Formation of CarbonâCarbon Triply Bonded Molecules from Two Free

Letter pubs.acs.org/JPCL

Formation of Carbon−Carbon Triply Bonded Molecules from Two Free Carbyne Radicals via a Conical Intersection David Danovich,†,‡ Avi Bino,*,† and Sason Shaik*,†,‡ †

Institute of Chemistry and ‡The Lise Meitner-Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, 91904 Jerusalem, Israel S Supporting Information *

ABSTRACT: The recent proposal (Bogoslavsky, B.; Levy, O.; Kotlyar, A.; Salem, M.; Gelman, F.; Bino, A. Angew. Chem., Int. Ed. 2012, 51, 90−94) that metallo−alkylidyne complexes decompose in aqueous solution and give rise to free carbynes, which couple to yield acetylenes, is examined here theoretically. On the basis of the known marker reactions of carbynes in the doublet and quartet state, it is concluded that most of the reactivity patterns observed in the Bino experiment arose from quartet carbynes. Indeed, theory shows that quartet carbynes can be funneled to acetylene via a conical intersection. Moreover, many of the minor products are also identified as markers of the quartet carbynes. Carbynes formation in their doublet state is a minor channel that branches from the conical intersection and leads to the formation of dienes and olefins in the Bino experiment. Thus, we show that conical intersections are important also in thermally initiated reactions. Coupled to the experimental approach, the study opens a window to studies of carbynes under mild conditions. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

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Indeed, these extremely reactive intermediates react with other carbyne radicals in solution to form alkynes according to: 2RC → RCCR. For example, the bis-ethylidyne trimolybdenum complex [Mo3(CCH3)2(O2CCH3)6(H2O)3]2+ (2) (Figure 1a) decomposes spontaneously in aqueous solution according to Scheme 1, producing 2-butyne and a large number of organic

he formation of a carbon−carbon triple bond in aqueous solution under mild conditions was reported in 2005,1 but the nature of the mechanism has been elucidated only recently by using isotope-labeling experiments.2 It was found that decomposition of trinuclear metal complexes that contain one or two triply bridging alkylidyne ligands or mononuclear transition metal complexes that contain a metal−carbon triple bond (Figure 1) leads to the formation of alkynes in aqueous

Scheme 1. Stoichiometric Production of Methyl-Carbyne Radical upon Decomposition of the Bis-ethylidyne Complex [Mo3(CCH3)2(O2CCH3)6(H2O)3]2+ (2)

substances of various chain lengths. The list includes acetic acid, acetaldehyde, and hydrogen that are formed by the reduction of water by CH3C radicals. It also includes ethylene and butadiene. More products, that are observed indicate extensive hydrogen, oxygen, and carbon atom abstractions, as expected from such a reactive intermediate. An electron count for the reaction depicted in Scheme 1 shows that the products have an excess of six d electrons on the metal vis-à-vis the reactants. Formally, these electrons originate from the two [CH 3 C]3‑ etylidyne ligands that, upon dissociation, are oxidized by the metal framework to two

Figure 1. Structures of metallo-alkylidyne complexes (a) bis-μ3ethylidyne trimolybdenum [Mo3(CCH3)2(O2CCH3)6(H 2 O) 3 ] 2 + (complex 2), (b) mono-μ 3 -ethylidyne tricobalt [(CO)9Co3CCH3], and (c) mononeopentylidyne monotungsten [(Me3CO)3WCCMe3]. Black, metal; green, carbon; red, oxygen. Hydrogen atoms are omitted for clarity.

solutions. On the basis of these results, it was suggested that the decomposition of the complexes produce free carbyne radicals (RC), in which the carbon atom is monovalent. Thus, these transition-metal complexes provide an entry for a new reactive intermediate of unique properties and reactivity patterns, which are outlined herein. © XXXX American Chemical Society

Received: October 17, 2012 Accepted: December 11, 2012

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dx.doi.org/10.1021/jz3016765 | J. Phys. Chem. Lett. 2013, 4, 58−64

The Journal of Physical Chemistry Letters

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carbynes [CH3C]0. Four electrons are transferred to the transition metals in complex 2, reducing them to complex 1, and two remain in complex 3 where two CH3C caps are replaced by two oxo ligands from the solvent. Interestingly, these radicals do not react with alkenes but react readily with alkynes to produce new alkynes and carbyne radicals.2 The “Fischer type” complex [(CO)9Co3CCH3] (Figure 1b) and the “Schrock type” complex [(Me3CO)3WCCMe3] (Figure 1c) decompose in aqueous solution, forming the corresponding coupling products 2-butyne and 2,2,5,5-tetramethyl-3-hexyne respectively along with other organic molecules.2 In nature, the methylidyne radical HC and acetylene were detected in interstellar matter.3,4 Free carbyne radicals can be also prepared in the laboratory by high-energy processes, such as flash and laser photolysis, pulsed radiolysis, and other highenergy process.5−14 These experimental results5−14 along with theoretical calculations15−18 indicate that the reactivity patterns of these radicals in their doublet (S = 1/2) and quartet (S = 3/ 2) states are different, and the products are diagnostic of the spin states. Thus, for example, in the doublet ground state such radicals are found to be very reactive toward alkenes10,11 and they insert into C−H bonds9 but are not prone to Habstraction reactions.9 By contrast, the quartet-excited state was reported to be long-lived12 and to prefer reactions with radicals, or H-abstraction. Because the carbyne radicals that are prepared by decomposition of metal complexes do not react with alkenes,2 and participate in H-abstraction, it is reasonable to assume that they are not formed in their doublet ground state but possess a quartet state. This intriguing conclusion has formed an incentive to test the mechanism and plausibility of generating acetylenes from carbynes in their two lowest spin states, which is done here by theoretical means. As shall be seen, whereas the reaction rate may well be limited by diffusion, the selectivity is controlled by a conical intersection (CI), which f unnels the coupling of two quartet carbynes directly to give acetylene, while producing minor amounts of doublet carbynes, which afford marker products of this spin state.2 To elucidate the mechanism that affords acetylene from free carbynes, we have examined here the coupling of the simplest carbyne radicals, namely, HC in their various spin states to produce acetylene. Scheme 2 shows the two lowest states of

Although the energy gap between the two states is sufficiently large to prevent fast 4Σ− → 2Π decay due to spin inversion, mediated by spin−orbit coupling, we cannot rule out the formation of both doublet and quartet states under the experimental conditions in the experimental study of one of us (A.B.).2 As such, we investigated those states that may arise during dimerization of 2Π methylidynes (Scheme 3a) as well as Scheme 3. (a) Singlet and Triplet States Nascent from 2Π-2Π Coupling of Methylidynes and (b) Singlet, Triplet, Quintet and Septet States Arising from 4Σ−4Σ− Methylidyne Coupling

of 4Σ− methylidynes (Scheme 3b). Thus, two 2Π methylidynes (Scheme 3a) can couple to singlet and triplet states. Initially, at long distances, these states are virtually degenerate. However, at shorter distances none of these states correlates directly to the ground state of acetylene. The singlet coupled 2Π-2Π (S = 0) state will rise in energy because it will include four electrons in the sigma frame, corresponding to σ2σ*2 occupation at short distances. The 4Σ−-4Σ− methylidyne coupling in Scheme 3b, generates four different spin states, having S = 0, 1, 2, and 3. At long distances these states are virtually degenerate. However, at short distances, the singlet-coupled state (S = 0) directly correlates to the ground state of acetylene. This, however, will have to occur by crossing or avoided crossing with the initially lower-lying singlet state arising from the 2Π-2Π singlet coupling, which correlates to the doubly excited σ2σ*2 configuration. Finding such a mechanism will reveal whether the dimerization of two quartet methylidynes can indeed generate acetylene. This information coupled to diagnostic reactivity patterns of the two spin states known from experiment and theory5−18 and comparison to the products detected in the Bino experiment may assist us in formulating a mechanism whereby free carbynes can couple. Our calculations are based on complete active space self-consistent field (CASSCF) calculations followed by multireference configuration interaction (MRCI).19 The technical details are given in the Methods section. All the numerical results are summarized in the Supporting Information (SI), while here we follow with the key results. Figure 1 shows the MRCI/6-31G* energy profile of the ground and triplet states along the minimum energy pathway (MEP), which couples the doublet methylidynes in an unconstrained manner. It is seen that the approach of the two methylidynes is not collinear. In fact, looking at the optimized geometries in this regions, it appears that the most favorable approach is when the vacant pπ orbital of one HC fragment points toward the filled σ orbital of the other, reminiscent of the insertion mechanism of singlet carbene into

Scheme 2. Methylidyne and Its Two Lowest States

HC. The ground state is the doublet 2Π state, which possesses two electrons in the σ-hybrid orbitals and one electron in one of the pπ orbitals. All calculations reveal a higher lying quartet 4 − Σ state,18 which possesses one electron in each of the valence orbitals, the σ-hybrid, and the two pπ orbitals. The experimental energy gap6 is 17.1 kcal mol−1, whereas full configuration interaction (FCI) calculations done here yield a value of 16.6 kcal mol−1 (FCI/cc-pVTZ). Because we cannot do the entire project at the FCI level with an extended basis set, we used the 6-31G* basis set. (The vertical FCI/6-31G* gap is 11.5 kcal mol−1.) 59



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Figure 2. MRCI/6-31G* energy profiles for 2Π-2Π methylidynes coupling along the MEP, wherein the two HC fragments approach one another in a nonlinear fashion: (a) Singlet ground state. Note that part of the energy curve, up to a C---C distance of 3.0 Å, is drawn in blue, whereas for shorter distances the curve is marked in red, and in between we use green. The different colors indicate that along the MEP there is an avoided crossing between the 2Π-2Π and 4Σ−-4Σ− singlet states; blue represents 2Π-2Π, red represents 4Σ−-4Σ−, and green represents a mixed character. (b) 2Π-2Π methylidynes coupling along the MEP in the singlet state (in blue/red) and the triplet state (in black). The relative energies (Erel) are given in eV units.

bonds,20 as is indeed noted for insertion and cycloaddition reactions of the S = 1/2 species.9 Thus, Figure 2a shows that along the MEP, the ground state of acetylene correlates smoothly with the ground state of the singlet-coupled 2Π-2Π methylidynes due to avoided crossing with the descending 4Σ−-4Σ− singlet state. Note also that 2Π-2Π methylidyne coupling on the triplet state, in Figure 2b (black curve), leads to an excited state of acetylene. Thus, an initial preparation of the HC fragments in their ground 2Π states will: (i) lead into partition of the 2Π-2Π complex into the singlet and the triplet manifolds and (ii) require a specific (noncollinear) trajectory to yield HCCH and will face an entropic barrier due to the loss of degrees of freedom. Figure 3 shows the MRCI/6-31G results for the 4Σ−-4Σ− methylidynes coupling along the collinear CH---CH approach

Note, however, from Figure 3 that the coupling of the HC quartet fragments leads to a few possible spin states that become excited states of acetylene, and hence the initially prepared the 4Σ−-4Σ− methylidynes will undergo partition into all of the spin state possibilities, which may have their own typical lifetimes. Additionally, the direct coupling to acetylene will encounter an entropic barrier due to the loss of degrees of freedom. (If the collision is diffusion-limited, then free energy barrier will be 5.2 kcal mol−1 at 300 K.) Figure 4 shows the 4Σ− 4Σ− and 2Π-2Π coupling curves (MRCI/6-31G*) along the collinear approach. It is seen that

Figure 4. MRCI/6-31G* energy curves showing the CH dimerization along the collinear approach for the 4Σ−-4Σ− (red) and 2Π-2Π (blue) singlet−coupled states. The relative energies (Erel) are in eV. Figure 3. MRCI/6-31G energy profiles for the 4Σ−-4Σ− methylidyne coupling along the collinear approach, in the various spin states noted in Scheme 3b. The Erel scale is in Hartrees relative to −76.0.

along the collinear pathway, the singlet coupled 4Σ−-4Σ− (red curve) and 2Π-2Π (blue curve) coupled-states undergo crossing or a very weak avoided crossing. Because the lack of mixing suggests that this is a CI22−29 or a point lying very near to a CI,30 we have optimized the geometry of the CI, along the collinear path, using state-averaged CASSCF(10,14)/6-31G*. The corresponding structure is shown in Figure 5a, along with the two vectors, which define the steepest descent paths from the CI to the ground states. It is seen that one vector (X1) will lead to coupling of the two carbynes, whereas the second (X2) will dissociate them. Figure 5b shows the product formation using arrows on the potential energy surface. Thus, after reaching the CI, one vector will

in all the possible spin states that arise from coupling of the six electrons (see Scheme 3 above). We can see clearly that the state of the fragments that correlates directly to acetylene (the red curve) involves the 4Σ−-4Σ− singlet coupling. Such a state correlation was noted by Carter and Goddard21 in the HCCH dissociation curve, studied using correlation-consistent configuration interaction (CCCI), based on a generalized valence bond wave function. 60



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Figure 5. CASSCF(10,14)/6-31G* characterization of the conical intersection (CI): (a) Geometry of the CI and the corresponding derivative coupling and gradient difference vectors, X1 and X2 (in mass weighted coordinates). (b) Surface crossing of the 4Σ−-4Σ− (red) and 2Π-2Π (blue) singlet−coupled states. Energies are in eV. The arrows emanating from the CI indicate the branching to acetylene and to two 2Π carbynes.

complexes.2 These experimentally generated species behave exactly opposite to the doublet carbynes: They do not react with alkenes, and they do abstract hydrogen atoms enthusiastically. Furthermore, the observation2 that these carbynes are capable of traveling long distances in water and couple to other carbynes at concentrations lower by at least 105 times that of the water concentration2 supports the assumption that these carbynes have a quartet spin state and are not in their doublet ground state. However, the yield of quartet−quartet coupling to acetylene will not be exclusive. Thus, as shown by the calculations (Figure 3), if the generated CH3C fragments are in their quartet states (S = 3/2), then the number of states that can be formed from their spin coupling at long distances is four, going from S = 0 to S = 3. Therefore, whereas the CI (Figure 5) offers a very efficient mechanism for 2-butyne production still the 4Σ−-4Σ− coupling manifold spreads into triplet, quartet, and septet and generate excited CH3CCCH3 molecules (Figure 3). These excited states, if formed, may react in different ways and give rise to more products; for example, the excited state may undergo addition to the O−H bond of a water molecule, giving rise to 2-butanone. Additionally, the heptet energy curve (S = 3) in Figure 3 is repulsive, generating back the free carbynes in the quartet state. These quartet carbynes in turn can lead to alkyne metathesis in the presence of alkynes and abstract hydrogen atoms from H2O or D2O, thereby giving rise to CH3CH3 or to CH3CD3 and hydroxide radicals, as observed experimentally.2 The intersystem crossing of free quartet state (S = 3/2) CH3C fragments to the corresponding doublet state does not appear to be fast.15,16 The CI in Figure 5 provides a clear mechanism for producing doublet carbynes in small amounts without a need for spin inversion. These doublet carbynes can in turn couple to CH3CCCH3 via a nonlinear trajectory, which is reminiscent of the Woodward−Hoffmann allowed20 reaction of singlet carbenes (see Figure 2). Even though the calculated energy barrier along this path is zero, there will be an entropic barrier (or a diffusion barrier) to form CH3CCCH3. This, together with the existence of a triplet-state (Figure 2), which is nascent from the triplet coupling of 2CH3C (S = 1/2),

couple the carbynes to acetylene, whereas the other will dissociate them to yield two doublet 2Π carbenes. Because the descent toward the acetylene is much steeper, acetylene will be a major product, whereas 2Π carbenes will be generated in small quantities, and their presence will be marked by their diagnostic follow-up reactions. Thus. based on Figure 5, if the carbynes fragments are prepared in the Bino experiment,2 in their quartet 4Σ− state, then the singlet coupling of the two 4Σ− fragments can be funneled via the CI22−29 between the 4Σ−-4Σ− and 2Π-2Π singlet-coupled states and decay fast on a time scale of several femtoseconds22 to yield acetylene. As such, the CI offers a fast channel to acetylene. Furthermore, because the CI also produces small quantities of the 2Π carbyne, this provides a spin-allowed mechanism that generates free 2Π carbynes from initially prepared 4Σ− carbynes. The formation of an alkyne molecule from two carbyne radicals is, in fact, an example of a new type of a coupling reaction in which a carbon−carbon triple bond is formed from its constituent fragments and does so in aqueous solution. Experimentally, this process has been discovered recently during the degradation of trinuclear molybdenum complexes containing ethylidyne ligands (see Scheme 1 above). Thus, the [CH3C]3‑ ligands are oxidized by the metal framework to neutral CH3C free intermediates that couple and form 2butyne. The very low reactivity of CH(4Σ−) toward water and other closed-shell molecules has been deduced from rate constants measurements by Hou and Bayes.12,14 By contrast, for the doublet-state species RC(2Π), Strausz et al.9,10 found that all reactions with olefins, arenes, and C−H (O−H) bonds are fast and stereo- and regioselective. They also found by calculations that the reaction resembles carbene insertion along the nonleast motion path (à la Woodward−Hoffmann rules20), and these reactions serve as markers for carbynes in the doublet ground state. Similarly, their and others’ calculations show that the quartet state carbynes engage in H-abstraction and in reactions with radicals.12,18 These differences along with the computational result in Figures 4 and 5 allow us to diagnose the methyl carbynes formed by the degradation of metal−alkylidyne 61



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in their doublet ground state as well as in their quartet states (see Schemes 2 and 3). In each case, we calculated the lowest spin-states, which can arise from coupling of the two methylidynes, as outlined in Scheme 3. The calculations were performed along two coupling coordinates: In one case, we used the least-motion coupling, which maintains the HC---CH moieties colinear (Figures 3−5). The state energies were calculated by changing the C−C distance starting from 1.25 to 4.0 Å in increments of 0.25 Å between RCC = 1.25−2.0 Å and 0.5 Å between RCC = 2.0−4.0 Å while optimizing the H−C bond length along the coupling coordinate. In a second case, we freed this constraint and optimized also the HCC angle for the same C−C bond lengths. This has resulted in a nonlinear coupling coordinate and an MEP in Figure 2. The MOLPRO2010.1 package42 was utilized to carry out the SS-CASSCF, SA-CASSCF, and MRCI calculations. Six and 10 electrons with different number of active orbitals [(6,6), (6,8), (6,12), (10,10), (10,14)] were tested in the CAS. Because the location of the CI changes with the CAS level, we show results only for the higher levels. The MRCI calculations in Figure 2 were based on SS-CASSCF(10,10)/6-31G*, whereas those in Figure 3 were based on SS-CASSCF(10,10)/6-31G calculations. Figure 5 corresponds to SA-CASSCF(10,14)/6-31G* calculations with the three lowest states being equally weighted. For the CI search, we used only the equally weighting SACASSCF wave function. To ascertain that the crossing point is maintained also at a higher level (Figure 4), we used MRCI employing the appropriate reference configurations and orbitals determined from the SA-CASSCF(10,14)/6-31G* calculations.43 To treat the long-range HC---CH species in a manner that can be recognizable in terms of the fragments in Scheme 3 we used localized orbitals, as depicted in Scheme 2. Thus, for example, the singlet coupling of the 2Π-2Π methylidyne includes four electrons in the sigma frame, which will eventually correlate to the doubly excited state of acetylene with σ2σ*2 occupation. We therefore followed all SA-CASSCF configurations wherein there are four electrons in the σ-type hybrids of the HC fragments. Similarly the 4Σ−-4Σ− methylidyne singlet coupling is typified by two electrons in the σ-type orbitals and four electrons in the pπ orbitals. For the linear HC----CH approach we used a D2h point group symmetry for the calculations, whereas for the nonlinear HC--CH coupling we utilized the Cs point group symmetry. Because the mechanistic question we propose here is qualitative, the complete set of calculations used the 6-31G* basis set,44 with which it was possible to follow the coupling reactions of the doublet and quartet carbynes easily. A marker reaction of the doublet CH3C species is rearrangement to vinyl radical (H2CCH), which dimerizes to butadiene and produces also ethylene. To test the barrier for this rearrangement in the two spin states of CH3C(2A″, 4A2), we used optimized CASSCF (11,11)/cc-pVTZ in the gas phase and in IEFPCM45 calculations with water as a solvent. In accord with previous results,17 we obtained small barriers for the doublet state and very large ones for the quartet state. Single point CCSD(T)/cc-pVTZ/IEFPCM calculations at the CASSCF geometry gave lower barriers of 5.7 and 54.3 kcal mol−1, respectively, for the doublet and quartet states. These calculations used Gaussian09.46 All results with solvent effect are given in the SI.

will endow the doublet fragments with sufficient lifetime to yield diagnostic products. One such product is H2CCH•, which is formed from CH3C (S = 1/2) via 1,2-H shift with a small barrier around 5.7 kcal mol−1 (see SI, Table S10). Subsequently, the so formed H2CCH• radicals can couple instantly to yield 1,3-butadiene or abstract H to yield ethylene. Experimentally, such products are formed in a very small yield,2 indicating the presence of small amounts of CH3C (S = 1/2) radicals, as predicted from the branching from the CI in Figure 5b. It is interesting that these carbynes that are generated by high-energy processes5−14 are normally in their doublet ground state, whereas the carbynes that result by decomposition of metal complexes under ambient conditions (Scheme 1) seem to be in the excited quartet state. A hint to this somewhat intriguing phenomenon might come from the work of Goddard and Carter,21 who showed that dissociating the triple bond in acetylene correlates smoothly to two CH fragments in the 4Σ− excited state. Although RCM3 and RCM systems are not exactly symmetrical RCCR systems, it is reasonable to invoke some analogy in the dissociation process. When the metallic systems dissociate, they do so in a pseudohomolytic fashion in which the metal portion is engaged in reductive processes where electrons are transferred to other species in solution and the direct production of quartet RC carbyne. In turn, these quartet carbynes collapse to acetylenes via the CI, along with minor production of doublet carbynes (Figure 5), which rearrange to vinyl radicals and generate their diagnostic products, for example, 1,3-butadiene and ethylene.2 In conclusion, the distinct chemical behavior of the carbyne radicals described here that includes slow reactions with water, high reactivity toward alkynes, extensive hydrogen atom abstraction, and the lack of reactivity toward alkenes that serves as a marker for doublet carbynes led us to deduce a quartet excited state for these radicals. By usage of theory, we showed here a conical-intersection mechanism whereby two carbynes in the excited state can couple to yield ground-state RCCR singlet species, along with minor production of doublet carbynes that rearrange and produce minor amounts of 1,3-butadiene and ethylene. To the best of our knowledge the coupling of carbyne radicals, especially in the S = 3/2 spin state to form acetylens, has never been substantiated experimentally or theoretically prior to our studies. Our study may contribute to the understanding of processes leading to the formation of carbon−carbon triple bonded molecules in space or in important reactions such as alkyne-metathesis. Carbynes are part of the repertoire of reactive intermediates of carbon, like C itself, C2 in different states,31−39 which exhibits spin-dependent reactivity, and carbenes, which have recently shown unusual selectivity.40,41 The ability to generate carbynes under mild conditions and the present study opens a window to mechanistic studies of carbynes under mild conditions.

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METHODS Many computational details are relegated to the SI, whereas here we describe the essential points. Because the methylidyne coupling to HCCH involves regions with strong multireference character (RCC > 1.75 Å), we applied single-state CASSCF (SS-CASSCF), state-averaged CASSCF (SA-CASSCF), and the internally contracted MRCI19 methods to calculate geometric and energetic features of the species along the coupling pathways of two methylidynes being 62



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(15) Peeters, J.; Ceursters, B.; Nguyen, H. M. T.; Nguyen, M. T. The Reaction of C2H with H2: Absolute Rate Coefficient Measurements and ab initio Study. J. Chem. Phys. 2002, 116, 3700−3709. (16) Lee, E. P. F.; Wright, T. G. Methylcarbyne Radical [CH3C(X2A”; ã4A2)] and the Chemiionization Reaction: CH3C + O → CH3CO+ + e−. J. Phys. Chem. A 1999, 103, 721−726. (17) Nielsen, I. M. B.; Janssen, C. L.; Burton, N. A.; Schaefer, H. F., III. (1,2)-Hydrogen Shift in Monovalent Carbon Compounds: the Methylcarbyne-Vinyl Radical Isomerization. J. Phys. Chem. 1992, 96, 2490−2494. (18) Kellogg, C. B.; Valeev, E.; Galbraith, J. M.; Fowler, J. E.; Schaefer, H. F., III. The Elementary Reaction of Quartet Methylidyne (CH) with Methane. Mol. Phys. 1996, 89, 1695−1705. (19) Werner, H.-J.; Knowles, P. J. An Efficient Internally Contracted Multiconfiguration-Reference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803−5814. (20) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry; Verlag Chemie −Academic Press: Weinheim, Germany, 1971; pp 152−156. (21) Carter, E. A.; Goddard, W. A. III. Correlation Consistent Configuration Interaction: Accurate Bond Dissociation Energies from Simple Wave Functions. J. Chem. Phys. 1988, 88, 3132−3140. (22) Köppel, H.; Cederbaurn, L. S.; Dorncke, W.; Shaik, S. S. Symmetry Breaking and Non-Born-Oppenheimer Effects in Radical Cations. Angew. Chem., Int. Ed. 1983, 22, 210−224. (23) Bernardi, F.; Olivucci, M.; Robb, M. A. Potential Energy Surface Crossings in Organic Photochemistry. Chem. Soc. Rev. 1996, 25, 321− 328. (24) Köppel, H.; J. Gronki, J.; Mahapatra, S. Construction Scheme for Regularized Diabatic States. J. Chem. Phys. 2001, 115, 2377−2388. (25) Conical Intersections. Electronic Structure, Dynamics & Spectroscopy; Domcke, W., Yarkony, D. R., Köppel, H., Eds.; Advanced Series in Physical Chemistry 15; World Scientific: River Edge, NJ, 2004. (26) Lan, Z.; Lu, Y.; Fabiano, E.; Thiel, W. QM/MM Nonadiabatic Decay Dynamics of 9H-Adenine in Aqueous Solution. ChemPhysChem. 2011, 12, 1989−1998. (27) Atchity, G. J.; Xantheas, S. S.; Ruedenberg, K. Potential Energy Surfaces Near Intersections. J. Chem. Phys. 1991, 95, 1862−1876. (28) Dixon, R. N.; Oliver, T. A. A.; Ashfold, M. N. R. Tunnelling Under a Conical Intersection: Application to the Product Vibrational State Distributions in the UV Photodissociation of Phenols. J. Chem. Phys. 2011, 134, 194303-1−194303-10. (29) Olsen, S.; McKenzie, R. H. A Diabatic Three-State Representation of Photoisomerization in the Green Fluorescent Protein Chromophore. J. Chem. Phys. 2009, 130, 184302−1− 184302-13. (30) Truhlar, D. G.; Mead, C. A. Relative Likelihood of Encountering Conical Intersections and Avoided Intersections on the Potential Energy Surfaces of Polyatomic Molecules. Phys. Rev. A 2003, 68, 032501−1−032501−2. (31) Pasternack, L.; Baronavski, A. P.; McDonald, J. R. Temperature Dependence of the C2 (a3Πu)+CH4 Reaction from 337 to 605 K. J. Chem. Phys. 2009, 73, 3508−3510. (32) Donnelly, V. M.; Pasternack, L. Reactions of C2 (a3Πu) with CH4, C2H2, C2H4, C2H6, and O2 Using Multiphoton UV Excimer Laser Photolysis. Chem. Phys. 1979, 39, 427−432. (33) Páramo, A.; Canosa, A.; Le Picard, S. D.; Sims, I. R. Rate Coefficients for the Reactions of C2(a3Πu) and C2(XΣ+g ) with Various Hydrocarbons(CH4, C2H2, C2H4, C2H6, and C3H8): A Gas-Phase Experimental Study Over the Temperature Range 24−300 K. J. Phys. Chem. A 2008, 112, 9591−9600. (34) Pasternack, L.; McDonald, J. R. Reactions of C2 (XΣ+g ) Produced by Multiphoton UV Excimer Laser Photolysis. Chem. Phys. 1979, 43, 173−182. (35) Skell, P. S.; Jackman, L. M.; Ahmed, S.; McKee, M. L.; Shedin, P. B. Some Reactions and Properties of Molecular C2. An Experimental and Theoretical Treatment. J. Am. Chem. Soc. 1989, 111, 4422−4429.

The FCI calculations of HC (with frozen 1s core for C) were done to test the method in reproducing the experimental spinstate gap. Using different basis set, 6-31G, 6-31G*, 6-311G*, 6311G**, and cc-pVTZ, we found that the latter one gave a value in close agreement with the experimental datum.

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ASSOCIATED CONTENT

S Supporting Information *

Results of FCI calculations for different basis sets, figures of natural orbitals for CASSCF(10,14)/6-31G* calculations, CSF and coefficients for MRCI/6-31G* calculations, Cartesian coordinates. This material is available free of charge via the Internet http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.S. acknowledges the Israel Science Foundation (grant 53/09). REFERENCES

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