Successive decarbonylation and cyclodimerization of the mono- and binuclear FeCp(PCO)(CO)2, Fe2Cp2(PCO)2(CO)4, and Fe2Cp2(CO)2(P2) complexes have been investigated using density functional theory calculations at the M06L/DZP level. For the mononuclear complexes, the lowest energy FeCp(PCO)(CO)m (m = 2, 1) structures always prefer the η-P(CO) bent configuration relative to other models. However, the lowest energy structure for the species of stoichiometry FeCp(PCO) is actually FeCp(P)(CO) with a formal Fe≡P triple bond. The binuclear complexes are much more complicated. The Fe2Cp2(PCO)2(CO)4 structure, highly entropy controlled, has a P2C2 ring originating from cyclodimerization of two P═C═O groups from two FeCp(PCO)(CO)2 monomers. The lowest energy Fe2Cp2(PCO)2(CO)3 structure has a μ-P(CO) group donating two lone-pair electrons to each iron atom in a nonbonded Fe···Fe unit. The most favorable structure for the species of stoichiometry Fe2Cp2(PCO)2(CO)2 has an end-to-end diphosphene P2 bridge connecting two FeCp(CO) fragments in a trans arrangement. The lowest energy Fe2Cp2(PCO)2(CO) structure has μ-P(P) and μ-C(O) groups bridging an Fe–Fe single bond. The lowest energy structures for the species of stoichiometries Fe2Cp2(P2)(CO)2 and Fe2Cp2(P2)(CO) have a central P2Fe2 tetrahedron as well as two or one CO group(s) bridging Fe–Fe or Fe═Fe bonds. The lowest energy carbonyl-free Fe2Cp2P2 structure has a rhombic Fe2P2 core with no direct P–P bond.

The tetrahedral Au20 cluster represents an outstanding landmark in cluster science. Its electronic structure can be described in terms of superatomic orbitals based on a 1s21p62s21d10 electronic configuration. Here we use the concentric bonding shell approach in order to rationalize Au20 in terms of a multilayered architecture accounting for its magic number of 20 valence electrons, which originates from the 2s antibonding combination between two structural layers. As the number of concentric structures increases from [Au4] → [Au4@Au12] → Au20, the superatomic shells are consequently expanded as, 1s1p → 1s1p1d2s2p1f → 1s1p2s1d2p3s1f3p. The role of spin–orbit coupling in affecting the electronic structure is also described. Our results suggest that Au20 can be conveniently viewed as the combination of concentric structures denoted by [{Au4@Au12}Au4] with considerable sharing of the electron density between the different concentric layers. Thus, the presence of the 2s antibonding combination originates from the interaction between two structural layers, ensuring the 20-ve count. Hence, both bonding and antibonding combinations of the s-type shells are populated, leaving both 1p and 1d shells as main superatomic bonding orbitals in the overall structure. Furthermore, the approach employed to rationalize the electronic structure of Au20 in terms of the interaction between layers is useful for the interpretation of larger thiolate-protected or bare gold clusters, among other species.

B3LYP/DZP level calculations are used to predict B2O2 cage oligomers, which are constructed from polyhedra by locating their B–B bonds at edge midpoints and three oxygen atoms at each degree 3 vertex. The stability of such cage oligomers depends highly on the B2nOn (n = 3, 4, 5) cavities corresponding to the polyhedral faces. All such polyhedral oligomers are found to have larger cohesive energies (Ec's) than corresponding planar structures, except for the smallest (B2O2)6 tetrahedron with extremely high strain arising from the four B6O3 cavities forming the tetrahedron faces. Promising (B2O2)n cages with the highest cohesive energies include pentagonal dodecahedral (B2O2)30 (c-B30) with B10O5 cavities, truncated octahedral (B2O2)36 (t-B36-2) with B8O4 cavities, and truncated icosahedral (B2O2)90 (t-B90) with B10O5 cavities. However, smaller (B2O2)n oligomers are also expected to exhibit cage structures having B8O4 or even B6O3 cavities because of their large Ec(s).

Binuclear chromium carbonyl complexes of the general type [MeN(PF2)2]mCr2(CO)n, including the experimentally known [MeN(PF2)2]3Cr2(CO)n (n = 6, 5) species, have been studied by density functional theory (DFT) methods. The lowest energy structures for the three series of [MeN(PF2)2]mCr2(CO)n (m = 1, 2, 3) structures can be grouped into three triads, namely [MeN(PF2)2]Cr2(CO)n (n = 10, 9, 8), [MeN(PF2)2]2Cr2(CO)n (n = 8, 7, 6), and [MeN(PF2)2]3Cr2(CO)n (n = 6, 5, 4). The carbonyl richest structures of each triad, namely [MeN(PF2)2]Cr2(CO)10, [MeN(PF2)2]2Cr2(CO)8, and [MeN(PF2)2]3Cr2(CO)6 have all terminal carbonyl groups, no chromium–chromium bond, and the MeN(PF2)2 ligands bridging the pair of chromium atoms. However, for [MeN(PF2)2]3Cr2(CO)6 a structure with two of the three MeN(PF2)2 ligands chelating to single chromium atoms are energetically competitive. Low-energy singlet spin state structures for the intermediate and carbonyl poorest members of each triad can incorporate a variety of features such as chromium–chromium single and double bonds, MeN(PF2)2 ligands split into bridging MeNPF2 + PF2 groups, and four-electron donor bridging η2-μ-CO groups as required to give each chromium atom the favored 18-electron configuration. Such four-electron donor bridging η2-μ-CO groups are not found in low-energy structures of related binuclear carbonyl complexes [MeN(PF2)2]mM2(CO)n (M = Fe, Ni; m = 1, 2) of the later transition metals iron and nickel.

The long-range characteristics of the induced magnetic field in the bare icosahedral [Al@Al12]− and [Si12]2− clusters reveal inherent characteristics for spherical aromatic and antiaromatic systems. Here, we extend the shielding cone property to these highly symmetrical inorganic examples to achieve a suitable indicator for aromaticity as a reliable method for evaluating the aromaticity of clusters containing interstitial atoms.

Reaction of (MePPh2)4WCl2 with C3O2 has been shown experimentally to result in stepwise cleavage of the two CC double bonds in C3O2 to give successively tungsten complexes containing phosphinoketenylidene and phosphinocarbyne ligands. The mechanism of such processes has been elucidated by density functional theory methods for the L4WCl2 (L = PMe3, PMePh2) systems. The triplet L4WCl2 reagents are found to proceed to singlet intermediates and products in a reaction sequence involving dissociation of a phosphine ligand, a triplet → singlet intersystem crossing, an initial CC bond cleavage and a free phosphine attachment transition state. The first step is the rate-determining step with a Gibbs free energy barrier of 19.8 kcal mol−1, and the formation of the stable phosphinoketenylidene intermediate is thermodynamically favorable. Further reaction of the phosphinoketenylidene intermediate to give the final phosphinocarbyne product is unusual because it is thermodynamically disfavored but kinetically feasible. The key steps involve loss of another phosphine ligand to give the transition state involving the cleavage of the second CC bond of C3O2.

A theoretical study of the cyclodimerization of (Cy3P)2Pt(BO)Br (1Br) and [(Cy3P)2Pt(BO)]+ (1) (Cy = cyclohexyl) suggests that the reactivity of the BO ligand is primarily controlled by M←BO σ donation. Therefore, increasing the electron density at the metal center through strong σ-donor and weak π-acceptor ancillary ligands and a low formal metal oxidation state are suggested to reduce the polarity of the boronyl ligand and thus lower its reactivity toward cyclodimerization. The stable 1Br has lower Pt←BO σ donation and thus a less electrophilic boron atom, leading to a less polarized BO ligand. However, 1 is unstable in dichloromethane, since the dicationic dimer and transition state are highly stabilized by strong electrostatic interactions.

The complete series of Cp2M2(μ-C6F6) (M = Ti, V, Cr, Mn, Fe, Co, Ni) structures have been examined theoretically for comparison with their unsubstituted Cp2M2(μ-C6H6) analogues. The singlet triple decker sandwich titanium complex Cp2Ti2(η6,η6-C6F6) with a closed shell electronic structure and a non-planar C6F6 ring is preferred energetically by a wide margin (>20 kcal mol−1) over other isomers and spin states. This is in contrast to the hydrogen analogue for which related triplet spin state structures are clearly preferred. A similar low-energy triple-decker sandwich Cp2V2(η6,η6-C6F6) structure is found for vanadium but with a quintet spin state. The later transition metals from Cr to Ni energetically prefer the so-called “rice-ball” cis-Cp2M2(μ-C6F6) structures with varying hapticities of metal-ring bonding, a range of formal orders of metal–metal bonding, and varying spin states depending on the metal atom. Thus the lowest energy Cp2Cr2(μ-C6F6) structures are triplet and quintet structures with pentahapto–trihapto η5,η3-μ-C6F6 rings and formal CrCr double bonds. This contrasts with the structure of Cp2Cr2(μ-C6H6) having a bis(tetrahapto) η4,η4-C6H6 ring and a formal Cr–Cr quadruple bond. The lowest energy Cp2Mn2(μ-C6F6) structures are trans and cis quintet spin state structures. This contrasts with Cp2Mn2(μ-C6H6) for which a closed-shell singlet triple decker sandwich structure is preferred. The lowest energy Cp2Fe2(μ-C6F6) structure is a triplet cis structure with a tetrahapto–dihapto η4,η2-μ-C6F6 ring and a formal Fe–Fe single bond. The lowest energy Cp2Co2(μ-C6F6) structures are singlet spin state structures with formal M–M single bonds and either bridging bis(trihapto) η3,η3-C6F6 or tetrahapto–dihapto η4,η2-C6F6 rings. For Cp2Ni2(μ-C6F6) low energy singlet cis and trans structures are both found. The singlet cis-Cp2Ni2(μ-C6F6) structure has a Ni–Ni single bond of length ∼2.5 Å and a bridging bis(dihapto) η2,η2-C6F6 ligand with an uncomplexed CC double bond. The singlet trans-Cp2Ni2(μ-C6F6) structure has a bis(trihapto) η3,η3-C6F6 ligand.

Alkali metal salts of the 2-phosphaethynolate anion PCO− synthesized from reactions of CO with NaPH2 or K3P7 have recently become available in quantities for the synthesis of transition metal complexes of the potentially ambidentate PCO ligand (Angew. Chem., Int. Ed., 2013, 38, 10064). This is exemplified by the recently reported rhenium carbonyl complex (triphos)Re(CO)2(PCO) (triphos = MeP(CH2PPh2)3). Density functional theory studies on the related manganese carbonyl complexes Mn(CO)n(PCO) (n = 5, 4, 3) and Mn2(CO)n(PCO)2 (n = 8, 7, 6, 5) are now reported. For the binuclear systems the low-energy Mn2(CO)8(PCO)2 structures are singlet spin state structures having two bridging P-bonded phosphaketenyl μ-PCO ligands without a direct Mn–Mn bond. Carbonyl loss from Mn2(CO)8(μ-PCO)2 is predicted to lead to migration of CO groups from phosphorus to manganese resulting in Mn2(CO)n+2(μ-P2) structures with bridging diphosphido groups as the lowest energy Mn2(CO)n(PCO)2 isomers (n = 7, 6, 5). Isomeric Mn2(CO)6(PCO)2 structures with dihapto bridging η2-μ-PCO ligands at ∼30 kcal mol−1 above the global minimum are also found representing intermediates in the migration of CO groups from phosphorus to manganese. For the mononuclear systems the P-bonded Mn(CO)n(PCO) (n = 5, 4) phosphaketenyl structures are found to lie 20 to 28 kcal mol−1 in energy below the isomeric O-bonded Mn(CO)n(PCO) phosphaethynoxy isomers consistent with previously reported results by Grützmacher and coworkers on R3E(PCO)–R3E(OCP) systems (R = iPr, Ph; E = Si, Sn, Ge, Pb). The lowest energy structure for the tricarbonyl Mn(CO)3(PCO) is a singlet structure with an unusual trihapto η3-PCO ligand. However, higher energy isomeric Mn(CO)3(PCO) structures with P-bonded phosphaketenyl or O-bonded phosphaethynoxy ligands and tetrahedral Mn coordination are also found.

The cyclopentadienyliron trifluorophosphine hydride CpFe(PF3)2H, in contrast to CpFe(CO)2H, is a stable compound that can be synthesized by reacting Fe(PF3)5 with cyclopentadiene. Theoretical studies on the binuclear Cp2Fe2(PF3)n (n = 5, 4, 3, 2) derivatives derived from CpFe(PF3)2H indicate the absence of viable structures having PF3 ligands bridging Fe–Fe bonds solely through the phosphorus atom. This contrasts with the analogous Cp2Fe2(CO)n systems for which the lowest energy structures have two (for n = 4 and 2) or three (for n = 3) CO groups bridging an iron–iron bond. Higher energy singlet Cp2Fe2(PF3)3 structures have a novel four-electron donor bridging η2-μ-PF3 ligand bonded to one iron atom through its phosphorus atom and to the other iron atom through a fluorine atom. Other higher energy triplet and singlet Cp2Fe2(PF3)2 structures are of the Cp2Fe2F2(μ-PF2)2 type having terminal fluorine atoms and bridging μ-PF2 ligands. The lowest energy Cp2Fe2(PF3)5 structure is actually Cp2Fe2(PF3)3(PF4)(μ-PF2) with a bridging PF2 group and a terminal PF4 group. Such structures are derived from a Cp2Fe2(PF3)4(μ-PF3) precursor by migration of a fluorine atom from the bridging PF3 group to a terminal PF3 group with a low activation energy barrier.

The pyrolysis of Cp2V2(CO)5 in tetrahydrofuran solution is reported by Herrmann and co-workers to give a tetranuclear Cp4V4(CO)4 cluster as a major product and the trinuclear Cp3V3(CO)9 as a minor product. Neither of these products has been characterized structurally. A theoretical study of the Cp4V4(CO)4 system reveals a complicated energy surface having 10 structures within 25 kcal mol−1 of the global minimum encompassing singlet, triplet, and quintet spin states. The lowest energy Cp4V4(CO)4 structures are nearly degenerate (within 1 kcal mol−1) triplet and singlet structures with a central V4 distorted tetrahedron with a μ3-CO group bridging each face. Higher energy singlet and triplet Cp4V4(CO)4 structures are also found with a central V4 butterfly and an unusual η2-μ4-CO group bridging all four vanadium atoms through four V–C bonds and one V–O bond. None of the ten Cp4V4(CO)4 structures has any terminal CO groups, which is totally different from the Cp4V4(CO)4 structure with exclusively terminal CO groups suggested from the experimental work. The lowest energy Cp3V3(CO)9 structure has a central equilateral V3 triangle and all terminal CO groups. However, this Cp3V3(CO)9 structure is disfavored by ∼34 kcal mol−1 relative to fragmentation into the stable compounds CpV(CO)4 + Cp2V2(CO)5 consistent with its low yield in the Cp2V2(CO)5 pyrolysis.

The Fe(CO)4(SiO), Co(CO)4(BO), and Co(CO)4(BNSiMe3) complexes analogous to the well-known Fe(CO)5 are predicted by density functional theory to undergo exothermic oligomerization to give the oligomers [Fe(CO)4]n(SinOn), [Co(CO)4]n(BnOn), and [Co(CO)4]2(B2N2Si2Me6) containing SinOn/BnOn/B2N2 rings with single bonds.

•The species Cp2Co2(BO)2(CO)n (Cp = η5-C5H5; n = 2, 1, 0) have been investigated by density functional theory.•The lowest energy Cp2Co2(BO)2(CO)2 structures are doubly bridged singlet trans and cis isomers.•The lowest energy Cp2Co2(BO)2(CO) structure is a triplet triply bridged structure.•The lowest energy Cp2Co2(BO)2 structure is a triplet state structure with a trans-η4-μ-B2O2 ligand.•The lowest energy singlet Cp2Co2(BO)2 structure has two bridging μ-BO groups and a formal CoCo triple bond.The structures and thermochemistry of the binuclear cyclopentadienylcobalt carbonyl boronyls Cp2Co2(BO)2(CO)n (Cp = η5-C5H5; n = 2, 1, 0) were investigated by density functional theory. Low energy structures were found of the following types: (1) Structures in which the BO groups are all one-electron donors analogous to the isoelectronic Cp2Fe2(CO)n+2 structures; (2) Structures in which the two BO groups have coupled to form bridging B2O2 ligands, which may be either four- or six-electron donors; (3) Structures with three-electron donor bridging BO groups, bonded to one metal through the boron atom and to the other metal through the oxygen atom. The lowest energy Cp2Co2(BO)2(CO)2 structures are singlet trans and cis isomers of doubly bridged structures analogous to the well-known isoelectronic Cp2Fe2(CO)2(μ-CO)2. The lowest energy Cp2Co2(BO)2(CO) structure is a triplet triply bridged structure analogous to the isoelectronic stable triplet state molecule Cp2Fe2(μ-CO)3. Higher energy Cp2Co2(BO)2(CO) structures have trans or cis bridging B2O2 ligands. The lowest energy Cp2Co2(BO)2 structure is a triplet state structure with a six-electron donor bridging trans-η4-μ-B2O2 ligand. The lowest energy singlet Cp2Co2(BO)2 structure has two one-electron donor bridging μ-BO groups and a formal CoCo triple bond similar to the predicted lowest energy Cp2Fe2(CO)2 structure.Low energy Cp2Co2(BO)2(CO)n (Cp = η5-C5H5; n = 2, 1, 0) structures are found of the following types: (1) Structures in which the BO groups are all one-electron donors; (2) Structures in which the two BO groups have coupled to form bridging B2O2 ligands; (3) Structures with three-electron donor bridging BO groups.

Binuclear palladium complexes of planar hydrocarbon ligands are of particular interest since both the coaxial structure (η5-Me5C5)2Pd2(μ-CO)2 and the perpendicular structure (μ-C6H6)2Pd2(Al2Cl7)2 have been synthesized as stable compounds. Here we report theoretical studies on a family of related compounds. For the formal Pd(II) derivatives Cp2Pd2X2 (Cp = η5-C5H5; X = F, Cl, CN) the perpendicular structures with direct Pd–Pd bonds are predicted to lie in energy below the isomeric coaxial structures. These coaxial structures have long Pd⋯Pd distances indicating the absence of palladium–palladium bonds. The lowest energy perpendicular Cp2Pd2X2 structures (X = F, CN) and a higher energy similar Cp2Pd2Cl2 structure contain a substituted η4-C5H5X cyclopentadiene ligand obtained by the addition of X to one of the Cp ligands. For the formal Pd(I) complexes Cp2Pd2L2 (L = CO and CS) the coaxial structures lie in energy below the isomeric perpendicular structures with a particularly large energy separation of ∼19 kcal mol−1 for the thiocarbonyl derivatives. However, for Cp2Pd2(CNCH3)2 the coaxial and perpendicular isomers have essentially the same energies.

The long-range characteristics of the induced magnetic field in the bare icosahedral [Al@Al12]− and [Si12]2− clusters reveal inherent characteristics for spherical aromatic and antiaromatic systems. Here, we extend the shielding cone property to these highly symmetrical inorganic examples to achieve a suitable indicator for aromaticity as a reliable method for evaluating the aromaticity of clusters containing interstitial atoms.

B3LYP/DZP level calculations are used to predict B2O2 cage oligomers, which are constructed from polyhedra by locating their B–B bonds at edge midpoints and three oxygen atoms at each degree 3 vertex. The stability of such cage oligomers depends highly on the B2nOn (n = 3, 4, 5) cavities corresponding to the polyhedral faces. All such polyhedral oligomers are found to have larger cohesive energies (Ec's) than corresponding planar structures, except for the smallest (B2O2)6 tetrahedron with extremely high strain arising from the four B6O3 cavities forming the tetrahedron faces. Promising (B2O2)n cages with the highest cohesive energies include pentagonal dodecahedral (B2O2)30 (c-B30) with B10O5 cavities, truncated octahedral (B2O2)36 (t-B36-2) with B8O4 cavities, and truncated icosahedral (B2O2)90 (t-B90) with B10O5 cavities. However, smaller (B2O2)n oligomers are also expected to exhibit cage structures having B8O4 or even B6O3 cavities because of their large Ec(s).

The complete series of Cp2M2(μ-C6F6) (M = Ti, V, Cr, Mn, Fe, Co, Ni) structures have been examined theoretically for comparison with their unsubstituted Cp2M2(μ-C6H6) analogues. The singlet triple decker sandwich titanium complex Cp2Ti2(η6,η6-C6F6) with a closed shell electronic structure and a non-planar C6F6 ring is preferred energetically by a wide margin (>20 kcal mol−1) over other isomers and spin states. This is in contrast to the hydrogen analogue for which related triplet spin state structures are clearly preferred. A similar low-energy triple-decker sandwich Cp2V2(η6,η6-C6F6) structure is found for vanadium but with a quintet spin state. The later transition metals from Cr to Ni energetically prefer the so-called “rice-ball” cis-Cp2M2(μ-C6F6) structures with varying hapticities of metal-ring bonding, a range of formal orders of metal–metal bonding, and varying spin states depending on the metal atom. Thus the lowest energy Cp2Cr2(μ-C6F6) structures are triplet and quintet structures with pentahapto–trihapto η5,η3-μ-C6F6 rings and formal CrCr double bonds. This contrasts with the structure of Cp2Cr2(μ-C6H6) having a bis(tetrahapto) η4,η4-C6H6 ring and a formal Cr–Cr quadruple bond. The lowest energy Cp2Mn2(μ-C6F6) structures are trans and cis quintet spin state structures. This contrasts with Cp2Mn2(μ-C6H6) for which a closed-shell singlet triple decker sandwich structure is preferred. The lowest energy Cp2Fe2(μ-C6F6) structure is a triplet cis structure with a tetrahapto–dihapto η4,η2-μ-C6F6 ring and a formal Fe–Fe single bond. The lowest energy Cp2Co2(μ-C6F6) structures are singlet spin state structures with formal M–M single bonds and either bridging bis(trihapto) η3,η3-C6F6 or tetrahapto–dihapto η4,η2-C6F6 rings. For Cp2Ni2(μ-C6F6) low energy singlet cis and trans structures are both found. The singlet cis-Cp2Ni2(μ-C6F6) structure has a Ni–Ni single bond of length ∼2.5 Å and a bridging bis(dihapto) η2,η2-C6F6 ligand with an uncomplexed CC double bond. The singlet trans-Cp2Ni2(μ-C6F6) structure has a bis(trihapto) η3,η3-C6F6 ligand.