Localized one-electron states

Chemically speaking there is little to say. Canonical Hartree-Fock molecular orbitals leave no place for classical chemical concepts such as bonds between atoms or groups, lone pairs, resonance hybrids, etc. However, chemists still utilize these concepts because they are extremely useful in correlating and understanding chemical facts. Even when one manages to localize the canonical molecular orbitals (which is not always straightforward) in regions such that they could be associated with lone pairs or individual chemical bonds, it is important to bear in mind that the orbitals represent localized one-electron states, and not a two-electron chemical bond between atoms or a lone pair of electrons, as will be discussed further. 

If the localized electron tunnels out through the barrier (state 1 in Fig. 12 b) a certain amount of f-f overlapping is present. States like 1 in Fig. 12 b are called sometimes resonant states or "virtually bound" states. In contrast with case 2 in Fig. 12b, which we may call of full localization , the wave function of a resonant state does not die out rapidly, but keeps a finite amplitude in the crystal, even far away from the core. For this reason, overlapping may take place with adjacent atoms and a band may be built as in ii. (If the band formed is a very narrow band, sometimes the names of localized state or of resonance band are employed, too. Attention is drawn, however, that in this case one refers to a many-electron, many-atoms wave function of itinerant character in the sense of band theory whereas in the case of resonant states one refers to a one-electron state, bound to the central potential of the core (see Chap. F)). 

According to it, the bond types known from theoretical chemistry are placed in relation to characteristics of the electronic structure of different classes of chemical species, and the delocalization pattern of the involved one-electron states is taken to be crucial. The first comment on this classification is based upon our vision of the electronic structure of organic compounds. In the Table these bonds are termed as valence ones and the corresponding MOs are considered to be localized. If the true MO picture based on the HFR model of electronic structure is employed, the corresponding MOs in CH4 or NII4 are in fact delocalized at least by symmetry the... 

Abstract. In frameworks of semi-empirical PM3-basis equilibrium configurations, total energy, heat of formation, energies of HOMO and LUMO orbitals, density of one-electron states (DOS) of open (12,0) carbon nanotubes with local vacancies and defects are obtained. 

It is often said that the band description of one-electron states is in terms of itinerant electrons and is mainly useful for solids, while the bond description looks at localized electrons and is appropriate for molecules. Since our subject concerns interactions between molecules and solid surfaces, we need to establish our vocabulary clearly. We will consider an electron as localized if it cannot participate in (electrical) transport phenomena otherwise it is itinerant. This is not the same as describing the one-electron orbitals by localized functions (such as the Wannier functions, introduced below) respectively by extended functions (such as the Bloch functions, see below). Nor is it simply a distinction between tight-binding orbitals constructed from (so-called localized) J-orbitals as opposed to those derived from (so-called extended) -orbitals. 

There is one localized,unpaired spin per TCNQ molecule. This presumably follows from 1. if the disorder is sufficiently great as to give complete localization of the one-electron states to a single site or if one has a Mott-Hubbard metal to insulator transition and is in the strong-coup ling limit. However, as we shall see, one does not necessarily have one unpaired spin per site when the disorder potential and interaction are comparable. 

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