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)

In the search for molecular species in the interstellar medium and extraterrestrial planetary atmospheres, theoretical methods continue to be an invaluable tool to astronomically minded chemists. Using state-of-the art methods, this doctoral work characterizes the electronically excited states of interstellar radicals, cations, and even rare anions and also predicts the gas phase fundamental vibrational frequencies of the cis and trans-HOCO radicals, as well as the cis-HOCO anion. First, open-shell coupled cluster methods of singles and doubles (CCSD) and singles and doubles with triples-inclusion (CC3) are tested on the C₂H and C₄H radicals. The significant double-excitation character, as well as the quartet multiplicity of some states yields inaccurate excitation energies and large spin contamination with CCSD. CC3 somewhat improves this for select states, but discrepancies between CC and multireference results for certain states exist and likely arise from the lack of spin adaptation in conventional spin-orbital CC. Next, coupled-cluster methods predict the presence of an excited state of the closed-shell allyl cation and its related H₂CCCHCH₂⁺ cousin at 443 nm near an unidentified laboratory peak at 442.9 nm which is also close to one of the largest unattributed interstellar absorption features. Additionally, the dipole moments, electron binding energies, and excited states of neutral radicals and corresponding closed-shell anions of interstellar interest are also computed. These are calibrated against experimental data for CH₂CN⁻ and CH₂CHO⁻. Since coupled cluster theory closely reproduces the known experimental data, dipole-bound excited states for eight previously unknown anions are predicted: CH2SiN⁻ , SiH₂CN⁻, CH₂SiHO⁻, SiN⁻, CCOH⁻, HCCO⁻, SiCCN⁻, and SiNC⁻. In addition, we predict the existence of one rare valence-bound excited state of CH₂SiN⁻ and also SiCCN⁻ as well as even rarer two valence-bound states of CCSiN⁻. Lastly, the reaction of CO + OH and its transient potential intermediate, the HOCO radical, may be responsible for the regeneration of CO₂ in the Martian atmosphere, but past spectroscopic observations have not produced a full gas-phase set of the fundamental vibrational frequencies of the HOCO radical. Using established, highly-accurate quantum chemical coupled cluster tech- niques and quartic force fields, all six fundamental vibrational frequencies for 1 ²A′ cis and trans-HOCO and 1 ¹A′ cis-HOCO⁻ are computed in the gas phase. / Ph. D.

No description available.

The Empirical Valence Bond (EVB) method has long been recognised as a reliable approach for the calculation of free energies of reactions in heterogeneous electrochemical environments. In spite of its established efficacy, existing implementations and protocols often pose challenges due to their tediousness or lack of transparency. This work introduces an open-source Python implementation of the EVB method, specifically designed to enhance accessibility and comprehension of the method making it highly suited for educational purposes. Recommendations are provided for integrating the methodology into the GROMACS application programming interface, to facilitate its integration into computational chemistry workflows and accellerating research. The program is demonstrated through various computations, including a short EVB study on the dissociation of \COt and tetraphenylporphyrin in the vicinity of a graphene sheet in water and dimethylformamide. Moreover, a novel analytical expression for computing the free energy profile is presented, showing promising agreement with the canonical discretised method.

This thesis presents an experimental and theoretical study of the collision dynamics of OH(A²Σ⁺) with Kr and Xe. These two systems both exhibit a significant degree of electronically non-adiabatic behaviour, and a particular emphasis of the work presented here is to characterise the competition and interplay between electronic quenching on the one hand, and electronically adiabatic collisional processes on the other. Quenching takes place close to the bottom of the deepest potential well for both systems. In collisions that remain in the excited electronic state, this same region of the potential is also largely responsible for rotational energy transfer (RET) and the collisional depolarisation of angular momentum. Therefore, the direct competition between these processes suppresses the cross-sections for RET and collisional depolarisation from their expected value in the absence of quenching. To investigate this, experiments were carried out to measure cross-sections for the collisional transfer of electronic, vibrational and rotational energy in OH(A, v=0,1) + Kr and OH(A, v=0) + Xe. In addition, measurements were made of the j-j' correlation -- that is, the relationship between the angular momentum of the OH radical before and after a collision -- in collisions with Kr and Xe, using the experimental technique of Zeeman quantum beat spectroscopy. Collisions with both Kr and Xe tend to effectively depolarise the angular momentum of the OH radical, due to the very anisotropic character of the potential on which the process occurs. Electronic quenching, which plays an essential role in both systems, is more prevalent with xenon as the crossing to the ground state potential is located in a more accessible location. These experimental results were compared with single surface quasi-classical trajectory (QCT) calculations, where the overestimate of rotational energy transfer or collisional depolarisation helps to elucidate the degree to which the presence of quenching suppresses these processes. Surface hopping QCT was then used to account for non-adiabatic transitions in the theory, which led to an improvement in agreement with experiment. However, standard surface hopping QCT theory failed to account for the full extent of quenching in these two systems. A major focus of this work is therefore on the development of an extension to standard surface hopping QCT theory to incorporate rovibronic couplings. In non-linear configurations, the excited state of the OH + Kr, Xe systems has A' symmetry, while the ground state is split into symmetric (A') and antisymmetric (A'') components. For these symmetry reasons, coupling is restricted to the two states of the same symmetry, however a rotation of the correct (A'') symmetry can induce transitions to the A'' state too. Inclusion of all three electronic states, and the relevant couplings between them, is found to be crucial for a proper description of experimental reality.

Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.

In this thesis a reduced dimensionality quantum scattering model is applied to the study of polyatomic reactions of type X + CH4 <--> XH + CH3. Two dimensional quantum scattering of the symmetric hydrogen exchange reaction CH3+CH4 <--> CH4+CH3 is performed on an 18-parameter double-Morse analytical function derived from ab initio calculations at the CCSD(T)/cc-pVTZ//MP2/cc-pVTZ level of theory. Spectator mode motion is approximately treated via inclusion of curvilinear or rectilinear projected zero-point energies in the potential surface. The close-coupled equations are solved using R-matrix propagation. The state-to-state probabilities and integral and differential cross sections show the reaction to be primarily vibrationally adiabatic and backwards scattered. Quantum properties such as heavy-light-heavy oscillating reactivity and resonance features significantly influence the reaction dynamics. Deuterium substitution at the primary site is the dominant kinetic isotope effect. Thermal rate constants are in excellent agreement with experiment. The method is also applied to the study of electronically nonadiabatic transitions in the CH3 + HCl <--> CH4 + Cl(2PJ) reaction. Electrovibrational basis sets are used to construct the close-coupled equations, which are solved via Rmatrix propagation using a system of three potential energy surfaces coupled by spin-orbit interaction. Ground and excited electronic surfaces are developed using a 29-parameter double-Morse function with ab initio data at the CCSD(T)/ccpV( Q+d)Z-dk//MP2/cc-pV(T+d)Z-dk level of theory, and with basis set extrapolated data, both corrected via curvilinear projected spectator zero-point energies. Coupling surfaces are developed by fitting MCSCF/cc-pV(T+d)Z-dk ab initio spin orbit constants to 8-parameter functions. Scattering calculations are performed for the ground adiabatic and coupled surface models, and reaction probabilities, thermal rate constants and integral and differential cross sections are presented. Thermal rate constants on the basis set extrapolated surface are in excellent agreement with experiment. Characterisation of electronically nonadiabatic nonreactive and reactive transitions indicate the close correlation between vibrational excitation and nonadiabatic transition. A model for comparing the nonadiabatic cross section branching ratio to experiment is discussed.

Careful treatment of water molecules in ligand-protein interactions is required in many cases if the correct binding pose is to be identified for molecular docking. Water can form complex bridging networks and can play a critical role in dictating the binding mode of ligands. A particularly striking example of this can be found in the ionotropic glutamate receptors (iGluRs), a family of ligand gated ion channels that are responsible for a majority of the fast synaptic neurotransmission in the central nervous system that are thought to be essential in memory and learning. Thus, pharmacological intervention at these neuronal receptors is a valuable therapeutic strategy. This thesis relies on various computational studies and X-ray crystallography to investigate the role of ligand-water mediated interactions in iGluRs bound to glutamate and α-amino-3-hydroxy-5-methyl-4- isoxazole-propionic acid (AMPA). Comparative molecular dynamics (MD) simulations of each subtype of iGluRs bound to glutamate revealed that crystal water positions were reproduced and that all but one water molecule, W5, in the binding site can be rearranged or replaced with water molecules from the bulk. Further density functional theory calculations (DFT) have been used to confirm the MD results and characterize the energetics of W5 and another water molecule implicated in influencing the dynamics of a proposed switch in these receptors. Additional comparative studies on the AMPA subtypes of iGluRs show that each step of the calculation must be considered carefully if the results are to be meaningful. Crystal structures of two ligands, glutamate and AMPA revealed two distinct modes of binding when bound to an AMPA subtype of iGluRs, GluA2. The difference is related to the position of water molecules within the binding pocket. DFT calculations investigated the interaction energies and polarisation effects resulting in a prediction of the correct binding mode for glutamate. For AMPA alternative modes of binding have similar interaction energies as a result of a higher internal energy than glutamate. A combined MD and X-ray crystallographic study investigated the binding of the ligand AMPA in the AMPA receptor subtypes. Analysis of the binding pocket show that AMPA is not preserved in the crystal bound mode and can instead adopt an alternative mode of binding. This involves a displacement of a key water molecule followed by AMPA adopting the pose seen by glutamate. Thus, this thesis makes use of various studies to assess the energetics and dynamics of water molecules in iGluRs. The resulting data provides additional information on the importance of water molecules in mediating ligand interactions as well as identifying key water molecules that can be useful in the de novo design of new selective drugs against iGluRs.

Electrochemistry is the science of electron transfer. The subject is of great importance and appeal because detailed information can be obtained using relatively simple experimental techniques. In general, the raw data is sufficiently complicated to preclude direct interpretation, yet is readily rationalised using numerical procedures. Computational analysis is therefore central to electrochemistry and is the main topic of this thesis. Chapters 1 and 2 provide an introductory account to electrochemistry and numerical analysis respectively. Chapter 1 explains the origin of the potential difference and describes its relevance to the thermodynamic and kinetic properties of a redox process. Voltammetry is introduced as an experimental means of studying electrode dynamics. Chapter 2 explains the numerical methods used in later chapters. Chapter 3 presents a review of the use of nanoparticles in electrochemistry. Chapter 4 presents the simulation of a random array of spherical nanoparticles. Conclusions obtained theoretically are experimentally confirmed using the Cr³⁺/Cr²⁺ redox couple on a random array of silver nanoparticles. Chapter 5 presents an investigation into the concentration of supporting electrolyte required to make a voltammetric experiment quantitatively diffusional. This study looks at a wide range of experimental conditions. Chapter 6 presents an investigation into the deliberate addition of insufficient supporting electrolyte to an electrochemical experiment. It is shown that this technique can be used to fully study a stepwise two electron transfer. Conclusions obtained theoretically are experimentally confirmed using the reduction of anthracene in acetonitrile. Chapter 7 presents a new method for simulating voltammetry at disc shaped electrodes in the presence of insufficient supporting electrolyte. It is shown that, under certain conditions, the results obtained from this complicated simulation can be quantitatively obtained by means of a much simpler ‘hemispherical approximation’. Conclusions obtained theoretically are experimentally confirmed using the hexammineruthenium ([Ru(NH₃)₆]³⁺/[Ru(NH₃)₆]²⁺) and hexachloroiridate ([IrCl₆]²⁻/[IrCl₆]³⁻) redox couples. Chapter 8 presents an investigation into the voltammetry of stepwise two electron processes using ionic liquids as solvents. It is shown that these solvents can be used to fully study a stepwise two electron transfer. Conclusions obtained theoretically are experimentally confirmed using the oxidation of N,N-dimethyl-p-phenylenediamine in the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([C₄ mim][BF₄]). The work presented in this thesis has been published as 7 scientific papers.