Vibrational symmetry breaking of NO₃^- in aqueous solution: NO asymmetric stretch frequency distribution and mean splitting

We apply a solute-solvent approach to a theoretical study of vibrational symmetry breaking in aqueous NO^-₃ solution. Experimental infrared and Raman spectra have shown that the NO asymmetric stretches, which are degenerate for the isolated anion, are split by 35-60 cm^-1 in dilute solution. As an initial step to calculating the spectra, we have computed the distribution of energies, or the "static spectrum"", and the resulting mean splitting of the two NO asymmetric stretch eigenstates in an aqueous milieu. These have been obtained in a two-mode treatment that considers only the NO asymmetric stretch mode pair as well as a full six-mode treatment. In both sets of calculations, six eigenstates, namely, the ground state, the two NO asymmetric stretch fundamentals, and its three overtones, were determined to suffice for converged energy distributions and mean splittings. The couplings between these six states are driven by the solvent forces on the anion's modes, which were extracted from molecular dynamics simulations. The solvent forces on the two central modes were found to give rise to a majority of the computed mean splitting of 21.7 cm^-1. The distribution of NO asymmmetric stretch excitation energies with these two modes alone was found to have a Maxwell-Boltzmann shape. The solvent forces on the in-plane bends were found to modestly reduce the splitting size and slightly alter the width of the parent distribution. The symmetric stretch force was found to have no effect on the splitting but instead resulted in a widening on the distribution shape. The force gradients were found to have a weak effect on both the eigenvalue distribution and the mean splitting.