I. V. Kochikov

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.

Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization

We describe a novel method for employing calculated ab initio potential data together with Tikhonov’s variational procedure to extract fundamental molecular force field parameters from experimental spectral data, the formal ‘‘inverse problem’’ of vibrational spectroscopy. In this approach, the ab initio quantities serve to ‘‘regularize’’ the initially ill‐posed problem (in the sense of Tikhonov), leading to variationally stable and unique force field parameters that optimally mimic overall patterns of the (approximate) ab initio quantities, but exactly reproduce the available experimental data within specified experimental precision. In this manner, ab initio and experimental data can be jointly combined to produce more stable and reliable force fields (improvable to any degree through higher level ab initio treatment, additional experimental data, etc.) than could be attained by theoretical or experimental methods alone. The proposed procedure allows use of any system of generalized coordinates, includin...

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.

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.

Equilibrium Structure and Internal Rotation in B2F4 from Electron Diffraction and Spectroscopic Data and Quantum Chemical Calculations

Electron diffraction (ED) data for B2F4 recorded by Hedberg et al. over the temperature range −80 to +150°C have been used to obtain equilibrium geometry of this molecule in the framework of a large-amplitude motion model. The torsional coordinate has been adiabatically separated from the rest of vibrations. Two types of constraints applied to obtain ab initio torsional potential energy function (PEF) and the parameters of the geometry relaxation are discussed. The relations between anharmonic interaction force constants and the parameters of the geometry relaxation are briefly considered. Ab initio force constant matrices for rigid vibrational coordinates as well as large-amplitude torsional PEF have been scaled in the procedure of simultaneous fitting to the ED data and experimental vibrational frequencies. The resulting equilibrium geometry and potential function provided good fit to both ED and spectroscopic data. As expected, the results for the equilibrium geometry obtained from separate ED patterns recorded at different temperatures did not show noticeable temperature trend. The determined equilibrium structural parameters for B2F4 are: re(B–B) = 1.719(4) Å, re(B–F) = 1.309(2) Å, ∠BBF = 121.1(1)°. Uncertainties given in parentheses include three times standard deviation and a systematic error. The rotational barrier height was evaluated as 160(50) cm−1.

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.

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.

High-performance atomistic modeling of optical thin films deposited by energetic processes

In this paper we present a computationally effective approach to classical molecular dynamic simulation of thin film growth with orientation on cluster supercomputing facilities. The goal of the developed approach is to investigate structural heterogeneities of thin films deposited on substrates at a nanoscale level. These heterogeneities depend on the experimental conditions of a deposition process being used. They have essential influence on practical properties of thin films and their modeling is important for achieving further progress in thin film optical technology. The presented research is focused on silicon dioxide thin films growth. A special force field, oriented on the atomistic description of the silicon dioxide deposition on fused silica substrate, has been developed and applied to the molecular dynamic simulation with the GROMACS package. The validity of the developed simulation approach is verified using atomic clusters consisting of up to 106 atoms and having characteristic dimensions of up to 30 nm. Its computational efficiency is tested using up to 2048 cores. The dependence of achievable efficiency on model parameters is discussed.