Anatoli A. Ischenko

A new intensity equation for electron diffraction analysis: A barrier to pseudorotation in PF5 from diffraction data

Abstract Using the cumulant expansion for the statistical average of the exponent the molecular intensity of scattered electrons is expressed in terms of the equilibrium internuclear distances and moments of the displacements of internuclear distances . The new intensity equation is suitable for practical analysis of diffraction data for any molecular system including those where anharmonicity factors are thought to be particularly important. The trigonal bipyramidal PF 5 molecule was chosen as a test system mainly with the aim of determining the barrier to pseudorotation which is thus estimated to be 3.41 kcal mol −1 , in excellent agreement with the recently available spectroscopy and ab initio values.

The cumulant method in diffraction analysis of polyatomic molecules

Abstract A method of analysis of molecules by electron diffraction in terms of the intramolecular potential function is presented. The method is based on the cumulant representation of the molecular scattering function and a perturbation solution of the vibrational problem. Special care has been taken in difficulties involving Fermi resonances. A test of the performance of the devised theory is provided by comparison of the calculated temperature dependence of ra distances in SF6 with available experimental data. The proposed scheme of diffraction analysis, providing due facility for incorporation of relevant spectroscopic information, is checked by treatment of published intensity data for SO2 and SF6.

The stroboscopic gas electron diffraction method for investigation of time-resolved structural kinetics in photoexcitation processes

Abstract The emergence of a novel tool of structural chemistry is reviewed; pulsed-electron beam (stroboscopic) gas electron diffraction (GED) synchronous with photoexcitation. About 10 years ago, the first stroboscopic electron diffraction experiments of irradiated gaseous species were performed at Moscow State University, yielding qualitative evidence that intensity changes upon irradiation can be detected in this way. More recently, development of prototype on-line GED data recording techniques at the University of Arkansas allowed for the first successful observations, with quantitatively model-fitted GED signals, of photochemical reactions, i.e. the 193 nm photodissociations of carbon disulfide and of chlorine-substituted ethenes. In addition to summarizing some of the current structural work, the paper describes the characteristic aspects of pulsed-beam GED, the requisite on-line data recording, and non-conventional data analysis techniques capable of interpreting GED signals from non-equilibrium ensembles in arbitrary vibrational states.

Structural and vibrational kinetics of photoexcitation processes using time resolved electron diffraction

Abstract This paper describes the historical background and current status of structural and vibrational kinetic studies of photoexcitation processes using pulsed beam gas electron diffraction. The development of time resolved electron diffraction (TRED) required essential changes in the traditional experimental and theoretical procedures of gas electron diffraction. On the experimental side, over the last decade or so, research at the University of Arkansas has led to construction of a prototype on-line data recording system that, combined with a laser-driven pulsed photocathode, enables time-resolved investigations spanning the time domain from microseconds to picoseconds. On the theoretical side, new techniques allow one to model TRED data in terms of a molecules potential energy surface or, alternatively, to apply stochastic procedures to solve the inverse problem, i.e. to determine the PES from the diffraction data. The importance of considering appropriate vibrational properties is demonstrated. Diverse aspects of TRED modeling of dissociation and pre-dissociation processes are described, including formalisms based on wave packet dynamics, spatial anisotropy, chaotic nuclear dynamics, Wigner distribution functions, tomographic reconstruction, and coherently excited molecular ensembles.

Vibronic effects in elastic scattering of electrons

Abstract A method for obtaining general equations for the scattered intensities from vibronic systems is given. The approximate formulas obtained are used to calculate the effects on the electron diffraction pattern for molecules with doubly degenerate electronic E terms interacting with e -type vibrations ( Ee -type of problem). The results of the approximate calculations are compared to more precise results, based on numerical solution of the vibronic problem.

Structural kinetics by time-resolved gas electron diffraction: coherent nuclear dynamics in laser excited spatially anisotropic molecular ensembles

Abstract Novel equations for molecular intensities are presented which can be used in analyses of time-resolved electron diffraction (TRED) data recorded from spatially oriented laser-excited molecules. The formalism is applicable to nondissociative processes and to studies of the nuclear dynamics of dissociation and predissociation phenomena. With the help of quantum dynamics, specific model calculations were performed with the new theoretical expressions for various purposes: to determine the effects of non-equilibrium vibrational distributions, of the vibrational recurrence of wave packets, and of isotopic substitution on TRED intensities; and to compare the quantum-dynamical calculations of TRED intensities with the previous Gaussian wave packet approach. The study is a continuation of ongoing efforts to create a theoretical base for structural kinetic studies of laser-excited species using gas electron diffraction.

Electron-diffraction study of the vibrational assignment, molecular structure and barrier to pseudorotation of gaseous tantalum pentabromide

Abstract Tantalum pentabromide has a trigonal bipyramidal structure (D 3h symmetry) with thermal average axial bonds longer than the equatorial ones by 0.061(10) A. The equatorial bonds are 2.412(4) A. The barrier to pseudorotation was estimated to be 1.3(0.6) kcal/mol from the electron-diffraction data.

Structural kinetics by stroboscopic gas electron diffraction Part 1. Time-dependent molecular intensities of dissociative states

Abstract Theoretical analyses and model calculations are presented for the application of stroboscopic gas electron diffraction as a technique to study the structural kinetics of transient species in the femtosecond time domain. An expression for the time-dependent molecular diffraction intensities is developed and used to model the dynamics of the laser-induced dissociations of IBr and ICN. It is found taht the molecular intensities can be directly expressed in terms of the potential function of the dissociative state and other parameters that characterize the transient state dynamics. Thus, the solution of the inverse structural problem seems feasible, i.e. the determination of transient state parameters from time-dependent intensity data. In addition it is found that structural details of the dissociative processes can be time-resolved on a scale that is significantly faster than that of the electron probe pulse width. Our study indicates that, by measuring directly the evolution of transient state geometries, time-resolved electron diffraction provides a new type of information complementary to that obtained by spectroscopic techniques.

Vibronic interactions and molecular structure of gaseous vanadium tetrabromide: An electron diffraction study

Abstract The molecular structure and vibronic interactions in vanadium tetrabromide have been studied by gas-phase electron diffraction. The gaseous sample of vanadium tetrabromide at 390°C was obtained by the thermal decomposition reaction 2VBr3 (solid) → VBr2 (solid) + VBr4 (gas) directly in the sample container of the vaporizer. The values of the internuclear distances rα (A) and of the mean amplitudes of vibration l(A) for the Td symmetry model are: rα (VBr) = 2.276(4), l(VBr) = 0.079(4), l(Br⋯Br) = 0.214(11). The uncertainties quoted include estimates of both random and systematic errors. Since VBr4 is considered to be in a doubly degenerate ground electronic state in a tetrahedral configuration the data obtained are rationalized in terms of the dynamic Jahn—Teller effect. Using this idea the recently developed theory of vibronic effects in elastic scattering of electrons is applied in the structural analysis. The experimental estimates of vibronic parameters are: the first-order vibronic interaction constant |aE| = 1.36 ± 0.07, the Jahn—Teller stabilization energy EJT = 62 ± 5 cm−1 and the dynamic distortion parameter ρ0 = 0.183 ± 0.007 A.

Structural kinetics by stroboscopic gas electron diffraction 2. Time-dependent molecular intensities of predissociation processes

Abstract Various attempts have been reported in the literature [1–3] to develop stroboscopic gas electron diffraction (GED) for time-resolved studies of dynamic phenomena in laser-excited molecular species. This novel applications of GED requires the formation of new expressions for the scattering intensities, since conventional equations for GED data analysis are based on models that are restricted to equilibrium ensembles and molecules exhibiting small amplitude motions. As a first example, the time-dependent molecular intensities for species in adiabatic dissociative states have recently been reported [4]. In the current study the molecular intensity expression for the evolution of internuclear distances in predissociation processes on a diabatic potential energy surface is presented and some model radial distribution curves are shown. The structural kinetics of the photodissociation of NaI are modeled on a femtosecond time-scale. The time-dependent molecular intensities of NaI are directly parameterized in terms of the intramolecular potential energy surfaces and other parameters which characterize the transient state dynamics, as taken from experimental spectroscopic investigations reported in the literature. The acute dependence of the molecular intensities and radial distribution curves on the PES shows that solution of the inverse problem, i.e. determination of potential parameters from time-dependent electron diffraction data, is feasible in principle. As in the previous model study of adiabatic dissociative processes, it is found that details of the dynamics of photo-predissociation can be resolved on a time-scale shorter than that of the probing electron pulse. Furthermore, our analysis demonstrates the fundamental difference between the observables obtained from spectroscopy and electron diffraction: whereas no explicit structural information on the time-evolution of the nuclear configuration is obtained from spectroscopy, the molecular intensities of scattered electrons depend directly on the structural kinetics; i.e. the time-evolution of the internuclear distances.