A local mode model for tetrahedral molecules

A three parameter coupled Morse oscillator model fitted to the known stretching vibrational energy levels is used to predict the energies of all stretching overtone bands with total quantum number ν ⩽ 5> for the molecules CH4, SiH4, GeH4 and their deuterium and 13C isotopic substituents. Close local mode degeneracies, with splittings of 3 cm-1 or less, are predicted at the highest energies for all molecules except CD4. Such degeneracies prevail at all excitation levels for SiH4 and GeH4, but those for ν ⩽ 3> are removed by deuterium substitution. The overtone splitting patterns of different molecules and the effects of isotopic substitution are rationalized by means of a correlation diagram, in which the ratio of bond anharmonicity to interbond coupling strength is used to rank the molecules on a scale running from local mode to harmonic normal mode limits. The ranking by local mode character is GeH4 > SiH4 > GeD4 > CH4 > SiD4 > CD4. A model intensity calculation for CH4 confirms the local mode picture with predominant intensity in the lowest frequency infrared bands for each overtone manifold except ν = 3 where the situation is complicated by intensity borrowing from the fundamental.