Randall B. Shirts

Department of Chemistry and Biochemistry, Brigham Young University Provo, Utah 84602 USA

We are interested in the spectra of molecules which are vibrationally excited to high levels. Because of the enormous number of states, the quantum mechanics of such systems is intractable, so we have been applying semiclassical methods. However, most coupled oscillator systems exhibit classically chaotic motion at high energies, and standard Einstein-Brillouin-Keller quantization is formally inapplicable. In 1982 however, W. P. Reinhardt and I [1] noted a surprising degree of intermediate-term order in classically chaotic coupled oscillator motion and dubbed the resulting phase space structure the "vague torus." At that time, we justified the success of several methods of semiclassical quantization on the existence of vague tori. In this poster, I will exhibit the explicit construction of vague tori and their use for semiclassical quantization [2]. In addition, I will demonstrate how the same Fourier transform formalism can be used to get approximate transition dipole matrix elements using the Heisenberg correspondence principle. The combination of semiclassical eigenvalues and matrix elements thus allow construction of approximate spectra using only Fourier transforms of classical trajectory data.

[1] R. B. Shirts and W. P. Reinhardt, J. Chem. Phys. 77, 5204 (1982)
[2] K. Sohlberg and R. B. Shirts, J. Chem. Phys. 101, 7763 (1994)