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 $v \leq 5$, for the molecules $CH_{4}$, $SiH_{4}$, $GeH_{4}$ and their deuterium and $^{13}C$ isotopic substituents. Close local mode degeneracica, with splittings of $3 cm^{-1}$ or less, are predicted at the highest energies for all molecules, except $CD_{4}$. Such degeneracies prevail at all excitation levels for $SiH_{4}$ and $GeH_{4}$, but those for $v \leq 3$ are removed by deuterium substitution. The overtone splitting patterns of different molecules and the effects of isotopic substitution are rationalised 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 $GeH_{4} > SiH_{4} > CeD_{4} > CH_{4} > SiD_{4} > CD_{4}$. A model intensity calculation for $CH_{4}$ confirms the local made picture with predominant intensity in the lowest frequency infrared bands for each overtone manifold except $v = 3$ where the situation is complicated by intensity borrowing from the fundamental