Circle mnemonic

The circle mnemonic was de vised by Arthur A Frost a theoretical chemist at North western University... 

The circle mnemonic was devised by Arthur A. Frost, a theoretical chemist at Northwestern University. 

For the special case of cyclic polyenes, (CH) , Frost and Musulin65 obtained the general circle mnemonic for the HMO eigenvalues in the form... 

Figure 3.48 The Frost-Musulin circle mnemonic (Eq. (3.141)) for HMO orbital energies ej of benzene, n = 6.

FIGURE 5.3 The VB structures for singlet and triplet states of C3H3 +, along with the graphical representation of their interaction matrix elements. The spread of the states is easily predicted from the circle mnemonic used in simple Hiickel theory. The expressions for the VB structures (dropping normalization) are deduced from each other by circular permutations 1 , = ab — ab, 1 <1>2 = bc — bc, 3 = ca — cI = ab, 34>2 = bc, 33 = ca. ... 

In a pericyclic reaction the array of basis orbitals of the reacting molecule is cyclic halfway along the reaction coordinate. The array will either be of the Mobius or the Hiickel type. Since the circle mnemonics give the distribution of MO energies... 

Fig. 35. Frost circle mnemonics for Huckel and Mobius energy levels illustrated with those for three and four membered rings...

The circle mnemonic has also been adapted for use with linear systems. A linear polyene with m p orbitals (where tn is an integer >1) is transformed... 

The circle mnemonic leads directly to a familiar result of HMO theory. As illustrated in Figure 4.25, the molecular orbitals of monocyclic conjugated n... 

As is often the case with simple HMO theory, it is the energy levels of the Mobius systems and not the MOs themselves that are of primary interest. Zimmerman developed a circle mnemonic, analogous to the circle mnemonic used with HMO theory in Chapter 4, which provides a shortcut to finding tt e Mobius energy levels. For Mobius MOs, the polygon corresponding to the cyclic molecule is inscribed in the circle of radius 26 with one side down (not with a comer down as was done for Huckel systems). This procedtue is illustrated in Figure 11.104 for both (a) Huckel MOs and (b) Mobius MOs for cyclopropenyl, cyclobutadiene, and benzene. 

Figure 11.101 (page 765), calculate the energy levels of a Mobius cyclopro-penyl system and verify that they are identical with those given by the circle mnemonic (Figure 11.104, page 767). 

The circle mnemonic for determining the tt system molecular orbital diagram for cyclic hydrocarbons at the HOckel level. 

The appropriate correlation diagrams can also be constructed for the Hiickel and Mobius closures in pericyclic processes where the system maintains some symmetry, and the method is capable of extension to include for unsymmetrical systems (Zimmerman, 1966, 1971). The molecular orbital energies of Hiickel- and Mobius-type cyclic polyenes are readily derived from the simple circle mnemonic discussed earlier (see pp. 43 and 55). 

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