S. V. Krasnoshchekov

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.

Scale factors as effective parameters for correcting nonempirical force fields

Sources of uncertainties that arise in the search for scale factors used to systematically correct theoretical quantum-mechanical force fields in the harmonic approximation are considered. The special features of various approaches to the traditional procedure for scaling according to Pulay are analyzed. It is suggested that scale factors be determined as quotients obtained by dividing the diagonal elements of the approximation to the exact matrix of force constants by their quantum-mechanical analogues. Using this approach obviates the necessity of solving the inverse problem. Perturbation theory is used to show that, when molecular geometric parameters and scale factors are varied jointly, an exact correlation can appear, which substantiates the effective character of force field corrections with the use of scale factors. The procedure for the scaling of generalized quantum-mechanical force fields based on the transition from the normal-coordinate to natural-coordinate representation is considered.

Internal rotation potential functions of the acryloyl chloride molecule in the ground (S 0) and excited (S 1) electronic states

The internal rotation potential function of the acryloyl chloride molecule in the S0 and S1 electronic states was reproduced using systems of torsional vibration levels obtained for its trans and cis isomers by analyzing the vibrational structure of the UV spectrum of the molecule. The kinematic factor F in the S0 ground state was calculated including geometric parameter relaxation as a function of internal rotation angle. The torsional potential parameters in the S0 state obtained in this work were substantially different from those determined from the infrared Fourier-transform spectrum ignoring the resonance perturbation of the level with v = 3. The form of the internal rotation potential function and the higher stability of the trans isomer (the main isomer) were substantiated by high-level quantum-mechanical calculations.

The Determination of the Equilibrium Geometry of a Molecule with the Use of Microwave Data and Theoretical Rotational-Vibrational Interaction Constants

The applicability of the classic method for calculating the equilibrium structure (re) of a polyatomic molecule with the use of experimental rotational constants and rotational-vibrational interaction constants (αrB) is considered. Direct minimization of the nonlinear functional of the sum of the squares of discrepancies by the Broyden-Fletcher-Goldfarb-Shanno method is suggested. Statistical parameters (confidence intervals and correlation coefficients) can be calculated by the double numerical differentiation of this functional. If the problem is ill-conditioned or some data are lacking, the Tychonoff regularization method can be used. The effectiveness of the suggested approach is demonstrated for the example of two molecules (cyclopropene and 3,3-difluorocyclopropene).

Vibrational spectra and conformational composition of ethylene glycol dinitrate in solid phases

8. J. A. Barltrop and J. D. Coyle, Excited States in Organic Chemistry [Russian transla- tion], Moscow (1978), pp. 6770. 9. I. S. Ioffe and V. F. Otten, Zh. Organ. Khim., 32, No. 4, 1196-1201 (1962). i0. I. S. Ioffe and V. F Otten, Zh. Organ. Khim., i, No. 2, 343-346 (1965). ii. Yu. Yu. Lure, Handbook on Analytical Chemistry [in Russian], Moscow (1979), p. 322. 12. B. Stevens, N. Conneily, and P. Suppan, Spectrochim. Acta, 2-2, No. 12, 2121-2122 (1966). 13. Sharma Ashutash and M. K. Machwe, Curr. Sci. (India), 5_~i, No. 13, 657-659 (1982). 14. M. D. Galanin, A. A. Kutenkov, V. N. Smorchkov, et al., Opt. Spektrosk., 53, No. 4, 683-689 (1982). 15. V. Ya. Artyukhov, R. T. Kuznetsova, and R. M. Fofonova, Zh. Prikl. Spektrosk., 37, No. 4, 576-580 (1982). 16. F. V. Schaefer (ed.), Dye Lasers, Springer, New York (1977). VIBRATIONAL SPECTRA AND CONFORMATIONAL C~9OSITION OF ETHYLENE GLYCOL DINITRATE IN SOLID PHASES G. A. Beresneva, L. V. Khristenko, UDC 539.194.01 S. V. Krasnoshchekov, and Yu. A. Pentin The authors of [i] studied the vibrational spectra of ethylene glycol dinitrate (EGDN) and showed that in the liquid state this compound consists of a mixture of conformers, while in the crystalline state it exists in the form of two modifications: a metastable one (crystal II), obtained by intense supercooling the liquid, and a stable modification (crystal I) obtained by either slowly cooling the liquid, or by heating the metastable modification to a temperature of -50~ If we assume that in a restrained internal rotation around the C--C and C--O bonds, the staggered conformations will be stable, while the --C-~NO= groups are planar, then EGDN can exist in the form of ten different nuclear equilibrium configurations. Figure i shows these possible conformations of EGDN. The authors of [i] suggested that each of the solid modifications is formed by only one of the ten possible conformers, which were identified from the data of rotation isomerism of ethyl nitrate [2] and the results of vibrational calculation carried out in [3], using force constants obtained by the MINDO/2 method. In this present work, the IR spectra of crystals I and II were recorded on a Bruker Fourier-type spectrometer with a higher,resolution than that obtained in [i], including the region below 400 cm -I, in which the IR spectra of crystals have not yet been studied. Figure 2 shows the IR spectra of a vitreous EGDN and two of its crystalline modifications (I and II). In the spectrum of crystal II in the 100-900 cm -I region, a region of skeletal stretch- ing and deformational vibrations, which are most sensitive to rotation isomerism, the number of bands exceeds that required for one nuclear configuration at equilibrium. On crystal II § crystal I transition, the bands at 213, 390, 588, 662, 715, 862, 928, i036,1237, 1392, 1431, 1460, and 1646 cm -i disappear. Bands at 364, 405, 581, 656, 680, 937, 1044, 1232, 1309, 1396, 1422, 1449, and 1666 cm -~, with a low intensity in the spectrum of crystal II, become markedly more intense, and the number of bands in the spectrum of crystal I in the 100-900 cm -i region corresponds to the number of bands for one Conformer. These facts indicate that crystal II is formed by at least two conformers, and crystal I by one conformer, and the conformer forming crystal I is also included in the composition of crystal II. For a more reliable identification of the conformers forming crystals I and II, we calculated the frequencies and forms of normal vibrations of all the ten possible conformers of EGDN. The calculations were carried out in an independent system of local symmetry co- ordinates, by a standard method [4]. The natural coordinates introduced, which are repre- Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 48, No. 6, pp. 946-952, June, 1988. Original article submitted April 8, 1987. 614 0021-9037/88/4806-0614512.50 x0e9 1988 Plenum Publishing Corporation

Vibrational spectra and calculation of the noemal vibrations of 1,3-dimethyl-1,1,3,3-tetrachlorodisiloxane

We have recorded the IR spectra of DMTChDS in the gaseous, liquid, and crystalline states and the Raman spectra in the liquid and crystalline states (Fig. I). The frequencies and forms of the normal vibrations of this molecule have been calculated in order to provide a more reliable interpretation of the vibrational spectra. On account of the lack of data concerning the geometry of this molecule, data on hexachlorodisiloxane (HChDS) and hexamethy~disiloxaneo(HMDS) from [2, 3] were employed. The following parameters were used: RSi 0 1.60 A, RSi C 1.88 A, RSiCI 2.01 ~, RCH 1.09 ~, SiOSi 146 ~ The angles at the Si atoms were assumed to be tetrahedral. Retarded internal rotation around the Si--O bonds is possible in DMTChDS as a result of which this molecule can exist in the form of several conformers of C~, Cs, C2~ and C~ v symmetry. In carrying out the calculations it was assumed that one of the SiC1 or SiC bonds of the CH3CI2Si-groups lies on the SiOSi plane in a trans-position with respect to the SiO bond (Fig. 2) althongh in [2] it was concluded that there is some deviation from the planar structure of the trans-chain in HChDS. We carried out calculations for all four conformers using the one and the same force constant matrix which was set up using data on the force fields obtained in [4] for HChDS and H}fDS. No additional refinement of the force field was carried out. The results of the calculations are shown in Table i. The calculation enabled one to assign the experimental frequencies using the calculated forms of the vibrations. There is no doubt concerning the assignment of tNe frequencies of 2990 and 2918 cm -I to the ~(CH)as and ~(CH) s valence vibrations respectively and the frequencies of 1405 and 1270 cm -I to the ~(CH3)as and ~(CH3)s deformation vibrations. The absorption bands in the 760-850 cm -I region are assigned to p(CH3) and, moreover, the vibration with a frequency at around 800 cm -: is very strongly mixed with v(SiO) s. The antisymmetric v(SiO)as vibration appears in the spectrum as a strong broad band the position of which varies somewhat upon passing from the liquid to the crystal (1095 cm -~ in the liquid and 1145 cm -: in the crystal) which may be associated with an increase in the SiOSi angle in the crystal in comparison with this angle in the liquid [5-7]~ Two frequencies, 680 and 645 cm -~, may be assigned to the ~(SiO) s vibration. The first only appears in the IR spectrum as a very weak band which is most probably a combination frequency or an overtone and it is therefore more reasonable to assign the weak band at 645 cm -~ in the IR and Raman spectra to ~(SiO) s. It is partially polarized in the Raman spectrum. The weak, depolarized band in the Raman spectrum at 755 cm -~ is assigned to the v(SiC) valence vibration. The assignment of the valence vibrations of the SIC12 groups, the vibrational frequencies of which are shown in Table i, also does not present any significant difficulty. The assignment of the deformation vibrations of the CH3CI2Si-fragment is considerably more difficult. These vibrations are very strongly mixed with one another and any specific assignments can only be made provisionally (Table i).

Potential function of the internal rotation of a methacrolein molecule in the ground (S 0) electronic state

The structural parameters of s-trans- and s-cis-isomers of a methacrolein molecule in the ground (S0) electronic state are determined by means of MP2 method with the cc-pVTZ basis set. Kinematic factor F(φ) is expanded in a Fourier series. The potential function of internal rotation (PFIR) of methacrolein in this state is built using experimental frequencies of transitions of the torsional vibration of both isomers, obtained from an analysis of the vibrational structure of the high-resolution UV spectrum with allowance for the geometry and difference between the energy (ΔH) of the isomers. It is shown that the Vn parameters of the potential function of internal rotation of the molecule, built using the frequencies of the transition of the torsional vibrations of s-trans- and s-cis-isomers of the methacrolein molecule, determined from vibrational structure of the high-resolution UV spectrum and the FTIR spectrum, are close.

The internal rotation potential functions of the methacryloyl chloride molecule in the ground and excited electronic states

The systems of torsional vibration levels of the trans and cis methacryloyl chloride isomers in the ground (S0) and excited (S1) electronic states obtained by analyzing the vibrational structure of the gas-phase UV spectrum were used to reproduce the internal rotation potential functions of the molecule in both electronic states. The kinematic F factor in the S0 and S1 electronic states was calculated taking into account the relaxation of geometric parameters depending on the internal rotation angle. The internal rotation potential function parameters in the S0 state are substantially different from the parameters obtained using the torsional levels of the IR Fourier transform spectrum; at the same time, they are substantiated by quantum-mechanical calculations.

Structure of the 3,3-dimethyl-3-silathietane molecule according to data from gas-phase electron diffraction analysis with consideration of vibrational effects

The 3,3-dimethyl-3-silathietane molecule has been investigated by gas-phase electron diffraction analysis with consideration of the vibrational effects. The following geometric parameters were obtained (the distances ra, the angles L~, the errors in the form of 3o in parentheses, for ~ 50): S-C 1.853(4), Si-C m 1.870(5) (m stands for methyl), Si-C r 1.916(3) (r stands for ring), C-H 1.086(3) ~, L(C-Si-C) m = 106.9(7), L(C-Si-C) r = 86.1(3), LSi-C-S = 90.5(5), and LC-S-C = 89.5(4) ~ The fourmembered ring is nonplanar; the angle 9 between the CSiC and CSC planes equals 2 0 . 3 ( 2 0 ) ~