DFT-calculation of the structural isomers of (1-methyl-4-phenyl-1-azabuta-1,3-diene)tetracarbonyliron(0) and (4-phenyl-1-oxabuta-1,3-diene)tetracarbonyliron(0)

DFT calculations (B3LYP/LANL2DZ/6-31 G*) were used to investigate the ways in which 1-methyl-4-phenyl-1-azabuta-1,3-diene and 4-phenyl-1-oxabuta-1,3-diene bind to a Fe(CO)(4) moiety. As possible coordination modes, eta(2)-coordination across the C=C or C=N/C=O bond, sigma-coordination to the lone pair of the heteroatom, or eta(3)-coordination through the C=C-C or the N=C-C/O=C-C moiety were considered. The latter forms involve coupling of the non-coordinated atom of the heterodiene with one of the carbonyl ligands to an acyl species. The calculated geometric parameters of all structures compare well with X-ray crystallographic data of similar complexes. The species in which the ligand is transoid and sigma-coordinated is lowest in energy, for both compounds studied. However, the eta(2)-alkene bound 1-oxabuta-1,3-diene complex is practically equal in energy to the sigma-transoid form and thus competes. This agrees with experimental observations that the heterodiene is sigma-bonded in Fe(CO)(4)(1-methyl-4-phenyl-1-azabuta-1,3-diene) but eta(2)-coordinated in Fe(CO)(4)(4-phenyl-1-oxabuta-1,3-diene). The solvent dependence was estimated from single point PCM calculations, for CH(2)Cl(2) as solvent. For the 1-azabuta-1,3-diene complexes, the relative energies of eta(2)-olefin and eta(3)-allyl forms are inverted, with the eta(3)-allyl form being more stable in polar solvents. The 1-oxabuta-1,3-diene complexes in their eta(2)-olefin and sigma-O forms change order of relative energy, and conversion to the sigma-O form is expected in a polar medium for these complexes. Calculated IR vibrational stretching frequencies of the carbonyl ligands and the C[double bond, length as m-dash]N/C[double bond, length as m-dash]O bond were compared with experimental data, to produce the best fits for the sigma-transoid form of Fe(CO)(4)(1-methyl-4-phenyl-1-azabuta-1,3-diene) and eta(2)-olefin bonded Fe(CO)(4)(4-phenyl-1-oxabuta-1,3-diene). These results are again consistent with the experiment and show that the DFT method applied in this work can be used as an aid for structural validation.     

Pinwheel motifs: formation of unusual homo- and hetero-nuclear aggregates via bridging thiolates

The homohexanuclear complexes [Ni2[Ni(L1)]4](BF4)4 x MeCN, 1, [Pd2(Pd(L2)]4](BF4)4, 2, and the heteropentanuclear aggregate [Cu2[Ni(L3)]3](PF6)2, 3, all adopt a 'pinwheel' type structural motif via thiolate bridging between square-planar Ni(II) or Pd(II) and between trigonal planar Cu(I) centres, respectively.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.     

DFT calculation and AIM-analysis of the substituent influence on the structure of (1-azabuta-1,3-diene)tetracarbonyliron(0) complexes

1-Azabuta-1,3-dienes can coordinate to the tetracarbonyliron(0) moiety in four ways, to form (1-azabuta-1,3-diene)tetracarbonyliron(0) complexes with the ligand bonded in an η² fashion through the alkene, η² coordinated through its CN bond, σ-bonded to the lone pair of the nitrogen atom, or η³ coordinated through the CC-C moiety under concomitant coupling of the imine nitrogen with one of the carbonyl ligands to a carbamoyl species. In the experiment, the equilibrium between these species strongly depends on factors such as the nature of the substituents at the ligand, the solvent and the temperature. In this work, DFT calculations (B3LYP/LANL2DZ/6-31G* and 6-311++G**) and an AIM-analysis of the topology of the charge density were used to investigate the influence of the substituents at the 1-azabuta-1,3-diene ligand on the structural, electronic and energetic properties of these constitutional isomers. In most cases, the calculations correctly predict the observed structure, even in situations where the energy differences between related species are rather small. Substituents larger than CH₃ at N and H at C2 disfavour the structures with an η² coordination to the CN bond to such an extent that they cease to exist as minimum energy structures. Also the σ-N forms distort significantly with the introduction of substituents at N or C2 and become energetically less favourable. The geometries of the η²-alkene form do not change much upon substitution, whereas the η³ form tolerates steric strain best and becomes most favourable when the substituent at C2 is large. The activation barrier between the η²-alkene and the η³-allyl form is low (7.5-1.4 kcal/mol) and allows for an equilibration between these species. The conversion of the η²-alkene into the σ-N form requires almost complete dissociation of the ligand from the Fe(CO)₄ moiety. Accordingly, its activation barrier is higher (approx. 14 kcal/mol) and fairly independent of the nature of the substituents at the azabutadiene ligand.