Determination of highly excited rovibrational states for N2O using generalized internal coordinates

Quantum Dynamics of Oblique Vibrational States in the Hénon-Heiles System

In this paper, we study the quantum time evolution of oblique nonstationary vibrational states in a Hénon-Heiles oscillator system with two dissociation channels, which models the stretching vibrational motions of triatomic molecules. The oblique nonstationary states we are interested in are the eigenfunctions of the anharmonic zero-order Hamiltonian operator resulting from the transformation to oblique coordinates, which are defined as those coming from nonorthogonal coordinate rotations that express the matrix representation of the second-order Hamiltonian in a block diagonal form characterized by the polyadic quantum number n = n1 + n2. The survival probabilities calculated show that the oblique nonstationary states evolve within their polyadic group with a high degree of coherence up to the dissociation limits on the short time scale. The degree of coherence is certainly much higher than that exhibited by the local nonstationary states extracted from the conventional orthogonal rotation of the original normal coordinates. We also show that energy exchange between the oblique vibrational modes occurs in a much more regular way than the exchange between the local modes.

Optimal internal coordinates, vibrational spectrum, and effective Hamiltonian for ozone

In this paper the authors use the optimal internal vibrational coordinates previously determined for the electronic ground state of the ozone molecule to study the vibrational spectrum of the molecule employing the second empirical potential energy surface calculated by Tyuterev et al. [Chem. Phys. Lett. 316, 271 (2000)]. First, the authors compute variationally all the bound vibrational energy levels of the molecule up to the dissociation limit and state the usefulness of the optimal coordinates in this respect, which allows us to converge all the bound levels using relatively small anharmonic basis sets. By analyzing the expansion coefficients of the wave functions, they show then that a large portion of the vibrational spectrum of O3 can be structured in nearly separable polyadic groups characterized by the polyad quantum number N=n1+n2+n(theta) corresponding to the optimal internal coordinates. Accordingly, they determine an internal effective vibrational Hamiltonian for O3 by fitting the effective Hamiltonian parameters to the experimental vibrational frequencies, using as input parameters in the fit those extracted from an analytical second-order Van Vleck perturbation theory calculation. It is finally shown that the internal effective Hamiltonian thus obtained accurately describes the vibrational spectrum of ozone in the low and medium energy regimes.

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.

Variational Calculations of Rovibrational Energies for CO(2)

Vibrational-rotational energy levels for the CO(2) molecule are computed variationally using an empirical potential energy surface previously determined. The calculations are carried out using a set of generalized internal coordinates properly optimized to describe the internuclear motions of the molecule. The rovibrational energies are used to determine the vibrational terms G(v) and the inertia constants B(v) for states with l = 0 to l = 6, and the values of these molecular constants are compared to those derived from the observed spectra. There exists excellent agreement between the calculated and the observed constants, which confirms the good quality of the potential energy surface used. Copyright 2001 Academic Press.