ROVIBRONIC PHASE PLOTS I: COMPUTER GRAPHICAL INSIGHTS INTO TENSOR SYMMETRY BREAKING, DYNAMICS AND SPIN-SYMMETRY-SPECIES CONVERSION EFFECTS

\underline{JUSTIN C. MITCHELL} and WILLIAM G. HARTER, Department of Physics, University of Arkansas, Fayetteville, AR 72701.

At the core of molecular spectral assignment (and quantum theory in general) is a process of matrix diagonalization for eigensolutions. An n-by-n matrix goes in and n eigenvalues with n(n − 1) eigenvector components come out. Yet one may be left mystified by both the numerical processes and the physical processes that the numbers supposedly represent. The n-values (or differences thereof) give spectra, but the bulk of the information about dynamics, intensity, symmetry, etc. lies in the n^{2} − n vector components. This and the following talk shows ways to understand and approximate results of rovibrational diagonalizations that insightfully display and relate e-values together with e-vectors. Centrifugal and Coriolis effects on rovibrational eigensolutions are often amenable to approximation by rotational-energy-surfaces (RES) that serve both as an angular phase space and as an Euler body-coordinate space. An illustration of RES views of SF_{6} fine and superfine spectral structure^{a} is reviewed and compared to extensions of this technique to higher rank tensor models.^{b} Of particular interest are spectral and RES regions with “big-pocket” suffering spontaneous symmetry breaking or phase localization effects including breakdown of Herzberg spin-species-conservation rules ^{c} ^{d} and superhyperfine clustering.^{e} The RES views help expose the wave interference phenomena that deeply underlie rovibronic dynamics as well as clarifying the matrix diagonalization methods that quantify them.

aW. G. Harter, in Handbook of Atomic, Molecular and Optical Physics, edited by G.W.F. Drake (Springer, Germany 2006)

Chapter 32. p. 501.

bW. G. Harter, J. Math. Phys. 20, 1453 (1979).

cG. Herzberg, Infrared and Raman Spectra (VanNostrand 1945) pp. 458,463.

dJ. T. Hougen, T. Oka, Science, 310, 1913 (2005)

eW. G. Harter, Phys. Rev. A24,192-262(1981)