Modified free-electron molecular orbital

The Kronig-Penney model, although rather crude, has been used extensively to generate a substantial amount of useful solid-state theory [73]. Simple free-electron models have likewise been used to provide logical descriptions of a variety of molecular systems, by a method known in modified form as the Hiickel Molecular Orbital (HMO) procedure [74]. 

There is much precedent but no particular justification for omitting the core orbitals from the molecular calculation. To determine the consequences of (6) separating the core orbitals and electrons, we divide the set of atomic orbitals into two classes, Xp, core orbitals with energies Ep, and valence orbitals for which we retain the symbol . Unlike the Crrti, the coefficients of the core orbitals are not free for variation to minimize the energy but are determined by requiring that arbitrary admixture of the core orbitals in the valence molecular orbitals do not change the energy of the latter. The final matrix equation (6) is of the order of the number of valence orbitals, but the definitions of the S and H matrix elements are modified ... 

Any molecular entity possessing an unpaired electron. The modifier unpaired is preferred over free in this context. The term free radical is to be restricted to those radicals which do not form parts of radical pairs. Further distinctions are often made, either by the nature of the central atom having the unpaired electron (or atom of highest electron spin density) such as a carbon radical (e.g., -CHs) or whether the unpaired electron is in an orbital having more s character (thus, radical molecular entity in a manuscript, the structure should always be written with a superscript dot or, preferably, a center-spaced bullet (e.g., -OH, -CHs, CF). 

The chemical reactivity of "molecular fragments depends upon the presence of unpaired electrons or the availability of low-lying unfilled orbitals. These electronic properties are also precisely the ones that cause molecular fragments to be of interest in spin resonance or in optical spectroscopic studies. Many of the physical properties of molecular fragments may be obtained very precisely from gas-phase optical spectroscopic measurements, since the line widths are very narrow. For the chemist, however, there is also interest in the question "In what way are the physical properties of free radicals modified by a high density environment ... 

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