Calculated absorption and vibrational circular dichroism spectra of fundamental and overtone transitions for a chiral HCCH molecular fragment in the hypothesis of coupled dipoles

We establish the general behavior of absorption and vibrational circular dichroism spectra (VCD) of a chiral HCCH fragment lacking all symmetry elements; the study is limited to CH-stretching modes, and the Hamiltonian employed is written in terms of normal-mode coordinates and momenta and approximates two different Morse oscillators interacting through a harmonic coupling term; rotational strengths are evaluated within a hypothesis of coupled electric dipoles. Van Vleck contact transformations written in terms of raising and lowering operators are used to calculate spectra up to the manifold Delta upsilon = 4. Three transformations are necessary to obtain fourth-order terms in the relevant operators, namely, the electric and magnetic dipole moments. The dynamics of the system exhibits 1:1 resonance terms in addition to the Darling-Dennison coupling term. We discuss the importance of coupling between CH stretches with respect to differences in their local mechanical characteristics in determining the aspect of the absorption and VCD fundamental and overtone spectra of increasing quantum number.