<title>New modeling of line positions and intensities for C<formula><inf><roman>s</roman></inf></formula>-type molecules: HDCO and HNO<formula><inf><roman>3</roman></inf></formula></title>

Abstract

The quality of the models used for the calculation of energy levels and line intensities is discussed for planar C_s type molecules in the case of strong resonances affecting the energy levels of at least two resonating states. The Hamiltonian model which is used classically to reproduce the energy levels involves for the v-diagonal blocks, rotational operators written in an orthorhombic reduced form as proposed by Watson [“Aspects of quartic and sextic centrifugal effects on rotational energy levels” J.K.G.Watson, Chap. 1, in “Vibrational spectra and structure”, J.Durig editor, Elsevier, (1977)]. This means that the non-orthorhombic character of the molecule is only accounted for through the operators off-diagonal in v. For example, for planar C_s type molecules the resonances which perturb the resonating levels are taken into account in these off-diagonal blocks either by both anharmonic and C-type Coriolis operators for vibrational states of the same symmetry species in C_s (A’ ↔ A’ or A” ↔ A>>) or by both A- and B-type Coriolis operators for resonating states with differing symmetries (A’ ↔ A”). For a well-identified scheme of resonances this “classical” model gives excellent results when the perturbations involving the perturbed energy levels are rather localized. On the other hand in case of overall strong resonances this “classical” model may fail and it is necessary to use a Hamiltonian which possesses also non-orthorhombic terms in the v-diagonal part of the Hamiltonian. This is because a common system of inertial axes cannot be used for the strongly resonating vibrational states. This effect has also to be accounted for during the calculation of line intensities.