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Density functional theory (DFT) is currently the most widely applied electronic structure theory in Chemistry. It is favoured for its computational efficiency, coupled with good accuracy. Although formally exact, approximations are required when practically applied. In the Kohn-Sham formalism, these approximations are contained within the exchange-correlation functional. Well established exchange-correlation functionals, such as the ubiquitous B3LYP, provide reasonable accuracy, but their continued use is increasingly based on the collective experience with the functional that has been accumulated, rather than the results that can be achieved. This thesis considers the circumstances under which conventional functionals fail and how a recent modification— coulomb attenuation—can resolve such issues. An outline of basic electronic structure theory is provided in chapter 1, particularly the formulation of the Hartree-Fock approach. This is extended to more sophisticated wavefunction based methods. Chapter 2 provides a formal proof for the validity of DFT as well as a framework for its implementation. A recently developed exchange-correlation functional (CAM-B3LYP) based on a varying quantity of exact exchange is outlined. Also discussed is the time-dependent DFT (TDDFT) approach to the determination of excitation energies, its failures and how such failures can be predicted and eliminated. The subsequent chapters consider the application of CAM-B3LYP to the description of weak interactions and excited states. Chapter 3 considers some key problems facing modern DFT—dispersion, fractional spins and fractional charges—in terms of the force and the Feynman electron density distortion, in addition to the conventional viewpoint of the energy. Two model systems, H2 and H+2 are employed to illustrate how increasing quantities of exact exchange can increase the fractional spin error while decreasing the fractional charge error, respectively. This is reflected in the improved description offered by CAM-B3LYP for H2 and the corresponding poor performance for H+2 . Chapter 4 takes a more detailed look at the dispersion interaction. C6 dispersion coefficients are calculated using a range of functionals—CAM-B3LYP showing a clear improvement over GGA and hybrid functionals. Dispersion corrected potential energy surfaces and interaction energies are determined with CAM-B3LYP providing comparable accuracy to other, existing long-range corrected functionals. Chapters 5 and 6 consider the application of CAM-B3LYP to the excited states of large systems of chemical and biological importance, respectively. In the former, the difficulty of comparing theoretically determined excitation energies with experimentally observed absorption spectra is of particular focus. In the latter, the failure of conventional functionals to correctly predict the energy and character of charge-transfer excitations is highlighted. For both cases, it is shown that CAM-B3LYP can provide a significant improvement over conventional functionals, all but eradicating the charge- transfer issue in the latter case. Chapter 7 further investigates the charge-transfer issue experienced by conventional functionals and illustrates how the error can manifest itself as an inaccuracy in the character of an excited state rather than the energy. CAM-B3LYP provides an accurate description of both aspects. Triplet excitation energies are determined from TDDFT and the ∆SCF approach—the latter providing improved results for conventional functionals.

Fairness in a non-interleaving semantic model for concurrency has been investigated. In contrast to the interleaving approach, which reduces non-sequential behaviours to a nondeterministic choice between possible interleavings of activities of concurrent processes, concurrency and causality were assumed as primitive notions. Mazurkiewicz's trace languages were chosen as behavioural representations of systems and Shields' asynchronous transition systems as their acceptors. The notion central to these two formalisms is one of causal independency, which determines trace equivalence (congruence) in the monoid of strings. Equivalence classes of strings are called traces. The quotient monoid of traces forms a poset with trace prefix ordering. First, trace languages have been enhanced to allow for infmite traces; this was achieved by introducing trace preorder relation on possibly infinite strings. It has been shown that the extension gives rise to the domain of traces and an infinitary monoid, which specializes to the domain and the infinitary monoid of strings of Nivat's, Asynchronous transition systems have been equipped with a notion of a process structure; a variety of process structures ordered by refinement relation are possible for a given system. Each process structure determines projective preorder and equivalence relations in the monoid of strings, which are shown to coincide with the trace preorder and trace equivalence. In this setting, a topological characterization of behavioural properties which includes safety, progress and fairness properties has been provided. Fairness properties form a subclass of infinitary progress properties that is closed under arbitrary union. Unconditional process fairness properties that are determined by process structures have been distinguished; they form a lattice with inclusion ordering. Finally, strength predicates were incorporated to allow for a variety of specific fairness properties such as weak and strong process fairness as well as equifairness and state fairness.

The reactions of chlorine with hydrogen and hydrocarbons have been widely studied and it is well established that they are chain reactions involving very long chains. There is general agreement as to the chain initiating and propagating steps but still considerable disagreement as to the chain terminating steps. The modern trend in kinetics has been away from the establishment of mechanism in detail and towards the determination of Arrhenius parameters for elementary reactions such as those involved in chain propagation. The present work was aimed at determining accurately the rate constants for the attack of chlorine atoms on different hydrocarbons (reaction(1)) Cl + R-H → R + H-Cl (1) and on different positions in the same hydrocarbon. This has been accomplished by employing a competitive technique in which reaction products are analysed for products characteristic of the initial chlorine atom attack. Absolute rate constants for each hydrocarbon are then found, if the absolute value for at least one of the substances studied is known. In this work the rate constant for the chlorine atom attack on hydrogen, which is reasonably well established, has been used as the standard value and all other absolute rate constants are obtained from this. The activation energies obtained from the rate constants have been explained in a qualitative manner, while the A factors have been used to test transition state theory.

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