Dynamics of Protonated Oxalate from Machine-Learned Simulations and Experiment: Infrared Signatures, Proton Transfer Dynamics and Tunneling Splittings

Abstract: The infrared spectroscopy and proton transfer dynamics together with the associated tunneling splittings for H/D-transfer in oxalate are investigated using a machine learning-based potential energy surface (PES) of CCSD(T) quality, calibrated against the results of new spectroscopic measurements. Second order vibrational perturbation calculations (VPT2) very successfully describe both the framework and H-transfer modes compared with the experiments. In particular, a new low-intensity signature at 1666 cm$^{-1}$ was correctly predicted from the VPT2 calculations. An unstructured band centered at 2940 cm$^{-1}$ superimposed on a broad background extending from 2600 to 3200 cm$^{-1}$ is assigned to the H-transfer motion. The broad background involves a multitude of combination bands but a major role is played by the COH-bend. For the deuterated species, VPT2 and molecular dynamics simulations provide equally convincing assignments, in particular for the framework modes. Finally, based on the new PES the tunneling splitting for H-transfer is predicted as $\Delta_{\rm H} = 35.0$ cm$^{-1}$ from ring polymer instanton calculations using higher-order corrections. This provides an experimentally accessible benchmark to validate the computations, in particular the quality of the machine-learned PES.