The vibrational eigenenergies of the deuterated forms of formic acid (DCOOD, HCOOD, and DCOOH) have been computed using the block-improved relaxation method as implemented in the Heidelberg multi-configuration time-dependent Hartree package on a previously published potential energy surface [J. Chem. Phys. 148, 064303 (2018)] generated at the CCSD(T)-F12a/aug-cc-pVTZ-F12 level of theory. Fundamental, combination band, and overtone transition frequencies of the trans isomer were computed up to ∼ 3000 cm-1 with respect to the zero point energy and assignments were determined by visualisation of the reduced densities. Root mean square deviation of computed fundamental transition frequencies with experimentally available gas-phase measurements are 8, 7, and 3 cm-1 for trans-DCOOD, HCOOD, and DCOOH, respectively. The fundamental transition frequencies are provided for the cis isomer of all deuterated forms; experimental measurements of these frequencies for the deuterated cis isotopologues are not yet available and the present work may guide their identification.

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

The intramolecular vibrational relaxation dynamics of formic acid and its deuterated isotopologues is simulated on the full-dimensional potential energy surface of Richter and Carbonnière [F. Richter and P. Carbonnière, J. Chem. Phys. 148, 064303 (2018)] using the Heidelberg MCTDH package. We focus on couplings with the torsion vibrational modes close to the trans- cis isomerisation coordinate from the dynamics of artificially excited vibrational mode overtones. The C-O stretch bright vibrational mode is coupled to the out-of-the plane torsion mode in HCOOH, where this coupling could be exploited for laser-induced trans-to- cis isomerisation. Strong isotopic effects are observed: deuteration of the hydroxyl group, i.e., in HCOOD and DCOOD, destroys the C-O stretch to torsion mode coupling whereas in DCOOH, little to no effect is observed.