Atomic orbitals highest occupied molecular

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... 

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.

What happens to electrons which are left over after all bonds have been formed Do they associate with individual atoms or are they spread uniformly throughout the molecule Draw a Lewis structure for trimethylamine. How many electrons are needed to make bonds How many are left over Where are they Display the highest-occupied molecular orbital (HOMO) for trimethylamine. Where is it located ... 

Another way to assess nucleophilic reactivity is to examii the shape of the nucleophile s electron-donor orbital (th is the highest-occupied molecular orbital or HOMC Examine the shape of each anion s HOMO. At which ato would an electrophile, like methyl bromide, find the be orbital overlap (Note This would involve overlap of tl the HOMO of the nucleophile and the lowest-unoccupif molecular orbital or LUMO of CH3Br.) Draw all of tl products that might result from an Sn2 reaction wi CHaBr at these atoms. 

Compare atomic charges for the enolate anion and the lithium salt. Are there major differences, in particular, for the oxygen and the a carbon Also compare the highest-occupied molecular orbital (HOMO) in the two molecules. This identifies the most nucleophilic sites, that is, the most likely sites for attack by electrophiles. Are the two orbitals similar or do they differ substantially Elaborate. 

Some electrophile-nucleophile reactions are guided more by orbital interactions than by electrostatics. The key interaction involves the donor orbital on the nucleophile, i.e., the highest-occupied molecular orbital (HOMO). Examine the HOMO of enamine, silyl enol ether, lithium enolate and enol. Which atom is most nucleophilic, i.e., which site would produce the best orbital overlap with an electrophile ... 

Aceording to Frontier Molecular Orbital (FMO) theory, thiophene s most reactive site can be identified by examining the shape of its highest-occupied molecular orbital (HOMO). Which atoms contribute to thiophene s HOMO Which atom(s) contributes the most Which nitration product should form preferentially ... 

In addition to electrophilic attack on the pyrrole ring in indole, there is the possibility for additions to the fused benzene ring. First examine the highest-occupied molecular orbital (HOMO) of indole. Which atoms contribute the most What should be the favored position for electrophilic attack Next, compare the energies of the various protonated forms of indole (C protonated only). These serve as models for adducts formed upon electrophilic addition. Which carbon on the pyrrole ring (C2 or C3) is favored for protonation Is this the same as the preference in pyrrole itself (see Chapter 15, Problem 2)1 If not, try to explain why not. Which of the carbons on the benzene ring is most susceptible to protonation Rationalize your result based on what you know about the reactivity of substituted benzenes toward electrophiles. Are any of the benzene carbons as reactive as the most reactive pyrrole carbon Explain. 

Figure 2. Minimum atomic localization energy in benzenoid hydrocarbons plotted against energy of the highest occupied molecular orbital (HOMO).

The rationale behind this choice of bond integrals is that the radical stabilizing alpha effect of such radicals are explained not by the usual "resonance form" arguments, but by invoking frontier orbital interactions between the singly occupied molecular orbital of the localized carbon radical and the highest occupied molecular orbital (the non-bonding electrons atomic orbital) of the heteroatom (6). For free radicals the result of the SOMO-HOMO interaction Ts a net "one-half" pi bond (a pi bond plus a one-half... 

Each energy level in the band is called a state. The important quantity to look at is the density of states (DOS), i.e. the number of states at a given energy. The DOS of transition metals are often depicted as smooth curves (Fig. 6.10), but in reality DOS curves show complicated structure, due to crystal structure and symmetry. The bands are filled with valence electrons of the atoms up to the Fermi level. In a molecule one would call this level the highest occupied molecular orbital or HOMO. 

Table 1 Calculation of some molecular-based descriptors for BOA, DIMBOA and MBOA. Physicochemical descriptor like logP (partition coefficient between octanol and water) constitutional descriptors like the number of a specified atoms or bonds (number of carbons, hydrogens, oxygens, nitrogens, single and aromatic bonds, the total number of atoms and bonds) and molecular weight quantum-mechanical descriptors like HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

Fig. 6. HOMO (left) and second highest occupied molecular orbital, sHOMO (right) of la predicted by DFT calculations. Hydrogen atoms and axial oxygens are not shown for clarity. From Ref. (27).

The nature of the electronic states for fullerene molecules depends sensitively on the number of 7r-electrons in the fullerene. The number of 7r-electrons on the Cgo molecule is 60 (i.e., one w electron per carbon atom), which is exactly the correct number to fully occupy the highest occupied molecular orbital (HOMO) level with hu icosahedral symmetry. In relating the levels of an icosahedral molecule to those of a free electron on a thin spherical shell (full rotational symmetry), 50 electrons fully occupy the angular momentum states of the shell through l = 4, and the remaining 10 electrons are available... 

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