MBD + C: How to Incorporate Metallic Character into Atom-Based Dispersion Energy Schemes.

The dispersion component of the van der Waals interaction in low-dimensional metals is known to exhibit anomalous "Type-C non-additivity" [Int. J. Quantum Chem. 2014, 114, 1157]. This causes dispersion energy behavior at asymptotically large separations that is missed by popular atom-based schemes for dispersion energy calculations. For example, the dispersion interaction energy between parallel metallic nanotubes at separation D falls off asymptotically as approximately D-2, whereas current atom-based schemes predict D-5 asymptotically. To date, it has not been clear whether current atom-based theories also give the dispersion interaction inaccurately at smaller separations for low-dimensional metals. Here, we introduce a new theory that we term "MBD + C". It permits inclusion of Type C effects efficiently within atom-based dispersion energy schemes such as many body dispersion (MBD) and universal MBD (uMBD). This allows us to investigate asymptotic, intermediate, and near-contact regimes with equal accuracy. (The large contact energy of intimate metallic bonding is not primarily governed by dispersion energy and is described well by the semi-local density functional theory.) Here, we apply a simplified version, "nn-MBD + C", of our new theory to calculate the dispersion interaction for three low-dimensional metallic systems: parallel metallic chains of gold atoms, parallel Li-doped graphene sheets, and parallel (4,4) armchair carbon nanotubes. In addition to giving the correct asymptotic behavior, the new theory seamlessly gives the dispersion energy down to near-contact geometry, where it is similar to MBD but can give up to 15% more dispersion energy than current MBD schemes, in the systems studied so far. This percentage increases with separation until nn-MBD + C dominates MBD at asymptotic separations.

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.

Exact Sum-Rule Approach to Polarizability and Asymptotic van der Waals Functionals─Derivation of Exact Single-Particle Benchmarks.

Using a sum-rule approach, we develop an exact theoretical framework for polarizability and asymptotic van der Waals correlation energy functionals of small isolated objects. The functionals require only monomer ground-state properties as input. Functional evaluation proceeds via solution of a single position-space differential equation, without the usual summations over excited states or frequency integrations. Explicit functional forms are reported for reference physical systems, including atomic hydrogen and single electrons subject to harmonic confinement, and immersed in a spherical-well potential. A direct comparison to the popular Vydrov-van Voorhis density functional shows that the best performance is obtained when density decay occurs at atomic scales. The adopted sum-rule approach implies general validity of our theory, enabling exact benchmarking of van der Waals density functionals and direct inspection of the subtle long-range correlation effects that constitute a major challenge for approximate (semi)local density functionals.

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.

Casimir-Polder Size Consistency: A Constraint Violated by Some Dispersion Theories.

A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this work we formulate the related idea of "Casimir-Polder size consistency" that manifests in long-range dispersion energetics. We show that local approximations in time-dependent density functional theory dispersion energy calculations violate the consistency condition because of incorrect treatment of highly nonlocal "xc kernel" physics, by up to 10% in our tests on closed-shell atoms.

Spooky correlations and unusual van der Waals forces between gapless and near-gapless molecules.

We consider the zero-temperature van der Waals (vdW) interaction between two molecules, each of which has a zero or near-zero electronic gap between a ground state and the first excited state, using a toy model molecule (equilateral H3) as an example. We show that the van der Waals energy between two ground state molecules falls off as D-3 instead of the usual D-6 dependence, when the molecules are separated by distance D. We show that this is caused by a perfect "spooky" correlation between the two fluctuating electric dipoles. The phenomenon is related to, but not the same as, the "resonant" interaction between an electronically excited and a ground state molecule introduced by Eisenschitz and London in 1930. It is also an example of "type C van der Waals non-additivity" recently introduced by one of us [J. F. Dobson, Int. J. Quantum Chem. 114, 1157 (2014)]. Our toy molecule H3 is not stable, but symmetry considerations suggest that a similar vdW phenomenon may be observable, despite Jahn-Teller effects, in molecules with a discrete rotational symmetry and broken inversion symmetry, such as certain metal atom clusters. The motion of the nuclei will need to be included for a definitive analysis of such cases, however.

Density functional theory analysis of structural and electronic properties of orthorhombic perovskite CH3NH3PbI3.

The organic-inorganic hybrid perovskite CH3NH3PbI3 is a novel light harvester, which can greatly improve the solar-conversion efficiency of dye-sensitized solar cells. In this article, a first-principle theoretical study is performed using local, semi-local and non-local exchange-correlation approximations to find a suitable method for this material. Our results, using the non-local optB86b + vdWDF functional, excellently agree with the experimental data. Thus, consideration of weak van der Waals interactions is demonstrated to be important for the accurate description of the properties of this type of organic-inorganic hybrid materials. Further analysis of the electronic properties reveals that I 5p electrons can be photo-excited to Pb 6p empty states. The main interaction between the organic cations and the inorganic framework is through the ionic bonding between CH3 and I ions. Furthermore, I atoms in the Pb-I framework are found to be chemically inequivalent because of their different chemical environments.

Binding and interlayer force in the near-contact region of two graphite slabs: experiment and theory.

Via a novel experiment, Liu et al. [Phys. Rev. B 85, 205418 (2012)] estimated the graphite binding energy, specifically the cleavage energy, an important physical property of bulk graphite. We re-examine the data analysis and note that within the standard Lennard-Jones model employed, there are difficulties in achieving internal consistency in the reproduction of the graphite elastic properties. By employing similar models which guarantee consistency with the elastic constant, we find a wide range of model dependent binding energy values from the same experimental data. We attribute some of the difficulties in the determination of the binding energy to: (i) limited theoretical understanding of the van der Waals dispersion of graphite cleavage, (ii) the mis-match between the strong bending stiffness of the graphite-SiO2 cantilever and the weak asymptotic inter-layer forces that are integrated over to produce the binding energy. We find, however, that the data do support determination of a maximum inter-layer force that is relatively model independent. We conclude that the peak force per unit area is 1.1 ± 0.15 GPa for cleavage, and occurs at an inter-layer spacing of 0.377 ± 0.013 nm.

Dispersion corrections in graphenic systems: a simple and effective model of binding.

We combine high-level theoretical and ab initio understanding of graphite to develop a simple, parametrized force-field model of interlayer binding in graphite, including the difficult non-pairwise-additive coupled-fluctuation dispersion interactions. The model is given as a simple additive correction to standard density functional theory (DFT) calculations, of form ΔU(D) = f(D)[U(vdW)(D) - U(DFT)(D)] where D is the interlayer distance. The functions are parametrized by matching contact properties, and long-range dispersion to known values, and the model is found to accurately match high-level ab initio results for graphite across a wide range of D values. We employ the correction on the bigraphene binding and graphite exfoliation problems, as well as lithium intercalated graphite LiC6. We predict the binding energy of bigraphene to be 0.27 J m(-2), and the exfoliation energy of graphite to be 0.31 J m(-2), respectively slightly less and slightly more than the bulk layer binding energy 0.295 J m(-2)/layer. Material properties of LiC6 are found to be essentially unchanged compared to the local density approximation. This is appropriate in view of the relative unimportance of dispersion interactions for LiC6 layer binding.

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients.

We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

The flexible nature of exchange, correlation, and Hartree physics: resolving "delocalization" errors in a "correlation free" density functional.

By exploiting freedoms in the definitions of "correlation," "exchange," and "Hartree" physics in ensemble systems, we better generalise the notion of "exact exchange" (EXX) to systems with fractional occupations of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the linear EXX ("LEXX") theory whose pair distribution and energy are explicitly piecewise linear in the occupations f(i)(σ). We provide explicit expressions for these functions for frontier s and p shells. Used in an optimised effective potential (OEP) approach the LEXX yields energies bounded by the piecewise linear "ensemble EXX" (EEXX) energy and standard fractional optimised EXX energy: E(EEXX) ≤ E(LEXX) ≤ E(EXX). Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that "ghost" Hartree interactions appear between opposite spin electrons in the usual formula. The energy E(LEXX) contains a cancellation term for the spin ghost case. It is evaluated for H, Li, and Na fractional ions with clear derivative discontinuities for all cases. The p-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again we find both derivative discontinuities and good agreement with exact results.

Electron affinities and ionisation potentials for atoms via "benchmark" tdDFT calculations with and without exchange kernels.

One of the known weaknesses of the adiabatic connection fluctuation dissipation (ACFD) correlation energy functional under the direct random-phase approximation (RPA) is its failure to accurately predict energy differences between dissimilar systems. In this work we evaluate ionisation potentials I and electron affinities A for atoms and ions with one to eighteen electrons using the ACFD functional under the RPA, and with the "PGG (Petersilka-Gossmann-Gross)" and "RXH (radial exchange hole)" model exchange kernels. All calculations are carried out using a real-space, all electron method with an exact exchange groundstate to minimise errors. As expected, the RPA is less accurate even than some regular density functional theory approaches, while the introduction of a dynamical exchange kernel improves results. In contrast to the case of atomic groundstate energies, the PGG kernel outperforms the RXH kernel for I and A. Mean absolute errors for I/A are found to be 3.27/2.38 kcal/mol, 4.38/5.43 kcal/mol, and 9.24/ 8.94 kcal/mol for the PGG, RXH, and RPA, respectively. We thus show that the inclusion of even the simple "RXH" kernel improves both quantities when compared to the RPA.

Shear induced formation of carbon and boron nitride nano-scrolls.

A 'top down' synthesis of carbon and hexagonal boron nitride (h-BN) nano-scrolls has been developed using the shear forces within dynamic thin films of N-methyl-2-pyrrolidone (NMP) generated on a rapidly rotating spinning disc processor (SDP), along with a theoretical understanding of the formation of the scrolls.

Quantum continuum mechanics made simple.

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

Vortex fluidic exfoliation of graphite and boron nitride.

Graphite is exfoliated into graphene by shearing vortex fluidic films of N-methyl-pyrrolidone (NMP), as a controlled process for preparing oxide free graphene, and for exfoliating the corresponding boron nitride sheets.

Calculation of dispersion energies.

We summarize the theory of van der Waals (dispersion) forces, with emphasis on recent microscopic approaches that permit the prediction of forces between solids and nanostructures right down to intimate contact and binding. Some connections are pointed out between microscopic theory and macroscopic Lifshitz theory.

Dispersion interaction in hydrogen-chain models.

We have investigated the dispersion interaction in hydrogen chain models via density functional theory-based symmetry-adapted perturbation theory using the asymptotically corrected PBE0 energy functional. The quasimetallic and the insulating prototype systems were chosen to be hydrogen chains with equally and alternately spaced H(2) units, respectively. The dependence of the dispersion energy on the chain length for quasimetallic and insulating cases has been determined for two chains arranged either in pointing or in parallel geometries. The results are compared with those previously calculated from a continuum coupled-plasmon approach [Phys. Rev. B 77, 075436 (2008)]. The interaction energy has also been modeled by pairwise summations over short fragments of the chains, demonstrating the failure of the additivity principle for the quasimetallic case, while confirming that the additivity is a qualitatively reasonable hypothesis for the insulating case.

Inhomogeneous STLS theory and TDCDFT.

We consider the inhomogeneous Singwi-Tosi-Land-Sjolander theory (ISTLS) of Dobson, Wang and Gould (Phys. Rev. B, 2002, 66, 081108(R)), and possible generalizations, in the context of time dependent current density functional theory (TDCDFT) and its tensor exchange correlation kernel fxc. We show that ISTLS corresponds to an fxc that is nonlocal in space but has only a trivial frequency dependence, and only a very simple tensorial structure. We propose approaches that may obtain more realistic structure while retaining the positive ISTLS features, namely that strong spatial inhomogeneity is allowed, with a kernel that contains physics specific to the inhomogeneous system under study, rather than being based on uniform-gas data.

Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals.

We show that the usual sum of R-6 contributions from elements separated by distance R can give qualitatively wrong results for the electromagnetically nonretarded van der Waals interaction between nonoverlapping bodies. This occurs for anisotropic nanostructures that have a zero electronic energy gap, such as metallic nanotubes or nanowires, and nanolayered systems including metals and graphene planes. In all these cases our analytic microscopic calculations give an interaction falling off with a power of separation different from the conventional value. We discuss implications for van der Waals energy functionals. The new nanotube interaction might be directly observable at submicron separations.