Equilibrium structures from gas-phase electron-diffraction data

Abstract

For the past 75 years gas-phase electron diffraction (GED) has remained the most valuable technique for determining structures of small molecules, free from intermolecular interactions. Throughout this period many improvements have been made to both the experimental and theoretical aspects of this technique, leading to the determination of more accurate structures. As the uncertainties associated with many stages of the process have been greatly reduced, errors introduced by assumptions, which were previously neglected, now play an important role in the overall accuracy of the determined structure. This work is focused on two such areas, namely the treatment of vibrational corrections and the vibrational effects on the scattering of individual electrons by multiple atoms. A novel method has been developed which allows the extraction of equilibrium structures (re) from distances obtained directly from GED experiments (ra). In unfavourable cases (such as small molecules with large-amplitude and / or highly anharmonic modes of vibration) traditional methods can introduce errors of comparable size to those obtained from the experiment. The newly developed method, EXPRESS (EXPeriments Resulting in Equilibrium StructureS), overcomes the problems which have plagued previous attempts through exploring a more extensive region of the potential-energy surface (PES), specifically regions relating to the normal modes of vibration. The method has been applied, initially, to sodium chloride in the gas phase as this contains dimer molecules with very low-frequency large-amplitude modes of vibration. The experimentally determined re structure gives good agreement with high-level ab initio calculations. Following this success, the EXPRESS method was then applied to sodium fluoride, sodium bromide and sodium iodide, giving similarly good agreement with theoretical calculations. The regular mixed alkali halide dimers (D2h symmetry) cannot be studied by microwave spectroscopy as they do not have a permanent dipole moment. However, vi mixed dimers (C2v) and asymmetric dimers (Cs) do not suffer from this constraint. Using insights learned from the ab initio studies of the sodium halides, geometries and dipole moments have been calculated for a range of mixed and asymmetric alkali halide dimers to enable their study by microwave spectroscopy. A multi-dimensional version of the EXPRESS method has been applied to the lowfrequency modes of chlorofluoroacetylene and chlorodifluoronitrosomethane to assess the effects of coupling between these modes of vibration in these structurally challenging systems. To obtain re structures of larger molecules a second method, using molecular dynamics (MD), has been developed and has been implemented on two test cases: the sodium chloride dimer and octasilsesquioxane. Traditional scattering theory used in GED employs the first-order Born approximation (FBO). However, this ignores any multiple scattering events, which are important for heavier atoms. Using a method similar in nature to EXPRESS a full vibrational analysis of three-atom scattering has been conducted on tellurium dibromide and tellurium tetrabromide.