The effects of rotation and vibration on the carbon-13 shielding, magnetizabilities and geometrical parameters of some methane isotopomers

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Abstract
An ab initio carbon-13 shielding surface to quadratic terms in displacement coordinates has been used to calculate the effects of temperature on the shielding in 13CH4 and its four deuterated isotopomers. Some of the second order terms are significant. For 3CH4 the total nuclear motion correction at 300 K is −3·695 ppm (−2%). The isotope effects observed by Alei and Wageman along the series 13CHnD4-n, are explained quantitatively to a high degree and the predictions of the temperature dependence of the shielding are in agreement with the meagre experimental data available. A similar calculation is reported for the temperature dependence of the molar magnetizabilities of 12CH4 and 12CD4 using an ab initio magnetizability surface to second order. Again some quadratic terms are important and the nuclear motion correction at 300 K is this time +2%. Modern SQUID magnetometers should be able to measure the variations predicted. Results are also given for the effects of vibration and rotation on the bond lengths and interbond angles of several methane isotopomers including some which contain tritium and muonium.