A Density Functional Theory for the Average Electron Energy.

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations.

An assessment of density functionals for predicting CO2 adsorption in diamine-functionalized metal-organic frameworks.

Diamine-functionalized M2(dobpdc) (M = Mg, Mn, Fe, Co, Zn) metal-organic frameworks (MOFs) are among a growing class of crystalline solids currently being intensively investigated for carbon capture as they exhibit a novel cooperative and selective CO2 adsorption mechanism and a step-shaped isotherm. To understand their CO2 adsorption behavior, ab initio calculations with near-chemical accuracy (∼6 kJ/mol, an average experimental error) are required. Here, we present density functional theory (DFT) calculations of CO2 adsorption in m-2-m-Zn2(dobpdc) (m-2-m = N,N'-dimethylethyle-nediamine and dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) with different exchange-correlation functionals, including semilocal functionals [Perdew-Burke-Ernzerhof (PBE) and two revised PBE functionals], semiempirical pairwise corrections (D3 and Tkatchenko-Scheffler), nonlocal van der Waals (vdW) correlation functionals-vdW-optB88 (or vdW-DF-optB88), vdW-DF1, vdW-DF2, vdW-DF2-B86R (or rev-vdW-DF2), vdW-DF-cx (and vdW-DF-cx0), and revised VV10-and the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA). Overall, we find that revPBE+D3 and RPBE+D3 show the best balance of performance for both the lattice parameters and the CO2 binding enthalpy of m-2-m-Zn2(dobpdc). revPBE+D3 and RPBE+D3 predict the m-2-m-Zn2(dobpdc) lattice parameters to within 1.4% of experiment and predict CO2 binding enthalpies of -68 kJ/mol, which compare reasonably well with the experiment (-57 kJ/mol). Although PBE (-57.7 kJ/mol), vdW-DF1 (-49.6 kJ/mol), and vdW-DF2 (-44.3 kJ/mol) are also found to predict the CO2 binding enthalpy with good accuracy, they overestimate lattice parameters and bond lengths. The other functionals considered predict the lattice parameters with the same accuracy as revPBE+D3 and RPBE+D3, but they overbind CO2 by around 26-50 kJ/mol. We find that the superior performance of revPBE+D3 and RPBE+D3 is sustained for the formation enthalpy and the lattice parameters of ammonium carbamate, a primary product of the cooperative CO2 insertion in diamine-functionalized M2(dobpdc) MOFs. Moreover, we find that their performance is derived from their larger repulsive exchange contributions to the CO2 binding enthalpy than the other functionals at the relevant range of the reduced density gradient value for the energetics of CO2 adsorption in the m-2-m-Zn2(dobpdc) MOF. A broader examination of the performance of RPBE+D3 for the structural parameters and CO2 binding enthalpies of 13 diamine-functionalized Mg2(dobpdc) MOFs further demonstrates that RPBE+D3 successfully reproduces experimental CO2 binding enthalpies and reveals a logarithmic relationship between the step pressure and the CO2 binding enthalpy of the diamine-functionalized Mg2(dobpdc) MOFs, consistent with experiments where available. The results of our benchmarking study can help guide the further development of versatile vdW-corrected DFT methods with predictive accuracy.

vdW-DF-ahcx: a range-separated van der Waals density functional hybrid.

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 Pet al1996Phys. Rev. Lett.773865), for example, as implemented in the HSE design (Heyd Jet al2003J. Chem. Phys.1188207). Here we define an analytical-hole (Henderson T Met al2008J. Chem. Phys.128194105) consistent-exchange RSH extension to the van der Waals density functional (vdW-DF) method (Berland Ket al2015Rep. Prog. Phys.78066501), launching vdW-DF-ahcx. We characterize the GGA-type exchange in the vdW-DF-cx version (Berland K and Hyldgaard P 2014Phys. Rev. B89035412), 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.

Screening nature of the van der Waals density functional method: a review and analysis of the many-body physics foundation.

We review the screening nature and many-body physics foundation of the van der Waals density functional (vdW-DF) method [Berland K et al 2015 Rep. Prog. Phys. 78 066501], 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 [Berland K and Hyldgaard P 2014 Phys. Rev. B 89 035412] and its spin extension [Thonhauser T et al 2015 Phys. Rev. Lett. 115 136402] 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 [Hyldgaard P et al 2014 Phys. Rev. B 90 075148], 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 [Goerigk L et al 2017 Phys. Chem. Chem. Phys. 19 32184] 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.

Extent of Fock-exchange mixing for a hybrid van der Waals density functional?

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.

Assessment of two hybrid van der Waals density functionals for covalent and non-covalent binding of molecules.

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.

Optimization of Norbornadiene Compounds for Solar Thermal Storage by First-Principles Calculations.

Molecular photoswitches capable of storing solar energy are interesting candidates for future renewable energy applications. Here, using quantum mechanical calculations, we carry out a systematic screening of crucial optical (solar spectrum match) and thermal (storage energy density) properties of 64 such compounds based on the norbornadiene-quadricyclane system. Whereas a substantial number of these molecules reach the theoretical maximum solar power conversion efficiency, this requires a strong red-shift of the absorption spectrum, which causes undesirable absorption by the photoisomer as well as reduced thermal stability. These compounds typically also have a large molecular mass, leading to low storage densities. By contrast, single-substituted systems achieve a good compromise between efficiency and storage density, while avoiding competing absorption by the photo-isomer. This establishes guiding principles for the future development of molecular solar thermal storage systems.

Comparative Ab-Initio Study of Substituted Norbornadiene-Quadricyclane Compounds for Solar Thermal Storage.

Molecular photoswitches that are capable of storing solar energy, so-called molecular solar thermal storage systems, are interesting candidates for future renewable energy applications. In this context, substituted norbornadiene-quadricyclane systems have received renewed interest due to recent advances in their synthesis. The optical, thermodynamic, and kinetic properties of these systems can vary dramatically depending on the chosen substituents. The molecular design of optimal compounds therefore requires a detailed understanding of the effect of individual substituents as well as their interplay. Here, we model absorption spectra, potential energy storage, and thermal barriers for back-conversion of several substituted systems using both single-reference (density functional theory using PBE, B3LYP, CAM-B3LYP, M06, M06-2x, and M06-L functionals as well as MP2 calculations) and multireference methods (complete active space techniques). Already the diaryl substituted compound displays a strong red-shift compared to the unsubstituted system, which is shown to result from the extension of the conjugated π-system upon substitution. Using specific donor/acceptor groups gives rise to a further albeit relatively smaller red-shift. The calculated storage energy is found to be rather insensitive to the specific substituents, although solvent effects are likely to be important and require further study. The barrier for thermal back-conversion exhibits strong multireference character and as a result is noticeably correlated with the red-shift. Two possible reaction paths for the thermal back-conversion of diaryl substituted quadricyclane are identified and it is shown that among the compounds considered the path via the acceptor side is systematically favored. Finally, the present study establishes the basis for high-throughput screening of norbornadiene-quadricyclane compounds as it provides guidelines for the level of accuracy that can be expected for key properties from several different techniques.

van der Waals forces in density functional theory: a review of the vdW-DF method.

A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals density functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasizing more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only for dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.

van der Waals density functionals built upon the electron-gas tradition: facing the challenge of competing interactions.

The theoretical description of sparse matter attracts much interest, in particular for those ground-state properties that can be described by density functional theory. One proposed approach, the van der Waals density functional (vdW-DF) method, rests on strong physical foundations and offers simple yet accurate and robust functionals. A very recent functional within this method called vdW-DF-cx [K. Berland and P. Hyldgaard, Phys. Rev. B 89, 035412 (2014)] stands out in its attempt to use an exchange energy derived from the same plasmon-based theory from which the nonlocal correlation energy was derived. Encouraged by its good performance for solids, layered materials, and aromatic molecules, we apply it to several systems that are characterized by competing interactions. These include the ferroelectric response in PbTiO3, the adsorption of small molecules within metal-organic frameworks, the graphite/diamond phase transition, and the adsorption of an aromatic-molecule on the Ag(111) surface. Our results indicate that vdW-DF-cx is overall well suited to tackle these challenging systems. In addition to being a competitive density functional for sparse matter, the vdW-DF-cx construction presents a more robust general-purpose functional that could be applied to a range of materials problems with a variety of competing interactions.

Physisorption of nucleobases on graphene: a comparative van der Waals study.

The physisorption of the nucleobases adenine (A), cytosine (C), guanine (G), thymine (T), and uracil (U) on graphene is studied using several variants of the density functional theory (DFT): the generalized gradient approximation with the inclusion of van der Waals interaction (vdW) based on the TS approach (Tkatchenko and Scheffer 2009 Phys. Rev. Lett. 102 073005) and our simplified version of this approach (here called sTS), the van der Waals density functional vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401) and vdW-DF2 (Lee et al 2010 Phys. Rev. B 82 081101), and DFT-D2 (Grimme 2006 J. Comput. Chem. 27 1787) and DFT-D3 (Grimme et al 2010 J. Chem. Phys. 132 154104) methods. The binding energies of nucleobases on graphene are found to be in the following order: G > A > T > C > U within TS, sTS, vdW-DF, and DFT-D2, and in the following order: G > A > T ~ C > U within DFT-D3 and vdW-DF2. The binding separations are found to be different within different methods and in the following order: DFT-D2 < TS < DFT-D3 ~ vdW-DF2 < vdW-DF. We also comment on the efficiency of combining the DFT-D approach and vdW-DF to study systems with van der Waals interactions.

Benchmarking van der Waals density functionals with experimental data: potential-energy curves for H2 molecules on Cu(111), (100) and (110) surfaces.

Detailed physisorption data from experiment for the H(2) molecule on low-index Cu surfaces challenge theory. Recently, density functional theory (DFT) has been developed to account for nonlocal correlation effects, including van der Waals (dispersion) forces. We show that the functional vdW-DF2 gives a potential-energy curve, potential-well energy levels and difference in lateral corrugation promisingly close to the results obtained by resonant elastic backscattering-diffraction experiments. The backscattering barrier is sensitive to the choice of exchange functional approximation. Further, the DFT-D3 and TS-vdW corrections to traditional DFT formulations are also benchmarked, and deviations are analyzed.

Do two-dimensional "noble gas atoms" produce molecular honeycombs at a metal surface?

Anthraquinone self-assembles on Cu(111) into a giant honeycomb network with exactly three molecules on each side. Here we propose that the exceptional degree of order achieved in this system can be explained as a consequence of the confinement of substrate electrons in the pores, with the pore size tailored so that the confined electrons can adopt a noble-gas-like two-dimensional quasi-atom configuration with two filled shells. Formation of identical pores in a related adsorption system (at different overall periodicity due to the different molecule size) corroborates this concept. A combination of photoemission spectroscopy with density functional theory computations (including van der Waals interactions) of adsorbate-substrate interactions allows quantum mechanical modeling of the spectra of the resultant quasi-atoms and their energetics.

Structure and binding in crystals of cagelike molecules: hexamine and platonic hydrocarbons.

In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF) [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)] permit the determination of molecular crystal structure within density functional theory (DFT). We study the crystal structures of hexamine and the platonic hydrocarbons (cubane and dodecahedrane). The calculated lattice parameters and cohesion energy agree well with experiments. Further, we examine the asymptotic accounts of the van der Waals forces by comparing full vdW-DF with asymptotic atom-based pair potentials extracted from vdW-DF. The character of the binding differs in the two cases, with vdW-DF giving a significant enhancement at intermediate and relevant binding separations. We analyze consequences of this result for methods such as DFT-D and question DFT-D's transferability over the full range of separations.

Understanding adhesion at as-deposited interfaces from ab initio thermodynamics of deposition growth: thin-film alumina on titanium carbide.

We investigate the chemical composition and adhesion of chemical vapour deposited thin-film alumina on TiC using and extending a recently proposed nonequilibrium method of ab initio thermodynamics of deposition growth (AIT-DG) (Rohrer and Hyldgaard 2010 Phys. Rev. B 82 045415). A previous study of this system (Rohrer et al 2010 J. Phys.: Condens. Matter 22 015004) found that use of equilibrium thermodynamics leads to predictions of a non-binding TiC/alumina interface, despite its industrial use as a wear-resistant coating. This discrepancy between equilibrium theory and experiment is resolved by the AIT-DG method which predicts interfaces with strong adhesion. The AIT-DG method combines density functional theory calculations, rate-equation modelling of the pressure evolution of the deposition environment and thermochemical data. The AIT-DG method was previously used to predict prevalent terminations of growing or as-deposited surfaces of binary materials. Here we extend the method to predict surface and interface compositions of growing or as-deposited thin films on a substrate and find that inclusion of the nonequilibrium deposition environment has important implications for the nature of buried interfaces.

Site determination and thermally assisted tunneling in homogenous nucleation.

A combined low-temperature scanning tunneling microscopy and density functional theory study on the binding and diffusion of copper monomers, dimers, and trimers adsorbed on Cu(111) is presented. Whereas atoms in trimers are found in fcc sites only, monomers as well as atoms in dimers can occupy the fcc as well as the metastable hcp site. In fact the dimer fcc-hcp configuration is only 1.3 meV less favorable with respect to the fcc-fcc configuration. This enables a confined intracell dimer motion, which at temperatures below 5 K is dominated by thermally assisted tunneling.