Stephen G. Dale

Extreme density-driven delocalization error for a model solvated-electron system

Delocalization (or charge-transfer) error is one of the scarce but spectacular failures of density-functional theory. It is particularly apparent in extensively delocalized molecules, and manifests in the calculation of bandgaps, reaction barriers, and dissociation limits. Even though delocalization error is always present in the self-consistent electron density, the differences from reference densities are often quite subtle and the error tends to be driven by the exchange-correlation energy expression. In this article, we propose a model system (the Kevan model) where approximate density functionals predict dramatically different charge distributions because of delocalization error. The model system consists of an electron trapped in a water hexamer and is a finite representation of an experimentally observed class of solids: electrides. The Kevan model is of fundamental interest because it allows the estimation of charge transfer error without recourse to fractional charge calculations, but our results are also relevant in the context of the modeling of confined electrons in density-functional theory.

Efficient basis sets for non-covalent interactions in XDM-corrected density-functional theory

In the development and application of dispersion-corrected density-functional theory, the effects of basis set incompleteness have been largely mitigated through the use of very large, nearly-complete basis sets. However, the use of such large basis sets makes application of these methods inefficient for large systems. In this work, we examine a series of basis sets, including Pople-style, correlation-consistent, and polarization-consistent bases, for their ability to efficiently and accurately predict non-covalent interactions when used in conjunction with the exchange-hole dipole moment (XDM) dispersion model. We find that the polarization-consistent 2 (pc-2) basis sets, and two modifications thereof with some diffuse functions removed, give performance of comparable quality to that obtained with aug-cc-pVTZ basis sets, while being roughly 12 to 23 times faster computationally. The behavior is explained, in part, by the role of diffuse functions in recovering small density changes in the intermolecular region. The general performance of the modified basis sets is tested by application of XDM to standard intermolecular benchmark sets at, and away from, equilibrium.

The explicit examination of the magnetic states of electrides.

Electrides are a unique class of ionic solids in which the anions are stoichiometrically replaced by electrons localised within the crystal voids. In this work, we present the first density-functional calculations to successfully reproduce the known anti-ferromagnetic behaviour of the organic electrides. Interrogation of the spin densities confirms that the localised, interstitial electrons are indeed the source of magnetism in the electride crystals. Comparison of the relative energies of the ferromagnetic and anti-ferromagnetic states allows prediction of the spin-coupling constants between electrons in neighbouring crystal voids. All major discrepancies between the calculated and experimentally-determined coupling constants reflect obvious deviations from the assumption of a simple, one-dimensional chain of interacting spins. For the electrides where such a model Hamiltonian is valid, the experimental ordering of the coupling constants is reproduced to a remarkable degree of accuracy.

Counterintuitive electron localisation from density-functional theory with polarisable solvent models.

Exploration of the solvated electron phenomena using density-functional theory (DFT) generally results in prediction of a localised electron within an induced solvent cavity. However, it is well known that DFT favours highly delocalised charges, rendering the localisation of a solvated electron unexpected. We explore the origins of this counterintuitive behaviour using a model Kevan-structure system. When a polarisable-continuum solvent model is included, it forces electron localisation by introducing a strong energetic bias that favours integer charges. This results in the formation of a large energetic barrier for charge-hopping and can cause the self-consistent field to become trapped in local minima thus converging to stable solutions that are higher in energy than the ground electronic state. Finally, since the bias towards integer charges is caused by the polarisable continuum, these findings will also apply to other classical polarisation corrections, as in combined quantum mechanics and molecular mechanics (QM/MM) methods. The implications for systems beyond the solvated electron, including cationic DNA bases, are discussed.

Kinetics of the Addition of Olefins to Si-Centered Radicals: The Critical Role of Dispersion Interactions Revealed by Theory and Experiment

Solution-phase rate constants for the addition of selected olefins to the triethylsilyl and tris(trimethylsilyl)silyl radicals are measured using laser-flash photolysis and competition kinetics. The results are compared with predictions from density functional theory (DFT) calculations, both with and without dispersion corrections obtained from the exchange-hole dipole moment (XDM) model. Without a dispersion correction, the rate constants are consistently underestimated; the errors increase with system size, up to 10(6) s(-1) for the largest system considered. Dispersion interactions preferentially stabilize the transition states relative to the separated reactants and bring the DFT-calculated rate constants into excellent agreement with experiment. Thus, dispersion interactions are found to play a key role in determining the kinetics for addition reactions, particularly those involving sterically bulky functional groups.

Theoretical Descriptors of Electrides

Electrides are ionic substances in which the anionic species is stoichiometrically replaced with localized electrons that reside within crystal voids. Originally discovered in 1983, the past decade has seen a sharp rise in the number of known electride materials, most notably the isolation of the first air- and water-stable electride. As the presence of localized interstitial electrons cannot be directly detected experimentally, researchers have turned to density-functional theory (DFT) to discover new electrides. In this work, we survey eight common theoretical descriptors of electrides for their efficacy in identifying these materials. Illustrative examples are presented for all classes of electrides: organic, inorganic, 2D, elemental, and molecular electrides. In general, density-based descriptors such as the electron localization function (ELF) and localized-orbital locator (LOL) are shown to be the most consistently reliable. Limitations of DFT treatments of electrides are also discussed.