Survey of correlation properties of polyatomic molecules vibrational energy levels using F. T. analysis

Abstract

In the last few years molecular spectroscopists have begun to study the highly excited vibrational levels of polyatomic molecules. In this high energy regime vibrational quantum numbers can no longer be intrinsically assigned (in contrast to vibrational levels at low energy). One can only characterize these levels by their correlation properties. The authors consider: short range correlations which are characterized by the next neighbor distribution, (NND). These correlations range from a Poisson (random or uncorrelated spectra) to a Wigner distribution (which shows 'level repulsion'); (ii) long range correlations are characterized by the$\mathrm{\Sigma ^{2}}$(L) and$\mathrm{\Delta _{3}}$(L) function. They describe the behavior which ranges from an uncorrelated spectra (Poisson statistic) to a spectra with 'spectral rigidity'.