Cumulant expansion and analytic continuation in Monte Carlo simulation of classical Lennard-Jones clusters.

The Monte Carlo (MC) estimates of thermal averages are usually functions of system control parameters λ, such as temperature, volume, and interaction couplings. Given the MC average at a set of prescribed control parameters λ{0}, the problem of analytic continuation of the MC data to λ values in the neighborhood of λ{0} is considered in both classic and quantum domains. The key result is the theorem that links the differential properties of thermal averages to the higher order cumulants. The theorem and analytic continuation formulas expressed via higher order cumulants are numerically tested on the classical Lennard-Jones cluster system of N=13, 55, and 147 neon particles.

Convergence characteristics of the cumulant expansion for Fourier path integrals.

The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables N included. It is proved that when the cumulant expansion is truncated at order p, the asymptotic convergence rate of the density matrix behaves like N(-(2p+1)). The complex algebra associated with the proof is simplified by introducing a diagrammatic representation of the contributing terms along with an associated linked-cluster theorem. The cumulant terms at each order are expanded in a series such that the asymptotic convergence rate is maintained without the need to calculate the full cumulant at order p. Using this truncated expansion of each cumulant at order p, the numerical cost in developing Fourier path integral expressions having convergence order N(-(2p+1)) is shown to be approximately linear in the number of required potential energy evaluations making the method promising for actual numerical implementation.

New signal processing method for the faster observation of natural-abundance 15N NMR spectra and its application to N5+.

The new harmonic inversion noise reduction method was applied to (15)N natural-abundance NMR spectroscopy and N(5)SbF(6). This method is superior to conventional Fourier transform methods for processing FIDs and permits the detection of natural abundance (15)N NMR signals with significantly reduced numbers of scans and improved sensitivity. In addition to the confirmation of the previously reported chemical shifts for N(5)(+), the one bond coupling between N(beta) and N(gamma) could be observed for the first time. Its absolute value is compared to known coupling constants of other covalent azides and the free azide ion.

An application of error reduction and harmonic inversion schemes to the semiclassical calculation of molecular vibrational energy levels.

A singular value decomposition based harmonic inversion signal processing scheme is applied to the semiclassical initial value representation (IVR) calculation of molecular vibrational states. Relative to usual IVR procedure of Fourier analysis of a signal made from the Monte Carlo evaluation of the phase space integral in which many trajectories are needed, the new procedure obtains acceptable results with many fewer trajectories. Calculations are carried out for vibrational energy levels of H2O to illustrate the overall procedure.