Benzenium−Ethene Complex: A Fundamental Problem for Standard Second-Order Møller−Plesset Theory

MOLECULAR BIOLOGY AT THE QUANTUM LEVEL: CAN MODERN DENSITY FUNCTIONAL THEORY FORGE THE PATH?

Recent years have seen vast improvements in the ability of rigorous quantum-mechanical methods to treat systems of interest to molecular biology. In this review article, we survey common computational methods used to study such large, weakly bound systems, starting from classical simulations and reaching to quantum chemistry and density functional theory. We sketch their underlying frameworks and investigate their strengths and weaknesses when applied to potentially large biomolecules. In particular, density functional theory — a framework that can treat thousands of atoms on firm theoretical ground — can now accurately describe systems dominated by weak van der Waals interactions. This newfound ability has rekindled interest in using this tried-and-true approach to investigate biological systems of real importance. In this review, we focus on some new methods within the density functional theory that allow for accurate inclusion of the weak interactions that dominate binding in biological macromolecules. Recent work utilizing these methods to study biologically relevant systems will be highlighted, and a vision for the future of density functional theory within molecular biology will be discussed.

Obtaining Good Performance With Triple-ζ-Type Basis Sets in Double-Hybrid Density Functional Theory Procedures

A variety of combinations of B-LYP-based double-hybrid density functional theory (DHDFT) procedures and basis sets have been examined. A general observation is that the optimal combination of exchange contributions is in the proximity of 30% Becke 1988 (B88) exchange and 70% Hartree-Fock (HF) exchange, while for the correlation contributions, the use of independently optimized spin-component-scaled Møller-Plesset second-order perturbation theory (SCS-MP2) parameters (MP2OS and MP2SS) is beneficial. The triple-ζ Dunning aug'-cc-pVTZ+d and Pople 6-311+G(3df,2p)+d basis sets are found to be cost-effective for DHDFT methods. As a result, we have formulated the DuT-D3 DHDFT procedure, which employs the aug'-cc-pVTZ+d basis set and includes 30% B88 and 70% HF exchange energies, 59% LYP, 47% MP2OS, and 36% MP2SS correlation energies, and a D3 dispersion correction with the parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.35. Likewise, the PoT-D3 DHDFT procedure was formulated with the 6-311+G(3df,2p)+d basis set and has 32% B88 and 68% HF exchange energies, 63% LYP, 46% MP2OS, and 27% MP2SS correlation energies, and the D3 parameters s6 = 0.5, sr,6 = 1.569, and s8 = 0.30. Testing using the large E3 set of 740 energies demonstrates the robustness of these methods. Further comparisons show that the performance of these methods, particularly DuT-D3, compares favorably with the previously reported DSD-B-LYP and DSD-B-LYP-D3 methods used in conjunction with quadruple-ζ aug'-pc3+d and aug'-def2-QZVP basis sets but at lower computational expense. The previously reported ωB97X-(LP)/6-311++G(3df,3pd) procedure also performs very well. Our findings highlight the cost-effectiveness of appropriate- and moderate-sized triple-ζ basis sets in the application of DHDFT procedures.

Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals-Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions

We present an extended and improved version of our recently published database for general main group thermochemistry, kinetics, and noncovalent interactions [J. Chem. Theory Comput. 2010, 6, 107], which is dubbed GMTKN30. Furthermore, we suggest and investigate two new double-hybrid-meta-GGA density functionals called PTPSS-D3 and PWPB95-D3. PTPSS-D3 is based on reparameterized TPSS exchange and correlation contributions; PWPB95-D3 contains reparameterized PW exchange and B95 parts. Both functionals contain fixed amounts of 50% Fock-exchange. Furthermore, they include a spin-opposite scaled perturbative contribution and are combined with our latest atom-pairwise London-dispersion correction [J. Chem. Phys. 2010, 132, 154104]. When evaluated with the help of the Laplace transformation algorithm, both methods scale as N(4) with system size. The functionals are compared with the double hybrids B2PLYP-D3, B2GPPLYP-D3, DSD-BLYP-D3, and XYG3 for GMTKN30 with a quadruple-ζ basis set. PWPB95-D3 and DSD-BLYP-D3 are the best functionals in our study and turned out to be more robust than B2PLYP-D3 and XYG3. Furthermore, PWPB95-D3 is the least basis set dependent and the best functional at the triple-ζ level. For the example of transition metal carbonyls, it is shown that, mainly due to the lower amount of Fock-exchange, PWPB95-D3 and PTPSS-D3 are better applicable than the other double hybrids. Finally, we discuss in some detail the XYG3 functional [Proc. Nat. Acad. Sci. U.S.A. 2009, 106, 4963], which makes use of B3LYP orbitals and electron densities. We show that it is basically a highly nonlocal variant of B2PLYP and that its partially good performance is mainly due to a larger effective amount of perturbative correlation compared to other double hybrids. We finally recommend the PWPB95-D3 functional in general chemistry applications.