In general, physical properties smoothly change with continuous variables such as distance and time. This is also true for electron density related properties, as those defined in the bond critical point (bcp).1-3 This can be illustrated using as an example the nature of the C-C bond. Recently, some of us reported unexpected long C-C bonds (>2.7 Å) in 1,3-metalladiyne complexes.4 They were characterized using the quantum theory of atoms in molecules and the electron localization function (ELF). Conce ing covalent C-C bonds, very short and very long bond lengths were reviewed by Hoffmann et al. in 2005,5 and other articles appeared afterward.6,7 This topic is related to C-C bond dissociation energies.8-14 Several articles also reported the existence of bond critical points in long C-C bonds: orthocarboranes, 15,16 π-π complexes,17 interactions of charged aromatic systems with neutral ones,18 and complexes of HNC with electron-deficient aromatic systems.19,20 The existence of two-electron/four-centers (2e/4c) long distance C-C bonds (g2.9 Å) has been explored experimentally21 and theoretically.22,23 These systems are formed by two anionic radicals stabilized by the presence of cationic counterions. The dispersive forces seem to be important in the proper description of the electronic state of these systems.23 These systems show the presence of bond critical points in the electron density topological analysis between the carbon atoms of both molecules.24 In the present article, we focused our attention in the interaction of closed shell systems where the interaction is due to the presence of an electron-excessive carbon atom, in one molecule, and an electron-deficient carbon atom in the other. An additional characteristic important for these molecules is the geometrical accessibility of both carbon atoms to form an interaction. Thus, as carbon-deficient systems, carbon dioxide (CO2) and cyanogen (NCCN) were chosen. As electronexcessive carbon atoms, those with carbene-type characteristic were selected, including in this group some simple carbenes (:CH2, :CF2, and :CCH2), carbon monoxide and carbon monosulfide (CO and CS), isocyanic acid derivatives (HNC and LiNC), and the two simplest multiple bonded C-C molecules, ethylene and acetylene. Methods The geometry of the systems was initially optimized at the M05-2x/6-311++G(d,p)25,26 computational level. This functional has shown to provide a good description for a large variety of molecular interaction complexes.27 Frequency calculations at this computational level were performed to confirm that the structures obtained correspond to energetic minima. Further optimization was performed with the MP2/aug-cc-pVTZ,28,29 and, for selected cases, with the CCSD(T)/aug-cc-pVTZ.30 All these calculations were carried out within the Gaussian 03 package.31 The interaction energy is defined as the difference between the total energy of the complexes minus the sum of the energies * To whom correspondence should be addressed. E-mail: ibon@iqm.csic.es. † Instituto de Quı´mica Me´dica, CSIC. ‡ Universidad de Granada. Figure 1. Geometry of some of the complexes optimized at the MP2/ aug-cc-pVTZ computational level. J. Phys. Chem. A XXXX, xxx, 000 A 10.1021/jp903016e CCC: $40.75 XXXX American Chemical Society Downloaded by AUSTRIA CONSORTIA on July 6, 2009 Published on July 1, 2009 on http://pubs.acs.org | doi: 10.1021/jp903016e of the isolated monomers. The basis sets used in this work are of sufficient quality, and thus basis set superposition errors (BSSEs) should be rather small.32 Moreover, it was shown that uncorrected MP2/aug-cc-pVTZ binding energies lie between corrected and uncorrected MP2/aug-cc-pVQZ energies.33 BSSE corrections may not always improve binding energies of weakly bonded complexes, since in the counterpoise method,34 a monomer may utilize the valence and core functions of its partner, which are not available to the monomer in the complex. The electron density topology and atomic properties were evaluated within the atoms in molecules (AIM) methodology35 with the AIMPAC36 and Morphy9837 programs. The calculation of the atomic properties was carried out by integration within the atomic basins using the default parameters, except in those cases where the integrated Laplacian was larger than 1 × 10-3 where more tight conditions were used. Previous reports showed small errors in the energy and charge for systems where all the values of the integrated Laplacian were smaller than the mentioned value.38 ELF, as interpreted by Silvi and Savin39 was computed with the ToPMoD software package.40 Isosurfaces represented were taken at the value of 0.75 and represented with the SciAn41 visualization software. The orbital interactions were analyzed within the natural bond orbital (NBO)42 framework and the NBO 5.0G program.43 This method allows the analysis of the interaction between filled and empty orbitals and associates them to charge-transfer processes. In addition, the natural energy decomposition analysis was carried out to gain insight into the source of the interactions. These calculations were performed using the optimized geometries at the M05-2x/6-311++G(d,p) at the same computational level within the Gamess program.44 Results and Discussion Geometry. The intermolecular distances obtained for the complexes are gathered in Table 1, and some of them are represented in Figure 1. To the best of our knowledge, no TABLE 1: Intermolecular C· · ·C Distances (Å) of the Minima Obtained complex M05-2x/6-311++G(d,p) MP2/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZ CO2:CCH2 3.041 3.055 3.034 CO2:CF2 3.155 3.158 CO2:CH2 3.017 3.049 3.066 CO2:CNH 3.116 3.088 3.089 CO2:CNLi 2.982 2.986 2.986 CO2:CO 3.241 3.181 3.183 CO2:CS 3.097 3.096 3.091 CO2:HCCH 3.414 3.367 CO2:H2CCH2 3.309 3.303 NCCN:CCH2 3.271 3.203 NCCN:CF2 3.394 3.316 NCCN:CH2 3.176 3.217 NCCN:CNH 3.330 3.224 NCCN:CNLi 3.208 3.114 NCCN:CO 3.450 3.343 NCCN:CS 3.306 3.218 NCCN:HCCH 3.352 3.258 NCCN:H2CCH2 3.403 3.320 TABLE 2: Interaction Energy (kJ mol-1) of the Energetic Minima Complexes Obtained complex M05-2x/6-311++G(d,p) MP2/aug-cc-pvtz CCSD(T)/aug-cc-pVTZ CO2:CCH2 -11.00 -10.66 -10.55 CO2:CF2 -6.92 -7.46 CO2:CH2 -14.52 -10.13 -11.20 CO2:CNH -8.68 -9.66 -9.45 CO2:CNLi -15.18 -15.60 -15.61 CO2:CO -4.69 -5.98 -5.74 CO2:CS -8.97 -9.58 -8.61 CO2:HCCH -4.70 -5.99 CO2:H2CCH2 -8.01 -9.04 NCCN:CCH2 -11.81 -14.58 NCCN:CF2 -6.92 -9.54 NCCN:CH2 -16.90 -15.44 NCCN:CNH -9.87 -13.50 NCCN:CNLi -18.09 -22.78 NCCN:CO -4.79 -7.52 NCCN:CS -9.92 -13.43 NCCN:HCCH -9.98 -13.50 NCCN:H2CCH2 -8.36 -12.15 TABLE 3: Term Contribution (kJ mol-1) to the Interaction of Energy (Ei) terms M05-2x/6-311++G(d,p) MP2/aug-cc-pvtz NCCN -1.6 -4.3 :CCH2 -10.6 -10.5 :CF2 -6.1 -6.4 :CH2 -14.9 -10.7 :CNH -8.5 -9.5 :CNLi -15.9 -17.1 :CO -4.0 -4.6 :CS -8.7 -9.4 :HCCH -6.6 -7.6 :H2CCH2 -7.4 -8.5 R2 0.994 0.994 B J. Phys. Chem. A, Vol. xxx, No. xx, XXXX Alkorta et al. Downloaded by AUSTRIA CONSORTIA on July 6, 2009 Published on July 1, 2009 on http://pubs.acs.org | doi: 10.1021/jp903016e experimental geometrical information for any of these complexes is available in the literature, but the related CO2:NCH complex shows a C2V symmetry with the nitrogen pointing toward the carbon atom of the CO2 and an intermolecular distance of 3.0 Å.45 A search in the literature indicates that only one of the complexes studied here, CO2:CO, was previously studied.46 The geometrical and energetic results reported for that complex are analogous to those described here. All the complexes obtained in the present work show C2V symmetry and correspond to energetic minima. Since the purpose of the article is to study C· · ·C interactions, other possible dispositions of the complexes were not explored. The intermolecular distances obtained range from 2.99 to 3.16 Å in the CO2 series and from 3.04 to 3.32 Å in the cyanogen one. In general, the observed intermolecular distances are longer in the cyanogen complexes than in the carbon dioxide ones with the exception of the complexes with :CH2. The three computational methods considered here provide similar intermolecular distances for a given complex. The interaction energy and symmetry of the complexes are reported in Table 2. The results obtained for the carbon dioxide complexes are very similar in the three computational methods, while for the cyanogen ones, the M05-2x/6-311++G(d,p), in general, slightly underestimate the ones obtained with the MP2/ aug-cc-pVTZ one. On the basis of these results, it can be concluded that the DFT method used here provides reasonable results and thus it can be used for larger systems.
