Infrared Spectra of Protonated Water Clusters, H+(H2O)4, in Eigen and Zundel Forms Studied by Vibrational Quasi-Degenerate Perturbation Theory

The infrared spectrum of H+(H2O)(4) recently observed in a wide spectral range has shown a series of bands in a range of 1700-2500 cm(-1), which can not be understood by the standard harmonic normal mode analysis. Here, we theoretically investigate the origin of these bands with a focus on (1) the possibility of coexistence of multiple isomers in the Eigen [H3O+(H2O)(3)] and Zundel [H5O2+(H2O)(2)] forms and (2) the effect of anharmonic coupling that gives rise to nonzero intensities for overtones and combination bands. Anharmonic vibrational calculations are carried out for the Eigen and Zundel clusters by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) based on optimized coordinates. The anharmonic potential energy surface and the dipole moment surfaces are generated by a multiresolution approach combining one-dimensional (1D) grid potential functions derived from CCSD(T)-F12, 2D and 3D grid potential functions derived from B3LYP for important coupling terms, and a quartic force field derived from B3LYP for less important terms. The spectrum calculated for the Eigen duster is in excellent agreement with the experiment, assigning the bands in the range of 1700-2500 cm(-1) to overtones and combination bands of a H3O+ moiety in line with recent reports [J. Phys. Chem. A 2015, 119, 9425; Science 2016, 354, 1131]. On the other hand, characteristic OH stretching bands of the Zundel cluster is found to be absent in the experimental spectrum. We therefore conclude that the experimental spectrum originates solely from the Eigen cluster. Nonetheless, the present calculation for the Eigen cluster poorly reproduces a band observed at 1765 cm(-1). A possible nature of this band is discussed.