Understanding and Quantifying London Dispersion Effects in Organometallic Complexes

Abstract

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...

A Universal Quantitative Descriptor of the Dispersion Interaction Potential

“…First, the ad hoc introduced pre‐factor A is replaced with a well‐defined physical quantity. Second, owing to the well established dispersion correction schemes such as TS, XDM, or D3/D4, C n coefficients can be computed readily and accurately for a wide range of elements. Hence, we could now test the potential of P as a general descriptor of dispersion interaction potentials.…”

Finding chemical concepts in the Hilbert space: Coupled cluster analyses of noncovalent interactions

“…In the large majority of cases, the magnitude of the force field term, for example, the D correction, is taken as a practical estimate of its value. Although this strategy has proven extremely useful for trend studies, it has two practical shortcomings: Being independent of the details of the electronic structure of the system, many force‐field corrections are uniquely determined by its geometry. Although some recent approaches like D4 and the Tkatchenko–Scheffler method incorporate density‐dependent terms in the dispersion energy expression, it is clear that a force field term is not the ideal tool for describing charge, spin or electronic state‐dependent effects on the dispersion energy.…”

Structure Optimisation of Large Transition‐Metal Complexes with Extended Tight‐Binding Methods

“…[8] Such compounds are not only highly interesting from af undamental chemistry point of view,b ut their unique properties also make them valuable for industrial technologies.T hey are used, for example,incatalysis, [9] for fuel storage, [10,11] as semi-conductor materials, [12] in ferroelectrics, [13] as filtration or selection materials,i nb iomedical applications such as bioimaging and sensing, [14] biomimetic mineralisation, [15] or as drug delivery systems. [26] Thefocus here is on demonstrating the quality of GFN2-xTB and its precursor GFN1-xTB for the structure optimisation of transition-metal complexes and in particular of very large organometallic systems,w hich are to date not possible otherwise.T he recently published GFN2-xTB approach features less empiricism, improved electrostatic interactions (multipole terms up to atomic dipolequadrupole interactions), as well as adensity (atomic charge)dependent London dispersion energy correction [27,28] at even slightly reduced computational cost. [26] Thefocus here is on demonstrating the quality of GFN2-xTB and its precursor GFN1-xTB for the structure optimisation of transition-metal complexes and in particular of very large organometallic systems,w hich are to date not possible otherwise.T he recently published GFN2-xTB approach features less empiricism, improved electrostatic interactions (multipole terms up to atomic dipolequadrupole interactions), as well as adensity (atomic charge)dependent London dispersion energy correction [27,28] at even slightly reduced computational cost.…”

“…[16,17] Thep otential field of application for efficient SQM methods is correspondingly large.However,universally applicable methods that are fully parameterised for transition metals are mostly limited to two method families,namely the already frequently used neglect of diatomic differential overlap (NDDO) based PMx (parametric method x)m ethods [4][5][6] and the recently introduced extended tight-binding methods GFNn-xTB, [1,2] (geometries,vibrational frequencies, and noncovalent interactions extended tight binding) from our laboratory.The robustness and quality of the GFNn-xTB methods has already been demonstrated in numerous applications with apredominant focus on organic chemistry.These applications include simulations of electron ionisation mass spectra, [18] fully automated computation of spin-spin-coupled nuclear resonance spectra, [19] including conformer-rotamer ensemble generation, atomic charge generation for the new D4 dispersion correction, [20,21] geometry optimisation of lanthanoid complexes, [22] automated determination of protonation sites, [23] pK a calculation in the SAMPL6 blind challenge, [24] metadynamics-based exploration of chemical compound conformation and reaction space, [25] and few studies on organometallic systems. [26] Thefocus here is on demonstrating the quality of GFN2-xTB and its precursor GFN1-xTB for the structure optimisation of transition-metal complexes and in particular of very large organometallic systems,w hich are to date not possible otherwise.T he recently published GFN2-xTB approach features less empiricism, improved electrostatic interactions (multipole terms up to atomic dipolequadrupole interactions), as well as adensity (atomic charge)dependent London dispersion energy correction [27,28] at even slightly reduced computational cost. Theoretically it seems interesting to investigate how this improved physical description effects the performance for large "real-life" applications.…”