V. P. Spiridonov

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 equilibrium structure of thiophene by the combined use of electron diffraction, vibrational spectroscopy and microwave spectroscopy guided by theoretical calculations

Abstract The equilibrium molecular geometry of thiophene has been determined from a combination of gas-phase electron diffraction, vibrational and microwave data and ab initio and DFT calculations. The quadratic and cubic force constants of thiophene calculated theoretically and empirically improved by harmonic scale factors were incorporated in the analysis in which equilibrium distances and harmonic scale factors were refined simultaneously. The diffraction intensities were calculated by the use of first-order perturbation theory. The commonly used r a distances and amplitudes of vibration were also estimated and found to agree reasonably well with those from an earlier investigation. Anharmonic phase shift parameters for all atom pairs and the various distance correction terms are presented.

Regularizing algorithm for determination of equilibrium geometry and harmonic force field of free molecules from joint use of electron diffraction, vibrational spectroscopy and ab initio data with application to benzene

Abstract A novel integrated algorithm is suggested for joint treatment of gas-phase electron diffraction and spectroscopic data. This algorithm develops the idea of the regularized quantum mechanical force field approach based on the theory of nonlinear illposed problems. The main advantage of the algorithm is that it provides a unique and stable solution for the equilibrium geometry and intramolecular harmonic force field of quasi-rigid systems. The check calculations were carried out with Oslo intensity data on benzene collected with improved precision. Infrared frequencies of benzene and its isotopomer were taken from the literature.

Molecular structure and vibrational potential function of HgI2: electron diffraction study

Abstract For the first time in electron diffraction structure analysis of polyatomic molecules the direct parameterization of an intensity function on force constants and equilibrium interatomic distances is applied. Following this procedure, all harmonic valence force constants of the HgI 2 molecule and the equilibrium interatomic distance HgI in the harmonic approximation have been determined by gas-phase electron diffraction assuming the equilibrium geometry to be linear. On the basis of vibrational frequencies calculated from the force constants thus obtained, a critical analysis of available spectroscopic data is given. By combined use of electron diffraction and most reliable spectroscopic data treated as independent observables the best values for harmonic valence force constants are obtained. The anharmonicity in the bending vibrational potential is also examined. It is shown that, to a good approximation, the bending vibration may be regarded as being harmonic at least for small vibrational quantum number 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.

Electron diffraction analysis of XY2 and XY3 molecules with large amplitude motion: Part II. Survey of experimental studies

Abstract A survey is given on the application of the interpretational scheme formulated in Paper I of this series to the analysis of gas phase electron diffraction data on MnF 2 , FeF 2 , CoF 2 , NiF 2 , CrF 2 and ZnF 2 conjointly with spectroscopic or estimated vibrational frequencies available from the literature. The results of an analysis by a conventional scheme of interpretation in terms of thermally averaged internuclear distances and amplitudes of vibration are also described. The bending potentials of all the above molecules were found to be shallow. Dynamical behavior of these systems conforms to the pattern of a fairly felxible quasi-linear molecule exhibiting large amplitude bending motion. The bending frequencies estimated independently from electron diffraction data are presented and the results of a numerical calculation of bending vibration spectra are reported. The equilibrium MeF distances, bond angle mean-square displacements and best fit stretching frequencies have also been given. A similar analysis of diffraction data on CrF 3 and LaCl 3 is described. CrF 3 is shown to be a planar molecule exerting large amplitude out-of-plane motion. By contrast, LaCl 3 appears to be pyramidal enough with four lowest doubly degenerated levels located inside both wells of the inversion potential. The fifth level exhibits apparent inversion splitting associated with tunneling of the metal atom, whereas at higher levels of excitation nearly free inversion motion is likely to occur. The equilibrium CrF and LaCl distances and best fit skeletal frequencies optimized against electron diffraction data and spectroscopic or estimated vibrational frequencies available from the literature are presented. The inversion frequencies estimated independently from electron diffraction are also given. By taking CrF 2 as an example, confirmative evidence is given for the potentially fruitful application in diffraction analysis of nonrigid molecules of multidimensional classical and semiclassical distribution functions in cases where appropriate conditions for their adequate use are satisfied.

Second-order perturbation approach to anharmonic analysis of molecules by electron diffraction: Part III. Morse-like potential function of SnCl2, SnBr2, SnI2, Ga2O and Tl2O

Abstract A practical procedure based on a second-order perturbation intensity equation derived in Part II of this series is developed for analysis of diffraction data from bent symmetric triatomic molecules in terms of the molecular potential function. With this procedure, diffraction data for SnCl 2 , SnBr 2 , SnI 2 , Ga 2 O and Tl 2 O obtained earlier were re-interpreted and the equilibrium geometrical parameters, harmonic force constants and Morse-like anharmonic parameters for both distances were determined. The frequencies of vibration were also evaluated and compared with spectroscopic and estimated values reported in the literature.

Extension of a regularizing algorithm for the determination of equilibrium geometry and force field of free molecules from joint use of electron diffraction, molecular spectroscopy and ab initio data on systems with large-amplitude oscillatory motion

Abstract The previously developed integrated algorithm for the joint treatment of gas-phase electron diffraction and vibrational spectroscopic data is extended to include systems with large-amplitude oscillatory motion. In addition, the treatment is augmented by the inclusion of microwave rotational constants. As in the previous work, the analysis of data from experimental sources is guided by quantum mechanical molecular geometry and force field optimization results. The computed force field matrix can be corrected empirically with the aid of suitable scale factors. Centrifugal distortion corrections to interatomic distances are included. The standard deviations of the parameters determined and the correlation coefficients can now be estimated. The principal design of the developed computer program is outlined, and some methodological problems associated with diffraction analysis of molecules with large-amplitude motion are discussed. To provide an example of a problem susceptible to attack by the present method an account is made of the re-analysis of diffraction data for 4-fluorobenzaldehyde collected earlier on the Balzers apparatus in Oslo.

Electron diffraction study and CNDO/2 calculations on the complex of aluminium trichloride with ammonia, Cl3Al.NH3

Abstract The molecular geometry of the complex of aluminium trichloride with ammonia, Cl 3 Al.NH 3 , has been studied by electron diffraction. The most important internuclear distances in terms of r a parameters are as follows: r (Al-Cl) = 2.100±0.005 A, r (Al-N) = 1.996±0.019 A, r (Cl·Cl) = 3.569±0.011 A and r (Cl·N) = 3.165±0.012 A. The Cl-Al-Cl bond angle in terms of an approximate r a structure is 116.9°. The assumptions of a staggered model in the structure analysis was justified by CNDO/2 calculations. The experimental data indicate strong linkage between the donor and acceptor parts. The flat pyramidal average configuration of the AlCl 3 part of the complex suggests planar equilibrium structure for free AlCl 3 . Variations in the bond configurations of the donor and acceptor parts, as compared with those of the respective free molecules, are discussed.