Linear Conjugated n Systems

For a linear conjugated n system the wave function yn will have n-1 nodes. If n 1 is zero or an even integer / would be symmetric with respect to m and antisymmetric with respect of C2. If n-1 is an odd integer fn will be having the symmetry exactly reversed. 

In electrocyclic reactions, a linear conjugated polyenyl system with n p orbitals is in equilibrium with a cyclic system with n — 2 p orbitals and one new a bond (Scheme 1.2). 

Although the Hiickel method has now been supplanted by more complete treatments for theoretical analysis of organic reactions, the pictures of the n orbitals of both linear and cyclic conjugated polyene systems that it provides are correct as to symmetry and the relative energy of the orbitals. In many reactions where the n system is the primary site of reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the reader should develop a familiarity with the qualitative description of the n orbitals of typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the basis for further discussion in Chapters 9 and 11. 

There are several general classes of pericyclic reactions for which orbital symmetry factors determine both the stereochemistry and relative reactivity. The first class that we will consider are electrocyclic reactions. An electrocyclic reaction is defined as the formation of a single bond between the ends of a linear conjugated system of n electrons and the reverse process. An example is the thermal ring opening of cyclobutenes to butadienes ... 

Acetylenes XCCY with n conjugated substituents, X and Y, on both carbon atoms have planar or perpendicular conformations. The substituents can be electron-donating or -accepting. The planar conformers are linear conjugate D-TI-D, D-IT-A, or A-IT-A systems whereas the perpendicular conformers are composed of ri-D and IT-A not in conjugation with each other. The orbital phase is continuous only in the planar conformations of D-TI-A (Scheme 23, cf. Scheme 4). The acetylenes with X=D (OR, NR ) and Y=A (RCO, ROCO) prefer planar conformations. When both substituents are electron-donating or accepting, the phase is discontinuous. The acetylenes then prefer perpendicular conformations. The predicted conformational preference was confirmed by ab initio molecular orbital calculations [32]. Diacetylenic molecules show similar conformational preference, which is, however, reduced as expected [32]. 

The results of the particle in a one-dimensional box problem can be used to describe the delocalized n electrons in (linear) conjugated polyenes. Such an approximation is called the free-electron model. Take the butadiene molecule CH2=CH-CH=CH2 as an example. The four n electrons of this system would fill up the [Pg.16]

There are a variety of methods for the computation of the MOs that interact in the transition states of [4+2]-cycloadditions. The LCAO method (linear combination of atomic orbitals) is often employed, and the basic idea is as follows. The MOs of the -systems of alkenes, conjugated polyenes, or conjugated polyenyl cations, radicals, or anions all are built by so-called linear combinations of 2p AOs. In a somewhat casual formulation, one might say that the MOs of these -systems are constructed with the help of the 2pz AOs. These AOs are centered at the positions of the n C atoms that are part of the -system. LCAO computations describe a conjugated -electron system that extends over n s/ 2-hybridized C atoms by way of n Ji-type MOs. 

The 7i orbitals of longer linear conjugated systems are derived in essentially the same way. The energies and coefficients of the n molecular orbitals for all six systems from an isolated p orbital up to hexatriene are summarised in Fig. 1.35. The viewpoint in this drawing is directly above the p orbitals, which appear therefore to be circular. This is a common simplification, rarely likely to lead to confusion between a p orbital and an s orbital, and we shall use it through much of this book. 

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