Torsional barriers of substituted biphenyls calculated using density functional theory: a benchmarking study

The barriers of torsional isomerization of 13 substituted biphenyls, ranging from 7.4 to 44 kcal mol(-1), were calculated using 9 density functionals (the BP86 and B97D GGAs, the meta-GGA TPSS, hybrids B3LYP, PBE0, ωB97XD, BMK and M06-2X, as well as the double-hybrid B2PLYP), some combined with D and D3 corrections for dispersive interactions, and results were compared with experimental data. As attractive dispersive interactions between substituents had a significant impact on the geometries and stabilities of the ground and transition states of the torsional isomerization pathways, the B3LYP-D, B97-D and TPSS-D3 functionals were identified as the most promising methods, and were used to determine the torsional barriers of 33 other substituted biphenyls with known Gibbs energies of activation (6.0 to 45 kcal mol(-1)). Throughout the 46-member ensemble, results were very accurate relative to experimental values (mean deviation between -0.38 and 0.24 kcal mol(-1)), and narrow distributions of errors were obtained (root-mean-square deviations between 0.14 and 0.16 kcal mol(-1); mean absolute deviations ranging from 0.61 to 0.75 kcal mol(-1)), as long as (1) large triple-ζ basis sets were used, (2) all conformations were screened at these levels of theory, (3) electronic energies were corrected with zero-point energies and entropic contributions, and (4) solvation effects were taken into account for biphenyl derivatives bearing charged ortho-substituents. With its simple procedures, this study is intended as a benchmark for future determinations of torsional barriers of various biphenyl derivatives.