Basis Set Superposition Error Effects Cause the Apparent Nonexistence of the Ethene/ Benzenium Ion Complex on the MP2 Potential Energy Surface Tanja van Mourik* School of Chemistry, UniVersity of St Andrews, North Haugh, St. Andrews, Fife KY16 9ST, Scotland, U.K. ReceiVed: August 05, 2008; ReVised Manuscript ReceiVed: September 29, 2008 In a recent Letter (J. Phys. Chem. A 2008, 112, 6399) Kolboe and Svelle reported that the ethene/benzenium ion complex found by B3LYP transforms into an ethylbenzenium ion when MP2 with a large basis set is used. We find that the failure of MP2 to locate the ethene/benzenium ion complex is due to large basis set superposition errors. Introduction In a recent Letter in this journal, 1 Kolboe and Svelle reported a case where B3LYP and MP2 calculations gave conflicting answers: B3LYP predicted the existence of an ethene/benzenium ion complex, whereas the structure transformed into an ethyl- benzenium ion when the MP2 method in combination with a large basis set including diffuse functions was employed. According to CCSD and QCISD calculations, the B3LYP result is correct. However, no explanation was given for the apparent failure of MP2. Over the past few years we have similarly encountered cases, all concerning molecules containing an aromatic ring, where B3LYP and MP2 give discrepant results. For example, for the indole-water complex B3LYP calculations yield two different π-bonded minima with the water molecule bonded to either the pyrrole or the phenol ring, 2 whereas MP2 yield only one minimum with the water molecule interacting with both rings simultaneously. 3,4 The different indole-water structures pre- dicted by MP2 and B3LYP are likely the result of missing dispersion interactions in the B3LYP calculations. More re- cently, we encountered discrepancies between structures opti- mized with B3LYP and MP2 while studying the tyrosyl-glycine (Tyr-Gly) dipeptide. In general, MP2 predicts more compact Tyr-Gly structures than B3LYP. 5 More detailed studies on the two conformers that changed most from B3LYP to MP2 geometry optimization showed that neither B3LYP nor MP2, when coupled with the medium-sized basis set 6-31+G(d), is able to predict the correct structures of these conformers. 6,7 B3LYP fails because it cannot describe the dispersion interac- tions that are important in interactions with aromatic rings, and MP2 fails because the potential energy surface is distorted by large intramolecular basis set superposition error (BSSE) effects (which are known to be large in MP2 but essentially negligible in B3LYP calculations). Similarly, Salvador et al. recently found that intramolecular BSSE effects are responsible for the non- planarity of benzene and other arenes obtained by correlated ab initio methods. 8 In the current paper we investigate the cause for the different results obtained by B3LYP and MP2 for the ethene/benzenium ion complex. As ethene/benzenium is a charged complex, it is expected that dispersion is less important than in the neutral systems mentioned above, suggesting that B3LYP may give correct results. Therefore, distortion of the MP2 potential energy surface by BSSE seems the likely reason for the discrepant results observed for the ethene/benzenium ion complex. We show that this is indeed the case, thereby issuing a warning against uncorrected MP2 geometry optimization of molecular systems where BSSE may be significant. Methodology Geometry optimizations of the ethene/benzenium ion complex and the ethylbenzenium ion were carried out with B3LYP and MP2, using the 6-31G(d) and 6-311++G(d,p) basis sets. The ethene/benzenium geometry optimizations used the CCSD/6- 311++G(d,p) structure provided in ref 1 as the starting geometry. For the ethene/benzenium ion complex, all energies were corrected for BSSE using the counterpoise procedure, taking the benzenium ion and ethene molecules as the fragments. Monomer deformation energies were taken into account. No counterpoise corrections were carried out for the ethylbenzenium ion. Counterpoise-corrected geometry optimizations of the ethene/ benzenium ion complex were carried out at the MP2/6- 311++G(d,p) level of theory. Potential energy curves were created by optimizing the C s -symmetric ethene/benzenium ion at fixed R CC distances between 2.8 and 4.5 Å (see Figure 1 for the definition of R CC ). The calculations were carried out with Gaussian 98 9 and Gaussian 03. 10 The B3LYP calculations employed Gaussian’s “ultrafine” integration grid. Results and Discussion Two dissimilar C s -symmetric ethene/benzenium ion com- plexes were found, labeled complex 1 and 2, which differ in the orientation of the ethene molecule with respect to the benzenium ion (see Figure 1). Both are true minima (with no imaginary frequencies) on the B3LYP/6-31G(d) and B3LYP/ 6-311++G(d,p) potential energy surfaces, with very similar energies (see Table 1). However, complex 1 is a transition state * To whom correspondence should be addressed. E-mail: tanja.vanmourik@st-andrews.ac.uk. 11017 10.1021/jp806986t CCC: $40.75  2008 American Chemical Society Published on Web 10/15/2008 2008, 112, 11017–11020