Sextet formula

A simple relation between regioselectivity of maleic anhydride addition to benzenoid hydrocarbons and Claris n sextet formulae has already previously been observed [65]. In cases where the addition can lead to several isomeric adducts, the adduct whose Clar formula has the largest number of inherent it sextets is always the only one to be formed. Scheme 6 gives some examples. A necessary and, usually, also adequate condition for the endocyclic Diels-Alder reaction of benzenoid hydrocarbons with maleic anhydride is that at least one n sextet be gained by the addition, i.e. that the number of sextets in the product be at least one more than in the reactant. 

Bamberger 1891-1893 Pre-sextet formulas for five-membered heterocycles... 

In the first step of the actual Ar-SE reaction, a substituted cyclohexadienyl cation is formed from the electrophile and the aromatic compound. This cation and its derivatives are generally referred to as a cr or Wheland complex. Wheland complexes are described in the language of the VB method by superpositioning mentally at least three carbenium ion resonance forms (Figure 5.1). In the following, these resonance forms are referred to briefly as sextet formulas. There is an additional resonance form for each substituent, which can stabilize the positive charge of the Wheland complex by a +M effect (see Section 5.1.3). This resonance form is an all-octet formula. 

Figure 4. Clar aromatic sextet formulas of anthracene...

Benzenoid hydrocarbons can be represented by ordinary graphs too. But the different Clar aromatic sextet formulas of the same conjugated molecule are presented one and the same graph. Figure 7 shows one and the same graph representation of two Clar aromatic sextet formulas of anthracene. 

Hypergraphs appear to be convenient for a description of Clar aromatic sextet formulas of conjugated molecules. In this case hyperedges correspond to aromatic sextets. Figure 18 shows two different... 

The results of comparative analysis of the invariants values for fully-benzenoid hydrocarbons (fully-benzenoid systems) are presented in this section [35]. Benzenoid systems in which there are no double bonds in the Clar aromatic sextet formulas, i.e., in which all tt—electrons belong to aromatic sextets, are called fully-benzenoid [32]. One example of fully-benzenoid system is shown in Figure 26. 

Figure 26. Clar aromatic sextet formula of dibenzo[/, op]naphthacene...

For the class of the 16 benzenoid systems with two or three aromatic sextets (hyperedges), which are not fully-benzenoid, but which have a unique Clar aromatic sextet formula we found... 

The definition of a Clar resonant sextet formula (of a benzendd hydrocarbon) can be found elsewhere [63,142]. Let G be the molecular graph of a benzenmd hydrocarbon and let s(G,k) be the number of Clar formulas of G with k sextets. 

The sextet formula for tetracene, for pentacene and for hexacene are respectively depicted in Fig.7 these structures correspond to the properties of the hydrocarbons. Anthracene is colourless but rather reactive and easily adds maleic anhydride tetracene is orange yellow and more reactive pentacene is violet and so reactive that it must be prepared under CO. ... 

The circle m a hexagon symbol was first suggested by the British chemist Sir Robert Robinson to represent what he called the aromatic sextet —the six delocalized TT electrons of the three double bonds Robinson s symbol is a convenient time saving shorthand device but Kekule type formulas are better for counting and keeping track of electrons especially m chemical reactions... 

The vast majority of aromatic compounds have a closed loop of six electrons in a ring (the aromatic sextet), and we consider these compounds first. It is noted that a formula periodic table for the benzenoid polyaromatic hydrocarbons has been developed. ... 

In principle, recently published19 rules for writing structural formulas have been adhered to in the present review with the one exception that a full circle in the cycle is used to denote not only a 7r-electron sextet but any number of 7r-electrons consistent with the Hiickel rule in general. 

Substituent increments are obtained as usual by subtracting the reference shifts of naphthalene (C-1,4,5,8 127.7 C-2,3,6,7 125.6 C-9,10 133.3 ppm) from the individual data of C-l to C-10 in the substituted derivatives given in Table 4.55. It turns out that comparable Zx, Zmthn, Zmrta, and Zpara increments in naphthalene and benzene differ substantially in magnitude, as exemplified in Table 4.56. In 1-substituted naphthalenes, C-9 increments are attenuated in favor of C-2 relative to comparable ortho effects known from benzene C-3 and C-1 in 2-substituted naphthalenes behave correspondingly (Table 4.56). This can be explained by the cannonical formulae c, which do not contribute so much to the actual molecular state due to disrupted % electron sextets. Full inter-... 

Simple relationships between molecular topology and reactivity can also be derived from the Clar formulae [20] of benzenoid hydrocarbons. For example, in a series of isomeric hydrocarbons the system with the largest number of inherent 7t-sextets is always the least reactive one. Due to the correspondence between number of 7i-sextets in Clar formulae and number of 120° angles [21] in the dualist graphs [22] of benzenoid hydrocarbons a similar relation holds for the dualist graphs. 

Many researchers tried to explain the secret of the Clar s aromatic sextet theory, or hypothesis from quantum-chemical points of view. However, those trials have been failing until the graph and combinatorial theories came to be applied to this challenging problem [9,10]. In the following discussion it will be shown how various techniques and concepts of the graph theory are useful for realizing and formulating not only the fantastic theory of Clar but also the mathematical beauty of the structural formula of aromatic hydrocarbons. 

In the theory known nowadays as the Clar theory of the aromatic sextet [12] a benzenoid system is represented by a Clar structure which is obtained by drawing circles in some of the hexagons of the corresponding benzenoid graph. These circles represent the aromatic sextets in the hydrocarbon. We consider here only Clar structures containing the maximum number of circles which are some times referred to as proper (or correct) Clar formulas. The rules for constructing such Clar structures are as follows [13]. 

Hosoyaand Yamaguchi generalized Clar structures by removing the restriction that Clar structures have to have the maximal number of rearomatic sextets. We will refer to these as HY-Clar structures, or briefly HY-structures (HY for Hosoya-Yamaguchi) in order to differentiate them from other generalizations of Clar structures that will be discussed later. In Fig. 13 we show the set of generalized HY-Clar formulas for... 

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