Understanding and Quantifying London Dispersion Effects in Organometallic Complexes

ConspectusQuantum 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.