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Fluorocarbons have been shown experimentally by Baker and coworkers to combine with the cyclopentadienylcobalt (CpCo) moiety to form fluoroolefin and fluorocarbene complexes as well as fluorinated cobaltacyclic rings. In this connection density functional theory (DFT) studies on the cyclopentadienylcobalt fluorocarbon complexes CpCo(L)(C n F 2n ) (L = CO, PMe 3 ; n = 3 and 4) indicate structures with perfluoroolefin ligands to be the lowest energy structures followed by perfluorometallacycle structures and finally by structures with perfluorocarbene ligands. Thus, for the CpCo(L)(C 3 F 6 ) (L = CO, PMe 3 ) complexes, the perfluoropropene structure has the lowest energy, followed by the perfluorocobaltacyclobutane structure and the perfluoroisopropylidene structure less stable by 8 to 11 kcal mol −1 , and the highest energy perfluoropropylidene structure less stable by more than 12 kcal mol −1 . For the two metal carbene structures Cp(L)CoC(CF 3 ) 2 and Cp(L)CoCF(C 2 F 5 ), the former is more stable than the latter, even though the latter has Fischer carbene character. For the CpCo(L)(C 4 F 8 ) (L = CO, PMe 3 ) complexes, the perfluoroolefin complex structures have the lowest energies, followed by the perfluorometallacycle structures at 10 to 20 kcal mol −1 , and the structures with perfluorocarbene ligands at yet higher energies more than 20 kcal mol −1 above the lowest energy structure. This is consistent with the experimentally observed isomerization of the perfluorinated cobaltacyclobutane complexes CpCo(PPh 2 Me)(–CFR–CF 2 –CF 2 –) (R = F, CF 3 ) to the perfluoroolefin complexes CpCo(PPh 2 Me)(RCFCF 2 ) in the presence of catalytic quantities of HN(SO 2 CF 3 ) 2 . Further refinement of the relative energies by the state-of-the-art DLPNO-CCSD(T) method gives results essentially consistent with the DFT results summarized above. 

Vanadium forms binuclear complexes with a variety of ligands often containing V≡V triple bonds. Many tetragonal divanadium paddlewheel complexes with bridging bidentate ligands have been experimentally characterized. This research exhaustively treats model tetragonal, trigonal, and digonal paddlewheel‐type divanadium complexes V₂L_x(L=formamidinate, guanidinate, and carboxylate;x=2, 3, 4), each in the three lowest‐energy spin states. The V−V formal bond orders are obtained from metal−metal MO diagrams for representative structures. A number of short V−V multiple bonds of order 3, 3.5, and 4 are found in these model complexes. The short V≡V triple bonds and singlet ground state predicted here for the model tetragonal complexes correspond well with the limited experimental results for the series of known tetragonal paddlewheels. Digonal divanadium lanterns with very short V−V quadruple bonds are predicted as interesting synthetic targets. The V−V bond distances are categorized into distinct ranges according to the formal bond order values from 0.5 to 4. These bond length ranges are compared with the ranges compiled for other divanadium complexes including carbonyl complexes.

 

Density functional theory studies show that the lowest energy C 4 F 8 Fe(CO) 4 structure is not the very stable experimentally known ferracyclopentane isomer (CF 2 CF 2 CF 2 CF 2 )Fe(CO) 4 obtained from Fe(CO) 12 and tetrafluoroethylene. Instead isomeric (perfluoroolefin)Fe(CO) 4 structures derived from perfluoro-2-butene, perfluoro-1-butene, and perfluoro-2-methylpropene are significantly lower energy structures by up to ∼17 kcal mol −1 . However, the activation energies for the required fluorine shifts from one carbon to an adjacent carbon atom to form these (perfluoroolefin)Fe(CO) 4 complexes from tetrafluoroethylene are very high ( e.g. , ∼70 kcal mol −1 ). Therefore the ferracyclopentane isomer (CF 2 CF 2 CF 2 CF 2 )Fe(CO) 4 , which does not require a fluorine shift to form from Fe 3 (CO) 12 and tetrafluoroethylene, is the kinetically favored product. The lowest energy structures of the binuclear (C 4 F 8 ) 2 Fe 2 (CO) n ( n = 7, 6) derivatives have bridging perfluorocarbene ligands and terminal perfluoroolefin ligands. 

The known sandwich compound [η 5 -(CH 2 ) 3 N 2 (BPh) 2 CMe] 2 Fe in which adjacent C 2 units are replaced by isoelectronic BN units can be considered as a boraza analogues of ferrocene similar to borazine, B 3 N 3 H 6 , considered as a boraza analogue of benzene. In this connection, the related bis(1,2,3,5-tetramethyl-1,2-diaza-3,5-diborolyl) derivatives (Me 4 B 2 N 2 CH) 2 M (M = Ti, V, Cr, Mn, Fe, Co, Ni) for all of the first row transition metals have been optimized using density functional theory for comparison with the isoelectronic tetramethylcyclopentadienyl derivatives (Me 4 C 5 H) 2 M. Low-energy sandwich structures having parallel B 2 N 2 C rings in a trans orientation are found for all seven metals. The 1,2-diaza-3,5-diborolyl ligand appears to be a weaker field ligand than the isoelectronic cyclopentadienyl ligand as indicated by higher spin ground states for some (η 5 -Me 4 B 2 N 2 CH) 2 M sandwich compounds relative to the corresponding metallocenes (η 5 -Me 4 C 5 H) 2 M. Thus (η 5 -Me 4 B 2 N 2 CH) 2 Cr has a quintet ground state in contrast to the triplet ground state of (η 5 -Me 4 C 5 H) 2 Cr. Similarly, the sextet ground state of (η 5 -Me 4 B 2 N 2 CH) 2 Mn lies ∼18 kcal mol −1 below the quartet state in contrast to the doublet ground state of the isoelectronic (Me 4 C 5 H) 2 Mn. These sandwich compounds are potentially accessible by reaction of 1,2-diaza-3,5-diborolide anions with metal halides analogous to the synthesis of [η 5 -(CH 2 ) 3 N 2 (BPh) 2 CMe] 2 Fe. 

Binuclear alkyne manganese carbonyls of the type (RC≡CR')Mn₂(CO)_n(R and R'=methyl or dimethylamino;n=8, 7, 6) and their isomers related to the experimentally known (MeC₂NEt₂)Mn₂(CO)_n(n=8, 7) structures have been investigated by density functional theory. The alkyne ligand remains intact in the only low energy (Me₂N)₂C₂Mn₂(CO)₈isomer, which has a central Mn₂C₂tetrahedrane unit and is otherwise analogous to the well‐known (alkyne)Co₂(CO)₆derivatives except for one more CO group per metal atom. The low‐energy structures of the unsaturated (Me₂N)₂C₂Mn₂(CO)_n(n=7, 6) systems include isomers in which the nitrogen atom of one of the dimethylamino groups as well as the C≡C triple bond of the alkyne is coordinated to the central Mn₂unit. In other low‐energy (Me₂N)₂C₂Mn₂(CO)_n(n=7, 6) isomers the alkyne C≡C triple bond has broken completely to form two separate bridging dimethylaminocarbyne Me₂NC ligands analogous to the experimentally known iron carbonyl complex (Et₂NC)₂Fe₂(CO)₆. The (alkyne)Mn₂(CO)_n(n=8, 7, 6) systems of the alkynes MeC≡CMe and Me₂NC≡CMe with methyl substituents have significantly more complicated potential surfaces. In these systems the lowest energy isomers have bridging ligands derived from the alkyne in which one or two hydrogen atoms have migrated from a methyl group to one or both of the alkyne carbon atoms. These bridging ligands include allene, manganallyl, and vinylcarbene ligands, the first two of which have been realized experimentally in research by Adams and coworkers. Theoretical studies suggest that the mechanism for the conversion of the simple alkyne octacarbonyl (MeC₂NMe₂)Mn₂(CO)₈to the dimethylaminomanganaallyl complex Mn₂(CO)₇[μ‐η⁴‐C₃H₃Me₂] involves decarbonylation to the heptacarbonyl and the hexacarbonyl complexes. Subsequent hydrogen migrations then occur through intermediates with C−H−Mn agostic interactions to give the final product. Eight transition states for this mechanistic sequence have been identified with activation energies of ∼20 kcal/mol for the first hydrogen migration and ∼14 kcal/mol for the second hydrogen migration.

 

Theoretical methods show that the lowest energy bis(butadiene)metal structures (C 4 H 6 ) 2 M (M = Ti to Ni) have a perpendicular relative orientation of the two butadiene ligands corresponding to a tetrahedral coordination of the central metal atom to the four CC double bonds of the butadiene ligands. Distribution of the metal d electrons in the resulting tetrahedral ligand field rationalizes the predicted spin states increasing monotonically from singlet to quartet from nickel to manganese and back from quartet to singlet from manganese to titanium.