Planarity and Nonplanarity

It should be made clear that the geometrical nonplanarity of helicenic polyhexes is not taken into account when the isomorphic systems of this category are enumerated and when symmetry groups are attributed to these systems. It has been ascertained, for instance, that all 

In (a) and (b) the coiled structure of [10]hdicene is suggested it gives rise to two enantiomorphic forms. However, these structures represent one system of symmetry. In (c) this symmetry is accentuated. Considerations of this kind apply also to primitive corohelicenes (and additions to such systems). The above principles have been followed in practically all works on enumerations of polyhexes cf., e.g. Cyvin BN, BrunvoU and Cyvin (1992b) with references cited therein. However, there is a notable exception described in the foUovdng. 

It remains to treat graph-theoretically nonplanar polyhexes. We shall not attempt to give any systematic classification of the variety of these systems, but present some examples in the next section. 

---

Cyclopentane is nonplanar, and the two minimum-energy geometries are the envelope and half-chair. In the envelope conformation, one carbon atom is displaced from the plane of the other four. In the half-chair conformation, three carbons are coplanar, vdth one of the remaining two being above the plane and the other below. The energy differences between the conformers are very small, and interconversion is rapid. All of the carbon atoms r idly move through planar and nonplanar positions. The process is called pseudorotation. 

P450s of gene family 2 (CYP 2) are more catholic, and can metabolize both planar and nonplanar PCBs. 

The Franck-Condon question is also an issue in diradical studies. It is particularly relevant in nonrigid systems, such as trimethylenemethane (TMM) and tetramethyleneethylene (TME), °° in which neutral and/or anion states can be planar or nonplanar. Thus, transitions can occur from planar anions to nonplanar neutral states, or from nonplanar anions to planar neutrals. In these cases, the energy differences between the planar and nonplanar states have generally been estimated by using quality electronic structure calculations. 

Figure 8.9 Rotomeric equilibrium between planar and nonplanar form of 2-(2 -hydroxyphenyl)benzotriazole UVAs. After DeBillis et al. [336]. Reprinted with permission from A.D. DeBellis et al., ACS Symposium Series, 805, 453-467. Copyright (2002), American Chemical Society...

CNDO/2 and extended Huckel calculations 74> of 13 (X = S) revealed a small difference in energy between the planar and nonplanar structure, both with bond alternation. These results can be translated into the valence bond structure corresponding to a cyclic thioether. 

Feltz, K.P., D.E. Tillitt, R.W. Gale, and PH. Peterman. 1995. Automated HPLC fractionation of PCDDs and PCDFs and planar and nonplanar PCBs on C18-dispersed PX-21 carbon. Environ. Sci. Technol. 29 709-718. 

Quantum chemical calculations on different levels have been reported for 2//-1,2,3-diazaphospholes (G) <83X1507), for 4,6-diamino-l,3,5-triaza-2-phosphapentalenes derived from 1,3,2-diazaphospholes (I) <86CB3213), for the tetrazaphospholium ion (S) <93CB1513), for 1//-1,2,3-azadiphosphole (U) <89NJC309), and for l//-l,2,3-benzazadiphosphole <93PS(76)45). Planar and nonplanar structures of 2/7-1,3,2-diazaphosphole and its 2-boryl derivative as well as of 4//-1,2,4-diazaphosphole and its 4-boryl and 3,5-diboryl derivatives are compared by correlated ab initio calculations <95JPC586). 

Planar and nonplanar polychlorinated biphenyls (Fig. 5.2) differ in the type of induction they will cause. Thus, 3, 3, 4, 4, 5, 5 -hexachlorobiphenyl is a planar molecule, which is an inducer of the polycyclic hydrocarbon type. 2, 2, 4, 4, 6, 6 -Hexachlorobiphenyl is a nonplanar molecule due to the steric hindrance between the chlorine atoms in positions 2 and 6 and is a phenobarbital type of inducer. The variety and type of inducing agents are shown in Table 5.21. Some compounds may indeed be mixed types of inducers, and thus mixtures of planar and nonplanar polychlorinated biphenyls are found to act as inducers of both the polycyclic and phenobarbital type. 

Theoretical investigation of the reaction between SiH2 and CO found a weakly bound structure, pyramidal at Si, with a nonlinear array of the heavy atoms that corresponds to lone pair donation from the carbon and very little backbonding249. The addition is predicted to be exothermic by only 16 kcalmol-1. Similar results have been reported, comparing the energies of planar and nonplanar adducts in which CO was coordinated to H2Si at C and O, respectively250. 

In this section, the current-potential curves of multi-electron transfer electrode reactions (with special emphasis on the case of a two-electron transfer process or EE mechanism) are analyzed for CSCV and CV. As in the case of single and double pulse potential techniques (discussed in Sects. 3.3 and 4.4, respectively), the equidiffusivity of all electro-active species is assumed, which avoids the consideration of the influence of comproportionation/disproportionation kinetics on the current corresponding to reversible electron transfers. A general treatment is presented and particular situations corresponding to planar and nonplanar diffusion and microelectrodes are discussed later. 

PGC sorbents have even more highly homogeneous hydrophobic surfaces than GCB sorbents. PGCs are macroporous materials composed of flat, two-dimensional layers of carbon atoms arranged in graphitic structure. The flat, homogeneous surface of PGC arranged in layers of carbons with delocalized n electrons makes it uniquely capable of selective fractionation between planar and nonplanar analytes such as the polychlorinated biphenyls [92,94,95],... 

Calculations at the MP2/6-31G07) level have indicated that planar and nonplanar conformers of thioxanthone differ in energy by less than 1 kcalmol-1 the dihedral angle of the latter is 173.3°. Computed and experimental ionization potentials and absorption spectra suggest contributions from both conformers and a dynamic model involving a butterfly-like motion is proposed <2006JPH(179)298>. 

There is some imbalance in studying and describing those two phenomena. In spite of that, both of them were first predicted computationally [11, 12] only nonplanarity of amino- group had been confirmed experimentally [13] and attracted considerable attention in the literature (see, for example [14, 15]). In case of conformational flexibility of DNA bases, only indirect experimental evidences have been revealed [16-18], Therefore, in this review, we discuss in detail the current status of investigations on the ability of pyrimidine ring of DNA bases to fluctuate between planar and nonplanar states. 

Build a model of cyclobutane. Examine the various types of strain present in the planar and nonplanar geometries. 

A comparison between a planarized and nonplanarized surface topography is shown in Fig. 1.2. By meeting the depth of focus requirement for the photolithographic step, CMP eliminated several yield-related issues such as missing contacts, undesired current leaks, and electromigrations [11-19]. 

Soc., 113, 4077 (1991). Relationships Between Structural Parameters and Raman Frequencies for Some Planar and Nonplanar Nickel(II) Porphyrins. 

RDF descriptors provide further valuable information, such as about bond distances, ring types, planar and nonplanar systems, and atom types. This is a valuable consideration for computer-assisted descriptor elucidation. 

Moreover, the RDF vectorial descriptor is interpretable by using simple rules and, thus, it provides a possibility of —> reversible decoding. Besides information about distribution of interatomic distances in the entire molecule, the RDF vector provides further valuable information for example, about bond distances, ring types, planar and nonplanar systems, and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

J. H. Chung, W. Zheng, T. J. Hatch, and H. O. Jacobs, Programmable reconfigurable self-assembly Parallel heterogeneous integration of chip-scale components on planar and nonplanar surfaces. J MEMS 15 p. 457-464 (2006). 

Table 13. Raman frequencies (in cm ) of the structure sensitive marker lines of various planar and nonplanar porphyrins (Numbers in parentheses for polycrystalline samples)...

---