B.S. Butayev

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.

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.

Electron diffraction evaluation of vibrational potentials of diatomic molecules

Abstract The application of modern electron diffraction to the determination of vibrational potential parameters of diatomic molecules is demonstrated. The vibrational potential of a diatomic system is directly introduced into the Debye intensity equation through the density matrix. Using the electron diffraction data for iodine at T = 294 K the vibrational potential parameters re, ωe, k3 and k4 are determined. These values were then used for calculating vibrational spectroscopic averages rv = 〈1/r2〉 −1 2 v for ν ⩽ 5. The results agree with those obtained by spectroscopy within the uncertainties quoted.

The morse-like model for the potential function of linear XY2 molecules

A Morse-like model with four adjustable constants is suggested for the potential function of linear XY2 molecules. By transferring the parameters from diatomic molecules the number of constants can be further reduced. It is shown that this model quantitatively reproduces the general valence force field of CO2 and CS2 established from spectroscopic data.

Second-order perturbation approach to anharmonic analysis of molecules by electron diffraction: Part II. Parr—Brown model potential of CO2

Abstract A new equation for molecular intensity of a general moderately anharmonic polyatomic system with non-degenerate normal vibrations and without accidental degeneracies has been derived by means of a second-order perturbation probability density function reported by Reitan. With this equation, diffraction data for CO 2 were interpreted in terms of the Parr—Brown potential function in two slightly different modifications W I and W II . The equilibrium internuclear distance CO ( r , A) and Parr—Brown coefficients W 11 (mdyn A 3 ), W 111 (mdyn A 4 ), W 3 (mdyn A 2 ), W 12 (mdyn A 3 ) and W γ (mdyn A 3 ) were found to be: W I , r e (CO) = 1.1603(8), W 11 = −13.7(1.2), W 111 = 8.25(0.3), W 12 = 4.5(0.5), W γ = 1.57(0.2); W II , r e (CO) = 1.1602(8), W 11 = −15.7(2.0), W 111 = 8.7(0.7), W 3 = 8.9(3.0), W 12 = 10.0(2.5), W γ = 3.8(1.0). Parenthesized values are estimated random errors. The error in r e is given in terms of the last significant figure stated. The results are compared with those obtained by spectroscopy.

Spectroscopic calculations of electron diffraction parameters of diatomic molecules

Abstract Using spectroscopic data, the electron diffraction parameters r g and l e for the iodine and oxygen molecules are calculated at various temperatures by numerical diagonalization of the vibrational hamiltonian matrix and by the density matrix approach. The results are discussed and compared with available experimental data. A comparison is also made with the results of second-order perturbation calculations for iodine reported in the literature.

Application of Schwinger perturbation theory in electron diffraction analysis Part II. Bent XY2-type molecules

Abstract The method of analysis of molecules by electron diffraction in terms of the intramolecular potential function based on Schwinger thermodynamic perturbation theory formulated in Paper I of this series is extended to include bent XY2-type molecules. A test of the performance of the analytical formulae derived is given by calculating various thermal average moments. These formulae, within the framework of the scheme of anharmonic diffraction analysis developed in Paper I, were applied to reinterpret the intensity data for Tl20, SnCl2, SnBr2 and SnI2 in conjunction with spectroscopic data.

Model potential functions of nonlinear XY2 molecules

Abstract Several simple anharmonic potential functions with a moderate number of adjustable parameters were considered for nonlinear XY 2 molecules. The ability of these functions to reproduce the general valence for field was tested by illustrative calculations for H 2 O, D 2 O, SO 2 , H 2 S, O 3 , NO 2 and ClO 2 . Evidence is presented that the diatomic model approach, which effectively reduces the number of adjustable parameters, is a reasonable approximation when a complete set of spectroscopic data is not available.

Application of the effective harmonic oscillator method to computing the thermal averages for a system of coupled anharmonic oscillators

Abstract By treating the Hamiltonian for coupled oscillators with polynomial anharmonicity by the Gibbs-Bogoliubov inequality, the effective harmonic oscillator (EHO) method is developed and applied to computing the thermal averages for polyatomic molecules. Practical utility is demonstrated with calculations of electron diffraction quantities, namely the distance r a and amplitude l , and of the vibrational partition functions for CO 2 , CS 2 , SO 2 and H 2 O from spectroscopic data on the force fields. The results are compared with those in the literature obtained by more accurate techniques. A comparison of r a and l was also made with the results of electron diffraction measurements.

Application of the effective harmonic oscillator in thermodynamic perturbation theory

Abstract The coordinate probability distribution function for a one-dimensional anharmonic oscillator is derived by application of the effective harmonic oscillator (EHO) density matrix in first-order thermodynamic perturbation theory. The practical utility of this approach is demonstrated by the calculation of quantities obtainable by electron diffraction, namely the distance r g and amplitude l e , and of vibrational partition functions for H 2 , N 2 and I 2 from the Morse potential.