A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions.

We present the GMTKN55 benchmark database for general main group thermochemistry, kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30 [Goerigk and Grimme J. Chem. Theory Comput., 2011, 7, 291], it allows assessment across a larger variety of chemical problems-with 13 new benchmark sets being presented for the first time-and it also provides reference values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calculations and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better reference values, and we re-emphasise the need for London-dispersion corrections in density functional theory (DFT) treatments of thermochemical problems, including Minnesota methods. We assessed 217 variations of dispersion-corrected and -uncorrected density functional approximations, and carried out a detailed analysis of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochemistry and noncovalent interactions, and they should be used whenever technically feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalised-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.

Automated Transition State Search and Its Application to Diverse Types of Organic Reactions.

Transition state search is at the center of multiple types of computational chemical predictions related to mechanistic investigations, reactivity and regioselectivity predictions, and catalyst design. The process of finding transition states in practice is, however, a laborious multistep operation that requires significant user involvement. Here, we report a highly automated workflow designed to locate transition states for a given elementary reaction with minimal setup overhead. The only essential inputs required from the user are the structures of the separated reactants and products. The seamless workflow combining computational technologies from the fields of cheminformatics, molecular mechanics, and quantum chemistry automatically finds the most probable correspondence between the atoms in the reactants and the products, generates a transition state guess, launches a transition state search through a combined approach involving the relaxing string method and the quadratic synchronous transit, and finally validates the transition state via the analysis of the reactive chemical bonds and imaginary vibrational frequencies as well as by the intrinsic reaction coordinate method. Our approach does not target any specific reaction type, nor does it depend on training data; instead, it is meant to be of general applicability for a wide variety of reaction types. The workflow is highly flexible, permitting modifications such as a choice of accuracy, level of theory, basis set, or solvation treatment. Successfully located transition states can be used for setting up transition state guesses in related reactions, saving computational time and increasing the probability of success. The utility and performance of the method are demonstrated in applications to transition state searches in reactions typical for organic chemistry, medicinal chemistry, and homogeneous catalysis research. In particular, applications of our code to Michael additions, hydrogen abstractions, Diels-Alder cycloadditions, carbene insertions, and an enzyme reaction model involving a molybdenum complex are shown and discussed.

Towards full Quantum-Mechanics-based Protein-Ligand Binding Affinities.

Computational methods play a key role in modern drug design in the pharmaceutical industry but are mostly based on force fields, which are limited in accuracy when describing non-classical binding effects, proton transfer, or metal coordination. Here, we propose a general fully quantum mechanical (QM) scheme for the computation of protein-ligand affinities. It works on a single protein cutout (of about 1000 atoms) and evaluates all contributions (interaction energy, solvation, thermostatistical) to absolute binding free energy on the highest feasible QM level. The methodology is tested on two different protein targets: activated serine protease factor X (FXa) and tyrosine-protein kinase 2 (TYK2). We demonstrate that the geometry of the model systems can be efficiently energy-minimized by using general purpose graphics processing units, resulting in structures that are close to the co-crystallized protein-ligand structures. Our best calculations at a hybrid DFT level (PBEh-3c composite method) for the FXa ligand set result in an overall mean absolute deviation as low as 2.1 kcal mol-1 . Though very encouraging, an analysis of outliers indicates that the structure optimization level, conformational sampling, and solvation treatment require further improvement.

Dispersion-corrected density functional theory for aromatic interactions in complex systems.

Aromatic interactions play a key role in many chemical and biological systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with standard wave function theory (WFT). Although density functional theory (DFT) can easily treat systems of more than 200 atoms, standard semilocal (hybrid) density functional approximations fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramolecular noncovalent interactions. Therefore dispersion-corrected DFT provides a unique tool for the investigation and analysis of a wide range of complex aromatic systems. In this Account, we start with an analysis of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The minima for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of saturated and aromatic model complexes, we show that increased dispersion coefficients for sp(2)-hybridized carbon atoms play a major role in aromatic stacking. Modern dispersion-corrected DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate reference data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, density-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramolecular interactions that arise in the molecular crystals of aromatic molecules. In studies of hexahelicene, dispersion-corrected DFT yields "the right answer for the right reason". By comparison, standard DFT calculations reproduce intramolecular distances quite accurately in single-molecule calculations while inter- and intramolecular distances become too large when dispersion-uncorrected solid-state calculations are carried out. Dispersion-corrected DFT can fix this problem, and these results are in excellent agreement with experimental structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calculations for the formation of a cationic, quadruply charged dimer of a porphyrin derivative, a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-corrected DFT with an adequate continuum solvation model can accurately reproduce experimental free association enthalpies in solution. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qualitatively or quantitatively correct picture of the interactions of this complex.

Splitting of dihydrogen by five-membered zirconacycloallenoids: a novel pathway to conjugated diene zirconocene complexes.

The five-membered zirconacycloallenoids 2 react rapidly with dihydrogen under mild conditions to yield the corresponding (s-cis-conjugated diene)zirconocenes 3. The reaction involves splitting of the H(2) molecule between the metal center and a ligand carbon atom.

A DFT-D study of structural and energetic properties of TiO2 modifications.

The structures and relative energies of the three naturally occurring modifications of titanium dioxide (rutile, brookite and anatase) were investigated. For an accurate description, atom-pairwise dispersion-corrected density functional theory (DFT-D) was applied. The DFT-D3 scheme was extended non-empirically to improve the description of Ti atoms in bulk systems. New dispersion coefficients were derived from TDDFT calculations for electrostatically embedded TiO(2) clusters. The dispersion coefficient [Formula: see text] is reduced by a factor of 18 compared to the free atom. The three TiO(2) modifications were optimized in periodic plane-wave calculations with dispersion-corrected GGA (PBE, revPBE) and hybrid density functionals (PBE0, revPBE0). The calculated lattice parameters are in good agreement with experimental data, in particular the dispersion-corrected PBE0 and revPBE0 hybrid functionals. Although the observed relative stabilities could not be reproduced in all cases, dispersion corrections improve the results. For an accurate description of bulk metal oxides, London dispersion is a prominent force that should not be neglected when energies and structures are computed with DFT. Additionally, the influence of dispersion interactions on the relaxation of the TiO(2)(110) surface is investigated.

System-dependent dispersion coefficients for the DFT-D3 treatment of adsorption processes on ionic surfaces.

Dispersion-corrected density functional theory calculations (DFT-D3) were performed for the adsorption of CO on MgO and C(2) H(2) on NaCl surfaces. An extension of our non-empirical scheme for the computation of atom-in-molecules dispersion coefficients is proposed. It is based on electrostatically embedded M(4)X(4) (M=Na, Mg) clusters that are used in TDDFT calculations of dynamic dipole polarizabilities. We find that the C(MM)(6) dispersion coefficients for bulk NaCl and MgO are reduced by factors of about 100 and 35 for Na and Mg, respectively, compared to the values of the free atoms. These are used in periodic DFT calculations with the revPBE semi-local density functional. As demonstrated by calculations of adsorption potential energy curves, the new C(6) coefficients lead to much more accurate energies (E(ads)) and molecule-surface distances than with previous DFT-D schemes. For NaCl/C(2) H(2) we obtained at the revPBE-D3(BJ) level a value of E(ads) =-7.4 kcal mol(-1) in good agreement with experimental data (-5.7 to -7.1 kcal mol(-1)). Dispersion-uncorrected DFT yields an unbound surface state. For the MgO/CO system, the computed revPBE-D3(BJ) value of E(ads) =-4.1 kcal mol(-1) is also in reasonable agreement with experimental results (-3.0 kcal mol(-1)) when thermal corrections are taken into account. Our new dispersion correction also improves computed lattice constants of the bulk systems significantly compared to plain DFT or previous DFT-D results. The extended DFT-D3 scheme also provides accurate non-covalent interactions for ionic systems without empirical adjustments and is suggested as a general tool in surface science.

Effect of the damping function in dispersion corrected density functional theory.

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.

The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.