The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

Conspectus Quantum chemical methods are nowadays able to determine properties of larger chemical systems with high accuracy and Kohn–Sham density functional theory (DFT) in particular has proven to be robust and suitable for everyday applications of electronic structure theory. A clear disadvantage of many established standard density functional approximations like B3LYP is their inability to describe long-range electron correlation effects. The inclusion of such effects, also termed London dispersion, into DFT has been extensively researched in recent years, resulting in some efficient and routinely used correction schemes. The well-established D3 method has demonstrated its efficiency and accuracy in numerous applications since 2010. Recently, it was improved by developing the successor (termed D4) which additionally includes atomic partial charge information for the generation of pairwise dispersion coefficients. These coefficients determine the leading-order (two-body) and higher-order (three- or many-body) terms of the D4 dispersion energy which is simply added to a standard DFT energy. With its excellent accuracy-to-cost ratio, the DFT-D4 method is well suited for the determination of structures and chemical properties for molecules of most kinds. While dispersion effects in organic molecules are nowadays well studied, much less is known for organometallic complexes. For such systems, there has been a growing interest in designing dispersion-controlled reactions especially in the field of homogeneous catalysis. Here, efficient electronic structure methods are necessary for screening of promising model complexes and quantifying dispersion effects. In this Account, we describe the quality of calculated structural and thermodynamic properties in gas-phase obtained with DFT-D4 corrected methods, specifically for organometallic complexes. The physical effects leading to London dispersion interactions are briefly discussed in the picture of second-order perturbation theory. Subsequently, basic theoretical aspects of the D4 method are introduced followed by selected case studies. Several chemical examples are presented starting with the analysis of transition metal thermochemistry and noncovalent interactions for small, heavy element containing main group compounds. Computed reaction energies can only match highly accurate reference values when all energy contributions are included in the DFT treatment, thus highlighting the major role of dispersion interactions for the accurate description of thermochemistry in gas-phase. Furthermore, the correlation between structural and catalytic properties is emphasized where the accessibility of high quality structures is essential for reaction planning and catalyst design. We present calculations for aggregates of organometallic systems with intrinsically large repulsive electrostatic interactions which can be stabilized by London dispersion effects. The newly introduced inclusion of atomic charge information in the DFT-D4 model robustly leads to quantitatively improved dis...

The calculation of redox potentials by semiempirical quantum mechanical (SQM) approaches is evaluated with a focus on the recently developed GFNn-xTB methods. The assessment is based on a data set comprising 313 experimental redox potentials of small to medium-sized organic and organometallic molecules in various solvents. This compilation is termed as ROP313 (reduction and oxidation potentials 313) and divided for analysis purposes into the organic subset OROP and the organometallic subset OMROP. Corresponding data for a few common density functional theory (DFT) functionals employing extended AO basis sets and small basis-set DFT composite schemes are computed for comparison. Continuum solvation models are used to calculate the important solvation free energy contribution. The results for ROP313 show that the GFNn-xTB methods provide a robust, efficient, and generally applicable workflow for the routine calculation of redox potentials. The GFNn-xTB methods outperform the PMx competitor for the OROP subset (mean absolute deviation from the experiment, MADGFN2‑xTB = 0.30 V, MADGFN1‑xTB = 0.31 V, PM6-D3H4 = 0.61 V, PM7 = 0.60 V), almost reaching low-cost DFT quality (MADB97‑3c = 0.25 V) at drastically reduced computational cost (2–3 orders of magnitude). All SQM methods perform considerably worse for the OMROP subset. Here, the GFN2-xTB still yields semiquantitative results slightly better and more robustly than with the PMx methods (MADGFN2‑xTB = 0.74 V, PM6-D3H4 = 0.78 V, PM7 = 0.82 V). The proposed workflow enables large-scale quantum chemical computations of organic and, to a lesser extent, organometallic molecule redox potentials on common laptop computers in seconds to minutes of computation time enabling, e.g., screening of extended compound libraries.

Large transition‐metal complexes are used in numerous areas of chemistry. Computer‐aided theoretical investigations of such complexes are limited by the sheer size of real systems often consisting of hundreds to thousands of atoms. Accordingly, the development and thorough evaluation of fast semi‐empirical quantum chemistry methods that are universally applicable to a large part of the periodic table is indispensable. Herein, we report on the capability of the recently developed GFNn‐xTB method family for full quantum‐mechanical geometry optimisation of medium to very large transition‐metal complexes and organometallic supramolecular structures. The results for a specially compiled benchmark set of 145 diverse closed‐shell transition‐metal complex structures for all metals up to Hg are presented. Further the GFNn‐xTB methods are tested on three established benchmark sets regarding reaction energies and barrier heights of organometallic reactions.

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange–correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree–Fock “exact” exchange (HFX). The resulting functionals r2SCANh (10% HFX), r2SCAN0 (25% HFX), and r2SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r2SCANh-D4), 16% (r2SCAN0-D4), and 1% (r2SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r2SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r2SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r2SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r2SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.