Vibrational analysis of HOCl up to 98% of the dissociation energy with a Fermi resonance Hamiltonian

Abstract

We have analyzed the vibrational energies and wave functions of HOCl obtained from previous ab initio calculations [J. Chem. Phys. 109, 2662 (1998); 109, 10273 (1998)]. Up to approximately 13 000 cm−1, the normal modes are nearly decoupled, so that the analysis is straightforward with a Dunham model. In contrast, above 13 000 cm−1 the Dunham model is no longer valid for the levels with no quanta in the OH stretch (v1=0). In addition to v1, these levels can only be assigned a so-called polyad quantum number P=2v2+v3, where 2 and 3 denote, respectively, the bending and OCl stretching normal modes. In contrast, the levels with v1⩾2 remain assignable with three vi quantum numbers up to the dissociation (D0=19 290 cm−1). The interaction between the bending and the OCl stretch (ω2≅2ω3) is well described with a simple, fitted Fermi resonance Hamiltonian. The energies and wave functions of this model Hamiltonian are compared with those obtained from ab initio calculations, which in turn enables the assignment of many additional ab initio vibrational levels. Globally, among the 809 bound levels calculated below dissociation, 790 have been assigned, the lowest unassigned level, No. 736, being located at 18 885 cm−1 above the (0,0,0) ground level, that is, at about 98% of D0. In addition, 84 “resonances” located above D0 have also been assigned. Our best Fermi resonance Hamiltonian has 29 parameters fitted with 725 ab initio levels, the rms deviation being of 5.3 cm−1. This set of 725 fitted levels includes the full set of levels up to No. 702 at 18 650 cm−1. The ab initio levels, which are assigned but not included in the fit, are reasonably predicted by the model Hamiltonian, but with a typical error of the order of 20 cm−1. The classical analysis of the periodic orbits of this Hamiltonian shows that two bifurcations occur at 13 135 and 14 059 cm−1 for levels with v1=0. Above each of these bifurcations two new families of periodic orbits are created. The quantum counterpart of periodic orbits are wave functions with “pearls” aligned along the classical periodic orbits. The complicated sequence of ab initio wave functions observed within each polyad is nicely reproduced by the wave functions of the Fermi resonance Hamiltonian and by the corresponding shapes of periodic orbits. We also present a comparison between calculated and measured energies and rotational constants for 25 levels, leading to a secure vibrational assignment for these levels. The largest difference between experimental and calculated energies reaches 22 cm−1 close to D0.