Ever since the advent of Quantum Mechanics, there has been a quest for a trajectory based formulation of quantum theory that is exact. In the 1950’s, David Bohm, building on earlier work of Madelung and de Broglie, developed an exact formulation of quantum mechanics in which trajectories evolve in the presence of the usual Newtonian force plus an additional quantum force. In recent years, there has been a resurgence of interest in Bohmian Mechanics (BM) as a numerical tool because of its apparently local dynamics, which could lead to significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared --- it has simply been swept under the rug into the quantum force. In this work, we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This requires the propagation of complex trajectories, but with the reward of a significantly higher degree of localization. For example, using strictly localized trajectories (no communication with their neighbors) we obtain extremely accurate quantum mechanical transmission probabilities down to 10-7. We have recently extended the formulation to include interference effects, which has been one of the major obstacles in conventional Bohmian mechanics. Applications to one- and two-dimensional transmission, thermal rate constants in one and two dimensions, the calculation of eigenvalues and nonadiabatic transitions will be presented. A variation on the method allows for the calculation of thermal rate constants and eigenvalues using just one or two zero-velocity trajectories. On the formal side, the approach is shown to be a rigorous extension of generalized Gaussian wavepacket methods to give exact quantum mechanics, and has intriguing implications for fundamental quantum mechanics.

We study resonant response of an oscillator with shot-noise type mass fluctuations. The model describes a nano-mechanical resonator with adsorbing and desorbing molecules. We derive an analytical expression for the spectrum of the oscillator. It applies to an arbitrary interrelation between the damping rate of the oscillator, the adsorption and desorption rates and the magnitude of frequency shift due to a single adsorption or desorption event. Depending on this interrelation the spectrum may display fine structure corresponding to variation of the number of adsorbed molecules or present a single asymmetric peak. The results can be used for high-precision fast measurements of molecular mass with nano-mechanical resonators.

MOPAC2009 is the most recent of the MOPAC semi-empirical molecular orbital programs, and represents the culmination of more than 28 years of work. A brief history of this research program will be presented along with some of the more recent developments. Among these are: The latest NDDO method, PM6: The status of this method, including applicability and accuracy considerations, will be described, along with some examples. The solid-state function within MOPAC: This function allows a wide range of crystalline solids to be modeled. Examples of minerals and organic and inorganic solids will be presented. The Localized Molecular Orbital method, MOZYME: A brief description of this method, and several examples illustrating the type of system that can be modeled using a PC will be given. Time permitting, the current status of the MOPAC2009 software will be outlined.