Quantum-chemical calculations with DFT (BP86) and ab initio methods [MP2, SCS-MP2, CCSD(T)] have been carried out for the molecules C(PH₃)₂ (1), C(PMe₃)₂ (2), C(PPh₃)₂ (3), C(PPh₃)(CO) (4), C(CO)₂ (5), C(NHC_H)₂ (6), C(NHC_Me)₂ (7) (Me₂N)₂CCC(NMe₂)₂ (8), and NHC (9), where NHC=N-heterocyclic carbene and NHC_Me=N-methyl-substituted NHC. The electronic structure in 1–9 was analyzed with charge- and energy-partitioning methods. The results show that the bonding situations in L₂C compounds 1–8 can be interpreted in terms of donor–acceptor interactions between closed-shell ligands L and a carbon atom which has two lone-pair orbitals LCL. This holds particularly for the carbodiphosphoranes 1–3 where L=PR₃, which therefore are classified as divalent carbon(0) compounds. The NBO analysis suggests that the best Lewis structures for the carbodicarbenes 6 and 7 where L is a NHC ligand have CCC double bonds as in the tetraaminoallene 8. However, the Lewis structures of 6–8, in which two lone-pair orbitals at the central carbon atom are enforced, have only a slightly higher residual density. Visual inspection of the frontier orbitals of the latter species reveals their pronounced lone-pair character, which suggests that even the quasi-linear tetraaminoallene 8 is a “masked” divalent carbon(0) compound. This explains the very shallow bending potential of 8. The same conclusion is drawn for phosphoranylketene 4 and for carbon suboxide (5), which according to the bonding analysis have hidden double-lone-pair character. The AIM analysis and the EDA calculations support the assignment of carbodiphosphoranes as divalent carbon(0) compounds, while NHC 9 is characterized as a divalent carbon(II) compound. The LC(¹D) donor–acceptor bonds are roughly twice as strong as the respective LBH₃ bond.

Quantum chemical calculations at the MP2/TZVPP//BP86/SVP level are reported for the first and second proton affinities (PAs) of divalent carbon-donor molecules. The molecules investigated are imidazol-2-ylidenes (“normal” NHCs) and the tautomeric imidazol-4/5-ylidenes (“abnormal” NHCs). PAs are also calculated for acyclic and cyclic carbodiphosphoranes, carbophosphoranesulfide, unsaturated and saturated carbodicarbenes, tetraaminoallenes and carbon suboxide. The results are discussed in terms of divalent carbon(II) compounds (carbenes) CR₂, which have one lone electron pair at carbon, and carbon(0) compounds CL₂, which have two lone pairs at carbon and two CL donor–acceptor bonds. Divalent C(0) compounds (carbones) not only have very high first PAs, but the second PA is also large and strong enough to isolate doubly protonated C(0) species as salts in a condensed phase. The first PA of divalent carbon(II) compounds (carbenes) are also large. However, they have much smaller second PAs than the divalent carbon(0) compounds. The divalent C(0) character of a compound is not always obvious when the bonding situation in the equilibrium geometry is considered. This is the case, for example, for tetraaminoallenes (TAAs). Protonation of TAAs changes the bonding situation of the central moiety from doubly bonded (R₂N)₂CCC(NR₂)₂ to a donor–acceptor description (R₂N)₂CC(H⁺)_nC(NR₂) [n=1, 2]. The atomic partial charge at the carbon donor atom does not correlate with the PA and the trend of the second PA may be quite different from the trend of the first. The trends of the first and second PA correlates quite well with the eigenvalues of the highest-lying carbon lone-pair orbitals.