Quadruple bonding in C2 and analogous eight-valence electron species

Abstract

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 theoretical methods, we show that C(2) 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 σ- and two π-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 mol(-1) for the isoelectronic species studied, and thus stronger than a hydrogen bond. In contrast, the analogues of C(2) that contain higher-row elements, such as Si(2) and Ge(2), exhibit only double bonding.

Communication: Chemical bonding in carbon dimer isovalent series from the natural orbital functional theory perspective

“…1. Note that the natural orbitals yield a representation with four bonding orbitals (quasi) doubly occupied, very supportive of a formal bond order of four, as claimed by Shaik et al 15 However, there is a number of differences between our description and that of the VB calculations of Shaik et al 15 which should be pointed out. Thus, the VB computations assume a sp hybridization scheme for each of the two carbon atoms and then four molecular bonding orbitals are set by combining the two (one on each carbon atom) σ -type orbitals inwardly pointing, the four (two on each carbon atom) π -type orbitals, and the fourth bond is made of the combination of the two σ -type outwardly pointing orbitals.…”

“…On the other hand, a deep inspection of the VB hybrid molecular orbitals pinpoints to a likely valence bond structure with a bond order of four, and it is claimed that the properties of C 2 can be predicted quite well using such quadruple bond valence bond structure. 15,17 Furthermore, for Si 2 and Ge 2 , inspection of both sets of orbitals agrees in assigning a bond order of two.…”

“…This approach has produced a number of pleasant outcomes, like the recent characterization of the quintuple bond of the uranium dimer, 14 but, as it has been stated above, it is subjected to some degree of arbritariness that for depending on which orbital set the inspected conclusion might be different. A nice example of the latter is the research by Shaik et al on the bond order of carbon dimer and its isovalent eight-valence electron species, 15 which has been recently enriched by an enlightening discussion with Rzepa and Hoffmann. 16 Thus, for C 2 , BN, CN + , and CB − , inspection of the orbitals computed from MO theory suggests a bond order of two.…”

“…Indeed, their estimated bond energies are 4.35 eV (100.4 kcal/mol) for the σ (C-C) bond, 4.08 eV (94.2 kcal/mol) for the two degenerate π (C-C) bonds, and 0.62 eV (14.3 kcal/mol) for the fourth weak bond. 15 It is worth noting that these orbital bond energies do not correspond to the ionization energies. 11 The natural orbitals found in the PNOF5 calculations are one of σ -type and three hybrid bent orbitals of pseudo-π symmetry, also referred as banana orbitals, 33 nodal plane is not a plane of symmetry, but they conserve an inversion point in such a way that bonding pseudo-π orbitals are of ungerade symmetry and antibonding pseudo-π orbitals are of gerade symmetry.…”

How valence bond theory can help you understand your (bio)chemical reaction

“…7). 42 The bond order of diatomic molecules with eight-valence electrons using the simple molecular orbital diagram is two, as in structure H (Fig. 7), because of the electron occupation of both 90 2σ g and 2σ u , which leaves only the contribution of the 4π electrons to the bond order.…”