Long-Range van der Waals Interactions in Density Functional Theory

The early difficulties in accounting for long-range van der Waals interactions in the framework of density functional theory (DFT) have been overcome to a certain extent in recent works by several groups, and those interactions can be computed numerically. In this paper a derivation of the analytical form of the attractive van der Waals interaction between two neutral atoms with polarizabilities α₁ and α₂ at large distance R, namely E _int=−C ₆ α₁ α₂/R ⁶ is performed within the context of DFT. Use is made of the properties of the Coulomb correlation hole, and it is shown that nonlocal Coulomb correlations are responsible for long-range dispersion interactions.     

Two-step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.     

Direct Measurement of Repulsive van der Waals Interactions Using an Atomic Force Microscope

The forces of interaction between a flat poly(tetrafluoroethylene) (PTFE) surface and gold spheres (of radii 3–8 μm) were measured as a function of apparent surface separation for different intervening media. For air, fluorinated alkanes, and polar liquids the interaction between the surfaces was found to be attractive. With intervening liquids of low-polarity the interaction was found to be repulsive. This repulsion is attributed to a negative composite Hamaker coefficient leading to van der Waals repulsion.     

Empirical bond-order potential for hydrocarbons: adaptive treatment of van der Waals interactions

Bond-order potentials provide a powerful class of models for simulating chemically reactive systems with classical potentials. In these models, the covalent bonding interactions adapt to the environment, allowing bond strength to change in response to local chemical changes. However, the non-bonded interactions should also adapt in response to chemical changes, an effect which is neglected in current bond-order potentials. Here the AIREBO potential is extended to include adaptive Lennard-Jones terms, allowing the van der Waals interactions to vary adaptively with the chemical environment. The resulting potential energy surface and its gradient remain continuous, allowing it to be used for dynamics simulations. This new potential is parameterized for hydrocarbons, and is fit to the energetics and densities of a variety of condensed phase molecular hydrocarbons. The resulting model is more accurate for modeling aromatic and other unsaturated hydrocarbon species, for which the original AIREBO potential had some deficiencies. Testing on compounds not used in the fitting procedure shows that the new model performs substantially better in predicting heats of vaporization and pressures (or densities) of condensed-phase molecular hydrocarbons.     

晶体中原子的平均范德华半径

根据晶体中原子的平均体积数据提出包括全部金属元素的原子平均范德华半径值.与现有几个重要的范德华半径体系进行了初步的比较,指出范德华半径值在应用中值得注意的问题,简要提出了有关范德华半径今后研究的方向.     

Van der Waals radii of metals from spectroscopic data

The lack of information about the van der Waals radii of metals can be compensated for by using the results of spectroscopic investigations of van der Waals molecules. It has been shown that the interatomic distances in these molecules obey an additive scheme if one allows for the polarization effects. The van der Waals radii of the alkali metals, Ag, Mg, Zn, Cd, Hg, B, Al, In, and Si, have been determined from the interatomic distances in their heteroatomic molecules with atoms of noble gases. Use of the obtained radii for crystal chemistry is discussed.Translated fromIzyestiya Akademil Nauk. Seriya Khimicheskaya, No. 8, pp. 1374–1378, August, 1994.     

晶体范德华半径的70年

对过去70年来发表的稀有气体、非金属元素和金属元素的晶体范德华半径重要数值进行了系统分析和总结.从常用的数值中推荐了最可靠值,并指出有关晶体范德华半径值及其应用中的若干问题,以及有待今后进一步研究的方向.     

A density functional theory study of van der Waals interaction in carbon nanotubes

In this article, we investigate the effect of van der Waals force in zigzag carbon nanotubes (CNTs) including single-wall CNT (SWCNT) and double-walled CNT (DWCNT) structures with several interaction configurations. The solid-state density functional theory is employed to calculate the geometric optimization, normal mode frequencies, and IR and Raman spectra with the periodic boundary condition. For SWCNTs, we find that the Raman intensity is not affected by the tube diameter or the electronic structure. The IR absorption, however, increases with the tube diameter. We find that the close metallicity of the electronic structure has a significant impact on the IR simulations. When the van der Waals force is applied outside the CNTs at a distance longer than 3.0, the effect on Raman spectra is minimal but some effects can still be confirmed by IR absorption. When the van der Waals force acts inside the CNTs, the effect on the spectrum can be observed, especially at a distance of 2.8 Å, both IR and Raman can be significantly enhanced in many modes.     

Accurate van der Waals force field for gas adsorption in porous materials

An accurate van der Waals force field (VDW FF) was derived from highly precise quantum mechanical (QM) calculations. Small molecular clusters were used to explore van der Waals interactions between gas molecules and porous materials. The parameters of the accurate van der Waals force field were determined by QM calculations. To validate the force field, the prediction results from the VDW FF were compared with standard FFs, such as UFF, Dreiding, Pcff, and Compass. The results from the VDW FF were in excellent agreement with the experimental measurements. This force field can be applied to the prediction of the gas density (H₂, CO₂, C₂H₄, CH₄, N₂, O₂) and adsorption performance inside porous materials, such as covalent organic frameworks (COFs), zeolites and metal organic frameworks (MOFs), consisting of H, B, N, C, O, S, Si, Al, Zn, Mg, Ni, and Co. This work provides a solid basis for studying gas adsorption in porous materials. © 2017 Wiley Periodicals, Inc.     

Novel van der Waals Deep-UV Nonlinear Optical Materials

Van der Waals (vdW) deep-UV (DUV) nonlinear optical (NLO) crystal is an important material system recently developed. Herein, we review its concept and original intention, and then summarized the discovery process of related materials, including the role of A-site cations and the resulting two-/one-dimensional vdW DUV NLO systems. Finally, we evaluate the practical DUV NLO performance and prospected the opportunities and challenges.     

Calculation of the van der Waals volumes of organic molecules

A new and more precise method is proposed for calculating van der Waals atomic and molecular volumes of organic compounds. The method provides for intersections of three or more spheres at one point of space. Such a possibility is essential for calculating the volumes of sterically overcrowded molecules and of molecules with intramolecular hydrogen bonds. A computer program for IBM PC/AT(XT) is developed. Depending on the atomic environment in the molecule, the average values of the volume increments for atoms C, N, O, H, F, Cl, and S are obtained using the data from the Cambridge Structural Database.N. S. Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow 117071. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 4, pp. 922–931, April, 1992.     

Calculation of van der Waals interactions involving lipid vesicles

Van der Waals energies of interaction involving vesicles and lipid layers are calculated for different geometries. Results from exact and approximate calculations are compared with some existing experimental data. It is shown that sufficient accuracy can be obtained using relatively simple ‘additivity’ approximations for the contribution of dispersion interactions. A set of calculated results is presented for a small unilamellar vesicle interacting with coated and uncoated metal and polymer surfaces. A lipid coating lowers magnitude of the interaction energy approximately two-fold. The procedure gives a simple possibility to estimate Hamaker constants (and ‘Hamaker functions’) from handbook data taking into account the existing uncertainity in the materials constants of the interacting substances.     

Augmented van der Waals equations of state: SAFT-VR versus Yukawa based van der Waals equation

Performance of the SAFT-VR equation of state developed for the hard sphere based simple fluids, namely the square-well, Sutherland and Yukawa fluids, is examined by comparing its results with simulation data and an augmented van der Waals (vdW) equation based on a Yukawa (Y) reference. Its shown that both for the equilibrium vapor-liquid data and data along selected isotherms in the liquid and supercritical fluid phases the vdW(Y) equation provides better results, particularly when going to lower temperatures.     

Phosphorene-Based van der Waals Heterojunction for Solar Water Splitting

As a clean and renewable future energy source, hydrogen fuel can be produced via solar water splitting. Two-dimensional (2D) black phosphorene (black-P) can harvest visible light due to the desirable band gap, which promises it as a metal-free photocatalyst. However, black-P can be only used to produce hydrogen since the oxidation potential of water locates lower than the position of the valence band maximum. To improve the photocatalytic performance of black-P, here, using black-P and blue phosphorene (blue-P) monolayers, we propose a 2D van der Waals (vdW) heterojunction. Theoretical results, including the band structures, density of states, Bader charge population, charge density di erence, and optical absorption spectra, clearly reveal that the visible light absorption ability is obviously improved, and the band edge alignment of the proposed vdW heterojunction displays a typical type-II feature to effectively separate the photogenerated carriers. At the same time, the built-in interfacialelectric field prevents the electron-hole recombination. These predictions suggest that the examined phosphorene-based vdW heterojunction is an efficient photocatalyst for solar water splitting.     

Efficient optimization of van der Waals parameters from bulk properties

Due to the computational cost involved, when developing a force field for new compounds, one often avoids fitting van der Waals (vdW) terms, instead relying on a general force field based on the atom type. Here, we provide a novel approach to efficiently optimize vdW terms, based on both ab initio dimer energies and condensed phase properties. The approach avoids the computational challenges of searching the parameter space by using an extrapolation method to obtain a reliable difference quotient for the parameter derivatives based on the central difference. The derivatives are then used in an active‐space optimization method which convergences quadratically. This method is applicable to polarizable and nonpolarizable force fields, although we focus on the parameterization of the AMBER force field. The scaling of the electrostatic potential (ESP) of the compounds is also studied. The algorithm is tested on 12 compounds, reducing the root mean squared error (RMSE) of the density from 0.061 g/cm³ with GAFF parameters to 0.004 g/cm³, and the heat of vaporization from 1.13 to 0.05 kcal/mol. This is done with only four iterations of molecular dynamic runs. Using the optimized vdW parameters, the RMSE of the self‐diffusion was reduced from 1.22 × 10^?9 to 0.78 × 10^?9 m² s^?1 and the RMSE of the hydration free energies was reduced from 0.30 to 0.26 kcal/mol. Scaling the ESP to improve dimer energies resulted in the RMSE improving to 0.77× 10^?9 m² s^?1, but the worsened to 0.33 kcal/mol. © 2013 Wiley Periodicals, Inc.     

Prediction of physicochemical properties of organic molecules using van der Waals surface electrostatic potentials

The generalized interaction properties function (GIPF) methodology developed by Politzer and coworkers, which calculated molecular surface electrostatic potential (MSESP) on a density envelope surface, was modified by calculating the MSESP on a much simpler van der Waals (vdW) surface of a molecule. In this work, vdW molecular surfaces were obtained from the fully optimized structures confirmed by frequency calculations at B3LYP/6-31G(d) level of theory. Multiple linear regressions for normal boiling point, heats of vaporization, heats of sublimation, heats of fusion, liquid density, and solid density were performed using GIPF variables from vdW model surface. Results from our model are compared with those from Politzer and coworkers. The surface-dependent beta (and gamma) values are dependent on the surface models but the surface-independent alpha and regression coefficients (r) are constant when vdW surface and density surface with 0.001 a.u. contour value are compared. This interesting phenomenon is explained by linear dependencies of GIPF variables.     

二维材料范德华间隙的利用

Since their discovery, two-dimensional (2D) materials have attracted significant research attention owing to their excellent and controllable physical and chemical properties. These materials have emerged rapidly as important material system owing to their unique properties such as electricity, optics, quantum properties, and catalytic properties. 2D materials are mostly bonded by strong ionic or covalent bonds within the layers, and the layers are stacked together by van der Waals forces, thereby making it possible to peel off 2D materials with few or single layers. The weak interaction between the layers of 2D materials also enables the use of van der Waals gaps for regulating the electronic structure of the system and further optimizing the material properties. The introduction of guest atoms can significantly change the interlayer spacing of the original material and coupling strength between the layers. Also, interaction between the guest and host atom also has the potential to change the electronic structure of the original material, thereby affecting the material properties. For example, the electron structure of a host can be modified by interlayer guest atoms, and characteristics such as carrier concentration, optical transmittance, conductivity, and band gap can be tuned. Organic cations intercalated between the layers of 2D materials can produce stable superlattices, which have great potential for developing new electronic and optoelectronic devices. This method enables the modulation of the electrical, magnetic, and optical properties of the original materials, thereby establishing a family of 2D materials with widely adjustable electrical and optical properties. It is also possible to introduce some new properties to the 2D materials, such as magnetic properties and catalytic properties, by the intercalation of guest atoms. Interlayer storage, represented by lithium-ion batteries, is also an important application of 2D van der Waals gap utilization in energy storage, which has also attracted significant research attention. Herein, we review the studies conducted in recent years from the following aspects: (1) changing the layer spacing to change the interlayer coupling; (2) introducing the interaction between guest and host atoms to change the physico-chemical properties of raw materials; (3) introducing the guest substances to obtain new properties; and (4) interlayer energy storage. We systematically describe various interlayer optimization methods of 2D van der Waals gaps and their effects on the physical and chemical properties of synthetic materials, and suggest the direction of further development and utilization of 2D van der Waals gaps.     

Accurate description of van der Waals complexes by density functional theory including empirical corrections

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.