7145
J. Phys. Chem. 1992,96,7145 (33) Allemand, P.-M.; Srdanov, G.;Koch, A,; Khemani, K.; Wudl, F.; Rubin, Y.;Diederich, F.; Alvarez, M. M.; Anz, S. J.; Whetten, R. L. J . Am. Chem. SOC.1991, 113, 2780. (34) Handbook of Chemistry and Physics, 66th ed.; CRC Press: Boca Raton, FL, 1985; pp E50-52. (35) Miller, B.; Rosamillia, J. M. Presented at the Symposium Fullerenes: Chemistry, Physics and New Directions of the 180th Meeting of The Elec-
trochemical Society, Phoenix, AZ, 1991. (36) Gill, D. S.; Singh, B. J. C h .Soc., Faraday Trans. I 19%8,84,4417. (37) Svorstd, I.; Sigvartsen, T.; Songstad, J. Acta Chem. Scand. 1988, B42, 133. (38) The effective donor numbers of the pyridine/acetonitrile mixtures were approximated as the weighed average of the donor numbers of both pure solvents.
COMMENTS Comment on "Accuracy of Counterpoise Corrections In Second-Order Intermolecular Potential Calculatlons. 1. Helium Dimer" Sir: A recent paper on the validity of counterpoise corrections in the intermolecular energy calculations was published by Yang and Kestner.' We are particularly interested in this work since we previously worked on the same topic with a different approach.* While we generally agree with their arguments and conclusions in the paper, we have found a few problems in some of the calculational results. It is the purpose of this comment to point out the possible errors in that paper. On the basis of our experience in the interaction energy calculations for "true" van der Waals molecules such as noble gases, we feel that it is impossible to reach the large depth of the He, interaction potential with the second-order theory of electron correlation with the contracted basis set [8s4p2d/2s4p2d]. To convince ourselves of this, we have repeated the same calculations and obtained the results shown in Table I. Since the paper did not mention which was the uncontracted single s gaussian function in the [8~4p2d/h4p2d]basis set, we have chosen the most diffuse one (with the smallest exponent) as the uncontracted s function accordii to common practice. (Other choices did not significantly change the results.) The calculations were carried out on a V A X mainframe with the GAUSSIAN 86 package. It is clear from Table I that considerable discrepancies exist between their results and ours. First the Hartree-Fock (HF) interaction energies are noticeably different: theirs are consistently larger than ours. For the correlation interaction energy calculations, they used the second-order localized orbital pair approach while we directly used the MP2 method. The two formalisms are not essentially different (the unitary transformation of molecular orbitals does not affect the total energy). So the large difference in the total interaction energies (HF plus correlation contribution) between theirs and ours is hardly understandable. Their values at the attractive region are almost twice ours. In order to confirm the reliability of our results, we have performed further calculations at higher levels of M~ller-Plesset perturbation theory and with use of a series of larger basis sets formed by gradual decontraction of the 8s primitive Gaussian functions. The HF and MP2 interaction energies remain nearly unchanged. The MP3, MP4SDQ, and MP4SDTQ values a t R = 3.0 A with [8s4p2d/2s4p2d] are -7.803, -8.064, and -8.843 K, respectively, and they remain nearly the same for the other basis sets. The slow convergence of the calculated interaction energy with the level of electron correlation theory for the noble gases was noted in our previous studies on Ne, and is consistent with other calculations in the l i t e r a t ~ r e . ~In - ~addition to the inadequacy of the MP2 theory, the basis set of spd quality is also likely far from sufficient for the accurate calculations. A study by Sauer et al.3 showed that hardly more than 65% of the stabilization energy could be recovered by the second-order theory, even if very extended basis sets are used. A possibility might be that the discrepancies of the reported values are due to random errors since they do not yield an upper
0022-365419212096-7 145$03.00/0
TABLE I: Comparison of the Calculated Interaction Energies at the HartreeFock and Second-Order Correlated Levels (BasisSet 18s4pM/Zs4pMl or ~~l/l:l:l:l/l:ll, Full CP Corrections for BSSE) results of Yang and Kestner' our results ~~
R(& 2.0
HF(K) 734.430
MP2(K) 609.21 1 35.931 -10.588
2.5 3 .O 3.5
78.666 9.736
4.0
0.138
-7.953 -4.450
4.5
0.010
-2.134
5.0
0.001
-0.966
1.638
HF(K) 724.604 77.782 7.864 0.762 0.0717 0.006 0.0003
MP2 (K) 598.649 40.242 -5.485 -4.447 -2.183 -1.070
-0.558
bound (the interaction energy by the perturbation theory is not a variational quantity). However, a study of the component contributions in the second-order theory showed that the major attractive contribution to the interaction energy is the dispersion energy evaluated at the second-order uncoupled HF level, which is advantageously a variational q ~ a n t i t y .As ~ a result, the second-order interaction energies should not allow such large random errors as those shown in the reported He, potential in that paper. As our frank conclusion, we consider that the reported He, potential in that paper is not possible under the described computational conditions and that the errors may be caused by some technical reasons. Note added in proof from the original authors (Yang and Kestner): This present study confirms that the counterpoise correction can lead to accurate results. The method of analysis used by Yang and Kestner is a good way to provide proof of its accuracy. However, in our helium work we modified an old version of the Gaussian program and something was not correct with our modifications, as this note has pointed out. The relative sizes of the components is valid but not their absolute values. The conclusions are also valid. The original program could not be checked as it will no longer run on our present computer. It is important to realize that this is not the program used in our paper part IL6 Those values are not subject to this problem. Registry No. He,, 12184-98-4.
References and Notes (1) Yang, J.; Kestner, N. R. J . Phys. Chem. 1991, 95, 9214. (2) Tao, F.-M.; Pan, Y.-K. J . Phys. Chem. 1991, 95, 3582; 9811. (3) Sauer, J.; Hobza, P.; Carsky, P.; Zahradnik, R. Chem. Phys. Lett. 1981, 134, 553. (4) Chalasinski, G.; Szczesniak, M. M. Mol. Phys. 1988, 63, 205. (5) Cybulski, S. M.; Chalasinski, G.; Moszynski, R.J . Chem. Phys. 1990, 92, 4357. ( 6 ) Yang, J.; Kestner, N. R. J. Phys. Chem. 1991, 95, 9221.
Department of Chemistry Brown University Providence, Rhode Island 0291 2 Department of Chemistry Boston College Chestnut Hill, Massachusetts 02167
Fu-Ming Tao Yuh-Kang Pan'
Received: April 30, 1992; In Final Form: June 24, 1992 0 1992 American Chemical Society
