Accuracy of Density Functionals in the Prediction of Electronic Proton Affinities of Amino Acid Side Chains

The ionization states of amino acids influence the structure, function, stability, solubility, and reactivity of proteins and are difficult to determine unambiguously by experimental means. Thus, it is very important to be able to determine them theoretically and with high reliability. We have analyzed how well DFT functionals, often used to characterize complex and large models such as proteins, describe the zero-point-exclusive proton affinity at 0 K, PA(el)(0K), for the ionizable side chains of lysine (Lys), histidine (His), arginine (Arg), and aspartate (Asp(-)) as well as the cysteine (Cys(-)), serine (Ser(-)), and tyrosine (Tyr(-)) anions. The reference values PA(el)(0K) were determined at the very accurate CCSD(T)/CBS level. Those values were obtained by the sum of the complete basis set limit of the MP2 energies plus a CCSD(T) correction term evaluated with the aug-cc-pVTZ basis set. The complete basis set limit of MP2 energies was determined using the Truhlar and Helgaker extrapolation schemes. A new, important, and consistent DFT benchmarking database for PA(el)(0K) and for proton transfer between two different ionizable side chains, Delta PA(el)(0K), is provided, making this work relevant to all studies with ionizable amino acids side chains that use DFT. Among the 64 density functionals tested, the MPW1B95-D3, XYG3, MPW1B95, B1B95-D3, BMK, BMK-D3, M06-2X, B1LYP, B1B95, PBE1PBE, CAM-B3LYP, B97-1, PBE1KCIS, B3P86, CAM-B3LYP-D3, B3LYP, B98, M06-L, and M06 provide the most accurate PA(el)(0K) values for all ionizable amino acids studied, with errors below 1.5 kcal/mol, which translate into an error of less than 1 pK(a) unit in solution. Furthermore, among the best rated to predict PA(el)(0K), we have found that M06-2X was the most accurate density functional for proton transfers between different amino acids.