A new method to obtain improved structural parameters by supplementing gas-phase electron diffraction (GED) data with restraints based on the results of ab initio calculations is proposed. The procedure involves the use of ab initio parameters with estimated uncertainties as additional observations; this allows previously fixed parameters to refine, with all geometrical parameters included in the final refinement. The refinement of the molecular structure of 2,5-dichloropyrimidine is used as an example to illustrate the principle of this technique. In this simple case, the effects are not very great, but this new approach allowed refinement of all structural parameters. The nine independent structural parameters (r R structure) were found to be: 6)-H( 10)] ) 109.9(12) pm, ∠[N(1)C( 2)N(3)] ) 127.9(4)°, ∠[C(2)N(3)C( 4)] ) 116.3(7)°, and ∠[N(3)C(4)H( 8)] ) 117.2(5)°. All structural parameters were found to be in good agreement with both ab initio and crystallographic values, which are presented for comparison.

Supplementing gas-phase electron-diffraction data with restraints derived from a graded series of ab initio calculations makes possible refinement of all geometrical parameters and amplitudes of vibration. By avoiding the need to fix some parameters, this technique yields structures which are more completely refined and thus have more reliable standard deviations than procedures used previously. It has been applied to the gas-phase structure of the urachno boron hydride tetraborane( lo), B,H,,. Salient structural parameters (rt structure) were found to be: r[ B( 1 )-B( 2)] 186.6(2), r[B( 1)-B( 3)] 173.7( 5), r[B( 1 )-H( 1,2)] 123.0( 1 5), r[B(2)-H( 1,2)] 14 1.7( 8), r[B( 1 )-H( 1 )] 119.8(8), r[B(2)-H(2)Iendn] 121.0(8) and r[B(2)-H(2),,,] 120.5(8) pm; butterfly angle 117.2( 4)". The crystal structure was also redetermined at 100 K. All gas-phase, crystallographic and ab initio structural parameters were found to be in good agreement. ~ ~~ ~~ ~~~~3 We use the term 'uncertainty' for the estimated possible error in a supplementary observation, and 'estimated standard deviation' for the error in a parameter derived in the least-squares refinements. The uncertainties, which give the weights assigned to additional observations, are, in the case of additional experimental data, the estimated standard deviations of those data. 9 'Restraint' is used for any additional information which is applied flexibly, 'constraint' for one which is applied rigidly, such as a fixed parameter or molecular symmetry.

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.

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