Spatial overlaps

Figure 6.12 Formation of a bonding 3-centre B-H-B orbital j1/ from an sp hybrid orbital on each of B(l), B(2) and the H Is orbital, (KH). The 3 AOs have similar energy and appreciable spatial overlap, but only the combination Vr(Bl)-l-Vr(B2) has the correct symmetry to combine linearly with i/r(H).

In systems such as [A... A ]+ where an electron (or a hole) hesitates or oscillates between two equivalent positions on subsystems A or A, symme breakings may occur when the effective transfer integral between the two sites is weak. Hiis will be the case when A and A are far apart, when they are bridged by an "insulating" ligand, or when the two localized MOs concerned by the electron transfer have a very we spatial overlap. 

Figure 2 Spatial overlap of low energy conformers of H-Hat-D-O rn-Aic-Glu-NH2 (heavy lines) with proposed models of the p-receptor-bound conformation (light lines) based on conformational analysis of H-Tyr-D-0 rn-Phe-As p-NH2 [24] (left panel) and H-Tyr-Pro-Phe(NMe)-D-Pro-NH2 (PL017) [29] (right panel). 

Obviously, it is of the utmost importance that the three input channels spatially overlap tightly, both in lateral and in axial direction. Co-registration (i.e., the precise, pixel-by-pixel correspondence of... 

The above analysis suggests that aromaticity or antiaromaticity in any system is the result of sequential aromatic and antiaromatic unions. The union which dominates and, thus, determines whether the system will be aromatic or antiaromatic, is the one which involves the greatest spatial overlap between the fragments. Accordingly, one can simplify the analysis by focusing exactly on this crucial union. However, exceptions to this generalization do exist and arise in a very predictable fashion. 

We can then say that planar cyclooctatetraene is antiaromatic because two antiaromatic unions dominate a single aromatic union. Alternatively, we can say that cyclooctatetraene is antiaromatic because the crucial union, Le. the union involving the greatest spatial overlap, is the (A + B + C) + D union which is antiaromatic. 

The nonbonded interactions of the fluorine 2s lone pairs can be neglected because F2s—F2s spatial overlap is poor. Even more important, the energy of the F2s orbital is extremely low so that interaction with the sigma vacant MO s of the coupling unit is negligible. 

A similar analysis can be given for the pi nonbonded interaction between the methylene group and the fluorine 2pz lone pair. However, due to much poorer spatial overlap, this interaction will be of limited significance compared to the sigma nonbonded interaction. 

The toxin content of Bay of Fundy zooplankton has reached high levels in most years since 1977 (Table IV). Yet, curiously, herring kills have not been observed in years other than 1976 and 1979. The occurrence of kills may depend upon the temporal and spatial overlapping of dense Gonyaulax blooms, highly toxic zooplankton, and actively feeding herring. 

In the typical setup, excitation light is provided by a pulsed (e.g., nanosecond) laser (emitting in the visible range, e.g., at 532 nm, if Mb is investigated), while the probe is delivered by a continuous-wave (cw) laser. The two beams are spatially overlapped in the sample, and the temporal changes in the optical properties (such as optical absorption or frequency shift) that follow the passage of the pump pulse are registered by a detector with short response time (relative to time scale of the processes monitored), such as a fast photodiode. 

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