A novel time-dependent quantum mechanical formulation of scattering theory is developed which is well suited for the calculation of individual S-matrix elements. Wave packets corresponding to well-defined reactant and product channel quantum numbers are propagated in to the interaction region using Mo/ller operators, the former forward in time and the latter backwards in time. The S-matrix element Sβα(E) is then simply related to the Fourier transform at energy E of the time-dependent correlation function between the two wave packets in the interaction region. The symmetric treatment of reactants and products allows the entrance and exit channel dynamics to be performed highly efficiently using different coordinate systems and different interaction representations. As a result, the formulation is expected to provide an improved route to the calculation of S-matrix elements using quantum mechanical, as well as semiclassical propagation methods. The new formulation combines elements of classical S-matrix theory, the wave packet correlation formulation of spectroscopy, and quantum transition state theory, and should be a good starting point for a variety of new approximations to and interpretations of individual S-matrix elements.

The icosahedral symmetry of molecules such as buckyball, B12H12−2, and C20H20, is analyzed using subgroup chain defined projection operators. The icosahedral analysis is used to determine the eigenvalues and eigenvectors of a classical spring mass model of buckyball. A spectrum of Raman and dipole active modes is given using the spring constants of benzene. Corresponding dipole active and Raman active normal modes are displayed stereographically. Several choices for springs constants are discussed and a comparison with spring mass systems of reduced symmetry is made.

The X(2)Σ(1/2)(+), A(2)Π(1∕2), A(2)Π(3∕2), and B(2)Σ(1/2)(+) potential energy curves and associated dipole matrix elements are computed for M + Ng at the spin-orbit multi-reference configuration interaction level, where M = K, Rb, Cs and Ng = He, Ne, Ar. Dissociation energies and equilibrium positions for all minima are identified and corresponding vibrational energy levels are computed. Difference potentials are used together with the quasistatic approximation to estimate the position of satellite peaks of collisionally broadened D2 lines. The comparison of potential energy curves for different alkali atom and noble gas atom combinations is facilitated by using the same level of theory for all nine M + Ng pairs.

Icosahedral symmetry analysis is developed for analyzing eigensolutions of rovibrational tensor Hamiltonians for molecules such as B12H12−2, C20H20, and C60. Simplified asymptotic formulas and procedures are developed for obtaining rotational spectral fine structure for high angular momentum. J=100 eigenlevels for sixth- and tenth-rank icosahedral tensors are discussed using different approximations and visualization schemes.