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We examine the properties of oblique coordinates. The coordinates, introduced by Zúñiga et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 055101, (2019)], reduce vibrational mode-mixing and enhance the quality of vibrational assignments in quantum mechanical investigations of two-dimensional model Hamiltonians. Oblique coordinates are obtained by making non-orthogonal rotations of the original coordinates that convert the matrix representation of the quadratic Hamiltonian operator into a block-diagonal matrix where the blocks are distinguished by the total quanta of vibrational excitation. Using techniques for the polar decomposition of matrices, we present a scheme for finding these coordinates for systems of arbitrary dimensions. Several molecular examples are presented that highlight the advantages of these coordinates. 

Vibrational fingerprints and combination bands are a direct measure of couplings that control molecular properties. However, most combination bands possess small transition dipoles. Here we use multiple, ultrafast coherent infrared pulses to resolve vibrational coupling between CH3CN fingerprint modes at 918 and 1039 cm(-1) and combination bands in the 2750-6100 cm(-1 )region via doubly vibrationally enhanced (DOVE) coherent multidimensional spectroscopy (CMDS). This approach provides a direct probe of vibrational coupling between fingerprint modes and near-infrared combination bands of large and small transition dipoles in a molecular system over a large frequency range. 

An approach for identifying resonances in vibrational perturbation theory calculations is introduced. This approach makes use of the corrections to the wave functions that are obtained from non-degenerate perturbation theory calculations to identify spaces of states that must be treated with degenerate perturbation theory. Pairs of states are considered to be in resonance if the magnitude of expansion coefficients in the corrections to the wave functions in the non-degenerate perturbation theory calculation is greater than a specified threshold, χ max . This approach is applied to calculations of the vibrational spectra of CH 4 , H 2 CO, HNO 3 , and cc-HOONO. The question of how the identified resonances depend on the value of χ max and how the choice of the resonance spaces affects the calculated vibrational spectrum is further explored for H 2 CO. The approach is also compared to the Martin test [J. M. L. Martin et al., J. Chem. Phys. 103, 2589–2602 (1995)] for calculations of the vibrational spectra of H 2 CO and cc-HOONO. 

We report vibrational spectra of the H 2 -tagged, cryogenically cooled X −  · HOCl (X = Cl, Br, and I) ion–molecule complexes and analyze the resulting band patterns with electronic structure calculations and an anharmonic theoretical treatment of nuclear motions on extended potential energy surfaces. The complexes are formed by “ligand exchange” reactions of X −  · (H 2 O) n clusters with HOCl molecules at low pressure (∼10 −2  mbar) in a radio frequency ion guide. The spectra generally feature many bands in addition to the fundamentals expected at the double harmonic level. These “extra bands” appear in patterns that are similar to those displayed by the X −  · HOD analogs, where they are assigned to excitations of nominally IR forbidden overtones and combination bands. The interactions driving these features include mechanical and electronic anharmonicities. Particularly intense bands are observed for the v = 0 → 2 transitions of the out-of-plane bending soft modes of the HOCl molecule relative to the ions. These involve displacements that act to break the strong H-bond to the ion, which give rise to large quadratic dependences of the electric dipoles (electronic anharmonicities) that drive the transition moments for the overtone bands. On the other hand, overtone bands arising from the intramolecular OH bending modes of HOCl are traced to mechanical anharmonic coupling with the v = 1 level of the OH stretch (Fermi resonances). These interactions are similar in strength to those reported earlier for the X −  · HOD complexes.