We present a study of the ground and triplet state properties of C$\sb{60}$O. UV-vis spectroscopy and a gravimetric analysis are used to produce a quantitative electronic absorption spectrum. Spectrofluorimetry reveals that the fluorescence quantum yield of C$\sb{60}$O is $8.1\times 10\sp{-4}$, which is a factor of 2.5 higher than that of C$\sb{60}$. Transient absorption spectroscopy is used to study the triplet state of C$\sb{60}$O, which is seen to exhibit complex decay kinetics. A possible explanation for this behavior involving triplet mediated epoxide ring opening is presented. The intrinsic triplet lifetime is determined to be 6.8 $\pm$ 0.3 $\mu$s, making C$\sb{60}$O the shortest lived fullerene derivative studied to date. Additional studies reveal that the decay of C$\sb{60}$O triplets has a mild temperature dependence corresponding to an E$\sb{\rm a}$ value of 4.5 $\mu$ 0.6 kJ/mol, whilt self-quenching is seen to play a negligible role. Furthermore, solutions of C$\sb{60}$O are shown to be unstable with respect to temperature, generating unknown impurities even at room temperature. Mass spectrometric studies failed to unambiguously identify the product contaminant.

Various density functional methods have been tested for the van der Waals interactions of the rare gas dimers He$\rm\sb2,\ Ne\sb2$ and Ar$\sb2$ as model compounds. Detailed analysis proved that all tested and commonly used functionals are not suitable for an appropriate description of the interactions, even if Hartree-Fock exchange is used in combination with a correlation functional. However, within the framework of long-range density functional theory, van der Waals coefficients are correctly reproduced by a density-density interaction term. Adding these interactions separately to the tested functionals, surprisingly good results are obtained by using exact exchange.

This thesis is composed of three parts. Part I describes a DFT study of the C60 dimer cations and anions which indicates that [2+2] isomers are lower in energy than single bond (SB) isomers. The center to center distances (CCD) of these two isomers calculated in our study are in fair agreement with experiment. Part II presents a good model (Fe+-oronene) and a scheme to simulate the binding of iron cations to [n, n] nanotubes. The binding energy from all DFT calculations increases as the nanotube diameter decreases, which can be explained by pi-orbital axis vector (POAV) theory. LSDA and PW91PW91 are believed to overestimate the binding energy while BPW91 and B3LYP are expected to give better results. Part III analyzes two possible patterns of fluorine addition to single wall carbon nanotube that have been proposed as 1,2 and 1,4 addition. Semi-empirical calculations indicate that the 1,4 isomer is lower in energy. Fluorine atoms prefer to grow along the tube for the 1,2 isomer whereas for the 1,4 isomer, they prefer to grow around the tube. This is consistent with results from a STM study of the fluorinated nanotubes.

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.