FEMO model

More recently a free electron version (PMO-F) of the first-order PMO method has been introduced [32, 33]. According to the branching conditions [34] of the FEMO model three types of resonance integral p are used ... 

Reference should also be made to a superdelocalizability index Sp derived within the frame of the simple FEMO model [35], Goodness of fit of correlations of SfE values with relative rate constants for electrophilic aromatic substitution was found to be comparable with those based on CNDO/2 calculations. 

Essential features of the electronic spectra of linear polyenes have already been mentioned in Chapter 1. The HOMO LUMO transition is shifted to longer wavelengths as the number of conjugated double bonds increases, and this is easy to rationalize in the FEMO model. However, the next transition that is to be expected from the simple MO model is only allowed if the molecule does not have a center of symmetry that is, if it is not in the all-trans configuration. (Cf. Example 1.7.) The absorption spectrum of /S-caro-... 

FEMO model predicts a linear relationship between A , and n. The HMO method yields a similar linear dependence of A, on n, as is also... 

Platt s original perimeter model was a free-electron (FEMO) model based on a one-dimensional circular potential along which the jt electrons can move freely. The orbitals of an electron confined to such a circular ring are given by... 

Translocation of formal charge, 214 Tricyclo(4.2.0.0- [octadiene, 409 Trienes, 112, 366, 444 Trimethinecyanine, FEMO model, 16 Trimelhylene biradical, 225, 227 Trinitrobenzene. DA complex, 125 Triphenyicne. 270, 276 Triphenylmethane dyes. 373, ... 

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. 

Delocalized systems are described in terms of a FEMO model (25-28). 

The FE-NBMO and HMO-NBMO coefficients of it radicals corresponding to a- and 0-substitutions in naphthalene are derived in Chart I to serve as examples. In the case of a-substitution, the FEMO model offers two possibilities for treating the effective potential at a bridge head atom adjacent to a substitution site, that is, either as a joint or a nonjoint atom. In the first case, an appendage of the free-electron pathway is considered to be pointing toward the a-position. In this chapter, these types of atoms in PAH fragments are taken to be joint positions. 

This key information about the butadiene molecule has been obtained at practically no cost from the primitive FEMO model. 

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