Accurate Equilibrium Structures Obtained from Gas-Phase Electron Diffraction Data:  Sodium Chloride

Abstract

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.

Experimental and theoretical studies of the vibrations and structure of 2,2,2-trifluoroethyl trifluoroacetate, CF3CO2CH2CF3

“…The structure obtained from the refinement is therefore of the type r a3,1 . For a full discussion of this nomenclature see reference [20].…”

Klein, aber oho: was die Nanowissenschaft von der Chemie lernen kann

“…[55,56] Wenn der Nanokristall vergrçßert wird, spielt sich die Rekonstruktion mehr auf der Oberfläche ab; das Innere nähert sich der Volumenstruktur an. [62] Ich habe hier keine Zeit, die faszinierende Frage zu diskutieren, ab welcher Grçße die Cluster von Edelgasen oder Metallen von ihrer ursprünglich ikosaedrischen Anordnung zur Translationssymmetrie und dichten Kugelpackungen übergehen. Es scheint Ausnahmen von dieser Regel zu geben -stabile Cluster von wohldefinierter Grçße, aber mit dramatischer Abweichung von der Festkçrperstruktur, so wie (CdSe) 34 .…”

Comparison of the molecular structures of five benzene derivatives as determined independently by gas-phase electron diffraction in two different laboratories: a perspective

“…[2] and [5]. The r hn notation, originally introduced by Sipachev [23], is described as follows by Rankin and co-workers [24]. The subscript h implies that the correction term K accounting for perpendicular vibrations is generated in the harmonic approximation, while n specifies the level of the correction, e.g., ''0'' indicates a zeroth-order rectilinear correction and ''1'' a first-order curvilinear correction.…”

“…The subscript h implies that the correction term K accounting for perpendicular vibrations is generated in the harmonic approximation, while n specifies the level of the correction, e.g., ''0'' indicates a zeroth-order rectilinear correction and ''1'' a first-order curvilinear correction. If the correction is calculated using third derivatives of energy, giving cubic anharmonicity terms, the subscript h is replaced by a3, e.g., as in r a3,1 [24]. At this point we would like to issue a caveat about the ever increasing proliferation of representations of and notations for internuclear distances, especially if they are used without a clear and unambiguous definition.…”