Approximations to complete basis set-extrapolated, highly correlated non-covalent interaction energies

The first-principles calculation of non-covalent (particularly dispersion) interactions between molecules is a considerable challenge. In this work we studied the binding energies for ten small non-covalently bonded dimers with several combinations of correlation methods (MP2, coupled-cluster single double, coupled-cluster single double (triple) (CCSD(T))), correlation-consistent basis sets (aug-cc-pVXZ, X = D, T, Q), two-point complete basis set energy extrapolations, and counterpoise corrections. For this work, complete basis set results were estimated from averaged counterpoise and non-counterpoise-corrected CCSD(T) binding energies obtained from extrapolations with aug-cc-pVQZ and aug-cc-pVTZ basis sets. It is demonstrated that, in almost all cases, binding energies converge more rapidly to the basis set limit by averaging the counterpoise and non-counterpoise corrected values than by using either counterpoise or non-counterpoise methods alone. Examination of the effect of basis set size and electron correlation shows that the triples contribution to the CCSD(T) binding energies is fairly constant with the basis set size, with a slight underestimation with CCSD(T)∕aug-cc-pVDZ compared to the value at the (estimated) complete basis set limit, and that contributions to the binding energies obtained by MP2 generally overestimate the analogous CCSD(T) contributions. Taking these factors together, we conclude that the binding energies for non-covalently bonded systems can be accurately determined using a composite method that combines CCSD(T)∕aug-cc-pVDZ with energy corrections obtained using basis set extrapolated MP2 (utilizing aug-cc-pVQZ and aug-cc-pVTZ basis sets), if all of the components are obtained by averaging the counterpoise and non-counterpoise energies. With such an approach, binding energies for the set of ten dimers are predicted with a mean absolute deviation of 0.02 kcal/mol, a maximum absolute deviation of 0.05 kcal/mol, and a mean percent absolute deviation of only 1.7%, relative to the (estimated) complete basis set CCSD(T) results. Use of this composite approach to an additional set of eight dimers gave binding energies to within 1% of previously published high-level data. It is also shown that binding within parallel and parallel-crossed conformations of naphthalene dimer is predicted by the composite approach to be 9% greater than that previously reported in the literature. The ability of some recently developed dispersion-corrected density-functional theory methods to predict the binding energies of the set of ten small dimers was also examined.     

Density-functional approaches to noncovalent interactions: a comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals

A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 - 0.38 kcal/mol.     

A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model chemistry yields MAD=0.68 kcal/mol, which represents a huge improvement over plain B3LYP/6-31G* (MAD=2.3 kcal/mol). Application of gCP-corrected B97-D3 and HF-D3 on a set of large protein-ligand complexes prove the robustness of the method. Analytical gCP gradients make optimizations of large systems feasible with small basis sets, as demonstrated for the inter-ring distances of 9-helicene and most of the complexes in Hobza's S22 test set. The method is implemented in a freely available FORTRAN program obtainable from the author's website.     

Semi-empirical molecular orbital methods including dispersion corrections for the accurate prediction of the full range of intermolecular interactions in biomolecules

Semi-empirical calculations including an empirical dispersive correction are used to calculate intermolecular interaction energies and structures for a large database containing 156 biologically relevant molecules (hydrogen-bonded DNA base pairs, interstrand base pairs, stacked base pairs and amino acid base pairs) for which MP2 and CCSD(T) complete basis set (CBS) limit estimates of the interaction energies are available. The dispersion corrected semi-empirical methods are parameterised against a small training set of 22 complexes having a range of biologically important non-covalent interactions. For the full molecule set (156 complexes), compared to the high-level ab initio database, the mean unsigned errors of the interaction energies at the corrected semi-empirical level are 1.1 (AM1-D) and 1.2 (PM3-D) kcal mol(-1), being a significant improvement over existing AM1 and PM3 methods (8.6 and 8.2 kcal mol(-1)). Importantly, the new semi-empirical methods are capable of describing the diverse range of biological interactions, most notably stacking interactions, which are poorly described by both current AM1 and PM3 methods and by many DFT functionals. The new methods require no more computer time than existing semi-empirical methods and therefore represent an important advance in the study of important biological interactions.     

Probing the effects of heterogeneity on delocalized pi...pi interaction energies

Dimers composed of benzene (Bz), 1,3,5-triazine (Tz), cyanogen (Cy) and diacetylene (Di) are used to examine the effects of heterogeneity at the molecular level and at the cluster level on pi...pi stacking energies. The MP2 complete basis set (CBS) limits for the interaction energies (E(int)) of these model systems were determined with extrapolation techniques designed for correlation consistent basis sets. CCSD(T) calculations were used to correct for higher-order correlation effects (deltaE(CCSD)(T)(MP2)) which were as large as +2.81 kcal mol(-1). The introduction of nitrogen atoms into the parallel-slipped dimers of the aforementioned molecules causes significant changes to E(int). The CCSD(T)/CBS E(int) for Di-Cy is -2.47 kcal mol(-1) which is substantially larger than either Cy-Cy (-1.69 kcal mol(-1)) or Di-Di (-1.42 kcal mol(-1)). Similarly, the heteroaromatic Bz-Tz dimer has an E(int) of -3.75 kcal mol(-1) which is much larger than either Tz-Tz (-3.03 kcal mol(-1)) or Bz-Bz (-2.78 kcal mol(-1)). Symmetry-adapted perturbation theory calculations reveal a correlation between the electrostatic component of E(int) and the large increase in the interaction energy for the mixed dimers. However, all components (exchange, induction, dispersion) must be considered to rationalize the observed trend. Another significant conclusion of this work is that basis-set superposition error has a negligible impact on the popular deltaE(CCSD)(T)(MP2) correction, which indicates that counterpoise corrections are not necessary when computing higher-order correlation effects on E(int). Spin-component-scaled MP2 (SCS-MP2 and SCSN-MP2) calculations with a correlation-consistent triple-zeta basis set reproduce the trends in the interaction energies despite overestimating the CCSD(T)/CBS E(int) of Bz-Tz by 20-30%.     

Stabilisation energy of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, I, CN) complexes: complete basis set limit calculations at MP2 and CCSD(T) levels

Stabilisation energies of stacked structures of C(6)H(6)...C(6)X(6) (X = F, Cl, Br, CN) complexes were determined at the CCSD(T) complete basis set (CBS) limit level. These energies were constructed from MP2/CBS stabilisation energies and a CCSD(T) correction term determined with a medium basis set (6-31G**). The former energies were extrapolated using the two-point formula of Helgaker et al. from aug-cc-pVDZ and aug-cc-pVTZ Hartree-Fock energies and MP2 correlation energies. The CCSD(T) correction term is systematically repulsive. The final CCSD(T)/CBS stabilisation energies are large, considerably larger than previously calculated and increase in the series as follows: hexafluorobenzene (6.3 kcal mol(-1)), hexachlorobenzene (8.8 kcal mol(-1)), hexabromobenzene (8.1 kcal mol(-1)) and hexacyanobenzene (11.0 kcal mol(-1)). MP2/SDD** relativistic calculations performed for all complexes mentioned and also for benzene[dot dot dot]hexaiodobenzene have clearly shown that due to relativistic effects the stabilisation energy of the hexaiodobenzene complex is lower than that of hexabromobenzene complex. The decomposition of the total interaction energy to physically defined energy components was made by using the symmetry adapted perturbation treatment (SAPT). The main stabilisation contribution for all complexes investigated is due to London dispersion energy, with the induction term being smaller. Electrostatic and induction terms which are attractive are compensated by their exchange counterparts. The stacked motif in the complexes studied is very stable and might thus be valuable as a supramolecular synthon.     

High-level ab initio computations of structures and interaction energies of naphthalene dimers: origin of attraction and its directionality

The intermolecular interaction energies of naphthalene dimers have been calculated by using an aromatic intermolecular interaction model (a model chemistry for the evaluation of intermolecular interactions between aromatic molecules). The CCSD(T) (coupled cluster calculations with single and double substitutions with noniterative triple excitations) interaction energy at the basis set limit has been estimated from the second-order M?ller-Plesset perturbation interaction energy near saturation and the CCSD(T) correction term obtained using a medium-size basis set. The estimated interaction energies of the set of geometries explored in this work show that two structures emerge as being the lowest energy, and may effectively be considered as isoenergetic on the basis of the errors inherent in out extrapolation procedure. These structures are the slipped-parallel (Ci) structure (-5.73 kcal/mol) and the cross (D2d) structure (-5.28 kcal/mol). The T-shaped (C2v) and sandwich (D2h) dimers are substantially less stable (-4.34 and -3.78 kcal/mol, respectively). The dispersion interaction is found to be the major source of attraction in the naphthalene dimer. The electrostatic interaction is substantially smaller than the dispersion interaction. The large dispersion interaction is the cause of the large binding energies of the cross and slipped-parallel dimers.     

Basis set convergence of the coupled-cluster correction, δ(MP2)(CCSD(T)): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δ(MP2)(CCSD(T)), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(T(*))-F12) correction, yielding a mean absolute deviation of 0.11 kcal mol(-1) for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(T)) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol(-1), respectively.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

The shape of gaseous n-butylbenzene: assessment of computational methods and comparison with experiments

Conformational landscape of neutral and ionized n-butylbenzene has been examined. Geometries have been optimized at the B3LYP/6-31G(d), B3LYP/6-31+G(d,p), B3LYP-D/6-31+G(d,p), B2PLYP/6-31+G(d,p), B2PLYP-D/6-31+G(d,p), B97-D/6-31+G(d,p), and M06-2X/6-31+G(d,p) levels. This study is complemented by energy computations using 6-311++G(3df,2p) basis set and CBS-QB3 and G3MP2B3 composite methods to obtain accurate relative enthalpies. Five distinguishable conformers have been identified for both the neutral and ionized systems. Comparison with experimentally determined rotational constants shows that the best geometrical parameters are provided by B3LYP-D and M06-2X functionals, which include an explicit treatment of dispersion effects. Composite G3MP2B3 and CBS-QB3 methods, and B2PLYP-D, B3LYP-D, B97-D, and M06-2X functionals, provide comparable relative energies for the two sets of neutral and ionized conformers of butyl benzene. An exception is noted however for conformer V(+) the stability of which being overestimated by the B3LYP-D and B97-D functionals. The better stability of neutral conformers I, III, and IV, and of cation I(+) , demonstrated by our computations, is in perfect agreement with conclusions based on micro wave, fluorescence, and multiphoton ionization experiments.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

New accurate benchmark energies for large water clusters: DFT is better than expected

In this work, we use MP2 and coupled‐cluster with single, double, and perturbative triple excitations [CCSD(T)] as well as their corresponding explicitly correlated (F12) counterparts to compute the interaction energies of water icosamers. The incremental scheme is used to compute benchmark energies at the CCSD(T)/CBS(45) and CCSD(T)(F12*)/cc‐pVQZ‐F12 level of theory. The four structures, dodecahedron, edge sharing, face sharing, and fused cubes, are part of the WATER27 test set and therefore, highly accurate interaction energies are required. All methods applied in this work lead to new benchmark energies for these four systems. To obtain these values, we carefully analyze the convergence of the interaction energies with respect to the basis set. Furthermore, we investigate the influence of the basis set superposition error and the core‐valence correlation. The interaction energies are: dodecahedron ?198.6 kcal/mol, edge sharing ?209.7 kcal/mol, face sharing ?208.0 kcal/mol, and fused cubes ?208.0 kcal/mol. For water clusters, we recommend to use the PW6B95 density functional of Truhlar in combination with Grimme's dispersion correction (D3), as the mean absolute error is 0.9 and the root mean‐squared deviation is only 1.4 kcal/mol. © 2014 Wiley Periodicals, Inc.     

Development of a 3-body:many-body integrated fragmentation method for weakly bound clusters and application to water clusters (H2O)(n = 3-10, 16, 17)

A 3-body:many-body integrated quantum mechanical (QM) fragmentation method for non-covalent clusters is introduced within the ONIOM formalism. The technique captures all 1-, 2-, and 3-body interactions with a high-level electronic structure method, while a less demanding low-level method is employed to recover 4-body and higher-order interactions. When systematically applied to 40 low-lying (H(2)O)(n) isomers ranging in size from n = 3 to 10, the CCSD(T):MP2 3-body:many-body fragmentation scheme deviates from the full CCSD(T) interaction energy by no more than 0.07 kcal mol(-1) (or <0.01 kcal mol(-1) per water). The errors for this QM:QM method increase only slightly for various low-lying isomers of (H(2)O)(16) and (H(2)O)(17) (always within 0.13 kcal mol(-1) of the recently reported canonical CCSD(T)/aug-cc-pVTZ energies). The 3-body:many-body CCSD(T):MP2 procedure is also very efficient because the CCSD(T) computations only need to be performed on subsets of the cluster containing 1, 2, or 3 monomers, which in the current context means the largest CCSD(T) calculations are for 3 water molecules, regardless of the cluster size.     

Performance of SM8 on a test to predict small-molecule solvation free energies

The SM8 quantum mechanical aqueous continuum solvation model is applied to a 17-molecule test set proposed by Nicholls et al. (J. Med. Chem. 2008, 51, 769) to predict free energies of solvation. With the M06-2X density functional, the 6-31G(d) basis set, and CM4M charge model, the root-mean-square error (RMSE) of SM8 is 1.08 kcal mol(-1) for aqueous geometries and 1.14 kcal mol(-1) for gas-phase geometries. These errors compare favorably with optimal explicit and continuum models reported by Nicholls et al., having RMSEs of 1.33 and 1.87 kcal mol(-1), respectively. Other models examined by these workers had RMSEs of 1.5-2.6 kcal mol(-1). We also explore the use of other density functionals and charge models with SM8 and the RMSE increases to 1.21 kcal mol(-1) for mPW1/CM4 with gas-phase geometries, to 1.50 kcal mol(-1) for M06-2X/CM4 with gas-phase geometries, and to 1.27-1.64 kcal mol(-1) with three different models at B3LYP gas-phase geometries.     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Computational methods to calculate accurate activation and reaction energies of 1,3-dipolar cycloadditions of 24 1,3-dipoles

Theoretical calculations were performed on the 1,3-dipolar cycloaddition reactions of 24 1,3-dipoles with ethylene and acetylene. The 24 1,3-dipoles are of the formula X≡Y(+)-Z(-) (where X is HC or N, Y is N, and Z is CH(2), NH, or O) or X═Y(+)-Z(-) (where X and Z are CH(2), NH, or O and Y is NH, O, or S). The high-accuracy G3B3 method was employed as the reference. CBS-QB3, CCSD(T)//B3LYP, SCS-MP2//B3LYP, B3LYP, M06-2X, and B97-D methods were benchmarked to assess their accuracies and to determine an accurate method that is practical for large systems. Several basis sets were also evaluated. Compared to the G3B3 method, CBS-QB3 and CCSD(T)/maug-cc-pV(T+d)Z//B3LYP methods give similar results for both activation and reaction enthalpies (mean average deviation, MAD, < 1.5 kcal/mol). SCS-MP2//B3LYP and M06-2X give small errors for the activation enthalpies (MAD < 1.5 kcal/mol), while B3LYP has MAD = 2.3 kcal/mol. SCS-MP2//B3LYP and B3LYP give the reasonable reaction enthalpies (MAD < 5.0 kcal/mol). The B3LYP functional also gives good results for most 1,3-dipoles (MAD = 1.9 kcal/mol for 17 common 1,3-dipoles), but the activation and reaction enthalpies for ozone and sulfur dioxide are difficult to calculate by any of the density functional methods.     

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.     

Experimentally-based recommendations of density functionals for predicting properties in mechanically interlocked molecules

Mechanically interlocked molecules (rotaxanes and catenanes) have already revolutionized molecular electronics and have the promise of a similar impact in other areas of nanotechnology, ranging from nanoactuators to in vivo drug nanocarriers. However, it would be most useful to have quantitative criteria for predicting structures, binding, and excitation energies for use in designing molecules with mechanical bonds. We assess here the use of density functional theory (DFT) to a noncovalently bound complex and find that no density functional is fully satisfactory. However, we find that the new M06-suite of density functionals, which include attractive medium-range interactions, leads to dramatic improvements in the structures (error of 0.04 A in the interplanar distances for M06-L compared to 0.42 A for B3LYP) and excitation energies (within 0.08 eV for TD-M06-HF without empirical correction compared to 2.2 eV error for TD-B3LYP). However, M06 predicts the complex to be too strongly bound by 22.6 kcal mol(-1) (B3LYP leads to too weak a bond by 29 kcal mol(-1)), while current empirical FF DREIDING is too weakly bound by only 15 kcal mol(-1).     

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.