Orbitals frontier

The reactive HOMO and LUMO of ethene (or of any other molecule) are referred to as frontier molecular orbitals (FMO), after the pioneering work of Fukui. Analyzing several different types of reactions with FMO 

Analysis of a reaction by frontier orbital theory has additional benefits, particularly for predicting reactivity and stereochemistry. Woodward and Hoffman pointed out that electrocyclic reactions followed the stereochemistry dictated by the symmetry, or nodal properties of the HOMO of the polyene .This concept of orbital symmetry will be important for discussions of all pericyclic reactions. Of particular importance is the difference in energy between the HOMO one Ji system and the LUMO of a second Jt-system, because this will be used to predict reactivity in pericyclic reactions (see below). 

Frontier molecular orbital (FMO) theory has been successful in rationalizing the reactivity, electroselectivity, and regioselectivity of many heterocycles, including mesomeric betaines. To apply FMO theory, some knowledge of the frontier orbital coefficients and energies is necessary, and it is useful to draw some general conclusions about the frontier orbitals in mesomeric betaines. 

Since the betaine HOMO is treated as a perturbed NBMO, the shape, as well as the energy, of this orbital might be expected to be close to that of a NBMO. Hiickel calculations on three betaines 427-429 (Fig. 4) lend support to this view. The following features of the calculated HOMOs are notable (i) 90% of the charge density is restricted to active positions (ii) the only 

The HOMO of a mesomeric betaine is similar in shape and energy to a NBMO. The energy of this pseudo-NBMO is lowered by replacing active carbon atoms by heteroatoms or by introducing electron-withdrawing substituents at active positions. 

The HOMO-LUMO separation of mesomeric betaines is relatively small. Heteroatoms and conjugated substituents at inactive positions will usually reduce this separation by lowering the energy of the LUMO without perturbing the HOMO. 

Build-up o dec iron density between nuclei (proportional lo V T) giving bonding 

Electron density between hydrogen nuclei diminished. Electrostatic repulsion between nuclei 

Q What will happen to the tr orbital energies if two hydrogen molecules approach side to side  

A As the molecules approach, their cr orbitals will overlap. Two orbitals will result the one with the phases the same will have a lower energy, whereas the one with different phases will have a higher energy. Since four electrons are involved, both new orbitals will be filled, so there will be no net increase in bonding. 

In most molecules, all the electrons are paired orbitals are either filled with two electrons or empty. If two molecules approach each other, all the orbitals in one molecule will interact with all those in the other. For complex molecules with a large number of orbitals, this gives rise to a very large number of interactions. Fortunately, it turns out that only one or two are important. 

They will be bonding in the central C=C region, helping to establish multiple bond character there. 

They will be antibonding in the C-C single bond regions, thereby cancelling out double-bond character from a lower set of 7r-type MOs. 

Notice that the HOMO of Fig. 14-16 is qualitatively similar to one of the leg — le HOMOs of ethane. The QMOT frontier orbital argument for the stability of staggered ethane is basically the same as that for the stability of form (a) in propene. Observe that this MO also resembles the HOMO of 1,3-butadiene, and would lead to the prediction that the trans form of this molecule is more stable than the cis. This is, in fact, observed to be the case. 

EXAMPLE 14-5 How should the bond lengths and angles of propene change if the methyl group rotates from the stable conformation (Fig. 14-16a) to the unstable one (Fig. 14-16b)  

---

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. 

The new bonds will be made between those two ends of the reactants where the orbital coefiicients of the frontier orbitals match best, where both have the largest coefficients. 

I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, New York, 1976. 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

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. 

Figure 1.3. Frontier orbital energies (eV) and confidents for acrolein and protonated acrolein. In the latter case the upper numbers refer to the situation where bond lengths and angles correspond to those of acrolein. The lower numbers are more suitable for a hydroxyallyl cation. The actual situation is assumed to be intermediate. The data are taken from ref. 104.

Note that the stereochemistry comes out right. H s a and b are cis because they were cis in the starting quinone and the Diels-Alder reaction is stereospecific in this respect. H is also cis to and H " because the Diels-Alder reaction is stereoselectively endo. These points are described in more detail in Norman p.284-6 and explained in Ian Fleming Frontier Orbitals and Organic Chemical Reactions, Wiley 1976, p. 106-109. How would you make diene A ... 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Use frontier orbital analysis to decide whether the dimeriza... 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

Frontier orbitals (Section 10 14) Orbitals involved in a chem ical reaction usually the highest occupied molecular orbital of one reactant and the lowest unoccupied molecular orbital of the other... 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

You can use the information obtained from semi-empirical calculations to investigate many thermodynamic and kinetic aspects of chemical processes. Energies and geometries of molecules have clear relation ships to chemical ph en om ena. 0ther quan tities, like atomic charges and Frontier Orbitals, are less defined but provide useful qualitative results. 

Other reactions are controlled kinetically, and the most stable product is not the major one observed. In these cases, you must look at the reactant side of the reaction coordinate to discover factors determining the outcome. Klopman and Salem developed an analysis of reactivity in terms of two factors an electrostatic interaction approximated by atomic charges and a Frontier orbital interaction. Fleming s book provides an excellent introduction to these ideas. 

You can interpret the stereochemistry and rates of many reactions involving soft electrophiles and nucleophiles—in particular pericyclic reactions—in terms of the properties of Frontier orbitals. This applies in particular to pericyclic reactions. Overlap between the HOMO and the LUMO is a governing factor in many reactions. HyperChem can show the forms of orbitals such as HOMO and LUMO in two ways a plot at a slice through the molecule and as values in a log file of the orbital coefficients for each atom. 

Frontier Orbital theory is qualitative, so there is no need for great accuracy in the calculation as long as it produces the approximate form of the orbitals. 

Btamp/e Another example of frontier orbital theory uses the reaction of phenyl-butadiene with phenylethylene. This reaction is a [4 + 2] pericyclic addition to form a six-membered ring. It could proceed with the two phenyl rings close to each other (head to head) or further away from each other (head to tail). 

This example uses AMI for optimization and orbital calculations. For more examples of Frontier Orbital theory, see Fleming sbook. ... 

Frontier orbital theory predicts that electrophilic substitution of pyrroles with soft electrophiles will be frontier controlled and occur at the 2-position, whereas electrophilic substitution with hard electrophiles will be charge controlled and occur at the 3-position. These predictions may be illustrated by the substitution behaviour of 1-benzenesulfonylpyr-role. Nitration and Friedel-Crafts acylation of this substrate occurs at the 3-position, whereas the softer electrophiles generated in the Mannich reaction (R2N=CH2), in formylation under Vilsmeier conditions (R2N=CHC1) or in formylation with dichloromethyl methyl ether and aluminum chloride (MeO=CHCl) effect substitution mainly in the 2-position (81TL4899, 81TL4901). Formylation of 2-methoxycarbonyl-l-methylpyrrole with... 

An alternative approach is in terms of frontier electron densities. In electrophilic substitution, the frontier electron density is taken as the electron density in the highest filled MO. In nucleophilic substitution the frontier orbital is taken as the lowest vacant MO the frontier electron density at a carbon atom is then the electron density that would be present in this MO if it were occupied by two electrons. Both electrophilic and nucleophilic substitution thus occur at the carbon atom with the greatest appropriate frontier electron density. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

K. Fukui, Acc. Chem. Res. 4 57 (1971) I. Fleming, Frontier Orbital and Organic Chemical Reactions, John Vfiiey St Sons, New Yodt, 1976 L. Salem, Electrons in Chemical Reactions, John Wil Sons, New Yoric, 1982, Chapter 6. 

Interaction of f. irmeilileliyde frontier orbitals with E and Nu Fig. 1.25. PMO description of interaction of ethylene and formaldehyde with an electrophile (E ) and a nucleophile (Nu ). 

The LUMO, which is the frontier orbital in reactions with nucleophiles, has a larger coefficient on the /3-carbon atom, whereas the two occupied orbitals are distorted in such a way as to have larger coefficients on oxygen. The overall effect is that the LUMO is relatively low-lying and has a high coefficient on the /3-carbon atom. The frontier orbital theory therefore predicts that nucleophiles will react preferentially at the /3-carbon atom. 

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

---