Highest occupied molecular orbitals HOMO

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

If the number of electrons, N, is even, you can have a closed shell (as shown) where the occupied orbitals each contain two electrons. For an odd number of electrons, at least one orbital must be singly occupied. In the example, three orbitals are occupied by electrons and two orbitals are unoccupied. The highest occupied molecular orbital (HOMO) is /3, and the lowest unoccupied molecular orbital (LUMO) is 11/4. The example above is a singlet, a state of total spin S=0. Exciting one electron from the HOMO to the LUMO orbital would give one of the following excited states ... 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

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.

It is now possible to "see" the spatial nature of molecular orbitals (10). This information has always been available in the voluminous output from quantum mechanics programs, but it can be discerned much more rapidly when presented in visual form. Chemical reactivity is often governed by the nature of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Spectroscopic phenomena usually depend on the HOMO and higher energy unoccupied states, all of which can be displayed and examined in detail. 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

FIGURE 13.38 The Tr Tr transition in ds,trans-, 3-cyclooctadiene involves excitation of an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). 

Draw a Lewis structure for singlet methylene, CH2 (all the electrons in singlet methylene are spin-paired). Ho many electrons remain after all bonds have been formei Where are the extra electrons located, in the plane the molecule or perpendicular to the plane Examine t highest-occupied molecular orbital (HOMO) of methyle to tell. 

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 ... 

Examine the highest-occupied molecular orbital (HOMO of cyanide anion. Is the larger lobe on carbon or nitrogen Would you expect cyanide to act as a carbon or nitrogei nucleophile Does this lead to the lower energy transitioi state (compare the energy of cyanide-l-methyl iodide ( attack and cyanide+methyl iodide N attack) ... 

Another measure of distortion is the shape of the highest-occupied molecular orbital (HOMO). This corresponds to the 7t bond. Is the orbital relatively undistorted in the cis compounds (as in cis-2-butene)l Is it more distorted in trans-cycloheptene than in trans-cyclooctene Explain why distortion in the HOMO is likely to be energetically unfavorable. 

Dimethylborane+propene Cl depicts the transition state for addition of dimethylborane onto the terminal alkene carbon of propene. Examine and describe the vibration with the imaginary frequency. Which bonds stretch and compress the most What simultaneous changes in bonding are implied by these motions Simultaneously display the highest-occupied molecular orbital (HOMO) of propene and the lowest-unoccupied molecular orbital (LUMO) of dimethylborane. Is the overall geometry of the transition state consistent with constructive overlap between the two Explain. 

Finally, display the highest-occupied molecular orbital (HOMO) of triphenylphosphinemethylidene. Is it primarily concentrated on the methylene carbon as would be expected of a fully-developed anion, or is it delocalized over both phosphorous and carbon Does this suggest that the molecule incorporates a n bond ... 

Examine electrostatic potential maps for dimethylsulfonium and dimethylsulfoxonium ylides. Which contains the more negatively-charged carbon Do either or both of the ylides incorporate a fully formed 7U bond Compare bond distances involving methylene and methyl carbons. Also examine the highest-occupied molecular orbital (HOMO) for evidence of 7U bonding. 

Next, examine the equilibrium structure of acetamide (see also Chapter 16, Problem 8). Are the two NH protons in different chemical environments If so, would you expect interconversion to be easy or difficult Calculate the barrier to interconversion (via acetamide rotation transition state). Rationalize your result. Hint Examine the highest-occupied molecular orbital (HOMO) for both acetamide and its rotation transition state. Does the molecule incorporate a n bond. If so, is it disrupted upon rotation ... 

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 ... 

Now, examine the orbital on cyclohexanone lithium enolate most able to donate electrons. This is the highest-occupied molecular orbital (HOMO). Identify where the best HOMO-electrophile overlap can occur. Is this also the most electron-rich site An electrophile will choose the best HOMO overlap site if it is not strongly affected by electrostatic effects, and if it contains a good electron-acceptor orbital (this is the lowest-unoccupied molecular orbital or LUMO). Examine the LUMO of methyl iodide and trimethylsilyl chloride. Is backside overlap likely to be successful for each The LUMO energies of methyl iodide and trimethylsilyl chloride are 0.11 and 0.21 au, respectively. Assuming that the lower the LUMO energy the more effective the interaction, which reaction, methylation or silylation, appears to be guided by favorable orbital interactions Explain. 

One way to anticipate the favored product is to consider the shape of naphthalene s best electron-donor orbital, the highest-occupied molecular orbital (HOMO). Display the HOMO in naphthalene and identify the sites most suitable for electrophilic attack. Which substitution product is predicted by an orbital-control mechanism Ts this the experimental result ... 

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. 

Examine pyrrole s highest-occupied molecular orbital (HOMO) to see if your can predict the most favorable protonation site. Which of the pyrrole s conjugate acids (N protonated, C2 proto noted, C3 proto noted pyrrole) is lowest in energy Examine electrostatic potential maps to see if the lowest-energy form is also that in which the positive charged is best delocalized. Rationalize your result using resonance arguments. What should be the favored substitution product ... 

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. 

Examine the highest-occupied molecular orbital (HOMO) of singlet methylene. Where is the pair of electrons, inplane or perpendicular to the plane Next, examine the electrostatic potential map. Where is the molecule most electron rich, in the o or the 7t system Where is the most electron poor Next, display the corresponding map for triplet methylene. Which molecule would you expect to be the better nucleophile The better electrophile Explain. Experimentally, one state of methylene shows both electrophilic and nucleophilic chemistry, while the other state exhibits chemistry typical of radicals. Which state does which Elaborate. 

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