Comment on “Beyond the Benzene Dimer: An Investigation of the Additivity of π−π...
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COMMENTS Comment on “Beyond the Benzene Dimer: An Investigation of the Additivity of π-π Interactions” Rafal Podeszwa Faculty of Chemistry, UniVersity of Warsaw, Pasteura 1, 02-093 Warsaw, Poland ReceiVed: April 9, 2008; ReVised Manuscript ReceiVed: July 9, 2008 In ref 1, Tauer and Sherrill presented nonadditive three-body energies for selected configurations of the benzene trimer using the supermolecular second-order Møller-Plesset (MP2) method with a small basis set. The justification for this approach is based on the idea sometimes used for the benzene dimer, that the application of small basis sets underestimate binding, whereas MP2 overestimates it. The authors compared this approach with the coupled cluster method with singles, doubles, and nonit- erative triples [CCSD(T)] for a single cyclic configuration representing the global minimum of the benzene trimer and for three stacked-trimer configurations. In all cases, the results of the MP2 approach were fairly accurate. It has already been pointed out in ref 2 that this approach “may prove to be incorrect if a broader range of configurations is considered” since the supermolecular MP2 method does not include the nonadditive dispersion energy and the first nonad- ditive dispersion contribution is present only in the third order of the Møller-Plesset perturbation theory. 3 However, for the cyclic configuration considered in ref 1, the contributions from orders higher than the third partially cancel out against the third- order dispersion contributions, 2 which explains the good per- formance of the MP2 method for this particular geometry. Moreover, for the stacked trimers, the nonadditive dispersion energy is significantly smaller than the other nonadditive contributions since the leading nonadditive dispersion term depends on all three intermolecular distances, whereas for other terms, two of them enter the energy expressions. 4 Therefore, testing MP2 on such configurations would not lead to large differences with CCSD(T). On the other hand, in a recent study of the benzene crystal, 5 using the nonadditive approach of ref 2, it has been found that the total nonadditive energy of the crystal is dominated by the positive dispersion contribution and the total nonadditive MP2 energy is only mildly positive since the MP2 contributions from individual trimers cancel out almost completely whereas majority of the dispersion contributions are of the same sign. The total nonadditive energy constitutes more than 10% of the total cohesion energy of the crystal, i.e. non- additive effects are more important for the crystal (and are of opposite sign) than for the minimum cyclic trimer considered in ref 1. Even taking into account that the method of ref 2 leads to a small overestimation of the nonadditive energy, such results contradict that of ref 6, where the approach of ref 1 was used for the benzene crystal resulting in a negligible three-body contribution. Moreover, it can be shown numerically that, for some configurations of the trimer, the approach suggested by Tauer and Sherrill leads to results of opposite sign to that of the CCSD(T). To look for such possible configurations, the asymptotic dispersion and induction three-body energies 4 (with multipole moments and polarizabilities taken from ref 7) were calculated for the cyclic configuration, varying the angle between the center of the mass of the trimer and the benzene planes. The results and the picture of the configuration are presented in Figure 1. One can see that some configurations are (asymp- totically) dominated by the induction whereas for different θ, the nonadditive energy is dominated by the dispersion. For a sample configuration from the latter regime, we calculated nonadditive energies by supermolecular methods and three-body dispersion from symmetry-adapted perturbation theory based on the Kohn-Sham description of the monomers [SAPT- (DFT)]. 2 The energies are presented in Table 1. The results clearly show that the MP2 approach fails in this case whereas MP2 + disp[3] or MP3 give reasonable accuracy. Due to the deficiencies of the supermolecular MP2 method for the bulk phase 5 and qualitative disagreements for certain configurations of the benzene trimer, the approach of ref 1 should not be used for the benzene trimer and for similar systems dominated by dispersion. Acknowledgment. This work was financed by the Polish Science Foundation grant Homing supported by Iceland, Liecht- enstein, and Norway through the EEA Financial Mechanism. References and Notes (1) Tauer, T. P.; Sherrill, C. D. J. Phys. Chem. A 2005, 109, 10475. (2) Podeszwa, R.; Szalewicz, K. J. Chem. Phys. 2007, 126, 194101. Figure 1. Asymptotic nonadditive three-body contributions for the benzene trimer in the cyclic C 3h configuration for R ) 3.695 Å. TABLE 1: Nonadditive Three-Body Energies (in kilocalories per mole) of the Benzene Trimer Structure from Figure 1 for θ ) 168° and the cc-pVDZ+ Basis Set of Reference 1 a SCF MP2 MP3 CCSD(T) MP2 + disp[3] -0.029 -0.030 0.051 0.035 0.056 a “disp[3]” corresponds to the three-body SAPT(DFT) dispersion. The MP2 + disp[3] was denoted MP2 + SDFT in ref 2. J. Phys. Chem. A 2008, 112, 8884–8885 8884 10.1021/jp803071f CCC: $40.75 2008 American Chemical Society Published on Web 08/27/2008
Transcript of Comment on “Beyond the Benzene Dimer: An Investigation of the Additivity of π−π...
COMMENTS
Comment on “Beyond the Benzene Dimer: AnInvestigation of the Additivity of π-πInteractions”
Rafał Podeszwa
Faculty of Chemistry, UniVersity of Warsaw, Pasteura 1,02-093 Warsaw, Poland
ReceiVed: April 9, 2008; ReVised Manuscript ReceiVed: July9, 2008
In ref 1, Tauer and Sherrill presented nonadditive three-bodyenergies for selected configurations of the benzene trimer usingthe supermolecular second-order Møller-Plesset (MP2) methodwith a small basis set. The justification for this approach is basedon the idea sometimes used for the benzene dimer, that theapplication of small basis sets underestimate binding, whereasMP2 overestimates it. The authors compared this approach withthe coupled cluster method with singles, doubles, and nonit-erative triples [CCSD(T)] for a single cyclic configurationrepresenting the global minimum of the benzene trimer and forthree stacked-trimer configurations. In all cases, the results ofthe MP2 approach were fairly accurate.
It has already been pointed out in ref 2 that this approach“may prove to be incorrect if a broader range of configurationsis considered” since the supermolecular MP2 method does notinclude the nonadditive dispersion energy and the first nonad-ditive dispersion contribution is present only in the third orderof the Møller-Plesset perturbation theory.3 However, for thecyclic configuration considered in ref 1, the contributions fromorders higher than the third partially cancel out against the third-order dispersion contributions,2 which explains the good per-formance of the MP2 method for this particular geometry.Moreover, for the stacked trimers, the nonadditive dispersionenergy is significantly smaller than the other nonadditivecontributions since the leading nonadditive dispersion termdepends on all three intermolecular distances, whereas for otherterms, two of them enter the energy expressions.4 Therefore,testing MP2 on such configurations would not lead to largedifferences with CCSD(T). On the other hand, in a recent studyof the benzene crystal,5 using the nonadditive approach of ref2, it has been found that the total nonadditive energy of thecrystal is dominated by the positive dispersion contribution andthe total nonadditive MP2 energy is only mildly positive sincethe MP2 contributions from individual trimers cancel out almostcompletely whereas majority of the dispersion contributions areof the same sign. The total nonadditive energy constitutes morethan 10% of the total cohesion energy of the crystal, i.e. non-additive effects are more important for the crystal (and are ofopposite sign) than for the minimum cyclic trimer consideredin ref 1. Even taking into account that the method of ref 2 leadsto a small overestimation of the nonadditive energy, such resultscontradict that of ref 6, where the approach of ref 1 was usedfor the benzene crystal resulting in a negligible three-bodycontribution.
Moreover, it can be shown numerically that, for someconfigurations of the trimer, the approach suggested by Tauer
and Sherrill leads to results of opposite sign to that of theCCSD(T). To look for such possible configurations, theasymptotic dispersion and induction three-body energies4 (withmultipole moments and polarizabilities taken from ref 7) werecalculated for the cyclic configuration, varying the angle betweenthe center of the mass of the trimer and the benzene planes.The results and the picture of the configuration are presentedin Figure 1. One can see that some configurations are (asymp-totically) dominated by the induction whereas for different θ,the nonadditive energy is dominated by the dispersion. For asample configuration from the latter regime, we calculatednonadditive energies by supermolecular methods and three-bodydispersion from symmetry-adapted perturbation theory basedon the Kohn-Sham description of the monomers [SAPT-(DFT)].2 The energies are presented in Table 1. The resultsclearly show that the MP2 approach fails in this case whereasMP2 + disp[3] or MP3 give reasonable accuracy. Due to thedeficiencies of the supermolecular MP2 method for the bulkphase5 and qualitative disagreements for certain configurationsof the benzene trimer, the approach of ref 1 should not be usedfor the benzene trimer and for similar systems dominated bydispersion.
Acknowledgment. This work was financed by the PolishScience Foundation grant Homing supported by Iceland, Liecht-enstein, and Norway through the EEA Financial Mechanism.
References and Notes
(1) Tauer, T. P.; Sherrill, C. D. J. Phys. Chem. A 2005, 109, 10475.(2) Podeszwa, R.; Szalewicz, K. J. Chem. Phys. 2007, 126, 194101.
Figure 1. Asymptotic nonadditive three-body contributions for thebenzene trimer in the cyclic C3h configuration for R ) 3.695 Å.
TABLE 1: Nonadditive Three-Body Energies (in kilocaloriesper mole) of the Benzene Trimer Structure from Figure 1for θ ) 168° and the cc-pVDZ+ Basis Set of Reference 1a
SCF MP2 MP3 CCSD(T) MP2 + disp[3]
-0.029 -0.030 0.051 0.035 0.056
a “disp[3]” corresponds to the three-body SAPT(DFT) dispersion.The MP2 + disp[3] was denoted MP2 + SDFT in ref 2.
J. Phys. Chem. A 2008, 112, 8884–88858884
10.1021/jp803071f CCC: $40.75 2008 American Chemical SocietyPublished on Web 08/27/2008
(3) Chalasinski, G.; Szczesniak, M.; Kendall, R. A. J. Chem. Phys. 1994,101, 8860.
(4) Stone, A. J. The Theory of Intermolecular Forces; Clarendon Press:Oxford, 1996.
(5) Podeszwa, R.; Rice, B. M.; Szalewicz, K. Phys. ReV. Lett., acceptedfor publication.
(6) Ringer, A. L.; Sherrill, C. D. Chem. Eur. J. 2008, 14, 2542.
(7) Podeszwa, R.; Bukowski, R.; Szalewicz, K. J. Phys. Chem. A 2006,110, 10345.
JP803071F
Comments J. Phys. Chem. A, Vol. 112, No. 37, 2008 8885
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