Identifying and embedding transferability in data-driven representations of chemical space.

Transferability, especially in the context of model generalization, is a paradigm of all scientific disciplines. However, the rapid advancement of machine learned model development threatens this paradigm, as it can be difficult to understand how transferability is embedded (or missed) in complex models developed using large training data sets. Two related open problems are how to identify, without relying on human intuition, what makes training data transferable; and how to embed transferability into training data. To solve both problems for ab initio chemical modelling, an indispensable tool in everyday chemistry research, we introduce a transferability assessment tool (TAT) and demonstrate it on a controllable data-driven model for developing density functional approximations (DFAs). We reveal that human intuition in the curation of training data introduces chemical biases that can hamper the transferability of data-driven DFAs. We use our TAT to motivate three transferability principles; one of which introduces the key concept of transferable diversity. Finally, we propose data curation strategies for general-purpose machine learning models in chemistry that identify and embed the transferability principles.

Size Isn't Everything: Geometric Tuning in Polycyclic Aromatic Hydrocarbons and Its Implications for Carbon Nanodots.

Recent developments in light-emitting carbon nanodots and molecular organic semiconductors have seen renewed interest in the properties of polycyclic aromatic hydrocarbons (PAHs) as a family. The networks of delocalized π electrons in sp2-hybridized carbon grant PAHs light-emissive properties right across the visible spectrum. However, the mechanistic understanding of their emission energy has been limited due to the ground state-focused methods of determination. This computational chemistry work, therefore, seeks to validate existing rules and elucidate new features and characteristics of PAHs that influence their emissions. Predictions based on (time-dependent) density functional theory account for the full 3-dimensional electronic structure of ground and excited states and reveal that twisting and near-degeneracies strongly influence emission spectra and may therefore be used to tune the color of PAHs and, hence, carbon nanodots. We particularly note that the influence of twisting goes beyond torsional destabilization of the ground-state and geometric relaxation of the excited state, with a third contribution associated with the electric transition dipole. Symmetries and peri-condensation may also have an effect, but this could not be statistically confirmed. In pursuing this goal, we demonstrate that with minimal changes to molecular size, the entire visible spectrum may be spanned by geometric modification alone; we have also provided a first estimate of emission energy for 35 molecules currently lacking published emission spectra as well as clear guidelines for when more sophisticated computational techniques are required to predict the properties of PAHs accurately.

Poisoning density functional theory with benchmark sets of difficult systems.

Large benchmark sets like GMTKN55 [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] let us analyse the performance of density functional theory over a diverse range of systems and bonding types. However, assessing over a large and diverse set can miss cases where approaches fail badly, and can give a misleading sense of security. To this end we introduce a series of 'poison' benchmark sets, P30-5, P30-10 and P30-20, comprising systems with up to 5, 10 and 20 atoms, respectively. These sets represent the most difficult-to-model systems in GMTKN55. We expect them to be useful in developing new approximations, identifying weak points in existing ones, and to aid in selecting appropriate DFAs for computational studies involving difficult physics, e.g. catalysis.

Single Excitation Energies Obtained from the Ensemble "HOMO-LUMO Gap": Exact Results and Approximations.

In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.

Linear fractional charge behavior in density functional theory through dielectric tuning of conductor-like polarizable continuum model.

A property of exact density functional theory is linear fractional charge behavior as electrons are added or removed from a molecule. Typical density functional approximations (DFAs) exhibit delocalization error, which overstabilizes this fractional charge. Conversely, solvent corrections have been shown to erroneously destabilize this fractional charge. This work will show that an implicit solvent correction with a tuned dielectric can be used as an ad hoc correction to offset the delocalizing character of DFAs and achieve linear fractional charge behavior. While desirable, in principle, we find that this linear charge behavior degrades the vertical ionization energies reported by DFAs. Our results reveal that the localizing character of the solvent correction and the Hartree-Fock (HF) exchange offset each other. This helps explain the decreased ratios of HF exchange to DFA exchange in long-range hybrid tuning studies that use a solvent correction.

Quantum Chemical Methods for Modeling Covalent Modification of Biological Thiols.

Targeted covalent inhibitor drugs require computational methods that go beyond simple molecular-mechanical force fields in order to model the chemical reactions that occur when they bind to their targets. Here, several semiempirical and density-functional theory (DFT) methods are assessed for their ability to describe the potential energy surface and reaction energies of the covalent modification of a thiol by an electrophile. Functionals such as PBE and B3LYP fail to predict a stable enolate intermediate. This is largely due to delocalization error, which spuriously stabilizes the prereaction complex, in which excess electron density is transferred from the thiolate to the electrophile. Functionals with a high-exact exchange component, range-separated DFT functionals, and variationally optimized exact exchange (i.e., the LC-B05minV functional) correct this issue to various degrees. The large gradient behavior of the exchange enhancement factor is also found to significantly affect the results, leading to the improved performance of PBE0. While ωB97X-D and M06-2X were reasonably accurate, no method provided quantitative accuracy for all three electrophiles, making this a very strenuous test of functional performance. Additionally, one drawback of M06-2X was that molecular dynamics (MD) simulations using this functional were only stable if a fine integration grid was used. The low-cost semiempirical methods, PM3, AM1, and PM7, provide a qualitatively correct description of the reaction mechanism, although the energetics is not quantitatively reliable. As a proof of concept, the potential of mean force for the addition of methylthiolate to methylvinyl ketone was calculated using quantum mechanical/molecular mechanical MD in an explicit polarizable aqueous solvent. © 2019 Wiley Periodicals, Inc.

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.

Density-functional description of alkalides: introducing the alkalide state.

Alkalides are crystalline salts in which the anion is a negatively charged alkali metal. A systematic investigation of the electronic structure of thirteen alkalides, with known crystal structures, is conducted using density-functional theory. For each alkalide, a high-lying valence state is identified that is localised on the alkali anions and is consistent with the low band gap and strong reducing power characteristic of these materials. This 'alkalide state' is compared to a similar state in the related class of electride materials, where the alkali anions are replaced by crystal voids occupied by localised, interstitial electrons. Finally, a thermodynamic cycle is constructed to examine the energy differences between the alkalides and electrides, revealing that the alkali-metal anion significantly stabilises the crystal.

Pervasive Delocalisation Error Causes Spurious Proton Transfer in Organic Acid-Base Co-Crystals.

Dispersion-corrected density-functional theory (DFT-D) methods have become the workhorse of many computational protocols for molecular crystal structure prediction due to their efficiency and convenience. However, certain limitations of DFT, such as delocalisation error, are often overlooked or are too expensive to remedy in solid-state applications. This error can lead to artificial stabilisation of charge transfer and, in this work, it is found to affect the correct identification of the protonation site in multicomponent acid-base crystals. As such, commonly used DFT-D methods cannot be applied with any reliability to the study of acid-base co-crystals or salts, while hybrid functionals remain too restrictive for routine use. This presents an impetus for the development of new functionals with reduced delocalisation error for solid-state applications; the structures studied herein constitute an excellent benchmark for this purpose.

Communication: Correct charge transfer in CT complexes from the Becke'05 density functional.

It has been known for over twenty years that density functionals of the generalized-gradient approximation (GGA) type and exact-exchange-GGA hybrids with low exact-exchange mixing fraction yield enormous errors in the properties of charge-transfer (CT) complexes. Manifestations of this error have also plagued computations of CT excitation energies. GGAs transfer far too much charge in CT complexes. This error has therefore come to be called "delocalization" error. It remains, to this day, a vexing unsolved problem in density-functional theory (DFT). Here we report that a 100% exact-exchange-based density functional known as Becke'05 or "B05" [A. D. Becke, J. Chem. Phys. 119, 2972 (2003); 122, 064101 (2005)] predicts excellent charge transfers in classic CT complexes involving the electron donors NH3, C2H4, HCN, and C2H2 and electron acceptors F2 and Cl2. Our approach is variational, as in our recent "B05min" dipole moments paper [Dale et al., J. Chem. Phys. 147, 154103 (2017)]. Therefore B05 is not only an accurate DFT for thermochemistry but is promising as a solution to the delocalization problem as well.

The ionic versus metallic nature of 2D electrides: a density-functional description.

The two-dimensional (2D) electrides are a highly unusual class of materials, possessing interstitial electron layers sandwiched between cationic atomic layers of the solid. In this work, density-functional theory, with the exchange-hole dipole moment dispersion correction, is used to investigate exfoliation and interlayer sliding of the only two experimentally known 2D electrides: [Ca2N]+e- and [Y2C]2+(2e-). Examination of the valence states during exfoliation identifies intercalated electrons in the bulk and weakly-bound surface-states in the fully-expanded case. The calculated exfoliation energies for the 2D electrides are found to be much higher than for typical 2D materials, which is attributed to the ionic nature of the electrides and the strong Coulomb forces governing the interlayer interactions. Conversely, the calculated sliding barriers are found to be quite low, comparable to those for typical 2D materials, and are effectively unchanged by exclusion of dispersion. We conjecture that the metallic nature of the interstitial electrons allows the atomic layers to move relative to each other without significantly altering the interlayer binding. Finally, comparison with previous works reveals the importance of a system-dependent dispersion correction in the density-functional treatment.

Interrogating the Becke'05 density functional for non-locality information.

In two papers, Becke [J. Chem. Phys. 119, 2972 (2003) and J. Chem. Phys. 122, 064101 (2005)] introduced Kohn-Sham density-functional approximations for static and dynamical correlation to be partnered with 100 percent exactly computed exchange. Known as "B05," this was the first non-local correlation model designed to work with the full non-locality of exact (or Hartree-Fock) exchange. Non-locality issues, often referred to as the "delocalization" problem, are among the most vexing problems in density-functional theory today. How much exact exchange should be used in a hybrid functional? What value of the range parameter should be used in a long-range corrected functional? Questions such as these abound, and the answers are system dependent. The physics of non-locality is built into the B05 functional in a natural way, and one wonders, therefore, if B05 might provide a mechanism to answer such questions. Here we explore a variational procedure, "B05min," to do so. We compute dipole moments of 52 small molecules and find that B05min delivers better moments than parent hybrid and long-range corrected functionals. Furthermore, B05min provides a priori optimum exact-exchange mixing fractions and range parameters for the parent functionals, whose values agree with literature values fit to experimental data.

Thermodynamic cycles of the alkali metal-ligand complexes central to electride formation.

Alkali metal-ligand complexes are the building blocks of the exotic organic alkalide and electride materials. In this work, density-functional theory is used to construct thermodynamic cycles for the alkali metal-ligand complexes, highlighting the energy changes that enable alkalide and electride formation. Strong alkali metal- and cation-to-ligand binding energies are predicted and Rydberg-like ground states of the alkali metal-ligand complexes are identified, consistent with previous work. Calculations on molecular electride species do not reveal consistency with the identified trends, suggesting that the molecular electrides are a class of material unto themselves. The ionisation potentials of the alkali metal-ligand complexes are calculated to be consistently between 1 and 2 eV, suggesting that a specific ionisation potential (IP) is central to electride formation. Further, the thermodynamic cycle for the simplest electride, Cs+(15C5)2e-, shows stabilisation of the solid crystal due to electride formation that is consistent in magnitude with the IP of the equivalent alkali metal-ligand complex. In light of this, computational screening of the alkali metal-ligand complexes' IP presents a new design criterion for alkalide and electride materials.

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.

Density-functional description of electrides.

Electrides are a unique class of ionic solids in which the anions are stoichiometrically replaced by electrons localised within the crystal voids. There are only nine electrides with known crystal structures and their study represents a challenge for theory. A systematic investigation of their electronic structure is conducted using semilocal density-functional theory (DFT) in this article. The band structure is calculated for each electride and a range of techniques including plots of the valence densities, procrystal densities, non-covalent interaction isosurfaces, and Bader's quantum-chemical topology are applied. All of these methods provide consistent results, confirming the presence of localised interstitial electrons and demonstrating that these crystals display a characteristic electronic structure.

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.

Anion photoelectron spectra and ab initio calculations of the iodide-carbon monoxide clusters: I(-)···(CO)(n), n = 1-4.

Anion photoelectron spectra are reported for the iodide-carbon monoxide clusters, with supporting ab initio calculations for the 1:1 dimer anion and neutral complexes. A C(s) minimum geometry is predicted for the anion complex, while for the neutral complex two linear van der Waals minima are predicted differing in the attachment point of the iodine, that is, I···CO and I···OC. The predicted adiabatic photodetachment energy agrees well with the experimental spectrum. The photoelectron spectra feature a vibrational progression in the CO stretching mode, which becomes more pronounced for the larger clusters.