Dispersed fluorescence spectroscopy of the SiCN Ã2Δ - X̃2Π system: Observation of some vibrational levels with chaotic characteristics.

The laser induced fluorescence (LIF) spectrum of the à 2Δ - X̃ 2Π transition was obtained for SiCN generated by laser ablation under supersonic free jet expansion. The vibrational structures of the dispersed fluorescence (DF) spectra from single vibronic levels (SVL's) were analyzed with consideration of the Renner-Teller (R-T) interaction. Analysis of the pure bending (ν2) structure by a perturbation approach including R-T, anharmonicity, spin-orbit (SO), and Herzberg-Teller (H-T) interactions indicated considerably different spin splitting for the µ and κ levels of the X̃ 2Π state of SiCN, in contrast to identical spin splitting for general species derived from the perturbation approach, where µ and κ specify the lower and upper levels, respectively, separated by R-T. Further analysis of the vibrational structure including R-T, anharmonicity, SO, H-T, Fermi, and Sears interactions was carried out via a direct diagonalization procedure, where Sears resonance is a second-order interaction combined from SO and H-T interactions with Δ K = ± 1, ΔΣ = ∓1, and Δ P = 0, and where P is a quantum number, P = K + Σ. The later numerical analysis reproduced the observed structure, not only the pure ν2 structure but also the combination structure of the ν2 and the Si-CN stretching (ν3) modes. As an example, the analysis demonstrates Sears resonance between vibronic levels, (0110) κ Σ(+) and (0200)µΠ12, with Δ K = ± 1 and Δ P = 0. On the basis of coefficients of their eigen vectors derived from the numerical analysis, it is interpreted as an almost one-to-one mixing between the two levels. The mixing coefficients of the two vibronic levels agree with those obtained from computational studies. The numerical analysis also indicates that some of the vibronic levels show chaotic characteristics in view of the two-dimensional harmonic oscillator (2D-HO) basis which is used as the basis function in the present numerical analysis; i.e., the eigen vectors for some of the observed levels have several components of the basis, and we have not been able to give precise vibronic assignments for the levels, but just vibronically labeled, referring the largest component in their vectors. (To emphasize this situation, we do not use the word "assignment," but prefer to use "label" as the meaning of just "label," but not "assign," throughout this paper.) The latter shows that the vibronic labels of the levels are meaningless, and the P quantum number and the order of their eigen states in the P matrix block derived in the numerical analysis only characterize the vibronic levels. Comparing the constants obtained for all of the interactions with those of species showing Sears resonance and studied previously, it is found that none of them are strong, but are moderate. It is thus concluded that the chaotic appearance is not derived by any strong interaction, but is induced by complex and accidental proximities of the vibronic levels caused by the moderate interactions.