Spectroscopy, dynamics, and chaos of the CS2 molecule: Fourier transform and phase‐space analysis

Quantum calculation of highly excited vibrational energy levels of CS2(X) on a new empirical potential energy surface and semiclassical analysis of 1:2 Fermi resonance

We report a refined potential energy function for the ground electronic state of CS2 based on a least-squares fitting to several low-lying experimental vibrational frequencies. Energy levels up to 20,000 cm(-1) have been obtained on this empirical potential using the Lanczos algorithm and potential optimized discrete variable representation. Among them, 329 levels below 10,000 cm(-1) are assigned with approximate normal mode quantum numbers (n1, n(0)2, n3), based on expectation values of one-dimensional (1D) reference Hamiltonians. An effective Hamiltonian is extracted from these assigned levels. The agreement with experimental data, including those of several isotopically substituted species, is excellent. In addition, some Fermi and anharmonic resonances are analyzed. The nearest neighbor level spacing and delta3 distributions indicated that the vibrational spectrum of CS2 is largely regular in the energy range up to 20,000 cm(-1). Semiclassical phase space analysis, including bifurcation analysis of the spectroscopic Hamiltonian, is used to interpret subtle anomalies signaled by expectation values used in normal mode assignments. The meaning of Fermi resonance is clarified by contrasting the semiclassical analysis of CS2 and CO2.

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.