Yu. I. Tarasov

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.

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.

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.

Large-amplitude motion in 1,4-cyclohexadiene and 1,4-dioxin: theoretical background for joint treatment of spectroscopic, electron diffraction and ab initio data

Abstract A flexible self-consistent approach based on the adiabatic separation between large- and small-amplitude motions has been developed for the joint treatment of gas-phase electron diffraction (ED) and spectroscopy data. The Hamiltonian developed gains versatility by directly proceeding from assumed model properties to energy levels and wavefunctions. In addition to the vibrational terms, it explicitly includes rotational effects as well as interactions between overall rotation and intramolecular motion. A particular form of a Hamiltonian is specified by the system to be considered. If the vibrational energy is much higher than rotational energy, the latter can be separated and treated conventionally as perturbation. Six-membered ring planar floppy molecules 1,4-cyclohexadiene and 1,4-dioxin (1,4-dioxacyclohexa-2,5-diene) were selected for illustration. Large-amplitude approach described below and previously developed technique based on the general framework of rigid molecules with account for anharmonicity have been compared in predicting theoretical ED intensities for these molecules. We conclude that no noticeable deviations between ED intensities obtained using the two mentioned theoretical approaches have been observed when large-amplitude vibrations were governed by the approximately quadratic potential function (the case of 1,4-cyclohexadiene) while the case of quartic potential (for 1,4-dioxin) resulted in significantly different ED patterns.

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.

Electron diffraction analysis for the molecules with multiple large-amplitude motions. 3-nitrostyrene--a molecule with two internal rotors.

Dynamic structural analysis of the molecules possessing large-amplitude degrees of freedom has been attempted by many researchers; however, so far, electron diffraction investigations involved only one large-amplitude coordinate (internal rotation or bending). The current state of computational facilities allows extending of the general dynamic approach to the systems possessing two or more large-amplitude motions. This paper presents the first practical implementation of the theoretical method developed previously by the authors for solving the dynamic-structural problem with two or more large-amplitude coordinates; the procedure is applied to a molecule of 3-nitrostyrene. The molecule is represented as a set of pseudoconformers built on a two-dimensional grid corresponding to both internal rotation coordinates present in the molecule (with 10-30° steps by each angle); altogether, up to 342 pseudoconformers were used. Structural analysis was based on the experimental electron diffraction data supported by quantum chemical calculations (at the MP2 and B3LYP levels of theory) and molecular spectroscopy data. Quantum chemistry predicts the planar structure of both syn- and anti- stable conformations with close energies and weak interaction between internal rotations of nitro and vinyl groups. The gas-phase electron diffraction experimental data are compatible with the quantum chemical predictions. The principal equilibrium geometry parameters of the molecule (syn- conformation) have been determined as follows: r(e)(C-C)(ring, avg.) = 1.391(1) Å, r(e)(C-C) = 1.477(5) Å, r(e)(C═C) = 1.333(7) Å, r(e)(C-N) = 1.463(5) Å, r(e)(N═O) = 1.227(3) Å, ∠e(O═N═O) = 124.3 (4)°. Experimental data for this molecule are insufficient to make estimates of the barrier heights of internal rotation; the population ratio of syn- and anti- conformations is evaluated as 50 ± 20%. Results of our investigation confirm the presence of significant internal rotations in the 3-nitrostyrene molecule.

Equilibrium structure and large amplitude motion investigation of 1,4-disilacyclohexa-2,5-diene by means of electron diffraction, vibrational spectroscopic data, and ab initio calculations

Abstract Equilibrium and thermal average structure of 1,4-disilacyclohexa-2,5-diene (DSCHD) was determined by applying procedures that have been recently developed for joint treatment of gas phase electron diffraction and molecular spectroscopy data guided by ab initio calculations. Both large amplitude motion and anharmonic vibrational effects were taken into account. Similar structural results were obtained by considering DSCHD molecule as a unique equilibrium conformer and as a set of quasi-conformers describing large amplitude motion. The determined equilibrium structural parameters for DSCHD (planar configuration) are: r e ( Si – C )=1.861(2) A , r e ( CC )=1.346(3) A , r e ( Si – H )=1.498(10) A , r e ( C – H )=1.074(10) A , ∠(C–Si–C)=109.9(3)°, ∠(H–CC)=116.7(10)°, and ∠(H–Si–H)=107.9(10)°. Uncertainties given in parentheses include three times standard deviation and a systematic error.

On the determination of equilibrium geometries and potential functions of simple polyatomic molecules from electron diffraction

The degree to which current electron diffraction (ED) techniques allow reliable determination of equilibrium geometries and potential functions of simple molecular systems is studied. Special attention is paid to the choice of the model potential function in the diffraction analysis. The main calculations were performed using accurate diffraction data on SO2 and SF6 available from the literature. Routine electron diffraction data on PbCl2 and PbBr2 obtained at Moscow University were also treated and found to be reasonably informative regarding bond stretching anharmonicity. Compelling evidence has been presented that any unfavorable situation in the ED analysis of equilibrium geometries and force fields of molecules can be substantially improved by augmenting scattering observations with reliable inferences from vibrational spectroscopy data. This useful cooperation of techniques is shown to be most powerful in efforts to solve equilibrium geometries and molecular dynamics.In addition, numerical simulation experiments were carried out with CO2 and SO2 as samples. It is shown that the high-temperature and hot-molecule techniques of electron diffraction may yield valuable information on anharmonicity.

An approximate approach to the anharmonic analysis of molecules by electron diffraction

Abstract An approximate approach to the structural analysis of molecules exerting moderately anharmonic motion based on the model potential function involving only a single Morse-like parameter for the bonded atom pair is developed. Also suggested is the simplified “quasi-diatomic” approximation. The natural curvilinear internal coordinates were used in formulating the molecular potential function. The check calculations were performed with non-photographic intensity data on CO2 and SO2 taken from the literature. It is shown that a sufficiently reliable determination of equilibrium geometry of molecules in anharmonic approximation is feasible provided that the diffraction technique is supplemented by spectroscopic methods.