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.     

Van der Waals interactions in aromatic systems: structure and energetics of dimers and trimers of pyridine.

Full geometry optimizations at the dispersion-corrected DFT-BLYP level of theory were carried out for dimers and trimers of pyridine. The DFT-D interaction energies were checked against results from single-point SCS-MP2/aug-cc-pVTZ calculations. Three stacked structures and a planar H-bonded dimer were found to be very close in energy (interaction energies in the range from -3.4 to -4.0 kcal mol(-1)). Two T-shaped geometries are higher lying, by about 1 kcal mol(-1), which is explained by the more favorable electrostatic interactions in the stacked and H-bonded arrangements. The DFT-D approach has proved to be a reliable and efficient tool to explore the conformational space of aromatic van der Waals complexes and furthermore provides interaction energies with errors of less than 10-20 % of DeltaE. Comparisons with previous results obtained by using only partially optimized model geometries strongly indicate that unconstrained optimizations are mandatory in such weakly bonded low-symmetry systems.     

Van der Waals complexes of polar aromatic molecules: unexpected structures for dimers of azulene

Full geometry optimizations at the dispersion corrected DFT-BLYP/TZV2P level of theory have been performed for dimers of azulene that may serve as a model system for the van der Waals complexes of polar pi systems. The structures and binding energies for 11 dimers are investigated in detail. The DFT-D interaction energies have been successfully checked against results from the accurate SCS-MP2/aug-cc-pVTZ approach. Out of the nine investigated stacked complexes, eight have binding energies larger than 7.4 kcal/mol (SCS-MP2) that exceed the value of 7.1 kcal/mol for the best naphthalene dimer. T-shaped arrangements (CH...pi) are significantly less stable. Two out of the three best structures have an antiparallel alignment of the monomer dipole moments in the complex, although the best ones with a parallel orientation are only about 0.5 kcal/mol less strongly bound which points to a minor importance of dipole-dipole interactions to binding. Quite surprisingly, the energetically lowest structure (DeltaE = -9.2 kcal/mol) corresponds to a situation where the two seven-membered rings are located almost on top of each other (7-7) and the long molecular axes are rotated against each other by 130 degrees. The 7-7 structural motif is found also in other energetically low-lying structures, and the expected 5-7 (two-side) arrangement is less strongly bound by about 2 kcal/mol. This can be explained by the electrostatic potential of azulene that only partially reflects the charge separation according to the common 4n + 2 pi electron rule. General rules for predicting stable van der Waals complexes of polar pi systems are discussed.     

Konformationen von 1,3-dioxanen nach der kraftfeldmethode. nichtbindende wechselwirkungen von sauerstoff

The treatment of oxygen lone pairs in force field calculations is discussed. The geometries of 1,3-dioxanes can be calculated well without explicit account of lone pairs. For the calculation of conformational energies in 5-alkyl-1,3-dioxanes electrostatic interactions between point charges taken from quantum mechanical calculations must be included. Addition of van der Waals interactions of lone pairs as weak potentials further improves the calculated conformational energies.     

On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level

The geometries and interaction energies of stacked and hydrogen-bonded uracil dimers and a stacked adeninecdots, three dots, centeredthymine pair were studied by means of high-level quantum chemical calculations. Specifically, standard as well as counterpoise-corrected optimizations were performed at second-order Moller-Plesset (MP2) and coupled cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)] levels with various basis sets up to the complete basis set limit. The results can be summarized as follows: (i) standard geometry optimization with small basis set (e.g., 6-31G(*)) provides fairly reasonable intermolecular separation; (ii) geometry optimization with extended basis sets at the MP2 level underestimates the intermolecular distances compared to the reference CCSD(T) results, whereas the MP2/cc-pVTZ counterpoise-corrected optimization agrees well with the reference geometries and, therefore, is recommended as a next step for improving MP2/cc-pVTZ geometries; (iii) the stabilization energy of stacked nucleic acids base pairs depends considerably on the method used for geometry optimization, so the use of reliable geometries, such as counterpoise-corrected MP2/cc-pVTZ ones, is recommended; (iv) the density functional theory methods fail completely in locating the energy minima for stacked structures and when the geometries from MP2 calculations are used, the resulting stabilization energies are strongly underestimated; (v) the self-consistent charges-density functional tight binding method, with inclusion of the empirical dispersion energy, accurately reproduces interaction energies and geometries of dispersion-bonded (stacked) complexes; this method can thus be recommended for prescanning the potential energy surfaces of van der Waals complexes.     

Electronic spectroscopy of benzo[g,h,i]perylene and coronene inside helium nanodroplets

We have recorded the electronic spectra of benzo[g,h,i]perylene and coronene and their van der Waals complexes with argon and oxygen with a helium-nanodroplet depletion spectrometer. These molecules differ by the addition of one and two fused benzene rings to perylene, which was previously studied in helium. The coronene spectrum is similar to a previously reported jet-cooled laser-induced fluorescence (LIF) spectrum. The van der Waals complexes with argon and oxygen show different complexation sites and maximum number of adsorbants. We report a vibronically resolved benzo[g,h,i]perylene S(1) <-- S(0) spectrum. The spectral lines are split in a similar way to that of several molecules studied before. However, surprisingly, while the van der Waals complexes with argon are free of the splitting, the complexes with oxygen retain the splitting, with increased linewidth and splitting. We could also observe the S(2) <-- S(0) origin transition of benzo[g,h,i]perylene which was previously observed by cavity ring down spectroscopy. While in general the two spectra are quite similar, the relative intensities and spectral shifts of several lines are different.     

Binding of hydrogen on benzene, coronene, and graphene from quantum Monte Carlo calculations

Quantum Monte Carlo calculations with the diffusion Monte Carlo (DMC) method have been used to compute the binding energy curves of hydrogen on benzene, coronene, and graphene. The DMC results on benzene agree with both M?ller-Plessett second order perturbation theory (MP2) and coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] calculations, giving an adsorption energy of ～25 meV. For coronene, DMC agrees well with MP2, giving an adsorption energy of ～40 meV. For physisorbed hydrogen on graphene, DMC predicts a very small adsorption energy of only 5 ± 5 meV. Density functional theory (DFT) calculations with various exchange-correlation functionals, including van der Waals corrected functionals, predict a wide range of binding energies on all three systems. The present DMC results are a step toward filling the gap in accurate benchmark data on weakly bound systems. These results can help us to understand the performance of current DFT based methods, and may aid in the development of improved approaches.     

Time dependent density functional theory calculations for electronic circular dichroism spectra and optical rotations of conformationally flexible chiral donor-acceptor dyad

Twelve conformations of a chiral donor-acceptor (charge-transfer) dyad and six conformations of its dimer complex were structurally optimized by using the Kohn-Sham density functional theory (BLYP/TZV2P) incorporating a recently developed empirical correction scheme that uses C6/R6 potentials for van der Waals interactions (DFT-D). Subsequent time-dependent DFT calculations with BH-LYP and B3-LYP functionals (with triple-zeta basis set) were performed to obtain theoretical circular dichroism (CD) spectra. The experimental CD spectra obtained independently were properly reproduced by averaging the calculated spectra of individual conformers according to a Boltzmann population derived from single-point SCS-MP2 energies. The optical rotations of the monomer were also calculated by using the same functionals with an aug-cc-pVDZ basis set. Dielectric continuum solvation models (COSMO) applied to correct the relative energies from the isolated molecule calculations resulted in conformer distributions that piled the same or even poorer level of agreement with the experimental CD spectrum. Our results clearly show the advantage of the DFT-D method for the geometry optimization of large systems with donor-acceptor interactions and the TD-DFT/BH-LYP calculations for reproducing the experimental CD spectra. As compared with the calculated optical rotations, the wealthy information embedded in the experimental/calculated CD spectra is requisite for the configurational and/or conformational analyses of relatively large and flexible chiral organic molecules in solution.     

Electronic structure and chemical bond in naphthalene and anthracene

We investigated the electronic structure of crystalline naphthalene and anthracene within the framework of density functional theory including van der Waals interactions (DFT-D). It is established that for better agreement with experimental values it is necessary to use the increased values of the van der Waals radii, which is caused by an overestimated value of the van der Waals interactions in crystalline linear oligoacenes. Utilization of the DFT-D leads to a correct account of the dispersion forces, which results in a high precision of the computed lattice parameters and cohesive energy. Based on the relaxed crystal structures, we have computed the total and deformation electron density and determined the mechanism of chemical bonds formation in crystals of naphthalene and anthracene. It has been established that the chemical bond in molecular crystals is formed under the influence of not only intramolecular but also intermolecular interactions. On the basis of the Mulliken population analysis it was revealed that two C(3) atoms in naphthalene (or C(3) and C(4) in anthracene) have a positive charge and the population of the rest of the carbon atoms increased, as compared with isolated molecule.     

Comparison of the performance of dispersion-corrected density functional theory for weak hydrogen bonds

Potential energy curves for five complexes with weak to medium strong hydrogen bonds have been computed with dispersion corrected DFT methods. The electronic density based vdW-DF2 and VV10 van der Waals density functionals have been tested, as well as an atom pair-wise correction method (DFT-D3). The short-range exchange-correlation components BLYP and rPW86-PBE together with the extended aug-cc-pVQZ basis sets have been employed. Reference data have been computed at the estimated CCSD(T)/CBS(aQ-a5) level of theory. The investigated systems are CH(4)·NH(3), Cl(3)CH·NH(3), NH(3)·NH(3), CH(3)F·C(2)H(2) and CH(3)F·H(2)O with binding energies ranging from -0.7 kcal mol(-1) to -5.5 kcal mol(-1). We find that all dispersion corrected methods perform reasonably well for these hydrogen bonds, but also observe distinct differences. The BLYP-D3 method provides the best results for three out of five systems. For the fluorinated complexes, the VV10 method gives remarkably good results. The vdW-DF2 method yields good interaction energies similar to the other methods (mean average deviation of 0.2-0.3 kcal mol(-1)), but fails to provide accurate equilibrium separations. Based on these results and previous experience with the computation of non-covalent interactions, for large-scale applications we can recommend DFT-D3 based structure optimizations with subsequent checking of interaction energies by single-point VV10 computations. Comparison of the DFT-D3 and VV10 results leads to the conclusion that the short-range exchange-correlation functional and not the dispersion correction mainly determines the achievable accuracy.     

Density functional theory with dispersion corrections for supramolecular structures, aggregates, and complexes of (bio)organic molecules

Kohn-Sham density functional theory (KS-DFT) is nowadays the most widely used quantum chemical method for electronic structure calculations in chemistry and physics. Its further application in e.g. supramolecular chemistry or biochemistry has mainly been hampered by the inability of almost all current density functionals to describe the ubiquitous attractive long-range van der Waals (dispersion) interactions. We review here methods to overcome this defect, and describe in detail a very successful correction that is based on damped -C(6).R(-6) potentials (DFT-D). As examples we consider the non-covalent inter- and intra-molecular interactions in unsaturated organic molecules (so-called pi-pi stacking in benzenes and dyes), in biologically relevant systems (nucleic acid bases/pairs, proteins, and 'folding' models), between fluorinated molecules, between curved aromatics (corannulene and carbon nanotubes) and small molecules, and for the encapsulation of methane in water clusters. In selected cases we partition the interaction energies into the most relevant contributions from exchange-repulsion, electrostatics, and dispersion in order to provide qualitative insight into the binding character.     

An ab initio study of van der Waals potential energy parameters for silver clusters

We employ ab initio calculations of van der Waals complexes to study the potential energy parameters (C(6) coefficients) of van der Waals interactions for modeling of the adsorption of silver clusters on the graphite surface. Electronic structure calculations of the (Ag(2))(2), Ag(2)-H(2), and Ag(2)-C(6)H(6) complexes are performed using a coupled-cluster approach that includes single, double, and perturbative triple excitations (CCSD(T)), M?ller-Plesset second-order perturbation theory (MP2), and spin-component-scaled MP2 (SCS-MP2) methods. Using the atom pair approximation, the C(6) coefficients for silver-silver, silver-hydrogen, and silver-carbon atom systems are obtained after subtracting the energies of quadrupole-quadrupole interactions from the total electronic energy.     

Interaction of anions with perfluoro aromatic compounds

The complexes formed by a variety of anions with perfluoro derivatives of benzene, naphthalene, pyridine, thiophene, and furan have been calculated using DFT (B3LYP/6-31++G**) and MP2 (MP2/6-31++G** and MP2/6-311++G**) ab initio methods. The minimum structures show the anion interacting with the pi-cloud of the aromatic compounds. The interaction energies obtained range between -8 and -19 kcal mol(-1). The results obtained at the MP2/6-31++G** and MP2/6-311++G** levels are similar. However, the B3LYP/6-31++G** results provide longer interaction distances and smaller interaction energies than do the MP2 results. The interaction energies have been partitioned using an electrostatic, polarization, and van der Waals scheme. The AIM analysis of the electron density shows a variety of topologies depending on the aromatic system considered.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

A density-functional study on pi-aromatic interaction: benzene dimer and naphthalene dimer

The long-range correction (LC) scheme of density-functional theory (DFT) was applied to the calculation of the pi-aromatic interaction of the benzene dimer and naphthalene dimer. In previous calculations, it was confirmed that the LC scheme [Iikura et al., J. Chem. Phys. 115, 3540 (2001)] gives very accurate potential- energy surfaces (PESs) of small van der Waals (vdW) complexes by combining with the Anderson-Langreth-Lundqvist (ALL) vdW correlation functional [Andersson et al., Phys. Rev. Lett. 76, 102 (1996)] (LC-DFT + ALL). In this study, LC-DFT+ALL method was examined by calculating a wide range of PES of the benzene dimer including parallel, T-shaped, and parallel-displaced configurations. As a result, we succeeded in reproducing very accurate PES within the energy deviance of less than 1 kcalmol in comparison with the results of high-level ab initio molecular-orbital methods at all reference points on the PES. It was also found that LC-DFT + ALL gave accurate results independent of exchange-correlation functional used, in contrast with the strong functional dependencies of conventional pure functionals. This indicates that both exchange repulsion and van der Waals attractive interactions should be correctly incorporated in conventional pure functionals in order to calculate accurate pi-aromatic interactions. We also found that LC-DFT + ALL method has a low basis-set dependency in the calculations of pi-aromatic interactions. The present scheme was also successfully applied to the pi,[ellipsis (horizontal)],pi stacking interactions of naphthalene dimer. This may suggest that LC-DFT + ALL method would be a powerful tool in the calculations of large molecules such as biomolecules.     

Dispersion interactions of carbohydrates with condensate aromatic moieties: theoretical study on the CH-π interaction additive properties

In this article we present the first systematic study of the additive properties (i.e. degree of additivity) of the carbohydrate-aromatic moiety CH-π dispersion interaction. The additive properties were studied on the β-D-glucopyranose, β-D-mannopyranose and α-L-fucopyranose complexes with the naphthalene molecule by comparing the monodentate (single CH-π) and bidentate (two CH-π) complexes. All model complexes were optimized using the DFT-D approach, at the BP/def2-TZVPP level of theory. The interaction energies were refined using single point calculations at highly correlated ab initio methods at the CCSD(T)/CBS level, calculated as E + (E(CCSD(T))-E(MP2))(Small Basis). Bidentate complexes show very strong interactions in the range from -10.79 up to -7.15 and -8.20 up to -6.14 kcal mol(-1) for the DFT-D and CCSD(T)/CBS level, respectively. These values were compared with the sum of interaction energies of the appropriate monodentate carbohydrate-naphthalene complexes. The comparison reveals that the bidentate complex interaction energy is higher (interaction is weaker) than the sum of monodentate complex interaction energies. Bidentate complex interaction energy corresponds to 2/3 of the sum of the appropriate monodentate complex interaction energies (averaging over all modeled carbohydrate complexes). The observed interaction energies were also compared with the sum of interaction energies of the corresponding previously published carbohydrate-benzene complexes. Also in this case the interaction energy of the bidentate complex was higher (i.e. weaker interaction) than the sum of interaction energies of the corresponding benzene complexes. However, the obtained difference is lower than before, while the bidentate complex interaction energy corresponds to 4/5 of the sum of interaction energy of the benzene complexes, averaged over all structures. The mentioned comparison might aid protein engineering efforts where amino acid residues phenylalanine or tyrosine are to be replaced by a tryptophan and can help to predict the changes in the interactions. The observed results also show that DFT-D correctly describes the CH-π interaction energy and their additive properties in comparison to CCSD(T)/CBS calculated interaction energies. Thus, the DFT-D approach might be used for calculation of larger complexes of biological interest, where dispersion interaction plays an important role.     

The non-covalent functionalisation of carbon nanotubes studied by density functional and semi-empirical molecular orbital methods including dispersion corrections

Density functional theory (DFT-D) and semi-empirical (PM3-D) methods having an added empirical dispersion correction have been used to study the binding of a series of small molecules and planar aromatic molecules to single-walled carbon nanotubes (CNTs). For the small molecule set, the PM3-D method gives a mean unsigned error (MUE) in the binding energies of 1.2 kcal mol(-1) when judged against experimental reference data for graphitic carbon. This value is close to the MUE for this method compared to high-level ab initio data for biological complexes. The PM3-D and DFT-D calculations describing the adsorption of the planar organic molecules (benzene, bibenzene, naphthalene, anthracene, TCNQ and DDQ) on the outer-walls of both semi-conducting and metallic CNTs give similar binding energies for benzene and DDQ, but do not display a stronger adsorption on [6,6] compared to [10,0] structures shown by another DFT study.     

Density functional theory modeling of the adsorption of small analyte and indicator dye 9-(diphenylamino)acridine molecules on the surface of amorphous silica nanoparticles

The adsorption of small analyte molecules (H(2)O, NH(3), C(2)H(5)OH, and (CH(3))(2)CO) and an indicator dye, 9-(diphenylamino)acridine (DPAA), on the surface of amorphous silica particles is studied using electronic structure calculations at the DFT-D level of theory taking into account explicit corrections for van der Waals forces. Cluster models of three different types are used; two of them have been constructed using classical MD methods. The effect of particle size, local environment, and the choice of the exchange-correlation functional and basis set on the adsorption energies is studied, and adsorption energies are extrapolated to nanosized clusters. It is shown that the dye is more strongly bound to amorphous silica particles than the studied analyte molecules and that the energy of DPAA adsorption increases with the particle size, being at least twice as high as the energy of analyte adsorption for nanosized clusters. Electrostatic interactions play an important role in the adsorption of acridine dyes on the surface of silica nanoparticles.     

High-resolution electron spectroscopy, preferential metal-binding sites, and thermochemistry of lithium complexes of polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons are model systems for studying the mechanisms of lithium storage in carbonaceous materials. In this work, Li complexes of naphthalene, pyrene, perylene, and coronene were synthesized in a supersonic metal-cluster beam source and studied by zero-electron-kinetic-energy (ZEKE) electron spectroscopy and density functional theory calculations. The adiabatic ionization energies of the neutral complexes and frequencies of up to nine vibrational modes in the singly charged cations were determined from the ZEKE spectra. The metal-ligand bond energies of the neutral complexes were obtained from a thermodynamic cycle. Preferred Li∕Li(+) binding sites with the aromatic molecules were determined by comparing the measured spectra with theoretical calculations. Li and Li(+) prefer the ring-over binding to the benzene ring with a higher π-electron content and aromaticity. Although the ionization energies of the Li complexes show no clear correlation with the size of the aromatic molecules, the metal-ligand bond energies increase with the extension of the π-electron network up to perylene, then decrease from perylene to coronene. The trends in the ionization and metal-ligand bond dissociation energies of the complexes are discussed in terms of the orbital energies, local quadrupole moments, and polarizabilities of the free ligands and the charge transfer between the metal atom and aromatic molecules.     

邻二甲苯…Ar, N2, NH3(ND3)范德华复合物的共振双光子电离光谱

在超声分子束中，使用双光子共振电离光谱技术和飞行时间质谱技术研究了复合物邻二甲苯…Ar．N2，NH3(ND3)．通过理论计算及同位素光谱效应．合理地归属了这些复合物的光谱．并由此获得这些复合物分子问各种模式的振动频率．