Localized molecular orbitals localization

Highest occupied molecular orbital Intermediate neglect of differential overlap Linear combination of atomic orbitals Local density approximation Local spin density functional theory Lowest unoccupied molecular orbital Many-body perturbation theory Modified INDO version 3 Modified neglect of diatomic overlap Molecular orbital Moller-Plesset... 

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. 

Fig. 7. Graphical representations of (a) the Highest Occupied Molecular Orbital (HOMO) and (b) the Lowest Unoccupied Molecular Orbital (LUMO) for ranitidine. It is possible, in the ordinarily visible color-coded data not shown here, to distinguish the strong localization (a) of the HOMO to the sulfur atom and adjacent nitroethyleneamine fragment and the contrasting localization (b) of the LUMO to the nitroethylenearnine fragment. Neither the LUMO not HOMO appear to have contributions from the dimethylaminomethyl-suhstitiited furan.

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

Further examination of Table 1.10 reveals that the lowest unoccupied molecular orbital, i/ 4, is a pure p orbital, localized on carbon, since the coefficients are zero for all but the 2p orbital. The MO picture is in agreement with the usual qualitative hybridization picture for the methyl cation. 

Carbon oxohalides are reactive gases or volatile liquids which feature planar molecules of C2t, symmetry they are isoelectronic with BX3 (p. 196) and the bonding is best described in terms of molecular orbitals spanning all 4 atoms rather than in terms of localized orbitals as... 

Compare atomic charges and electrostatic potential maps for the three cations. For each, is the charge localized or delocalized Is it associated with an empty a-type or Tt-type orbital Examine the lowest-unoccupied molecular orbital (LUMO) of each cation. Draw all of the resonance contributors needed for a complete description of each cation. Assign the hybridization of the C" atom, and describe how each orbital on this atom is utilized (o bond, n bond, empty). How do you explain the benzene ring effects that you observe ... 

Another useful way to think about carbon electrophilicity is to compare the properties of the carbonyls lowest-unoccupied molecular orbital (LUMO). This is the orbital into which the nucleophile s pair of electrons will go. Examine each compound s LUMO. Which is most localized on the carbonyl group Most delocalized Next, examine the LUMOs while displaying the compounds as space-filling models. This allows you to judge the extent to which the LUMO is actually accessible to an approaching nucleophile. Which LUMO is most available Least available ... 

Finally, examine the highest-occupied molecular orbital (HOMO) of phenoxide anion. Is the HOMO the best electron-donor orbital Is the orbital localized primarily on oxygen or on carbon Is the observed product consistent with orbital control Explain your answers. 

Woodward and Hoffmann pointed out that the Diels-Alder reaction involved bonding overlap of the highest-occupied molecular orbital (HOMO) on the diene and the lowest-unoccupied molecular orbital (LUMO) on the dienophile. Display the HOMO for 2-methoxybutadiene. Where is it localized Display the LUMO for acrylonitrile. Where is it localized Orient the two fragments such that the HOMO and LUMO best overlap (A clearer picture is provided by examining-the HOMO map for 2-methoxybutadiene and the LUMO map for acrylonitrile.) Which product should result ... 

One of the goals of Localized Molecular Orbitals (LMO) is to derive MOs which are approximately constant between structurally similar units in different molecules. A set of LMOs may be defined by optimizing the expectation value of an two-electron operator The expectation value depends on the n, parameters in eq. (9.19), i.e. this is again a function optimization problem (Chapter 14). In practice, however, the localization is normally done by performing a series of 2 x 2 orbital rotations, as described in Chapter 13. 

An error function depending on parameters. Only minima are of interest, and the global minimum is usually (but not always) desired. This may for example be determination of parameters in a force field, a set of atomic charges, or a set of localized Molecular Orbitals. 

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