| The calculation of real time correlation functions remains a difficult problem in the field of quantum dynamics, mainly due to the multidimensional integrals that are necessary when investigating chemically relevant systems (such as neat fluids). Forward-backward semiclassical dynamics (FBSD) provides a rigorous and powerful methodology for calculating time correlation functions. By taking advantage of the phase space density of the multidimensional integrand resulting from the FBSD formulation, the convergence properties of various correlation functions are examined and a novel, optimal Monte Carlo sampling scheme that leads to a significant reduction of statistical error is introduced.;Differing from the real time formulation, the symmetrized correlation function provides an alternate route for calculating the real time correlation function due to the unique Fourier relations between the two functions. The pair-product approximation to the complex-time quantum mechanical propagator is utilized to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. Static equilibrium properties are calculated simultaneously and compared to Path Integral Monte Carlo results, and in doings so the method is shown to yield quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.;A more direct calculation using the pair-product approximation to the propagator is also discussed. Using single-step approximations to the propagator, it is shown that real-time correlation functions can be expressed as integrals of smooth functions, and thus can be efficiently evaluated by Monte Carlo methods. Tests on a model anharmonic system coupled to a bath of 25 harmonie oscillators are presented, and in spite of the large number of degrees of freedom associated with such a setting, the method allows direct calculation of correlation functions at intermediate temperatures over short to intermediate time lengths. Initial work into applying the single step propagator methodology to a Lennard-Jones fluid is also discussed. The efforts to evaluate the multidimensional integral associated with the unique matrix elements present in such a high dimensional system are explained, along with preliminary results. |
