Effect of the damping function in dispersion corrected density functional theory

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.     

Dispersion Interaction Stabilizes Sterically Hindered Double Fullerenes

By state‐of‐the‐art quantum chemical methods, we show that for bulky functional groups like cyclohexane, [20]fullerene, dodecahedrane, and C₆₀, the attractive dispersion interaction can have a greater impact on stereochemistry than the repulsive steric effect, making the compact isomer the more stable one. In particular, for the double C₆₀ adduct of pentacene 1 , the syn isomer should be the main product instead of the anti one inferred in the original synthesis experiment (Y. Murata et al., J. Org. Chem.­ 1999 , 64, 3483). With and without dispersion interactions taken into account, the Gibbs energy difference ΔG(syn?anti) is ?6.36 and +1.15 kcal mol^?1, respectively. This study reminds us that dispersion interactions as well as electrostatic or hyperconjugation effects, etc. can lead to some unusual stereochemical phenomena.     

Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP-and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s(R), scaling globally the vdW radii. For good results, a basis set of at least triple-zeta quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.     

Noncovalent interactions in inorganic supramolecular chemistry based in heavy metals. Quantum chemistry point of view

Complexity is a concept that is being considered in chemistry as it has shown potential to reveal interesting phenomena. Thus, it is possible to study chemical phenomena in a new approach called systems chemistry. The systems chemistry has an organization and function, which are regulated by the interactions among its components. At the simplest level, noncovalent interactions between molecules can lead to the emergence of large structures. Consequently, it is possible to go from the molecular to the supramolecular systems chemistry, which aims to develop chemical systems highly complex through intra- and intermolecular forces. Proper use of the interactions previously mentioned allow a glimpse of supramolecular system chemistry in many tasks such as structural properties reflecting certain behaviors in the chemistry of materials, for example, electrical and optical, processes of molecular recognition and among others. In the last time, within this area, inorganic supramolecular systems chemistry has been developed. Those systems have a structural orientation which is defined by certain forces that predominate in the associations among molecules. It is possible to recognize these forces as hydrogen bonding, π-π stacking, halogen bonding, electrostatic, hydrophobic, charge transfer, metal coordination, and metallophilic interactions. The presence of these forces in supramolecular system yields certain properties such as light absorption and luminescence. The quantum theoretical modeling plays an important role in the designing of the supramolecular system. The goal is to apply supramolecular principles in order to understand the associated forces in many inorganic molecules that include heavy metals for instance gold, platinum, and mercury. Relevant systems will be studied in detail, considering functional aspects such as enhanced coordination of functionalized molecular self-assembly, electronic and optoelectronic properties.     

On the van der Waals interactions and the stability of polypeptide chains in helical conformations

In this work, we aim to investigate the contribution of van der Waals (vdW) interactions to the stability of polypeptides in helical conformations studying infinitely long chains of alanine and glycine with density functional theory. To account for vdW interactions, we have used the interatomic pairwise dispersion approach proposed by Tkatchenko–Scheffler (TS), the TS approach with self‐consistent screening (SCS) that self‐consistently includes long‐range electrostatic effects (TS + SCS), the D2 and D3 methods of Grimme et al., and the Langreth–Lundqvist procedure that treats nonlocally the correlation part of the approximation to the exchange‐correlation (xc) functional (called DF). First, we have tested the performance of these strategies studying a set of representative hydrogen bonded dimers. Next, we have studied polyalanine and polyglicine in π‐helix, α‐helix, ‐helix, 2₇, and polyproline‐II conformations and in a fully extended structure. We have found that the DF methodology in combination with a modified version for the Becke approximation to the exchange (optB86b), the D2, D3, TS, and TS + SCS strategies in combination with the Perdew–Burke–Ernzerhof approximation to the xc functional, describe fairly well dimer association energies. Furthermore, the DF method and the D2, D3, TS, and TS + SCS strategies predict very similar helical stabilities even though the approximation used in DF for describing the long‐range dispersion interactions is different that the one used in D2/D3 and TS/TS + SCS. We found that the stability doubles for π and α helices if vdW interactions are taken into account. © 2015 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.     

Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.     

Reparameterization of a meta-generalized gradient approximation functional by combining TPSS exchange with τ1 correlation

We present a new local meta-GGA exchange-correlation density functional by combining the TPSS meta-GGA exchange and the τ1 meta-GGA correlation functionals. The TPSS meta-GGA exchange-correlation and the τ1 meta-GGA correlation functionals have been implemented in the deMon code. The parameters in the τ1 meta-GGA correlation model are reoptimized in a synchronized way to match the original TPSS meta-GGA exchange counterpart. This reparametrized meta-GGA functional is referred to as “TPSSτ3”. The TPSSτ3 and TPSSτ1 meta-GGAs are validated using a test set that consists of covalent molecules, hydrogen-bonded complexes, and van der Waals interactions. The calculated results from TPSSτ1 and TPSSτ3 are analyzed and compared with reliable experimental data and theoretical data, as well as with those from Bmτ1 and TPSS calculations. The τ1 correlation model describes the aromatic compounds better than TPSS. TPSSτ3 yields satisfactory results for the covalent molecules, the hydrogen-bonded complexes, and the van der Waals complexes in the test set compared with TPSS, Bmτ1 and TPSSτ1. Contribution to the Serafin Fraga Memorial Issue.     

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.     

Modeling chemical reactions on surfaces: The roles of chemical bonding and van der Waals interactions

Chemical reactions on surfaces play central roles in heterogeneous catalysis, and most reactions involve the formation and/or the cleavage of bonds. At present, density functional theory (DFT) has become the workhorse for computational investigation of reaction mechanisms, but its predictive power has been severely limited by the lack of appropriate exchange-correlation functionals. Here, we show that there are many cases where the chemical bonding and van der Waals (vdW) interactions both play a key role in chemical reactions on surfaces. After briefly introducing some DFT methods and basic theory in chemical reactions, we first demonstrate that DFT can help to understand the mechanisms of “classic” reactions that mainly dominated by covalent bonding and vdW forces, as exemplified in electrocatalytic reduction of CO₂ and the fabrication of 2D materials on metal substrates. We next show that DFT calculations can help to uncover the tautomerization reactions of molecules on metal surfaces, wherein the hydrogen bonding and vdW forces would largely affect the reaction process. More importantly, we show that in some cases, the vdW interactions can become the decisive effect that determines the adsorption configuration, energy hierarchy, and the potential-energy surface of chemical reactions, yielding distinct pathways and products. Additionally, we highlight the importance of more realistic conditions, such as surface defects, finite coverage, and temperature effects, in accurate modeling of chemical reactions. Finally, we summarize some challenges in modeling catalysis, which include many-body dispersive correction, strong correlation effect, and non-adiabatic approximations.     

Interesting periodic variations in physical and chemical properties of homonuclear diatomic molecules

We carry out a systematic study of various ground state and response properties of homonuclear diatomic molecules (from hydrogen to rubidium, including transition metals) as a function of atomic number of constituent atoms. We perform the ground state and response property calculations by using state of the art density functional theory/time dependent density functional theory. We observe that several properties of homonuclear diatomic molecules show periodic variations along rows and columns of the periodic table. The periodic variations in the ground state properties of diatomic molecules may be explained by the nature and type of the bond that exists between the constituent atoms. Similarly, the periodic variations in the response properties such as static dipole polarizability and strength of the van der Waals interaction between diatomic molecules have been correlated with the variations in metallic/nonmetallic character of the elements along the periodic table. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Molecular mechanics studies of the conformations of metal complexes of 1,4,7,10,13,16-hexaazacyclooctadecane: Calculations of macrocyclic cavity size

Molecular mechanics calculations are reported on metal complexes of 18-azacrown-6. Four possible conformations are considered which encapsulate the metal in different geometric environments, namely, chiral octahedral, meso octahedral, trigonal prismatic, and hexagonal bipyramidal. Crystal structures are available for all but the last geometry, and molecular mechanics calculations show an excellent fit to the experimental data. The strain energy of the macrocycle has been calculated for a range of M-N distances, and thus the hole size of the macrocycle has been obtained for various conformations. Two different methods were used to calculate the strain energy of the metal environment. We either used the conventional molecular mechanics term for angle bending,k _b — ₀)², and chose the ideal angles to fit the particular metal geometry, or we set the angle force constants to zero and introduced 1,3 van der Waals interactions between the ligand donor nitrogen atoms. Results from the two methods are compared.     

Sensing Characteristics of a Graphene‐like Boron Carbide Monolayer towards Selected Toxic Gases

By using first‐principles calculations based on density functional theory, we study the adsorption efficiency of a BC₃ sheet for various gases, such as CO, CO₂, NO, NO₂, and NH₃. The optimal adsorption position and orientation of these gas molecules on the BC₃ surface is determined and the adsorption energies are calculated. Among the gas molecules, CO₂ is predicted to be weakly adsorbed on the graphene‐like BC₃ sheet, whereas the NH₃ gas molecule shows a strong interaction with the BC₃ sheet. The charge transfer between the molecules and the sheet is discussed in terms of Bader charge analysis and density of states. The calculated work function of BC₃ in the presence of CO, CO₂, and NO is greater than that of a bare BC₃ sheet. The decrease in the work function of BC₃ sheets in the presence of NO₂ and NH₃ further explains the affinity of the sheet towards the gas molecules. The energy gap of the BC₃ sheets is sensitive to the adsorption of the gas molecules, which implies possible future applications in gas sensors.     

Improved parameterization of the quantum harmonic oscillator model based on localized wannier functions to describe Van der Waals interactions in density functional theory

Recently, the quantum harmonic oscillator model has been combined with maximally localized Wannier functions to account for long‐range dispersion interactions in density functional theory calculations (Silvestrelli, J. Chem. Phys. 2013, 139, 054106). Here, we present a new, improved set of values for the three parameters involved in this scheme. To test the new parameter set we have computed the potential energy curves for various systems, including an isolated Ar2 dimer, two N2 dimers interacting within different configurations, and a water molecule physisorbed on pristine graphene. While the original set of parameters generally overestimates the interaction energies and underestimates the equilibrium distances, the new parameterization substantially improves the agreement with experimental and theoretical reference values. © 2016 Wiley Periodicals, Inc.     

3D-Graphene/Boron Nitride-stacking Material: a Fundamental van der Waals Heterostructure

The 3D periodic graphene/h-BN(G/BN) heterostuctures were studied. The stacking forms between the graphene and h-BN layers were discussed. The varieties of the geometric and electronic configurations at the interface between graphene and h-BN layers were also reported. The metal-semiconductor transform of the G/BN material can be achieved by adjusting the stacking form of the h-BN layers or changing the proportion of graphene layers in the unit cell. An electrostatic potential well was found at the interface. Due to the potential well and the only dispersion correlation at the interface, the dielectric constant ε_zz in vertical direction was independent on the variety of the thickness or the proportion of the compositions in an unit cell.     

Adsorption of Large Hydrocarbons on Coinage Metals: A van der Waals Density Functional Study

The adsorption of organic molecules onto the close‐packed facets of coinage metals is studied, and how accurately adsorption heights can be described by using recent advances of the van der Waals density functional (vdWDF), with optPBE/vdWDF, optB86b/vdWDF, vdWDF2, and rev/vdWDF2 functionals is illustrated. The adsorption of two prototypical aromatic hydrocarbons is investigated, and the calculated adsorption heights are compared to experimental literature values from normal incident X‐ray standing wave absorption and a state‐of‐the‐art semi‐empirical method. It is shown that both the optB86b/vdWDF and rev/vdWDF2 functionals describe adsorption heights with an accuracy of 0.1 Å, compared to experimental values, and are concluded as reliable methods of choice for related systems.     

Towards Predicting the Sequential Appearance of Zeolitic Imidazolate Frameworks Synthesized by Mechanochemistry

We use computational materials methods to study the sequential appearance of zinc-based zeolitic imidazolate frameworks (ZIFs) generated in the mechanochemical conversion process. We consider nine ZIF topologies, namely RHO, ANA, QTZ, SOD, KAT, DIA, NEB, CAG and GIS, combined with the two ligands 2-methylimidazolate and 2-ethylimidazolate. Of the 18 combinations obtained, only six (three for each ligand) were actually observed during the mechanosynthesis process. Energy and porosity calculations based on density functional theory, in combination with the Ostwald rule of stages, were found to be insufficient to distinguish the experimentally observed ZIFs. We then show, using classical molecular dynamics, that only ZIFs withstanding quasi-hydrostatic pressure P ≥ 0.3 GPa without being destroyed were observed in the laboratory. This finding, along with the requirement that successive ZIFs be generated with decreasing porosity and/or energy, provides heuristic rules for predicting the sequences of mechanically generated ZIFs for the two ligands considered.