Dewar-Zimmerman rule

The Dewar-Zimmerman rule specifies that the reaction is allowed in the ground state if ... 

The Woodward-Hoffmann rule states that the reaction is allowed in the ground state if m + u is odd. The Dewar-Zimmerman rule states that the reaction is forbidden in the ground state if... 

Give examples of possible reactions of each of the following types, and determine whether each is forbidden or allowed in the ground state, using both the Woodward-Hoffmann and the Dewar-Zimmerman rules. 

Cheletropic reactions are cyclizations - or the reverse fragmentations - of conjugated systems in which the two newly made o bonds terminate on the same atom. However, a cheletropic reaction is neither a cycloaddition nor a cycloreversion. The reason is that the chelating atom uses two AOs whereas in cycloadditions, each atom uses one and only one AO. Therefore, Dewar-Zimmerman rules cannot apply to cheletropic reactions. Selection rules must be derived using either FO theory or correlation diagrams 38 The conjugated fragment39 of 4n + 2 electron systems reacts in a disrotarory (conrotarory) mode in linear (nonlinear) reactions. In 4n electron systems, it reacts in a disrotarory (conrotarory) mode in nonlinear (linear) reactions. 

It is much simpler, however, to use Dewar-Zimmerman rules or PMO to treat these systems. 

Cation radicals react with a variety of nucleophiles. Substitution often occurs, but there are many examples in which electron transfer occurs either entirely or in part. Eberson (1975) has provided a theoretical explanation for a number of reactions, based 5n the Dewar-Zimmerman rules. 

Theoretical Aspects, Calcidatioiis and Physical Data.—Probably the most significant paper on theory this year is the one in which Day puts the flesh on the bones of the tacit assumptions that many chemists have been making, namely that the Wood-ward-Hoffmann rules for pericyclic reactions and the Dewar-Zimmerman rules for... 

Euler-Lagrange equations, electron nuclear dynamics (END), time-dependent variational principle (TDVP) basic ansatz, 330-333 free electrons, 333-334 Evans-Dewar-Zimmerman approach, phase-change rule, 435... 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offiilminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4-6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

COMPARISON OF THE WOODWARD-HOFFMANN AND DEWAR-ZIMMERMAN PERICYCLIC SELECTION RULES... 

In the aromatic transition state approach, the basic criterion was that a reaction is allowed in the ground state if and only if there occurs in the transition state aromatic stabilization. This criterion led to the Dewar-Zimmerman selection rule (Equation 11.36), where p. i. = 0 signifies an even number of phase inversions, p. i. = 1 signifies an odd number of phase inversions, and N is the total number of electrons. 

Several very popular and successful interpretations of electronic reaction mechanisms employ orbital models, for example, the Woodward-Hoffmann rules, Fukui s frontier orbital theory, " the Dewar-Zimmerman treatment. 

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogen shift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-HQckel system (with n = 1), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase. 

Using the nomenclature of Dewar and Zimmerman, the transition state for the 2, + 2S cycloaddition is a 4n Hiickel system (zero nodes) and is antiaromatic in the ground state and aromatic in the excited state. The transition state for the 2S + 20 cycloaddition is a 4n Mobius system (one node) and is aromatic in the ground state and antiaromatic in the excited state (see Chapter 8). The general cycloaddition rules are given in Table 9.5. 

Dewar [16] and Zimmerman [17] proposed selection rules based on the cyclic transition state. A Hiickel transition state is one in which there are zero or an even number of phase transitions perpendicular to the plane of the reaction and is the allowed condition for thermal cases in which there are 4n-n2 electrons. These reactions occur in a suprafacial manner. A Mobius transition state, in which there is one or an odd number of phase transitions perpendicular to the plane of the reaction, predicts thermally allowed reactions when there are An electrons involved. These reactions have an antarafacial component. The advantage of this transition state analysis is that all types of concerted reactions are covered by basically one selection rule. If a continuous loop of overlap through all the... 

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