Long-range Dispersion Corrections Research Articles

Thermal expansion of free-standing graphene: benchmarking semi-empirical potentials

The thermodynamical properties of free-standing graphene have been investigated under constant zero pressure as a function of temperature using Monte Carlo simulations. A variety of atomistic models have been used, including the simple three-body Stillinger potential and a series of bond-order many-body potentials based on the Tersoff–Brenner seminal models, with recent reparametrizations dedicated to graphene, extensions to medium-range or long-range dispersion corrections. In addition, we have also tested a tight-binding potential in the fourth-moment approximation. The simulations reveal significant discrepancies in the in-plane lattice parameter and the thermal expansion coefficient, which despite showing monotonically increasing variations with temperature, can be positive, negative or change sign at moderate temperature depending on the potential. Comparison with existing experimental and theoretical data obtained from complementary approaches indicates that empirical potentials limited to nearest-neighbour interactions give rather dispersed results, and that van der Waals corrections generally tend to flatten the variations of the in-plane lattice constant, in contradiction with experiment. Only the medium-range corrected potentials of Los and Fasolino, as well as the tight-binding model in the fourth-moment approximation, are reasonably close to the reference results near room temperature. Our results suggest that classical potentials should be used with caution for thermal properties.

The adsorption of h-BN monolayer on the Ni(111) surface studied by density functional theory calculations with a semiempirical long-range dispersion correction

The geometric and spin-resolved electronic structure of a h-BN adsorbed Ni(111) surface has been investigated by density functional theory calculations. Two energy minima (physisorption and chemisorption) are obtained when the dispersive van der Waals correction is included. The geometry of N atom on top site and B atom on fcc site is the most energetically favorable. Strong hybridization with the ferromagnetic Ni substrate induces considerable gap states in the h-BN monolayer. The induced π* states are spin-polarized.

A Metal-Capped Conjugated Polyyne Threaded through a Phenanthroline-Based Macrocycle. Probing beyond the Mechanical Bond to Interactions in Interlocked Molecular Architectures

DFT calculations with long-range dispersion corrections have been used to analyze the structures and binding energies of rotaxanes featuring dimetal polyynediyl Pt2Cn dumbbells threaded through a 1,10-phenanthroline-based macrocycle. Results indicate that (i) the threading of the organometallic wire hardly affects its geometric and electronic properties and (ii) the noncovalent binding energies between the axle and macrocycle not only arise from mechanical bonding enforced weak interactions derived from the close proximity of the sp carbon chain to the macrocycle atoms, but also include hydrogen-bonding contacts involving hydrogen atoms of the metal bound phosphine ligands of the former and the nitrogen and oxygen atoms of the latter. The optimized geometries of the rotaxane and macrocycle are compared to the corresponding crystal structures where available.

Spin polarization study of graphene on the Ni(111) surface by density functional theory calculations with a semiempirical long-range dispersion correction

The geometric and spin-resolved electronic structure of a graphene-adsorbed Ni(111) surface has been investigated by density functional theory (DFT) calculations without and with a semiempirical long-range dispersion correction (DFT-D). DFT calculations with generalized gradient approximation (GGA) functional cannot predict well about the adsorption properties of graphene to the Ni(111) surface. While DFT-D calculations with the same GGA functional give reasonable values of the adsorption energy and layer distance from graphene to the substrate. The geometry of top_fcc is the most energetically favorable in all geometries. Strong hybridization of graphene with the ferromagnetic Ni substrate induces significant shift partially in graphene π states towards the Fermi level yielding spin polarization. The spin polarization is positive at the shallow levels of modified π states and slightly negative at the deeper levels of fundamental π states, which is indicated by the calculated spin density distributions and plane-averaged density of states at the vacuum side. The opposite spin polarization is consistent with our experimental result of spin asymmetry obtained by spin-polarized metastable-atom de-excitation spectroscopy measurements.

A first-principles-based correlation functional for harmonious connection of short-range correlation and long-range dispersion

We present a physically motivated correlation functional belonging to the meta-generalized gradient approximation (meta-GGA) rung, which can be supplemented with long-range dispersion corrections without introducing double-counting of correlation contributions. The functional is derived by the method of constraint satisfaction, starting from an analytical expression for a real-space spin-resolved correlation hole. The model contains a position-dependent function that controls the range of the interelectronic correlations described by the semilocal functional. With minimal empiricism, this function may be adjusted so that the correlation model blends with a specific dispersion correction describing long-range contributions. For a preliminary assessment, our functional has been combined with an atom-pairwise dispersion correction and full Hartree-Fock (HF)-like exchange. Despite the HF-exchange approximation, its predictions compare favorably with reference interaction energies in an extensive set of non-covalently bound dimers.

Performance of meta-GGA Functionals on General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions.

Among the computationally efficient semilocal density functionals for the exchange-correlation energy, meta-generalized-gradient approximations (meta-GGAs) are potentially the most accurate. Here, we assess the performance of three new meta-GGAs (revised Tao-Perdew-Staroverov-Scuseria or revTPSS, regularized revTPSS or regTPSS, and meta-GGA made simple or MGGA_MS), within and beyond their "comfort zones," on Grimme's big test set of main-group molecular energetics (thermochemistry, kinetics, and noncovalent interactions). We compare them against the standard Perdew-Burke-Ernzerhof (PBE) GGA, TPSS, and Minnesota M06L meta-GGAs, and Becke-3-Lee-Yang-Parr (B3LYP) hybrid of GGA with exact exchange. The overall performance of these three new meta-GGA functionals is similar. However, dramatic differences occur for different test sets. For example, M06L and MGGA_MS perform best for the test sets that contain noncovalent interactions. For the 14 Diels-Alder reaction energies in the "difficult" DARC subset, the mean absolute error ranges from 3 kcal mol(-1) (MGGA_MS) to 15 kcal mol(-1) (B3LYP), while for some other reaction subsets the order of accuracy is reversed; more generally, the tested new semilocal functionals outperform the standard B3LYP for ring reactions. Some overall improvement is found from long-range dispersion corrections for revTPSS and regTPSS but not for MGGA_MS. Formal and universality criteria for the functionals are also discussed.

Atomic-scale friction in graphene oxide: An interfacial interaction perspective from first-principles calculations

Atomic-scale friction in graphene oxide is investigated using density functional theory calculation including a long-range dispersion correction (DFT-D). The sliding behaviors between two graphene oxide layers with different functional groups or oxidation levels are quantitatively studied based on the constructed potential energy surfaces. Sliding paths with minimum energy corrugations and the corresponding static lateral forces and shear strengths for different systems are derived, suggesting moderately higher friction in graphene oxide compared with graphene. The effects of load on friction in different graphene oxide models are also investigated. Moreover, the largest lateral force existing in the graphene oxide system with both epoxide and hydroxyl groups is dominated by the interlayer hydrogen bond interaction, the instability of which also simultaneously leads to dissipation and hence gives rise to the friction. An in-depth understanding of the relationship between atomic-scale friction and interfacial interactions reveals that certain levels of friction can be achieved by controllable structural and chemical modifications to the sliding surfaces, which sheds light on friction control and design of new lubricant materials.

Adsorption of Hydrocarbons in Metal–Organic Frameworks: A Force Field Benchmark on the Example of Benzene in Metal–Organic Framework 5

For the application of metal–organic frameworks (MOFs), the understanding of host–guest interactions on a molecular level is crucial, and often only theoretical methods allow such an insight. However, to obtain quantitative information from such calculations, a validation of the applied methods is indispensable. In this work we investigate for the first time the physisorption of benzene, as a probe molecule for larger guest molecules, within the matrix of MOF-5 using high-level quantum mechanical methods. The calculations reveal a large contribution of dispersion effects on the host–guest interaction. The importance of both reliable and efficient quantum mechanical techniques, which are able to properly cover these effects, is discussed. We find that in particular a double-hybrid functional together with an empirical long-range dispersion correction is an accurate and robust method for the rather large model systems. In addition, our quantum mechanical results enabled us to benchmark for the first time th...

Hybrid Graphene and Graphitic Carbon Nitride Nanocomposite: Gap Opening, Electron–Hole Puddle, Interfacial Charge Transfer, and Enhanced Visible Light Response

Opening up a band gap and finding a suitable substrate material are two big challenges for building graphene-based nanodevices. Using state-of-the-art hybrid density functional theory incorporating long-range dispersion corrections, we investigate the interface between optically active graphitic carbon nitride (g-C(3)N(4)) and electronically active graphene. We find an inhomogeneous planar substrate (g-C(3)N(4)) promotes electron-rich and hole-rich regions, i.e., forming a well-defined electron-hole puddle, on the supported graphene layer. The composite displays significant charge transfer from graphene to the g-C(3)N(4) substrate, which alters the electronic properties of both components. In particular, the strong electronic coupling at the graphene/g-C(3)N(4) interface opens a 70 meV gap in g-C(3)N(4)-supported graphene, a feature that can potentially allow overcoming the graphene's band gap hurdle in constructing field effect transistors. Additionally, the 2-D planar structure of g-C(3)N(4) is free of dangling bonds, providing an ideal substrate for graphene to sit on. Furthermore, when compared to a pure g-C(3)N(4) monolayer, the hybrid graphene/g-C(3)N(4) complex displays an enhanced optical absorption in the visible region, a promising feature for novel photovoltaic and photocatalytic applications.

Physisorption of helium on a TiO2(110) surface: Periodic and finite cluster approaches

As a proto-typical case of physisorption on an extended transition-metal oxide surface, the interaction of a helium atom with a TiO2(110)-(1×1) surface is studied here by using finite cluster and periodic approaches and both wave-function-based (post-Hartree–Fock) quantum chemistry methods and density functional theory. Both classical and advanced finite cluster approaches, based on localized Wannier orbitals combined with one-particle embedding potentials, are applied to provide (reference) coupled-cluster and second-order Möller–Plesset interaction energies. It is shown that, once the basis set is specifically tailored to minimize the basis set superposition error, periodic calculations using the Perdew–Burke–Ernzerhof functional yield short and medium-range interaction potentials in very reasonable agreement with those obtained using the correlated wave-function-based methods, while small long-range dispersion corrections are necessary to reproduce the correct asymptotic behavior. This study is aimed at a subsequent simulation of helium mediated deposition on oxide surfaces.

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long-range and/or empirical dispersion corrections, including LC-ωPBE, B97-D, ωB97X-D, M06-2X, B2PLYP-D, and mPW2PLYP-D functionals, are assessed for their ability to describe the conformational preferences of Ac-Ala-NHMe (the alanine dipeptide) and Ac-Pro-NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22-0.40 kcal/mol in conformational energy and 2.0-3.2° in torsion angles φ and ψ using these functionals with the 6-311++G(d,p) basis set against the reference values calculated at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP-D ≈ mPW2PLYP-D > ωB97X-D ≈ M06-2X > MP2 > LC-ωPBE > B3LYP with the 6-311++G(d,p) basis set. The SMD model at the M06-2X/6-31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP-D/6-311++G(d,p)//SMD M06-2X/6-31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values.

Application of semiempirical long‐range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from Møller-Plesset second-order perturbation theory with basis set extrapolation.

Theoretical Investigation of Clusters of Phosphorus and Arsenic: Fascination and Temptation of High Symmetries

We present a theoretical study of the energetic and thermodynamic stability of selected phosphorus and arsenic clusters containing 18 to 168 atoms. For this purpose we employ MP2 as well as DFT functionals BP86 and B3LYP with extended basis sets. All procedures predict the family of one-dimensional polymers X18+12n, each with 2n-1 isomers of virtually identical energy, to be more stable than other structures investigated so far. Furthermore, islands of stability result for ring-shaped clusters X24n with Dnd symmetry for n=4 (only for arsenic), 5, 6, and 7. Phosphorus and arsenic show otherwise a very similar behavior. An investigation of basis set effects shows that a doubly polarized triple zeta valence basis (TZVPP) is both necessary and sufficient. In comparison to the reliable spin component scaled MP2 (SCS-MP2) procedure, DFT methods underestimate and MP2 overestimates the stability of larger clusters; the discrepancy increases with the number of atoms. The addition of a long-range dispersion correction to B3LYP energies does not rectify the shortcomings of DFT in comparison with SCS-MP2.

Application of Ewald summations to long-range dispersion forces

Results illustrating the effects of using explicit summation terms for the r(-6) dispersion term on the interfacial properties of a Lennard-Jones fluid and SPC/E water are presented. For the Lennard-Jones fluid, we find that the use of long-range summations, even with a short "crossover radius," yields results that are consistent with simulations using large cutoff radii. Simulations of SPC/E water demonstrate that the long-range dispersion forces are of secondary importance to the Coulombic forces. In both cases, we find that the ratio of the box size L( parallel) to the crossover radius r(c) (k) plays an important role in determining the magnitude of the long-range dispersion correction, although its effect is secondary when Coulombic interactions are also present.

Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability

The objective of this work is the further systematic improvement of the accuracy of Double-Hybrid Density Functionals (DHDF) that add non-local electron correlation effects to a standard hybrid functional by second-order perturbation theory (S. Grimme, J. Chem. Phys., 2006, 124, 034108). The only known shortcoming of these generally highly accurate functionals is an underestimation of the long-range dispersion (van der Waals) interactions. To correct this deficiency, we add a previously developed empirical dispersion term (DFT-D) to the energy expression but leave the electronic part of the functional untouched. Results are presented for the S22 set of non-covalent interaction energies, the G3/99 set of heat of formations and conformational energies of a phenylalanyl-glycyl-glycine peptide model. We furthermore propose seven hydrocarbon reactions with strong intramolecular dispersion contributions as a benchmark set for newly developed density functionals. In general, the proposed composite approach is for many chemically relevant properties of similar quality as high-level coupled-cluster treatments. A significant increase of the accuracy for non-covalent interactions is obtained and the corrected B2PLYP DHDF provides one of the lowest ever obtained Mean Absolute Deviations (MAD) for the S22 set (0.2-0.3 kcal mol(-1)). Unprecedented high accuracy is also obtained for the relative energies of peptide conformations that turn out to be very difficult. The significant improvements found for the G3/99 set (reduction of the MAD from 2.4 to 1.7 kcal mol(-1)) underline the importance of intramolecular dispersion effects in large molecules. In all tested cases the results from the standard B3LYP approach are also significantly improved, and we recommend the general use of dispersion corrections in DFT treatments.