New bonding modes of carbon and heavier group 14 atoms Si–Pb

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 s donor ligands L in the donor–acceptor complexes L - E ’ L. Tetrylones EL 2 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 ER 2 (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 EL 2 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 s and p J electron-sharing bonds TM–E and p > 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.


Introduction
This review summarizes recent theoretical work which deals with molecules where novel types of chemical bonds of group 14 atoms C-Pb in main group compounds and transition metal complexes were found. Experimental and theoretical evidence suggest that there are carbon compounds such as carbodiphosphorane C(PPh 3 ) 2 -known since 1961 1 -which are best described in terms of donor-acceptor interactions L-C'L between a bare carbon atom in the excited 1 D state and two strong s donors L, namely divalent carbon(0) compounds CL 2 . The term carbone has been suggested for these molecules which exhibit a chemical reactivity that is clearly different from carbenes CR 2 . The same bonding situation may also be found in the heavier tetrylone homologues EL 2 (E = Si-Pb). Stable silylones SiL 2 and germylones GeL 2 could become synthesized after theoretical studies suggested that they might exist.
We also review theoretical studies of transition metal complexes [TM]-C which have a bare carbon atom as ligand. Examples of such carbon complexes have been synthesized in 2002 where the ruthenium species [(PCy 3 ) 2 Cl 2 Ru(C)] could become isolated. 2 A formal electron count which takes the carbon atom as two-electron donor suggests that the molecule is a 16 valence-electron complex. The bonding analysis shows that the bare carbon atom which is isolobal to CO binds through its 3 P ground state to the transition metal which yields two electron-sharing bonds and one donor-acceptor bond. This makes carbon a formal four-electron donor which indicates that [(PCy 3 ) 2 Cl 2 Ru(C)] is actually a Ru(IV) compound. Theoretical studies of carbon complexes [TM]-C and heavier group 14 homologues [TM]-E (E = Si-Pb) which are experimentally not known are discussed here.

Divalent carbon(0) compounds (carbones)
The vast majority of organic compounds which until 1988 were known as stable species in condensed phase exhibit carbon atoms that use all four valence electrons in single, double or triple bonds with other elements across the periodic table (Scheme 1a). Except for a very few special cases such as the notorious CO, 3 carbon appears nearly always as tetravalent C(IV) 4 in stable organic compounds. The situation changed when Bertrand 5 in 1988 and Arduengo 6 in 1991 isolated compounds which are now recognized 7 as stable carbenes CR 2 . In carbenes, carbon uses only two of its valence electrons while the remaining two retain as a lone electron pair (Scheme 1b). The chemistry of N-heterocyclic carbenes (NHCs) has become a particular focus of synthetic chemistry because NHCs are versatile ligands in transition metal complexes which were found very useful as powerful catalysts. 8 The carbene chemistry of divalent carbon(II) compounds is now well established in organic synthesis. 9 It has recently been recognized that there are organic compounds in which carbon exhibits yet another bonding situation. Divalent carbon(0) compounds CL 2 possess a carbon atom which retains all four valence electrons as two lone pairs and where the bonding to the s donor ligands L occurs through donor-acceptor interactions L-C'L (Scheme 1c). The electronic reference state of carbon in CL 2 is the excited 1 D singlet state with the electron configuration 1s 2 2s 2 2p x 0 2p y 0 2p z 2 which is 29.1 kcal mol À1 higher in energy than the 3 P ground state (Fig. 1). 10 The donation from the lone-pair electrons of the ligands takes place from the in-phase (+,+) combination of the donor orbitals into the vacant 2p x orbital (s symmetry) and Gernot Frenking from the out-of-phase (+,À) combination of the donor orbitals into the vacant 2p y orbital (in-plane p J symmetry). The orientation of the carbon 2p z 2 orbital is orthogonal to the CL 2 plane, i.e.
it becomes the out-of-plane p(p > ) lone pair orbital. The excitation energy 3 P -1 D is compensated by the strong donoracceptor bonding between the Lewis base L and the (double) Lewis acid ( 1 D) carbon. The name carbone has been suggested 11 for the latter divalent carbon(0) compounds in analogy to the name carbene for divalent carbon(II) compounds CR 2 which have only one lone pair and two electron-sharing bonds C-R.
Another important difference between carbones and carbenes is that the former compounds are p donors while the latter are usually weak p acceptors. The first carbone was already synthesized in 1961 when Ramirez reported about the isolation of the carbodiphosphorane C(PPh 3 ) 2 . 1 The chemistry of carbodiphosphoranes was systematically explored in experimental work in the following years. 12 A critical examination of the bonding description in the past literature shows that the carbon-phosphorous bond in carbodiphosphoranes is usually classified as diylide which is sketched Scheme 1 Schematic representation of (a) tetravalent carbon(IV) compounds; (b) divalent carbon(II) compounds (carbenes), (c) divalent carbon(0) compounds (carbones). Fig. 1 Schematic presentation of the orbital interactions between carbon atom in the (1s 2 2s 2 2p x 0 2p y 0 2p z with mesomeric structures as shown in Fig. 2a. This picture was already suggested by Ramirez in his 1961 publication 1 when the structure of hexaphenylcarbodiphosphorane was not known yet. It was not until 1978 when the first X-ray structural analysis revealed that C(PPh 3 ) 2 has a strongly bent P-C-P angle of 131.71. 13 Recent DFT calculations gave a geometry which is in very good agreement with the experimental data (Fig. 2b). 14 Inspection of the frontier orbitals of C(PPh 3 ) 2 showed that the HOMO is a p-type lone pair orbital while the HOMOÀ1 is a s-type lone pair orbital ( Fig. 2c and d). 15 The description of the bonding situation in carbodiphosphoranes in terms of donor-acceptor interactions Ph 3 P-C'PPh 3 was put forward in 2006 in a combined theoretical and experimental study by Tonner et al. 16 providing crucial support for the postulated Lewis structure by Kaska et al. from 1973. 17 The authors had analyzed in a preceding study the nature of the carbon-carbon bond between carbodiphosphorane and CO 2 as well as CS 2 yielding the adducts X 2 C-C(PPh 3 ) 2 (X = O, S) which were isolated and characterized through an X-ray structure analysis (Fig. 3). 18 The complexes possess rather short carbon-carbon bonds which are shorter than a standard single bond. With the help of charge-and energy decomposition analyses, they identified a donor-acceptor bond X 2 C'C(PPh 3 ) 2 which has a dominant s component and a weaker p component. It was concluded that carbodiphosphoranes C(PR 3 ) 2 are double electron pair donors having sand p-carbon lone-pair orbitals. 18 The latter finding was elaborated in the 2006 theoretical study where the twofold donor strength of carbodiphosphoranes C(PR 3 ) 2 with different substituents R with respect to H + and the Lewis acids BH 3 , BCl 3 and AlCl 3 was estimated and analyzed using ab initio and DFT methods. 16 The calculations showed that carbodiphosphoranes have not only a very large first proton affinity (PA) which classifies them as very strong bases. They also have a very large second PA which agrees with the notion of two lone pairs. A subsequent theoretical study of the first and second proton affinities of carbon bases showed that the first PA of carbodiphosphoranes C(PR 3 ) 2 has a similar strength as the first PA of NHCs but that C(PR 3 ) 2 exhibit a significantly higher second PA than NHCs. 19 Pertinent examples are shown in Table 1. The calculations also predicted that the double Lewis base C(PPh 3 ) 2 is capable of binding two BH 3 molecules at the carbon lone pairs in the stable complex (H 3 B) 2 -C(PPh 3 ) 2 while NHC binds only one BH 3 at the carbon atom. 16 (Fig. 4b).
The double donor ability of the carbodiphosphoranes C(PPh 3 ) 2 and the contrast to the carbene NHC was convincingly demonstrated in a joint experimental/theoretical work by Alcarazo, Thiel and co-workers. 21 The authors realized that the s and p lone    (Fig. 4d). The calculations of carbodiphosphoranes C(PR 3 ) 2 were the starting point for further theoretical studies of divalent carbon(0) compounds CL 2 with other ligands than phosphanes. Inspection of the literature revealed that the carbonyl homologues C(PPh 3 )(CO) 22 and C(CO) 2 23 which is usually described as carbon suboxide OQCQCQCQO are experimentally known for a long time. The bonding model in terms of donor-acceptor interactions L-C'L easily explains the finding that the divalent C(0) compounds with the better p acceptor ligands CO have larger bending angles t for C(PPh 3 )(CO) (t = 145.51) 22 and C(CO) 2 (t = 156.01). 24 There is a correlation between the p-acceptor strength of ligand L and the bending angle L-C-L in carbones CL 2 . Stronger p-acceptor ligands L induce more obtuse bending angles in CL 2 . The deviation from linearity and the very shallow bending potential of carbon suboxide is difficult to explain with the standard bonding model of a cumulene OQCQCQCQO while it becomes plausible when the donor-acceptor model L-C'L is employed. The litmus test for the predictive power of the donor-acceptor model L-C'L was provided by the theoretical study of the hitherto unknown class of carbodicarbenes C(NHC) 2 which were suggested by Tonner and Frenking as stable molecules. 25 Chemical experience has shown that NHCs have comparable donor properties as phosphanes which initiated a theoretical study of CL 2 with NHC ligands L. The optimized geometry of C(NHC Me ) 2 (Fig. 5) shows a bending angle at the central carbon atom of 131.81, which is similar to the value that is calculated for C(PPh 3 ) 2 . The experimental verification of the theoretical work followed shortly after. Bertrand and co-workers isolated the benzoannelated carbodicarbene C(NHC Bz ) 2 which is also shown in Fig. 5. 26 The bending angle in C(NHC Bz ) 2 is 134.81 which is close to the calculated value for C(NHC Me ) 2 . Fürstner et al. reported at the same time about protonated carbon complexes which carry C(NHC) 2 as ligands. 27 The latter group recently synthesized a series of mixed carbones with one phosphane and various other ligands C(PPh 3 )(L) where L is CO, CNPh, PPh 3 or a carbene CR 2 with different substituent R. 28 The authors investigated experimentally and theoretically the monoaurated and diaurated complexes (ClAu) 2 -C(PPh 3 )(L). It was suggested that the binding strength toward a second AuCl molecule should be used as measure of the carbone character of a compound CL 2 . Fig. 5 shows also the optimized geometry of C[C(NMe 2 ) 2 ] 2 which has a nearly linear C-C-C structure and a geometry where the C(NMe 2 ) 2 moieties are orthogonal to each other. The molecule may thus become identified as tetraaminoallene (TAA) (NMe 2 ) 2 CQCQC(NMe 2 ) 2 . However, the calculations predict that not only the first but also the second PA of the TAA which are very large have values similar to carbodicarbenes. The analogous TAA with ethyl groups instead of methyl has even a second PA of 175.8 kcal mol À1 . 19 Protonation at the central carbon atom is in both cases favoured over protonation at nitrogen. It has therefore been suggested that TAAs have ''hidden carbone character'' and that the bonding situation may also be described in terms of donor-acceptor interactions (NMe 2 ) 2 C-C'C(NMe 2 ) 2 . 14 The chemical reactivity of TAAs supports the suggestion. The X-ray structure of doubly protonated TAAs where both protons bind to the central carbon atom has been reported. 29 Even more convincing evidence for the ''hidden carbone character'' comes from the work of Viehe et al. who found that methyl and ethyl substituted TAAs react ''extremely readily and in good yields with carbon dioxide'' to give adducts which are analogous to the CO 2 adduct of C(PPh 3 ) 2 which is shown in Fig. 3. 30 It becomes obvious that the nature of the ligand L has a very strong influence on the structure and reactivity of carbon compounds CL 2 . The methylene group L = CH 2 has a triplet ground state which binds a carbon atom in its ( 3 P) triplet ground state yielding the parent allene H 2 CQCQCH 2 . The first PA (182.4 kcal mol À1 ) and particularly the second PA (À5.2 kcal mol À1 ) are strikingly different to the first and second PA of TAAs. 25a Diaminocarbenes C(NR 2 ) 2 have a singlet ground state and a very large singlet-triplet gap which supports donor-acceptor binding with a carbon atom in the ( 1 D) excited state. The correlation between singlet-triplet gap and donor-acceptor bond will be further discussed in the section about the heavy group 14 homologues EL 2 which is given below. TAAs have a very shallow bending mode like C(CO) 2 and other compounds CL 2 where L is a s donor. Table 2 gives the calculated energies that are necessary to stretch the bending angle of various compounds CL 2 from the equilibrium structure to the linear form or to the value of 136.91 which is the energy minimum value for C(PPh 3 ) 2 . The calculated data indicate that very little energy is required for bending the molecules over a wide range.
The structures and bonding situation in divalent carbon(0) parent compounds CL 2 where L = PH 3 , PMe 3 , PPh 3 , CO, C(NHC) 2 , C(NHC Me ) 2 , C(NMe 2 ) 2 and the first and second proton affinities and bond strengths of complexes of CL 2 with main group Lewis acids BH 3 , CO 2 and transition metal species W(CO) 5 and Ni(CO) n (n = 2, 3) have been investigated in a series of theoretical studies by our group. 14,31,32 The results show that carbones possess characteristic properties as double Lewis base which distinguishes them from carbenes. This was recognized in a comment article by Bertrand entitled ''Rethinking carbon'' where the author expressed his belief that the new concept may lead to ''new chemistry and applications for carbon, the basic element for all known life.'' 33 Very recently, another set of carbones has been investigated with quantum chemical methods which show that there are not only new examples of the class of compounds that may become synthesized, but that molecules which have been isolated in the past were not recognized as  carbones. Fig. 6 shows the calculated geometries of compounds 1-10 which have been studied. Compound 1 is the saturated homologue of the unsaturated carbodicarbene C(NHC Me ) 2 which is discussed above while 2 is the benzoannelated carbodicarbene that was synthesized by Bertrand et al. 26 Compounds 3 and 4 may be considered as ''bent allenes'' or alternatively as cyclic carbones where the dicoordinated C(0) atom binds to two diaminocarbene ligands (3a and 3b) or to two aminooxocarbene ligands (4a and 4b). The molecules have recently become synthesized. 34 Because amino groups are better donors than oxo groups it can be expected that the carbone character of 3a and 3b is stronger than that of 4a and 4b. Compounds 5-10 exhibit various combinations of CL 1 L 2 where L 1 , L 2 are CO, N 2 , NHC or phosphane. Substituted homologues of compound 9 have been synthesized more than 20 years ago but they were introduced as phosphacumulenes. 35 Fig. 7 shows the frontier orbitals HOMO and HOMOÀ1 of 1-10. It becomes obvious that the two highest lying MOs of all molecules appear like sand p-type lone-pair orbitals which suggest that the compounds may have chemical properties of carbones. Table 3 gives the calculated first and second PAs and the bond dissociation energy of complexes of 1-10 with one and with two BH 3 ligands. The second PA of all compounds is rather high except for complexes CL 1 L 2 where L 1 is N 2 or CO. However, all molecules 1-10 bind two Lewis acids BH 3 in adducts, whichexcept for 4a and 4b -may be stable enough to become isolated in condensed phase. We are convinced that carbone chemistry is a very fruitful area of chemical research that waits to be explored.
The nature of the donor-acceptor interaction in carbones L-C'L can be analyzed in great detail with the EDA (Energy Decomposition Analysis) method that was developed independently by Morokuma 36 and by Ziegler and Rauk. 37 The EDA analyzes the instantaneous interactions in a chemical bond A-B via a breakdown of the total interaction energy DE int between the frozen fragments A and B in the electronic reference state in three major terms: (a) the electrostatic interactions DE elstat between the frozen electronic charges and nuclei of the fragments; (b) the Pauli repulsion (exchange repulsion) DE Pauli between electrons having the same spin; (c) the attractive orbital interactions DE orb which arise from the mixing of the occupied and vacant orbitals between and within the fragments.
The orbital term DE orb can be further partitioned into contributions from orbitals which belong to different irreducible representations of the point group. The combination of the EDA with the NOCV (Natural Orbitals for Chemical Valence) 38 charge partitioning method makes it possible to separate DE orb into pairwise contributions of the orbitals of the interacting fragments. 39 The energy difference between the frozen fragments A and B in the electronic reference state and their equilibrium structures in the ground state gives the preparation energy DE prep . The sign converted sum of DE int + DE prep gives the bond dissociation energy D e . Further details  and pertinent examples for EDA and EDA-NOCV calculations are available from the literature. 14,40 The EDA and EDA-NOCV methods can also be used to analyze the interactions between two fragments such as the carbon atom in the 1 D electronic reference state and two ligands L in carbones CL 2 . The EDA-NOCV results for the carbodiphosphorane C(PPh 3 ) 2 and the carbodicarbene C(NHC Me ) 2 are shown in Table 4.
The upper part of the table shows schematically the orbital interactions between the ligands and the carbon atom which are expected to be the most important contributions to DE orb . The in-phase (+,+) combination of the s donor orbitals donate into the vacant p x (s) AO of C while the (+,À) out-of-phase combination donates electronic charge into the p y (p J ) orbital of carbon. Some p backdonation L'C-L from the occupied p z (p > ) AO of carbon into vacant ligand orbitals may also be found. The EDA-NOCV data in Table 4 provide a quantitative estimate of the different types of orbitals interactions as well as the other energy terms which are relevant for the carbon-ligand bonding.
The calculations suggest that C-NHC Me bonds in the carbodicarbene C(NHC Me ) 2 are significantly stronger than the C-PPh 3 bonds in C(PPh 3 ) 2 . This holds for both, the intrinsic interaction energies DE int as well as for the bond dissociation energies D e ( Table 4). Inspection of the different energy terms indicate that the nature of the carbon-ligand bonding in the two complexes is very similar. Both L-C'L donor-acceptor bonds have B70% covalent character. The breakdown of the orbital term into the pairwise interactions shows that the major contribution comes from the in-phase (+,+) s donation which provides B60% to DE orb while the out-of-phase (+,À) donation provides B30% (L = NHC Me ) and B24% (L = PPh 3 ) to the attractive orbital interactions. The p > backdonation L'C-L is only a minor component in both complexes while the remaining orbital interactions are negligible. The EDA-NOCV results in Table 4 are a striking example for the strength of modern methods of bonding analysis to provide quantitative insight into the nature of chemical bonding which is based on accurate quantum chemical methods.

Divalent E(0) compounds (E = Si-Pb)
Is divalent E(0) chemistry of the group 14 elements restricted to E = C or is it also found for the heavier elements E = Si-Pb? Are there compounds EL 2 for the latter tetrele 41 atoms which can be described as donor-acceptor complexes L-E'L? Recent theoretical studies strongly suggest that divalent E(0) compounds EL 2 are stable species which have already become synthesized. Like carbodiphosphoranes which were not recognized as divalent C(0) compounds, a similar situation exists for the heavier group 14 homologues. 42 Scheme 2a shows three recently synthesized compounds which were introduced by Kira et al. as the first examples of heavier group 14 homologues of allenes that are stable in a condensed phase. 43 The authors named the molecules trisilaallene, trigermaallene and 1,3-digermasilallene although the equilibrium geometries of the compounds are strongly bent with bond angles (cyc)E-E-E(cyc) between 122.61 (E = Ge) and 136.51 (E = Si). The bending angles are similar to the P-C-P angle in C(PPh 3 ) 2 of 131.71 and to the C-C-C angle of 131.81 which was calculated for C(NHC Me ) 2 and the experimental value of 134.81 for C(NHC Bz ) 2 . Scheme 2a sketches the bonding situation of trisilaallene, trigermaallene and 1,3-digermasilallene as they were suggested by Kira et al. 43 The similar bending angle implies that the bonding of the (cyc)E-E-E(cyc) moiety might be described Table 3 First and second proton affinities PA and bond dissociation energies D e of complexes (L 1 L 2 )C-BH 3 and (L 1 L 2 )C-(BH 3 ) 2 at the MP2/ TZVPP//BP86/SVP level of theory. All energies are given in kcal mol À1 32 a The geometries of 1-10 are shown in Fig. 6. Table 4 Energy decomposition analysis at BP86/TZ2P with the EDA-NOCV method of the carbon-ligand interactions in carbodiphosphorane C(PPh 3 ) 2 and carbodicarbene C(NHC Me ) 2 . All values in kcal mol À1 where E = Si, Ge is not a minimum on the potential energy surface (PES). Geometry optimization of the D 2d form A of E(EH 2 ) 2 without symmetry constraints gives a strongly bent equilibrium structure B for H 2 E-E-EH 2 with bending angles of B701 where the planes of the EH 2 moieties are strongly rotated from the E 3 plane (Fig. 8). The latter energy minima are B20 kcal mol À1 (E = Si) and B25 kcal mol À1 (E = Ge) 45c lower lying than the D 2d form which is a second-order saddle point with a degenerate imaginary frequency. Another energy minimum of E(EH 2 ) 2 is the cyclic form C (Fig. 8) which is separated by only a small energy barrier from structure B which has a similar energy as C. Apeloig and co-workers pointed out that B and C are bond-stretch isomers on the Si 3 H 4 PES. 44 It becomes obvious that the equilibrium geometry B bears little resemblance to a classical allene. A similar situation is found for acetylene and its heavier group 14 homologues E 2 H 2 (E = Si-Pb) where the linear form HEREH is a second-order saddle point. 46, 47 The rather unusual energy minimum structures of the latter species and the difference to the carbon systems have been explained with the doublet/quartet gap of the EH fragments which yield the E 2 H 2 structures. 47 Petrov and Veszprémi recognized the connection between the strongly bent equilibrium structure of the ''trisilaallene'' R 2 Si-Si-SiR 2 and the carbones CL 2 and they calculated various systems SiL 2 where L = SiR 2 , NH 3 , PH 3 . 45c The latter two compounds Si(EH 3 ) 2 which are related to carbodiphosphoranes have strongly bent geometries where the bending angle is 89.11 (E = N) and 88.21 (E = P). The NBO 48 analysis predicts two lonepairs at the silicon atom which let the authors suggest that the bonding situation should be written in analogy to the carbones as H 3 E-Si'EH 3 . The authors also calculated the structures of compounds R 2 Si-Si-SiR 2 with acyclic and cyclic moieties SiR 2 which are model substituents for the real substituent of the experimental ''trisilaallene'' of Kira et al. Table 5 shows the most important results. It becomes obvious that the bending angle of 136.51 which was measured for the isolated compound is due to steric repulsion between the bulky substituents. The agreement between the latter value and the bending angles of C(PPh 3 ) 2 (131.71) and C(NHC Bz ) 2 (134.81) is fortuitous.
Another experimental finding which is relevant for the present work concerns the synthesis of the first ''tristannaallene'' [(t-but) 3 Si] 2 SnQSnQSn[(t-but) 3 Si] 2 which was already reported by Wiberg et al. in 1999 prior to the synthesis of the trisilaallene and trigermaallene. 49 The X-ray structure analysis shows that the compound has a Sn-Sn-Sn bending angle of 156.01. The authors noted that the 119 Sn NMR signal of the central dicoordinated tin atom appears at a very low field which is more typical for a stannylene SnR 2 . On the basis of the experimental geometry and the NMR signal it was proposed that the bonding situation in the compounds is best described by the resonance formulae shown in Fig. 9.
The bonding situation in the carbodicarbene homologues 11E and in the ''bent allenes'' 12E with E = C-Pb has been investigated in recent theoretical studies by Takagi et al. who reported also about theoretical results of the related systems 13E-15E (Scheme 3). 50 The results strongly suggest that the    0) compounds. Fig. 10 shows the optimized geometries of 11E-15E (E = C-Sn). The carbon compounds 11C-15C possess much wider bending angles at the dicoordinated central atom than the heavier homologues. The difference is particularly striking between 12C, which shows the typical feature of an allene, i.e. a linear CQCQC moiety and an orthogonal alignment of the cyclopentyl ligands (dihedral angle of 901/2701), and the heavier homologues 12E (E = Si-Sn) which have very acute bending angles E-E-E between 76.41 (E = Sn) and 79.41 (E = Ge). The cyclic ligands in the latter compounds are slightly twisted with respect to each other with dihedral angles between 31.01 (E = Ge, Sn) and 34.01 (E = Si). Inspection of the highest occupied orbitals of 11E-15E showed that all compounds possess highlying MOs which can be identified as sand p-type lone-pair orbitals. 50 The bending angles of the experimentally observed ''trisilaallene'' and ''trigermaallene'' which carry bulky trimethylsilyl groups at a and a 0 position of the cyclic ligands are much wider than in 12E. Geometry optimizations of the compounds 12E 0 (E = Si, Ge, Sn) which have trimethylsilyl groups at the a and a 0 position show (Fig. 11) that the bending angles of 12E 0 are much larger than those of 12E. The calculated values for 12Si 0 (135.71) and 12Ge 0 (123.81) are in very good agreement with the experimental values for the ''trisilaallene'' (136.51) and However, the much more acute bonding angles in the parent systems 12E (E = Si-Sn) which are o801 raise serious doubt whether these compounds should be considered as allenes.
Moreover the calculations show that the molecules 11E-14E are rather flexible with respect to the bending angles at the central dicoordinated atom and the rotation of the cyclic ligands about the central E 1 -E 2 -E 3 plane. Fig. 11 shows also the calculated geometries of the singly and doubly protonated compounds 12E 0 (H + ) and 12E 0 (H + ) 2 (E = Si-Sn) and the theoretically predicted first and second proton affinities. It becomes obvious that the ''heteroallenes'' 12E 0 possess not only very large first PAs but also the second PAs are very big. The calculated values for the second PA (168.1-187.2 kcal mol À1 ) are similar to the second PA of C(PPh 3 ) 2 (185.6 kcal mol À1 ) and for C(NHC Me ) 2 (168.4 kcal mol À1 ). The geometries of the singly protonated compounds 12E 0 (H + ) exhibit a particular feature. The E-H + bond is not coplanar to the E 1 -E 2 -E 3 plane which means that the central tetrele atom is protonated through the p-type orbital. The same situation is found in the protonated compounds of the parent systems 11E(H + )-15E(H + ) (E = Si-Sn). 50a,b This is strikingly different to the carbone compounds where carbon is always protonated at the s lone pair yielding a C-H + bond in 11C(H + ), 12C(H + ) and 15C(H + ) which is coplanar to the central E-C-E plane.
Takagi et al. reported also about complexes of 11E-15E with one and with two Lewis acids BH 3 as ligands. 50b They also calculated transition metal complexes (CO) 5 W-D and (CO) 3 Ni-D with the ligands D = 11E-15E. Table 6 summarizes the theoretically predicted bond dissociation energies (BDEs) and proton affinities of the compounds. The calculated data suggest that the heavy-atom homologues 11E-15E (E = Si-Sn) possess not only large values for the first and second PAs. They also yield strongly bonded complexes with one but also with two BH 3 Lewis acids. Surprisingly, the BDE of the second BH 3 is in several complexes even higher than the BDE of the first BH 3 ! The binding of the first BH 3 ligand in 11E(BH 3 )-15E(BH 3 ) prepares the central atom E quite well for the interaction with the second borane ligand. It should be noted that the BH 3 ligands in some complexes are Z 3 coordinated to the E 3 moiety while in other complexes they bind Z 1 to the central atom E. A detailed discussion of the geometries of the complexes is given in the paper by Takagi et al. 50b Finally, we note that the compounds 11E-15E are strongly bonded ligands D in complexes (CO) 5 W-D and (CO) 3 Ni-D where their BDE is comparably strong as that of CO.
What is the reason for the drastically different equilibrium geometries and chemical properties of 11E-15E which show typical features of an allene when E = C while they exhibit divalent E(0) properties when E = Si-Pb? A straightforward answer to this question can be given when the relative energies of the interacting fragments L and E in the species EL 2 in the lowest lying singlet and triplet states of the carbon compounds are compared with the heavier homologues. The explanation is based on the model which was introduced earlier by Trinquier and Malrieu 51a,b and by Carter and Goddard 51c,d who discussed the unusual structures of the heavy-atom homologues of ethylene E 2 H 4 (E = Si-Pb) using the electronic singlet and triplet states of EH 2 . Fig. 12 shows qualitatively the orbital interactions in divalent E(0) compounds (top) and in allenes (bottom). The donor-acceptor bonds in the former species come from the interactions between singlet fragments ER 2 and a group 14  atom E in the singlet ( 1 D) state. The double bonds in allenes come from the electron-sharing interactions between triplet fragments ER 2 and a group 14 atom E in the triplet ( 3 P) state. Table 7 gives the calculated energy differences for atoms E, for NHC and cyclopentylidene (cycC) and their heavier homologues (E = Si-Pb). Table 7 shows that the singlet fragments in C(NHC) 2 are energetically favored over the triplet fragments by (2 Â 84.1 kcal mol À1 ) À 29.1 kcal mol À1 = 139.1 kcal mol À1 . This is in contrast to C(cycC) 2 where the triplet fragments are favored over the singlet fragments by 29.1 kcal mol À1 À (2 Â 7.4 kcal mol À1 ) = 14.3 kcal mol À1 . The situation for the heavier group 14 homologues is different because the tripletsinglet excitation energy of atom E = Si-Pb is smaller than for carbon atom and the singlettriplet excitation energy of cycE is clearly higher than that of cycC. For example, the singlet fragments in Si(NHSi) 2 are favored over the triplet fragments by (2 Â 60.8 kcal mol À1 ) À 18.0 kcal mol À1 = 103.6 kcal mol À1 and they are favored in Si(cycSi) 2 by (2 Â 27.1 kcal mol À1 ) À 18.0 kcal mol À1 = 36.2 kcal mol À1 . A similar situation is found for the heavier homologues E = Ge-Pb. The bonding situation of a genuine allene in E(cycE) 2 would only be possible if stronger binding interactions between the triplet fragments than the binding interactions between the singlet fragments compensate for the differences in the excitation energies. It has been shown, however, that E-E (E = Si-Pb) donoracceptor interactions between singlet fragments may have the same strength as E-E electron-sharing interactions between openshell fragments. 47 The differences between the bonding situation in the heavier tetrele compounds and the carbon molecules can thus be attributed to the nature and energy levels of the electronic ground and excited states of the bonding fragments and to the strength of the interactions in the different electronic states.
The experimental work about ''trisilaallene'' and ''trigermaallene'' 43 and the theoretical studies of the parent systems Table 7 Energy differences (in kcal mol À1 ) between different spin multiplicities at BP86/TZVPP  11E-15E 50 gave rise to the question about the heavy group 14 homologues of carbodiphosphorane E(PPh 3 ) 2 (E = Si-Pb). The structures, bonding situation and double-donor properties were investigated in a theoretical study by Takagi,Tonner and Frenking. 52 The experimentally yet unknown compounds were shown to be genuine examples of tetrylones EL 2 which are predicted to have large first and second proton affinities as well as large bond dissociation energies of one and two Lewis acids BH 3 and AuCl. Fig. 13 shows the calculated equilibrium geometries of E(PPh 3 ) 2 and the singly and doubly protonated species E(PPh 3 ) 2 -(H + ) and E(PPh 3 ) 2 -(H + ) 2 . The calculations predict that the bending angle P-E-P in all systems becomes more acute for the heavier group-14 complexes where E = Si-Pb than for the parent carbone. The shape of the highest lying orbitals HOMO and HOMO À 1 of the neutral parent systems E(PPh 3 ) 2 exhibits the typical features of p lone-pair (HOMO) and s lone-pair (HOMO À 1) (Fig. 14). Table 8 gives the calculated proton affinities of E(PPh 3 ) 2 in comparison with the PA values for the homologues E(NHC) 2 (14E) and the divalent E(II) compounds NHE. It becomes obvious that the first PAs but particularly the second PAs of E(NHC) 2 and E(PPh 3 ) 2 are much higher than those of the NHE compounds. This clearly identifies E(PPh 3 ) 2 and E(NHC) 2 as divalent E(0) compounds while the NHE molecules are divalent E(II) compounds.
Further relevant information about the tetrele phosphoranes E(PPh 3 ) 2 are given in Table 9. The calculated bond dissociation energies for breaking the E-PPh 3 bonds become significantly smaller for the heavier systems C c Si 4 Ge 4 Sn 4 Pb but protonation at atom E strongly enhances the E-PPh 3 bonds. This is a hint for possible synthesis of the neutral compounds which might becomes isolated via deprotonation of the cations E(PPh 3 ) 2 -(H + ) and E(PPh 3 ) 2 -(H + ) 2 . The calculated data also suggest that the tetrylones E(PPh 3 ) 2 are very strong donors toward one and two Lewis acids BH 3 and AuCl. Unlike the proton affinities where the carbon system has larger first and second PAs than the heavier homologues, the bond strengths of E(PPh 3 ) 2 toward one and two BH 3 53 There is a wealth of experimental and theoretical results which support the identification of a new class of tetrele compounds which are stable in a condensed phase where the group-14 atom has a divalent E(0) valence state. The bonding situation in the tetrylones EL 2 should be described in terms of donor-acceptor interaction L-E'L where the tetrele atom E = C-Pb retains its valence electrons as two lone pairs. The suggested nomenclature for the tetrylones EL 2 is shown in Table 10. Very recently, the first heavier homologues of carbodicarbenes C(NHC) 2 could become synthesized and structurally characterized by X-ray analysis. Roesky and co-workers reported  about the isolation of the silylone and germylones E(CAAC) 2 (E = Si, Ge) where the ligand CAAC (Cyclic Alkyl Amino Carbene) has only one nitrogen atom in the N-heterocyclic carbene moiety (Fig. 15a). 54 The silylone and germylone complexes E(NHC-NHC) where the NHC fragments are bonded to each other in a bidentate ligand have been synthesized by Driess et al. (Fig. 15b) 60,61 should be considered as electronsharing interactions between triplet (for carbenes) and quartet (for carbynes) fragments (Fig. 16). 63 The final member in the series of metal-carbon bonds has a naked carbon atom as ligand [TM]-C. Until recently, no such compounds were experimentally known. In 1997, Cummins and co-workers reported a structurally characterized 14 valence electron (VE) anion [(NRAr) 3 Mo(C)] À (R = C(CD 3 ) 2 CH 3 , Ar = C 6 H 3 Me 2 -3,5). 64 It was the first representative example of transition metal complex bearing a naked carbon atom as ligand. 65 The compound is isoelectronic with the nitrido complex [(NRAr) 3 Mo(N)]. 66 The bonding situation in the anion is very similar to the neutral nitrogen homologues which indicates that the anion [(NRAr) 3 Mo(C)] À should be considered as metal carbide that possesses a TMRC À electron-sharing triple bond. It may also be viewed as the anion of Schrock-type carbynes [TM]RCR where the positively charged substituent R + has dissociated. The bonding model for Schrock carbynes (Fig. 16d) may therefore be used for the metal-carbon bonding in the carbide anion.
Neutral complexes with bare carbon atoms were first studied with theoretical methods by Chen et al. in 2000. 67 The authors showed that the carbon atom in the 1 D excited state which has the valence configuration (2s) 2 (2p z(s) ) 2 (2p x(p) ) 0 (2p y(p) ) 0 is perfectly suited for donor-acceptor interactions. The [(CO) 4 Fe]-C bond can thus be Table 9 Calculated energies at BP86/TZVPP of tetrelediphosphoranes E(PPh 3 ) 2 (E = C-Pb). Bond dissociation energies D e for the E-(PPh 3 ) 2 bonds. Bond dissociation energies D e of the complexes E(PPh 3 ) 2 with one and two Lewis acids BH 3     described with the DCD model where the carbon ligand is bonded to the metal with a triple bond retaining a s lone-pair orbital. A charge decomposition analysis showed that the singly coordinated carbon atom is a strong s donor but also a strong p acceptor. The bond dissociation energy for the [(CO) 4 Fe]-C bond was calculated at CCSD(T) to be 94.5 kcal mol À1 which suggests that the bond is very strong. 67 The authors concluded that the molecule might be too reactive to become isolated in a condensed phase. Because of the s lone-pair orbital at the terminal carbon atom the compound should be a strong Lewis base. Calculations of the complex [(CO) 4 FeC-BCl 3 ] showed that it is a minimum on the PES with a BDE of 25.6 kcal mol À1 (B3LYP). 67 The latter species might be stable enough to become isolated in a condensed phase. The first synthesis of a neutral transition metal compound with a terminal carbon ligand which could become fully characterized by X-ray structure analysis was reported in 2002 by Heppert and co-workers. 2 68 In 2005 the same group reported about more versatile routes to the air-and moisture-stable [(PCy 3 ) 2 Cl 2 Ru(C)], opening the way for broader research on the chemistry of complexes with terminal C. 69 To the best of our knowledge, no further transition metal carbon complexes could become isolated. There are reports in the literature about the synthesis of other carbon complexes but there is no X-ray structure available. 70 The chemical reactivity of the carbon complexes was experimentally studied which sheds light on the bonding situation. Grubbs and his group reported that the complex (A) can act as a s-donor towards Mo(CO) 5 and Pd(SMe 2 )Cl 2 via the terminal carbon atom. 71 75 The carbon ligand is always in the equatorial position which concurs with the experimental observations for A-C. The calculated interatomic distances and angles of 16RuC, 16RuCO and 17RuCO are in good agreement with the experimental values of the real compounds which carry more bulky substituents. 2,76a,b The most important difference between the 16VE complexes 16TMC and the 18VE species 17TMC (TM = Ru, Fe) is the TM-C bond length. The 18VE complexes have a significantly longer metal-carbon bond than the 16VE species.
The TM-C bond in the former species is also clearly weaker than in the latter compounds. Table 11 shows that the calculated   BDEs of 16RuC and 16FeC are significantly higher than for 17RuC and 17FeC. It is interesting to note that, for the 18VE complexes 17TMC, the Fe-C bond is stronger than the Ru-C bond while for the 16VE compounds 16TM the Fe-C bond is weaker than the Ru-C bond. All metal-carbon bonds are very strong. The calculations predict that the BDE in the 16VE and 18VE complexes is 4100 kcal mol À1 . It is interesting to compare the calculated geometries and bond energies of the carbon complexes 16TMC and 17TMC with the results for the corresponding carbonyl complexes 16TMCO and 17TMCO. Fig. 17 gives for the latter species experimental data of the bond lengths and angles which show that the calculated values are quite accurate. The metal-CO bonds in 16TMCO and 17TMCO are significantly longer and weaker than the metal-C bonds in 16TMC and 17TMC. Table 11 shows that the calculated BDEs of the CO ligand in the former complexes are between D e = 38.2 kcal mol À1 (16FeCO) to 55.3 kcal mol À1 (17RuCO) which is much less than the BDEs of the metal-C bonds. Note that the trend of the calculated values for the dissociation energies of the carbonyl complexes 16FeCO o 16RuCO and 17FeCO 4 17RuCO is the same as for the carbon complexes 16TMC and 17TMC. The 16VE iron complexes have weaker bonds than the 16VE ruthenium complexes while in the 18VE complexes iron binds stronger than ruthenium. A comparison of the metal-ligand bond lengths in the carbonyl complexes 16TMCO and 17TMCO with the carbon complexes 16TMC and 17TMC indicates that the substitution of the equatorial CO ligand in the former compounds by a carbon ligand elongates the axial but particularly the other equatorial metal-ligand bonds. Fig. 18 shows the optimized geometries of the carbon complexes [(CO) 4 TM(C)] (18RuC and 18FeC) and the pentacarbonyls [TM(CO) 5 ] (18RuCO and 18FeCO). 75 As noted before, the carbon ligand in 18RuC and 18FeC is in the axial position. The equatorial forms of the latter compounds are not minima on the PES. The TM-C bonds in 18RuC and 18FeC are much shorter and possess a significantly higher BDE (Table 11)  There are seven valence orbitals in 16RuC which contribute to the [Ru]-C bond, two s orbitals and five p orbitals. The HOMO À 3 (15a 1 ) and HOMO À 6 (14a 1 ) orbitals which come from the bonding and antibonding combination of the d z 2 ruthenium orbital with the chlorine p(s) lone-pair orbitals contribute to the Ru-C s bond. Two orbitals, i.e. HOMO À 2 (10b 1 ) and HOMO À 9 (8b 1 ) MOs, describe the Ru-C p bonding in the Cl-Ru-Cl plane (p J ). The HOMO À 8 (9b 2 ) orbital is a Ru-C p orbital in the P-Ru-P plane (p > ). The remaining p orbitals HOMO À 4 (9b 1 ) and HOMO À 5 (10b 2 ) have only small contributions at the carbon ligand atom. Fig. 19 shows also the three lowest lying vacant orbitals of 16RuC. Note that the LUMO (16a 1 ), which has a small coefficient at C, is antibonding with respect to the Ru-C bond. This is important for understanding the changes in the bonding situation of the 18VE complexes where this orbital is occupied and becomes the HOMO. The p orbitals LUMO + 1 (12b 2 ) and LUMO + 2 (11b 1 ) and the occupied s orbital HOMO À 3 (15a 1 ) are perfectly suited to serve as ligand orbitals for binding of 16RuC to another transition metal fragment. As noted above, the complex [16RuC-Mo(CO) 5 ] where 16RuC binds with Mo(CO) 5 through the carbon atom has been synthesized. 71 It is interesting to compare the frontier orbitals of the 16VE carbon complex [(PMe 3 ) 2 Cl 2 Ru(C)] (16RuC) with the most relevant MOs of the 18VE species [(PMe 3 ) 2 (CO) 2 Ru(C)] (17RuC) and with the corresponding CO 16VE complex [(PMe 3 ) 2 Cl 2 Ru(CO)] (16RuCO) as well as the 18VE complex [(PMe 3 ) 2 (CO) 2 Ru(CO)] (17RuCO). Fig. 20 shows that the HOMO of the 18VE species 17RuC and 17RuCO closely resembles the LUMO of the respective 16VE complexes 16RuCO and 16RuC (Fig. 19). The occupation of the Ru-C and Ru-CO antibonding orbital explains why the bonds in the 18VE compounds are clearly longer than in the 16VE homologues. Table 12 summarizes the results of a charge-partitioning analysis of the carbon and CO complexes 16TMC-18TMC and 16TMCO-18TMCO which shed further light on the bonding situation. The calculated values for P(TM-L) suggest that the TM-C bonds have a clearly higher bond order than the TM-CO Fig. 20 Plot of some relevant molecular orbitals of 17RuC, 16RuCO and 17RuCO. The calculated eigenvalues (BP86/TZ2P) of the orbitals are given in parentheses (in eV). 75 The figure has been adapted from ref. 75. bonds. Not surprisingly, the 16VE complexes have larger bond orders for the TM-L bonds than the 18VE species. The carbon and CO ligands carry a small positive charge in the 16VE complexes but they are negatively charged in the 18VE species. This indicates that the donor/acceptor ratio of the ligands L = C, CO in the 16VE complexes changes towards more [TM]'L net donation. The latter donation does not reside at the metal atoms. Table 12 shows that the metal atoms in the 16VE complexes are less negatively charged than in the 18VE compounds. The stronger [TM]'L net donation in the former species is conveyed to the CO ligands. We want to point out that the partial charges of the carbon and CO ligands in the 16 and 18VE compounds are not very different from each other. The question remains about the correct description of the [TM]-C interactions. A very detailed answer to this question was given by the EDA results of KPF 75 which shall now be summarized.
What is the best description for the metal-ligand orbital interactions in the carbon complexes [(PR 3 ) 2 Cl 2 Ru(C)], which have been synthesized by Heppert et al.? Fig. 21 shows five different scenarios which are possible for the [TM]-C interactions. Model A sketches the situation which was already mentioned above for (CO) 2 Fe-C. Here, the carbon atom in the 1 D excited state serves as two-electron s donor while the empty p(p) AOs serve as p acceptors. This is the classical DCD bonding model which is valid for the bonding for metal-CO and Fischertype metal-carbyne bonds. Model E describes the bonding in terms of three electron-sharing interactions which yield one s-bond and two p-bonds. The latter description applies to Schrock-type metal carbynes which are better termed metal alkylidynes. Note that the two p bonds in the donor-acceptor model A and the electron-sharing model E are not the same. This is because the ligands in the two planes are different. The plane which contains the chlorine ligands is designated as p J while the plane containing the phosphane ligands is designated as p > (see Fig. 21). The orbital models B, C and D describe intermediate cases where one bonding component comes from donor-acceptor interactions while the other two come from electron-sharing bonding.
The EDA results which are given in Table 13 make it possible to quantitatively estimate the strength of the different orbital interactions which are shown in Fig. 21. The EDA data refer to the instantaneous interactions between the carbon atom and the metal fragment (PMe 3 ) 2 Cl 2 Ru which are calculated with the frozen geometry in the complex 16RuC. Five EDA calculations  (Table 13). were carried out where the electron configurations of the fragments are chosen in accordance with models A-E. 75 Since 16RuC has C 2v symmetry there are orbitals with a 1 (s), a 2 (d), b 1 (p J ) and b 2 (p > ) symmetry which directly relate the calculated values for the orbital terms with the respective orbital interactions that are shown in Fig. 21. But which of the models A-E gives the best description for the orbital interactions in 16RuC?
The answer is given by the absolute values of the total orbital interaction term DE orb . Those fragment pairs whose orbital relaxation in the final step of the EDA gives the smallest DE orb value provide the best description of the interacting species because their electronic structure is closest to the bonding situation in the molecule after bond formation. Table 13 shows that the best model for the (PMe 3 ) 2 Cl 2 Ru-C bond formation is given by the fragment pair B. According to this model, the metal-carbon bond in 16RuC is a mixture of electronsharing interactions and donor-acceptor bonding. This makes sense because 16RuC has electron-sharing Ru-Cl bonds as well as donor-acceptor Ru-PR 3 bonds. Model B suggests that the Ru-C bond has about one half electrostatic character and one half covalent character. This comes from the EDA values for DE elstat and DE orb which contribute 48.4% and 51.6% to the total attractive interactions. The orbital interactions DE orb come mainly from the electron-sharing s bond (45.9%). The electronsharing p J bond contributes 24.4% which is somewhat weaker than the donor-acceptor p > bond which contributes 29.7% to DE orb . The occurrence of two electron-sharing interactions which comprise one s and one p bond in the bonding model B (Fig. 21) suggest 16RuC and thus, the isolated carbon complexes 2,68,69 are actually Ru(IV) and Os(IV) compounds.
The EDA calculations of the complexes 17RuC-18RuCO revealed that the Ru-C and Ru-CO bonds are better described by model A than model B, because the absolute values for DE orb were slightly lower when the former pair of interacting fragments was employed. 75 It is therefore appropriate to compare the bonding interactions between the [Ru]-C and [Ru]-CO bonds using the EDA results for model A. Since the carbon and CO ligands in 16RuC-17RuCO are in the equatorial position, KPF optimized (CO) 4 RuC (18RuC) where C is equatorial (18RuC-eq) and analyzed the equatorial Ru-C bond with the EDA method. Structure 18RuC-eq is a transition state but it is the appropriate species for comparison with the equatorial Ru-C and Ru-CO bonds of the other species. Table 14 shows the EDA results using model A for the equatorial Ru-C and Ru-CO bonds of 16RuC-18RuCO. Note that the Table 13 Energy decomposition analysis at BP86/TZ2P of the ruthenium-carbon bond in the complex 16RuC using different fragment pairs A-E as shown in Fig. 21 .0 (45.9%) À144.9 (43.4%) À210.5 (57.5%) À146.6 (43.2%) À105.1 (31.5%) À75.4 (24.4%) À108.6 (32.5%) À75.2 (20.5%) À90.5 (26.7%) The value in parentheses gives the percentage contribution to the total orbital interactions. Table 14 Energy decomposition analysis at BP86/TZ2P of the equatorial Ru-C and Ru-CO bonds in the complexes 16RuC-18RuCO using model A (Fig. 21). All energies in kcal mol À1 75 equatorial isomer of (CO) 4 ReC (18RuC-eq) which is 5.2 kcal mol À1 higher in energy than axial 16RuC-ax is not a minimum on the potential energy surface. 75 Since the comparison is made for equatorial ligands, 18RuC-eq must be used as the appropriate isomer. The comparison of the 16VE complex pair 16RuC-16RuCO and the 18VE pairs 17RuC-17RuCO as well as 18RuC-18RuCO suggests that the interaction energies of the Ru-C bonds in the carbon complexes 16RuC, 17RuC and 18RuC are much stronger than those of the Ru-CO bonds in 16RuCO, 17RuCO and 18RuCO. This comes from a rather uniform increase of all attractive components of DE int : The carbon ligand is a much stronger s donor as well as a better p acceptor as CO. The s-donor/p-acceptor ratio is shifted toward greater s-donor strength and less p acceptor strength of C compared with CO but the overall nature of the Ru-C and Ru-CO bonds does not change dramatically. The EDA results shed light on the question why the 18VE complex 17RuC could not become isolated while the 16VE complex 16RuC is stable in the condensed phase. A comparison of the EDA results using the same model A for both complexes shows (Tables 10 and 11) that the [Ru]-C binding interactions in 17RuC are much weaker than in 16RuC mainly because the a 1 (s) contribution which comes from the [Ru]'C donation in the 18VE species is significantly smaller than in the 16VE compound. The much weaker Ru-C s bonding in 17RuC can be explained with the occupation of the s antibonding LUMO (16a 1 ) of 16RuC (Fig. 19) which becomes the HOMO in 17RuC (Fig. 20).  5 38.9 0.20 (PMe 3 ) 2 Cl 2 RuC-W(CO) 5 45.3 0.17 (PMe 3 ) 2 Cl 2 FeC-W(CO) 5 45.1 0.15 (PMe 3 ) 2 Cl 2 OsC-W(CO) 5 47.1 0.20 (PMe 3 ) 2 F 2 RuC-W(CO) 5 39.7 0.21 (PMe 3 ) 2 Br 2 RuC-W(CO) 5 44.8 0.16 (PMe 3 ) 2 I 2 RuC-W(CO) 5 44.3 0.15 (Por)FeC-W(CO) 5 52.6 0.09 (Por)RuC-W(CO) 5 51.6 0.14 (Por)OsC-W(CO) 5 53.8 0.17 (PMe 3 ) 2 Cl 2 RuC-BH 3 47.0 0.43 (PMe 3 ) 2 Cl 2 RuC-BCl 3 13.5 0.51 OC-Cr(CO) 5 43.2 0.28 OC-Mo(CO) 5 39.6 0.18 OC-W(CO) 5 45.7 0.13 OC-BH 3 42.6 0.39 OC-BCl 3 À6.8 0.38

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The metal-carbon bonding situation in [(PR 3 ) 2 Cl 2 Ru(C)] is very similar to the bonding in CO. This finding was pointed out by KPF 75 and also by Johnson and co-workers 74 in their theoretical studies of carbon complexes. The isolobal 77 relationship between carbon complexes and carbon monoxide was the topic of a very detailed theoretical work by Krapp and Frenking (KF). 78 These workers calculated the group-8 carbon complexes [(L) 2 X 2 TM(C)] for various combinations where L = PH 3 , PMe 3 , PPh 3 , PCy 3 , NHC and X = F, Cl, Br, I with the metals TM = Fe, Ru, Os which are related to the complexes that have been isolated so far. 2,68,69 They also investigated the ironporphyrin complexes with carbon ligands [(Por)TM(C)] (TM = Fe, Ru, Os; Por = Porphyrin) for which adducts with the Lewis acid Ru 2 (CO) 9 were reported by Beck and co-workers. 73 KF calculated the carbon complexes [(L) 2 X 2 TM(C)] and [(Por)TM(C)] as well as the adducts with the Lewis acids BH 3 , BCl 3 , PdCl 2 SMe 2 and TM(CO) 5 (TM = Cr, Mo, W). The latter structures were compared with the corresponding carbonyl complexes. In order to test whether the carbon complexes can also serve as bridging ligands like CO, the authors calculated the complex [Fe 2 (CO) 9 ] and the analogues molecule [RuCl 2 (PMe 3 ) 2 (C)-Fe 2 (CO) 8 ] where the carbon compound [RuCl 2 (PMe 3 ) 2 (C)] binds in the Z 2 -coordination mode. The bonding situation in the compounds was investigated with charge-and energy decomposition methods. 78 The most important result will shortly be summarized. Table 15 8 ] is a minimum on the PES which shows that the carbon complex like CO may bind in an Z 2 -fashion to the Fe 2 (CO) 8 . A closer examination of the donor-acceptor bonds in [(PMe 3 ) 2 Cl 2-RuC-LA] and [OC-LA] reveals that the carbon complexes exhibit slightly longer C-LA bonds than CO (Fig. 23).
The strongly isolobal relationship between CO and the carbon complexes [TM]C becomes clearly apparent by comparing the EDA results for transition metal complexes which carry CO and [TM]C as ligands. Table 16 shows the EDA results for  (covalent) interactions DE orb to the total attraction of the metalcarbon ligands are also quite similar to the results for CO. The most significant difference concerns the ratio of s-donation/ p-backdonation. The EDA results suggest that (CO) 5 W-CO p-backdonation is a bit stronger than (CO) 5 W'CO s-donation. The opposite trend is calculated for the metal-carbon complexes where the (CO) 5 W'C[TM] s-donation is clearly stronger than (CO) 5 W-C[TM] p-backdonation. 78

Transition metal-tetrele complexes [TM]-E (E = Si, Ge, Sn)
The first purposeful synthesis of a transition metal carbene complex in 1964 by Fischer 57,58 was soon followed by experimental research with the aim to isolate the heavier group-14 homologues [TM]QER 2 (E = Si-Pb). 79 The first examples of stannylene and plumbylene complexes were reported in 1976 by Lappert and co-workers. 80 One year later, the first transition metal complex with a germylene ligand could become isolated by the same group. 81 The first (unsupported) 82 silylene complex which was structurally characterized by X-ray analysis was reported in 1990 by Tilley. 83 Table 17 shows an overview of the first syntheses of transition metal carbene and carbyne complexes and heavier group-14 homologues. We want to point out that unlike the lighter homologues, until today no X-ray structure for a plumbylene complex has been reported.
A similar time-delayed history exists for the experimental attempts to synthesis the heavy group-14 homologues of transition metal carbyne complexes. 84 Following the first synthesis of a carbyne complex by Fischer in 1973, 59 the next member in the series which could become characterized by X-ray analysis was a germylyne complex which was reported by Power in 1996. 85 The other three members of the group of heavier carbyne homologues for which X-ray structure analyses have been synthesized by Filippou. The first isolation of a stannylene complex in 2003 86 was followed by the first synthesis of a plumbylyne complex in 2004. 87 Very recently, the first X-ray structure analysis of a silylyne complex was reported by Filippou. 88 It is foreseeable that the first synthesis of a carbon complex by Heppert 2 in 2002 also triggers intensive efforts to isolate the heavier group-14 homologues [TM]-E. Until today, all attempts have not been successful. This is not surprising when one looks at the history of carbyne homologues where it took 23 years after the work of Fischer before the first heavier homologue could be isolated (Table 17).
Theoretical studies have been published which could be helpful as a guideline for further experimental work. The geometries and bonding situation of the heavier homologues of the model carbon complex [(PMe 3 ) 2 Cl 2 TM(E)] (16TME) with TM = Fe, Ru, Os and E = Si, Ge, Sn has been the topic of a   89 The most important results will shortly be summarized. Fig. 24 shows the optimized geometries of the 16-electron tetrele complexes 16TME and the calculated BDEs for the (PMe 3 ) 2 Cl 2 TM-E bonds with E = C-Sn. The carbon complexes are shown for comparison with the heavier homologues. It becomes obvious that the heavier tetrele complexes have weaker bonds than the lighter ones but even the stannylene complexes have BDEs which are 450 kcal mol À1 which indicates that the TM-Sn bonds are quite strong. The bond orders drops from 2.2 for the Os-C bond to 1.4 for the Fe-Sn bond which suggests a sizeable multiple-bond character. PF1 calculated also the 18-electron complexes [(PR 3 ) 2 (CO) 2 TM(E)] (17TME) which exhibit interesting differences compared with the 16-electron species 16TME. 89 The optimized geometries and the calculated BDEs for the compounds 17TME are shown in Fig. 25.
A comparison of the theoretically predicted TM-E bond lengths and bond orders of the 18-electron complexes 17TME with the 16-electron species 16TME reveals that the former molecules have always longer bonds and smaller bond orders than the latter species. The two series of complexes exhibit distinctively different trends for the bond dissociation energy of the TM-E bond which are shown in Fig. 26. The BDEs of the 16-electron complexes 16TME increase for the heavier transition metals in the order Fe o Ru o Os while the trend for the ligand atoms E is C c Si 4 Ge 4 Sn. The latter trend is also calculated for the 18-electron complexes 17TME but the transition metals exhibit the order Ru o Os o Fe. This is the well-known V-shaped sequence for the bond strength of the first, second and third row of transition metals. 63b The calculations suggest that iron has the strongest TM-E bond in 17TME while it has the weakest bond in 16TME. This is an important result for experimental studies aiming at the synthesis of 18-electron complexes 17TME.
The nature of the TM-E bond in 16TME and 17TME has been analyzed by PF1 89 with the EDA method in order to investigate the changes in the metal-ligand interactions when the tetrele atom becomes heavier. Table 18 shows the results for the ruthenium complexes. The data for the iron and osmium species which were reported by PF1 are not very different from the ruthenium complexes. EDA calculations using the interacting fragments according to bonding models A-E (Fig. 21) showed that the bonding situation in all 16-electron species 16TME is best described by model B while the TM-E bond in the 18-electron complexes 17TME can be described by the classical DCD model which is given by the fragment pair A. 75 The results in Table 18 indicate that the Ru-E bond in 16RuE and 17RuE is less covalent and has a higher electrostatic character when E = Si, Ge, Sn compared with the carbon complexes. The percentage p-backbonding [Ru]'E of the heavier atoms Si-Sn in the 18-electron complexes 17RuE becomes smaller compared with 17RuC which means that the heavier tetrele atoms Si, Ge, Sn are weaker p-acceptors than C. There is an interesting change in the weight of the two components Db 1 (p J ) and Db 2 (p > ) to the p-backbonding [Ru]'E for 16RuE and 17RuE. Table 18 shows that the contribution of Db 1 (p J ) increases from 16RuE to 17RuE for each atoms E while the strength of Db 2 (p > ) clearly decreases. The Db 1 (p J ) orbital interactions in 16RuE come from the electronsharing p bonds (see Fig. 21, model B) while the Db 1 (p J ) term in 17RuE comes from the donor-acceptor p bonds (see Fig. 21, model A). The TM-C p J interactions in 16RuE compete with the strongly electron withdrawing TM-chlorine bonds while the TM-C p J interactions in 17RuE compete with TM-CO p backdonation. As noted above, the carbon ligand is a much stronger p acceptor than CO. This explains why the Db 1 (p J ) contribution to the TM-C bond increases from 16RuE to 17RuE. Note that the intrinsic interaction energies DE int in the 18VE complexes 17RuE are larger than in the 16VE species 16RuE (Table 18) but the BDEs of 17RuE are clearly smaller than for 16RuE. This comes from the significantly higher preparation energies DE prep in the former species, because the atoms E are in the excited 1 D state in the EDA calculations using model A (Fig. 21).
In a second paper by Parameswaran and Frenking (PF2) 90 the authors calculated the structures of the adducts 16TME-W(CO) 5 and 17TME-W(CO) 5 where the tetrele complexes 16TME and 17TME are two-electron donor ligands. The nature of the E-W bonds was investigated with charge-and energy decomposition analyses and the results were compared with the E-W bonds in OE-W(CO) 5 . The theoretical study could be helpful for the synthesis of the adducts which might be easier than isolating the free tetrele complexes. Fig. 27 shows the optimized geometries of the complexes 16TME-W(CO) 5 which possess a linear coordination at the two coordinated tetrele atom C. A comparison with the structures of the free molecules 16TME (Fig. 24) shows that the TM-E bonds become mostly longer in the adducts 16TME-W(CO) 5 but the bond lengthening gets smaller for the heavier atoms E and they become even shorter for the tin complexes and for 16OsGe-W(CO) 5 . The calculations predict that the TM-PMe 3 bonds become always slightly longer in 16TME-W(CO) 5 while the TM-Cl bonds become a bit shorter. The E-W distances in 16TME-W(CO) 5 may be compared with the calculated E-W bond lengths in OE-W(CO) 5 which are shown in Fig. 28. The theoretical data suggest that the OE-W bonds in the latter complexes are clearly shorter than the E-W distances in 16TME-W(CO) 5 .
The nature of the E-W bonds in 16TME-W(CO) 5 and 17TME-W(CO) 5 was analyzed by PF2 90 with the EDA method. Table 20 gives the results for the ruthenium complexes 16RuE-W(CO) 5 and 17RuE-W(CO) 5 and for OE-W(CO) 5 . The data indicate that the nature of the bonding is not very different from each other. The covalent character of the bonds which is given by the percentage values of DE orb in the tetrele complexes 16TME-W(CO) 5 is nearly the same as in OE-W(CO) 5 while it is somewhat smaller in 17TME-W(CO) 5 . All ligands 16RuE, Fig. 27 Optimized geometries and E-W bond dissociation energies D e (BP86/TZ2P) of the tetrele complexes 16TME-W(CO) 5 . Bond lengths are given in Å, angles in degree, energies in kcal mol À1 . 90 The figure has been adapted from ref. 90.  5 . Bond lengths are given in Å, angles in degree, energies in kcal mol À1 . 90 The figure has been adapted from ref. 90. 17RuE and OE are stronger s donors than p acceptors except CO which is calculated to be a stronger p acceptor. 92

Summary and conclusion
The theoretical work which is reviewed here shows that the naked group-14 atoms E = C-Pb in the singlet 1 D state behave as bidentate Lewis acids which strongly bind two s donor ligands L in the donor-acceptor complexes L-E'L. Tetrylones EL 2 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 ER 2 (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 they become obvious by a distinctively different chemical reactivity. The unusual structures and chemical behaviour of tetrylones EL 2 can be understood in terms of the donor-acceptor interactions L-E'L. Tetrylones are potential donor ligand in main group compounds and transition metal complexes which are experimentally not yet known. The theoretical studies which are presented and discussed in this review provide an outlook over a wide area which awaits to be explored.
The second part of the review 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 Fig. 29 Optimized geometries and E-W bond dissociation energies D e (BP86/TZ2P) of the tetrele complexes 17TME-W(CO) 5 . Bond lengths are given in Å, angles in degree, energies in kcal mol À1 . 90 16TME + W(CO) 6 -16TME-W(CO) 5 + CO (1) 17TME + W(CO) 6 -17TME-W(CO) 5 + CO (2) 16TME + (CO) 5 W-EO -16TME-W(CO) 5 + EO (3) 17TME + (CO) 5 W-EO -17TME-W(CO) 5 + EO (4) transition metal in a combination of s and p J electron-sharing bonds TM-E and p > 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. This is also a large field of promising experimental research which awaits to become explored.