Relative energetics of acetyl-histidine protomers with and without Zn2+ and a benchmark of energy methods

We studied acetylhistidine (AcH), bare or microsolvated with a zinc cation by simulations in isolation. First, a global search for minima of the potential energy surface combining both, empirical and first-principles methods, is performed individually for either one of five possible protonation states. Comparing the most stable structures between tautomeric forms of negatively charged AcH shows a clear preference for conformers with the neutral imidazole ring protonated at the N-epsilon-2 atom. When adding a zinc cation to the system, the situation is reversed and N-delta-1-protonated structures are energetically more favorable. Obtained minima structures then served as basis for a benchmark study to examine the goodness of commonly applied levels of theory, i.e. force fields, semi-empirical methods, density-functional approximations (DFA), and wavefunction-based methods with respect to high-level coupled-cluster calculations, i.e. the DLPNO-CCSD(T) method. All tested force fields and semi-empirical methods show a poor performance in reproducing the energy hierarchies of conformers, in particular of systems involving the zinc cation. Meta-GGA, hybrid, double hybrid DFAs, and the MP2 method are able to describe the energetics of the reference method within chemical accuracy, i.e. with a mean absolute error of less than 1kcal/mol. Best performance is found for the double hybrid DFA B3LYP+XYG3 with a mean absolute error of 0.7 kcal/mol and a maximum error of 1.8 kcal/mol. While MP2 performs similarly as B3LYP+XYG3, computational costs, i.e. timings, are increased by a factor of 4 in comparison due to the large basis sets required for accurate results.