Canadian Journal of Chemistry. Van der Waals Potential Energy Surfaces from the Exchange-Hole Dipole Moment Dispersion Model

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1 Van der Waals Potential Energy Surfaces from the Exchange-Hole Dipole Moment Dispersion Model Journal: Manuscript ID cjc r1 Manuscript Type: Article Date Submitted by the Author: 0-Jul-2016 Complete List of Authors: Dizon, Joseph; San Francisco State University, Department of Mathematics Johnson, Erin; Dalhousie University, Department of Chemistry Keyword: density-functional theory, van der Waals complexes, potential energy surfaces, London dispersion, non-covalent interactions

2 Page 2 of 22 Van der Waals Potential Energy Surfaces from the Exchange-Hole Dipole Moment Dispersion Model Joseph B. Dizon Department of Mathematics, San Francisco State University, 1600 Holloway Ave, San Francisco, CA, USA 912 Erin R. Johnson Department of Chemistry, Dalhousie University, 627 Coburg Road, Halifax, Nova Scotia, Canada BH R2 The potential energy surfaces (PES) of 28 simple van der Waals complexes, consisting of a rare-gas (Rg) atom interacting with a linear molecule, are calculated using the exchange-hole dipole moment (XDM) dispersion model in conjunction with three base density functionals (HFPBE, PW86PBE, and a commensurate hybrid functional). Results are compared with literature coupled-cluster reference data. The quality of the computed PES is assessed based on the positions of the global minima and the corresponding binding energies. Only the hybrid functional is found to provide generally reliable PES. Dispersion-corrected HFPBE strongly underestimates the equilibrium intermolecular separations and predicts different global minima than the reference PES for Rg-HCl, Rg-HBr, and two of the Rg-HCN complexes. Analysis of the binding-energy errors reveals that the performance of HFPBE degrades as the size of the Rg atoms increase down the group, while the performance of PW86PBE is significantly worse for strongly-polar molecules. PW86PBE, and to a lesser extent the hybrid, strongly overbind Kr-HF due to charge-transfer error. Despite this, the XDM-corrected hybrid functional displays the best overall error statistics and provides binding energies to within ca. 10 cm 1 of the coupled-cluster reference data at a greatly reduced computational cost. Keywords: density-functional theory, London dispersion, non-covalent interactions, van der Waals complexes, potential energy surfaces

3 Page of 22 2 I. INTRODUCTION Accurate computational modeling of van der Waals (vdw) interactions is a challenging task with widespread applications in chemistry, physics, and biology. One particularly sensitive test of computational methods concerns reproduction of high-level ab initio potential-energy surfaces (PES), which map the interaction energies between two closedshell molecules in terms of the relative orientations and distance between the monomers. 1 Such vdw complexes are bound by a balance between long-range and short-range contributions to the overall interaction energy. 1,2,6 Long-range interactions include electrostatic interactions, which arise from the interaction between the permanent charge distributions of the two monomers (i.e. atoms or molecules); induction, which comes from the distortion of the monomer charge distribution in response to the electric field of the other monomer s electrons; and dispersion, which arises due to instantaneous fluctuations in the charge distribution of each monomer. Short-range exchange-repulsion interactions are also present due to the overlap of the electron density between monomers as they come into close contact. Treating these effects accurately is essential in computational chemistry because the structures of many systems of interest are determined, in part, by vdw interactions. Examples include bioorganic molecules, molecular crystals, and surface adsorbates, in addition to the prototypical gas-phase molecular dimers. 6,7 Reference PES of complexes of Rg atoms and linear molecules have been determined with particularly high precision from both experimental spectroscopic measurements and correlated wavefunction-theory calculations. 1,8 In recent years, researchers have employed coupled-cluster methods to calculate highly accurate PES for Rg-linear complexes that reproduce experimental PES. The popular CCSD(T) method (coupled-cluster theory with single and double excitations and a non-iterative perturbation treatment of triple excitations) 9 reproduces appropriate behavior of the PES at both short- and long-range. CCSD(T) calculations are typically employed with large basis sets including midbond functions to speed the convergence of computed binding energies (BEs). Computed PES are commonly used to determine the most stable, lowest-energy configurations of the vdw complex and its rovibrational properties. 1,2,,8 However, the construction of PES with CCSD(T) is extremely computationally demanding and it is impractical for larger systems. Due to its high accuracy, CCSD(T) is the standard source of reference data to assess the overall performance of

4 Page of 22 other promising (and more efficient) methods for computing PES. Density-functional theory (DFT) methods have gained tremendous attention in recent years for treatment of vdw interactions. 7,10,11 DFT is widely used in computational chemistry because it performs well for thermochemistry with a relatively-low computational cost. 10,11 However, popular conventional functionals such as the local density approximation (LDA) and generalized gradient approximations (GGA) have serious drawbacks for describing dispersion. 12 Problems with these functionals were revealed from computational studies of Rg dimers, where functionals either predicted the interaction between the Rg dimers to be significantly overbound or underbound depending on their treatment of exchange-repulsion. This was, in turn, shown to be directly related to the form of the enhancement factor used in the construction of the functional. 12,1 Additionally, the long-range decay behavior of the PES has an exponential decay rather than the correct 1/R 6 behavior characteristic of the dispersion energy. 1 This occurs because conventional functionals do not describe the highly non-local dynamical-correlation effects that give rise to dispersion. A number of dispersioncorrected density-functional theory methods have since been developed 1 27 although there have been comparatively few assessments of their performance for full PES. 28 This work will focus on one dispersion-correction approach, the exchange-hole dipole moment (XDM) dispersion model of Becke and Johnson. 1,16,6 0 In XDM, the potential that gives rise to dispersion is taken as the interaction between the multiple moments of an electron plus its corresponding exchange hole at position r A in monomer A and the multiple moments of the electron plus the hole at position r B in monomer B. Secondorder perturbation theory was used to evaluate the dispersion energy and obtain dispersion coefficients that depend on the multipole moments and atomic polarizabilities. The XDM dispersion energy is written as an asymptotic series 6 0 involving a sum over all atomic pairs: E disp = n=6,8,10 ij C n,ij f(r ij ) R n ij The C n are the dispersion coefficients and R ij is the inter-nuclear distance. Divergence of the dispersion energy for small R ij is prevented by the damping function: (1) f(r ij ) = R n ij R n vdw,ij +Rn ij (2)

5 Page of 22 R vdw,ij is the effective vdw separation and is dependent on two universal fit parameters a 1 and a 2, whose values are optimized for use with a given base exchange-correlation functional. The XDM model has been shown to be highly versatile and provides excellent performance for small-molecule complexes, 16 halogen-bonding, 1 metallophilic interactions, 2 surface adsorption, graphite, and molecular crystals.,6 In this work we compile a benchmark set of Rg linear-molecule complexes, for which accurate CCSD(T) reference data is available, as a sensitive test of dispersion-corrected DFT. 7 The set includes 28 complexes of noble-gas atoms (He, Ne, Ar, and Kr) and linear molecules of varying size and polarity (H 2, N 2, CO, CO 2, OCS, C 2 H 2, HF, HCl, HBr, and HCN). This set is then used to assess the quality of intermolecular PES computed using XDM in conjunction with three base density-functional approximations, ranging from 0-100% exact-exchange mixing. It is shown that the performance of the GGA functional suffers for the strongly-polar molecules, while the full exact-exchange method yields poor results for the heavier Rg elements. Ultimately, the hybrid provides the best compromise and, with this base functional, the XDM dispersion model is able to predict reliable PES, and binding energies to ca. 10 cm 1 accuracy. II. COMPUTATIONAL DETAILS All calculations in this work were performed using Gaussian 09 8 and postg 16,9,0, an external program for XDM computations. Since the PES are generally quite flat for Rg-linear complexes, a large integration grid is necessary 1,2 and the Lebedev (200,97) quadrature scheme was used for all of the calculations. The aug-cc-pvz basis set was used for all Rg atoms, as in our previous work. 16 For the Rg-diatomic complexes, the aug-cc-pvz basis set was also assigned to the linear molecule. For the larger linear molecules, a mixed basis set was used with the aug-cc-pvqz basis set assigned to the triatomic and tetraatomic linear molecules. Counterpoise (CP) corrections were not included since DFT methods are much less susceptible to basis-set superposition error than correlated-wavefunction methods, like CCSD(T). Moreover, XDM is not parameterized to work with CP corrections in order to treat intermolecular and intramolecular interactions on equal footing. The XDM dispersion correction can be used reliably with any number of base density functionals, provided that they recover correct exchange-repulsion behavior similar to Hartree

6 Page 6 of 22 TABLE I. Exact-exchange mixing fractions (c X ) and XDM damping parameters (a 1 and a 2 ) for each base functional considered in this work. Functional c X a 1 a 2 PW86PBE PW1PBE HFPBE Fock. 16, Assuch,calculationswereperformedusingthreedifferentbasefunctionalsdiffering in their treatment of exchange. These are PW86PBE,6, a GGA that reproduces Hartree- Fockexchange-repulsionatshortrangeforPESofRgdimers; HFPBE,whichusesfullexact exchange; andapw86pbehybrid 7 functional(denotedhereaspw1pbe).forthishybrid, the exact-exchange mixing fraction (17%) was optimized for main-group thermochemistry by fitting to the atomization energies of the G/99 set. 8 The XDM damping parameters used with each base functional are provided in Table I and were obtained by minimizing the root-mean-square (RMS) percent error in the calculated BEs, relative to reference data, for a given training set. Optimized damping parameters for PW86PBE 16 and PW1PBE were obtained using the KB6 set of molecular dimers 9, which includes hydrogen-bonding, dipole-dipole, π-stacking, and dispersion interactions. The damping parameters for HFPBE weredeterminedbyfittingonlytothesetof10rgdimersduetothepoorperformanceofthe HFPBE functional for hydrogen-bonded systems. Although the XDM dispersion correction is used with all functionals, it will not appear in the functional acronyms for brevity. The vdw complexes included in this benchmark set were selected based on the availability of CCSD(T) reference data. 7 The full list is given in Tables II and III, which include reference geometries and BEs for the global minimum of each complex. Jacobi coordinates were used to generate the configuration space of each PES and their definitions are shown in Figure 1. The PES of a prototypical Rg linear-molecule complex contains two independent degrees of freedom: the intermolecular distance from the Rg atom to the center-of-mass of the linear molecule (normally denoted as R) and the angle between the axis of the linear molecule, its center of mass, and the Rg atom (denoted as θ). The intramolecular bond lengths are generally fixed to reduce the number of degrees of freedom. Note that, in the calculation of the reference CCSD(T) PES for Kr-HF, 9 the definition of the angle in Jacobi

7 Page 7 of 22 6 FIG. 1. Definition of the Jacobi coordinates for the Rg linear-molecule complexes. coordinates appears to have been accidentally reversed. A test calculation for Kr-HF with CCSD(T) 7,8 verified that the minimum-energy arrangement corresponds to the pseudohydrogen-bonded Kr H-F geometry, which occurs at an angle of 0. The geometries of the linear molecules were optimized with each functional to determine the fixed bond lengths (tabulated in the Supporting Information) to be used in generation

8 Page 8 of 22 7 of the PES. 7 The energy at each point on the PES was computed as the energy difference between the vdw complex and the sum of monomer energies for each intermolecular separation, R, and angle, θ. For consistency, the range of points was chosen to match the boundaries and dimensions of the reference CCSD(T) PES. For geometry optimizations of the vdw complexes, the coordinates of the linear molecules were held fixed and only the positions of the Rg atoms were allowed to optimize. III. RESULTS AND DISCUSSION A. Comparison of PES A satisfactory PES must reproduce the correct anisotropy of the vdw interaction, which means that it must contain the correct number of minima, with the geometries and BEs in agreement with the CCSD(T) reference data. In this section, the quality of the computed PES is assessed by comparing the position of the global minima, as well as the overall appearance and anisotropy, with the reference PES. Noteworthy examples of PES of certain vdw complexes are highlighted and the remaining PES plots for all vdw complexes are shown in the Supporting Information. The reader is also directed to Ref. 7 for a more detailed comparison between the calculated and reference PES. As discussed previously, base functionals without XDM fail to give reasonable vdw PES, normally predicting very weak binding interactions or unbound complexes. The XDMcorrected functionals perform relatively well overall, reproducing the correct shape and anisotropy of the PES for Rg-N 2, Rg-H 2, Rg-CO 2, Rg-CO, and Rg-OCS complexes and obtaining satisfactory global minimum BEs in comparison with CCSD(T). The one exception is Kr-N 2, for which PW86PBE predicts a distorted T-shaped geometry instead of a perfect T-shape arrangement. 60 The PES for Ne-N 2, is shown in the top row of Figure 2 as a representative example. The contour lines represent the interaction energy relative to the infinitely-separated monomers. The remaining complexes (Rg-HX, Rg-HCN, and Rg- C 2 H 2 ) represent more challenging tests of dispersion-corrected DFT and will be discussed in sequence in the remainder of this section. The Rg-hydrogen halide dimers are relatively stable due to both induction and dispersion interactions, owing to the permanent dipole moments of the hydrogen halide molecules.

9 Page 9 of 22 8 FIG. 2. PES for Ne with N 2 (top), HCl (center), and HBr (bottom) with XDM-corrected functionals. The units of the Jacobi coordinates, R and θ, corresponding to the intermolecular distances and angles are given in Ångstroms and degrees, respectively. The contours of all PES are in terms of wavenumbers (cm 1 ). PW86PBE PW1PBE HFPBE PW86PBE PW1PBE HFPBE PW86PBE PW1PBE HFPBE Two minima are present: the first where the Rg atom aligns nearest the H atom (pseudohydrogen-bonding) and the second structure where the Rg atom aligns nearest the halogen (F, Cl, and Br), where dispersion dominates due to the polarizability of the heavier halogens. This is illustrated for the two examples of Ne-HCl and Ne-HBr in Figure 2. Since HCl and HBr are only moderately-polar molecules, the two collinear minima are competing structures and can be nearly degenerate. For He-HCl, all functionals favor pseudo-hydrogen-bonding between the He atom and the H atom, which is the opposite to what is observed in the CCSD(T) PES of He-HCl, although the two minima are predicted to differ in energy by only 1.8 cm However, for Ne-HCl and Ne-HBr, the behavior is reversed and CCSD(T) favors the global minimum configuration as the pseudo-hydrogen

10 Page 10 of 22 9 bonding interaction. 62,6 For these two complexes, HFPBE incorrectly predicts the global minimum to be the Ne X-H configuration, favoring dispersion between the halogen atom and Ne, as shown in Figure 2. Although, for Ne-HCl, the two minima are again nearly degenerate. The Rg-HF dimer is a particularly problematic case for XDM-corrected functionals. Since HF is quite polar, the pseudo-hydrogen-bonding interaction between the Rg atom and H at the collinear geometry is strongly favored and is the global minimum 9,6. While all of the functionals perform reasonably well for He-HF, PW86PBE severely overbinds the Kr-HF interaction and the secondary Kr F-H local minimum is not even present. The addition of exact exchange to PW86PBE slightly improves the BE for Kr-HF, but does restore the secondary minimum. This error can be understood by noting that both PW86PBE and the hybrid predict a strong binding interaction in Kr-HF even without the XDM dispersion correction. This occurs because the relatively small energy difference between the HOMO of Kr and the LUMO of HF causes GGAs and hybrid functionals (with low percentages of exact exchange) to succumb to delocalization error 7,10,11,6 for this complex. Both PW86PBE and PW1PBE predict nonphysical, fractional charge transfer from Kr to HF, which leads to artificiallylarge binding energies. At the minimum-energy configuration, the Mulliken charge on the Kr atom is predicted to be 0.08 e with PW86PBE and 0.0 e with PW1PBE. Moreover, intermolecular delocalization indices (DIs) have been shown to be excellent predictors of delocalization error 1 and are higher for this complex (viz with PW86PBE and 0.09 with PW1PBE, computed using the aimall program 71 ) than for any other complex in our benchmark set. Note that the next highest intermolecular DI is 0.06 for Kr-HCN with PW86PBE and this complex is also significantly overbound. HFPBE, which contains no density-functional exchange and hence does not suffer from delocalization error, performs well for Kr-HF and provides a PES comparable to CCSD(T). The Rg-HCN complexes also reveal some difficulties with the dispersion-corrected functionals in reproducing the reference PES, although not to the same extent as for the hydrogen halides. All PES for the Rg-HCN complexes have a global minimum at the collinear Rg- HCN arrangement 72 where hydrogen bonding is favored due to the high polarity of the HCN molecule. Most of the functionals obtain the correct, linear global minimum and also identify the second, distorted T-shaped local minimum with the Rg atom interacting with

11 Page 11 of FIG.. PES of Rg-C 2 H 2 with XDM-corrected functionals for He, Ne, Ar, and Kr (top to bottom). The units of the Jacobi coordinates, R and θ, corresponding to the intermolecular distances and angles are given in Ångstroms and degrees, respectively. The contours of all PES are in terms of wavenumbers (cm 1 ). PW86PBE PW1PBE HFPBE PW86PBE PW1PBE HFPBE PW86PBE PW1PBE PW86PBE PW1PBE HFPBE HFPBE the π system. However, HFPBE incorrectly predicts this distorted T-shaped geometry to be the global minimum for Ar-HCN and Kr-HCN. The relatively-high polarizability of Ar and Kr might influence the global minimum for HFPBE, which seems to favor dispersion interactions over pseudo-hydrogen-bonding, as seen earlier for the Ne-HX complexes.

12 Page 12 of TABLE II. Jacobi coordinates corresponding to the global minima of the vdw complexes with XDM-corrected functionals and CCSD(T). The intermolecular distances, R, are given in Ångstroms and the angles, θ, are given in degrees. Rg Molecule PW86PBE PW1PBE HFPBE CCSD(T) PW86PBE PW1PBE HFPBE CCSD(T) Ne H Kr H Ne N Ar N Kr N He CO Ne CO Ar CO Kr CO He HF Kr HF He HCl Ne HCl Ne HBr He HCN Ne HCN Ar HCN Kr HCN He CO Ne CO Kr CO Ne OCS Ar OCS Kr OCS He C 2 H Ne C 2 H Ar C 2 H Kr C 2 H MAE Finally, the Rg-C 2 H 2 dimers are challenging cases for predicting correct anisotropies with all functionals due to the flatness of the PES 89, as shown in Figure. Both PW86PBE and PW1PBE predict incorrect anisotropies as follows: a distorted T-shape secondary minimum for He-C 2 H 2 ; a perfect T-shape global minimum for Ne-C 2 H 2 ; and insufficiently-distorted T- shape global minima for Ar-C 2 H 2 and Kr-C 2 H 2, at ca. 7 to the axis of the C 2 H 2 molecule. It is possible that PW86PBE has difficulties in treating interactions involving the π system of

13 Page 1 of the C-C bond in C 2 H 2 and the addition of a small portion of exact exchange does not fix the incorrect anisotropy, unlike the Kr-N 2 case. Only HFPBE predicts the correct anisotropies for these complexes, in agreement with the CCSD(T) PES. 87,88 Because the PES are so flat around the π region of C 2 H 2, the results are susceptible to small errors in the repulsive exchange-only curves from the base functional. However, full exact exchange is capable of providing a qualitatively correct picture of these PES when paired with XDM. Optimized Jacobi coordinates for the global minima of each PES are summarized in Table II. In general, PW1PBE and PW86PBE provide reasonable intermolecular distances, while HFPBE predicts much shorter distances than CCSD(T). In terms of the intermolecular angles, all dispersion-corrected functionals provide relatively good agreement with CCSD(T) for most of the complexes, although there are cases where one or more of the functionals obtain a global minimum at a completely different geometry, as described above. B. Binding energies Binding energies obtained at the optimized geometries for the full set of vdw complexes are collected in Table III. HFPBE performs worse than the other functionals and tends to overestimate the BEs. PW86PBE and PW1PBE provide lower mean absolute errors (MAE) and addition of a small fraction of exact exchange appears to improve the binding energies formostofthevdwcomplexes. Asnotedabove, Kr-HFisaratherpathologicalcaseforboth PW86PBE and PW1PBE due to the effects of the density-functional delocalization error. Eliminating this dimer from the set results in a large decrease in the MAE for PW86PBE and a proportionately smaller decrease for the hybrid. PW1PBE provides the lowest MAE of 12 cm 1. This error approaches the anticipated errors for CCSD(T) calculations with moderate basis sets and without midbond functions, 7,87,90 while possessing the superior scaling of DFT as compared to coupled-cluster theory. However, using the MAE alone is not the most effective approach to gauge the performance of these functionals since the BEs span such a large range. The mean absolute percent error (MAPE) is more appropriate to describe the trends in the BE errors for each functional. We assess the error trends with respect to the size of the Rg atom and with respect to the polarity of the linear molecule in Table IV. In our set of vdw complexes, there are

14 Page 1 of 22 1 TABLE III. Binding energies, in cm 1, corresponding to the global minima of the vdw complexes with XDM-corrected functionals and CCSD(T). Rg Molecule PW86PBE PW1PBE HFPBE CCSD(T) Ne H Kr H Ne N Ar N Kr N He CO Ne CO Ar CO Kr CO He HF Kr HF He HCl Ne HCl Ne HBr He HCN Ne HCN Ar HCN Kr HCN He CO Ne CO Kr CO Ne OCS Ar OCS Kr OCS He C 2 H Ne C 2 H Ar C 2 H Kr C 2 H MAE Without Kr HF six molecules that pair with He, nine with Ne, five with Ar, and eight with Kr. The linear molecules are grouped as those with low polarity (H 2, N 2, CO 2, C 2 H 2, CO, and OCS) and those with higher polarity which are capable of pseudo-hydrogen-bonding interactions (HF, HCl, HBr, and HCN). Inspection of Table IV shows that the errors for HFPBE increase with increasing size of the Rg atom. Since HFPBE pairs non-local Hartree-Fock exchange with local GGA

15 Page 1 of 22 1 TABLE IV. Mean Absolute Percent Error (MAPE) of the BEs for the XDM-corrected functionals with respect to the size of the Rg atom and the polarities of the linear molecule. Type PW86PBE PW1PBE HFPBE All He Ne Ar Kr Weakly-polar Strongly-polar correlation, this method does not provide a balanced treatment of electron correlation. Thus, it is reasonable that it performs worse for larger Rg atoms, where electron correlation becomes more important. PW86PBE performs somewhat erratically and there is no clear trend with respect to the identity of the Rg atom. Finally, the BE errors for PW1PBE are consistently lower than with the other two functionals. This indicates that the hybrid compensates for the errors in the GGA by including some exact exchange, while retaining a large fraction of local exchange to pair well with the local correlation functional. PW86PBE performs quite well for the vdw complexes involving only weakly-polar molecules, but tends to perform worse for highly-polar molecules capable of forming pseudo hydrogen-bonds to the Rg atom. Excessive charge-transfer caused by delocalization error can overstabilize these complexes, resulting in the large MAPE. Thus, the errors of PW86PBE are not dependent on the size of the Rg atom, but vary depending on the polarity of the linear molecule and the ability of the complex to experience spurious charge transfer. Conversely, HFPBE gives larger errors for the vdw complexes involving weaklypolar linear molecules where dispersion is the dominant interaction. This is again likely due to a relatively poor treatment of electron correlation affecting the energetics for interaction of the Rg atom with an electron-rich π-system. On the other hand, for the highly-polar molecules, HFPBE performs comparatively well since it does not suffer from delocalization error, unlike functionals that incorporate GGA exchange. Finally, PW1PBE performs better than the other two functionals and is the only method that provides a balanced distribution of errors with respect to the polarity of the linear molecule. However, as noted previously, the hybrid also overestimates binding energies when delocalization error is present, although to a lesser extent than with the GGA. One may ask what is the optimum mixing fraction of exact exchange to minimize the

16 Page 16 of 22 1 TABLE V. Mean absolute percent errors (MAPE) of the BEs for the XDM-corrected PW86PBEbased hybrid functionals with varying fractions of exact exchange mixing. Results are shown for the full set of vdw complexes, as well as for the weakly-polar and strongly-polar subsets. c X a 1 a 2 Weakly-polar Strongly-polar Overall binding-energy errors for this data set. To address this, additional full geometry optimizations were performed for all dimers using PW86PBE-based hybrid functionals with the exact-exchange mixing fraction ranging from 0-0% in 10% increments. The computed binding energies vary smoothly with the change in exchange functional, as noted in our previous work on molecular clusters. 91 The resulting errors for the full benchmark set, as well as the weakly-polar and strongly-polar subsets are shown in Table V. The treatment of the highlypolar systems is typically better for higher fractions of exact-exchange mixing than for the weakly-polar systems due to the effects of delocalization error. It is found that the overall MAPE is minimized with 20% Hartree-Fock exchange. This is quite close to the mixing fraction of 17% chosen for the PW1PBE hybrid by fitting to the G atomization-energy set. Thus, PW1PBE includes a near-optimal exact-exchange mixing fraction for these vdw complexes and it exhibits good performance for both main-group thermochemistry and weak non-covalent interactions. IV. SUMMARY Full PES, as well as binding energies at the optimized global-minimum geometries, were computed for a set of 28 vdw complexes involving interaction of a rare-gas atom with a linear molecule. Three XDM-corrected functionals were considered and it was determined that the PW1PBE hybrid provides the best performance for BEs, intermolecular distances and angles, typically reproducing the shapes of the reference coupled-cluster PES. The performance of the XDM-corrected functionals was compared by highlighting trends inthebinding-energyerrorsintermsoftherelativesizesofthergatomsandthepolaritiesof

17 Page 17 of the linear molecules. HFPBE was found to perform poorly for larger noble gas atoms, while PW86PBE performed poorly for more polar molecules, such as HF. The principal sources of error are the delocalization (or charge-transfer) error of the GGA functional and the unbalanced treatment of electron correlation with HFPBE. Using a relatively-small mixing fraction of exact exchange in the hybrid functional reduces both errors and the quality of the results from the hybrid is effectively invariant with respect to both Rg-atom size and molecular polarity. However, this functional does not correct all of the features of the PES, such as the incorrect anisotropy of the Rg-C 2 H 2 interaction, and significant charge-transfer error remains for Kr-HF due to the large contribution of PW86 exchange. Nevertheless, we conclude that the PW1PBE hybrid is best choice of the functionals considered for vdw complexes, due to its ability to provide consistently accurate PES for the majority of this benchmark set. Once known errors from the base functional are taken into account, the present results show that the XDM model is able to treat dispersion interactions accurately, even for very weakly-bound vdw complexes, and can generally be applied to obtain PES in satisfactory agreement with CCSD(T) reference data. This implies that the XDM dispersion model can be extended to provide reliable PES for larger vdw complexes beyond the current reach of coupled-cluster theory. erin.johnson@dal.ca erin.johnson@dal.ca 1 Buckingham, A. D.; Fowler, P. W.; Hutson, J. M. Chem. Rev. 1988, 88, Cha lasiński, G.; Szczȩśniak, M. M. Chem. Rev. 199, 9, Hutson, J. M. Ann. Rev. Phys. Chem. 1990, 1, Blaney, B. L.; Ewing, G. E. Ann. Rev. Phys. Chem. 1976, 27, 8. Xie, D.; Ran, H.; Zhou, Y. Int. Rev. Phys. Chem. 2007, 26, Stone, A. J. The theory of intermolecular forces, 2nd ed.; International Series of Monographs on Chemistry; Clarendon Press: Oxford, 201.

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