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.     

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.     

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.     

van der Waals corrected density functional calculations of the adsorption of benzene on the Cu (111) surface

We investigate the performance of several van der Waals (vdW) functionals at calculating the interactions between benzene and the copper (111) surface, using the local orbital approach in the SIESTA code. We demonstrate the importance of using surface optimized basis sets to calculate properties of pure surfaces, including surface energies and the work function. We quantify the errors created using (3 × 3) supercells to study adsorbate interactions using much larger supercells, and show non‐negligible errors in the binding energies and separation distances. We examine the eight high‐symmetry orientations of benzene on the Cu (111) surface, reporting the binding energies, separation distance, and change in work function. The optimized vdW‐DF(optB88‐vdW) functional provides superior results to the vdW‐DF(revPBE) and vdW‐DF2(rPW86) functionals, and closely matches the experimental and experimentally deduced values. This work demonstrates that local orbital methods using appropriate basis sets combined with a vdW functional can model adsorption between metal surfaces and organic molecules.     

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.     

Optimization of a molecular mechanics force field for type-II polyoxometalates focussing on electrostatic interactions: a case study

In this study, we have focussed on type-II polyanions such as [M(7)O(24)](6-), and we have developed and validated optimized force fields that include electrostatic and van der Waals interactions. These contributions to the total steric energy are described by the nonbonded term, which encompasses all interactions between atoms that are not transmitted through the bonds. A first validation of a stochastic technique based on genetic algorithms was previously made for the optimization of force fields dedicated to type-I polyoxometalates. To describe the new nonbonded term added in the functional, a fixed-charged model was chosen. Therefore, one of the main issues was to analyze that which partial atomic charges could be reliably used to describe these interactions in such inorganic compounds. Based on several computational strategies, molecular mechanics (MM) force field parameters were optimized using different types of atomic charges. Moreover, the influence of the electrostatic and van der Waals buffering constants and 1,4-interactions scaling factors used in the force field were also tested, either being optimized as well or fixed with respect to the values of CHARMM force field. Results show that some atomic charges are not well adapted to CHARMM parameters and lead to unrealistic MM-optimized structures or a MM divergence. As a result, a new scaling factor has been optimized for Quantum Theory of Atoms in Molecules charges and charges derived from the electrostatic potential such as ChelpG. The force fields optimized can be mixed with the CHARMM force field, without changing it, to study for the first time hepta-anions interacting with organic molecules.     

An analysis of an induced-fit type inclusion phenomenon of a paracyclophane with benzene by means of van der waals potential calculations

The binding process of the paracyclophane 1 with benzene is classified into two types; namely simple fit and induced fit. In the former case, it is assumed that the geometry of the host is fixed to that in the free state during complexation. On the basis of the MMP2 calculations, the induced fit type process, allowing all motional freedoms of the host and the guest, is essential in forming the stable inclusion complex with benzene. By the use of van der Waals potential maps, it is confirmed that the force-field inside the cavity of the host is effective for the inclusion of benzene.     

van der Waals corrections to density functional theory calculations: Methane,ethane, ethylene,benzene, formaldehyde,ammonia, water,PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

Different van der Waals radii for organic and inorganic halogen atoms: a significant improvement in IMOMM performance

The discrepancies between X-ray and integrated molecular orbital molecular mechanics computed geometries for Os(H)₂Cl₂(PⁱPr₃)₂ and Ir(H)₂Cl(P^tBu₂ Ph)₂ are explained by the inadequacy of the default molecular mechanics van der Waals radii for halogen elements. A simple procedure is proposed for the calculation of corrected van der Waals radii, and the application of the corrected radius for chloride is shown to improve substantially the results for the systems under test. Received: 25 February 1997 / Accepted: 7 April 1997     

Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions

The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor = 13.772 at or near the equilibrium and = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.     

Predicting whether aromatic molecules would prefer to enter a carbon nanotube: A density functional theory study

The interaction of a carbon nanotube (CNT) with various aromatic molecules, such as aniline, benzophenone, and diphenylamine, was studied using density functional theory able to compute intermolecular weak interactions (B3LYP-D3). CNTs of varying lengths were used, such as 4-CNT, 6-CNT, and 8-CNT (the numbers denoting relative lengths), with the lengths being chosen appropriately to save computation times. All aromatic molecules were found to exhibit strong intermolecular binding energies with the inner surface of the CNT, rather than the outer surface. Hydrogen bonding between two aromatic molecules that include N and O atoms is shown to further stabilize the intermolecular adsorption process. Therefore, when benzophenone and diphenylamine were simultaneously allowed to interact with a CNT, the aromatic molecules were expected to preferably enter the CNT. Furthermore, additional calculations of the intermolecular adsorption energy for aniline adsorbed on a graphene surface showed that the concavity of graphene-like carbon sheet is in proportion to the intermolecular binding energy between the graphene-like carbon sheet and the aromatic molecule.     

Ring formation mechanism of single-walled carbon nanotubes: Energy conservation between curvature elasticity and inter-tube adhesion

Rings of single-walled carbon nanotubes (SWNTs) exist widely during water evaporation from their dispersions at low concentration on such substrates as silica wafer. We examine the phenomenon in terms of energy conservation between the increased significant curvature energy and the inherent inter-tube van der Waals (vdW) attraction potentials. And thereby, the observed multi ring structures for coarse and long SWNT bundles have also gained detailed interpretation. We conclude that carbon nanotubes (CNTs) coil into rings by their own elastic mechanism. The formed rings with different width and diameters originate from appropriate sizes of SWNTs or the bundles. Specially, the associated elasticity may have prospective potentials to reveal other fascinating self-assembling phenomenon on CNTs, for instance, the known liquid crystallinity of them. Besides, we have also analyzed the external factors to the ring formation, both statistically and dynamically.     

Dual-hybrid direct random phase approximation and second-order screened exchange with nonlocal van der Waals correlations for noncovalent interactions

We have added the nonlocal van der Waals correlation energy functional of Vydrov and Van Voorhis in 2010 (VV10NL) to the dual-hybrid direct random phase approximation (dRPA75) and second-order screened exchange (SOSEX75) for noncovalent interactions. The obtained methods are denoted as dRPA75-NL and SOSEX75-NL, and the corresponding short-range attenuation parameters are fitted with the large aug-cc-pV5Z basis set against the S66 dataset. Therefore, the dRPA75-NL method overcomes the error cancellation problem of the dRPA75 method with the relatively small aug-cc-pVTZ basis set for noncovalent interactions. Based on our benchmark computations, the dRPA75-NL and SOSEX75-NL methods perform very well on evaluating noncovalent interaction energies. Compared with the double-hybrid density functionals (DHDFs) of DSD-PBEP86-NL and DOD-PBEP86-NL, the dRPA75-NL and SOSEX75-NL methods perform much better on charge transfer interactions. Furthermore, the SOSEX75-NL method also gives insight into the development of computational methods for both closed-shell and open-shell noncovalent interactions. In summary, our computations demonstrate that even the full dRPA and SOSEX correlations still need additional dispersion corrections for noncovalent interactions.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999