déphaseurs et des détections homodynes. Pour atteindre l'universalité, nous avons également besoin d'effets non gaussiens, qui peuvent être fournis par des détecteurs résolvant le nombre de photons. Nous concevons des circuits à partir de cette boîte à outils et les optimisons pour diverses applications en utilisant divers algorithmes de descente de gradient, dont certains que nous avons adaptés à notre objectif.Les principaux apports sont :1. En photonique, les représentations de l'espace de Fock et de l'espace de phase sont des formalismes utiles pour décrire les états et les transformations quantiques. Nous introduisons une représentation unifiée dans l'espace de Fock de tous les objets gaussiens en termes d'une seule relation de récurrence linéaire qui peut générer de manière récursive leurs amplitudes dans l'espace de Fock.2. On retrouve la règle de composition des opérations gaussiennes dans l'espace de Fock, qui permet d'obtenir la bonne phase globale lors de la composition des opérations gaussiennes (normalement absente), et donc d'étendre notre modèle à des états qui s'écrivent comme combinaisons linéaires de gaussiennes.3. Notre représentation récursive est différentiable, permettant à calculer des gradients. Nous adaptons ensuite l'optimisation basée sur les gradients au problème d'optimisation des circuits. Nous implémentons un optimiseur Euclidien afin d'optimiser chaque composant. Ensuite, nous étudions deux manières de prendre en compte la géométrie: d'abord, nous appliquons l'optimisation Riemannienne, en combinant toutes les opérations gaussiennes en une transformation globale pour trouver ensuite la transformation optimisée, et la décomposer en composants optiques fondamentaux. Deuxièmement, nous généralisons une version complexe du gradient naturel pour les circuits afin d'accélérer le processus d'apprentissage.4. Nous donnons également quelques stratégies optimales basées sur les tâches pour utiliser nos relations de récurrence. De nouveaux algorithmes sont proposés pour calculer, par exemple, les amplitudes d'un état mixte et la matrice de transformation des interféromètres. De plus, nous dérivons un algorithme de contraction rapide pour les transformations gaussiennes, qui nous permet de "fusionner" le calcul des amplitudes d'une transformation gaussienne et son action sur n'importe quel état.5. Avec la simulation sur des circuits quantiques photoniques différentiables construits à partir de la relation de récurrence, nous pouvons concevoir automatiquement des circuits quantiques photoniques. Nous donnons la préparation de l'état comme premier exemple ; nous trouvons des circuits capables de produire des états de haute fidélité dans un temps raisonnable. Nous pouvons aussi optimiser un interféromètre à 216 modes pour rendre une expérience d'échantillonnage de boson gaussien difficile à usurper.6. Nous avons rendu ce travail accessible dans diverses bibliothèques open source: TheWalrus, StrawberryFields, Poenta et MrMustard
Quantum computing is based on quantum physics phenomena, such assuperposition and entanglement and it promises to revolutionize the world of computing. Photonics is a prominent platform for realizing fault-tolerant quantum computing. It has various qualities: working at room temperature, large-scale manufacturability using existing foundries for silicon chips, and compatibility with optical communication to interconnect different quantum computers.Our main goal is to automate the design of photonic quantum circuits and of their interconnects. Before a real photonic quantum computer can be manufactured, it is essential to numerically simulate and optimize the corresponding circuits, which in practice are built out of Gaussian components such as squeezers, beam-splitters, phase shifters, and homodyne detectors. To achieve universality, we also need non-Gaussian effects, which can be supplied by photon-number-resolving detectors. We design circuits from this toolbox and optimize them for various applications using various gradient descent algorithms, some of which we adapted to our purpose.The main contributions are:1. In photonics, Fock space and phase space representations are both useful formalisms to describe quantum states and transformations. We introduce a unified Fock space representation of all Gaussian objects in terms of a single linear recurrence relation that can recursively generate their Fock space amplitudes.2. We find the composition rule of Gaussian operations in Fock space, which allows us to obtain the correct global phase when composing Gaussian operations (normally absent from the phase space description), and therefore to extend our model to states that can be written as linear combinations of Gaussians.3. Our recursive representation is differentiable, allowing for a straightforward computation of the gradients of a Gaussian object with respect to any parametrization. We then adapt gradient-based optimization to the problem of circuit optimization. We implement a Euclidean optimizer (i.e. which doesn't take the geometry of parameter space unto account) in order to optimize each parametrized component of a circuit. Then we study two ways to account for geometry: first we apply Riemannian optimization, by combining all the Gaussian operations into a global transformation and following a geodesic on the manifold of symplectic matrices to find the optimized transformation, at which point we can decompose it back into fundamental optical components. Second, we generalize a complex version of the natural gradient for optical quantum circuits to accelerate the convergence of the training process.4. We also give some optimal task-based strategies for using our recurrence relations. New algorithms are proposed to calculate, for instance, the amplitudes of a mixed state and the transformation matrix of interferometers. In addition, we derive a fast contraction algorithm for Gaussian transformations, which allows us to "fuse" the computation of the amplitudes of a Gaussian transformation and its action on any state.5. With the simulation on differentiable photonic quantum circuits built from the recurrence relation, we can design photonic quantum circuits automatically. We give state preparation as the first example; we find circuits that can produce high-fidelity states in a reasonable time, such as cat states with mean photon number 4, fidelity 99.38%, and success probability 7.3%. We can also optimize a 216-mode interferometer to make a Gaussian Boson Sampling experiment harder to spoof.6. We made this work available in various open-source libraries: TheWalrus, StrawberryFields, Poenta, and MrMustard

Orientador: Marcos Cesar de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Resumo: Estudamos estados Gaussianos quânticos e as propriedades físicas associadas a operações sobre tal classe de estados que preservam a sua natureza Gaussiana. Propriedades gerais de matrizes de covariância globais representando estados Gaussianos bipartidos de dois modos podem ser decompostas em propriedades de matrizes de covariância locais e seus complementos de Schur. Demonstramos que dado um estado Gaussiano de dois modos r12 descrito por uma matriz de covariância V 4 × 4, o complemento de Schur de uma submatriz de covariância local V2 2 × 2 pode ser interpretado como uma nova matriz de covariância representando um operador Gaussiano do modo 1 condicionado a medições de paridade no modo 2. Como o valor médio da paridade está relacionado com a determinação da função de Wigner de um estado na origem do espaço de fase, que pode ser obtido facilmente através de experimentos de fotocontagem, este resultado nos permite estudar propriedades desta função em termos das probabilidades de medições pares e ímpares no modo local. Também generalizamos este procedimento para um estado Gaussiano de n modos e demonstramos que o operador dos n - 1 sistemas condicionado a projeções parciais de paridade está relacionado com uma matriz de covariância tal que seus elementos bloco 2 × 2 são complementos de Schur de matrizes especiais locais. A determinação da relação entre uma estrutura matemática (o complemento de Schur) com um processo físico permitiram a construção de um protocolo para a identificação de propriedades de emaranhamento de um estado Gaussiano de dois modos via apenas medições/operações locais e um canal de comunicação clássica entre as duas partes. Este protocolo se baseia na obtenção dos quatro invariantes simpléticos locais do grupo Sp(2, R) que determinam as propriedades de emaranhamento e de pureza do sistema Gaussiano de dois modos. Além disso, para uma classe de estados Gaussianos simétricos, que inclui por exemplo o estado comprimido com ruído térmico e o estado EPR, este protocolo também é útil para a reconstrução de sua matriz de covariância
Abstract: We study quantum Gaussian states and the physical properties associated to operations over such class of states, which preserve the respective Gaussian nature. General properties of global covariance matrices representing two-mode bipartite Gaussian states can be decomposed into properties of local covariance matrices and their Schur complements. We demonstrate that given a two-mode Gaussian state r12 described by a 4 × 4 covariance matrix V, the Schur complement of a 2 × 2 local covariance sub-matrix V2 of it can be interpreted as a new covariance matrix representing a Gaussian operator of party 1 conditioned to local parity measurements on party 2. As the parity mean value is related to the determination of the Wigner function of a state at the origin of the phase-space, which can be achieved straightforwardly by photocounting experiments, this result allow us to study properties of this function in terms of the odd and even measurements probabilities of the local mode. We also generalize this procedure to a n partite Gaussian state and we demonstrate that a n - 1 system operator conditioned to a partial projection is given by a covariance matrix such as its 2 × 2 block elements are Schur complements of special local matrices. The determination of the relation between a mathematical structure (the Schur complement) with a physical process allowed us to construct a protocol to identify the two-mode Gaussian state entanglement properties via only local measure-ments/ operations and a classical communication channel between the two parties. This protocol is established from the achievement of the four local sympletic invariants of the Sp(2, R) group, which determines the entanglement and purity properties of a two-mode Gaussian state. Moreover, for the symmetric Gaussian states class, which include for example the squeezed thermal state and the EPR state, this protocol is also uselfull for the covariance matrix reconstruction
Mestrado
Física
Mestre em Física

The development of the correlation consistent basis sets, cc-pVnZ (where n = D, T, Q, etc.) have allowed for the systematic elucidation of the intrinsic accuracy of ab initio quantum chemical methods. In density functional theory (DFT), where the cc-pVnZ basis sets are not necessarily optimal in their current form, the elucidation of the intrinsic accuracy of DFT methods cannot always be accomplished. This dissertation outlines investigations into the basis set requirements for DFT and how the intrinsic accuracy of DFT methods may be determined with a prescription involving recontraction of the cc-pVnZ basis sets for specific density functionals. Next, the development and benchmarks of a set of cc-pVnZ basis sets designed for the s-block atoms lithium, beryllium, sodium, and magnesium are presented. Computed atomic and molecular properties agree well with reliable experimental data, demonstrating the accuracy of these new s-block basis sets. In addition to the development of cc-pVnZ basis sets, the development of a new, efficient formulism of the correlation consistent Composite Approach (ccCA) using the resolution of the identity (RI) approximation is employed. The new formulism, denoted 'RI-ccCA,' has marked efficiency in terms of computational time and storage, compared with the ccCA formulism, without the introduction of significant error. Finally, this dissertation reports three separate investigations of the properties of FOOF-like, germanium arsenide, and silicon hydride/halide molecules using high accuracy ab initio methods and the cc-pVnZ basis sets.

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.

Estudamos as excitações de baixa energia, presentes em um gás de bosons homogêneo, de spin nulo, sujeitos a uma interação de dois corpos repulsiva e a temperatura zero, utilizando a aproximação gaussiana, que consiste num caso particular de aproximação de campo médio. As equações dinâmicas resultantes foram linearizadas ao redor da solução estática de Hartree-Fock-Bogoliubov. Obtivemos uma banda contínua e limitada inferiormente, além de um segundo ramo discreto, que define um limite inferior para as excitações e que, ao contrário do resultado proveniente do tratamento de Hartree-Fock-Bogoliubov, possui um comportamento linear sem gap com respeito ao momento da excitação no limite de grandes comprimentos de onda, ou seja, possui uma equação de dispersão do tipo fônon. Discutimos também a forma através da qual é possível gerar desvios do equilíbrio, vinculados aos estados excitados, e concluímos haver restrições sobre os possíveis desvios das grandezas características em campo médio gaussiano, quando tais desvios são gerados por transformações infinitesimais unitárias de um corpo tomadas até primeira ordem.
We study low-lying excitations of a spinless, homogeneous bose gas, with repulsive interaction, at zero temperature, in terms of a gaussian mean field approximation. The dynamical equations of this approximation have been linearized in small displacements from the well known static Hartree-Fock-Bogoliubov solution. We obtain a gapped continous band of excitations above a discrete branch with phonon behavior at large wavelengths. We also discuss the allowed forms of excitations and conclude that restrictions exist for the allowed deviations of the general set of gaussian mean field parameters, when they are generated in first orders by infinitesimal unitary transformations.

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Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
Considering a quantum gas, the foundations of standard thermostatistics are investigated in the context of non-Gaussian statistical mechanics introduced by Tsallis and Kaniadakis. The new formalism is based on the following generalizations: i) Maxwell- Boltzmann-Gibbs entropy and ii) deduction of H-theorem. Based on this investigation, we calculate a new entropy using a generalization of combinatorial analysis based on two different methods of counting. The basic ingredients used in the H-theorem were: a generalized quantum entropy and a generalization of collisional term of Boltzmann equation. The power law distributions are parameterized by parameters q;, measuring the degree of non-Gaussianity of quantum gas. In the limit q ?1; ?0, the gaussian thermostatistics is recovered. A complementary study is related to a perfect gas in the context of general relativity. Using the non-Gaussian effects on the concept of entropy flux, and on the collisional term of the Boltzmann equation, we generalize the H-theorem within the Tsallis and Kaniadakis frameworks. In the first one, the nonextensive parameter is constrained to the interval [0,2]
Considerando um g?s qu?ntico, os fundamentos da termoestat?stica padr?o s?o investigados no contexto da mec?nica estat?stica n?o-gaussiana introduzida por Tsallis e Kaniadakis. O novo formalismo ? baseado nas seguintes generaliza??es: i) entropia de Maxwell-Boltzmann-Gibbs e ii) dedu??o do Teorema-H. Com base neste estudo, calculamos uma nova entropia usando a generaliza??o da an?lise combinat?ria baseadas em dois diferentes m?todos de contagem. Os ingredientes b?sicos usados no teorema-H foram: uma entropia qu?ntica generalizada e uma generaliza??o do termo colisional da equa??o de Boltzmann. As distribui??es lei de pot?ncia calculadas s?o parametrizadas pelos par?metros q; , medindo o grau de n?o-gaussianidade do sistema. No limite q ?1; ?0, a termoestat?stica gaussiana ? recuperada. Um estudo complementar est? relacionado com um g?s perfeito no contexto da relatividade geral. Utilizando os efeitos n?o-gaussiano no conceito de fluxo de entropia, e no termo colisional da equa??o de transporte de Boltzmann, n?s generalizamos o teorema- H nos formalismos de Tsallis e Kaniadakis. No formalismo de Tsallis, o par?metro n?o extensivo est? restrito ao intervalo [0,2]

Chien Siu-Hung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract (English)
Abstract (Chinese)
Acknowledgements
Table of Contents
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian-2 Method
Chapter 1.2 --- The Gaussian-3 Method
Chapter 1.3 --- The G3 Method with Reduced Moller-Plesset Order and Basis Set
Chapter 1.4 --- Calculated Thermochemical Data
Chapter 1.5 --- Remark on the Location of Transition State
Chapter 1.6 --- Scope of the Thesis
Chapter 1.7 --- References
Chapter Chapter 2 --- "Energetics and Structures of the Carbonyl Chloride Radical, Oxalyl Chloride, and Their Cations" --- p.6
Chapter 2.1 --- Introduction
Chapter 2.2 --- Computational Methods
Chapter 2.3 --- Results and Discussion
Chapter 2.3.1 --- Carbonyl Chloride and Its Cation
Chapter 2.3.2 --- The anti and syn Conformers of Oxalyl Chloride and Oxalyl Chloride Cation
Chapter 3.3.3 --- The anti and gauche Conformers of (ClCO) 2 and the TS Linking Them
Chapter 2.4 --- Conclusions
Chapter 2.5 --- Publication Note
Chapter 2.6 --- References
Chapter Chapter 3 --- "An Isomeric Study of N5, N5+，and N5- : A Gaussian-3 Investigation" --- p.17
Chapter 3.1 --- Introduction
Chapter 3.2 --- Computational Methods
Chapter 3.3 --- Results and Discussion
Chapter 3.3.1 --- "The N5 Isomers """
Chapter 3.3.2 --- The N5+ Isomers
Chapter 3.3.3 --- The N5- Isomers
Chapter 3.3.4 --- Comparison of the G3 and G3(MP2) Results
Chapter 3.4 --- Conclusions
Chapter 3.5 --- Publication Note
Chapter 3.6 --- References
Chapter Chapter 4 --- Thermochemistry of Hydrochlorofluorosilanes : An Ab Initio Gaussian-3 Study --- p.28
Chapter 4.1 --- Introduction
Chapter 4.2 --- Computational Methods
Chapter 4.3 --- Results and Discussion
Chapter 4.3.1 --- Heats of Formation for Neutral HCFSis
Chapter 4.3.2 --- Ionization Energies
Chapter 4.3.3 --- Electron Affinities
Chapter 4.3.4 --- Proton Affinities
Chapter 4.3.5 --- Acidities
Chapter 4.3.6 --- G3 versus G3(MP2)
Chapter 4.4 --- Conclusions
Chapter 4.5 --- Publication Note
Chapter 4.6 --- References
Chapter Chapter 5 --- A Gaussian-3 Study of the Photodissociation Channels of Thiirane --- p.48
Chapter 5.1 --- Introduction
Chapter 5.2 --- Computational Methods
Chapter 5.3 --- Results and Discussion
Chapter 5.3.1 --- The Heats of Reactions
Chapter 5.3.2 --- The Dissociation Channels Taking Place at the Ground State
Chapter 5.3.3 --- The Dissociation Channels Taking Place at Excited States
Chapter 5.4 --- Conclusions
Chapter 5.5 --- References
Chapter Chapter 6 --- A Gaussian-3 Study of the VUV Photoionization and Photodissociation of Chloropropylene Oxide --- p.59
Chapter 6.1 --- Introduction
Chapter 6.2 --- Computational Methods
Chapter 6.3 --- Results and Discussion
Chapter 6.3.1 --- Ionization Energy
Chapter 6.3.2 --- Dissociation Channels
Chapter 6.4 --- Conclusions
Chapter 6.5 --- Publication Note
Chapter 6.6 --- References
Chapter Chapter 7 --- Conclusions --- p.69
Appendix A The Gaussian-n (n=l-3) Theoretical Models --- p.71
Chapter A.1 --- The G1 and G2 Theories
Chapter A.2 --- The G3 Theory
Chapter A.3 --- The G3(MP2) Theory
"Appendix B Calculation of Enthalpy at 298 K,H298" --- p.74

It remains questionable whether all physically realizable computational model can be simulated by currently available digital computer in an efficient manner. The theory of Quantum Mechanics offers an answer to this question through one of its branches that intersects with Computer Science, known as Quantum Computing. It claims that current computers, which is operating based on classical mechanics cannot efficiently simulate quantum mechanical process. Under this claim, a computer that is operating based on quantum mechanics holds more computational power than classical computers, promising a possibility to computationally solve problems that are classically intractable. To show that this claim holds, numerous quantum computational models have been proposed and analyzed through the lens of Computational Complexity Theory, providing a rigorous notion of efficiency. Models that are more feasible experimentally, although not necessarily universal, have also been of a particular interests given the numerous complicated challenges surrounding the experimental implementation of a universal quantum computer. One of this non-universal models is called Gaussian Boson Sampling (GBS), which embraces the methods of Quantum Optics by sampling the number of photon outputs from a linear optical network as a means to process quantum information. Compared to its prototype model, Boson Sampling, GBS is more experimentally feasible due to its method of generating photon that is based on the Continuous Variable (CV) paradigm of Quantum Information. Nevertheless as with Boson Sampling, it was also shown that classical simulation of GBS cannot be performed efficiently under some highly plausible conjectures. In the work presented in this thesis, we probe the complexity of classically constructing the probability distribution induced by GBS using the method of Quantum Homodyne Tomography. Instead of photon number measurement, this method further embraces the CV paradigm in the measurement of GBS by using Homodyne measurements that outputs real numbers. Sample data obtained from the measurement outcomes is then classically processed using Pattern Functions, which we use to approximate the probability distribution of GBS. A series of computer simulations that approximates some probability values of GBS are presented here, which shows that the number of samples needed to decrease the error of the approximation increases rapidly for more accurate approximation. We have derived a bound for the approximation error which can be achieved given that the sampled data satisfies a certain statistical property. This statistical property can eventually be satisfied as the number of Homodyne samples increases. Having shown another evidence for the complexity of approximating GBS using Homodyne Tomography, we further investigate the nature of the complexity of GBS by analyzing its classical-quantum computational boundary in the spectrum of amount of noise present in a GBS setup. In doing this, we built our discussions on the measure of non-classicality using the presence of negative values in the Quasi-probability distribution (QPD) representation of states of a quantum system. We then discuss existing results that shows the possibility of efficient classical simulation of a quantum computational model given a sufficient amount of noise. These results impose a necessary criteria of the minimum amount of noise that an experiment has to surpass in order for it to be impossible to simulate classically in an efficient manner. We extend this idea for GBS, where we propose a modified GBS where we consider noise in its measurements that opens a way for a possible formulation of a noise condition that a GBS experiment has to fulfill to rule out possible efficient classical simulation. To further probe the classical-quantum computational boundary, we also propose a different quantum computational model called the Photon-added Thermal State CV-Sampling (PATS CVS), which can be formulated similarly to our noisy GBS model. We then discuss existing results that analyzes the negativity of the QPD representation of a noisy Photon-added Thermal state (PATS), which constitutes the inputs for PATS CVS. Using the result that shows the quantum-classical transition in terms of the QPD negativity for a PATS state when the amount of noise changes, we discuss the potential of PATS CVS model as a possible avenue to further probe the transition between efficiently simulable and non-efficiently simulable quantum mechanical experiment.

Lau Kai-Chi.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Table of Contents --- p.iv
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1
Chapter 1.2 --- The G3 Method with Reduced MΦ ller-Plesset Order and Basis Set --- p.2
Chapter 1.3 --- The Gaussian-3X Method --- p.2
Chapter 1.4 --- The Modified G2 Method --- p.3
Chapter 1.5 --- Calculation of Thermodynamical Data --- p.3
Chapter 1.6 --- Remark on the Location of Transition Structures --- p.4
Chapter 1.7 --- Scope of the Thesis --- p.4
Chapter 1.8 --- References --- p.4
Chapter Chapter 2 --- "A Gaussian-2 and Gaussian-3 Study of Alkoxide Anion Decompositions. I. H2 and CH4 Eliminations of the Methoxide, Ethoxide, i-Propoxide, and t-Butoxide Anions" --- p.6
Chapter 2.1 --- Introduction --- p.6
Chapter 2.2 --- Methods of Calcuations --- p.7
Chapter 2.3 --- Results and Discussion --- p.8
Chapter 2.3.1 --- Nature of ion-neutral complex --- p.8
Chapter 2.3.2 --- Initial bond cleavage of alkoxide anions --- p.9
Chapter 2.3.3 --- Dissociation of alkoxide anions --- p.10
Chapter 2.4 --- Conclusions --- p.23
Chapter 2.5 --- Publication Note --- p.25
Chapter 2.6 --- References --- p.25
Chapter Chapter 3 --- A Gaussian-2 and Gaussian-3 Study of Alkoxide Anion Decompositions. II. Alkane Eliminations of (CH3)2(C2H5)CO- and (i-Pr)(C2H5)2CO- --- p.28
Chapter 3.1 --- Introduction --- p.28
Chapter 3.2 --- Methods of Calculations --- p.29
Chapter 3.3 --- Results and Discussion --- p.29
Chapter 3.3.1 --- Initial bond cleavage of alkoxide anions --- p.30
Chapter 3.3.2 --- Dissociation of alkoxde anions --- p.31
Chapter 3.3.3 --- General dissociation mechanism of alkoxide anions --- p.35
Chapter 3.4 --- Conclusions --- p.37
Chapter 3.5 --- References --- p.37
Chapter Chapter 4 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Dimethyl Disulfide --- p.40
Chapter 4.1 --- Introduction --- p.40
Chapter 4.2 --- Methods of Calculations --- p.41
Chapter 4.3 --- Results and Discussion --- p.41
Chapter 4.3.1 --- Bond cleavage reactions --- p.44
Chapter 4.3.2 --- Dissociation channels involving transition structures --- p.45
Chapter 4.4 --- Conclusions --- p.48
Chapter 4.5 --- References --- p.48
Chapter Chapter 5 --- A Gaussian´ؤ3 Study of the Photodissociation Channels of Propylene Sulfide --- p.50
Chapter 5.1 --- Introduction --- p.50
Chapter 5.2 --- Methods of Calculations --- p.51
Chapter 5.3 --- Results and Discussion --- p.51
Chapter 5.3.1 --- The dissociation channels involving transition structures --- p.53
Chapter 5.3.2 --- The dissociations of sulfur atom --- p.56
Chapter 5.4 --- Conclusions --- p.58
Chapter 5.5 --- References --- p.59
Chapter Chapter 6 --- Thermochemistry of Phosphorus Fluorides: A Gaussian´ؤ3 and Gaussian´ؤ3X Study --- p.60
Chapter 6.1 --- Introduction --- p.60
Chapter 6.2 --- Methods of Calculations --- p.62
Chapter 6.3 --- Results and Discussion --- p.62
Chapter 6.3.1 --- Comparison of the G3 and G3X methods --- p.62
Chapter 6.3.2 --- Assessments of the experimental results --- p.65
Chapter 6.4 --- Conclusions --- p.71
Chapter 6.5 --- References --- p.71
Chapter Chapter 7 --- Conclusions --- p.74
Appendix A --- p.75
Appendix B --- p.78

Optomechanics has made great strides in theory and experiments over the past decade, which culminated in the first direct detection of gravitational waves in 2015 by LIGO. This thesis explores how optomechanics can be used to test fundamental physics other than the theory of general relativity. Our emphasis will be on falsifiable theories (ultimately, only experiments can decide whether a theory is correct) that address two outstanding issues in quantum mechanics: the measurement problem, and reconciling quantum mechanics with the theory of general relativity. In particular, we show that the space experiment LISA pathfinder places aggressive bounds on two objective collapse models, which are non-linear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that state-of-the-art torsion pendulum experiments can test the Schroedinger-Newton theory, which is the non-relativistic limit of a non-linear theory combining quantum mechanics with a fundamentally classical spacetime.

Along the way, we propose how to resolve two major difficulties with determining the predictions of non-linear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in non-linear quantum mechanics and so we have to suggest and justify a particular ensemble for the thermal bath. Separating out quantum and classical fluctuations helped us propose a reasonable ensemble. Second, most researchers believe that deterministic non-linear quantum mechanics must violate the no-signaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics. We propose an interpretation, the causal-conditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many non-linear theories is equivalent to evolution under a linear Hamiltonian with feedback. The mapping allows us to leverage the tools of quantum control, and it tells us that if the non-linear parameters of a non-linear Hamiltonian respond causally (i.e. with an appropriate delay) to measurement results, then the theory can be made causal.

We also contribute to the theory of quantum optomechanics. We introduce two new bases that one can view environment modes with. In linear optomechanics a system interacts with an infinite number of bath modes. We show that the interaction can be reduced to one with finite degrees of freedom. Moreover, at any particular time, the system is correlated with only a finite number of bath modes. We show that if we make the assumption that we can measure any commuting environment modes, then this basis allows us to understand the one-shot quantum Cramer-Rao bound in a simple way, and allows us to sweep large parameter regimes and so find promising optomechanics topologies for quantum state preparation tasks that we can then analyze without the assumption of being able to measure any observable of the environment. We also use this basis to show that when we are interested in the conditional dynamics of a test mass, we can only adiabatically eliminate a lossy cavity when we measure the optomechanical system at a slow enough rate. Finally, we develop an analytic filter for obtaining the state of a generic optomechanical system that interacts linearly with its environment and is driven by Gaussian states, and where the outgoing light is measured with a non-linear photon-counting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.

Li Chi-Lun.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Table of Contents --- p.iv
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Remark on the Location of Transition Structures --- p.1
Chapter 1.2 --- Scope of the Thesis --- p.1
Chapter 1.3 --- References --- p.2
Chapter Chapter 2 --- "A Gaussian-3 Study on the Photodissociation of Phenylacetylene and Formation of 1,3,5-Hexatriyne" --- p.5
Chapter 2.1 --- Introduction --- p.6
Chapter 2.2 --- Computational Method --- p.7
Chapter 2.3 --- Results and Discussion --- p.8
Chapter 2.3.1 --- Phenylacetylene → Acetylene + Benzyne --- p.8
Chapter 2.3.2 --- "Phenylacetylene → Acetylene + (Z)-3 -Hexene- 1,5-diyne" --- p.9
Chapter 2.3.3 --- "(Z)-3-Hexene-l,5-diyne / (E)-3 -Hexene-1,5-diyne → 1,3,5-Hexatriyne and Molecular Hydrogen" --- p.9
Chapter 2.3.4 --- Evaluation of Thermochemical Data --- p.10
Chapter 2.3.5 --- Evaluation of Ion Energetics Data --- p.10
Chapter 2.4 --- Conclusions --- p.10
Chapter 2.5 --- References --- p.11
Chapter Chapter 3 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Cyanoethylene --- p.21
Chapter 3.1 --- Introduction --- p.22
Chapter 3.2 --- Computational Method --- p.22
Chapter 3.3 --- Results and Discussion --- p.23
Chapter 3.3.1 --- Bond Cleavage Reactions --- p.23
Chapter 3.3.2 --- Dissociation Channels Involving Transition Structures --- p.25
Chapter 3.4 --- Conclusions --- p.25
Chapter 3.5 --- References --- p.26
Chapter Chapter 4 --- "A Gaussian´ؤ2 Study of Structures, Energetics, and Reactions of C2H3S- Anions" --- p.34
Chapter 4.1 --- Introduction --- p.35
Chapter 4.2 --- Computational Method --- p.35
Chapter 4.3 --- Results and Discussion --- p.36
Chapter 4.3.1 --- Thioformylmethyl Anion --- p.37
Chapter 4.3.2 --- Thioacetyl Anion --- p.37
Chapter 4.3.3 --- Cyclic C2H3S- Ions --- p.37
Chapter 4.3.4 --- CH2SCH- --- p.38
Chapter 4.3.5 --- 2-Thiovinyl Anion --- p.38
Chapter 4.3.6 --- 1-Thiovinyl Anion --- p.39
Chapter 4.3.7 --- Intramolecular Rearrangements of 1- --- p.39
Chapter 4.3.8 --- Intramolecular Rearrangements of Cyclic C2H3S- ions and 1´ؤThiovinyl Anion --- p.39
Chapter 4.4 --- Conclusions --- p.40
Chapter 4.5 --- References --- p.40
Chapter Chapter 5 --- "Theoretical Studies of Transition Metal Complexes: Bond Energies for Fe+-D, Fe+-H2O, and Fe+-CO" --- p.51
Chapter 5.1 --- Introduction --- p.52
Chapter 5.2 --- Computational Method --- p.53
Chapter 5.3 --- Results and Discussion --- p.54
Chapter 5.3.1 --- Fe+-D --- p.54
Chapter 5.3.2 --- Fe+-CO --- p.54
Chapter 5.3.3 --- Fe+-H2O --- p.55
Chapter 5.4 --- Conclusions --- p.56
Chapter 5.5 --- References --- p.57
Chapter Chapter 6 --- Ab Initio Study of the Charge-Delocalized and -Localized Form of the Rhodizonate Dianion --- p.61
Chapter 6.1 --- Introduction --- p.62
Chapter 6.2 --- Computational Method --- p.63
Chapter 6.3 --- Results and Discussion --- p.64
Chapter 6.3.1 --- Charge-Localized C6062- --- p.64
Chapter 6.3.2 --- Charge-Delocalized C6062- --- p.64
Chapter 6.4 --- Conclusions --- p.65
Chapter 6.5 --- References --- p.66
Chapter Chapter 7 --- "Franck-Condon Factor Simulated Spectra of the Cations of cis-2-Butene,trans-2-Butene, Isobutene, cis-Dichloroethene, and trans-Dichloroethene" --- p.71
Chapter 7.1 --- Introduction --- p.72
Chapter 7.2 --- Computational Method --- p.72
Chapter 7.3 --- Results and Discussion --- p.73
Chapter 7.3.1 --- cis-2-Butene Cation --- p.73
Chapter 7.3.2 --- trans-2-Butene Cation --- p.74
Chapter 7.3.3 --- cis-Dichloroethene Cation --- p.75
Chapter 7.3.4 --- trans-Dichloroethene Cation --- p.76
Chapter 7.3.5 --- Isobutene --- p.76
Chapter 7.4 --- Conclusions --- p.77
Chapter 7.5 --- References --- p.77
Chapter Chapter 8 --- Conclusions --- p.88
Appendix A --- p.89
Appendix B --- p.91
Appendix C --- p.92

Lam Chow Shing.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references.
Abstracts in English and Chinese.
Thesis Examination Committee --- p.i
Abstract --- p.ii
Acknowledgements --- p.iv
Table of Contents --- p.v
List of Tables --- p.vii
List of Figures --- p.viii
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian-3 Method --- p.1
Chapter 1.2 --- The G3 Method with Reduced MΦller- Plesset Order and Basis Set --- p.2
Chapter 1.3 --- Density Functional Theory (DFT) --- p.3
Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3
Chapter 1.5 --- Remark on the Location of Transition Structures --- p.3
Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4
Chapter 1.7 --- Scope of the Thesis --- p.4
Chapter 1.8 --- References --- p.5
Chapter Chapter 2 --- Theoretical Study of Tri-s-triazine and Its Derivatives --- p.7
Chapter 2.1 --- Introduction --- p.7
Chapter 2.2 --- Methods of Calculation --- p.9
Chapter 2.3 --- Results and Discussion --- p.9
Chapter 2.3.1. --- Property of Tri-s-triazine --- p.9
Chapter 2.3.2. --- Substituent Effects on the Properties of the Tri-s-triazine Parent Molecule --- p.10
Chapter 2.3.3. --- Heats of Formation of Derivatives of Tri-s-triazine --- p.20
Chapter 2.4 --- Conclusion --- p.22
Chapter 2.5 --- References --- p.22
Chapter Chapter 3 --- A Gaussian-3 Study of the Dissociative Photoionization of Acetone --- p.25
Chapter 3.1 --- Introduction --- p.25
Chapter 3.2 --- Methods of Calculation --- p.26
Chapter 3.3 --- Results and Discussion --- p.26
Chapter 3.3.1. --- "Formation of m/z = 42 (CH2CO+.),43 (CH3CO+) Ions" --- p.31
Chapter 3.3.2. --- Formation of m/z = 43 (c-CH2CHO+) and m/z = 15 (CH3+) Ions --- p.32
Chapter 3.3.3. --- Formation of m/z = 57 (CH3COCH2+) Ions --- p.37
Chapter 3.3.4. --- Formation of m/z = 39 (C3H3+) Ions --- p.38
Chapter 3.4 --- Conclusion --- p.40
Chapter 3.5 --- Publication Note --- p.40
Chapter 3.6 --- References --- p.40
Chapter Chapter 4 --- "A G3(MP2) Study of the C3H60+. Isomers Fragmented from l,4-Dioxane+" --- p.42
Chapter 4.1 --- Introduction --- p.42
Chapter 4.2 --- Methods of Calculation --- p.43
Chapter 4.3 --- Results and Discussion --- p.44
Chapter 4.3.1. --- "Formation of C3H60+. Isomers 1 and 2 via Fragmentation of 1,4-Dioxane+" --- p.44
Chapter 4.3.2. --- Reaction with Acetonitrile --- p.55
Chapter 4.3.3. --- Reaction with Formaldehyde --- p.57
Chapter 4.3.4. --- Reaction with Ethylene --- p.61
Chapter 4.3.5. --- Reaction with Propene --- p.63
Chapter 4.4 --- Conclusion --- p.67
Chapter 4.5 --- Publication Note --- p.68
Chapter 4.6 --- References --- p.68
Chapter Chapter 5 --- A Computational Study of the Photodissociation Channels of Chloroiodomethane --- p.71
Chapter 5.1 --- Introduction --- p.71
Chapter 5.2 --- Methods of Calculation --- p.73
Chapter 5.3 --- Results and Discussion --- p.74
Chapter 5.3.1 --- CH2C1 + I(2P1/2) and CH2C1 + I(2P3/2) Channels --- p.77
Chapter 5.3.2 --- "CH2I + C1(2P3/2,1/2) Channel" --- p.78
Chapter 5.3.3 --- CHI + HC1 Channel --- p.80
Chapter 5.3.4 --- CH2 + IC1 Channel --- p.81
Chapter 5.4 --- Conclusion --- p.82
Chapter 5.5 --- Publication Note --- p.83
Chapter 5.6 --- References --- p.83
Chapter Chapter 6 --- Conclusion --- p.86
Appendix A --- p.87
Appendix B --- p.89

Law Chi-Kin.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Table of Contents --- p.iv
List of Tables --- p.vi
List of Figures --- p.viii
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian´ؤ3 Method --- p.1
Chapter 1.2 --- The G3 Method with Reduced Mφller-Plesset Order and Basis Set --- p.2
Chapter 1.3 --- The Gaussian-3X Method --- p.2
Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3
Chapter 1.5 --- Remark on the Location of Equilibrium and Transition Structures --- p.3
Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4
Chapter 1.7 --- Scope of the Thesis --- p.4
Chapter 1.8 --- References --- p.5
Chapter Chapter 2 --- Gaussian´ؤ3 Heats of Formation for (CH)6 Isomers --- p.6
Chapter 2.1 --- Introduction --- p.6
Chapter 2.2 --- Methods of Calculation and Results --- p.7
Chapter 2.3 --- Discussion --- p.9
Chapter 2.4 --- Conclusion --- p.11
Chapter 2.5 --- Publication Note --- p.12
Chapter 2.6 --- References --- p.12
Chapter Chapter 3 --- A Gaussian-3 Investigation of N7 Isomers --- p.14
Chapter 3.1 --- Introduction --- p.14
Chapter 3.2 --- Computational Method and Results --- p.16
Chapter 3.3 --- Discussion --- p.16
Chapter 3.4 --- Conclusion --- p.24
Chapter 3.5 --- Publication Note --- p.24
Chapter 3.6 --- References --- p.24
Chapter Chapter 4 --- A Gaussian-3 Study of N7+ and N7- Isomers --- p.27
Chapter 4.1 --- Introduction --- p.27
Chapter 4.2 --- Computational Method and Results --- p.29
Chapter 4.3 --- Discussion --- p.30
Chapter 4.3.1 --- The N7+ isomers --- p.30
Chapter 4.3.2 --- The N7- isomers --- p.37
Chapter 4.4 --- Conclusion --- p.41
Chapter 4.5 --- Publication Note --- p.41
Chapter 4.6 --- References --- p.41
Chapter Chapter 5 --- "Thermochemistry of Chlorine Fluorides ClFn, n = 1-7, and Their Singly Charged Cations and Anions: A Gaussian-3 and Gaussian-3X Study" --- p.45
Chapter 5.1 --- Introduction --- p.45
Chapter 5.2 --- Methods of Calculations --- p.47
Chapter 5.3 --- Results and Discussion --- p.48
Chapter 5.3.1 --- Comparison of the G3 and G3X methods --- p.48
Chapter 5.3.2 --- Assessments of the experimental results --- p.54
Chapter 5.3.3 --- "Bond dissociation energies of ClFn, ClFn+, and ClFn-" --- p.57
Chapter 5.3.4 --- Summary of the thermochemical data --- p.58
Chapter 5.4 --- Conclusion --- p.59
Chapter 5.5 --- Publication Note --- p.60
Chapter 5.6 --- References --- p.60
Chapter Chapter 6 --- A Gaussian-3 Study of the Photoionization and Dissociative Photoionization Channels of Dimethyl Sulfide --- p.63
Chapter 6.1 --- Introduction --- p.63
Chapter 6.2 --- Methods of Calculations --- p.64
Chapter 6.3 --- Results and Discussion --- p.64
Chapter 6.3.1 --- Bond cleavage reactions --- p.67
Chapter 6.3.2 --- Dissociation channels involving transition structures --- p.68
Chapter 6.4 --- Conclusion --- p.70
Chapter 6.5 --- Publication Note --- p.70
Chapter 6.6 --- References --- p.70
Chapter Chapter 7 --- "Theoretical Study of the Electronic Structures of Carbon and Silicon Nanotubes, Carbon and Silicon Nanowires" --- p.72
Chapter 7.1 --- Introduction --- p.72
Chapter 7.2 --- Models and Computational Methods --- p.74
Chapter 7.3 --- Results and Discussion --- p.75
Chapter 7.4 --- Conclusion --- p.87
Chapter 7.5 --- Publication Note --- p.87
Chapter 7.6 --- References --- p.87
Chapter Chapter 8 --- Conclusion --- p.90
Appendix A --- p.91
Appendix B

Cheng Mei-Fun.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgements --- p.iii
Table of Contents --- p.iv
List of Tables --- p.vi
List of Figures --- p.viii
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian-3 Method --- p.1
Chapter 1.2 --- The G3 Method with Reduced Mφller-Plesset Order and Basis Set --- p.2
Chapter 1.3 --- Density Functional Theory (DFT) --- p.3
Chapter 1.4 --- Calculation of Thermodynamical Data --- p.3
Chapter 1.5 --- Remark on the Location of Transition Structures --- p.3
Chapter 1.6 --- Natural Bond Orbital (NBO) Analysis --- p.4
Chapter 1.7 --- Scope of the Thesis --- p.4
Chapter 1.8 --- References --- p.5
Chapter Chapter 2 --- Heats of Formation for the Azine Series: A Gaussian-3 Study --- p.7
Chapter 2.1 --- Introduction --- p.7
Chapter 2.2 --- Methods of Calculation and Results --- p.8
Chapter 2.3 --- Discussion --- p.8
Chapter 2.4 --- Conclusion --- p.9
Chapter 2.5 --- Publication Note --- p.10
Chapter 2.6 --- References --- p.10
Chapter Chapter 3 --- Heats of Formation for Some Boron Hydrides: A Gaussian-3 Study --- p.16
Chapter 3.1 --- Introduction --- p.16
Chapter 3.2 --- Methods of Calculation and Results --- p.18
Chapter 3.3 --- Discussion --- p.19
Chapter 3.4 --- Conclusion --- p.21
Chapter 3.5 --- Publication Note --- p.21
Chapter 3.6 --- References --- p.21
Chapter Chapter 4 --- Structural and Energetics Studies of Tri- and Tetra-tert-butylmethane --- p.30
Chapter 4.1 --- Introduction --- p.30
Chapter 4.2 --- Methods of Calculation and Results --- p.32
Chapter 4.3 --- Discussion --- p.34
Chapter 4.3.1 --- Mono-tert-butylmethane --- p.34
Chapter 4.3.2 --- Di-tert-butylmethane --- p.35
Chapter 4.3.3 --- Tri-tert-butylmethane --- p.37
Chapter 4.3.4 --- Tetra-tert-butylmethane --- p.38
Chapter 4.4 --- Conclusion --- p.39
Chapter 4.5 --- Publication Note --- p.40
Chapter 4.6 --- References --- p.40
Chapter Chapter 5 --- A Computational Study of the Diels-Alder Reactions Involving Acenes: Reactivity and Aromaticity --- p.49
Chapter 5.1 --- Introduction --- p.49
Chapter 5.2 --- Methods of Calculation and Results --- p.50
Chapter 5.3 --- Discussion --- p.51
Chapter 5.4 --- Conclusion --- p.53
Chapter 5.5 --- Publication Note --- p.53
Chapter 5.6 --- References --- p.53
Chapter Chapter 6 --- A Computational Study of the Charge- Delocalized and Charge-Localized Forms of the Croconate and Rhodizonate Dianions --- p.65
Chapter 6.1 --- Introduction --- p.65
Chapter 6.2 --- Methods of Calculation and Results --- p.67
Chapter 6.3 --- Discussion --- p.68
Chapter 6.3.1 --- Charge-Localized Forms of C5052- (C2v) and C6O6 2-(C2v) --- p.68
Chapter 6.3.2 --- Charge-Delocalized Forms of C5052- (D5h) and C6062- (D6h) --- p.71
Chapter 6.4 --- Conclusion --- p.72
Chapter 6.5 --- Publication Note --- p.73
Chapter 6.6 --- References --- p.74
Chapter Chapter 7 --- Conclusion --- p.89
Appendix A --- p.90
Appendix B --- p.92

Lau Kai-Chung.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.
Includes bibliographical references.
Abstracts in English and Chinese.
Abstract
Acknowledgements
Table of Contents
Chapter Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- The Gaussian-2 Method
Chapter 1.2 --- The G2 Method with Reduced M φller-Plesset Order and Basis Set
Chapter 1.3 --- The Gaussian-3 Method
Chapter 1.4 --- Our Modified G2 Methods
Chapter 1.5 --- Calculation of Thermodynamical Data
Chapter 1.6 --- Scope of the Thesis
Chapter 1.7 --- Remark on the Location of Transition Structures
Chapter 1.8 --- References
Chapter Chapter 2 --- A Gaussian-2 Study of the [C2H5O-] Potential Energy Surface and the Fragmentation Pathways of the Ethoxide Anion --- p.7
Chapter 2.1 --- Introduction
Chapter 2.2 --- Theoretical Methods
Chapter 2.3 --- Results and Discussion
Chapter 2.3.1 --- Stable Isomers and TSs for the [C2H50-] Anions
Chapter 2.3.2 --- Fragmentation Pathways of the Ethoxide Anion (1-)
Chapter 2.4 --- Conclusions
Chapter 2.5 --- Publication Note
Chapter 2.6 --- References
Chapter Chapter 3 --- A Gaussian-2 Study of Isomeric C2H2N and C2H2N+ --- p.20
Chapter 3.1 --- Introduction
Chapter 3.2 --- Theoretical Methods
Chapter 3.3 --- Results and Discussion
Chapter 3.3.1 --- The C2H2N and C2H2N+ Isomers
Chapter 3.3.2 --- The Cyanomethyl Radical (1) and Cation (1+)
Chapter 3.3.3 --- The Isocyanomethyl Radical (2) and Cation (2+)
Chapter 3.3.4 --- The lH-Azirinyl Radical (5) and Cation (5+)
Chapter 3.3.5 --- Other C2H2N and C2H2N+ Isomers
Chapter 3.3.6 --- The Unidentified C2H2N Isomer Formed in N + CH=CH2
Chapter 3.4 --- Conclusions
Chapter 3.5 --- Publication Note
Chapter 3.6 --- References
Chapter Chapter 4 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Ethylene Oxide --- p.35
Chapter 4.1 --- Introduction
Chapter 4.2 --- Theoretical Methods
Chapter 4.3 --- Results and Discussion
Chapter 4.3.1 --- Bond Cleavage Reactions
Chapter 4.3.2 --- Dissociation Channels Involving Transition Structure(s)
Chapter 4.4 --- Conclusions
Chapter 4.5 --- Publication Note
Chapter 4.6 --- References
Chapter Chapter 5 --- A Gaussian-2 Study of the Photoionization and Dissociative Photoionization Channels of Propylene Oxide --- p.47
Chapter 5.1 --- Introduction
Chapter 5.2 --- Theoretical Methods
Chapter 5.3 --- Results and Discussion
Chapter 5.3.1 --- Bond Cleavage Reactions
Chapter 5.3.2 --- Dissociation Channels Involving Transition Structure(s)
Chapter 5.4 --- Conclusions
Chapter 5.5 --- Publication Note
Chapter 5.6 --- References
Chapter Chapter 6 --- A Gaussian-3 Study of the Thermochemistry of Chlorofluoromethanes (CFnCl4-n) and Their Cations (CFnCl4_n+)， n =0-4 --- p.61
Chapter 6.1 --- Introduction
Chapter 6.2 --- Theoretical Methods
Chapter 6.3 --- Results and Discussions
Chapter 6.3.1 --- Heats of Formation of Chlorofluoromethanes and Their Cations
Chapter 6.3.2 --- Ionization Energies of Chlorofluoromethanes
Chapter 6.3.3 --- Proton Affinities of Chlorofluoromethanes
Chapter 6.4 --- Conclusions
Chapter 6.5 --- Publication Note
Chapter 6.6 --- References
Chapter Chapter 7 --- "A Gaussian-2 and Gaussian-3 Study of the Energetics and Structures of Cl2On and Cl2On+, n = 1，4, 6，and7" --- p.69
Chapter 7.1 --- Introduction
Chapter 7.2 --- Theoretical Methods
Chapter 7.3 --- Results and Discussion
Chapter 7.3.1 --- Cl20 and Cl20+
Chapter 7.3.2 --- Cl204 and Cl204+
Chapter 7.3.3 --- Cl206 and Cl206+
Chapter 7.3.4 --- Cl207 and Cl207+
Chapter 7.4 --- Conclusions
Chapter 7.5 --- Publication Note
Chapter 7.6 --- References
Chapter Chapter 8 --- Conclusions --- p.81
Chapter Appendix A --- The Gaussian-n (n = 1 - 3) Theoretical Models --- p.82
Chapter A.1 --- The G1 and G2 theories
Chapter A.2 --- The G2(MP2) theory
Chapter A.3 --- "The G2(MP2,SVP) theory"
Chapter A.4 --- The G3 theory
Chapter Appendix B --- "Calculation of Enthalpy at 298 K, H298" --- p.86

This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

Ab initio molecular orbital theory has been successful in predicting the stabilities of many weak complexes; typical of these are the complexes formed between water and various small molecules. To account for the correlation effect, Moller-Plesset perturbation theory truncated at the second order level was employed. In order to account for the hydrogen bonding, the 6-3lG** basis set was used. The geometry optimisations of the complexes were carried out using the Gaussian-92 suite of programs installed on a Hewlett-Packard 720 computer operating under UNIX. The interaction energies of the complexes were subjected to further analysis by applying the Morokuma decomposition scheme. The electrostatic interaction component accounts for over 40% of the total stabilisation energy in all the typical hydrogen bonded complexes. Gas phase enthalpies were computed and compared with the experimental values of similar systems. For the systems studied here, the prediction is that all complexes are stable at 25° C. A second program, Vibra, was used for carrying out a normal coordinate analysis. A third computer program for the graphical representation of molecular and crystallographic models, Schakal-92, was employed to illustrate the predicted equilibrium geometries and the fundamental vibrational modes. The predicted geometries, interaction energies, charge redistributions, vibrational wave numbers, infrared intensities and force constants are listed and compared with those in the literature, where applicable. Correlations between the various predicted properties show some interesting chemistry.
Thesis (Ph.D.)-University of Natal, Durban, 1996.