Potential energy surfaces from highly excited spectra using the bootstrap fitting method: Two‐dimensional surfaces for water and ozone

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.

Determination of the Effective Ground State Potential Energy Function of Ozone from High-Resolution Infrared Spectra

The effective ground state potential energy function of the ozone molecule near the C(2v) equilibrium configuration was obtained in a least-squares fit to the largest sample of experimental, high-resolution vibration-rotation data used for this purpose so far. The fitting is based on variational calculations carried out with the extended Morse Oscillator Rigid Bender Internal Dynamics model. The potential function is expanded in Morse-type functions of the stretching variables and in cosine of the bending angle. The present calculation produces results in significantly better agreement with experiment than previous determinations of the potential energy surface, and the energies predicted with the new surface are sufficiently accurate to be useful for the assignment of new high-resolution spectra. The rms (root-mean-square) deviation of the fit of rovibrational data up to J = 5 is 0.02 cm(-1). For the set of all 60 band centers of the (16)O(3) molecule included in the Atlas of Ozone Line Parameters, the rms deviation is 0.025 cm(-1), and for all band centers determined so far from high-resolution spectra, including those recently observed and assigned in Reims corresponding to highly excited stretching and bending vibrations (v(1) + v(2) + v(3) = 6), the rms deviation is 0.1 cm(-1). The "dark states" that produce resonance perturbations in the observed bands are described with experimental accuracy up to the (v(1)v(2)v(3)) = (080) state. Extrapolation tests demonstrate the predictive power of the potential function obtained: rotational extrapolation up to J = 10 for the 11 lowest vibrational states results in an rms deviation of 0.06cm(-1). Also, vibrational energies measured by low-resolution Raman spectroscopy (which were not included in the input data for the fit) are calculated within the experimental accuracy (rms = 1.6 cm(-1)) of the experimental values up to the dissociation limit. The statistical analysis suggests that the accuracy of the equilibrium geometry and force constants of the molecule is considerably improved relative to previous determinations. The long-range behavior of the fitted potential at the dissociation limit O(3) --> O(2) + O shows very good agreement with experimental data. The new potential energy surface was used to predict the band centers of the isotopomers (17)O(3) and (18)O(3). Copyright 1999 Academic Press.