Orbital Compatibility

The adherence of the large number of polyhedral boranes, metallaboranes, and heteroboranes to the set of electron-counting rules was a triumph. Later, chemistry witnessed the advent of a series of electron-deficient metallaboranes, in relation to 

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An essential characteristic of the Fock equations resides in the fact that each individual operator F depends on all the orbitals which are occupied in the system (on account of the explicit inclusion of the interaction terms). Thus, each is given by an equation which depends on all the s. The way out of this difficulty is to choose arbitrarily a starting set of s, calculate the F(v) s, solve the series of equations for a new set of s, and go over the same series of operations again and again until the pth set of < s reproduce the (p— l)th set with good accuracy—hence the name self-consistent given to the procedure. The orbitals obtained in this fashion are, in principle, the best possible orbitals compatible with a determinantal W. 

Figure 5.28 Orbital compatibility indicates preference of the larger cluster to condense with the smaller ones.

Jemmis, E.D. and Schleyer, P.v.R. (1982) Aromaticity in three dimensions. 4. Influence of orbital compatibility on the geometry and stability of capped annu-lene rings with six interstitial electrons. J. Am. Chem. Soc., 104 (18), 4781-4788. 

Shameema, O. and Jemmis, E.D. (2009) Relative stability of closo-closo, closo-nido, and nido-nido macropolyhedral boranes the role of orbital compatibility. Chem. Asian J., 4 (8), 1346-1353. 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

The observed bond lengths in some intermetallic compounds can be made compatible with those in the constituent metals by consideration of the possibility of distributing the d character unequally among the bond orbitals of an atom. 

The wave functions for the two inner-core spherons can, of course, be described as the symmetric and antisymmetric combinations of l.t and Ip-functions. The Nilsson (19) treatment of neutron and proton orbitals in deformed nuclei is completely compatible with the foregoing discussion, which provides a structural interpretation of it. 

This might be compatible with the electrostatic model in that the radial extensions of Ad and 5d orbitals are greater than that of 3d but then the diffuseness of these orbitals increases along the series in Eq. (6.10) and that would tend to decrease the Zioct values. 

This reviews contends that, throughout the known examples of facial selections, from classical to recently discovered ones, a key role is played by the unsymmetri-zation of the orbital phase environments of n reaction centers arising from first-order perturbation, that is, the unsymmetrization of the orbital phase environment of the relevant n orbitals. This asymmetry of the n orbitals, if it occurs along the trajectory of addition, is proposed to be generally involved in facial selection in sterically unbiased systems. Experimentally, carbonyl and related olefin compounds, which bear a similar structural motif, exhibit the same facial preference in most cases, particularly in the cases of adamantanes. This feature seems to be compatible with the Cieplak model. However, this is not always the case for other types of molecules, or in reactions such as Diels-Alder cycloaddition. In contrast, unsymmetrization of orbital phase environment, including SOI in Diels-Alder reactions, is a general concept as a contributor to facial selectivity. Other interpretations of facial selectivities have also been reviewed [174-180]. 

These observations are compatible with the model for the carbene complex presented in Section II,A. Both metal and w-donor substituents compete to donate electron density to unfilled carbenepz orbitals, and with good 7r-donors such as nitrogen, the metal is less effective. In terms of resonance formalism, the resonance hybrid 39 makes a more significant contribution than 40 to the structure of the carbene ligands in these compounds. Similar conclusions are reached when the structures of Group 6, 7, and other Group 8 heteroatom-substituted carbene complexes are considered. 

Next we must select a hybridization scheme for the Br atom that is compatible with the predicted shape. It turns out that only sp3d hybridization will provide the necessary trigonal bipyramidal distribution of electron pairs around the bromine atom. In this scheme, one of the sp3d hybrid orbitals is filled while the remaining four are half-occupied. 

There are two other mechanistic possibilities, halogen atom abstraction (HAA) and halonium ion abstraction (EL), represented in Schemes 4.4 and 4.5, respectively, so as to display the stereochemistry of the reaction. Both reactions are expected to be faster than outer-sphere electron transfer, owing to stabilizing interactions in the transition state. They are also anticipated to both exhibit antiperiplanar preference, owing to partial delocalization over the C—C—Br framework of the unpaired electron in the HAA case or the electron pair in the EL case. Both mechanisms are compatible with the fact that the activation entropies are about the same as with outer-sphere electron donors (here, aromatic anion radicals). The bromine atom indeed bears three electron pairs located in two orthogonal 4p orbitals, perpendicular to the C—Br bond and in one s orbital. Bonded interactions in the transition... 

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