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.     

A van der Waals density functional study of ice Ih

Density functional theory with the van der Waals density functional (vdW-DF) is used to calculate equilibrium crystal structure, binding energy, and bulk modulus of ice Ih. It is found that although it overestimates the equilibrium volume, vdW-DF predicts accurate binding energy of ice Ih, as compared with high level quantum chemistry calculations and experiment. Inclusion of the nonlocal correlation, i.e., van der Waals interaction, leads to an overall improvement over the standard generalized gradient approximation in describing water ice.     

An application of the van der Waals density functional: Hydrogen bonding and stacking interactions between nucleobases

We apply the van der Waals density functional (vdW-DF) to study hydrogen bonding and stacking interactions between nucleobases. The excellent agreement of our results with high level quantum chemical calculations highlights the value of the vdW-DF for first-principles investigations of biologically important molecules. Our results suggest that, in the case of hydrogen-bonded nucleobase pairs, dispersion interactions reduce the cost of propeller twists while having a negligible effect on buckling. Furthermore, the efficient scaling of DFT methods allowed for the easy optimization of separation distance between nucleobase stacks, indicating enhancements in the interaction energy of up to 3 kcalmol over previous fixed distance calculations. We anticipate that these results are significant for extending the vdW-DF method to model larger vdW complexes and biological 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.     

One-dimensional molecular zippers

We synthesized an azobenzene derivative to demonstrate a one-dimensional molecular zipper. The formation and underlying mechanism of the molecular zipper formed by combined hydrogen-bonding and van der Waals interactions between adjacent molecules were investigated on a Au(111) surface using scanning tunneling microscopy and density functional theory calculations.     

Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set

Nearly all common density functional approximations fail to properly describe dispersion interactions responsible for binding in van der Waals complexes. Empirical corrections can fix some of the failures but cannot fully grasp the complex physics and may not be reliable for systems dissimilar to the fitting set. In contrast, the recently proposed nonlocal van der Waals density functional (vdW-DF) was derived from first principles, describes dispersion interactions in a seamless fashion, and yields the correct asymptotics. Implementation of this functional is somewhat cumbersome: Nonlocal dependence on the electron density requires numerical double integration over the space variables and functional derivatives are nontrivial. This paper shows how vdW-DF can be implemented self-consistently with Gaussian basis functions. The gradients of the energy with respect to nuclear displacements have also been derived and coded, enabling efficient geometry optimizations. We test the vdW-DF correlation functional in combination with several exchange approximations. We also study the sensitivity of the method to the basis set size and to the quality of the numerical quadrature grid. For weakly interacting systems, acceptable accuracy in semilocal exchange is achieved only with fine grids, whereas for nonlocal vdW-DF correlation even rather coarse grids are sufficient. The current version of vdW-DF is not well suited for pairing with Hartree-Fock exchange, leading to considerable overbinding.     

van der Waals interactions of polycyclic aromatic hydrocarbon dimers

Density functional theory is in principle exact and includes also long-range interactions, such as the van der Waals interactions. These are, however, part of the exchange-correlation energy functional that needs to be approximated, and are absent in the local and semilocal standard implementations. Recently a density functional which includes van der Waals interactions for planar systems has been developed, which we show can be extended to provide a treatment of planar molecules. We use this functional to calculate binding distances and energies for dimers of three of the smallest polycyclic aromatic hydrocarbons (PAHs)--naphthalene, anthracene, and pyrene.     

Amalgamating at the molecular level. A study of the strong closed-shell Au(I)···Hg(II) interaction

Complex {[Hg(C(6)F(5))(2)][Au(C(6)F(5))(PMe(3))](2)}(n)2 displays unsupported Au(I)···Hg(II) and Au(I)···Au(I) interactions. Its crystal structure displays a polymeric -(Au-Hg-Au-Au-Hg-Au)(n)- disposition. Ab initio calculations show very strong Au(I)···Hg(II) and Au(I)···Au(I) closed-shell interactions of -73.3 kJ mol(-1) and -57.0 kJ mol(-1), respectively, which have a dispersive (van der Waals) nature and are strengthened by large relativistic effects (>20%).     

Density, structure, and dynamics of water: the effect of van der Waals interactions

It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.     

The van der Waals Interactions of n‐Alkanethiol‐Covered Surfaces: From Planar to Curved Surfaces

The van der Waals (vdW) interactions of n ‐alkanethiols (ATs) adsorbed on planar Au(111) and Au(100) surfaces and curved Au nanoparticles of different diameters are reported. By means of electrochemical measurements and molecular dynamic calculations, the increase in the average geometrical curvature of the surface influences the global interactions, that is, decreasing vdW interactions between neighboring molecules. Small NPs do not present the same electrochemical behavior as planar surfaces. The transition between nanoparticle to flat surface electrochemical response is estimated to occur at a circa 13–20 nm diameter range.     

Reactions of B atoms and clusters with NO: experimental and theoretical characterization of novel molecules containing B, N, and O

Reactions of boron atoms and clusters with NO molecules in solid argon have been studied using matrix isolation infrared absorption spectroscopy. The reaction products were identified by isotopic substitution ((10)B, (11)B, (15)N(16)O, (14)N(18)O, and mixtures) and comparison with density functional calculations of isotopic frequencies. In solid argon, boron atoms spontaneously reacted with NO to form the insertion molecule NBO. The BNBO and OBNNO molecules were formed by the B and NO addition reactions to NBO. The linear BBNO and BBBNO nitrosyls also were formed spontaneously on annealing. These molecules photochemically rearranged to the more stable BNBO and BNBBO isomers, which have linear polyyne-like structures. The photosensitive OBNNO molecule decomposed to form the NNBO(2) van der Waals complex. In addition, the novel OBON diradical was also formed on photolysis in high-concentration NO experiments.     

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.     

Competition between van der Waals and hydrogen bonding interactions: structure of the trans-1-naphthol/N(2) cluster

The excitation energy in the multiphoton ionization spectrum of the trans-1-naphthol/N(2) cluster shows only a small red shift with respect to isolated naphthol, indicating a van der Waals pi-bound structure rather than a hydrogen-bonded one. To confirm this interpretation, high-level electronic structure calculations were performed for several pi- and hydrogen-bonded isomers of this cluster. The calculations were carried out at the second order M?ller-Plesset (MP2) level of perturbation theory with the family of correlation consistent basis sets up to quintuple-zeta quality including corrections for the basis set superposition error and extrapolation to the MP2 complete basis set (CBS) limit. We report the optimal geometries, vibrational frequencies, and binding energies (D(e)), also corrected for harmonic zero-point energies (D(0)), for three energetically low-lying isomers. In all calculations the lowest energy structure was found to be an isomer with the N(2) molecule bound to the pi-system of the naphthol ring carrying the OH group. In the CBS limit its dissociation energy was computed to be D(0) = 2.67 kcal/mol (934 cm(-1)) as compared to D(0) = 1.28 kcal/mol (448 cm(-1)) for the H-bound structure. The electronic structure calculations therefore confirm the assignment of the experimental electronic spectrum corresponding to a van der Waals pi-bound structure. The energetic stabilization of the pi-bound isomer with respect to the hydrogen-bonded one is rather unexpected when compared with previous findings in related systems, in particular phenol/N(2).     

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.     

Adsorption of square and rectangular plate-like molecules on a planar surface

A mean-field statistical thermodynamic analysis of monolayer adsorption of rigid square and rectangular plate-like molecules on a homogeneous planar surface is developed. The analysis is simplified by only considering facewise and edgewise modes of adsorption in restricted orthogonal orientations parallel to the surface. The free energy density, adsorbate population distribution and surface spreading pressure are obtained as a function of adsorbate density and compared for square plate molecules using three different sequences of adsorbate molecule placement on the surface to evaluate the configurational degeneracy. It is found that edgewise adsorbed molecules can be anisotropically ordered if the edge length of square and rectangular plate-like molecules exceeds three length units in the absence of anisotropic dispersion interactions. If intermolecular dispersion interactions are present and of sufficient strength, the spreading pressure-density isotherms can exhibit one or two van der Waals loops for square plate molecules with three van der Waals loops possible for rectangular plate adsorbate molecules. The phase transitions for the adsorbed monolayer corresponding to the appearance of these van der Waals loops are discussed.     

Inelastic neutron scattering,Raman, vibrational analysis with anharmonic corrections,and scaled quantum mechanical force field for polycrystalline l-alanine

A scaled quantum mechanical harmonic force field (SQMFF) corrected for anharmonicity is obtained for the 23 K l-alanine crystal structure using van der Waals corrected periodic boundary condition density functional theory (DFT) calculations with the PBE functional. Scale factors are obtained with comparisons to inelastic neutron scattering (INS), Raman, and FT-IR spectra of polycrystalline l-alanine at 15–23 K. Calculated frequencies for all 153 normal modes differ from observed frequencies with a standard deviation of 6 wavenumbers. Non-bonded external k = 0 lattice modes are included, but assignments to these modes are presently ambiguous. The extension of SQMFF methodology to lattice modes is new, as are the procedures used here for providing corrections for anharmonicity and van der Waals interactions in DFT calculations on crystals. First principles Born–Oppenheimer molecular dynamics (BOMD) calculations are performed on the l-alanine crystal structure at a series of classical temperatures ranging from 23 K to 600 K. Corrections for zero-point energy (ZPE) are estimated by finding the classical temperature that reproduces the mean square displacements (MSDs) measured from the diffraction data at 23 K. External k = 0 lattice motions are weakly coupled to bonded internal modes.     

Weakly interacting molecular layer of spinning C60 molecules on TiO2 (110) surfaces

The adsorption of C(60), a typical acceptor organic molecule, on a TiO(2) (110) surface has been investigated by a multitechnique combination, including van der Waals density functional calculations. It is shown that the adsorbed molecules form a weakly interacting molecular layer, which sits on the fivefold-coordinated Ti that is confined between the prominent bridging oxygen rows (see figure).