A p r i o r i rates of phonon-assisted v–v transfers among CO and N2 molecules in N2 matrices

Abstract

The method of computing matrix shifts, splittings, and sideband intensities of the vibrational fundamental bands in solid N2 and CO has been extended to the calculation of resonant and off-resonant v–v transfer rates. The contribution of mechanical anharmonicity, i.e., vibron–phonon coupling through third- and higher-order terms in the potential, is found to be negligible for phonon-assisted transfer rates, similar to the situation in ir and Raman sideband intensities. Electrical anharmonicity, i.e., the modulation of vibron resonance energies by phonon-type motions, produces off-resonant v–v rates which are larger than those due to mechanical anharmonicity by two orders of magnitude. Analytical expressions have been derived for the quantitative determination of rates based on static multipole–multipole interactions, and contributions by repulsive exchange forces have been calculated numerically. The calculated rates are consistent with observations in a system of CO diluted in N2 and they explain the observed temperature behavior of endothermic v–v processes in pure solid N2 where two and more phonons are involved. It is found that molecular librations dominate over translational motions in all of these phonon-assisted rates, even in the repulsive contributions.