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.

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.

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.

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.

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.

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.

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.

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.

Faraday cage screening reveals intrinsic aspects of the van der Waals attraction.

General properties of the recently observed screening of the van der Waals (vdW) attraction between a silica substrate and silica tip by insertion of graphene are predicted using basic theory and first-principles calculations. Results are then focused on possible practical applications, as well as an understanding of the nature of vdW attraction, considering recent discoveries showing it competing against covalent and ionic bonding. The traditional view of the vdW attraction as arising from pairwise-additive London dispersion forces is considered using Grimme's "D3" method, comparing results to those from Tkatchenko's more general many-body dispersion (MBD) approach, all interpreted in terms of Dobson's general dispersion framework. Encompassing the experimental results, MBD screening of the vdW force between two silica bilayers is shown to scale up to medium separations as 1.25 de/d, where d is the bilayer separation and de is its equilibrium value, depicting antiscreening approaching and inside de Means of unifying this correlation effect with those included in modern density functionals are urgently required.

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.

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.

What do we learn from the classical turning surface of the Kohn-Sham potential as electron number is varied continuously?

The classical Kohn-Sham turning radius Rt of an atom can be defined as the radius where the Kohn-Sham potential is equal to the negative ionization potential of the atom, i.e., where vs(Rt) = ϵh. It was recently shown [E. Ospadov et al., Proc. Natl. Acad. Sci. U. S. A. 115, E11578-E11585 (2018)] to yield chemically relevant bonding distances, in line with known empirical values. In this work, we show that extension of the concept to non-integer electron number yields additional information about atomic systems and can be used to detect the difficulty of adding or subtracting electrons. Notably, it reflects the ease of bonding in open p-shells and its greater difficulty in open s-shells. The latter manifests in significant discontinuities in the turning radius as the electron number changes the principal quantum number of the outermost electronic shell (e.g., going from Na to Na2+). We then show that a non-integer picture is required to correctly interpret bonding and dissociation in H2 +. Results are consistent when properties are calculated exactly or via an appropriate approximation. They can be interpreted in the context of conceptual density functional theory.

Density-Driven Correlations in Many-Electron Ensembles: Theory and Application for Excited States.

Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and offers useful formal and demonstrated practical benefits. The correlation energy functional in the generalized case acquires higher complexity than its ground state counterpart, however. Little is known about its internal structure nor how to effectively approximate it in general. Here we show that such a functional can be broken down into natural components, including what we call "state-" and "density-driven" correlations, with the former amenable to conventional approximations, and the latter being a unique feature of ensembles. Such a decomposition provides us with a pathway to general approximations that are able to routinely handle low-lying excited states. The importance of density-driven correlations is demonstrated, and an approximation for them is introduced and shown to be useful.

Asymptotic behavior of the Hartree-exchange and correlation potentials in ensemble density functional theory.

We report on previously unnoticed features of the exact Hartree-exchange and correlation potentials for atoms and ions treated via ensemble density functional theory, demonstrated on fractional ions of Li, C, and F. We show that these potentials, when treated separately, can reach non-vanishing asymptotic constant values in the outer region of spherical, spin unpolarized atoms. In the next leading order, the potentials resemble Coulomb potentials created by effective charges which have the peculiarity of not behaving as piecewise constants as a function of the electron number. We provide analytical derivations and complement them with numerical results using the inversion of the Kohn-Sham equations for interacting densities obtained by accurate quantum Monte Carlo calculations. The present results expand on the knowledge of crucial exact properties of Kohn-Sham systems, which can guide development of advanced exchange-correlation approximations.

Range-separation and the multiple radii functional approximation inspired by the strongly interacting limit of density functional theory.

The strongly interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [S. Vuckovic and P. Gori-Giorgi, J. Phys. Chem. Lett. 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyze the MRF in exactly solvable one-dimensional molecules to uncover how it matches and deviates from exact results and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. We show that range-separated treatment of the MRF can offer advantages over a full treatment, by using MRF for short-ranged and/or midranged interactions only. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.

'Diet GMTKN55' offers accelerated benchmarking through a representative subset approach.

The GMTKN55 benchmarking protocol introduced by [Goerigk et al., Phys. Chem. Chem. Phys., 2017, 19, 32184] allows comprehensive analysis and ranking of density functional approximations with diverse chemical behaviours. But this comprehensiveness comes at a cost: GMTKN55's 1500 benchmarking values require energies for around 2500 systems to be calculated, making it a costly exercise. This manuscript introduces three subsets of GMTKN55, consisting of 30, 100 and 150 systems, as 'diet' substitutes for the full database. The subsets are chosen via a stochastic genetic approach, and consequently can reproduce key results of the full GMTKN55 database, including ranking of approximations. Some results are also included for the recent MGCDB84 database.

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory.

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Benchmarking several van der Waals dispersion approaches for the description of intermolecular interactions.

Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.'s "blind" test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.