Effect of the damping function in dispersion corrected density functional theory

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

Sensitivity analysis and uncertainty calculation for dispersion corrected density functional theory

The precision of binding energies and distances computed with dispersion-corrected density functional theory (DFT-D) is investigated by propagation of uncertainties, yielding relative uncertainties of several percent. Sensitivity analysis is used to calculate the geometry-dependent relative importance of each input parameter for the dispersion correction. While DFT-Ds are exact at asymptotically large distances, their damping functions are shown to play a significant role in binding geometries. This is demonstrated in detail for the interlayer binding of graphite. The techniques presented allow practitioners to quickly compute error bars and to get an a posteriori estimate about the transferability of their results. They can also aid the development of future dispersion corrections.     

低阶煤中氢键作用的色散校正密度泛函理论研究

本研究以苯酚…苯酚、苯酚…苯、苯酚…二苯醚、苯酚…喹啉和苯甲酸…苯甲酸为对象，采用色散校正的密度泛函理论分别研究褐煤中自缔合OH、OH-π、OH-醚O、OH-N和COOH-COOH之间形成的氢键。此外，还研究了氢键供体中取代基(CH₃-、CH₃O-、OH-、NH₂-、COOH-和NO₂-)对氢键的影响。对上述复合物进行了几何优化，并计算了能量、Mulliken电荷分布及振动频率。从优化的结构中可以看出上述复合物之间都存在氢键，所有复合物中O-H键键长都比苯酚中自由羟基的长，这表明这些复合物之间存在相互作用。其中，羧酸…羧酸复合物中O-H键的键长最长。此外，通过Mulliken电荷分布可看出上述复合物之间存在电荷转移。基于振动频率分析，所有的O-H键伸缩振动都发生了红移，尤其是羧酸…羧酸和苯酚…喹啉复合物，这可为煤中羟基振动的红外光谱分析提供依据。根据键能不同氢键强度按以下顺序依次递减：COOH-COOH>OH-N > 自缔合OH≈OH-醚O > OH-π，这与振动频率的分析结果一致。此外，不同取代基对氢键作用的影响不同。     

A systematic study of rare gas atoms encapsulated in small fullerenes using dispersion corrected density functional theory

The most stable fullerene structures from C₂₀ to C₆₀ are chosen to study the energetics and geometrical consequences of encapsulating the rare gas elements He, Ne, or Ar inside the fullerene cage using dispersion corrected density functional theory. An exponential increase in stability is found with increasing number of carbon atoms. A similar exponential law is found for the volume expansion of the cage due to rare gas encapsulation with decreasing number of carbon atoms. We show that dispersion interactions become important with increasing size of the fullerene cage, where Van der Waals forces between the rare gas atom and the fullerene cage start to dominate over repulsive interactions. The smallest fullerenes where encapsulation of a rare gas element is energetically still favorable are He@C₄₈, Ne@C₅₂, and Ar@C₅₈. While dispersion interactions follow the trend Ar > Ne > He inside C₆₀ due to the trend in the rare gas dipole polarizabilities, repulsive forces become soon dominant with smaller cage size and we have a complete reversal for the energetics of rare gas encapsulation at C₅₀. © 2014 Wiley Periodicals, Inc.     

Wetting behavior of spherical nanoparticles at a vapor-liquid interface: a density functional theory study

The wetting behavior of spherical nanoparticles at a vapor-liquid interface is investigated by using density functional theory, and the line tension calculation method is modified by analyzing the total energy of the vapor-liquid-particle equilibrium. Compared with the direct measurement data from simulation, the results reveal that the thermodynamically consistent Young's equation for planar interfaces is still applicable for high curvature surfaces in predicting a wide range of contact angles. The effect of the line tension on the contact angle is further explored, showing that the contact angles given by the original and modified Young's equations are nearly the same within the region of 60° < θ < 120°. Whereas the effect is considerable when the contact angle deviates from the region. The wetting property of nanoparticles in terms of the fluid-particle interaction strength, particle size, and temperature is also discussed. It is found that, for a certain particle, a moderate fluid-particle interaction strength would keep the particle stable at the interface in a wide temperature range.     

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT‐D3) is used for fully ab initio protein‐ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three‐body and higher many‐body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side‐chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full‐system calculation for the 1060 atoms containing PL complex. For charged amino acid side‐chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (? = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (?30 and ?54 kcal/mol). © 2012 Wiley Periodicals, Inc.     

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.     

Water cluster anions studied by the long-range corrected density functional theory

Long-range corrected density functional theory (LC-DFT) is applied to a series of small water cluster anions(n= 2-6) to compute their vertical detachment energies (VDEs). The LC scheme is shown to eliminate an unphysical overestimation of the electron-water attraction in the hybrid functional by properly accounting for the long-range exchange repulsions. It is shown that a correct correlation energy behavior for a rapidly varying density is also important for describing a spatially extent, excess electron. The one-parameter progressive (OP) correlation functional, which satisfies this condition, leads to a remarkable improvement in the calculated VDE over the conventional one. The LC-BOP method produces highly accurate VDEs with a mean absolute deviation of 13.8 meV from the reference CCSD(T) results, reducing the error of B3LYP by more than 15 times. LC-BOP is found to be more accurate than MP2 which yields an excess electron underbound by 43.6 meV. The effect of basis sets on the calculated VDE is also examined. The aug-cc-pVDZ basis set with an extra diffuse function is found to be more accurate and reliable than the extended Pople-type basis sets used in the previous works. The extrapolation of the calculated VDE of different electron binding motifs is compared with the VDEs of experimentally observed three isomers (Verlet, J. R. R.; Bragg,A. E.; Kammrath, A.; Cheshnovsky, O.; Neumark, D. M. Science 2005, 307, 93).     

Intermolecular dispersion energies from time-dependent density functional theory

Non-expanded dispersion energies are calculated from time-dependent coupled-perturbed density functional theory (DFT) employing various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel. Considering the dimer systems He₂, Ne₂, Ar₂, NeAr, NeHF, ArHF, (H₂)₂, (HF)₂, and (H₂O)₂ it is shown that the effects of intramonomer electron correlation on the dispersion energy are accurately reproduced with the PBE0AC exchange-correlation potential. In contrast, the uncoupled sum-over-states approximation yields inacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and therefore, not substantially improved through an asymptotic correction of the exchange-correlation potential.     

Calculation of some atomic properties by gradient corrected density functional method

Using thePerdew andPerdew-Wang Yue gradient expansion functionals the total electronic binding energies, the ionization potentials and the KL transitin energies are calculated for the atoms of elements from Be to Cu, and the 3d–4s transition energies are determined for the third row elements. There is a general improvement with respect to the results found without gradient corrections. However the asymptotic behavior of the potential does not changes.     

Chiroptical properties of artemisinin and artemether investigated using time-dependent density functional theory

Chiroptical properties including electronic circular dichroism(ECD) and optical rotatory dispersion(ORD) of artemisinin and artemether have been fully studied using quantum-chemical calculation based on time-dependent density functional theory.Both theoretical ECD and ORD of these two compounds were in good match with the experimental data.ECD spectrum of artemether could be totally attributed to the peroxide group,and that of artemisinin was an overlay of contribution from δ-lactone and peroxide moieties,which leading to a positive maximum at 260 nm.Our results showed that peroxide group could produce a broad ECD band in the far-UV region originated from electron transitions of HOMO →LUMO,HOMO-1 →LUMO and HOMO-2 →LUMO in the case of artemether.This work provided a theoretical interpretation of the ECD behavior of peroxide bond.     

Prediction of formation constants of metal-ammonia complexes in aqueous solution using density functional theory calculations

Density functional theory calculation of gas-phase Delta G of replacement of a water molecule by NH(3) on [M(H(2)O)(6)](n+)(g) for 19 different metal ions correlates well with Delta G of formation of mono NH(3) complexes of these ions in water, suggesting this approach will permit prediction of formation constants in aqueous solution, and produce insights into theories of metal complex formation reactions.     

Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results.     

Implementation of empirical dispersion corrections to density functional theory for periodic systems

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT‐D3) is implemented in the plane‐wave program package VASP. The DFT‐D3 implementation is compared with an implementation of the earlier DFT‐D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT‐D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three‐center terms as implemented in the original molecular DFT‐D3 version is investigated. The empirical parameters are taken from the original DFT‐D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid‐state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT‐D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106). © 2012 Wiley Periodicals, Inc.     

Self-interaction corrected density functional theory for the study of intramolecular electron transfer dynamics in radical carbocations

We derived an orbital dependent Kohn-Sham based scheme for the correction of the self-interaction error in DFT, which is particularly suited for the study of open shell molecular systems. Our approach is based on a weighted form of the Perdew and Zunger (PZ) self-interaction correction scheme, in which an empirical coefficient is introduced in front of the SIC term to remove overcorrections. The method is used to investigate the first principle molecular dynamics of the intramolecular electron transfer (IET) in bis(methylene) adamanthyl radical cation and allows the analysis of the free energy surface that governs the IET process at room temperature (300 K). Indeed, the thermal activation of all molecular degrees of freedom provides important additional information about the mechanisms involved in the IET process. Our study confirms and extends previous results obtained with CASSCF and shows that there is no predominant degeneracy-lifting mode even at room temperature. However, we also identified regions in the phase space for which there is a significant probability for a productive IET event. In addition, we performed thermodynamic integrations along selected reaction coordinates to determine an estimate of the activation free energy barrier for the IET process.     

Approximate scaling properties of the density functional theory Tc for atoms

Revealed are scaling properties for T(c)[rho], the kinetic-energy component of the correlation energy density functional for atoms, in terms of the total number of electrons N, the nuclear charge Z, and the total electron density at the nucleus rho(0). T(c) scales well as Nrho(0)/Z(8/3) for both neutral atoms up to Z=18 and the four-electron Be-like cationic species. A model is given that describes these findings, involving a density encoding the cusp information and an effective potential going like r(-4/3).     

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.     

Application of semiempirical long-range dispersion corrections to periodic systems in density functional theory

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from M?ller-Plesset second-order perturbation theory with basis set extrapolation.     

Methylation of zebularine investigated using density functional theory calculations

Deoxyribonucleic acid (DNA) methylation is an epigenetic phenomenon, which adds methyl groups into DNA. This study reveals methylation of a nucleoside antibiotic drug 1‐(β‐D ‐ribofuranosyl)‐2‐pyrimidinone (zebularine or zeb) with respect to its methylated analog, 1‐(β‐D ‐ribofuranosyl)‐5‐methyl‐2‐pyrimidinone (d5) using density functional theory calculations in valence electronic space. Very similar infrared spectra suggest that zeb and d5 do not differ by types of the chemical bonds, but distinctly different Raman spectra of the nucleoside pair reveal that the impact caused by methylation of zeb can be significant. Further valence orbital‐based information details on valence electronic structural changes caused by methylation of zebularine. Frontier orbitals in momentum space and position space of the molecules respond differently to methylation. Based on the additional methyl electron density concentration in d5, orbitals affected by the methyl moiety are classified into primary and secondary contributors. Primary methyl contributions include MO8 (57a), MO18 (47a), and MO37 (28a) of d5, which concentrates on methyl and the base moieties, suggest certain connection to their Frontier orbitals. The primary and secondary methyl affected orbitals provide useful information on chemical bonding mechanism of the methylation in zebularine. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011