Electron diffraction studies of hot molecules. I. Observed and calculated thermal expansions of SF6, CF4, and SiF4

A new method is described for the rapid heating (10−5–10−6 s) of gas molecules for study by electron diffraction. Laser irradiation of the tip of a micronozzle makes it possible to determine structures, amplitudes of vibrations, and aspects of anharmonicity of molecules at temperatures much higher than those at which decomposition occurs in conventional oven nozzles. The vibrations and thermal expansions of SF6, CF4, and SiF4 have been investigated up to 1700, 1600, and 1200 K, respectively. Clear evidence for effects of anharmonicity was observed in amplitudes of vibration as well as mean bond lengths. Various models proposed for the treatment of increases in bond length have been assessed, among which an anharmonic Urey–Bradley field accounted well for results. Comparisons are made with the predictions of Heenan and Robiette based on spectroscopic analyses. The diffraction approach offers a promising method for augmenting spectroscopy in the investigation of intramolecular forces.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69996/2/JCPSA6-77-4-1866-1.pd

Electron diffraction studies of hot molecules. II. ‘‘Anharmonic shrinkage effects’’ in SF6, CF4, and SiF4

Least squares refinements of diffraction intensities for SF6, CF4, and SiF4 yielded nonbonded internuclear distances that lagged increasingly behind values expected from the bond lengths, the higher the temperature. The observation that observed nonbonded shrinkages greatly exceed calculated shrinkages cannot be attributed to a deficiency in the theoretical expressions customarily invoked. It is explained, instead, by anharmonic effects in bending modes that give the illusion of anomalous shrinkage where it does not, in fact, exist. These effects, which skew the nonbonded distribution functions and displace the true mean distances from the peak maxima, contain heretofore unexploited information about anharmonic potential constants.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70624/2/JCPSA6-77-4-1874-1.pd

Effects of Electron Correlation in X‐Ray and Electron Diffraction. IV. Approximate Treatment for Many‐Electron Atoms

A simple scheme is proposed for predicting effects of electron correlation on intra‐atomic electron—electron radial distribution functions and on intensities of x rays scattered by gas atoms. It makes use of a relationship connecting the Coulomb hole function for an electron pair with the corresponding correlation energy. The method is applied to the beryllium atom in its ground state. Results compare favorably with results calculated directly from correlated and Hartree—Fock wavefunctions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71228/2/JCPSA6-45-12-4700-1.pd

Molecular Structure of XeF6. II. Internal Motion and Mean Geometry Deduced by Electron Diffraction

The distribution of internuclear distances in gaseous XeF6 exhibits unusually diffuse XeF6 bonded and F–F geminal nonbonded peaks, the latter of which is severely skewed. The distribution proves the molecule cannot be a regular octahedron vibrating in independent normal modes. The instantaneous molecular configurations encountered by the incident electrons are predominantly in the broad vicinity of C3υC3υ structures conveniently described as distorted octahedra in which the xenon lone pair avoids the bonding pairs. In these distorted structures the XeF bond lengths are distributed over a range of approximately 0.08 Å with the longer bonds tending to be those adjacent to the avoided region of the coordination sphere. Fluorines suffer angular displacements from octahedral sites which range up to 5° or 10° in the vicinity of the avoided region.Alternative interpretations of the diffraction data are developed in detail, ranging from models of statically deformed molecules to those of dynamically inverting molecules. In all cases it is necessary to assume that t1ut1u bending amplitudes are enormous and correlated in a certain way with substantial t2gt2g deformations. Notwith‐standing the small fraction of time that XeF. spends near OhOh symmetry, it is possible to construct a molecular potential‐energy function more or less compatiable with the diffraction data in which the minimum energy occurs at OhOh symmerty. The most notable feature of this model is the almost vanishing restoring force for small t1ut1u bending distortions. Indeed, the mean curvature of the potential surface for this model corresponds to a υ4υ4 force constant F44F44 of 10−2 mdyn/Å or less. Various rapidly inverting non‐OhOh structures embodying particular combinations of t2gt2g and t1ut1u deformations from OhOh symmetry give slightly better radial distribution functions, however. In the region of molecular configuration where the gas molecules spend most of their time, the form of the potential‐energy function required to represent the data does not distinguish between a Jahn–Teller first‐order term or a cubic V445V445 term as the agent responsible for introducing the t2gt2g deformation. The Jahn–Teller term is consistent with Goodman's interpretation of the molecule. On the other hand, the cubic term is found to be exactly analogous to that for other molecules with stereochemically active lone pairs (e.g., SF4, ClF3). Therefore, the question as to why the XeF6 molecule is distorted remains open. The reported absence of any observable gas‐phase paramagnetism weighs against the Jahn–Teller interpretation.The qualitative success but quantitative failure of the valence‐shell–electron‐pair‐repulsion theory is discussed and the relevance of the “pseudo‐Jahn–Teller” formalism of Longuet‐Higgins et al. is pointed out. Brief comparisons are made with isoelectronic ions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70641/2/JCPSA6-48-6-2466-1.pd

Refined Procedure for Analysis of Electron Diffraction Data and Its Application to CCl4

A refined procedure for obtaining the structure of free molecules from electron diffraction data is described which compensates for the interference arising from non‐nuclear scattering. The procedure is applied to CCl4 using somewhat more extensive rotating sector data than has hitherto been published for this molecule. Estimates are made for the first time in electron diffraction results of the effect of anharmonicity of vibration on the measurement of internuclear distance and of the effect of the failure of the Born approximation on the measurement of amplitudes of vibration. A method of estimating the reliability of the results is described.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71343/2/JCPSA6-23-10-1854-1.pd

Inference of vibrational anharmonicity in hot SF6: An electron diffraction study

In an investigation of gaseous SF6 at temperatures ranging from 298 to almost 1000 K, the observed thermal expansion of the mean bond length as a function of the mean‐square amplitude of vibration was found to be much too large to be accounted for by the commonly invoked model of Morse anharmonicity. Experimental results can be reproduced quantitatively, however, with the aid of existing potential constants fed into an anharmonic, modified Urey–Bradley force field proposed previously.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69831/2/JCPSA6-70-10-4585-1.pd