Symmetry properties, tunneling splittings of some vibrational energy levels and torsional IR spectra of the trans – and cis – conformers of hydroquinone molecule

Torsional vibrational states of trans − and cis − conformers belonging to point symmetry groups C_2H and C_2V, respectively, of hydroquinone molecules are classified according to the irreducible representations of the molecular symmetry group D_2H(M). A correspondence has been established between the symmetry elements of the D_2H(M) group and the symmetry elements on the torsional coordinate plane for two-dimensional surfaces of potential energy, wave functions, kinetic coefficients and dipole moment projections. A correspondence has been established between the symmetry species of the point symmetry groups C_2H, C_2V and the symmetry species of the molecular symmetry group D_2H(M). Conformational states, barriers to internal rotation and the above-mentioned characteristics of the hydroquinone molecule were calculated at the MP2/Aug-cc-pVDZ, MP2/Aug-cc-pVQZ, MP2/Aug-cc-pVTZ, MP2/CBS(aD,aT,aQ), and CCSD(T)/dAug-cc-pVDZ levels of theory. The calculated data sets were approximated using symmetry-adapted sets of basis functions. Using a numerical solution of the vibrational Schrödinger equation of restricted dimensionality, the energies and wave functions of 50 stationary torsional states of the hydroquinone molecule were determined for the first time. The values of tunneling splittings of the ground vibrational and a number of excited torsional states of trans − and cis − conformers were determined. In particular, when calculating at the MP2/CBS(aD,aT,aQ) level of theory, the values of tunneling splittings of the ground vibrational states of trans − and cis − conformers turned were 1.32*10^-6 and 1.62*10^-6 cm⁻¹, which is consistent with the experimentally established upper limit for this value in the cis − conformer by authors of [W. Caminati, S. Melandri, L. B. Favero, J.Chem.Phys., 100 (1994) 8569 – 8572] (0.2 MHz or 6.67*10^-6 cm⁻¹). The calculations of the matrix elements of the dipole moment operator and the partition function made it possible to simulate the torsional IR spectra of the molecule’s conformers at different temperatures. The frequencies of fundamental torsional vibrations in the trans – (267.1 and 269.0 cm⁻¹) and cis – (269.5 and 270.9 cm⁻¹) conformers, calculated at the MP2/CBS(aD,aT,aQ) level of theory, are in good agreement with the experimental value of frequency of this vibration (266 cm⁻¹), established in [W.G. Fateley, G.L. Carlson, F.F. Bentley, J.Phys.Chem., 79 (1975) 199–204.].