Collisional broadening and spectral line shape of an entire rotational band

The impact approximation is applied to the classical binary collision operator making it possible to derive an expression for the dipole correlation function for real systems in a form which is computationally tractable and contains no adjustable parameters. Trajectory calculations are performed (in order to evaluate the microscopic expression for the relaxation parameter in the correlation function) for the system CO in dense Ar gas. Comparison is made with experimental data and excellent agreement is found for certain densities when a quantum correction is included. At higher densities (i.e., ρ^(−1/3)< "the range of the potential") one approximation is not valid and comparison with experiment illustrates this point

Cross-correlation trajectory study of V-V energy transfer in HF-HF and DF-DF

Results of a fully three‐dimensional classical trajectory calculation of vibrational energy transfer are presented for the collision of HF(v=1) with HF(v=1) and its deuterium analog. A cross‐correlation method, together with quasiclassical trajectories, is introduced to relate the changes in vibrational states of the two molecules to probabilities and rate constants. Multiple collisions are found to make an important contribution to the vibrational energy transfer cross‐sections for the present potential surface. Vibrational anharmonicity is shown to decrease the energy transfer rate constant by a factor of ten, by causing the process to be further from exact resonance. Excellent agreement with experiment is obtained for the HF–HF and DF–DF systems

A spectral analysis method of obtaining molecular spectra from classical trajectories

Vibrational classical trajectories of anharmonic molecules are used here to obtain the classical vibrational autocorrelation function and, via a Fourier transform, the power (or infrared) spectrum of the dynamical variables. In the vibrationally quasiperiodic regime the spectrum consists of sharp lines, for any given initial amplitude. The initial amplitudes are chosen semiclassically. The spectral lines are compared with quantum mechanical calculations for systems with two and three coordinates, with excellent agreement. The method is also useful for obtaining a classical spectrum in the ergodic regime; the spectral lines are then ''broad'' rather than narrow. The method can be used in the analysis of trajectories for unimolecular reactions, infrared multiphoton dissociations, and for obtaining molecular spectra from force fields. The spectral analysis itself has implications for the theory of unimolecular reactions

Semiclassical calculation of bound states in multidimensional systems with Fermi resonance

A method is devised to calculate eigenvalues semiclassically for an anharmonic system whose two unperturbed modes are 2:1 degenerate. For some special states the periodic energy exchange between unperturbed modes is found to be very large. The quantum mechanical wave functions are examined and a correlation with the classical trajectories is described, both for quasiperiodic and the stochastic cases. A method used in the literature for calculating the stochastic limit is tested and found to break down when the present anharmonic system is separable

Comparison of quantal, classical, and semiclassical behavior at an isolated avoided crossing

The quantal and classical/semiclassical behavior at an isloated avoided crossing are compared. While the quantum mechanical eigenvalue perturbation parameter plots exhibit the avoided crossing, the corresponding primitive semiclassical eigenvalue plots pass through the intersection. Otherwise, the eigenvalues agree well with the quantum mechanical values. The semiclassical splitting at the intersection is calculated from an appropriate Fourier transform. In the quasiperiodic regime, a quantum state near an avoided crossing is seen to exhibit typically more delocalization than the classical state. However, trajectories near the ‘‘separatrix’’ display a quasiperiodic ‘‘transition’’ between two zeroth order classical states

On correlation functions and the onset of chaotic motion

A variety of correlation functions computed over a microcanonical ensemble for the Hénon–Heiles system are investigated. We find the general trend is that of a gradual change to some form of decaying behavior as the motion becomes predominantly chaotic. The decay of a mode energy correlation function indicates a time scale for intramolecular energy redistribution

Semiclassical calculation of eigenvalues for a three-dimensional system

A method utilizing integration along invariant curves on Poincaré's surfaces of section is described for the semiclassical calculation of eigenvalues for three and higher dimensional systems, supplementing thereby our previous work in two dimensions. The eigenvalues calculated for anharmonically coupled oscillators agree well with the exact quantum eigenvalues