Orbital control

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... 

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 ... 

Next, consider the reactivity of phenyl diazonium ion. Are either of the reactions shown above consistent with nucleophilic attack at the ion s most electron-poor site Examine the lowest-unoccupied molecular orbital (LUMO) of phenyl diazonium ion. What electrophilic sites are identified by the LUMO Are either of the reactions shown above consistent with an orbital-controlled addition ... 

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. 

If we are comparing reactions which have approximatively the same steric requirements, the first term is roughly constant. If the species are very polar the second term will dominate, and the reaction is charge controlled. This means for example that an electrophihc attack is likely to occur at the most negative atom, or in a more general sense, along a path where the electrostatic potential is most negative. If the molecules are non-polar, the third term in (15.1) will dominate, and the reaction is orbital controlled. 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

Compound N-1 Values of A when a molecule of NH N-5 C-2 C-3 C-4 (C-5) i attacks position N-6 N-7 (C-6) (C-7) N-8 (C-8) Preferable positions for NH3 attack under orbital control Experimental data... 

A fundament of the quantum chemical standpoint is that structure and reactivity are correlated. When using quantum chemical reactivity parameters for quantifying relationships between structure and reactivity one has the advantage of being able to describe the nature of the structural influences in a direct manner, without empirical assumptions. This is especially valid for the so-called Salem-Klopman equation. It allows the differentiation between the charge and the orbital controlled portions of the interaction between reactants. This was shown by the investigation of the interaction between the Lewis acid with complex counterions 18> (see part 4.4). 

The carbonyl n orbital is also assumed to be unsymmetrized arising from the out-of-phase interaction of the orbital attached to the more electron-donating aryl group (9 and 10). These unsymmetrizations of the carbonyl k orbital correspond well to syn addition (9) and anti addition (10), respectively. Thus, the electron-donation of the p-a orbitals controls the facial selectivities. The cyclopentane system was more sensitive to stereoelectronic effects, showing larger induced biases, than the adamantanone system [63]. 

As mentioned above, the unpaired electrons of diradicals may interact with each other through bonds. The orbital phase relationships between the involved orbitals control the effectiveness of the cyclic orbital interactions underlying the through-bond coupling. 

Thus the calculations indicate that the direct through-space bonding between the pnictogen atom p-orbitals controls the conformations of the heavier diheteroferrocenes. 

The importance of both frontier orbital-controlled and electronic charge-controlled factors in determining chemical reactivity has been recognized (16). These concepts are the key to interpreting two types of reactivity expected for carbene complexes, i.e., reactions with nucleophilic... 

Self-consistent field molecular orbital calculations by Fenske and coworkers have confirmed that nucleophilic additions to Fischer and related complexes [e.g., (CO)sCr=CXY, (T)5-C5H5)(CO)2Mn=CXY], are frontier orbital-controlled rather than charge-controlled reactions (7-9). Interaction of the HOMO of the nucleophile with the carbene complex LUMO (localized on Ca) destroys the metal-carbon w-interaction and converts the bond to a single one. 

The model predicts that frontier orbital-controlled addition at position (1) should be favorable for octahedral or pseudooctahedral complexes of... 

In some cases the site of attack is in no doubt, e.g., 9 adds PMe3 at the carbyne carbon in an orbital-controlled reaction (29,31) ... 

The preferred orientation for electrophiles is out of the plane defined by the Y-S-Z bonds, and about 20° from the normal (n) to the plane [50], whereas nucleophiles tend to lie in the plane, and cluster close to the line defined by the extension of the Y-S (or Z-S) bond. Similar interactions have been observed for selenium (Ramasubbu and Parthasarathy, 1984). The conclusion, as before, is that these interactions are frontier-orbital controlled, with the HOMO being a sulphur lone pair, and the LUMO an antibonding o- C-y(Z) orbital. 

The reactions of electrogenerated cation radicals of diarylsulfldes are mainly orbital-controlled and at this level the electronic structure of their frontier orbitals (HOMO-SOMO) has very interesting synthetic consequences. The 3p orbitals of sulfur are conjugated with only one aromatic ring even if there are two aryls bound to sulfur. Therefore, only one ring can be activated electrochemically. The degree of the charge delocalization in the ArS moiety of a cation radical on the one hand, and the availability of p- and o-positions for the substitution on the other, determine quite different reactivity of such species. 

This reactivity pattern is certainly unexpected. Why should low-valent complexes react as electrophiles and highly oxidized complexes be nucleophilic Numerous calculations on model compounds have provided possible explanations for the observed chemical behavior of both Fischer-type [3-8] and Schrock-type [9-17] carbene complexes. In simplified terms, a rationalization of the reactivity of carbene complexes could be as follows. The reactivity of non-heteroatom-stabilized carbene complexes is mainly frontier-orbital-controlled. The energies of the HOMO and LUMO of carbene complexes, which are critical for the reactivity of a given complex, are determined by the amount of orbital overlap and by the energy-difference between the empty carbene 2p orbital and a d orbital (of suitable symmetry) of the group L M. 

Dnring an electron transfer, the acceptor places its LUMO at the electron disposal and the donor releases an electron that is located on its HOMO. These orbitals are frontier orbitals. In the corresponding ion-radicals, the distribution of an unpaired electron proceeds, naturally, under frontier-orbital control. This definitely reflects in the ion-radical reactivity and not always by a self-obvions manner. Let ns concisely trace peculiarities of ion-radical fragmentation reactions that are very important in organic synthesis. 

There have been discussions whether the amide addition at C-6 is charge-controlled or orbital-controlled. Charge density calculations in 4-phenylpyrimidine (MNDO method) predict that the addition of the amide ion would preferably take place at position 2 (95UP1) this, however, does not agree with the experimental results. Therefore, the conclusion seems justified that the addition is not charge-controlled. Frontier orbital calculations, using the SCF-PPP method, show that the frontier orbital densities in the LUMO of pyrimidine are zero at C-2 and C-5, making these positions... 

Various reasons have been advanced for the relative accuracy of spin-polarized Kohn-Sham calculations based on local (spin) density approximations for E c- However, two very favourable aspects of this procedure are clearly operative. First, the Kohn-Sham orbitals control the physical class of density functions which are allowed (in contrast, for example, to simpler Thomas-Fermi theories). Second, local density approximations for are mild-mannered,... 

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