Understanding and Quantifying London Dispersion Effects in Organometallic Complexes

A generally applicable atomic-charge dependent London dispersion correction

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.

Rotational dynamics of the organic bridging linkers in metal–organic frameworks and their substituent effects on the rotational energy barrier

Organic bridging linkers or ligands play an important role in gas and fuel storage, CO₂ capture, and controlling the radical polymerization reactions in metal–organic frameworks (MOFs) nanochannels. The rotation of the linkers causes the expansion of the pore size and pore volume in MOFs. To understand the rotational behavior of organic linkers in MOFs and the substituent effects of the linkers, we investigated the equilibrium structure, stability, potential energy curves (PECs), and rotational energy barriers of the organic bridging linkers of a series of MOF model systems imposing three constrained imaginary planes. Both the dispersion-uncorrected and dispersion-corrected density functional theory (DFT and DFT-D i.e. B3LYP and B3LYP-D3) methods with the correlation consistent double-ζ quality basis sets have been applied to study the model MOF systems [Cu₄(X)(Y)₆(NH₃)₄] (where X = organic bridging linker, and Y = HCO₂). The present study found that the structural parameters and rotational energy barrier of the model MOF containing 1,4-benzendicarboxylate (BDC) linker are in accord with previous experiments. This study reveals that rotational barriers significantly differ depending on the substituents of organic linkers, and the linker dynamical rotation provides information about the framework flexibility with various potential applications in porous materials science. Changing the linkers in the MOFs could be helpful for designing various new kinds of flexible MOFs which will have many important applications in gas storage and separation, catalysis, polymerization, sensing, etc.

Organic bridging linkers or ligands play an important role in gas and fuel storage, CO₂ capture, and controlling the radical polymerization reactions in metal–organic framework (MOF) nanochannels.

London dispersion effects in the coordination and activation of alkanes in σ-complexes: a local energy decomposition study

The coupled-cluster-based local energy decomposition (LED) analysis is used to elucidate the nature of the TM–alkane interaction in alkane σ-complexes.