Topological type

Conical intersections can be broadly classified in two topological types peaked and sloped [189]. These are sketched in Figure 6. The peaked case is the classical theoretical model from Jahn-Teller and other systems where the minima in the lower surface are either side of the intersection point. As indicated, the dynamics of a system through such an intersection would be expected to move fast from the upper to lower adiabatic surfaces, and not return. In contrast, the sloped form occurs when both states have minima that lie on the same side of the intersection. Here, after crossing from the upper to lower surfaces, recrossing is very likely before relaxation to the ground-state minimum can occur. 

These loops ean be seen in Figures 3-59 a, b, and e for the three major switeh-ing power supply topology types. 

Figure 3-59 The major current loops within the major switching power supply topology types (a) the nonisolated buck converter (h) the nonisolated boost converter (c) the transformer-isolated converter.

The grounds for the three major switehing power supply topology types ean be seen in Figure 3-61. 

The bicyclic 5-5 heterocycles with 1 2-heteroatom orientation cover a range of known topological types the parent aromatic heterocycles for which derivatives are currently known are shown in Figure 1. The chemistry of the heterocycles covered in this chapter is exceptionally diverse and various aspects were discussed in CHEC(1984)... 

Weakness of the theory. Lipscomb s theory based on the assumption of localized three-centre bonds becomes inadequate as the number of hydrogen and boron atoms in molecules grows, increasing dramatically the number of possible resonance structures that should be taken into account when composing the total wave function of the molecule. Inevitably, the number of possible topological types of the molecule also grows with the increase in p and q. 

Number of 3i-electrons Topological type of system Character of system... 

Evans-Dewar-Zimmerman criterion. In accordance with this criterion the pericyclic reactions proceed through the cyclic transition state of the Htickel topological type if it contains AN + 2) jt-electrons, and through the state with anti-Hiickel (Mobius) topology if it contains AN ji-electrons. 

To determine the topological type of a transition state, one should walk around the cycle and count how many times the AO changes its sign. This sign changes occur-... 

Carlucci L., Ciani G., Proserpio D. M. and Rizzato S. Interlinked molecular squares with [Cu(2,2 -bipy)] coners generating a three-dimensional network of unprecedented topological type, J. Chem. Soc., Chem. Chem. Commun. (2001) pp. 1198-1199. 

Figure 1. A. Computer graphic portion of a periodic surface of constant mean curvature, having the same space group and topological type as the Schwarz D minimal surfhce. This surbce, together with an identical displaced copy, would represent the polar/apolar dividing surface in a cubic phase with space group 224 (Pn3m). The two graphs shown would thread the two aqueous subspaces. B. Computer graphic of a portion of the Schwarz D minimal sur ce (mean curvature identically zero). In the 224 cubic phase structure, this sur ce would bisect the surfactant bilayer.

Early in the development of the process, we determined that silicalite, a MFl structure type adsorbent, is suitable for the process. Silicalite is crystalline silica, which has a novel topologic type of tetrahedral framework similar to aluminosilicate molecular sieves. 

A function/of the essential variables, is said to be of finite co-dimension if a small perturbation of/gives rise to only a finite number of topological types. It is in this case that a map / of co-rank k can be embedded in a family of deformations (/, x R), parametrized by q variables which form the control space a R. By definition, q, the dimension of the control space, is the co-dimension of the singularity represented by /. The family of functions (/, / X R R) thus defined, describes the universal unfolding of /, in which the function/itself is the member associated with the origin of control space. In our applications the control space is a subset of the nuclear configuration space. 

Sites of type (e) are occupied between all successive pairs of layers in a-Al2 03 and related structures to which we refer shortly, while occupation of sites (e ) between all successive pairs of layers gives the h.c.p. MX3 structure of trifluorides such as Rhp3. In this structure each MXg octahedron is linked to six others through shared vertices (X atoms) there is no c.c.p. structure of the same topological type, for in the Re03 structure the 0 atoms occupy only three-quarters of the positions of cubic closest packing (see MSIC, p. 61). 

Inorganic acids provide a number of examples of layer structures. The layers in H2Se03, H2Se04, and H2SO4 are all of the same topological type, being based on the simplest 4-connected plane net, but whereas in acids H2XO4 (Fig. 8.11(a))... 

Then the results can be compared with a list of known nets (e.g. more than 1300 nets described in RCSR and the zeolite databases are stored in TOPOS) to find (if any) the topological type, with its given name and ideally most symmetrical structure. 

Hgure 3b. The solution with H = 1.0, same space group and topological type as the Schwarz P minimal surface. 

Figure 4b. Solution with H = 3.8, same space group and topological type is the Schwarz D minimal surface.

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