Coupling Across Bonds: Ab Initio Calculations for the Anharmonic Vibrational Resonance Dynamics of the Coupled OH and CH Chromophores in Trans Formic Acid HCOOH

We report high level ab initio calculations (treating correlation by second order Møller-Plesset perturbation theory, MP2) of various two-dimensional (2D), three-dimensional (3D) and four-dimensional (4D) normal coordinate subspaces of the full 12D coordinate space of trans formic acid, HCOOH. With the resulting potential and electric dipole hyper-surfaces accurate vibrational variational calculations are carried out using a discrete variable representation (DVR) for the anharmonically coupled modes. The full absorption spectra are calculated and the overtone spectra of the OH chromophore, which clearly dominates the entire absorption spectrum, are analyzed in detail with respect to their anharmonic resonance dynamics. We have investigated the OH/CH stretching coupling, which is an example for a coupling across bonds, in terms of direct and indirect coupling terms. A close resonance coupling of 5 ν_OH (5 ν₁) with 4 ν_OH + ν_CH (4 ν₁ + ν₂) leads to short time (250 fs) intramolecular vibrational redistribution (IVR). Using the various multidimensional normal coordinate calculations we have investigated in detail the role of the "skeletal" modes. A sequence of calculations including various subspaces (two-dimensional up to four-dimensional) leads to the conclusion that the resonance includes important contributions from coupling to the CH and OH bending modes and C-O stretching mode in addition to the direct coupling of the CH- and OH stretching modes. The time dependent population dynamics further demonstrate that the IVR cannot be explained by a simple direct high order potential coupling. Important resonances are predicted between OH stretching and CH bending, OH bending, and C-O stretching modes. These resonances significantly contribute to IVR at higher levels of OH stretching excitation. The results provide an example for a more general "through-bond" coupling mechanism with wider implications for the understanding of IVR in multiple chromophore systems.