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.     

Host-guest complex of nabumetone: β-cyclodextrin: quantum chemical study and QTAIM analysis

The aim of the present work is the investigation of the inclusion complex of nabumetone (NAB) and β-cyclodextrin (β-CD) using PM3, DFT, DFT-D and ONIOM2 methods. The results indicate that the most energetically favorable structure predicts a preference of the methoxy group to enter the cavity of β-CD from its wide rim. Consequently, the butanone moiety is positioned outside the cavity on the side of the secondary hydroxyls, with a total insertion of naphthalene group. The semi-empirical PM3 results are in good agreement with those obtained by the DFT optimization (with and without dispersion correction). The donor–acceptor interactions between drug and the cavity wall of the host, studied on the basis of natural bonding orbital (NBO) analysis, show the presence of weak intermolecular hydrogen bonds in addition to the most important van der Waals interactions. Furthermore, it is revealed that among the DFT and DFT-D techniques selected to quantify these interactions, WB97X-D functional provides the greatest values of stabilization energies E⁽²⁾. Finally, a detailed topological charge density analysis based on the quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, has been accomplished using the WB97X-D and B3LYP methods on the most favorable complexes. A good correlation between the structural parameters and the electronic density is found.     

甲烷晶体的晶格能和弹性性质: 不同方法及泛函的评估

通过对甲烷晶体进行结构、晶格能和弹性特性的研究, 评估了不包含和包含色散能量修正的密度泛函理论的性能. 我们分别利用不包含色散能量修正的密度泛函理论(DFT) (包含不同的标准泛函和杂化泛函)和包含色散能量修正的密度泛函理论(DFT-D)计算了甲烷晶体特性, 并与实验作对比. 尽管DFT-D 与传统密度泛函理论及杂化密度泛函理论相比, 修正了甲烷晶体中的范德华(vdW)相互作用, 但是一些修正方案过分修正了这种相互作用. 因此, 人们在使用DFT-D方法时务必谨慎.     

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.     

Linear response time-dependent density functional theory for van der Waals coefficients

A linear response time-dependent density functional theory is described and used to calculate the dynamic polarizabilities and van der Waals C(6) coefficients of complex atom pairs. We present values of C(6) for dimers of main group atoms and the first row of transition metal atoms.     

Phase transition and chemical decomposition of shocked CO-N(2) mixture

Using quantum molecular dynamics simulations based on density functional theory including dispersion corrections (DFT-D), we have studied the thermophysical properties of liquid carbon monoxide and nitrogen (CO-N(2)) mixture under extreme conditions. Density functional theory (DFT) method significantly overestimates the pressure as compared to DFT-D. It is demonstrated that the van der Waals (vdW) interaction has a negative contribution to the pressure and tends to reduce the overestimation of the equilibrium volume. We also demonstrate that a negative slope of Hugoniot curve could possibly be caused by both the absorption of dissociation energy and the uncertainties in composition. As density and temperature increase along the Hoguniot curve, the system appears to undergo a continuous transition and provides for a much richer set of dissociation products. The influence of dissociated carbon and oxygen atoms on nitrogen molecules is also discussed.     

Structures and Chemical Bonding in Antimony(III) Bromide Complexes with Pyridine

Weakly or “partially” bonded molecules are an important link between the chemical and van der Waals interactions. Molecular structures of six new SbBr₃-Py complexes in the solid state have been determined by single-crystal X-ray diffraction analysis. In all complexes all Sb atoms adopt a pseudo-octahedral coordination geometry which is completed by additional Sb⋅⋅⋅Br contacts shorter than the sum of the van der Waals radii, with Br−Sb⋅⋅⋅Br angles close to 180°. To reveal the nature of Sb–Br and Sb–N interactions, the DFT calculations were performed followed by the analysis of the electrostatic potentials, the orbital interactions and the topological analysis. Based on Natural Bond Orbital (NBO) analysis, the Sb–Br interactions range from the covalent bonds to the pnictogen bonds. A simple structural parameter, non-covalence criterion (NCC) is defined as a ratio of the atom-atom distance to the linear combination of sums of covalent and van der Waals radii. NCC correlates with E(2) values for Sb−N, Sb−Cl and Sb−Br bonds, and appears to be useful criterion for a preliminary evaluation of the bonding situation.     

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.     

From weak interactions to covalent bonds: a continuum in the complexes of 1,8-bis(dimethylamino)naphthalene

Experimental charge density distributions in a series of ionic complexes of 1,8-bis(dimethylamino)naphthalene (DMAN) with four different acids: 1,2,4,5-benzenetetracarboxylic acid (pyromellitic acid), 4,5-dichlorophthalic acid, dicyanoimidazole, and o-benzoic sulfimide dihydrate (saccharin) have been analyzed. Variation of charge density properties and derived local energy densities are investigated, over all inter- and intramolecular interactions present in altogether five complexes of DMAN. All the interactions studied [[O...H...O](-), C[bond]H...O, [N[bond]H...N](+), O[bond]H...O, C[bond]H...N, C pi...N pi, C pi...C pi, C[bond]H...Cl, N[bond]H(+)] follow exponential dependences of the electron density, local kinetic and potential energies at the bond critical points on the length of the interaction line. The local potential energy density at the bond critical points has a near-linear relationship to the electron density. There is also a Morse-like dependence of the laplacian of rho on the length of interaction line, which allows a differentiation of ionic and covalent bond characters. The strength of the interactions studied varies systematically with the relative penetration of the critical points into the van der Waals spheres of the donor and acceptor atoms, as well as on the interpenetration of the van der Waals spheres themselves. The strong, charge supported hydrogen bond in the DMANH(+) cation in each complex has a multicenter character involving a [[Me(2)N[bond]H....NMe(2)](+)....X(delta-)] assembly, where X is the nearest electronegative atom in the crystal lattice.     

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron ab initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C(6) of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation [Phys. Rev. 3, 360 (1948)]. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation [Can. J. Phys. 58, 1200 (1980)] of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C(6) and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient, and find that to a very high degree of correlation C(6) scales as the square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N(2) molecule interactions.     

Anisotropic adsorption of molecular assemblies on crystalline surfaces

Orientational order of surfactant micelles and proteins on crystalline templates has been observed but, given that the template unit cell is significantly smaller than the characteristic size of the adsorbate, this order cannot be attributed to lattice epitaxy. We interpret the template-directed orientation of rodlike molecular assemblies as arising from anisotropic van der Waals interactions between the assembly and crystalline surfaces where the anisotropic van der Waals interaction is calculated using the Lifshitz methodology. Provided the assembly is sufficiently large, substrate anisotropy provides a torque that overcomes rotational Brownian motion near the surface. The probability of a particular orientation is computed by solving a Smoluchowski equation that describes the balance between van der Waals and Brownian torques. Torque aligns both micelles and protein fibrils; the interaction energy is minimized when the assembly lies perpendicular to a symmetry axis of a crystalline substrate. Theoretical predictions agree with experiments for both hemi-cylindrical micelles and protein fibrils adsorbed on graphite.     

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.     

Anharmonic infrared and Raman spectra in Car-Parrinello molecular dynamics simulations

The infrared and Raman spectra of naphthalene crystal with inclusion of anharmonic effects have been calculated by adopting the generalized variational density functional perturbation theory in the framework of Car-Parrinello molecular dynamics simulations. The computational approach has been generalized for cells of arbitrary shape. The intermolecular interactions have been analyzed with and without the van der Waals corrections, showing the importance of such interactions in the naphthalene crystal to reproduce the structural, dynamical, and spectroscopic properties.     

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.     

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.     

Evaluation of the role of “dilution” in ionic crystal formation by analysis of electron density distribution for two solvatomorphs of 4-amino-3,5-dinitropyrazole ammonium salt

The influence of “dilution” on the peculiarities of supramolecular organization in ionic crystals was analyzed by a detailed analysis of the electron density distribution function recovered by high-resolution X-ray diffraction experiments for two solvatomorphs of 4-amino-3,5-dinitropyrazole ammonium salt. The obtained results show that a decrease in the number of solvate water molecules unexpectedly increases the contribution from the anion-anion interactions to the lattice energy mainly due to the interactions between the π-systems of anions and between the nitro groups, which additionally confirms their binding nature. The latter indicates the general character of tendencies observed for hydrogen bonds and van der Waals interactions in the formation of crystalline materials in molecular and ionic crystals.     

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.     

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.