Effects of an electric field on interaction of aromatic systems

The effect of uniform external electric field on the interactions between small aromatic compounds and an argon atom is investigated using post‐HF (MP2, SCS‐MP2, and CCSD(T)) and density functional (PBE0‐D3, PBE0‐TS, and vdW‐DF2) methods. The electric field effect is quantified by the difference of interaction energy calculated in the presence and absence of the electric field. All the post‐HF methods describe electric field effects accurately although the interaction energy itself is overestimated by MP2. The electric field effect is explained by classical electrostatic models, where the permanent dipole moment from mutual polarization mainly determines its sign. The size of π‐conjugated system does not have significant effect on the electric field dependence. We found out that PBE0‐based methods give reasonable interaction energies and electric field response in every case, while vdW‐DF2 sometimes shows spurious artifact owing to its sensitivity toward the real space electron density. © 2015 Wiley Periodicals, Inc.     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

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.     

The Nature of the Binding of Au, Ag, and Pd to Benzene, Coronene, and Graphene: From Benchmark CCSD(T) Calculations to Plane-Wave DFT Calculations

The adsorption of Ag, Au, and Pd atoms on benzene, coronene, and graphene has been studied using post Hartree-Fock wave function theory (CCSD(T), MP2) and density functional theory (M06-2X, DFT-D3, PBE, vdW-DF) methods. The CCSD(T) benchmark binding energies for benzene-M (M = Pd, Au, Ag) complexes are 19.7, 4.2, and 2.3 kcal/mol, respectively. We found that the nature of binding of the three metals is different: While silver binds predominantly through dispersion interactions, the binding of palladium has a covalent character, and the binding of gold involves a subtle combination of charge transfer and dispersion interactions as well as relativistic effects. We demonstrate that the CCSD(T) benchmark binding energies for benzene-M complexes can be reproduced in plane-wave density functional theory calculations by including a fraction of the exact exchange and a nonempirical van der Waals correction (EE+vdW). Applying the EE+vdW method, we obtained binding energies for the graphene-M (M = Pd, Au, Ag) complexes of 17.4, 5.6, and 4.3 kcal/mol, respectively. The trends in binding energies found for the benzene-M complexes correspond to those in coronene and graphene complexes. DFT methods that use empirical corrections to account for the effects of vdW interactions significantly overestimate binding energies in some of the studied systems.     

氢气在Na-MAZ和Li-MAZ沸石原子簇上的吸附

采用基于密度泛函理论(DFT)的广义梯度近似(GGA)/PBE(Perdew-Burke-Ernzerhof)交换相关泛函和双数值基加p极化(DNP)基组对氢气分子在Na-MAZ和Li-MAZ沸石原子簇上的吸附进行了研究, 计算得到吸附复合物的平衡几何结构参数、振动频率以及吸附能等数据. 结果表明: MAZ沸石中存在四个稳定的吸附位点, 分别为SI′、SI″、SII′和SII″位点; 氢气分子在Na-MAZ沸石的SII″位点吸附时最稳定, 而在Li-MAZ沸石中, 氢气分子处于SI″和SII″位点时最稳定. 吸附能越大, 氢气分子键长越长, 振动频率减少也越多. Li-MAZ沸石对氢气的吸附能力要明显强于Na-MAZ沸石的吸附能力, 理论上Li-MAZ沸石具有更高的氢气储量, 可能是一种潜在的储氢材料.     

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.     

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.     

Understanding the Effect of the Exchange-Correlation Functionals on Methane and Ethane Formation over Ruthenium Catalysts

Density functional theory (DFT) has been established as a powerful research tool for heterogeneous catalysis research in obtaining key thermodynamic and/or kinetic parameters like adsorption energies, enthalpies of reaction, activation barriers, and rate constants. Understanding of density functional exchange-correlation approximations is essential to reveal the mechanism and performance of a catalyst. In the present work, we reported the influence of six exchange-correlation density functionals, including PBE, RPBE, BEEF+vdW, optB86b+vdW, SCAN, and SCAN+rVV10, on the adsorption energies, reaction energies and activation barriers of carbon hydrogenation and carbon-carbon couplings during the formation of methane and ethane over Ru(0001) and Ru(1011) surfaces. We found the calculated reaction energies are strongly dependent on exchange-correlation density functionals due to the difference in coordination number between reactants and products on surfaces. The deviation of the calculated elementary reaction energies can be accumulated to a large value for chemical reaction involving multiple steps and vary considerably with different exchange-correlation density functionals calculations. The different exchange-correlation density functionals are found to influence considerably the selectivity of Ru(0001) surface for methane, ethylene, and ethane formation determined by the adsorption energies of intermediates involved. However, the influence on the barriers of the elementary surface reactions and the structural sensitivity of Ru(0001) and Ru(1011) are modest. Our work highlights the limitation of exchange-correlation density functionals on computational catalysis and the importance of choosing a proper exchange-correlation density functional in correctly evaluating the activity and selectivity of a catalyst.     

Adsorption of liquid-phase alkane mixtures in silicalite: simulations and experiment

A combination of experimental and computational studies of adsorption from liquid-phase mixtures of linear alkanes in the zeolite silicalite is presented here. Configurational biased grand canonical Monte Carlo simulations combined with identity-swap moves are used to equilibrate the simulations in reasonable times. Interesting trends observed in experiments have been captured quantitatively by simulations. A siting analysis of the simulation data reveals that, during adsorption from a liquid mixture, shorter alkanes prefer the zigzag channels and longer alkanes concentrate in the straight channels of silicalite.     

A balanced procedure for the treatment of cluster–ligand interactions on gold phosphine systems in catalysis

Ligand‐protected metal clusters are difficult to describe within density functional theory due to the need to treat the electronic structure of the cluster, possible charge transfer between the ligands and the cluster, and weak ligand–ligand interactions in a balanced manner. We demonstrate the use of an appropriate, stepwise benchmarking process that accounts for the nonadditivity of these different contributions to stability and catalytic activity. We consider both open‐ and closed‐shell clusters, differently charged systems, and ligands of increasing complexity for gold phosphine systems. The use of a dispersion correction to density functional calculations was found to be crucial for both structure optimization and the calculation of binding energies. We find that PBE‐D3 performs well with a variation in energetics of 0.7–10.9 kcal/mol, PBE0‐D3 better with 0.0–3.3 kcal/mol, and B2PLYP‐D3 the best with 0.2–2.4 kcal/mol, when compared to the best available benchmark [CCSD(T) or SCS‐MP2]. Our systematic procedure clarifies that these functionals all give accurate results for certain cases, but for the total performance over a range of interactions, they perform in accordance with Jacob's ladder. © 2014 Wiley Periodicals, Inc.     

Influence of Van der Waals Interactions on the Solvation Energies of Adsorbates at Pt-Based Electrocatalysts

Solvation can significantly modify the adsorption energy of species at surfaces, thereby influencing the performance of electrocatalysts and liquid-phase catalysts. Thus, it is important to understand adsorbate solvation at the nanoscale. Here we evaluate the effect of van der Waals (vdW) interactions described by different approaches on the solvation energy of *OH adsorbed on near-surface alloys (NSAs) of Pt. Our results show that the studied functionals can be divided into two groups, each with rather similar average *OH solvation energies: (1) PBE and PW91; and (2) vdW functionals, RPBE, PBE-D3 and RPBE-D3. On average, *OH solvation energies are less negative by ∼0.14 eV in group (2) compared to (1), and the values for a given alloy can be extrapolated from one functional to another within the same group. Depending on the desired level of accuracy, these concrete observations and our tabulated values can be used to rapidly incorporate solvation into models for electrocatalysis and liquid-phase catalysis.     

Heats of adsorption of methanol and ethanol on high-silicon ZSM-5 zeolite

The heats of adsorption of lower alcohols on NaZSM-5 have a stepwise appearance and each step corresponds to the stoichiometric formation of adsorption complexes of Na⁺ ions with from one to four alcohol molecules. All the adsorption complexes are located at zeolite channel intersections, while the alkyl groups enter these channels. The heats of adsorption of alcohols on NaZSM in the region of the formation of adsorption complexes with cations markedly exceed the heats of adsorption on silicalite, while on the noncationic part of the NaZSM-5 structure, they are identical to the heats of adsorption on silicalite. The mean molar integral adsorption entropies of alcohols are significantly less than the entropy of the liquid. The adsorbed molecules are in a solidlike state. The isotherms for the adsorption of alcohols on NaZSM-5 are completely described by VMOT equations.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2633–2635, November, 1989.     

Assessment of density functional theory to calculate the phase transition pressure of ice

To assess the accuracy of density functional theory (DFT) methods in describing hydrogen bonding in condensed phases, we benchmarked their performance in describing phase transitions among different phases of ice. We performed DFT calculations of ice for phases Ih, II, III, VI and VII using BLYP, PW91, PBE, PBE-D, PBEsol, B3LYP, PBE0, and PBE0-D, and compared the calculated phase transition pressures between Ih-II, Ih-III, II-VI, and VI-VII with the 0 K experimental values of Whalley [J. Chem. Phys., 1984, 81, 4087]. From the geometry optimization of many different candidates, we found that the most stable proton orientation as well as the phase transition pressure does not show much functional dependence for the generalized gradient approximation and hybrid functionals. Although all these methods overestimated the phase transition pressure, the addition of van der Waals (vdW) correction using PBE-D and PBE0-D reduced the transition pressure and improved the agreement for Ih-II. On the other hand, energy ordering between VI and VII reversed and gave an unphysical negative transition pressure. Binding energy profiles of a few conformations of water dimers were calculated to understand the improvement for certain transitions and failures for others with the vdW correction. We conclude that vdW dispersion forces must be considered to accurately describe the hydrogen bond in many different phases of ice, but the simple addition of the R(-6) term with a small basis set tends to over stabilize certain geometries giving unphysical ordering in the high density phases.     

CO2 capture by metal-organic frameworks with van der Waals density functionals

We use density functional theory calculations with van der Waals corrections to study the role of dispersive interactions on the structure and binding of CO(2) within two distinct metal-organic frameworks (MOFs): Mg-MOF74 and Ca-BTT. For both classes of MOFs, we report calculations with standard gradient-corrected (PBE) and five van der Waals density functionals (vdW-DFs), also comparing with semiempirical pairwise corrections. The vdW-DFs explored here yield a large spread in CO(2)-MOF binding energies, about 50% (around 20 kJ/mol), depending on the choice of exchange functional, which is significantly larger than our computed zero-point energies and thermal contributions (around 5 kJ/mol). However, two specific vdW-DFs result in excellent agreement with experiments within a few kilojoules per mole, at a reduced computational cost compared to quantum chemistry or many-body approaches. For Mg-MOF74, PBE underestimates adsorption enthalpies by about 50%, but enthalpies computed with vdW-DF, PBE+D2, and vdW-DF2 (40.5, 38.5, and 37.4 kJ/mol, respectively) compare extremely well with the experimental value of 40 kJ/mol. vdW-DF and vdW-DF2 CO(2)-MOF bond lengths are in the best agreement with experiments, while vdW-C09(x) results in the best agreement with lattice parameters. On the basis of the similar behavior of the reduced density gradients around CO(2) for the two MOFs studied, comparable results can be expected for CO(2) adsorption in BTT-type MOFs. Our work demonstrates for this broad class of molecular adsorbate-periodic MOF systems that parameter-free and computationally efficient vdW-DF and vdW-DF2 approaches can predict adsorption enthalpies with chemical accuracy.     

Assessment of density functional methods for reaction energetics: Iridium‐catalyzed water oxidation as case study

We investigate basis set convergence for a series of density functional theory (DFT) functionals (both hybrid and nonhybrid) and compare to coupled‐cluster with single and double excitations and perturbative triples [CCSD(T)] benchmark calculations. The case studied is the energetics of the water oxidation reaction by an iridium‐oxo complex. Complexation energies for the reactants and products complexes as well as the transition state (TS) energy are considered. Contrary to the expectation of relatively weak basis set dependence for DFT, the basis set effects are large, for example, more than 10 kcal mol^?1 difference from converged basis for the activation energy with “small” basis sets (DZ/6‐31G** for Ir/other atoms, or SVP) and still more than 6 kcal mol^?1 for def2‐TZVPP/6‐31G**. Inclusion of the dispersion correction in DFT‐D3 schemes affects the energies of reactant complex (RC), TS, and product complex (PC) by almost the same amount; it significantly improves the complexation energy (the formation of RC), but has little effect on the activation energy with respect to RC. With converged basis, some pure GGAs (PBE‐D3, BP86‐D3) as well as the hybrid functional B3LYP‐D3 are very accurate compared to benchmark CCSD(T) calculations. © 2012 Wiley Periodicals, Inc.     

Water monomer interaction with gold nanoclusters from van der Waals density functional theory

We investigate the interaction between water molecules and gold nanoclusters Au(n) through a systematic density functional theory study within both the generalized gradient approximation and the nonlocal van der Waals (vdW) density functional theory. Both planar (n = 6-12) and three-dimensional (3D) clusters (n = 17-20) are studied. We find that applying vdW density functional theory leads to an increase in the Au-Au bond length and a decrease in the cohesive energy for all clusters studied. We classify water adsorption on nanoclusters according to the corner, edge, and surface adsorption geometries. In both corner and edge adsorptions, water molecule approaches the cluster through the O atom. For planar clusters, surface adsorption occurs in a O-up/H-down geometry with water plane oriented nearly perpendicular to the cluster. For 3D clusters, water instead favors a near-flat surface adsorption geometry with the water O atom sitting nearly atop a surface Au atom, in agreement with previous study on bulk surfaces. Including vdW interaction increases the adsorption energy for the weak surface adsorption but reduces the adsorption energy for the strong corner adsorption due to increased water-cluster bond length. By analyzing the adsorption induced charge rearrangement through Bader's charge partitioning and electron density difference and the orbital interaction through the projected density of states, we conclude that the bonding between water and gold nanocluster is determined by an interplay between electrostatic interaction and covalent interaction involving both the water lone-pair and in-plane orbitals and the gold 5d and 6s orbitals. Including vdW interaction does not change qualitatively the physical picture but does change quantitatively the adsorption structure due to the fluxionality of gold nanoclusters.