A combined experimental/theoretical study gives strong evidence that carbodiphosphoranes are divalent carbon(0) compounds. The calculations show that carbodiphosphoranes have two lone pairs of electrons (see picture), which give rise to unusual properties as confirmed by experiment. The synthesis of a triply charged molecules in which two protonated carbodiphosphoranes serve as donor ligands to an Ag+ center supports the bonding model.

Quantum-chemical calculations with DFT (BP86) and ab initio methods [MP2, SCS-MP2, CCSD(T)] have been carried out for the molecules C(PH(3))(2) (1), C(PMe(3))(2) (2), C(PPh(3))(2) (3), C(PPh(3))(CO) (4), C(CO)(2) (5), C(NHC(H))(2) (6), C(NHC(Me))(2) (7) (Me(2)N)(2)C=C=C(NMe(2))(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 L(2)C 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 L-->C<--L. This holds particularly for the carbodiphosphoranes 1-3 where L=PR(3), 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 C==C==C 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 L-->C((1)D) donor-acceptor bonds are roughly twice as strong as the respective L-->BH(3) bond.

Future targets: Quantum‐chemical calculations predict that the experimentally still unknown carbodicarbenes C(NHC)2 (NHC=N‐heterocyclic carbene; see picture for example) are a synthetically accessible class of divalent carbon(0) compounds which are very strong nucleophiles and bases that may be useful ligands for transition‐metal complexes.

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) CR(2), which have one lone electron pair at carbon, and carbon(0) compounds CL(2), which have two lone pairs at carbon and two C<--L 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 (R(2)N)(2)C=C=C(NR(2))(2) to a donor-acceptor description (R(2)N)(2)C-->C(H(+))(n)<--C(NR(2)) [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.

DFT calculations at the BP86/TZ2P level were carried out to analyze quantitatively the metal-ligand bonding in transition-metal complexes that contain imidazole (IMID), imidazol-2-ylidene (nNHC), or imidazol-4-ylidene (aNHC). The calculated complexes are [Cl4TM(L)] (TM = Ti, Zr, Hf), [(CO)5TM(L)] (TM = Cr, Mo, W), [(CO)4TM(L)] (TM = Fe, Ru, Os), and [ClTM(L)] (TM = Cu, Ag, Au). The relative energies of the free ligands increase in the order IMID < nNHC < aNHC. The energy levels of the carbon sigma lone-pair orbitals suggest the trend aNHC > nNHC > IMID for the donor strength, which is in agreement with the progression of the metal-ligand bond-dissociation energy (BDE) for the three ligands for all metals of Groups 4, 6, 8, and 10. The electrostatic attraction can also be decisive in determining trends in ligand-metal bond strength. The comparison of the results of energy decomposition analysis for the Group 6 complexes [(CO)5TM(L)] (L = nNHC, aNHC, IMID) with phosphine complexes (L = PMe3 and PCl3) shows that the phosphine ligands are weaker sigma donors and better pi acceptors than the NHC tautomers nNHC, aNHC, and IMID.

The many-body expansion V int = ͚ iϽj V ͑2͒ ͑r ij ͒ + ͚ iϽjϽk V ͑3͒ ͑r ij , r ik , r jk ͒ +¯, in terms of interaction potentials between rare-gas atoms converges fast at distances r Ͼ r HS , with r HS being the hard-sphere radius at the start of the repulsive wall of the interaction potential. Hence, for the solid state where the minimum distance is always above r HS , a reasonable accuracy is already obtained for the lattice parameters and cohesive energies of the rare-gas elements using precise two-body terms. All tested two-body potentials show a preference of the hcp over the fcc structure. We demonstrate that this is always the case for the Lennard-Jones potential. We extend the Lennard-Jones potential to obtain analytical expressions for the lattice parameters, cohesive energy, and bulk modulus using the solid-state parameters of Lennard-Jones and Ingham ͓Proc. R. Soc. London, Ser. A 107, 636 ͑1925͔͒, which we evaluate up to computer precision for the cubic lattices and hcp. The inclusion of three-body terms does not change the preference of hcp over fcc, and zero-point vibrational effects are responsible for the transition from hcp to fcc as shown recently by Rosciszewski et al. ͓Phys. Rev. B 62, 5482 ͑2000͔͒. More precisely, we show that it is the coupling between the harmonic modes which leads to the preference of fcc over hcp, as the simple Einstein approximation of moving an atom in the static field of all other atoms fails to describe this difference accurately. Anharmonicity corrections to the crystal stability are found to be small for argon and krypton. We show that at pressures higher than 15 GPa three-body effects become very important for argon and good agreement is reached with experimental high-pressure density measurements up to 30 GPa, where higher than three-body effects become important. At high pressures we find that fcc is preferred over the hcp structure. Zero-point vibrational effects for the solid can be successfully estimated from an extrapolation of the cluster zero-point vibrational energies with increasing cluster size N. For He, the harmonic zero-point vibrational energy is predicted to be always above the potential energy contribution for all cluster sizes up to the solid state at structures obtained from the two-body force. Here anharmonicity effects are very large which is typical for a quantum solid.

Recent theoretical studies are reviewed which show that the naked group 14 atoms E = C-Pb in the singlet (1)D state behave as bidentate Lewis acids that strongly bind two σ donor ligands L in the donor-acceptor complexes L→E←L. Tetrylones EL2 are divalent E(0) compounds which possess two lone pairs at E. The unique electronic structure of tetrylones (carbones, silylones, germylones, stannylones, plumbylones) clearly distinguishes them from tetrylenes ER2 (carbenes, silylenes, germylenes, stannylenes, plumbylenes) which have electron-sharing bonds R-E-R and only one lone pair at atom E. The different electronic structures of tetrylones and tetrylenes are revealed by charge- and energy decomposition analyses and they become obvious experimentally by a distinctively different chemical reactivity. The unusual structures and chemical behaviour of tetrylones EL2 can be understood in terms of the donor-acceptor interactions L→E←L. Tetrylones are potential donor ligands in main group compounds and transition metal complexes which are experimentally not yet known. The review also introduces theoretical studies of transition metal complexes [TM]-E which carry naked tetrele atoms E = C-Sn as ligands. The bonding analyses suggest that the group-14 atoms bind in the (3)P reference state to the transition metal in a combination of σ and π∥ electron-sharing bonds TM-E and π⊥ backdonation TM→E. The unique bonding situation of the tetrele complexes [TM]-E makes them suitable ligands in adducts with Lewis acids. Theoretical studies of [TM]-E→W(CO)5 predict that such species may becomes synthesized.

The formal cycloaddition between 1,3-diaza-2-azoniaallene salts and alkynes or alkyne equivalents provides an efficient synthesis of 1,3-diaryl-1H-1,2,3-triazolium salts, the direct precursors of 1,2,3-triazol-5-ylidenes. These N,N-diarylated mesoionic carbenes (MICs) exhibit enhanced stability in comparison to their alkylated counterparts. Experimental and computational results confirm that these MICs act as strongly electron-donating ligands. Their increased stability allows for the preparation of ruthenium olefin metathesis catalysts that are efficient in both ring-opening and ring-closing reactions.