Knowledge Bank

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 $v\le 5$, for the molecules $CH4$, $SiH4$, $GeH4$ and their deuterium and $\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}C$ isotopic substituents. Close local mode degeneracica, with splittings of $3cm-1$ 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 $v\le 3$ 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 $GeH4>SiH4>CeD4>CH4>SiD4>CD4$. A model intensity calculation for $CH4$ 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.