Mean and Equilibrium Molecular Structures of Methane and Deuteromethane as Determined by Electron Diffraction

Abstract

The structural parameters of methane and methane-d4 were determined with the new rotating-sector electron diffraction apparatus of Iowa State University. The results demonstrated, for the first time by electron diffraction, the existence of isotope effects on structure. Mean internuclear distances were C–H=1.1068±0.001 A, C—D=1.1027±0.001 A, H···H=1.811±0.007 A and D···D=1.805±0.008 A. Mean amplitudes, reckoned from mean positions, were C–H=0.0751±0.002 A, C—D=0.0663±0.002 A, H···H=0.120±0.006 A, and D···D=0.105±0.006 A. The isotope effects were just those expected for atoms of different mass vibrating in identical anharmonic force fields. Vibrational anharmonicity led to measurable phase shifts in the molecular diffraction patterns from which the asymmetry of the internuclear distribution functions could be determined. This allowed a direct experimental determination of the approximate equilibrium C–H and C—D bond lengths, giving 1.082 A. Somewhat more rigorous calculations of the correction from mean to equilibrium distances based on an anharmonic Urey-Bradley field led to equilibrium C–H and C—D bond lengths of 1.0847 A and 1.0863 A, respectively. Corresponding equilibrium bond lengths computed from the spectroscopic r0 values of 1.0940 A and 1.0923 A, respectively, were 1.0850 A and 1.0856 A. The comparison clearly illustrates the appreciable difference between electron diffraction and spectroscopic methods in the manner of averaging over molecular motions, but also confirms the essential equivalence of molecular information derived, if suitable corrections are applied to each.