Self-interaction error appears because the exchange interaction of a system does not cancel the self-coulomb energy of its electron density, yet this exchange interaction contributes to the non-dynamical correlation interaction of the system. The use of exact Hartree-Fock (HF) exchange can correct the self-interaction error, but does not include any non-dynamical correlation required to correctly model the system. This thesis presents a novel approach for constructing hybrid functionals using variable amounts of regular density functional theory (DFT) exchange and exact HF exchange according to the local properties of each system. The idea behind this local mix is to allow for the inclusion of non-dynamical correlation when required, and the correction of the self-interaction error when needed. In this work, the local mix of HF and DFT exchange is driven by the ratio of the Weizsacker approximation to the kinetic energy density with the exact kinetic energy density. This particular choice of local mix yields 100% of exact exchange in one-electron regions, which reduces the self-interaction error. Exact exchange is introduced in this scheme using the exact exchange energy density derived from the definition of the non-local exchange energy density. Unlike other works that tried to correct self-interaction error, this local hybrid approach is computationally feasible for a wide range of molecules. Dissociation energy curves, binding energies, and equilibrium geometries for two-center, three-electron symmetric radical cations can be modeled accurately using this scheme, something that cannot be done accurately with traditional density functionals. This work also presents examples of reaction energy barriers showing a significantly closer agreement to experimental results than traditional density functionals. Calculations of properties of radicals, charge transfer complexes, and Rydberg excited states interactions could also benefit from the flexibility of our local hybrid scheme.

Equilibrium geometries and binding energies (corrected for basis set superposition error) of single and multiple noble gas atom complexes of C$\sb{60}$ are calculated at DFT and MP2 levels of theory using basis sets including polarization functions. B3LYP and MP2 give similar van der Waals dispersion interactions, predicting repulsive energies for the He and Ne complexes of about 1 kcal/mol, and higher energies for the larger noble gas atom complexes. As expected, C$\sb{60}$ is resilient to deformation in all cases studied, with the geometry of the fullerene cage barely affected by the presence of multiple noble gas atoms inside.

The convergence of the Self Consistent Field (SCF) iteration process is one of the most commonly encountered problems in quantum chemistry calculations. Numerous cases are known in which calculations (both Hartree-Fock and Density Functional Theory), even when using extrapolation techniques, converge extremely slowly or do not converge at all. Many of these cases include molecules that contain transition metals. During my research, I developed two techniques that fractionally occupy orbitals around the Fermi energy during the SCF cycles. Both methods use fractionally occupied orbitals to aid in the iterative process, but the occupations at convergence are forced to be ones and zeros. I investigated how by using these fractionally occupied orbitals, convergence was improved for a number of difficult cases. There is also no significant overhead in the number of SCF cycles for molecules that easily converge with standard techniques. On the other hand, I also studied cases where the lowest energy solutions may be fractionally occupied. I implemented numerous methods to optimize the fractional orbital occupations in various Density Functional Theory methods. These methods, which included steepest descent and conjugate gradient techniques, are based on Janak's theorem. In general, the lowest energy solution is fractionally occupied if a solution containing an aufbau principle violation is lower in energy than a typical solution. In these cases, a fractionally occupied solution is indeed the lowest self-consistent field energy solution. New methods to optimize the fractional occupations based on optimizing a trigonometric or Fermi-Dirac based function of the orbital occupations are also discussed and compared.

Ground- and excited-state studies of ill-characterized fullerenes are presented. The first isomerically enriched study of C84's major isomers finds they differ significantly in T1 energies. Their T 1 lifetimes span two orders of magnitude, from 643 mus for D 2(IV) to 5 mus for D2d(II). The minor isomer, Cs(a), has a 127 mus T1 lifetime. Temperature-dependent decay kinetics and triplet-triplet spectra also show clear isomeric variations. These changes are remarkable, since they originate in subtle geometry differences. The C80{D5d} isomer lacks appreciable transient absorption. Its slow quenching of 1Deltag O 2 emission indicates C80{D5d}'s T1 state is within 1 kT (∼300 cm-1) of 7880 cm -1. O2-quenching experiments showed that Ho 3N C80 {Ih}'s T1 energy lies above 7880 cm-1. This incar quenches C 70 triplet states, and data suggest their T1 energies are similar. The ground-state optical behavior of n-C60 (aq) is dominated by scattering effects. This colloid's transient attenuation is primarily refractive. Redshifted 1Deltag O2 emission from the colloid indicates the polarizable C60 environment lowers electronic energy levels. The "bucky amino acid" (BAA) shows derivatization-blueshifted transient absorption. This derivative has a T1 level substantially higher than 7880 cm-1, and is only a modest quencher of singlet oxygen.

The reaction dynamics of realistic molecular Hamiltonians including both mode coupling and anharmonicity may be profitably explored by classical trajectories. However even if such trajectories begin in phase the energy dependence of individual orbital periods of anharmonic oscillators quickly results in an incoherent ensemble, thereby obscuring organization present in the reaction dynamics of a given Hamiltonian. One solution to these difficulties is to compare trajectories in phase on a cycle by cycle basis (i.e. coherently). In this work a model independent means for phase based, or coherent, comparison was developed utilizing the Hilbert transform. Phase based analysis reveals that in particular unimolecular reactions correlated motion occurs when energy transfer between an orthogonal mode and the reaction coordinate forces synchronization in their motions, resulting in convergence of their phases. Thus a restricted and systematic set of states (i.e. points in phase space) precedes reaction, apparently contradicting the RRKM assumption that all states are equally likely to react. Detailed examination of the fundamental RRKM equation shows that this assumption differs from requiring that all states are equally likely to react per unit of time. States involved in correlated motion react sooner than others, but all states ultimately react, so their reaction probabilities are equal, therefore correlated motion can be consistent with RRKM kinetics. To explore the properties of different distributions of internal energy within a microcanonical ensemble a variant of phase space is proposed wherein every point is indexed by time remaining until reaction. (In the absence of trapping all unimolecular trajectories reside in the bound region of phase space for only a finite duration.) Under this variant points belonging to a particular allocation of internal energy are not scattered randomly across the lifetime distribution mapping (e.g. states in close time proximity to the transition state obviously all share the property of having sufficient energy in the reaction coordinate to clear the barrier). The microcanonical rate constant is an average of those for all component distributions of available internal energy, so the existence of rate constants with mode specificity can also be consistent with RRKM kinetics.

We report methodological and computational details of our Kohn-Sham density functional method with Gaussian orbitals for systems with periodic boundary conditions (PBC). When solving iterative self-consistent field (SCF) equations of density functional theory (DFT), the most computationally demanding tasks are Kohn-Sham (or Fock) matrix formation and the density matrix update step. The former requires evaluation of the Coulomb interactions and the exchange-correlation quadrature, and in our code both of them are computed via O (N) techniques. An O (N) approach for the Coulomb problem in electronic structure calculations with PBC is developed here and is based on the direct space fast multipole method (FMM). The FMM achieves not only linear scaling of computational time with system size but also high accuracy, which is pivotal for avoiding numerical instabilities that have previously plagued calculations with large bases, especially those containing diffuse functions. The density matrix update step is carried out via the conventional O (N3) diagonalization of the Fock matrix, which for systems with less than ≈3000 basis functions is cheaper than the recently developed O (N) algorithms. In addition to evaluating energy, our code also computes analytic energy gradients with respect to atomic positions and cell dimensions (forces). Combining the latter with the developed in this work redundant internal coordinate algorithm for optimization of periodic systems, it becomes possible to optimize geometries of periodic structures with great efficiency and accuracy. We demonstrate the capabilities of our method with benchmark calculations on polyacetylene, poly(p-phenylenevinylene) (PPV), and a series of carbon and boron-nitride single wall nanotubes employing basis sets of double zeta plus polarization quality, in conjunction with generalized gradient approximation and kinetic energy density dependent functionals. We also present vibrational frequencies for PPV obtained from finite differences of forces. The largest calculation reported in this work contains 244 atoms and 1344 contracted Gaussians in the unit cell.

The Coupled Cluster theory has proven itself as an effective method for the accurate calculations of correlation energy. A computational program for the full coupled-cluster model (CCSDT) single, double and triple excitation method has been integrated into the Gaussian program. This interface is based on original code that had been developed in late 80's. Single point energy calculations for the HF and OH- molecules verify the accuracy and stability of the newly developed code compared to the old one. Research on the potential energy curve of the MnO-4 anion has been conducted. Energy calculations for various Mn-O bond lengths using Hartree-Fock, MP2, MP3, MP4(SDQ), CCSDT), B3LYP, VSXC, PBE and CCSDT method exist. The CCSDT result is in excellent agreement with the experimental value of the Mn-O bond length.

A beam of symmetric top (CX3Y) molecules is state-selected using an inhomogeneous hexapole electric field and then oriented by homogeneous electric fields. A fast neutral atomic potassium beam produced via charge-exchange crosses the molecular beam at a right angle. Continuous electric fields extract ion pair products as they are formed into dual time-of-flight (TOF) mass spectrometers, where the arrival time difference is characteristic of the mass difference of the particles. The positive product (K+) is known for these reactions, allowing identification of the negative products based on the time difference. Construction of the dual time-of-flight (TOF) mass spectrometers is described, with an explanation of how coincidence detection is used to identify the negative ion products of reactions between fast neutral K atoms and small molecules (≤7 atoms). Examination of the results of initial characterization studies including reactions with CH3Cl, CH3Br, CH3I, CF 3Br, and SF6 indicate that coincidence TOF should be a powerful tool for investigations into the dynamics of these reactions. Preliminary results suggest that orientation data will be obtainable to address the question of whether different approach vectors result in different product channels. The importance of a well-calibrated alkali source, well-defined electric fields, and a good vacuum is indicated. An appendix discusses radio-frequency (RF) spectroscopy experiments performed to explore characteristics of the rotational distribution in the molecular beam. A possible application of RF spectroscopy to "tag" single quantum states is discussed.

The technique of infrared kinetic spectroscopy has been used to study the production of the propargyl radical from the reaction of singlet methylene with acetylene. The rate constant for this product channel was measured as $\rm(3.5\pm0.7)\times10\sp{-10}\ cm\sp3\ molecule\sp{-1}\ s\sp{-1}$ at 295 K, relative to the known rate for $\rm\sp1CH\sb2$ with H$\sb2$ or CH$\sb4.$ Methylene was produced in the singlet state by excimer laser photolysis of ketene at 308 nm in the presence of acetylene and either $\rm H\sb2$ or $\rm CH\sb4.$ Reaction of $\sp1CH\sb2$ with acetylene produces propargyl, and reaction of $\sp1CH\sb2$ with either $\rm H\sb2$ or CH$\sb4$ produces CH$\sb3.$ The intensity of a propargyl infrared absorption line was compared with that of a methyl infrared absorption line, and the rate of formation of propargyl was determined from the ratio of these two intensities and the known rates of reaction of singlet methylene. The relative peak infrared absorption cross-sections of methyl and propargyl were calibrated under the conditions of the experiment by photolyzing crotyl bromide at 193 nm to produce methyl and propargyl in equal concentrations. The reaction of the cyanomethylene (HCCN) radical with nitric oxide (NO) and oxygen (O$\sb2)$ has also been investigated using infrared kinetic spectroscopy. The overall rate constants for each reaction have been determined. For the reaction with NO, the rate constant was determined to be $\rm(3.5\pm0.6)\times10\sp{-11}\ cm\sp3\ molecule\sp{-1}\ s\sp{-1},$ for reaction with O$\sb2,$ the rate constant was $\rm(1.8\pm0.4)\times10\sp{-12}\ cm\sp3\ molecule\sp{-1}\ s\sp{-1}.$ Several products were observed, but not quantified for either reaction. In the case of reaction with NO, hydrogen cyanide (HCN) and fulminic acid (HCNO) were observed. During reaction with O$\sb2,$ HCN, hydrogen isocyanide (HNC) and carbon dioxide (CO$\sb2)$ were observed. Species looked for but not observed include isocyanic acid (HNCO), ethynyl (C$\sb2$H) radical, cyanic acid (HOCN) and isofulminic acid (HONC). Under the conditions of our experiments, no reaction was observed between HCCN and the following: methane (CH$\sb4),$ CO$\sb2,$ acetylene $\rm(C\sb2H\sb2),$ ethylene $\rm(C\sb2H\sb4),$ carbon monoxide (CO) and hydrogen (H$\sb2).$

The optical properties of metal nanostructures are related to their plasmon response, which is sensitively dependent on nanostructure geometry and environment. The metallodielectric, core-shell structure of nanoshells represents a unique geometry allowing for the systematic tunability of the plasmon resonance of the nanostructure. This is accomplished by varying the relative dimensions of the core and shell layers. Fabrication of a nanoshell particle with a strong plasmon resonance is dependent on shell quality, which is strongly dependent on the careful preparation of the metal shell. The resonant response of metal nanostructures can also be modified through plasmon-plasmon interactions. This work focuses on the fabrication of nanoparticles with a multilayer, concentric-shell structure consisting of a silica core, inner gold shell layer, silica spacer layer, and an outer gold shell layer. This concentric nanoshell particle is fabricated through the controlled growth of a nanometer-scale silica layer around a preformed nanoshell. The silica layer was found to increase the thermal and chemical stability of the nanoshell particles. A second gold shell could be grown on this layer to generate the concentric nanoshell particle. This layered nanoparticle geometry has a plasmon resonance dependent on the interaction between the inner and outer shell plasmons. This interaction can be explained in terms of a sphere-cavity model of plasmon hybridization derived from a semi-classical model of the plasmon resonance. Varying the dimensions of the concentric shell layers can independently and systematically control the plasmon resonance of the inner and outer shell, which effects the interaction between the two plasmons. The coupling between the inner and outer shell plasmons was investigated experimentally by varying the concentric nanoshell dimensions, specifically examining how the spectral detuning of the inner and outer shell resonances and spatial interaction between inner and outer shell plasmons determine the nanoparticle's optical properties. Calculations using Mie scattering theory to model the nanoshell plasmon response agree quantitatively with experimental measurements of the nanoshell plasmon resonance in both the single-layer and multi-layer regime.