Multilevel and Density Functional Electronic Structure Calculations of Proton Affinities and Gas-Phase Basicities Involved in Biological Phosphoryl Transfer † Kevin Range, ‡,§ Carlos Silva Lo ´ pez, # Adam Moser, ‡ and Darrin M. York* ,‡ Department of Chemistry, UniVersity of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, and Departamento de Quı ´mica Orga ´ nica, UniVersidade de Vigo, Lagoas Marcosende, 36200 Vigo, Galicia, Spain ReceiVed: August 5, 2005; In Final Form: September 9, 2005 Five multilevel model chemistries (CBS-QB3, G3B3, G3MP2B3, MCG3/3, and MC-QCISD/3) and seven hybrid density functional methods (PBE0, B1B95, B3LYP, MPW1KCIS, PBE1KCIS, and MPW1B95) have been applied to the calculation of gas-phase basicity and proton affinity values for a series of 17 molecules relevant to the study of biological phosphoryl transfer. In addition, W1 calculations were performed on a subset of molecules. The accuracy of the methods was assessed and the nature of systematic errors was explored, leading to the introduction of a set of effective bond enthalpy and entropy correction terms. The multicoefficient correlation methods (MCG3/3 and MC-QCISD), with inclusion of specific zero-point scale factors, slightly outperform the other multilevel methods tested (CBS-QB3, G3B3, and G3MP2B3), with significantly less computational cost, and in the case of MC-QCISD, slightly less severe scaling. Four density functional methods, PBE1KCIS, MPW1B95, PBE0, and B1B95 perform nearly as well as the multilevel methods. These results provide an important set of benchmarks relevant to biological phosphoryl transfer reactions. 1. Introduction Proton affinities and gas-phase basicities are important thermochemical quantities required for the calculation of pK a values 1,2 and linear free energy relations. 3 Biological phosphoryl transfer reactions 4 are particularly sensitive to the protonation state. The utility of theoretical methods to provide detailed atomic-level information that may aid in the interpretation and refinement of experimental data is intimately linked to the accuracy of the underlying models. Consequently, it is important to establish benchmark comparisons between theory and experi- ment such that the limitations of current models can be characterized, and new-generation models with increased reli- ability and computational performance can be developed. A promising strategy toward the elucidation of complex chemical mechanisms of RNA catalysis, for example, is to derive highly accurate quantum models for phosphoryl transfer reactions that are sufficiently fast to be applied in linear-scaling electronic structure methods 5-8 or hybrid quantum mechanical/molecular mechanical (QM/MM) simulations. 9-11 Significant effort has been made to develop electronic structure methods that achieve chemical accuracy ((1 kcal/mol) for thermochemical properties. 12 Among two of the most promising classes of model chemistries for thermochemistry and kinetics are so-called “multilevel” and density functional methods. There is generally a tradeoff between accuracy and computational efficiency that often motivates a hierarchical strategy where a more affordable level of theory is first calibrated against experiment and/or higher level methods to establish error limits and determine sources of systematic errors. “Multilevel” methods are model chemistries that combine the results of several electronic structure calculations, and in some cases additional empirical terms, to predict energies and related quantities to high accuracy. The multilevel methods discussed in the present work include the CBS methods by Petersson and co-workers, 13-16 the Gaussian-n methods by Pople and co- workers, 17-19 the Weizmann-n methods by Martin and co- workers, 20,21 and the multicoefficient correlation methods (MCCMs) of Truhlar and co-workers. 22-25 These methods have been extensively tested and shown to be generally reliable; however, they are too computationally intensive to apply to many large biological model systems. Methods based on Kohn- Sham density functional theory (DFT) 26 provide practical alternative to the multilevel methods for larger systems. The formal O(N 3 ) scaling of DFT methods 26 is much less severe than that of most multilevel methods, and continue to improve in performance for thermochemistry and kinetics. 27,28 In the present work, five multilevel and seven hybrid density functional methods have been applied to the calculation of gas- phase basicity and proton affinity values for a series of 17 molecules relevant to the study of biological phosphoryl transfer. In addition, W1 calculations were performed on a subset of molecules that warranted further study. The accuracy of the methods was assessed and the nature of systematic errors was explored, leading to the introduction of a set of effective bond enthalpy and entropy correction terms. 2. Methods 2.1. Multilevel Methods. All electronic structure and ther- mochemical calculations were performed using the GAUSSI- AN03 (G03) suite of programs, 29 except for the coupled cluster † Part of the special issue “Donald G. Truhlar Festschrift”. * Corresponding author: Phone: (612)624-8042. Fax: (612)626-7541. E-mail: york@chem.umn.edu. Web site: http://theory.chem.umn.edu. ‡ University of Minnesota. § Present address: Department of Chemistry, Lock Haven University of Pennsylvania, Lock Haven, PA 17745. # Universidade de Vigo. 791 J. Phys. Chem. A 2006, 110, 791-797 10.1021/jp054360q CCC: $33.50 © 2006 American Chemical Society Published on Web 12/02/2005