Energy levels linear polyenes

The most easily obtained information from such calculations is the relative orderings of the eneigy levels and the atomic coefficients. Solutions are readily available for a number of frequently encountered delocalized systems, which we will illustrate by referring to some typical examples. Consider, first, linear polyenes of formula C H 2 such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such compounds are given by the expression... 

The spectra of linear polyenes are modelled well as one-dimensional free-electron systems. The cyanine dyes are a classical example. They constitute a class of long chain conjugated systems with an even number n of 7r-electrons distributed over an odd number N = n — 1 of chain atoms. The cyanine absorption of longest wavelength corresponds to promotion of an electron from the highest occupied energy level, En/2 to the lowest unoccupied level, such that in terms of a free-electron model... 

V-UV Application First Excited State of Linear Polyenes. The first electronic absorption band of perfect linear aromatic polyenes (CH)X, or perfect polyacetylene shifts to the red (to lower energies) as the molecule becomes longer, and the bond length alternation (BLA) would be zero. This was discussed as the free-electron molecular orbital theory (FEMO) in Section 3.3. If this particle-in-a-box analysis were correct, then as x > oo, the energy-level difference between ground and first excited state would go to zero. This does not happen, however first, because BLA V 0, next, because these linear polyenes do not remain linear, but are distorted from planarity and linearity for x > 6. 

The conjugated polyene systems taking part in pericyclic reactions are linear, so all the tt molecular orbitals of the starting materials have a different energy. The distribution of energy levels is important because it affects the electronic configuration of the starting materials (see Example 6.19) and consequently the course of the reaction. 

The first (bonding) and the last (antibonding) energy levels of the linear polyene chain are reported with respect to Nin Table 3.1 in units of (3. In the last column of the table is the difference in energy between two successive levels. The asymptotic approach of x towards 2 and of % towards -2 is apparent from the numbers given in the table, as well as is the decreasing distance between two successive levels, which tends to zero for N —> oo. 

Table 3.1 Orbital energies (units of /3) of first and last level and energy difference between two successive levels in a linear polyene chain as a function of the number of carbon atoms N...

D Amico KL, Manos C and Christensen RL (1980) Electronic energy levels in a homologous series of unsuhstituted linear polyenes. J Am Chem Soc 102 1777-1782... 

---