Geometry factors determination

In this equation E is the modulus of the beam arms, b is the thickness of the beam, and m is a geometry factor, determined by the shape of the arms. 

From a synthetic point of view, the regioselectivity and stereoselectivity of the cyclization are of paramount importance. As discussed in Section 11.2.3.3 of Part A, the order of preference for cyclization of alkyl radicals is 5-exo > 6-endo 6-exo > 7-endo S-endo > 1-exo because of stereoelectronic preferences. For relatively rigid cyclic structures, proximity and alignment factors determined by the specific geometry of the ring system are of major importance. Theoretical analysis of radical addition indicates that the major interaction of the attacking radical is with the alkene LUMO.321 The preferred direction of attack is not perpendicular to the it system, but rather at an angle of about 110°. 

An interesting application of these principles is the prediction of CO dissociation routes on the closed-packed (111) surface of rhodium (see Fig. A.17). Two factors determine how the dissociation of a single CO molecule proceeds. First, the geometry of the final situation must be energetically more favorable than that of the initial one. This condition excludes final configurations with the C and the O atom on adjacent Rh atoms, because this would lead to serious repulsion between the C and O atoms. A favorable situation is the one sketched in Fig. A.17, where initially CO occupies a threefold hollow site, and after dissociation C and O are in opposite threefold sites. The second requirement for rupture of the CO molecule is that the C-0 bond is effectively weakened by the interaction with the metal. This is achieved when the C-O bond stretches across the central Rh atom. In this case there is optimum overlap between the d-electrons of Rh in orbitals, which extend vertically above the surface, and the empty antibonding orbitals of the CO molecule. Hence, the dissociation of CO requires a so-called catalytic ensemble of at least 5 Rh atoms [8,21,22]. 

Atoms form bonds with each other based on a variety of factors determined by their need for electrons. You can depict these structures by drawing Lewis structures to determine polarity and geometry. 

The ability of heavy Group V ligands and transition metals to form stable L M—ER3 (E = P, As, Sb, Bi M = transition metal L = other ligands) is determined by the synergic interplay of their respective donor-acceptor properties, subtly modulated by steric influences. The electronic and steric factors determining the electron availability on the transition metal are determined by the oxidation state, coordination number, orbital geometry and the ligand effects of the other substituents in the coordination sphere. These factors will be discussed later. 

Coordination and geometry are determined by size and bonding factors. 

The Franck-Condon factors determination is of special interest when the two electronic states, involved in the transition exhibit very different geometries. This is especially the case of electronic transition in the valence shell such as n — tt, which induces conjugation change, as well as geometrical change, in the molecular system. This phenomenon was studied in the fluorescence spectra of acetaldehyde and acetone [62,63], and in the phosphorescence spectra of thioacrolein and thioacetaldehyde [64,65] and thioacetone [66]. 

Coordination geometries are determined by ligand steric factors rather than crystal field effects. 

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