Atom confinement localization

Furthermore, the observed absorption bands are often found to have fine structure that is, they are composed of two or more different energies lying very close together. This splitting results from interactions between the spin of the unpaired electron and the spins of one or more nuclei. By analysis of the fine structure (and this is sometimes quite difficult) it is often possible to learn something about the environment of the unpaired electron (s), in particular whether unpaired electron density is spread over a number of atoms or localized on a single atom. Thus, electron spin resonance studies on the peroxodicobalt complex, III, indicate that the one unpaired electron is spread over the area between the two cobalt atoms, rather than being confined to just one of the cobalts. 

The Hamiltonian integrals and the overlap integrals are calculated with atom-centered localized atomic orbitals under a two-center approximation. These atom-centered orbitals are constructed by solving modified KS equations of spherical pseudoatoms with confinement potentials ... 

In molecular orbital theory, electrons occupy orbitals called molecular orbitals that spread throughout the entire molecule. In other words, whereas in the Lewis and valence-bond models of molecular structure the electrons are localized on atoms or between pairs of atoms, in molecular orbital theory all valence electrons are delocalized over the whole molecule, not confined to individual bonds. 

An LVM is a vibration of a light impurity atom that does not propagate in the lattice. The atom motions are confined primarily to the impurity itself and its nearest neighbors, with rapidly decaying vibrational amplitude for more distant host atoms. Usually, the lighter the impurity, the higher the frequency of the vibration and the more localized the mode. 

Substituted ethylenes, with hydrogen atoms replaced by various alkyl groups, have a common feature in their electronic spectra, i.e. an absorption band at ca. 164 — 180 nm. This band is interpreted to show that the delocalization of the electron pair is largely confined to the vicinity of the unsaturated centre, commonly referred to as the C=C double bond. If the de-localization is assumed not to exceed a linear distance of one bond length on either side of the double bond, the electron pair remains in a linear potential box of width 3d, with allowed energy levels of... 

For the driven atom, we developed an accurate approach without any adjustable parameter, and with no other approximation than the confinement of the accessible configuration space to two dimensions. This method was successfully applied for the study of the near resonantly driven frozen planet configuration. Floquet states were found that are well localized in the associated phase space and propagate along near-... 

The magnetic moments of the Ni clusters are dominated by the contribution from surface atoms.48,69 The analysis of Wan et al. indicates that the orbital and spin local moments of cluster atoms with atomic coordination 8 or larger are similar to those in the bulk (p spin 0.55 and orb 0.05 pB) 73 that is, the orbital moment is almost quenched for internal cluster atoms. In contrast, there is a large enhancement of the spin and orbital moments for atoms with coordination less than 8. This enhancement increases with the coordination deficit, and it is larger for the orbital moment. Wan et al.48 also analyzed the quantum confinement effect proposed by Fujima and Yamaguchi,56 i.e., the... 

Many molecules that have several double bonds are much less reactive than might be expected. The reason for this is that the double bonds in these structures cannot be localized unequivocally. Their n orbitals are not confined to the space between the double-bonded atoms, but form a shared, extended Tu-molecular orbital. Structures with this property are referred to as resonance hybrids, because it is impossible to describe their actual bonding structure using standard formulas. One can either use what are known as resonance structures—i. e., idealized configurations in which n electrons are assigned to specific atoms (cf pp. 32 and 66, for example)—or one can use dashed lines as in Fig. B to suggest the extent of the delocalized orbitals. (Details are discussed in chemistry textbooks.)... 

Structural and/or spectroscopic investigations have shown that the local symmetries around the metal atoms in the M(PF3)4 (189,215), M(PF3)5(2), and M(PF3)6 compounds are Td, D3h, and Oh, respectively. Unfortunately theoretical studies on trifluorophosphine complexes are confined to CNDO/2 calculations on Ni(PF3)4, Fe(PF3)5, and Cr(PF3)6 (251). In view of the discussion of relaxation effects and basis set dependences presented in Section II the CNDO/2 results (Table XXVI) should be used only as a qualitative guide to spectral assignment. 

---