Ab initio Calculations of the Internal Rotation Barrier in the Dimethylacetylene Molecule

Abstract

Ab initio quantum-chemical calculations have been successfully used to study the torsional potentials of molecules (for example, [1]). At the same time, there are few calculations for compounds whose internal rotation barriers are less than kT . This is due to the fact that a comparison of the total energies of conformations with a small energy difference is insufficiently reliable. Recently, there have been a number of papers devoted to both quantum-chemical and experimental investigations of the torsional potentials of molecules with practically free internal rotation [2, 3]. The goal of the present study is to estimate the potentials of ab initio quantum-chemical calculations of internal rotation barriers well below kT . We studied dimethylacetylene (DMA), which has one of the lowest rotation barriers known in organic chemistry. DMA is a classical example of practically free relative internal rotation of methyl groups [4]. The rotation barrier for this compound is rather low, and attempts at determining its value have long been unsuccessful [5–7]. The rotation barrier for the methyl groups in DMA was first determined in 1971 [8]. According to the results of this work, it is ∼ 48 J/mole. Later, owing to the development of spectral techniques, the value of the rotation barrier in DMA was established more reliably. According to the data based on interpretation of a vibrational spectrum of DMA in the region 1000–1100 cm−1 taken with a resolution of 0.0014 cm−1, the internal rotation barrier is 62.2 ± 1.0 J/mole [9, 10]. In addition, in the papers cited, it is noted that the position of the minimum of the torsional potential cannot be determined by IR spectroscopy. In another study, an analysis of an IR spectrum of DMA recorded in the range 2955–3065 cm−1 with a resolution of 0.0028 cm−1 gave a value of 75.60± 0.41 J/mole for the rotation barrier [11]. In the first ab initio quantum-chemical investigations, the internal rotation of the methyl groups of DMA was ignored. In papers describing calculations for DMA, the type of conformation (eclipsed or skewed) considered is not indicated and the rotation of the substituent around the threefold axis of the acetylene bond is ignored [12, 13]. In [14], the difference in energy between the DMA conformations is estimated in ab initio calculations. For the skew conformation, the value of the barrier calculated by the HF/4-31G method is 30 kJ/mole. In the present work, we calculated the energy difference between the skew (D3d) and eclipsed (D3h) conformations of DMA. The GAUSSIAN-94 software package was used [15]. The geometry was optimized using the HF, BLYP, B3LYP, and MP2 methods and sets of basis functions from 6-31G(d) to 6-311G++(3df , 3p). Calculations of the conformers with a fixed torsion angle were carried out with full optimization of the remaining geometrical parameters. The energies of the conformers were refined by the MP4 method, and their structures were optimized by the MP2 method. The calculations showed that the eclipsed conformer of symmetry D3h is more stable. This agrees with the conclusion of [14]. The difference in bond lengths between the examined structures of the DMA molecule is extremely small and does not exceed 0.004–0.006 pm for different methods. The variations in the electronic structure of DMA for the values of the torsion angle considered are also inappreciable.