Calculation of the energies of torsional states for dihydroxybenzenes

Abstract

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]:

Dynamics of wavepacket tunneling in a periodic double-well potential

“…For most non-rigid molecules with internal rotation, the inertial parameter B(γ) is an even periodic function with a weak dependence on the torsion angle. However, an uneven term can appear in the Fourier expansion of B(γ) for objects with two internal tops [10]. We note that the asymmetry of the inertial parameter, like the potential function, destroys the coherent tunneling conditions.…”

Calculation of transition intensities for torsional vibrations in IR and Raman spectra of dihydroxybenzenes

“…2 and 3, a). The transitions 11 → 13, 12 → 14, 12 → 23, 21 → 41, 21 → 32, and 22 → 24 are connected with the most intense bands in the IR spectrum of hydroquinone, where each pair of numbers determines the numbering of unperturbed torsional states of the hydroxyl groups [27]. The most intense Raman lines are due to the transitions 11 → 41, 11 → 32, 21 → 24, 22 → 41, and 22 → 32.…”

“…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…”

“…For calculation of integrals (2) and (5), we used zero-th approximation torsional functions [27], since using first-approximation functions requires a significant increase in the calculation time and does not lead to a qualitative or substantial quantitative change in the intensity distribution in the spectrum. We used a Lorentzian function for the contour functions L(ν ij , ν).…”

“…1a. The experimental structural geometry from [10] was used to calculate the torsional inertial parameters B g 1 g 1 and B g 2 g 2 [27].…”