Understanding and Quantifying London Dispersion Effects in Organometallic Complexes.

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 dispersion energies in particular for metallic systems. By construction it yields results which are easily understandable due to a clear separation into hybridization and charge (oxidation) state and two- and many-body effects, respectively. Due to its high computational efficiency, the D4 dispersion model is even applicable to low-cost classical and semiempirical theoretical methods.