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We investigate the vibrational shift of beryllium oxide (BeO) in Xe matrix as well as in Ar matrix environments by mixed quantum-classical simulation and examine the origin of spectral shift in details. BeO is known to form strong chemical complex with single rare gas atom, and it is predicted from the gas phase calculations that vibrational frequencies are blueshifted by 78 cm^[-1] and 80 cm^[-1] upon formation of XeBeO and ArBeO, respectively. When the effects of other surrounding rare gas atoms are included by Monte Carlo simulations, it is found that the vibrational frequencies are redshifted by 21 cm^[-1] and 8 cm^[-1] from the isolated XeBeO and ArBeO complexes, respectively. The vibrational shift of XeBeO in Ar matrix is also calculated and compared with experimental data. In all simulations examined in this paper, the calculated vibrational frequency shifts from the isolated BeO molecule are in reasonable agreement with experimental values. The spectral shift due to the rare-gas-complex formation of RgBeO (Rg = Xe or Ar) is not negligible as seen in the previous studies, but it is shown in this paper that the effects of other surrounding rare gas atoms should be carefully taken into account for quantitative description of the spectral shifts and that these two effects are competing in vibrational spectroscopy of BeO in matrix environments.

In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schrodinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schrodinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes in this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.