A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

/pdf/the-m06-suite-of-density-functionals-for-main-group-1748swzp1l.pdf

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT:  B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

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)...

Density functionals with broad applicability in chemistry.

Density functional approximations for the exchange‐correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≊EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling‐constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Gorling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence Exc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.

/pdf/rationale-for-mixing-exact-exchange-with-density-functional-19evr7wlkm.pdf

Rationale for mixing exact exchange with density functional approximations

Although the three-dimensional structures of mouse and Torpedo californica acetylcholinesterase are very similar, their responses to the covalent sulfonylating agents benzenesulfonyl fluoride and phenylmethylsulfonyl fluoride are qualitatively different. Both agents inhibit the mouse enzyme effectively by covalent modification of its active-site serine. In contrast, whereas the Torpedo enzyme is effectively inhibited by benzenesulfonyl fluoride, it is completely resistant to phenylmethylsulfonyl fluoride. A bottleneck midway down the active-site gorge in both enzymes restricts access of ligands to the active site at the bottom of the gorge. Molecular dynamics simulations revealed that the mouse enzyme is substantially more flexible than the Torpedo enzyme, suggesting that enhanced ‘breathing motions’ of the mouse enzyme relative to the Torpedo enzyme might explain why phenylmethylsulfonyl fluoride can reach the active site in mouse acetylcholinesterase, but not in the Torpedo enzyme. Accordingly, we performed docking of the two sulfonylating agents to the two enzymes, followed by molecular dynamics simulations. Whereas benzenesulfonyl fluoride closely approached the active-site serine in both mouse and Torpedo acetylcholinesterase in such simulations, phenylmethylsulfonyl fluoride was able to approach the active-site serine of mouse acetylcholinesterase - but remained trapped above the bottleneck in the case of the Torpedo enzyme. Our studies demonstrate that reliance on docking tools in drug design can produce misleading information. Docking studies should, therefore, also be complemented by molecular dynamics simulations in selection of lead compounds. Author summary Enzymes are protein molecules that catalyze chemical reactions in living organisms, and are essential for their physiological functions. Proteins have well defined three-dimensional structures, but display flexibility; it is believed that this flexibility, known as their dynamics, plays a role in their function. Here we studied the neuronal enzyme acetylcholinesterase, which breaks down the neurotransmitter, acetylcholine. The active site of this enzyme is deeply buried, and accessed by a narrow gorge. A particular inhibitor, phenylmethylsulfonyl fluoride, is known to inhibit mouse acetylcholinesterase, but not that of the electric fish, Torpedo, even though their structures are very similar. A theoretical technique called molecular dynamics (MD) shows that the mouse enzyme is more flexible than the Torpedo enzyme. Furthermore, when the movement of the inhibitor down the gorge towards the active site is simulated using MD, the phenylmethylsulfonyl fluoride can reach the active site in the mouse enzyme, but not in the Torpedo enzyme, in which it remains trapped midway down the gorge. Our study emphasizes the importance of taking into account not only structure, but also dynamics, in designing drugs targeted towards proteins.

/pdf/molecular-dynamics-simulations-of-the-interaction-of-mouse-1s1vbc7wbw.pdf

Molecular Dynamics Simulations of the Interaction of Mouse and Torpedo Acetylcholinesterase with Covalent Inhibitors Explain Their Differential Reactivity: Implications for Drug Design

The heats of formation of haloacetylenes are evaluated using the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects, and (where relevant) first-order spin-orbit coupling. The heats of formation determined using W2 theory are: \hof(HCCH) = 54.48 kcal/mol, \hof(HCCF) = 25.15 kcal/mol, \hof(FCCF) = 1.38 kcal/mol, \hof(HCCCl) = 54.83 kcal/mol, \hof(ClCCCl) = 56.21 kcal/mol, and \hof(FCCCl) = 28.47 kcal/mol. Enthalpies of hydrogenation and destabilization energies relative to acetylene were obtained at the W1 level of theory. So doing we find the following destabilization order for acetylenes: FCCF $>$ ClCCF $>$ HCCF $>$ ClCCCl $>$ HCCCl $>$ HCCH. By a combination of W1 theory and isodesmic reactions, we show that the generally accepted heat of formation of 1,2-dichloroethane should be revised to -31.8$\pm$0.6 kcal/mol, in excellent agreement with a very recent critically evaluated review. The performance of compound thermochemistry schemes such as G2, G3, G3X and CBS-QB3 theories has been analyzed.

The heats of formation of the haloacetylenes XCCY [X, Y = H, F, Cl]: basis set limit ab initio results and thermochemical analysis

On the effect of core correlation on geometries and harmonic frequencies of small polyatomics

We have investigated the title question for the W4-08 thermochemical benchmark using l-saturated truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root-mean-square (RMS) contribution of i functions to the MP2-F12 total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol for P2 and P4. However, even for these cases, basis set extrapolation from {g,h} basis sets adequately addresses the problem. Using basis sets insufficiently saturated in the spdfgh angular momenta may lead to exaggerated i function contributions. For extrapolation from spdfg and spdfgh basis sets, basis set convergence appears to be quite close to the theoretical asymptotic ∝ L–7 behavior. We hence conclude that h functions are sufficient even for highly demanding F12 applications. With one-parameter extrapolation, spdf and spdfg basis sets are adequate, aug-cc-pV{T,Q}Z-F12 yielding a RMSD = 0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b suggests our conclusions are applicable to higher-level F12 methods as well.

/pdf/mp2-f12-basis-set-convergence-near-the-complete-basis-set-104d1f2b.pdf

MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient?

For a number of different structures and states of B/sub 3/, B/sub 2/N, BN/sub 2/, and N/sub 3/, optimum geometries and harmonic spectra were obtained at the HF/6-31G* level. The relative stability of the isomers was determined using full fourth-order Moeller--Plesset theory, both with and without spin projection, as well as coupled cluster methods. Estimates for the dissociation energies are based on scaled CCD+ST(CCD) binding energies. Koopmans' vertical ionization potentials and Mulliken charge distributions, both at the UHF/6-31G* level, are quoted for the most stable isomers. B/sub 3/ is found to be an equilateral triangle in its /sup 2/A/sup '//sub 1/ ground state. B/sub 2/N has a symmetric linear arrangement in its /sup 2/..sigma../sup +//sub u/ ground state with an extremely low bending frequency (73 cm/sup -1/), and an unusually low vertical ionization potential (6.75 eV). Its asymmetric stretching (2021 cm/sup -1/) is found to be extremely intense (8782 km mol/sup -1/). BN/sub 2/ has four rather closely spaced states, of which an isosceles triangle is the absolute minimum (/sup 2/A/sub 1/ state). However, at high temperatures, an asymmetric linear arrangement (/sup 2/Pi state) is found to have equal importance, whereas a /sup 4/..sigma../sup -/ state plays a role theremore » too. The same theoretical methods correctly predict for N/sub 3/ a symmetric linear arrangement in the /sup 2/Pi/sub g/ ground state; the spectroscopic constants are found to be in reasonable agreement with experiment. Estimated dissociation energies (expected accuracy +- 4 kcal mol/sup -1/) are: B/sub 3/ 197.9, B/sub 2/N 265.0, BN/sub 2/ 224.9, N/sub 3/ 210.1 kcal mol/sup -1/.« less

Jan M. L. Martin

Papers

Molecular Dynamics Simulations of the Interaction of Mouse and Torpedo Acetylcholinesterase with Covalent Inhibitors Explain Their Differential Reactivity: Implications for Drug Design

The heats of formation of the haloacetylenes XCCY [X, Y = H, F, Cl]: basis set limit ab initio results and thermochemical analysis

On the effect of core correlation on geometries and harmonic frequencies of small polyatomics

MP2-F12 Basis Set Convergence near the Complete Basis Set Limit: Are h Functions Sufficient?

Ab initio study of boron, nitrogen, and boron--nitrogen clusters. I. Isomers and thermochemistry of B/sub 3/, B/sub 2/N, BN/sub 2/, and N/sub 3/