We present theoretical models and results of calculations of the energies of torsional states of dihydroxybenzenes: flexible molecules with two non-coaxial internal tops of low symmetry.Introduction. Dihydroxybenzenes (dihydric phenols), containing a six-membered ring in their molecules, are aromatic compounds widely distributed in nature and used for practical purposes. Thus dihydroxybenzenes are included as a basic structural unit in gas-filled polymers (foam plastics) which, owing to their unique combination of low density and high strength with exceptionally good soundproofing and thermal insulation properties, have been widely used in various areas of human activity [1].The properties of dihydroxybenzenes vary depending on the relative positions of the OH groups (1,2-, 1,3-, or 1,4-substitution), which also affects the properties of the final product (the polymer). The relative positions of the OH groups also has a substantial effect on the torsional spectra of the dihydroxybenzenes resulting from internal rotations of the hydroxyl groups relative to the core of the molecule (the benzene ring).Spectral structural analysis of dihydroxybenzenes and their derivatives has mainly been carried out with respect to the fundamental vibrational frequencies [2]. Until recently, there was virtually no proper attention paid to the problem of calculating and interpreting the high-resolution torsional spectra, lying in the far IR and microwave regions, for flexible molecules with two non-coaxial internal tops. The major approaches making it possible to calculate the energy states for multi-dimensional torsional motion do not differ in principle from the one-dimensional case [3,4]. However, their application at the moment is limited to compounds containing highly symmetric internal tops (with a three-fold symmetry axis) [5], because the mathematical apparatus needed for the calculation becomes considerably more complicated when going to a two-dimensional model.In this paper, we present the results of a theoretical calculation of the energies of the torsional states of 1,2-, 1,3-, and 1,4-dihydroxybenzene molecules, taking into account interaction between the hydroxyl groups.Procedure. The rotational-torsional Hamiltonian (in cm -1 ) of a flexible molecule with two internal tops has the form [4]:

We present the calculated intensity distributions in torsional-rotational IR absorption bands of hydrogen peroxide. The torsional components of the band intensities have been calculated based on the appropriate matrix element computations. The contribution of the rotational components has been calculated using the 3j-symbols technique. The calculations have proved the reliability of available data on rotational constants, barrier heights of internal rotation, and locations of torsional-rotational levels of hydrogen peroxide.Introduction. Hydrogen peroxide is the simplest non-rigid molecule and has served for a long time [1][2][3][4][5] and continues to serve [6-9] as the subject of spectral research and quantum-chemical calculations of the geometry and electronic structure [10-15]. On one hand, this is due to the comparative simplicity of the molecular structure; on the other, to the ability of the hydroxyls to rotate internally and form a complicated torsional-rotational spectrum. Research of the last decades has shown convincingly that very simple peroxides and their fragments that are present in trace quantities in the upper layers of the atmosphere have a destructive effect on the ozone layer of the earth [12,16]. Therefore, the study of the spectral characteristics of these compounds is of great interest.Energy states, frequencies of torsional and torsional-rotational transitions, and group theory approaches to establishing selection rules in IR and Raman spectra have been calculated several times [4,5,7,8,[17][18][19][20]. Nevertheless, intensities of rotational components of torsional transitions of hydrogen peroxide in the far IR region have not been calculated. Because heights of torsional barriers, the position of torsional-rotational energy levels, and rotational constants of H 2 O 2 are used as starting data to calculate absorption band intensities due to torsional-rotational transitions, the agreement of the calculated and experimental band intensities would provide additional confirmation that the calculated frequencies of torsional-rotational spectra that were calculated earlier are correct.Herein the intensity distribution in the torsional-rotational IR absorption of hydrogen peroxide is calculated based on computation of matrix elements of the dipole moment components and use of the 3j-symbols technique.Experimental. It is known [21] that the integral extinction coefficient, which is responsible for the intensity distribution in the IR absorption spectrum, is defined by the expression

We have obtained an analytical expression for the two-dimensional potential energy function for internal rotation in 1,2-dihydroxybenzenes, allowing us to use perturbation theory methods to calculate and interpret the torsional spectra of these compounds.

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