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 Dv = 4. Three transformations are necessary to obtain fourthorder
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.