Density Functionals with Broad Applicability in Chemistry

Abstract

Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy "across-the-board" for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06-2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate functional for transition metals and is the only local functional (no Hartree-Fock exchange) with better across-the-board average performance than B3LYP; this is very important because only local functionals are affordable for many demanding applications on very large systems; (d) M06-HF has good performance for valence, Rydberg, and charge transfer excited states with minimal sacrifice of ground-state accuracy. In this Account, we compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases. The tests include barrier heights, conformational energy, and the trend in bond dissociation energies of Grubbs' ruthenium catalysts for olefin metathesis. Based on these tests, we recommend (1) the M06-2X, BMK, and M05-2X functionals for main-group thermochemistry and kinetics, (2) M06-2X and M06 for systems where main-group thermochemistry, kinetics, and noncovalent interactions are all important, (3) M06-L and M06 for transition metal thermochemistry, (4) M06 for problems involving multireference rearrangements or reactions where both organic and transition-metal bonds are formed or broken, (5) M06-2X, M05-2X, M06-HF, M06, and M06-L for the study of noncovalent interactions, (6) M06-HF when the use of full Hartree-Fock e...

Enzyme Promiscuity in Enolase Superfamily. Theoretical Study of o-Succinylbenzoate Synthase Using QM/MM Methods

“…[48][49][50] In equation 1, HL stands for the high level chosen to obtain the corrected estimation of the activation free energy. In our case M06-2X/6-31+G(d,p) 34,35 has been used. HL calculations are carried out under the effect of the field created by the MM environment, where the electrostatic coupling between the QM and MM subsystems is calculated using point charges on the QM atoms.…”

Stereoselectivity induced by support confinement effects. Aza-pyridinoxazolines: A new family of C1-symmetric ligands for copper-catalyzed enantioselective cyclopropanation reactions

“…Quantum chemical calculations were carried out by means of the B3LYP 49,50 and M05-2X [41][42][43][44][45][46][47][48] hybrid functionals. Full geometrical optimizations using the 6-31G(d) basis set were carried out with the Gaussian 03 package.…”

“…Thus, a methyl 60 group in the oxazoline ring (ligand 10a') is enough to model the reaction experimentally carried out with 10a and 10b, but a bulkier tert-butyl group is necessary to account for the experimental behavior of 10c and 10d (ligand 10c' bearing a methyl group gives worse results). From the methodological 65 point of view, single-point energy calculations using the M05-2X functional [41][42][43][44][45][46][47][48] carried out on B3LYP 49,50 optimized geometries led to much better relative energies, which is necessary to account for the subtle energy differences involved in enantioselective processes. It has been reported that the hybrid meta functional M05-2X shows a superior 5 performance with respect to classical functional in the field of transition metal thermochemistry, which is of particular interest in our theoretical study.…”

“…It has been reported that the hybrid meta functional M05-2X shows a superior 5 performance with respect to classical functional in the field of transition metal thermochemistry, which is of particular interest in our theoretical study. [41][42][43][44][45][46][47][48] Figure 4 shows some selected examples of calculated TS structures and the relative energies of all the calculated TS (a few structures could not be 10 properly converged) are gathered in Table 2, together with the calculated enantioselectivities. The first observation made from the energy values in Table 2 is that conformations labeled as Λ are always less favored than the corresponding V. In addition, an inspection of the 20 transition structures revealed that the lowest energy conformations are always associated to a distal disposition of the carbonyl group with regard to the incoming alkene.…”

Reversibility and Diffusion in Mandelythiamin Decarboxylation. Searching Dynamical Effects in Decarboxylation Reactions

“…where the first term in the right-hand side of equation (2) the HL energies where obtained at the M06/6-31+G* level 24,25 of theory using Gaussian09. 26 The selected QM configurations were obtained along the AM1/MM minimum energy path traced down from the transition structure to the product and reactant valleys.…”