Theoretical Spectroscopic Characterization at Low Temperatures of Dimethyl Sulfoxide: The Role of Anharmonicity.

The structural and spectroscopic parameters of dimethyl sulfoxide (DMSO) are predicted from CCSD(T)-F12 calculations that can help to resolve the outstanding problem of the rovibrational spectroscopy. DMSO is a near oblate top that presents a trigonal pyramidal geometry. Rotational parameters are determined at the equilibrium and in selected vibrational states. For the ground state, the rotational constants were calculated to be A0 = 7031.7237 MHz, B0 = 6920.1221 MHz, and C0 = 4223.3389 MHz, at few megahertz from the previous experimental measurements. Ab initio calculations allow us to assert that DMSO rotational constants are strongly dependent on anharmonic effects. Asymmetry increases with the vibrational energy. Harmonic frequencies, torsional parameters, and a two-dimensional potential energy surface (2D-PES) focused to describe the internal rotation of the two methyl groups are determined at the CCSD(T)-F12 level of theory. For the medium and small amplitude motions, anharmonic effects are estimated with MP2 theory getting an excellent agreement with experimental data for the ν11 and ν23 fundamentals. Torsional energies and transitions are computed variationally form the 2D-PES that denotes strong interactions between both internal tops. The vibrationally corrected V3 torsional barrier is evaluated to be 965.32 cm(-1). The torsional splitting of the ground vibrational state has been estimated to be lower than 0.01 cm(-1). Although the ν13 torsional fundamental is found at 229.837 cm(-1) in good agreement with previous assessment, there is not accord for the low intense transition ν24. A new assignment predicting ν24 to lie between 190 and 195 cm(-1) is proposed.

Most typical 1 ratio 2 resonant perturbation of the hydrogen atom by weak electric and magnetic fields.

We study a perturbation of the hydrogen atom by small homogeneous static electric and magnetic fields in a specific mutual alignment with angle approximately pi/3 which results in the 1 ratio 2 resonance of the linearized Keplerian n-shell approximation. The bifurcation diagram of the classical integrable approximation has for most such field configurations the same typical structure that we describe. The structure of the corresponding quantum energy spectrum, which we describe in detail, is in certain ways an analogue of the well-known degeneracy found by Herrick [Phys. Rev. A 26, 323 (1982)] for the quadratic Zeeman effect.

Assigning vibrational polyads using relative equilibria: application to ozone.

We demonstrate how relative equilibria of a vibrating molecule, which are families of principal periodic orbits otherwise known as nonlinear normal modes, can be used to describe the global polyad structure of vibrational energy levels. The classical action integral n(E) computed along these orbits at different energies E corresponds to the polyad quantum number n so that the energy En of different relative equilibria describes the splitting of n-polyads. Further information on the internal polyad structure can be driven from the stability analysis of relative equilibria. We use the ozone molecule as a concrete example where n-polyads or "hyperpolyads" should be distinguished from the well-known polyads of the 1:1 stretching mode resonance; the stretching polyads are structural elements of hyperpolyads. We give dynamical interpretation of the relation between relative equilibria and n-polyads based on the normal form reduction in the limit of small vibrations near the equilibrium.

CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy.

We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO2 molecule. We uncover quantum monodromy of CO2 as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.

Analysis of the "Unusual" Vibrational Components of Triply Degenerate Vibrational Mode nu(6) of Mo(CO)(6) Based on the Classical Interpretation of the Effective Rotation-Vibration Hamiltonian.

Rotational structure of the triply degenerate vibrational state nu(6)(F(1u)) of the octahedral molecule Mo(CO)(6) is analyzed qualitatively on the basis of classical mechanics. We show that the energy level redistribution between the vibrational components of nu(6)(F(1u)) occurs due to rotational excitation and is related to the formation of singular points of classical rotational energy surfaces. The singularity is stable under small variations of parameters of the effective rovibrational Hamiltonian. Parameters responsible for the persistence of this phenomenon are specified. Comparison with quantum calculations demonstrates the high qualitative and quantitative accuracy of our classical analysis. Copyright 2000 Academic Press.