CALCULATION OF TRANSITION INTENSITIES FOR TORSIONAL VIBRATIONS IN IR AND RAMAN SPECTRA OF DIHYDROXYBENZENES M. B. Shundalov, *1 G. A. Pitsevich, 1 M. A. Ksenofontov, 2 and D. S. Umreiko 2 UDC 539.19 We present the calculated intensity distribution for bands and lines in torsional IR and Raman spectra of di- hydroxybenzenes. The calculations were based on calculated matrix elements for the components of the dipole moment and the polarizability tensor. Key words: dihydroxybenzenes, torsional IR and Raman spectra, intensity calculations, dipole moment, polarizability tensor. Introduction. Dihydroxybenzenes, as representatives of a broad class of flexible molecules with two non-co- axial internal tops of low symmetry, having considerable practical importance [1, 2], have been the subject of many spectral studies [3–18] and also quantum chemical calculations at different levels [8, 14, 17–25]. Nevertheless, the problem of interpretation of the torsional IR and Raman spectra of dihydroxybenzenes in the 100–500 cm –1 region is far from resolved. In this work, we have calculated the intensity distribution in the torsional IR and Raman spectra of dihy- droxybenzenes, based on calculation of the matrix elements for the components of the dipole moment and the po- larizability tensor. Procedure. As we know [26], the absorption coefficient for an electric dipole transition between nondegener- ate states i → j is determined by the expression κ ij (ν) = Cν ij exp ⎛ ⎜ ⎝ − E i − E 0 kT ⎞ ⎟ ⎠ ⎡ ⎢ ⎣ 1 − exp ⎛ ⎜ ⎝ − E j − E i kT ⎞ ⎟ ⎠ ⎤ ⎥ ⎦ ⏐ µ ij⏐ 2 L (ν ij , ν) , (1) where C is some constant; the exponential factors take into account the population of the i-th state and the probability of stimulated emission, respectively; µ ij is the dipole moment matrix element; L(ν ij , ν) is the line-shape function for the contour of the spectral line for the transition. The energies of the torsional states for dihydroxybenzenes were determined using the procedure described in [27]. Calculation of the intensities in the torsional IR spectrum is thus reduced to calculation of integrals of the form (µ α ) ij = ∫ g 1 ∫ g 2 Ψ i ∗ µ α Ψ j dg 1 dg 2 , (2) where µ α are the components of the dipole moment of the molecule in a coordinate system fixed to the molecule, α = x, y, z; Ψ i and Ψ j are the torsional wavefunctions of the combining states; g 1 and g 2 are the angles of internal rotation for the hydroxyl groups. Obviously for dihydroxybenzene molecules, the dipole moment is mainly determined by the charge distribu- tion on the hydroxyl groups. If we assume that the charges vary little in transitions between different rotamers (which is confirmed by ab initio calculations), then the dipole moment of the molecule depends on the change in the coordi- * To whom correspondence should be addressed. 1 Belorussian State University, 4 prosp. Nezavisimosti, Minsk 220030. E-mail: shundalov@bsu.by, pitsevich@ bsu.by. 2 A. N. Sevchenko Institute of Applied Physical Problems (Research Institution), Belorussian State University, Minsk. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 598–603, September–October, 2007. Original article submitted May 18, 2007. Journal of Applied Spectroscopy, Vol. 74, No. 5, 2007 0021-9037/07/7405-0659 ©2007 Springer Science+Business Media, Inc. 659