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Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates the develop of accurate, but approximate, ways to parametrize the wavefunction, including methods like couple cluster theory and correlator product states (CPS). Recently, there has been interest in approaches based on machine learning both direct applications of neural network architecture and the combinations of conventional wavefunction parametrizations with various Boltzmann machines. While all these methods can be exact in principle, they are usually applied with only a polynomial number of parameters, limiting their applicability. This research's objective is to present a fresh approach to wavefunction parametrization that is size-consistent, rapidly convergent, and robust numerically. Specifically, we propose a hierarchical ansatz that converges rapidly (with respect to the number of least-squares optimization). The general utility of this approach is verified by applying it to uncorrelated, weakly-correlated, and strongly-correlated systems, including small molecules and the one-dimensional Hubbard model., Comment: 18 pages

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

Quantitative correlation of several theoretical electrophilicity measures over different families of organic compounds are examined relative to the experimental values of Mayr et al. Notably, the ability to predict these values accurately will help to el

Chemical reactivity towards electron transfer is captured by the Fukui function. However, this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states. In such a case, the first-order chemical response is not in

Background: The nuclear many-body system is a strongly correlated quantum system, posing serious challenges for perturbative approaches starting from uncorrelated reference states. The last decade has witnessed considerable progress in the accurate treatment of pairing correlations, one of the major components in medium-sized nuclei, reaching accuracies below the 1% level of the correlation energy. Purpose: Development of a quantum many-body method for pairing correlations that is (a) competitive in the 1% error range, and (b) can be systematically improved with a fast (exponential) convergence rate. Method: The present paper capitalizes upon ideas from Richardson-Gaudin integrability. The proposed method is a two-step approach. The first step consists of the optimization of a Richardson-Gaudin ground state as variational trial state. At the second step, the complete set of excited states on top of this Richardson-Gaudin ground state is used as an optimal basis for a Configuration Interaction method in an increasingly large effective Hilbert space. Results: The performance of the variational Richardson-Gaudin (varRG) and Richardson-Gaudin Configuration Interaction (RGCI) method is benchmarked against exact results using an effective $G$-matrix interaction for the Sn region. The varRG already reaches accuracies around the 1% level of the correlation energies, and the RGCI step sees an additional improvement scaling exponentially with the size of the effective Hilbert space. Conclusions: The Richardson-Gaudin models of integrability provide an optimized complete basis set for pairing correlations.

International audience

National audience; The PUREX process has been designed for the reprocessing of spent nuclear fuel to separate uranium and plutonium from the fission products. Following the dissolution of the irradiated fuel in aqueous nitric acid, uranium and plutonium are transferred to an organic phase by intensive mixing with an organic solvent extraction (tributyl phosphate in kerosene), while fission products remain in the aqueous nitric phase. The degradation products of TBP by hydrolysis can react with nitric acid through very exothermic chemical reactions that can lead to a rapid increase of temperature in the reprocessing vessels. In the worse cases, the in-cell solvent fire is considered to be an important postulated accident even if its probability is low. In such cases plutonium is released in volatile forms such as PuO2, PuO3 or PuO2(OH)2. Ourtheoretical study focusses on the thermodynamics properties of those molecules, in particular the former two species for which large experimental uncertainties remain.

International audience

We review information on methods for constructing the exact density functional mathematically and computationally. While it is generally accepted that no explicit analytic form for the exact functional exists, we argue, based on what is known about the classical many-body problem, that is not necessarily the case.

A new method for optimizing transition state and minima structures using redundant internal coordinates is presented. The new method is innovative because it allows the user to select a few key reduced coordinates, whose Hessian components will be accurately computed by finite differencing; the remaining elements of the Hessian are approximated with a quasi-Newton method. Usually the reduced coordinates are the coordinates that are involved in bond breaking/forming. In order to develop this method, several other innovations were made, including ways to (a) select the key reduced coordinates automatically, (b) guess the transition state quickly and efficiently, (c) choose dihedrals so that the “linear angle problem” is avoided, (d) robustly convert redundant internal coordinates to Cartesian coordinates. These, and other technical developments (e.g., new quasi-Newton Hessians, new trust-radius updates), were validated using a database of 7000 initial transition-state guesses for a diverse set of 140 chemical reactions.

It is well known that the Electrongativity Equalization Mtehod (EEM) fails to describe the charge distribution upon bond dissocation. In this presentation, the bond dissocation is studied with the Atom-Condensed Kohn-Sham DFT approximated to second order (ACKS2). After reviewing the basic equations, a two-fragment system is studied in the dissociation limit. The limiting behavior of the Coulomb interaction (1/r) and the Kohn-Sham matrix elements (exponentially decaying) are plugged into the equations. The solution exhibits integer dissocuation limits, in line with high-level ab initio computations. A direct fit of the ACKS2 model to reproduce constrained CAS-SCF reference data yield parameters that are in line with experimental atomic data.

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges., 10 pages, 3 figures, preprint, communication

We have implemented the single-site density matrix renormalization group algorithm for the variational optimization of SU(2) \times U(1) (spin and particle number) invariant matrix product states for general spin and particle number symmetric fermionic Hamiltonians. This class also includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are obtained with the algorithm. A comparison with other methods is made., Comment: 4 pages, 5 figures, Poster presentation at the 16th International Conference on Recent Progress in Many-Body Theories, Nov. 28 to Dec. 2, 2011, Bariloche, Argentina

Orbital-free density functional theory requires accurate approximations for the noninteracting kinetic energy as a functional of the ground-state electron den- sity. For explicit functionals in real space, it has proved difficult to supersede the quality of the gradient expansion, truncated at second order. This is partly because the gradient expansion diverges for atomic and molecular densities. In an effort to include information about higher-order terms in the gradient expansion but avoid divergences, we consider resummations for the series using Padé approximants and Meijer-G functions. To regularize terms that appear in the denominator, we consider various damping functions, which introduces parameter(s) that can be fit to atomic data. These results improve upon the second-order truncation, but do not achieve the exquisite accuracy that would be required for practical orbital-free density-functional theory calculations. Thesis Master of Science (MSc)

Atom is not an observable of the molecular wavefunction, in quantum chemistry there are myriad ways of defining an atom in a molecule. Partitioning a molecule’s electrons between its atomic constituents (population analysis) remains a challenge. A popular approach is based on Mulliken’s overlap-based population analysis, which exploits the fact that molecular orbitals can be expressed as linear combinations of user-defined functions: atomic orbitals. In turn, this creates a dependency on the selection of the predetermined atomic orbitals that are used to expand the molecular orbitals. Chemically intuitive atomic orbitals like Minimal Atomic Orbitals (minAO) produces chemically intuitive atomic charges but a non-accurate wave function. Accurate wave functions can be obtained from large atomic basis sets like def2-QZVPd at the cost of chemically unintuitive atomic charges. With this problem in sight, Quasi-Atomic Orbitals (QAO) are constructed from the accurate wave function to resemble the minAO and maximally span the molecular orbital space. The key idea is Mulliken population analysis can be carried out for wave functions with the chemical intuitive power of minAO, without sacrificing the wave function’s accuracy by using QAO. To ensure that overlaps of QAO are divided between different atoms without bias. Zero-Bond Dipole (ZBD) orthogonalization is proposed as a novel way to orthogonalize QAO. Common population analysis from literature: Charge Model 5 (CM5), QH, Hu-Lu-Yang (ESP), Mulliken, NPA atomic charges will be compared to QAO (Mulliken with QAO) and ZBD-QAO (Mulliken after ZBD orthogonalization of QAO) and tested for mathematical accuracy and expected chemical trends. Thesis Master of Science (MSc)

This thesis discusses Kaplan, a free conformer searching package, available at github.com/PeaWagon/Kaplan Conformer searching algorithms find minima in the Potential Energy Surface (PES) of a molecule, usually by following a torsion-driven approach. The minima represent conformers, which are interchangeable via free rotation around bonds. Conformers can be used as input to computational analyses, such as drug design, that can convey molecular reactivity, structure, and function. With an increasing number of rotatable bonds, finding optima in the PES becomes more complicated, as the dimensionality explodes. Kaplan is a new, free and open-source software package written by the author that uses a ring-based Evolutionary Algorithm (EA) to find conformers. The ring, which contains population members (or pmems), is designed to allow initial PES exploration, followed by exploitation of individual energy wells, such that the most energetically-favourable structures are returned. The strengths and weaknesses of existing publicly available conformer searchers are discussed, including Balloon, RDKit, Openbabel, Confab, Frog2, and Kaplan. Since RDKit is usually considered to be the best free package for conformer searching, its conformers for the amino acids were optimised using the MMFF94 forcefield and compared to the conformers generated by Kaplan. Amino acid conformers are well characterised, and provide insight for protein substructure. Of the 20 molecules, Kaplan found a lower energy minima for 12 of the structures and tied for 5 of them. Kaplan allows the user to specify which dihedrals (by atom indices) to optimise and angles to use, a feature that is not offered by other programs. The results from Kaplan were compared to a known dataset of amino acid conformers. Kaplan identified all 57 conformers of methionine to within 1.2Å, and found identical conformers for the 5 lowest-energy structures (i.e. within 0.083Å), following forcefield optimisation. Thesis Master of Science (MSc) A conformer search affords the low-energy arrangements of atoms that can be obtained via rotation around bonds. Conformers provide insight about the chemical reactivity and physical properties of a molecule. With increasing molecule size, the number of possible conformers increases exponentially. To search the space of possible conformers, this thesis presents Kaplan, which is a software package that implements a novel directed, stochastic, sampling technique based on an Evolutionary Algorithm (EA). Kaplan uses a special type of EA that stores sets of conformers in a ring-based structure. Unlike other conformer-specific packages, Kaplan provides the means to analyse and interact with found conformers. Known conformers of amino acids are used to verify Kaplan. Other tools for generating conformers are discussed, including a comparison of freely available software. Kaplan effectively finds the conformers of small molecules, but requires additional parametrisation to find the conformers of mid-sized molecules, such as Penta-Alanine.

Orbital-based methods for electronic-structure calculations are limited to atoms or molecules with up to about 50 electrons. This limitation comes from the requirement of a long expansion in basis functions to approximate correctly the wave function. Replacing the Coulomb interaction with a smooth model potential has two main consequences: first, the wave function becomes cuspless and the expansion in basis functions converges more rapidly, and second, the smooth potential describes a weaker interaction at the electronic coalescence point, which leads to the loss of accuracy. This work explores whether one can construct models with smooth, non-singular, potentials, but without compromising accuracy. The key idea is to use extrapolation procedures to predict the energy for the Coulomb interaction from a sequence of (cheaper) calculations for smooth potentials. By replacing the Coulomb electron-electron interaction with a smooth potential, using the semi-stochastic heat-bath configuration interaction method (SHCI) to select key configurations, and extrapolating to the limiting (non-smoothed) Coulomb potential, we were able to retain the accuracy of full configuration interaction (FCI) calculations, at reduced computational cost. Thesis Doctor of Philosophy (PhD)

Molecular nonlinear optical (NLO) properties are extensively studied using both theory and experiment because of their use in myriad applications. Experimental measurements of the most interesting molecules’ NLO properties are difficult, so experimental data for molecules with desirable NLO properties is scarce. Theoretical tools don’t suffer from the same limitations and can provide significant insights into the physico-chemical phenomena underlying the nonlinear responses, can help in interpreting response behaviour of molecules, and can guide design the materials with desirable response properties. Here, I present my work on developing methods for accurately calculating the NLO properties of molecules using the finite field (FF) approach. The first chapter provides a background for the finite field and electronic structure methods used in this dissertation. Chapter two is a thorough investigation of the finite field method. The limitations of the method are highlighted and the optimal conditions for overcoming its drawbacks and obtaining meaningful and accurate results are described. Chapter three presents the first systematic study of the dependence of optimal field strengths on molecular descriptors. The first protocol for predicting the optimal field for the second hyperpolarizability is presented and successfully tested, and the dependence of the optimal field strength for the first hyperpolarizability on the molecular structure is investigated. Chapter four is an assessment of various DFT functionals in calculating the second hyperpolarizabilities of organic molecules and oligomers. This study shows the limitations of conventional DFT methods and the importance of electron correlation to response properties. In chapter five we present a new method of calculating NLO properties using a rational function model that is shown to be more robust and have lower computational cost than the traditional Taylor expansion. Finally, chapter six includes a summary of the thesis and an overview of future work. Thesis Doctor of Philosophy (PhD)

Standard approaches to approximating solutions to the Schroedinger equation rely upon the assumption that there is a single dominant electronic configuration with a small number of low-lying excited states. As such, they are referred to as single reference approaches and are accurate only when the band gap is small in comparison with the inter-electronic repulsion of the valence electrons. Systems for which this is the case are weakly-correlated. If the inter-electronic repulsion larger than the band gap, then a single electronic reference is not an appropriate ansatz for the physical wavefunction. As the strength of the interaction is increased many Slater determinants become near-degenerate, each providing non-negligible contributions. Such systems are strongly-correlated. The goal of the thesis was to employ wavefunctions which are: non-trivial, tractable, size-consistent and extensive, and not given in an active space. We have outlined approaches based on wavefunction forms more suited to describe strong correlation. Built on the Lie algebra su(2), our first trial wavefunction was the Bethe ansatz solution to the reduced BCS Hamiltonian derived by Richardson. This wavefunction is expressed as a product of quasi-particles each parametrized in terms of quasi-momenta. Consistency among the quasi-momenta is ensured by a set of non-linear equations to be solved numerically. This approach is feasible in both variational and projected flavours. We next considered a wavefunction of the same form without requiring it to be an eigenvector of the reduced BCS Hamiltonian. A variational approach in this case is only feasible provided there are two equivalent descriptions in terms of particles and holes. In any case, a bivariational principle and a projected approach are both feasible. Also based on su(2), there is AP1roG (coupled cluster pair doubles). Open-shell singlets and triplets were constructed with the Lie algebras sp(N) and so(4N). The resulting formulae appear to be infeasible unless it is possible to efficiently compute generalizations of determinants to three-dimensional objects. Treating each spatial orbital individually, all four possible occupations close the Lie superalgebra gl(2|2). Thesis Doctor of Philosophy (PhD)

Geometry optimization is a key step in the computational modeling of chemical reactions because one cannot model a chemical reaction without first accurately determining the molecular structure, and electronic energy, of the reactants and products, along with the transition state that connects them. These structures are stationary points— the reactant and product structures are local minima, and the transition state is a saddle point with one negative-curvature direction—on the molecular potential energy surface. Over the years, many methods for locating these stationary points have been developed. In general, the problem of finding reactant and product structures is relatively straightforward, and reliable methods exist. Converging to transition states is much more challenging. Because of the difficulty of transition-state optimization, researchers have designed optimization methods specifically for this problem. These methods try to make good choices for the initial geometry, the system of coordinates used to represent the molecule, the initial Hessian, the Hessian updating method, and the step-size. The transition-state optimization method developed in this thesis required considering all of these methods. Specifically, a new method for finding an initial guess geometry was developed in chapter 2; good choices for a coordinate system for representing the molecule were explored in chapters 2 and 6; different choices for the initial Hessian are considered in chapter 5; chapters 3 and 4 present, and test, a sophisticated new method for updating the Hessian and controlling the step-size during the optimization. iv The methods created in the process of this research led to the development of Saddle, a general-purpose geometry optimizer for transition states and stable structures, with and without constraints on the molecular coordinates. Saddle can be run in conjunction with the Gaussian program or almost any other quantum chemistry program, and it converges significantly more often than the other traditional methods we tested. Thesis Doctor of Science (PhD)

Understanding and predicting chemical phenomena is the main goal of computational chemistry. In this thesis I present my work on applying computational approaches to study chemical processes in biological and supramolecular systems. pH-responsive molecular tweezers have been proposed as an approach for targeting drug-delivery to tumors, which tend to have a lower pH than normal cells. In chapter 2 I present a computational study I performed on a pH-responsive molecular tweezer using ab initio quantum chemistry in the gas phase and molecular dynamics simulations in solution. The binding free energy in solution was calculated using Steered Molecular Dynamics. We observe, in atomistic detail, the pH-induced conformational switch of the tweezer and the resulting release of the drug molecule. Even when the tweezer opens, the drug molecule remains near a hydrophobic arm of the molecular tweezer. Drug release cannot occur, it seems, unless the tweezer is a hydrophobic environment with low pH. The protonation state of amino acid residues in proteins depends on their respective pKa values. Computational methods are particularly important for estimating the pKa values of buried and active site residues, where experimental data is scarce. In chapter 3 I used the cluster model approach to predict the pKa of some challenging protein residues and for which methods based on the numerical solution of the Poisson-Boltzmann equation and empirical approaches fail. The ionizable residue and its close environment were treated quantum mechanically, while the rest of the protein was replaced by a uniform dielectric continuum. The approach was found to overestimate the electrostatic interaction leading to predicting lower pKa values. Master of Science (MSc)

In this thesis, we investigate the properties of a model of an anti-phase modulated d-wave superconductor, particularly in the presence of a magnetic field. This so-called model of $\pi$-striped superconductor has been proposed to describe the decoupling between Cu-O planes in $1/8$ doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. The d-wave superconducting order parameter in a $\pi$-striped superconductor oscillates spatially with period 8 and zero average value. Unlike a uniform d-wave superconductor, this model has non-zero density of states at zero energy and exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to $B$, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are also discussed in the context of experiments which observe quantum oscillations in the cuprates. Furthermore, within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in this model. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surface sections as well as between them via magnetic breakdown. Oscillations periodic in 1/B are found in both the positions and widths of the lowest Landau levels. The area corresponding to these quantum oscillations for intermediate pairing interaction is similar to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al. Doctor of Philosophy (PhD)

Approximating the exchange-correlation energy in density functional theory (DFT) is a crucial task. As the only missing element in the Kohn-Sham DFT, the search for better exchange-correlation functionals has been an active field of research for fifty years. Many models and approximations are known and they can be summarized in what is known as the Jacob’s ladder. All the functionals in that ladder are local in the sense that they rely on the information of only one electronic coordinate. That is, even though the exchange-correlation hole, the cornerstone in density functional theory, is a two-electron coordinate quantity, one of the coordinates is averaged over in “Jacob’s ladder functionals.” This makes the calculations considerably more efficient. On the other hand, some of the important constraints on the form of the exchange-correlation functional become inaccessible in the one-point forms. The violation of these constraints leads to functionals plagued by systematic errors, leading to qualitatively incorrect descriptions of some chemical and physical processes. In this thesis the idea of a weighted density approximation (WDA) is explored. More specifically, a symmetric and normalized two-point functional is proposed for the exchange-correlation energy functional. The functional is based entirely on the hole for the uniform electron gas. By construction, these functionals fulfill two of the most important constraints: the normalization of the exchange-correlation hole and the uniform electron gas limit. The findings suggest that we should pursue a whole new generation of “new Jacob’s ladder” functionals. A further step was considered. Given the relevance of the long-range behavior of the exchange-correlation hole, a study of the electronic direct correlation function was performed. The idea was to build up the long-range character of the hole as convoluted pieces of the simple and short-ranged direct correlation function. This direct correlation function provides better results, at least for the correlation energy in the spin-polarized uniform electron gas. The advantage of one-point functionals is their computational efficiency. We therefore attempted to develop new methods that mitigate the relative computational inefficiency of two-point functionals. This led to new methods for evaluating the six-dimensional integrals that are inherent to the exchange-correlation energy. Doctor of Philosophy (PhD)

Approximating the kinetic energy as a functional of the electron density is a daunting, but important, task. For molecules in equilibrium geometries, the kinetic energy is equal in magnitude to the total electronic energy, so achieving the exquisite accuracy in the total energy that is needed for chemical applications requires similar accuracy for the kinetic energy functional. For this reason, most density functional theory (DFT) calculations use the Kohn-Sham method, which provides a good estimate for the kinetic energy. But the computational cost of Kohn-Sham DFT calculations has a direct dependence on the total number of electrons because the Kohn-Sham method is based on the orbital picture, with one orbital per electron. Explicit density functionals, where the kinetic energy is written explicitly in terms of the density, and not in terms of orbitals, are much faster to compute. Unfortunately, the explicit density functionals in the literature had disappointing accuracy. This dissertation introduces several new approaches for orbital-free density functional methods. One can try to include information about the Pauli principle using the exchange hole. In the weighted density approximation (WDA), a model for the exchange hole is used to approximate the one-electron density matrix, which is then used to compute the kinetic energy. This thesis introduces a symmetric, normalized, weighted density approximation using the exchange hole of the uniform electron gas. Though the key results on kinetic energy are not accurate enough, an efficient algorithm is introduced which, with a more sophisticated hole model, might give better results. The effects of electron correlation on the kinetic energy can be modeled by moving beyond the one-electron distribution function (the electron density) to higherorder electron distributions (k-electron DFT). For example, one can model electron correlation directly using the pair electron density. In this thesis, we investigated two different functionals of the pair density, the Weizsäcker functional and the March-Santamaria functional. The Weizsäcker functional badly fails to describe the accurate kinetic energy due to the N-representability problem. The March-Santamaria functional is exact for a single Slater determinant, but fails to adequately model the effects of electron correlation on the kinetic energy. Finally, we established a relation between Fisher information and Weizsäcker kinetic energy functional. This allowed us to propose generalisations of the Weizsäcker kinetic energy density functional. It is hoped that the link between information theory and kinetic energy might provide a new approach to deriving improved kinetic energy functionals. Keywords: Kinetic energy functional, Density functional theory (DFT), von-Weizsäcker functional, March-Santamaria functional, Thomas-Fermi model, density matrix, Twopoint normalization, Pair-density functional theory (PDFT). Doctor of Science (PhD)

The prediction and characterisation of chemical and biochemical processes are fundamental tasks in computational chemistry. Small chemical systems can be characterised by the stationary points on potential energy surface and reaction paths linking them. For large biological systems, statistical sampling is required to characterising their average properties. This thesis presents my Ph.D. work on developing new methods to predict and characterise chemical and biological processes. Two path-finding methods for finding the minimum energy reaction path and alternative reaction paths for small gas-phase reactions have been elucidated with examples, and molecular dynamic simulations have been used to characterise the binding affinity of protein-ligand complex and the free energy of protonation processes in a protein. Specifically, the fast marching method (FMM) has been used to find the minimum energy path (MEP) on the potential energy surface (PES) for small gas-phase reactions. In this thesis, FMM is shown to be one of the most general and reliable surface-walking algorithms for finding the MEP. However, it is an expensive method. Some improvements have been illustrated in chapter 2 and chapter 3. I also proposed a new method (called QSM-NT) for finding all stationary points, accordingly all alternative reaction paths on the PES. Unlike other path-finding methods, QSM-NT overcomes the need of an initial guess of the path, and it can find all stationary points on the PES. QSM-NT has been proven to be efficient and reliable through applications on analytical PES and real chemical reaction. The difficulties and pitfalls associated with QSM-NT have been elucidated with examples. Molecular dynamic (MD) simulation and associated postprocessing procedures have been used to study the binding properties of caffeine-A2A complex. The binding affinities of different binding modes have been calculated using MM/PBSA method. The binding pocket has been characterised with MM/GBSA energy decomposition. Our computational work provides significant insight to the targeted drug design of the adenosine A2A receptor. The pH-dependent properties of a protein play important roles in the fundamental biological processes. The protonation states, namely, the pKa values of ionisable residues, especially active-site residues are the prerequisites to understanding of the mechanisms of many biological processes. In this thesis, acetoacetate decarboxylase (AADase) is used as a test case for studying different types of pKa prediction methods. Our computational results have shown that the site-site interactions from other ionisable residues are crucial to the pKa prediction of the target residue. This thesis covers the range from small gas phase reaction prediction to large complex biological systems characterisation using quantum mechanical and molecular mechanical methods. Doctor of Philosophy (PhD)

Understanding the chemical and physical properties of molecules and materials at a fundamental level often requires quantum-mechanical models for these substance's electronic structure. This type of many body quantum mechanics calculation is computationally demanding, hindering its application to substances with more than a few hundreds atoms. The supreme goal of many researches in quantum chemistry-and the topic of this dissertation-is to develop more efficient computational algorithms for electronic structure calculations. In particular, this dissertation develops two new numerical integration techniques for computing molecular and atomic properties within conventional Kohn-Sham-Density Functional Theory (KS-DFT) of molecular electronic structure. The first of these grid-based techniques is based on the transformed sparse grid construction. In this construction, a sparse grid is generated in the unit cube and then mapped to real space according to the pro-molecular density using the conditional distribution transformation. The transformed sparse grid was implemented in program deMon2k, where it is used as the numerical integrator for the exchange-correlation energy and potential in the KS-DFT procedure. We tested our grid by computing ground state energies, equilibrium geometries, and atomization energies. The accuracy on these test calculations shows that our grid is more efficient than some previous integration methods: our grids use fewer points to obtain the same accuracy. The transformed sparse grids were also tested for integrating, interpolating and differentiating in different dimensions (n = 1, 2, 3, 6). The second technique is a grid-based method for computing atomic properties within QTAIM. It was also implemented in deMon2k. The performance of the method was tested by computing QTAIM atomic energies, charges, dipole moments, and quadrupole moments. For medium accuracy, our method is the fastest one we know of. Thesis Doctor of Philosophy (PhD)