Periodic orbit analysis of molecular vibrational spectra: Spectral patterns and dynamical bifurcations in Fermi resonant systems

Raman spectroscopy study on the ν1-2ν2 Fermi resonance of liquid carbon disulfide in binary solutions: effect of the weak hydrogen bond formation on the Fermi resonance

We have measured the Raman spectra of liquid CS(2) at different volume concentrations in CHCl(3) and CH(2)Cl(2) solutions. With decreasing the volume concentration of CS(2), a noticeable growth in the 2ν(2) band frequency was observed, while the ν(1) band location remained practically unchanged. This asymmetric wavenumber shift phenomenon of the Fermi doublet ν(1) and 2ν(2) of CS(2) has been ascribed to weak, non-conventional hydrogen bonds formed between the CS(2) and the solvent molecules. These weak hydrogen bonds were also responsible for significant decreases in the C-H bond symmetric stretching vibration band frequencies of CHCl(3) and CH(2)Cl(2). The values of the ν(1)-2ν(2) FR parameters of CS(2) in CH(2)Cl(2) and CHCl(3) at different volume concentrations were calculated according to the FR theory. The magnitude of the FR coupling coefficient W of CS(2) increases upon dilution with CH(2)Cl(2) and CHCl(3), indicating that the vibrational anharmonicity is relatively sensitive to variations in the weak hydrogen bonding. Compared with the changing tendencies of Fermi coupling coefficient W of CS(2) in CH(2)Cl(2) and CHCl(3) at different volume concentrations, we discussed the effect of the weak hydrogen bond formation on the FR and the asymmetric wavenumber shift phenomenon of the Fermi doublet ν(1) and 2ν(2) of CS(2).

The effect of the Fermi resonance on the Raman scattering cross sections of the Fermi doublet ν1 and 2ν2 of liquid carbon disulfide in benzene

The effect of the Fermi resonance (FR) on the Raman scattering cross sections (RSCSs) of the Fermi doublet ν1, 2ν2 of liquid CS2 in C6H6 using the method of changing the volume concentration of the solution is investigated. We have calculated the RSCSs of the Fermi doublet ν1, 2ν2 using Onsager's theory with the 992 cm(-1) Raman line of C6H6 as the internal standard. The result shows that the RSCS of the ν1 line decreases with decreasing the volume concentration of CS2, while that of the 2ν2 line unexpectedly increases. With decreasing the volume concentration of CS2, two main effects of the solvent effect (SE) and the FR in binary solution that can make the ν1, 2ν2 RSCSs change: the SE, as calculated, reduces both the ν1 and 2ν2 RSCSs; the FR plays a significant role in reducing the ν1 RSCS and enhancing the 2ν2 RSCS. In comparison with our previous investigation [J. Raman Spectrosc. 41 (2010) 776-779], it was found that the stronger the FR is, the more the RSCS of the ν1 decreases and the 2ν2 increases. Thus, we proposed that the result can be best explained by taking into account the effect of the FR on the RSCSs of the Fermi doublet. In addition, this paper also gives an explanation to the experimental results deviating from the theoretical results of the scattering coefficients of CS2 in solvent C6H6 as mentioned in Fini's paper.

Semiclassical trace formulas for noninteracting identical particles

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.

Global analysis of periodic orbit bifurcations in coupled Morse oscillator systems: time-reversal symmetry, permutational representations and codimension-2 collisions

In this paper we study periodic orbit bifurcation sequences in a system of two coupled Morse oscillators. Time-reversal symmetry is exploited to determine periodic orbits by iteration of symmetry lines. The permutational representation of Tsuchiya and Jaffe is employed to analyze periodic orbit configurations on the symmetry lines. Local pruning rules are formulated, and a global analysis of possible bifurcation sequences of symmetric periodic orbits is made. Analysis of periodic orbit bifurcations on symmetry lines determines bifurcation sequences, together with periodic orbit periodicities and stabilities. The correlation between certain bifurcations is explained. The passage from an integrable limit to nointegrability is marked by the appearance of tangent bifurcations; our global analysis reveals the origin of these ubiquitous tangencies. For period-1 orbits, tangencies appear by a simple disconnection mechanism. For higher period orbits, a different mechanism involving 2-parameter collisions of bifurcations is found. (c) 1999 American Institute of Physics.

HCP CPH ISOMERIZATION: Caught in the Act

▪ Abstract  In this overview we discuss the vibrational spectrum of phosphaethyne, HCP, in its electronic ground state, as revealed by complementary experimental and theoretical examinations. The main focus is the evolution of specific spectral patterns from the bottom of the potential well up to excitation energies of approximately 25,000 cm−1, where large-amplitude, isomerization-type motion from H–CP to CP–H is prominent. Distinct structural and dynamical changes, caused by an abrupt transformation from essentially HC bonding to mainly PH bonding, set in around 13,000 cm−1. They reflect saddle-node bifurcations in the classical phase space—a phenomenon well known in the nonlinear dynamics literature—and result in characteristic patterns in the spectrum and the quantum-number dependence of the vibrational fine-structure constants. Two polar opposites are employed to elucidate the spectral patterns: the exact solution of the Schrödinger equation, using an accurate potential energy surface and an effective or resonance Hamiltonian (expressed in a harmonic oscillator basis set and block diagonalized into polyads), which is defined by parameters adjusted to fit either the measured or the calculated vibrational energies. The combination of both approaches—together with classical mechanics and semiclassical analyses—provides a detailed spectroscopic picture of the breaking of one bond and the formation of a new one.