Geometric constraints

Taylor H and Simons J 1985 Imposition of geometrical constraints on potential energy walking procedures J. Phys. Chem. 89 684... 

Further evidence of the efficacy of the algorithm for locating points of conical intersection is provided in Figure 3, which reports additional points on the 2E 2E intersection seam, detemiined by introducing the geometrical constraint. 

O. Lund, J. Hansen, S. Brunak and J. Bohr, Relationship between protein structure and geometrical constraints. Protein Sci. 5 (1996), 2217-2225. 

For intramolecular D-A rxns, geometric constraints can now reverse the normal regiochemistry of the addition as compared to the intermolecular rxn. 

Richmond, T.J., Richards, EM. Packing of a-helices geometrical constraints and contact areas. /. Mol. Biol. 119 537-555, 1978. 

How do you interpret the values of p and r in these equations Which system is more sensitive to the aryl substituent How would you explain this difference in sensitivity Sketch the resonance, field and hyperconjugative interactions which you believe would contribute to these substituent effects. What, if any, geometric constraints would these interactions place on the ions ... 

To illustrate this theory, we consider a one-component fluid with the interaction between the same species given by Eq. (36). Obviously, the model differs from that described in Sec. (II Bl). In particular, the geometrical constraints, which determine the type of association products in the case of a two-component model, are no longer valid. If we restrict ourselves to the case L < cr/2, only dimers and -mers built up of rigid, regular polygons are possible. 

The properties of flexible polymer chains moving in porous structures, that is, in structures with geometric constraints such as tubes or slits, apart from their Tclevance for various applications such as filtration, gel permeation chromatography, oil recovery, etc., pose an exciting problem of statistical... 

FIG. 15 The projected surface area per unit volume S, divided by the surfactant volume fraction for different structures along the bifurcation line as a function of surfactant volume fraction Note that due to the geometrical constraints this quantity cannot exceed the length of the surfactant a. Here we set a = 1 for convenience. 

Reactions of the metallocene derivatives of molybdenum with pyrazole lead to the mononuclear complexes of the type 22. Structure 22 shows that it cannot be used as a ligand for the preparation of dinuclear complexes owing to geometric constraints [80JOM( 197)291 83JOM(253)53]. In acetone, an unusual complex 23 is formed [83JOM(253)53]. The bidentate ligand is the product of the reaction of pyrazole and acetone. 

Note that both suprafacial and antarafacial cycloadditions are symmetry-allowed. Geometric constraints often make antarafacial reactions difficult, however, because there must be a twisting of the it orbital system in one of the reactants. Thus, suprafacial cycloadditions are the most common for small tt systems. 

In contrast with the thermal [4 + 2] Diels-Alder reaction, the 2 + 2 cycloaddition of two alkenes to yield a cvclobutane can only be observed photo-chemically. The explanation follows from orbital-symmetry arguments. Looking at the ground-state HOMO of one alkene and the LUMO of the second alkene, it s apparent that a thermal 2 + 2 cycloaddition must take place by an antarafacial pathway (Figure 30.10a). Geometric constraints make the antarafacial transition state difficult, however, and so concerted thermal [2 + 2j cycloadditionsare not observed. 

A further example of the importance of this type of stereoelectronic effect is seen in the reactions of /-butoxy radicals with spiro[2,n]alkanes (22) where it is found that hydrogens from the position a- to the cyclopropyl ring arc specifically abstracted. This can be attributed to the favorable overlap of the breaking C-H bond with the cyclopropyl cr bonds.120131 No such specificity is seen with bicyclo[n, 1,0]alkanes (23) where geometric constraints prevent overlap. 

Suggest a synthesis for (29), needed to explore geometrical constraints on Diels-Alder reactions. 

It is not the catalytic activity itself that make zeolites particularly interesting, but the location of the active site within the well-defined geometry of a zeolite. Owing to the geometrical constraints of the zeolite, the selectivity of a chemical reaction can be increased by three mechanisms reactant selectivity, product selectivity, and transition state selectivity. In the case of reactant selectivity, bulky components in the feed do not enter the zeolite and will have no chance to react. When several products are formed within the zeolite, and only some are able to leave the zeolite, or some leave the zeolite more rapidly, we speak about product selectivity. When the geometrical constraints of the active site within the zeolite prohibit the formation of products or transition states leading to certain products, transition state selectivity applies. 

The rotating-disk CVD reactor (Fig. 1) can be used to deposit thin films in the fabrication of microelectronic components. The susceptor on which the deposition occurs is heated (typically around lOOOK) and rotated (speeds around 1000 rpm). A boundary layer is formed as the gas is drawn in a swirling motion across the spinning, heated susceptor. In spite of its three-dimensional nature, a peculiar property of this flow is that, in the absence of buoyant forces and geometrical constraints, the species and temperature gradients normal to the disk are the same everywhere on the disk. Consequently, the deposition is highly uniform - an especially desirable property when the deposition is on a microelectronic substrate. 

In Eq. (12), l,m are the photoelectron partial wave angular momentum and its projection in the molecular frame and v is the projection of the photon angular momentum on the molecular frame. The presence of an alternative primed set l, m, v signifies interference terms between the primed and unprimed partial waves. The parameter ct is the Coulomb phase shift (see Appendix A). The fi are dipole transition amplitudes to the final-state partial wave I, m and contain dynamical information on the photoionization process. In contrast, the Clebsch-Gordan coefficients (CGC) provide geometric constraints that are consequent upon angular momentum considerations. 

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