Localized orbital model

When the electron configurations of the elements were worked out, it became clear that the valence electrons of the period 2 elements must be accommodated in just four orbitals, the 2s and the three 2p orbitals. In the localized orbital model it is assumed that each bond can be described by a localized orbital formed by the overlap of one orbital on each of the bonded atoms. According to this model, therefore, a period 2 element can form bonds with at most four ligands so that electron configurations appeared to provide a justification for the octet rule. 

Both models can be extended. The localized orbital model is improved by allowing for the interaction between the locally excited benzene states and the CT state, and the isoconjugate hydrocarbon model is improved by taking into account the electronegativity change upon the replacement of the C atom in the benzyl anion by an N atom in aniline. Good agreement with experiment is obtained in both cases. 

Both models are useful, but the localized orbital model has the advantage that it is more easily extended to more complicated molecules. The Cl... 

Light, circularly polaridzed, 41, 139-44. 154, 158, 162-63 elUplically polarized, 139-43 linearly polarized, 1-3, 5, 38-41, 139-41 Light-gathering antennae, 473 Linear momentum operator. 22. 24, 56, 145 Line-shape function, 156 Liquid crystals, 272 Localized orbital model, 115-16... 

Szostak et al 52 have made calculations of the /Miyperpolarizability of 2-nitroaniline and 2 nitrophenol and for their radical ions and suggest that the latter might have a role in the nonlinear optical response. A localized orbital model of the response of the barium titanate crystal has been developed by Khatib et al 253 Lacroix et al.254 have performed INDO calculations on crystal structures for a highly polarizable zwitterionic merocyanine dye. 

Head J D and Silva S J 1996 A localized orbitals based embedded cluster procedure for modeling chemisorption on large finite clusters and infinitely extended surfaces J. Chem. Phys. 104 3244... 

Molecular orbitals are not unique. The same exact wave function could be expressed an infinite number of ways with different, but equivalent orbitals. Two commonly used sets of orbitals are localized orbitals and symmetry-adapted orbitals (also called canonical orbitals). Localized orbitals are sometimes used because they look very much like a chemist s qualitative models of molecular bonds, lone-pair electrons, core electrons, and the like. Symmetry-adapted orbitals are more commonly used because they allow the calculation to be executed much more quickly for high-symmetry molecules. Localized orbitals can give the fastest calculations for very large molecules without symmetry due to many long-distance interactions becoming negligible. 

We cannot generate a tetrahedron by simple overlap of atomic orbitals, because atomic orbitals do not point toward the comers of a tetrahedron. In this section, we present a modification of the localized bond model that accounts for tetrahedral geometry and several other common molecular shapes. 

The molecular orbital model developed in this section is more elaborate than the localized bonds described earlier in this chapter. Is this more complicated model necessary to give a thorough picture of chemical bonding Experimental evidence for molecular oxygen suggests that the answer is yes. 

The n molecular orbitals described so far involve two atoms, so the orbital pictures look the same for the localized bonding model applied to ethylene and the MO approach applied to molecular oxygen. In the organic molecules described in the introduction to this chapter, however, orbitals spread over three or more atoms. Such delocalized n orbitals can form when more than two p orbitals overlap in the appropriate geometry. In this section, we develop a molecular orbital description for three-atom n systems. In the following sections, we apply the results to larger molecules. 

Although, as proposed by Lewis, the octet rule is a purely empirical rule, the advent of orbital models appeared to add some theoretical support to the octet rule. For period 2 elements a maximum of only four orbitals, the 2s and the three 2p orbitals, are available for describing the bonds in terms of localized bonding and nonbonding orbitals, because other orbitals such as 3s, 3p, and 3d have energies that are too high. As a consequence, the octet rule came to be regarded more as a physical law than as a purely empirical rule. So it was... 

Several methods have been used for analyzing the electron density in more detail than we have done in this paper. These methods are based on different functions of the electron density and also the kinetic energy of the electrons but they are beyond the scope of this article. They include the Laplacian of the electron density ( L = - V2p) (Bader, 1990 Popelier, 2000), the electron localization function ELF (Becke Edgecombe, 1990), and the localized orbital locator LOL (Schinder Becke, 2000). These methods could usefully be presented in advanced undergraduate quantum chemistry courses and at the graduate level. They provide further understanding of the physical basis of the VSEPR model, and give a more quantitative picture of electron pair domains. 

It has also to be remembered that the band model is a theory of the bulk properties of the metal (magnetism, electrical conductivity, specific heat, etc.), whereas chemisorption and catalysis depend upon the formation of bonds between surface metal atoms and the adsorbed species. Hence, modern theories of chemisorption have tended to concentrate on the formation of bonds with localized orbitals on surface metal atoms. Recently, the directional properties of the orbitals emerging at the surface, as discussed by Dowden (102) and Bond (103) on the basis of the Good-enough model, have been used to interpret the chemisorption behavior of different crystal faces (104, 105). A more elaborate theoretical treatment of the chemisorption process by Grimley (106) envisages the formation of a surface compound with localized metal orbitals, and in this case a weak interaction is allowed with the electrons in the metal. 

Scheme la shows the approximate molecular orbital model for the hypervalent X-E-X 3c-4e in EX4, such as SC14. Characters of the three molecular orbitals are bonding (v /i), nonbonding (v /2), and anti-bonding (v /3). Two electrons are in and two in v 2. Electrons in v 2 localize on X of X-E-X and the hypervalent bonds are mainly characterized by v 2. Consequently,... 

We shall consider here in more detail two models first a dynamic coupling approach, due to Weigang33, who considered optical activity deriving from the coupling of electric dipoles (the diene chromophore and the polarizable bonds around it) and second, a localized orbital investigation, which permits one to separate the contributions from the intrinsic diene optical activity and from the axial substituents. 

This transformation leaves invariant all observable molecular properties of ground-state norbornadiene that can be derived from our SCF model. Note that the two localized orbitals describing a double bond are two banana LMOs Xb,Up and Xb.down, as shown on the left of Figure 17, Their normalized, out-of-phase linear combination... 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

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