Perspective: Explicitly correlated electronic structure theory for complex systems Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H Today's quantum chemistry methods are extremely powerful but rely upon complex quantities such as the massively multidimensional wavefunction or even the simpler electron density. Consequently, chemical insight and a chemist's intuition are often lost in this complexity leaving the results obtained difficult to rationalize. To handle this overabundance of information, computational chemists have developed tools and methodologies that assist in composing a more intuitive picture that permits better understanding of the intricacies of chemical behavior. In particular, the fundamental comprehension of phenomena governed by non-covalent interactions is not easily achieved in terms of either the total wavefunction or the total electron density, but can be accomplished using more informative quantities. This perspective provides an overview of these tools and methods that have been specifically developed or used to analyze, identify, quantify, and visualize non-covalent interactions. These include the quantitative energy decomposition analysis schemes and the more qualitative class of approaches such as the Non-covalent Interaction index, the Density Overlap Region Indicator, or quantum theory of atoms in molecules. Aside from the enhanced knowledge gained from these schemes, their strengths, limitations, as well as a roadmap for expanding their capabilities are emphasized. ©2017Author(s).All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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.

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.

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.

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.

The electronic correlation energy is a quantum mechanically modulated many-particle effect. In order to quantitatively describe chemical processes by quantum theory, their accurate computation is mandatory. However, (so-called) correlation is also very important for the understanding of chemistry. An example is the omnipresent van der Waals (vdW) forces that hold together most non-covalently bound matter. At large interatomic distances they are a pure correlation effect called London dispersion energy (or force).[1] If perturbation theory is applied to the electrons of interacting atoms, [2,3] two regimes can be identified (Scheme 1).At large distances, the dispersion energy is given by the well-known ÀC 6 /R 6 dependence on the interaction distance, where C 6 is a (computable) atomic or molecular dispersion coefficient.[2] In this region dispersion can be considered as the attractive part of a typical Lennard-Jones (model) potential. According to less well-known analyses, [3] at small distances, the dispersion energy becomes constant and part of the normal correlation energy. Herein, we want to establish the notion that the dispersion energy is a continuous quantity that represents a meaningful concept for all values of R (i.e. including the dashed line in Scheme 1). It can be expected that in intermediate regions, it influences the electronic energy of molecules significantly and hence has to be considered in computational thermochemistry. Note that this is not only defined for the intermolecular(atomic) situation but also for the interaction of fragments (functional groups) because of the locality of electronic structure for most chemical systems (intramolecular dispersion energy).In recent years it has become clear that standard approximations of density functional theory (DFT) not only miss the longrange dispersion energy [4][5][6] (the right part in Scheme 1) but also "under-correlate" at intermediate or short distances (originally termed "medium-range correlation" [7] or "overlap-dispersion" [8] ). Because DFT calculations are so widely used in chemistry nowadays, this topic is not only of theoretical but also of high practical interest [9] if one wants to obtain accurate chemical energetics (computational thermochemistry). Note that wavefunction-based methods such as coupled-cluster (CC) or perturbation (MP) theory naturally include dispersion (correlation) at all ranges and are free of these problems. However, because of the high computational demands, the very accurate CC theory is currently not routinely applicable to many interesting problems in supramolecular and biochemistry, surface science or for solid materials, for which DFT is often the method of choice.Although we recently published some work regarding the importance of the dispersion energy for DFT-based thermochemistry, [10][11][12] many chemists still refuse to accept the underlying concept or paradigm change. In the area of nanochemistry it is becoming more and more clear that dispersion (analogous to gravitation) is omnipresent and always...

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.

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.