FEMO theory

The free electron (FEMO) theory had its origins in work on the conduction electrons of metals in the 1940s, when several workers independently recognised the close analogy between these and the delocalised Jt-electrons of polyene dyes. The method was extended to many other classes of dyes, notably by Kuhn in the 1950s, but it has not found general acceptance for spectroscopic calculations, since it lacks adaptability by simple parameter adjustment. 

Many of the colors of vegetation are due to electronic transitions in conjugated 7c-electron systems. In thefree-electron molecular orbital (FEMO) theory, the electrons in a conjugated molecule are treated as independent particles in a box of length L. Sketch the form of the two occupied orbitals in butadiene predicted by this model and predict the minimum excitation energy of the molecule. The tetraene CH2=CHCH=CHCH=CHCH=CH2 can be treated as a box of length 8R, where R = 140 pm (as in this case,... 

The FEMO theory Problem 10.32) of conjugated molecules is rather crude and better results are obtained with simple Hiickel theory, (a) For a linear conjugated polyene with each of Nq carbon atoms contributing an electron in a 2p orbital, the energies of the resulting % molecular orbitals are given by... 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

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 basic differences between the FEMO and the HMO methods are (1) the FEMO method presumes the electron exists in a space (box) of continuous potential and (2) the FEMO method contains only one parameter, the neighboring distance D, rather than two parameters as in the HMO method. The meaning of the parameter D in terms of measurable quantities is defined more precisely than the integral parameters in the HMO method, and the FEMO model is closer to being an absolute theory with no adjustable parameters. When the existence of the free electron is restricted to the onedimensional carbon-bond skeleton of the molecule, one obtains the free-electron network model. Depending upon the conditions imposed at the branch points of the C skeleton, a very close relationship between the FEMO and HMO methods and results can be demonstrated. 

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