Torsional vibrations of two thiol groups in the HSOSH, DSOSH, and DSOSD molecules: 2D PES study in CBS limit

https://doi.org/10.1016/j.vibspec.2021.103208Get rights and content

Highlights

  • Internal rotation of the two thiol groups in the HSOSH, DSOSH and DSOSD molecules was analyzed at MP2/CBS level of theory.

  • The energies of the stationary torsional states and tunneling frequencies of the trans- and cis- conformers were found.

  • The torsional wave functions were classified.

  • Features of the torsional vibrations in analyzed molecules are discussed.

Abstract

2D surfaces of potential energy, dipole moment, and kinetic coefficients associated with internal rotation of the thiol groups in the HSOSH molecule were calculated and analyzed at MP2/CBS level of theory. Two stable conformers (trans- and cis-) with very close energies were found. Torsional vibrations of the HSOSH, DSOSH, and DSOSD molecules were calculated at harmonic and anharmonic approximations as well as by numerically solving of the 2D torsional Schrödinger equation using the Fourier method for the first time. The tunneling splitting of the first thirty torsional energy levels was found. The torsional IR spectra of the trans- and cis- conformers of the three analyzed molecules were calculated at different temperatures.

Introduction

The HSOSH molecule belongs to a group of molecules described by the general formula HXYXH, where X is some atom, and Y is some atom or functional group. These molecules are characterized by the presence of two stable conformers, where tunneling is feasible between these structurally equivalent states. It can also be argued that they all belong to the C2V(M) molecular symmetry group [[1], [2], [3], [4], [5], [6]]. The structure and conformational properties of many members of this group are being actively studied. In particular, in several papers, 2D potential energy surfaces (PES) caused by the internal rotation of hydroxyl (OH) and thiol (SH) groups around single bonds were calculated in molecules: HO(CH2)OH [1,7,8], HOOOH [2,9,10], HOSOH [5], and HSSSH [11]. These studies show that the heights of potential barriers separating the conformers, their stability, and the difference in energies of the ground states of the trans- and cis- conformers differ significantly. Molecules with mixed symmetric combinations of O and S atoms (HOSOH and HSOSH), which also belong to this group, have received much less attention in the literature. Although, it is known that these molecules can be formed during volcanic eruptions [12], as well as in interstellar space [[13], [14], [15]]. In paper [16] the geometric parameters of the equilibrium configurations of the trans- and cis- conformers of the HSOSH molecule at the MP2/6-311G** level of theory were calculated. It was found that the energies of their ground states differ insignificantly. Based on the results in [16], the trans- conformer is energetically moderately preferable than the cis- conformer. At the same time, the barriers to internal rotation of thiol groups in the HSOSH molecule have yet to be calculated. The energies of the torsional states and frequencies of tunneling between the structurally equivalent configurations of the conformers of this molecule have not been found yet.

In this work, the 2D PES due to the rotation of thiol groups in the HSOSH molecule is calculated for the first time. Besides, 2D surfaces of the kinetic coefficients and components of the dipole moment of this molecule were calculated. The energies of the first thirty stationary torsional states were found and determined their symmetry ыз, which further enabled us to compute the torsional IR spectra of the trans- and cis- conformers of the molecule at different temperatures. A comparison of the kinetic coefficients, barriers to internal rotation, as well as the frequencies of torsional vibrations and tunneling frequencies of the HSOSH molecule with the comparable characteristics of the molecules of methanediol [1,3] and hydrogen trioxide [2,4], is performed.

Section snippets

Symmetry properties

Fig. 1 shows the equilibrium configurations of the trans- and cis-conformers of the HSOSH molecule.

Considering Fig. 1, it helps to see the trans- conformer of the HSOSH molecule belongs to the C2 point group, and the cis- conformer belongs to the CS point group. However, as shown in detail in [[1], [2], [3], [4]], the fact that the tunneling is feasible between structurally equivalent configurations in both conformers enables us to assign HSOSH and DOSOD molecules to the C2V(M) molecular

Calculation details

The potential energy of the HSOSH molecule and its other physical characteristics, as functions of the angles of internal rotation Uγ1,γ2, were calculated at the nodes of a two-dimensional uniform grid. The values of the torsional coordinates γ1 and γ2 on the grid were varied from 4° to 356° in steps of 8°. Thus, molecular parameters were calculated at 45 * 45 = 2025 nodes on the coordinate plane γ1,γ2. In each node, when calculating the molecular characteristics, values of the torsional

Discussion of the results

The optimization of the structure of the HSOSH molecule was performed at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of the theory. Then the values of the equilibrium geometric parameters of the trans- and cis-conformers of the molecule were extrapolated to the complete basis set (CBS) limit. Table 1, Table 2 represent the values of the geometric parameters, rotational constants, and kinetic parameters of the two conformers of the HSOSH molecule obtained at the MP2/CBS level of theory.

As follows

Conclusions

This paper is a pioneering analysis of torsional vibrations of HSOSH, DSOSH, and DSOSD molecules in the anharmonic approximation and by constructing 2D PES at the MP2/CBS level of theory, caused by rotation of thiol groups. It was found that in the analyzed molecule the energies of the trans- and cis- conformers are quite close, and the energy of the latter in the ground torsional state is only 35.6 cm−1 higher than the corresponding energy of the trans- conformer.

It was shown that the kinetic

Autors statement

G. Pitsevich - Statement of the problem, theoretical justification of the calculations, analysis of the results

A. Malevich – Development of software codes in the Mathematica shell for processing the results of calculations of 2D PES and kinematic coefficients and numerical solution of the Schrödinger equation

V. Zheutok – 2D PES calculations, visualization of results

A. Khrapunova – 2D PES calculations, contributed to the discussion of materials

U. Sapeshka – 2D PES calculations, analysis of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

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