ARTICLES PUBLISHED ONLINE: 29 JANUARY 2012 | DOI: 10.1038/NCHEM.1263 Quadruple bonding in C2 and analogous eight-valence electron species Sason Shaik1*, David Danovich1,WeiWu2,PeifengSu2, Henry S. Rzepa3 and Philippe C. Hiberty4 Triple bonding is conventionally considered to be the limit for multiply bonded main group elements, despite higher metal–metal bond orders being frequently observed for transition metals and lanthanides/actinides. Here, using high-level 1 2 theoretical methods, we show that C2 and its isoelectronic molecules CN , BN and CB (each having eight valence electrons) are bound by a quadruple bond. The bonding comprises not only one s -andtwop-bonds, but also one weak ‘inverted’ bond, which can be characterized by the interaction of electrons in two outwardly pointing sp hybrid orbitals. A simple way of assessing the energy of the fourth bond is proposed and is found to be ∼12–17 kcal mol21 for the isoelectronic species studied, and thus stronger than a hydrogen bond. In contrast, the analogues of C2 that contain higher-row elements, such as Si2 and Ge2, exhibit only double bonding. he interest in multiple bonding has been on the rise ever since directionality of these hybrids is the main factor that dictates why it was demonstrated that transition metals and lanthanides/ this ‘inverted’ fourth bond is commonly ruled out by chemists. Tactinides can form metal–metal bonding in which the However, a recent estimate of the bonding in [1.1.1]propellane24 maximum practical bond order reaches four to six bonds1–8.In shows that such outwardly pointing hybrids may nevertheless main elements, however, the maximum number of bonds between maintain a highly significant bonding interaction. Indeed, if the two atoms has remained three9–13, this being composed of one two odd electrons in the outwardly pointing hybrids were very s- and two p-bonds. Nevertheless, there are diatomic molecules weakly coupled, the molecule would have exhibited a diradicaloid þ such as C2,Si2,CN and BN, which, by having eight valence elec- character with a closely lying triplet state. However, the diradicaloid trons, could at least formally express quadruple bonding between character is absent25. More compelling is the fact that the corre- 3 þ the two atoms (H. S. Rzepa, www.ch.imperial.ac.uk/rzepa/blog/ sponding triplet state c Su , in which these electrons are unpaired, ?p=3065). One might then ask, no matter how naively, can the lies 26.4 kcal mol21 above the ground state15,16, indicating that eight valence electrons (for example, between the two carbon these electrons maintain a significant bonding interaction in the atoms in C2) couple to create four bonds and, if so, what is the ground state. Therefore, one cannot rule out the inference that C2 bonding energy of the putative fourth bond? This is the focus of has a quadruple bond, as depicted by structure 3 in Fig. 1b. Here, the present article, which uses valence bond (VB) theory12,14 and we test this hypothesis. We present an assessment of the energy of full configuration interaction (FCI) calculations to determine the the fourth bond by means of VB and FCI calculations, and we bonding energy of the fourth bond in C2 and its absence or presence demonstrate the quadruple bonding from the FCI wavefunction. þ 2 in some of its isoelectronic species. As we shall show, although C2,CN , BN and CB definitely have C2 has been extensively investigated using a variety of methods, a fourth bond, higher-row analogues such as Si2 or Ge2 have only which have provided valuable information on its ground state a double bond. 1 þ 15–22 (X Sg ) and 17 of its excited states . Nevertheless, C2 continues to challenge our understanding of bonding14. A nominal a π b 1 g CC consideration of the bond order in the molecular orbital diagram 1 23 σ in Fig. 1a would suggest a bond order of two , as in structure 1 3 g CC in Fig. 1b, and, because the 2sg and 2su orbitals are both filled, π 2 the molecule would then have two p-bonds unsupported by an 1 u underlying s-bond (or a weak one assuming that 2su is rather σ CC 2 u weakly antibonding), and two s lone pairs. In contrast, using 3 sp-hybridized carbons would suggest that it is possible to form a σ 2 g strong triple bond composed of one s- and two p-bonds, with X 1Σ+ two electrons remaining in the outwardly pointing hybrids, as in g structure 2 (Fig. 1b). 14 A recent VB theory study has shown that, by using structure 2, Figure 1 | Representations of bonding in C2. a, Molecular orbital diagram. the properties of C2 can be predicted quite well, and that its two The shapes of the 2su and 3sg molecular orbitals, as determined from FCI electrons in the outwardly pointing hybrids are singlet-paired, calculations, are also represented together with their respective energy 1 þ thus yielding the known singlet ground state X Sg . The levels. b, Three simplified bonding cartoons. 1Institute of Chemistry and The Lise Meitner-Minerva Center for Computational Quantum Chemistry, Hebrew University of Jerusalem, 91904, Jerusalem, Israel, 2The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China, 3Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, UK, 4Laboratoire de Chimie Physique, UMR CNRS 8000, Universite´ de Paris Sud, 91405 Orsay Ce´dex, France. *e-mail: [email protected] NATURE CHEMISTRY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturechemistry 1 © 2012 Macmillan Publishers Limited. All rights reserved. ARTICLES NATURE CHEMISTRY DOI: 10.1038/NCHEM.1263 a c 12,14,24,26 only classical interactions, which sum to zero . In turn, Din Ψ = a Ψ + b (Ψ + Ψ' ) Ψ bond cov ion,l ion,r T AB is the energy difference (Fig. 2b) of the CQC and of Cbond states. Figure 2c shows another way of estimating Din by calculating the D ª ΔE Ψ in 1/2 ST corresponding triplet state, C , which uncouples the electrons of the cov = (A B) = (A B) (A B) T Ψ Ψ' fourth bond to a triplet state with two identical spins. As has been QC QC Ψ 28 bond AB discussed previously (see ref. 26, p. 131), the singlet-to-triplet Ψ + Ψ ion,l = (A: B ) 'ion,r = (A B: ) excitation of a bond is approximately twice the desired Din. Figure 2d shows the symbols for the C2 states that are involved in this particular singlet-to-triplet excitation. b d Figure 2e shows the relationship between the total Din and BDE Ψ c3Σ+ σ2π4 σ1 σ1 QC A B CC2 2 3 u g u u g for all the electron pairs in C2. The BDE involves the relaxation of D the fragments and their electronic demotion to the corresponding cov electronic ground states, which in the case of C atoms are the 3P D ª ΔE Ψ D in 1/2 ST cov AB in states. However, Din (total) measures the stabilization energy due to bond-pairing of the ‘prepared’ 5S states of C, without any REcov-ion effects associated with the relaxation of the fragments electronically Ψ σ2π4 σ2 bond CC2 g u2 u (or geometrically if applicable). We shall refer to D (total) as the Ψ in bond AB ‘intrinsic bonding energy’. The first two entries in Table 1 list the Din values for C2 from e VB theory. The two methods give values for Din of the fourth C C–C bond of 14.30 and 11.64 kcal mol21, respectively. We note that the VB-calculated DE value (23.28 kcal mol21) is quite 5S ST 2 C ( ) close to the experimental value of the vertical excitation from ΔE 1 þ 3 þ 21 15,16 prom X Sg to the c Su state (26.4 kcal mol ) . This is expected, D D (total) because the VB calculation of EST is entirely equivalent to the in 1 þ 3 þ X Sg c Su excitation that uncouples the singlet pair of the fourth-bond electrons to a triplet spin, as shown in Fig. 2c,d29 (see also ref. 26, pp. 57,79,88,188). 2 C (3P) Using molecular orbital-based FCI computations of DE is a BDE ST convenient alternative way to obtain Din data. Indeed, our FCI 1 þ calculations for these states in C2 show that the ground-state X Sg C C 3 þ 2 4 2 and the triplet-state c Su are dominated by the 2sgpu 2su and 2 4 1 1 C (X 1Σ+) 2sgpu2su3sg configurations (Supplementary Section II.2). The cal- 2 g 21 culated FCI value of DEST is 29.6 kcal mol , slightly higher than the Figure 2 | VB wavefunctions and energy terms. a, The full-bond state experimental value. Using the relation of Din to DEST in Fig. 2c, we list the corresponding Din values in Table 1 (last two entries), estimated (Cbond) for bond A–B, with covalent (Ccov) and two ionic (Cion) from the experimental and FCI DEST quantities. These values are contributions, and the spin arrangement patterns that make up the covalent 21 structure. b, Definition of the in situ bond energy (D ) as the energy gap 13.2 and 14.8 kcal mol . Thus, four different methods bracket in the intrinsic bonding energy of the fourth bond in the range between Cbond and the QC state CQC.REcov-ion is the covalent–ionic 21 resonance energy.