G. M. Kuramshina

Inverse problems of vibrational spectroscopy

Physical model of molecular vibrations full statement of the vibrational problem consideration of the mathematical model for molecular vibration analysis - direct and inverse problems vibrational problems in internal coordinates - use of the redundant coordinate system vibrational problems in symmetry coordinates ill-posed problems and the regularization method - regularizing algorithms for constructing force fields of poly-atomic molecules on the base of experimental data numerical methods analysis of band intensities in vibrational spectra of poly-atomic molecules numerical implementation of algorithms for solving problems of vibrational spectroscopy examples of molecular force field calculations on the basis of experimental data joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonovs method of regularization. Appendix: systems of units used in vibrational spectroscopy.

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.

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.

The use of ab initio anharmonic force fields in experimental studies of equilibrium molecular geometry

Abstract The use of ab initio methods has been investigated for obtaining physically meaningful anharmonic force fields applicable in structure analysis of molecules by electron diffraction. The quadratic and cubic force constants for the sample molecule SF 6 chosen as a suitable test case were theoretically estimated and improved by an empirical scaling based on a quadratic force constant scale factors. It was confirmed that if theoretical calculations are made with well selected basis sets the accuracy of the individual values of the computed cubic constants established by reference to precise spectroscopic data is practically sufficient to experimentally determine the accurate equilibrium S–F distance and to theoretically estimate the amplitudes of vibration and the phase shift parameters for all internuclear distances. Calculations based on a Morse-like anharmonic model function were also performed for comparison. The present calculations show that determination of an accurate equilibrium molecular structure by electron diffraction is possible through the appropriate combination of experimental and theoretical data. The best equilibrium geometry results, if empirically scaled ab initio quadratic and cubic force constants are used in a regularizing algorithm developed earlier for the effective interaction of electron diffraction with vibrational and microwave spectroscopy techniques.

A priori constraints in the force field calculations of polyatomic molecules

An inverse problem on calculating the force field parameters of a molecule from experimental data and its solution using regularizing algorithms are considered The choice of a priori constraints that may be imposed on solutions of the inverse vibrational problem is analyzed in terms of quantum mechanical calculations of some polyatomic molecules at different levels of theory, including electron correlation.

Stable numerical methods of solving certain inverse problems of vibrational spectroscopy

Abstract Stable numerical methods of constructing the force fields of multi-atomic molecules from experimental data based on Tikhonovs method of regularization of ill-posed problems are proposed.

Calculation of force fields of chromium, molybdenum and tungsten hexafluorides and dioxodifluorides by means of the Tikchonov regularization method

Abstract Force fields and mean amplitudes of vibration of chromium, molybdenum and tungsten hexafluorides and dioxodifluorides are calculated using Tikchonovs regularization method and are compared with those for oxotetrafluorides.

Regularizing algorithms for molecular force field calculations

Abstract Stable numerical methods for constructing molecular force fields on the basis of experimental data using Tikhonovs regularization method of ill-posed problems are proposed.

Normal coordinate analysis of CH2ClSiX3, CHCl2SiX3, CCl3SiX3 (X = H, D, F, Cl) Molecules using Tikhonov's regularization method

Abstract Force fields and mean amplitudes of vibration of CH2ClSiH3, CHCl2SiH3, CCl3, SiCl3 and CCl3SiF3 are calculated using Tikhonovs regularization method. The transferability of calculated force constants is examined by normal coordinate calculations for CH2ClSiF3, CH2ClSiCl3, CHCl2SiF3, CHCl2SiCl3 and CCl3SiH3.