7r-Bonding theory

Ring has saddle conformation. 139, Variation in P-N bond lengths 141 consistent with 7r-bonding theory... 

Several theories have been proposed to explain this trans effect, but at present only the polarization and the 7r-bonding theories are commonly used. 

For bonded atoms, the off-diagonal terms (where i j) are taken to depend on tjje type and length of the bond joining the atoms on which the basis functions y- and Xj 0 centred. The entire integral is written as a constant, 0ij, which is not the same as the fixY in Hiickel 7r-electron theory. The are taken to be parameters, fixed by calibration against experiment. It is usual to set Pij to zero when the pair of atoms are not formally bonded. 

Theoretical explanation of the trans-effect (and /rans-influence) has centred on two theories, one based on cr-bonding the other on 7r-bonding. The tr-bonding argument considers two frans-ligands sharing a metal p orbital (Figure 3.83). 

Molecular orbital theory may provide an explanation for stereochemical differences between carboxylate-metal ion and phosphate-metal ion interactions. Detailed ab initio calculations demonstrate that the semipo-lar 1 0 double bond of RsP=0 is electronically different from the C=0 double bond, for example, as found in H2C=0 (Kutzelnigg, 1977 Wallmeier and Kutzelnigg, 1979). The P=0 double bond is best described as a partial triple bond, that is, as one full a bond and two mutually perpendicular half-7r bonds (formed by backbonding between the electrons of oxygen and the empty d orbitals of phosphorus). Given this situation, a lone electron pair should be oriented on oxygen nearly opposite the P=0 bond, and these molecular orbital considerations for P=0 may extend to the phosphinyl monoanion 0-P=0. If this extension is valid, then the electronic structure of 0-P=0 should not favor bidentate metal complexation by phosphate this is in accord with the results by Alexander et al. (1990). 

Briefly, as Prof. Basolo points out in his paper, and Prof. Basolo and Pearson pointed out nicely in a review on the trans effect, the situation in the ir-bonding theory is a stabilization of the trigonal bipyramidal intermediate because there are more orbitals in the trigonal plane available for 7r-bonding in the trigonal bipyramid than in the square planar complex. The same is also true in the --system. The trans effect is directional, and in my opinion, it has to be orbital or quantum mechanical. 

Neither of the above species is a ground-state quintet (four unpaired electrons). The pairing indicated by the valence bond structures shown above apparently occurs, leaving the unpaired electrons localized in a orbitals that are approximately orthogonal to the n system. The very small zero-field splitting is perhaps a measure of the validity of the o—7r separation which constitutes the basic assumption of 7r-electron theory. 

Anisotropic 7r-bonding and phase coupling can each lead to splittings far in excess of what is predicted by classical ligand field theory. When the AOM matrix M10 is used, the ligand field potential matrix for M(A-A)3 assumes the form... 

The electronic spectrum is yet another property which illustrates the similarities between the metallocenes and (7r-ollyl) metal compounds. In Table VI are listed some data for a series of Coin(absorption bands with the small extinction coefficients are probably two of the spin-allowed d-d transitions. Scott (34) has developed an approximate axial ligand field model for the carborane-transition metal complexes and has discussed the optical spectra in relation to this bonding theory. The actual assessment of bonding in the (7r-ollyl) metal compound as well as the metallocenes would be greatly aided by accurate assignments of the electronic spectra. 

Dimeric 7r-arene-bridged samarium anilide [Sm(NHArl Pr,H)3]2 was employed in the isolation and characterization of a dimeric amido-imido compound. Addition of 4 equivalents of TMA led to (1) cleavage of one of the Ln-NHPh bonds, (2) deprotonation, and (3) adduct formation. Density functional theory calculations, carried out in order better to understand the nature of the imido bonding, revealed the presence of Sm - N 7r-bonding interactions involving the samarium 5d orbitals [218]. 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

Covalent bonding depends on the presence of two atomic receptor sites. When the electron reaches one of these sites its behaviour, while in the vicinity of the atom, is described by an atomic wave function, such as the ip(ls), (l = 0), ground-state function of the H atom. Where two s-type wave functions serve to swap the valence electron the interaction is categorized as of a type. The participating wave functions could also be of p, (l = 1), or d, (/ = 2) character to form 7r or 6 bonds respectively. The quantum number l specifies the orbital angular momentum of the valence electron. A common assumption in bonding theory is that a valence electron with zero angular momentum can be accommodated in a p or d state if a suitable s-state is not available. The reverse situation is not allowed. 

Single-wall carbon nanotubes are new types of nanomaterial, the study of which generates about five research papers [234] from around the world, each day. An important feature of these structures is that the aromatic rings of the folded graphite sheet that constitutes the tube, are no longer planar. This feature represents a new challenge for accepted theories of 7r-bonding. 

Resonance between three 7r-complex structures might lead to stabilization of 1 in the sense of 7r-aromatic stabilization involving the six CC bond electrons. Therefore, Dewar has discussed the stability of in terms of a c-aromatic stabilization (Section V). However, spin-coupled valence bond theory clearly shows that 1 cannot be considered as the cr-aro-matic analogue to 7r-aromatic benzene The 7r-complex description of 1 is a (very formal) model description, which should be discarded as soon as it leads to conflicting descriptions of the properties of 1. This will be discussed in Section V. 

The Mills-Nixon hypothesis had, as its foundation, certain differences in the chemical behaviour of indan (3) and tetralin (4) from which a localization of the aromatic 7r-bonds was predicted to occur in the direction depicted by la rather lb. The original experimental evidence upon which the effect was based was shown to be erroneous, but calculations at various levels of theory indicated that aromatic bond localization should exist and become more pronounced as the size of the annelated ring decreases In essence one can recognize that the structure of benzene has a symmetry such that both Kekule structures must contribute equally. With Q tetralin (4) (and the lower homologues) no such symmetry requirement exists and ring annelation could induce bond length alternation within the arene nucleus. As the strain imposed by the fused ring increases, the Mills-Nixon effect should increase. The hypothesis has been the subject of considerable discussion and the controversy is far from settled. 

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