Dipole and rotational strengths for overtone transitions of a C2-symmetry HCCH molecular fragment using Van Vleck perturbation theory

Contact transformation theory up to second order is employed to treat CH-stretching overtone
transitions and to calculate dipole and rotational strengths. A general Hamiltonian describing two
interacting CH-stretching oscillators is considered, and the Darling–Dennison resonance is
appropriately taken into account. The two CH bonds are supposed to be dissymmetrically disposed,
so as to represent a chiral HCCH fragment, endowed with C2 symmetry. Analytical expressions of
transition moments and dipole and rotational strengths are given in the hypothesis of general electric
and magnetic dipole moments with quadratic dependence on coordinates and momenta. Dipole and
rotational strengths are then calculated together with frequencies for the fundamental and first three
overtone regions in the simplifying hypothesis of the valence optical approach on the
coupled-oscillator framework. Simplified analytical expressions thereof in the relevant parameters
are presented.