Volume delocalization

Another characteristic property of the electron density of 1 is its relatively high value at the centre e of the ring (more than 80% of that at the CC bond critical point). Density is smeared out over the ring surface and concentrated at its centre because of the occupation of the w0 -orbital (MO 8, 3a(, Figure 6), which has the character of a surface orbital . Cremer and Kraka9, n 13 have termed this phenomenon surface delocalization of electrons, to be distinguished from ribbon delocalization and volume delocalization of electrons (Figure 12)12. 

Extension of the concepts of ribbon and surface delocalization of electrons to three-dimensions leads to volume delocalization and covers cases of radial aromaticity and three-dimensional (3D) aromaticity . As we will show later the most convicing example of radial aromaticity, namely the l,3-dehydro-5,7-adamantanediyl cation (Figure 2), is actually an example of homoradial aromaticity. Also, there exist several examples of homo-3D aromaticity that are normally listed under 3D-aromaticity (for an example, see Figure 2). Finally, a number of examples have been investigated that can be classified as homoheteroaromatic systems (Figure 2). It may be only a matter of time until the first molecule with homospherical aromaticity has been synthesized and investigated. 

Molecules have some occupied and some unoccupied orbitals. There occur diverse interactions (Scheme 1) when molecules undergo reactions. According to the frontier orbital theory (Sect 3 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume), the HOMO d) of an electron donor (D) and the LUMO (fl ) of an electron acceptor (A) play a predominant role in the chemical reactions (delocalization band in Scheme 2). The electron configuration D A where one electron transfers from dio a significantly mixes into the ground configuration DA where... 

Thermal dimerization of ethylene to cyclobutane is forbidden by orbital symmetry (Sect 3.5 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). The activation barrier is high E =44 kcal mof ) [9]. Cyclobutane cannot be prepared on a preparative scale by the dimerization of ethylenes despite a favorable reaction enthalpy (AH = -19 kcal mol" ). Thermal reactions between alkenes usually proceed via diradical intermediates [10-12]. The process of the diradical formation is the most favored by the HOMO-LUMO interaction (Scheme 25b in chapter Elements of a Chemical Orbital Theory ). The intervention of the diradical intermediates impfies loss of stereochemical integrity. This is a characteric feature of the thermal reactions between alkenes in the delocalization band of the mechanistic spectrum. 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

This almost distance independent hole transfer over (A T)n sequences where adenines are charge carriers is very surprising. Maybe the transfer of a positive charge between adenines of an (A T)n sequence is extremely fast, as recent calculations of M.D. Sevilla predicted [20], One could also speculate that the positive charge is delocalized over more than one A T base pair so that polaron hopping, which is discussed in this volume by G.B. Schuster as well as E.N. Conwell, might make the hole transport in oxidized (A T)n sequences very efficient. 

Since the tensor D is strictly proportional to the inverse cube of the distance between the unpaired electrons for two spin systems and is regarded as a measure of the inverse volume of the delocalized spins in higher-spin systems, the absolute Z)-values become smaller as S increases. Since the epr spectral width is approximated by 2D, it is customarily the case that the g = 2 region becomes crowded with spectral peaks with increasing S. 

For two and three dimensions, it provides a crude but useful picture for electronic states on surfaces or in crystals, respectively. Free motion within a spherical volume gives rise to eigenfunctions that are used in nuclear physics to describe the motions of neutrons and protons in nuclei. In the so-called shell model of nuclei, the neutrons and protons fill separate s, p, d, etc orbitals with each type of nucleon forced to obey the Pauli principle. These orbitals are not the same in their radial shapes as the s, p, d, etc orbitals of atoms because, in atoms, there is an additional radial potential V(r) = -Ze2/r present. However, their angular shapes are the same as in atomic structure because, in both cases, the potential is independent of 0 and (f>. This same spherical box model has been used to describe the orbitals of valence electrons in clusters of mono-valent metal atoms such as Csn, Cu , Na and their positive and negative ions. Because of the metallic nature of these species, their valence electrons are sufficiently delocalized to render this simple model rather effective (see T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange, J. Phys. Chem. 95, 6421 (1991)). 

The triplet state of NH is 36 kcal/mol lower in energy than the singlet state. The triplet state is favored because, on the average, electrons with parallel spin spend less time in proximity with each other than electrons with antiparallel spin. Consequently, the Coulombic electron-electron repulsion in the triplet state is less severe than in the singlet state (cf. Borden, Chapter 22 in this volume.) As we will see in vinyl- and phenylnitrene, delocalization of an unpaired electron by conjugation dramatically stabihzes the singlet relative to the triplet states of nitrenes. 

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