Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains.

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.

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.

Deep Mind 21 functional does not extrapolate to transition metal chemistry.

The development of density functional approximations stands at a crossroads: while machine-learned functionals show potential to surpass their human-designed counterparts, their extrapolation to unseen chemistry lags behind. Here we assess how well the recent Deep Mind 21 (DM21) machine-learned functional [Science, 2021, 374, 1385-1389], trained on main-group chemistry, extrapolates to transition metal chemistry (TMC). We show that DM21 demonstrates comparable or occasionally superior accuracy to B3LYP for TMC, but consistently struggles with achieving self-consistent field convergence for TMC molecules. We also compare main-group and TMC machine-learning DM21 features to shed light on DM21's challenges in TMC. We finally propose strategies to overcome limitations in the extrapolative capabilities of machine-learned functionals in TMC.

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.

Permeability of Dermatological Solutes through the Short Periodicity Phase of Human Stratum Corneum Lipid Bilayers.

Determining the permeability of drug-like solutes through the densely packed and heterogeneous stratum corneum lipid layer presents a significant challenge. In this study, we employed umbrella sampling with a periodic weighing function applied to the center of mass of the lipid bilayers. Precise umbrella sampling was conducted with an interframe distance of 0.5 Å, spanning from the bilayer center to the water phase, and each frame was simulated for at least 20 ns. Autocorrelation functions, potential of mean force (PMF), and diffusivity profiles were analyzed for six solutes (testosterone, benzene, caffeine, ethanol, mannitol, and histidine). The results revealed that autocorrelations were dependent solely on the medium, whether water or lipid phase. Diffusivity and PMF profiles along the reaction coordinate were influenced by the hydrophilicity of the solute rather than its size. For hydrophobic solutes, the PMF curves exhibited a minimum at the bilayer center, while for hydrophilic solutes, the PMFs peaked at the bilayer center and lipid tails (where the lipid tails are not interacting with the cholesterol). Diffusivity curves were low at the bilayer center and water phase, with peaks observed at the headgroup or the boundary between fatty acid and cholesterol (1 nm from the bilayer center). The quantitative findings presented in this work hold significance for pharmacists and drug designers.

A step toward density benchmarking-The energy-relevant "mean field error".

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn.

Permeable Cornified Envelope Layer Regulates the Solute Transport in Human Stratum Corneum.

To unravel the diffusion mechanisms of percutaneous drug delivery, suitable numerical analysis of stratum corneum structure is essential. In this research paper, we accounted for the permeable envelope layer in the brick-and-mortar finite element models of human stratum corneum. Both penetration and desorption experiments for tritiated water were simulated by transient finite element analysis. Rivet-shaped corneodesmosomes were included in the brick and mortar model. Results showed that cornified lipid permeability (Penv) is a determinant in desorption of the solute, while lipid transverse diffusion coefficient (Dlip-trans) is prominent during penetration. These two major unknowns (Penv and Dlip-trans) were obtained by extensive fitting of the finite element model to the experimental water data. Penv and Dlip-trans were determined to be 1×10-2 cm/s and 5.7×10-10 cm2/s, respectively.

Electronic Excited States in Extreme Limits via Ensemble Density Functionals.

Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable ab initio calculations by models based on paradigmatic physics from high- and low-density limits. But, a comparable treatment of excited states lags behind. Here, we solve this outstanding problem by employing a generalization of density functional theory to ensemble states (EDFT). We thus address important paradigmatic cases of all electronic systems in strongly (low-density) and weakly (high-density) correlated regimes. We show that the high-density limit connects to recent, exactly solvable EDFT results. The low-density limit reveals an unnoticed and most unexpected result-density functionals for strictly correlated ground states can be reused directly for excited states. Nontrivial dependence on excitation structure only shows up at third leading order. Overall, our results provide foundations for effective models of excited states that interpolate between exact low- and high-density limits, which we illustrate on the cases of singlet-singlet excitations in H_{2} and a ring of quantum wells.

Toward routine Kohn-Sham inversion using the "Lieb-response" approach.

Kohn-Sham (KS) inversion, in which the effective KS mean-field potential is found for a given density, provides insights into the nature of exact density functional theory (DFT) that can be exploited for the development of density functional approximations. Unfortunately, despite significant and sustained progress in both theory and software libraries, KS inversion remains rather difficult in practice, especially in finite basis sets. The present work presents a KS inversion method, dubbed the "Lieb-response" approach, that naturally works with existing Fock-matrix DFT infrastructure in finite basis sets, is numerically efficient, and directly provides meaningful matrix and energy quantities for pure-state and ensemble systems. Some additional work yields potential. It thus enables the routine inversion of even difficult KS systems, as illustrated in a variety of problems within this work, and provides outputs that can be used for embedding schemes or machine learning of density functional approximations. The effect of finite basis sets on KS inversion is also analyzed and investigated.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

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.

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.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in ionic liquids.

We test a number of dispersion corrected versatile Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol-1 of benchmarks. This compares favorably with an accurate dispersion corrected hybrid, ωB97X-V. Our tests also reveal that PBE (Perdew-Burke-Ernzerhof GGA) calculations using the plane-wave projector augmented wave method and Gaussian Type Orbitals (GTOs) differ by less than 0.6 kJ mol-1 for ionic liquids, despite ions being difficult to evaluate in periodic cells - thus revealing that GTO benchmarks may be used also for plane-wave codes. Finally, the relatively high success of explicit van der Waals density functionals, compared to elemental and ionic dispersion models, suggests that improvements are required for low-cost dispersion correction models of ions.

Health Impact Assessment of the 2020 Washington State Wildfire Smoke Episode: Excess Health Burden Attributable to Increased PM2.5 Exposures and Potential Exposure Reductions.

Major wildfires starting in the summer of 2020 along the west coast of the United States made PM2.5 concentrations in this region rank among the highest in the world. Washington was impacted both by active wildfires in the state and aged wood smoke transported from fires in Oregon and California. This study aims to estimate the magnitude and disproportionate spatial impacts of increased PM2.5 concentrations attributable to these wildfires on population health. Daily PM2.5 concentrations for each county before and during the 2020 Washington wildfire episode (September 7-19) were obtained from regulatory air monitors. Utilizing previously established concentration-response function (CRF) of PM2.5 (CRF of total PM2.5) and odds ratio (OR) of wildfire smoke days (OR of wildfire smoke days) for mortality, we estimated excess mortality attributable to the increased PM2.5 concentrations in Washington. On average, daily PM2.5 concentrations increased 97.1 µg/m3 during the wildfire smoke episode. With CRF of total PM2.5, the 13-day exposure to wildfire smoke was estimated to lead to 92.2 (95% CI: 0.0, 178.7) more all-cause mortality cases; with OR of wildfire smoke days, 38.4 (95% CI: 0.0, 93.3) increased all-cause mortality cases and 15.1 (95% CI: 0.0, 27.9) increased respiratory mortality cases were attributable to the wildfire smoke episode. The potential impact of avoiding elevated PM2.5 exposures during wildfire events significantly reduced the mortality burden. Because wildfire smoke episodes are likely to impact the Pacific Northwest in future years, continued preparedness and mitigations to reduce exposures to wildfire smoke are necessary to avoid excess health burden.

Self-Interaction-Corrected Random Phase Approximation.

The short-range correlation energy of the random phase approximation (RPA) is too negative and is often corrected by local or nonlocal methods. These beyond-RPA corrections usually lead to a mixed performance for thermodynamics and dissociation properties. RPA+ is an additive correction based on density functional approximations that often gives realistic total energies for atoms or solids. RPA+ adds a moderate correction to the ionization energies/electron affinities of RPA but does not yield an improvement beyond RPA for atomization energies of molecules. This incompleteness results in severely underestimated atomization energies just like in RPA. Exchange-correlation kernels within the Dyson equation could simultaneously improve atomization, ionization energies, and electron affinities, but their implementation is computationally less feasible in localized basis set codes. In preceding work ( Phys. Rev. A 100, 2019022515), two of the authors proposed a computationally efficient generalized RPA+ (gRPA+) that changes RPA+ only for spin-polarized systems by making gRPA+ exact for all one-electron densities. gRPA+ was found to yield a large improvement of ionization energies and electron affinities of light atoms over RPA, and a smaller improvement over RPA+. Within this work, we investigate to what extent this improvement transfers to atomization energies, ionization energies, and electron affinities of molecules, using a modified gRPA+ (mgRPA+) method that can be applied in codes with localized basis functions. We thereby aim to understand the applicability of beyond-RPA corrections based on density functional approximations.

Ensemble generalized Kohn-Sham theory: The good, the bad, and the ugly.

Two important extensions of Kohn-Sham (KS) theory are generalized: KS theory and ensemble KS theory. The former allows for non-multiplicative potential operators and greatly facilitates practical calculations with advanced, orbital-dependent functionals. The latter allows for quantum ensembles and enables the treatment of open systems and excited states. Here, we combine the two extensions, both formally and practically, first via an exact yet complicated formalism and then via a computationally tractable variant that involves a controlled approximation of ensemble "ghost interactions" by means of an iterative algorithm. The resulting formalism is illustrated using selected examples. This opens the door to the application of generalized KS theory in more challenging quantum scenarios and to the improvement of ensemble theories for the purpose of practical and accurate calculations.

Ensemble Density Functional Theory: Insight from the Fluctuation-Dissipation Theorem.

Density functional theory can be generalized to mixtures of ground and excited states, for the purpose of determining energies of excitations using low-cost density functional approximations. Adapting approximations originally developed for ground states to work in the new setting would fast-forward progress enormously. But, previous attempts have stumbled on daunting fundamental issues. Here we show that these issues can be prevented from the outset, by using a fluctuation dissipation theorem (FDT) to dictate key functionals. We thereby show that existing exchange energy approximations are readily adapted to excited states, when combined with a rigorous exact Hartree term that is different in form from its ground state counterpart, and counterparts based on ensemble Ansatzë. Applying the FDT to correlation energies also provides insights into ground statelike and ensemble-only correlations. We thus provide a comprehensive and versatile framework for ensemble density functional approximations.

Approximately Self-Consistent Ensemble Density Functional Theory: Toward Inclusion of All Correlations.

Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground states to the practical resolution of excited states, provided newly discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of low-lying excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations.

Health Impact Assessment of PM2.5 attributable mortality from the September 2020 Washington State Wildfire Smoke Episode.

Major wildfires that started in the summer of 2020 along the west coast of the U.S. have made PM2.5 concentrations in cities in this region rank among the highest in the world. Regions of Washington were impacted by active wildfires in the state, and by aged wood smoke transported from fires in Oregon and California. This study aims to assess the population health impact of increased PM2.5 concentrations attributable to the wildfire. Average daily PM2.5 concentrations for each county before and during the 2020 Washington wildfire episode were obtained from the Washington Department of Ecology. Utilizing previously established associations of short-term mortality for PM2.5, we estimated excess mortality for Washington attributable to the increased PM2.5 levels. On average, PM2.5 concentrations increased 91.7 µg/m3 during the wildfire episode. Each week of wildfire smoke exposures was estimated to result in 87.6 (95% CI: 70.9, 103.1) cases of increased all-cause mortality, 19.1 (95% CI: 10.0, 28.2) increased cardiovascular disease deaths, and 9.4 (95% CI: 5.1, 13.5) increased respiratory disease deaths. Because wildfire smoke episodes are likely to continue impacting the Pacific Northwest in future years, continued preparedness and mitigations to reduce exposures to wildfire smoke are necessary to avoid this excess health burden.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in biomolecules.

Biomolecules have complex structures, and noncovalent interactions are crucial to determine their conformations and functionalities. It is therefore critical to be able to describe them in an accurate but efficient manner in these systems. In this context density functional theory (DFT) could provide a powerful tool to simulate biological matter either directly for relatively simple systems or coupled with classical simulations like the QM/MM (quantum mechanics/molecular mechanics) approach. Additionally, DFT could play a fundamental role to fit the parameters of classical force fields or to train machine learning potentials to perform large scale molecular dynamics simulations of biological systems. Yet, local or semi-local approximations used in DFT cannot describe van der Waals (vdW) interactions, one of the essential noncovalent interactions in biomolecules, since they lack a proper description of long range correlation effects. However, many efficient and reasonably accurate methods are now available for the description of van der Waals interactions within DFT. In this work, we establish the accuracy of several state-of-the-art vdW-aware functionals by considering 275 biomolecules including interacting DNA and RNA bases, peptides and biological inhibitors and compare our results for the energy with highly accurate wavefunction based calculations. Most methods considered here can achieve close to predictive accuracy. In particular, the non-local vdW-DF2 functional is revealed to be the best performer for biomolecules, while among the vdW-corrected DFT methods, uMBD is also recommended as a less accurate but faster alternative.