Mutual conjugation

A +E substituent R and a — E substituent T can conjugate mutually through an odd alternant hydrocarbon radical S if R, T are both attached to active atoms in S. 

This is written in terms of zt-, the moduli of the roots Zk-, since the roots are either real or come in mutually complex conjugate pairs. In any case, this constant term can be absorbed in the polynomial P t) in Eq. (15).]... 

Some liquids are practically immiscible e.g., water and mercury), whilst others e.g., water and ethyl alcohol or acetone) mix with one another in all proportions. Many examples are known, however, in which the liquids are partially miscible with one another. If, for example, water be added to ether or if ether be added to water and the mixture shaken, solution will take place up to a certain point beyond this point further addition of water on the one hand, or of ether on the other, will result in the formation of two liquid layers, one consisting of a saturated solution of water in ether and the other a saturated solution of ether in water. Two such mutually saturated solutions in equilibrium at a particular temperature are called conjugate solutions. It must be mentioned that there is no essential theoretical difference between liquids of partial and complete miscibility for, as wdll be shown below, the one may pass into the other with change of experimental conditions, such as temperature and, less frequently, of pressure. 

In the second, which belongs to a systematic study of the transmission of substituent effects in heterocyclic systems, Noyce and Forsyth (384-386) showed that for thiazole, as for other simple heterocyclic systems, the rate of solvolysis of substituted hetero-arylethyl chlorides in 80% ethanol could be correlated with a constants of the substituent X only when there is mutual conjugation between X and the reaction center. In the case of thiazole this situation corresponds to l-(2-X-5-thiazolyl)ethyl chlorides (262) and l-(5-X-2-thiazolyl)ethyl chlorides (263). 

The example of COj discussed previously, which has no vibrations which are active in both the Raman and infrared spectra, is an illustration of the Principle of Mutual Exclusion For a centrosymmetric molecule every Raman active vibration is inactive in the infrared and any infrared active vibration is inactive in the Raman spectrum. A centrosymmetric molecule is one which possesses a center of symmetry. A center of symmetry is a point in a molecule about which the atoms are arranged in conjugate pairs. That is, taking the center of inversion as the origin (0, 0, 0), for every atom positioned at (au, yi, z ) there will be an identical atom at (-a ,-, —y%, —z,). A square planar molecule XY4 has a center of symmetry at atom X, whereas a trigonal planar molecule XYS does not possess a center of symmetry. 

The classic example of this group is l-phenyl-3-methyl-5-pyrazolone (12.60), which was mentioned previously. The question of whether this compound and its derivatives react as enols or ketones, which was fervently discussed in former years, is now irrelevant, since it is known that normally only the mutual conjugate base of enol and ketone in the equilibrium (Scheme 12-33) participates in the actual substitution step. 

From the orbital phase theory an outstanding electron-donating (accepting) bond toward both the C-H and C-C bonds is predicted to prefer as long sequential conjugation of mutually antiperiplanar bonds as possible. The electron delocalization... 

The logical continuation of the stepladder strategy outlined above for minimizing the mutual distorsion of adjacent main chain phenylene units was the incorporation of the complete PPP-parent chromophore into the network of a completely planar ladder polymer. The complete flattening of the conjugated 7T-system by bridging of all the subunits should then lead to maximum conjuga-tive interaction. As with the PTHP 11 systems, alkyl or alkoxy side chains should lead to solubilization of the polymers. 

Copulation Sexual union of male and female coitus sexual intercourse also, conjugation between two cells that do not fuse but separate after mutual fertilization. 

B) From the foregoing, it is clear that the Arrhenius or solvents theory cannot work for aprotic solvents most adequate here is the Bransted-Lowry or proton theory, in which an acid is defined as a proton donor and a base as a proton acceptor, and under conditions such that the acid by donating its proton is converted into its conjugate base, and the base by accepting a proton is converted into its conjugate acid. This mutual relationship is illustrated by the following equilibrium reaction ... 

As free proton cannot exist alone in solution, reactions in which a proton is split off from an acid to form a conjugate base cannot occur in an isolated system (in a homogeneous solution although this is possible in electrolysis (Section 5.7.1)). The homogeneous solution must contain another base Bn that accepts a proton from the acid HAr (acid HA is, of course, not conjugate with base Bn). It will be seen that this second base can even be the solvent molecule, provided it has protophilic properties. Acid-base reactions thus depend on the exchange of a proton between an acid and a base that are not mutually conjugate ... 

If an amphiprotic solvent contains an acid and base that are neither mutually conjugate nor are conjugated with the solvent, a protolytic reaction occurs between these dissolved components. Four possible situations can arise. If both the acid and base are strong, then neutralization occurs between the lyonium ions and the lyate ions. If the acid is weak and the base strong, the acid reacts with the lyate ions produced by the strong base. The opposite case is analogous. A weak acid and a weak base exchange protons ... 

If P and Q are both conjugate to the same element W, they are mutually conjugate. This relation can be demonstrated as follows. Given P = S ]WS and 0 = TWT where 5 and T are also members of the croup,... 

The ensemble of elements that are mutually conjugate form a class TJje concept of a class is most easily demonstrated by an example. The multiplication table for the group of matrices defined by Eq. (2) is given in Table 3. With its use the relations... 

Before going on to consider applications of group theory in physical problems, it is necessary to discuss several general properties of irreducible representations. First, suppose that a given group is of order g and that the g operations have been collected into k different classes of mutually conjugate operations. It can be shown that the group Q possesses precisely k nonequivalent irreducible representations, T(1), r(2).r(t>, whose dimen-... 

As there are 6 ir electrons to accommodate—two per orbital—the HOMO will be ip3 (11). To form the C—C a bond on cyclisation, the orbital lobes on the terminal carbon atoms of the conjugated system (C2 and C7—the C atoms carrying the Me substituents) must each rotate through 90° if mutual overlap is to occur (p/sp2— sp3 re-hybridisation must also occur). This necessary rotation could be either (a) both in the same direction—conrotatory (12), or (b) each in opposite directions—disrotatory (13) ... 

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