Maximum overlapping

The overlap in the shifted curves as shown in Fig. 6.15a means that heat transfer is infeasible. At some point this overlap is a maximum. This maximum overlap is added as a hot utility to correct the overlap. The shifted curves now touch at the pinch, as shown in Fig. 6.156. Since the shifted curves just touch, the actual curves are separated by AT ,in at this point (see Fig. 6.156). 

In Fig. 13.7d, the grand composite curve for the reactor and that for the rest of the process are superimposed. To obtain maximum overlap, one of the curves must be taken as a mirror image. It can be seen in Fig. 13.7d that the reactor is appropriately placed relative to the rest of the process. Had the reactor not been appropriately placed, it would have been extremely... 

Figure Bl.10.10. Schematic diagram of the effect of detector view angles on coincidence rate. The view angles of two detectors are shown along with the common view angle. Maximum signal collection efficiency is achieved when the individual view angles have the maximum overlap and when the overlap coincides with the maximum density of the incident beam.

An initial assumption is that the reaction takes place with maximum overlap between the HOMO on one molecule and the LUMO on the other. The HOMO ofphenylbutadiene has most density on the terminal carbon atom. 

It is apparent that Corey s rule requires modification when strong steric opposition to axial attack exists. In an attempt to unify the conflicting views, Valls has suggested that Corey s principle of preferred axial attack, which ensures maximum overlap, be extended. 

All atoms taking part in the resonance, that is, covered by delocalized electrons, must lie in a plane or nearly so (see p. 42). This, of course, does not apply to atoms that have the same bonding in all the canonical forms. The reason for planarity is maximum overlap of the p orbitals. 

A basis set ofhybrid AOs,having o, tt or n character, is prepared by the Slater s,p valence set according to the maximum overlap criterion [31,46]. An extension to d orbitals is in progress. 

Figure 16.15 The utility target can be determined from the maximum overlap between the shifted composite curves.

It is thus evident that the reaction path is controlled by the frontier-orbital interaction. The position of reaction will be determined by the rule of maximum overlapping of frontier orbitals, that is, HO and LU MO s of the two reacting molecules. Sometimes SO takes the place of HO or LU in radicals or excited molecules. Hence, the general orientation principle would be as follows ... 

This reflects the maximum overlapping principle between HO and LU. 

Theoretical considerations in the same fashion enable predication of the possible configuration of the transition state. Eq. (3.25 b) for the multicentre interaction is utilized. Hoffmann and Woodward 136> used such methods to explain the endo-exo selectivity of the Diels-Alder reaction (Fig. 7.28). The maximum overlapping criteria of the Alder rule is in this case valid. The prevalence of the endo-addition is experimentally known 137>. 

Localized bonding orbitals are then constructed from a linear combination of the orbital on each of the paired atoms. To do this we use the principle of maximum overlap, which states... 

Figure 3.13 shows approximate representations of the 2px and 2p orbitals. To construct the two bonding orbitals b] and b2 we place the H atoms along the directions of the 2p and 2pv orbitals of the O atom to give maximum overlap of a Is orbital of H with the 2p, and 2py 0 orbitals (Figure 3.13). This bonding model implies a bond angle of 90° for the water molecule, which is not in very good agreement with the observed angle of 104.5°.

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

Maximum overlap between the p orbitals of a k bond occurs when the axes of the... 

Therefore, in the final analysis, the quadruple bond consists of one a bond, two it bonds, and one S bond. The configuration in which the Cl atoms are in eclipsed positions provides maximum overlap. From the rather intuitive analysis provided here, it is possible to arrive at a qualitative molecular orbital diagram like that shown in Figure 21.23 to describe the Re-Re bond. 

Although structures involving methyl groups bonded simultaneously to two carbon atoms by means of an overlap between the hydrogen orbitals and the />-orbitals of the carbon atoms may be readily enough assimilated, the state of structural theory is such that most of the cyclic intermediate or transition state structures are dubbed non-classical. In many cases they are best depicted by molecular orbitals, usually by diagramming the component atomic orbitals in the best position for overlap. Since maximum overlap of the component atomic orbitals imposes certain geometric requirements, pre-... 

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