Yang Jiao

We introduce and illustrate use of two closely related range-separated hybrid (RSH) van der Waals density functionals (vdW-DFs), denoted AHBR-mRSH and AHBR-mRSH*, for total-energy and quasiparticle characterizations of molecules using generalized Kohn–Sham (gKS) density functional theory (DFT). For comparison, we also introduce and document a traditional design for a long-range corrected (LRC) vdW-DF, denoted ‘B86R-LRC’. All three new vdW-DFs set the exchange potential as free of asymptotic screening in the coupling between the electron and its associated exchange hole. Our two AHBR-mRSHs are key members of a broader class ‘AHBR-mRSH(γ)’ defined by an inverse length scale γ for a crossover in weighting short- and long-ranged exchange contributions; we obtain a highly accurate predictor of general molecular-energy differences by keeping γ = 0.106 (inverse Bohr) deliberately fixed in AHBR-mRSH. We obtain an optimally tuned (OT) form AHBR-mRSH* = AHBR-mRSH( γ ∗ ) by computing a plausible value of γ ∗ for specific types of systems. This AHBR-mRSH* permits characterizations of molecular quasiparticles and generalizes (1) the existing ‘OT-RSH’ (Stein et al 2010 Phys. Rev. Lett. 105 266802; Rafaely–Abramson et al 2012 Phys. Rev. Lett. 109 226405) approach by a systematic inclusion of truly nonlocal correlations, and (2) more traditional LRC forms (e.g. B86R-LRC) by setting the short-range exchange description as in vdW-DF2-ahbr (Shukla et al 2022 Phys. Rev. X 12 041003). Importantly, we may view AHBR-mRSH and AHBR-mRSH* as internally consistent functionals for gKS-DFT, being simultaneously accurate on molecular energies and quasiparticles. This is possible because the ‘AHBR-mRSH(γ)’ class has enough transferability to almost always limit adverse impacts of tuning γ, as tested here on the GMTKN55 benchmark suite (Goerigk et al 2017 Phys. Chem. Chem. Phys. 19 32184). We find that AHBR-mRSH generally outperforms B86R-LRC on molecular problems. To illustrate usage, we complete the OT design of an AHBR-mRSH* for nucleobases and show that it provides quasiparticle predictions that are in good agreement with both literature theory and experimental values for adenine, thymine, cytosine, and guanine.

The forefoot is the foot part most affected by ill-fitting shoes. Footwear fitting considers the measurements of length, width and arch length. Toe shape has not yet been used in sizing feet and fitting shoes. This study aims to investigate the variation in toe shape, as measured by the hallux valgus angle. An automatic and reproducible hallux valgus angle measuring method using 3D foot scans with no palpation markers is proposed and applied to about half a million samples collected across North America, Europe and Asia. The measuring method is robust and can detect the medial contour along the proximal phalanx even in extreme cases. The hallux valgus angle has a normal distribution with long tails on both sides in the general population. Large dispersions of HVA values were observed for both genders, and in all 3 geographical regions. The hallux valgus angle has a broad distribution in the general population. Females have larger hallux valgus angles than males, and people from Asia have larger hallux valgus angles than people from North America and Europe. Shoe toe boxes should be designed to fit the actual shapes of shoppers’ toes. The proposed method for measuring HVA opens a new opportunity to study the causal relationship between shoe wearing habits and HVA on a large scale.

Background The forefoot is the foot most affected part by ill-fitting shoes. Footwear fitting standards have the measurements of length, width and arch length. Toe shape has not yet been used in footwear measurement. This study aims at investigating the variation in toe shape, as measured by the hallux valgus angle. Methods An automatic and reproducible hallux valgus angle measuring method using 3D foot scans with no palpation markers is proposed and applied to about half a million samples collected across North America, Europe and Asia. The measuring method is robust, it can detect the medial contour along the proximal phalanx even in extreme cases. Results The hallux valgus angle has a normal distribution with long tails on both sides in the general population. In the three regions (North America, Europe, Asia), the mean and standard deviation of this angle are 9° ± 6°, 8 ° ± 6°, 12° ± 6° for males and 11 ° ± 7°, 12 ° ± 7°, 16° ± 7° for females. Conclusions The hallux valgus angle has a broad distribution in the general population. Females have larger hallux valgus angle than males, and people from Asia have larger hallux valgus angle than people from North America and Europe.

Hybrid density functionals replace a fraction of an underlying generalized-gradient approximation (GGA) exchange description with a Fock-exchange component. Range-separated hybrids (RSHs) also effectively screen the Fock-exchange component and thus open the door for characterizations of metals and adsorption at metal surfaces. The RSHs are traditionally based on a robust GGA, such as PBE (Perdew J P et al 1996 Phys. Rev. Lett. 77 3865), for example, as implemented in the HSE design (Heyd J et al 2003 J. Chem. Phys. 118 8207). Here we define an analytical-hole (Henderson T M et al 2008 J. Chem. Phys. 128 194105) consistent-exchange RSH extension to the van der Waals density functional (vdW-DF) method (Berland K et al 2015 Rep. Prog. Phys. 78 066501), launching vdW-DF-ahcx. We characterize the GGA-type exchange in the vdW-DF-cx version (Berland K and Hyldgaard P 2014 Phys. Rev. B 89 035412), isolate the short-ranged exchange component, and define the new vdW-DF hybrid. We find that the performance vdW-DF-ahcx compares favorably to (dispersion-corrected) HSE for descriptions of bulk (broad molecular) properties. We also find that it provides accurate descriptions of noble-metal surface properties, including CO adsorption.

We review the screening nature and many-body physics foundation of the van der Waals density functional (vdW-DF) method [ROPP 78, 066501 (2015)], a systematic approach to construct truly nonlocal exchange-correlation energy density functionals. To that end we define and focus on a class of consistent vdW-DF versions that adhere to the Lindhard screening logic of the full method formulation. The consistent-exchange vdW-DF-cx version [PRB 89, 035412 (2014)] and its spin extension [PRL 115, 136402 (2015)] represent the first examples of this class; In general, consistent vdW-DFs reflect a concerted expansion of a formal recast of the adiabatic-connection formula [PRB 90, 075148 (2014)], an exponential summation of contributions to the local-field response, and the Dyson equation. We argue that the screening emphasis is essential because the exchange-correlation energy reflects an effective electrodynamics set by a long-range interaction. Two consequences are that 1) there are, in principle, no wiggle room in how one balances exchange and correlation, for example, in vdW-DF-cx, and that 2) consistent vdW-DFs have a formal structure that allows them to incorporate vertex-correction effects, at least in the case of levels that experience recoil-less interactions (for example, near the Fermi surface). We explore the extent to which the strictly nonempirical vdW-DF-cx formulation can serve as a systematic extension of the constraint-based semilocal functionals. For validation, we provide a complete survey of vdW-DF-cx performance for broad molecular processes, for the full set of 55 benchmarks in GMTKN55 [PCCP 19, 32181 (2017)] and comparing to the quantum-chemistry calculations that are summarized in that paper. We also provide new vdW-DF-cx results for metal surface energies and work functions that we compare to experiment. Finally, we use the screening insight to separate the vdW-DF nonlocal-correlation term into pure-vdW-interaction and local-field-susceptibility effects and present tools to compute and map the binding signatures.

The vdW-DF-cx0 exchange-correlation hybrid design [K. Berland et al., J. Chem. Phys. 146, 234106 (2017)] has a truly nonlocal correlation component and aims to facilitate concurrent descriptions of both covalent and non-covalent molecular interactions. The vdW-DF-cx0 design mixes a fixed ratio, a, of the Fock exchange into the consistent-exchange van der Waals density functional, vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)]. The mixing value a is sometimes taken as a semi-empirical parameter in hybrid formulations. Here, instead, we assert a plausible optimum average a value for the vdW-DF-cx0 design from a formal analysis; A new, independent determination of the mixing a is necessary since the Becke fit [A. D. Becke, J. Chem. Phys. 98, 5648 (1993)], yielding a′ = 0.2, is restricted to semilocal correlation and does not reflect non-covalent interactions. To proceed, we adapt the so-called two-legged hybrid construction [K. Burke et al., Chem. Phys. Lett. 265, 115 (1997)] to a starting point in the vdW-DF-cx functional. For our approach, termed vdW-DF-tlh, we estimate the properties of the adiabatic-connection specification of the exact exchange-correlation functional, by combining calculations of the Fock exchange and of the coupling-constant variation in vdW-DF-cx. We find that such vdW-DF-tlh hybrid constructions yield accurate characterizations of molecular interactions (even if they lack self-consistency). The accuracy motivates trust in the vdW-DF-tlh determination of system-specific values of the Fock-exchange mixing. We find that an average value a′ = 0.2 best characterizes the vdW-DF-tlh description of covalent and non-covalent interactions, although there exists some scatter. This finding suggests that the original Becke value, a′ = 0.2, also represents an optimal average Fock-exchange mixing for the new, truly nonlocal-correlation hybrids. To enable self-consistent calculations, we furthermore define and test a zero-parameter hybrid functional vdW-DF-cx0p (having fixed mixing a′ = 0.2) and document that this truly nonlocal correlation hybrid works for general molecular interactions (at reference and at relaxed geometries). It is encouraging that the vdW-DF-cx0p functional remains useful also for descriptions of some extended systems.

Two hybrid van der Waals density functionals (vdW-DFs) are developed using 25% Fock exchange with (i) the consistent-exchange vdW-DF-cx functional [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)] and (ii) with the vdW-DF2 functional [K. Lee et al., Phys. Rev. B 82, 081101 (2010)]. The ability to describe covalent and non-covalent binding properties of molecules is assessed. For properties related to covalent binding, atomization energies (G2-1 set), molecular reaction energies (G2RC set), and ionization energies (G21IP set) are benchmarked against experimental reference values. We find that hybrid-vdW-DF-cx yields results that are rather similar to those of the standard non-empirical hybrid PBE0 [C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999)], with mean average deviations (MADs) of 4.9 and 5.0 kcal/mol for the G2-1 set, respectively. In this comparison, experimental reference values are used, back corrected by wavefunction-based quantum-chemistry calculations of zero-point energies. Hybrid vdW-DF2 follows somewhat different trends, showing on average significantly larger deviations from the reference energies, with a MAD of 14.5 kcal/mol for the G2-1 set. Non-covalent binding properties of molecules are assessed using the S22 benchmark set of non-covalently bonded dimers and the X40 set of dimers of small halogenated molecules, using wavefunction-based quantum chemistry results as references. For the S22 set, hybrid-vdW-DF-cx performs better than standard vdW-DF-cx for the mostly hydrogen-bonded systems, with MAD dropping from 0.6 to 0.3 kcal/mol, but worse for purely dispersion-bonded systems, with MAD increasing from 0.2 to 0.6 kcal/mol. Hybrid-vdW-DF2 offers a slight improvement over standard vdW-DF2. Similar trends are found for the X40 set, with hybrid-vdW-DF-cx performing particularly well for binding energies involving the strongly polar hydrogen halides, but poorly for systems with tiny binding energies. Our study of the X40 set reveals the potential of mixing Fock exchange with vdW-DF, but also highlights shortcomings of the hybrids constructed here. The solid performance of hybrid-vdW-DF-cx for covalent-bonded systems, as well as the strengths and issues uncovered for non-covalently bonded systems, makes this study a good starting point for developing even more accurate hybrid vdW-DFs.

The formation of a Schottky barrier at the metal-semiconductor interface is widely utilised in semiconductor devices. With the emerging of novel Schottky barrier based nanoelectronics, a further microscopic understanding of this interface is in high demand. Here we provide an atomistic insight into potential barrier formation and band bending by ab initio simulations and model analysis of a prototype Schottky diode, i.e., niobium doped rutile titania in contact with gold (Au/Nb:TiO₂). The local Schottky barrier height is found to vary between 0 and 1.26 eV depending on the position of the dopant. The band bending is caused by a dopant induced dipole field between the interface and the dopant site, whereas the pristine Au/TiO₂ interface does not show any band bending. These findings open the possibility for atomic scale optimisation of the Schottky barrier and light harvesting in metal-semiconductor nanostructures.

Emission of photoexcited hot electrons from plasmonic metal nanostructures to semiconductors is key to a number of proposed nanophotonics technologies for solar harvesting, water splitting, photocatalysis, and a variety of optical sensing and photodetector applications. Favorable materials and catalytic properties make systems based on gold and TiO₂ particularly interesting, but the internal photoemission efficiency for visible light is low because of the wide bandgap of the semiconductor. We investigated the incident photon-to-electron conversion efficiency of thin TiO₂ films decorated with Au nanodisk antennas in an electrochemical circuit and found that incorporation of a Au mirror beneath the semiconductor amplified the photoresponse for light with wavelength λ = 500–950 nm by a factor 2–10 compared to identical structures lacking the mirror component. Classical electrodynamics simulations showed that the enhancement effect is caused by a favorable interplay between localized surface plasmon excitations and cavity modes that together amplify the light absorption in the Au/TiO₂ interface. The experimentally determined internal quantum efficiency for hot electron transfer decreases monotonically with wavelength, similar to the probability for interband excitations with energy higher than the Schottky barrier obtained from a density functional theory band structure simulation of a thin Au/TiO₂ slab.