The accurate structures of silsesquioxanes Si8O12H8 and Si8O12Me8 have been determined by gas-phase electron diffraction methods in order to obtain experimental data on single molecules unconstrained by a crystal lattice for comparison with data obtained by theoretical methods. For Si8O12H8 the experimentally determined structure shows ideal O h symmetry with Si−O distances and Si−O−Si angles of 161.41(3) pm and 147.9(2)° [r e, uncertainties (σ) in parentheses] compared with 162.9 pm and 147.8° for theoretical results from MP2/6-311++G(3df,3pd) calculations. In Si8O12Me8 a similar O h symmetry model gave experimental values of 161.74(5) pm and 148.9(2)° for the Si−O distances and Si−O−Si angles compared with calculated values of 163.2 pm and 148.6°, respectively.

A novel method has been developed to allow the accurate determination of equilibrium gas-phase structures from experimental data, thus allowing direct comparison with theory. This new method is illustrated through the example of sodium chloride vapor at 943 K. Using this approach the equilibrium structures of the monomer (NaCl) and the dimer (Na(2)Cl(2)), together with the fraction of vapor existing as dimer, have been determined by gas-phase electron diffraction supplemented with data from microwave spectroscopy and ab initio calculations. Root-mean-square amplitudes of vibration (u) and distance corrections (r(a) - r(e)) have been calculated explicitly from the ab initio potential-energy surfaces corresponding to the vibrational modes of the monomer and dimer. These u and (r(a) - r(e)) values essentially include all of the effects associated with large-amplitude modes of vibration and anharmonicity; using them we have been able to relate the ra distances from a gas-phase electron diffraction experiment directly to the re distances from ab initio calculations. Vibrational amplitudes and distance corrections are compared with those obtained by previous methods using both purely harmonic force fields and those including cubic anharmonic contributions, and the differences are discussed. The gas-phase equilibrium structural parameters are r(e)(Na-Cl)(monomer) = 236.0794(4) pm; r(e)(Na-Cl)(dimer) = 253.4(9) pm; and <(e)ClNaCl = 102.7(11) degrees. These results are found to be in good agreement with high-level ab initio calculations and are substantially more precise than those obtained in previous structural studies.

A general method is described that allows experimental equilibrium structures to be determined from gas electron diffraction (GED) data. Distance corrections, starting values for amplitudes of vibration and anharmonic "Morse" constants (all required for a GED refinement) have been extracted from molecular dynamics (MD) simulations. For this purpose MD methods have significant advantages over traditional force-field methods, as they can more easily be performed for large molecules, and, as they do not rely on extrapolation from equilibrium geometries, they are highly suitable for molecules with large-amplitude and anharmonic modes of vibration. For the test case Si(8)O(12)Me(8), where the methyl groups rotate and large deformations of the Si(8)O(12) cage are observed, the MD simulations produced results markedly superior to those obtained using force-field methods. The experimental equilibrium structure of Si(8)O(12)H(8) has also been determined, demonstrating the use of empirical potentials rather than DFT methods when such potentials exist. We highlight the one major deficiency associated with classical MD--the absence of quantum effects--which causes some light-atom bonded-pair amplitudes of vibration to be significantly underestimated. However, using C(3)N(3)Cl(3) and C(3)N(3)H(3) as examples, we show that path-integral MD simulations can overcome these problems. The distance corrections and amplitudes of vibration obtained for C(3)N(3)Cl(3) are almost identical to those obtained from force-field methods, as we would expect for such a rigid molecule. In the case of C(3)N(3)H(3), for which an accurate experimental structure exists, the use of path-integral methods more than doubles the C-H amplitude of vibration.

Gas-phase electron-diffraction scattering data and dipolar couplings from NMR experiments in four different liquid crystal solvents have been combined to give a high-accuracy molecular structure of 1,4-difluorobenzene. The anisotropic components of the CF and FF indirect couplings have been deduced directly from the experimental data. The resultant structure has standard deviations of around 0.2 pm for interatomic distances and less than 0.20 for inter-bond angles.

Within the independent atom scattering model, we derive an approximate formula for the rotationally and vibrationally averaged three-atom terms in the series expansion of the electron scattering cross section. This formula uses the atomic scattering factors as well as the atomic scattered wavefunctions as input, and rotational averaging is performed numerically. We compare our results to previous theoretical multiple scattering approaches for the molecules F(3), F(4), and SF(6) and to experimental data for TeF(6). Our results are consistent with those of previous calculations and inclusion of the three-atom term produces a dramatically better least squares fit of the TeF(6) data. The algorithm presented here is sufficiently fast and simple to be incorporated easily into existing electron diffraction codes.

ABSTRACT:The alkali halides sodium fluoride, sodium bromide and sodium iodide exist in the gas phase as both monomer and dimer species. A reanalysis of gas electron diffraction (GED) data collected earlier has been undertaken for each of these molecules using the EXPRESS method to yield experimental equilibrium structures.EXPRESS allows amplitudes of vibration to be estimated and corrections terms to be applied to each pair of atoms in the refinement model. These quantities are calculated from the ab initio potential-energy surfaces corresponding to the vibrational modes of the monomer and dimer. Because they include many of the effects associated with large-amplitude modes of vibration and anharmonicity we have been able to determine highly accurate experimental structures. These results are found to be in good agreement with those from high-level core-valence ab initio calculations and are substantially more precise than those obtained in previous structural studies.