Orbital Considerations

Whereas it is clear that a free carbenium ion should experience nucleophilic attack equally well from either face because it has a plane of symmetry, it may not be clear why an Sim2 reaction has to proceed via backside attack only. Leaving groups generally have electronegative atoms. This produces a polar C-LG bond, with a 5+ on carbon. Simple electrostatic considerations thus predict a nucleophile should attack carbon, but they really cannot rationalize why the attack must be on the backside. Considering potential donor-acceptor interactions, however, nicely rationalizes the result. 

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R. Gleiter, Stmcture and Bonding in Cyclic Sulfur-Nitrogen Compounds Molecular Orbital Considerations, Angew. Chem. Int. Ed. Engl., 20, 444 (1981). 

The Hiickel method is essentially only used for educational purposes or for veiy qualitative orbital considerations. It has the ability to produce qualitatively correct MOs involving a computational effort which is within reach of doing by hand. 

To explain tlie stereodieniistiy of tlie allylic substitution reaction, a simple stereoelectronic model based on frontier molecular orbital considerations bas been proposed fl55. Fig. G.2). Organocopper reagents, unlike C-nudeopbiles, possess filled d-orbitals fd - configuration), wbidi can interact botli witli tlie 7t -fC=C) orbital at tlie y-carbon and to a minor extent witli tlie cr -fC X) orbital, as depicted... 

When enantiomerically pure allyl p-tolyl sulfoxide is deprotonated and then treated with electrophilic 2-cyclopentenone, a conjugate addition occurs forming a new carbon-carbon bond with very high control of absolute stereochemistry (equation 25)65. See also Reference 48. Similarly, using more substituted enantiomerically pure allylic sulfoxides leads to virtually complete diastereocontrol, as exemplified by equations 26 and 27 the double bond geometry in the initial allylic sulfoxide governs the stereochemistry at the newly allylic carbon atom (compare equations 26 vs. 27)66. Haynes and associates67 rationalize this stereochemical result in terms of frontier molecular orbital considerations... 

According to these consideration the diamino-substituted phosphenium (an alternative suggestion for its nomenclature is phosphanylium) cation, 5, and the phosphanetriylammonium (iminophosphenium) cation, 6, possess the largest intrinsic (gas phase) stabihties. Since in the X-ray structures the molecules are to a first-order isolated, this theoretical stability scale determined for the gas phase should also mimic the various trends of the stabilities of the cations and their chelation behaviour. The methylenephosphenium, 7, and the PjH cations, 8, suffer from poor stabihties. On the other hand the phosphirenium cation, 11, is considered to be fairly well stabilized. It is due to n-electron delocalisation of the positive charge in the phosphirenium cation. Intermediate cases in stabihty are the PO+ (9) and PS+ cations (10). Of further interest are the frontier orbital considerations, as shown in Fig. 2. 

Chemical Reactivity Aspects and Frontier Orbital Considerations... 

Theoretical calculations have also permitted one to understand the simultaneous increase of reactivity and selectivity in Lewis acid catalyzed Diels-Alder reactions101-130. This has been traditionally interpreted by frontier orbital considerations through the destabilization of the dienophile s LUMO and the increase in the asymmetry of molecular orbital coefficients produced by the catalyst. Birney and Houk101 have correctly reproduced, at the RHF/3-21G level, the lowering of the energy barrier and the increase in the endo selectivity for the reaction between acrolein and butadiene catalyzed by BH3. They have shown that the catalytic effect leads to a more asynchronous mechanism, in which the transition state structure presents a large zwitterionic character. Similar results have been recently obtained, at several ab initio levels, for the reaction between sulfur dioxide and isoprene1. ... 

As in benzene, the substituents in ortho and para will be better conjugated than those in meta. These qualitative aspects of regioselectivity have been studied quantitatively by quantum mechanical studies. Further the molecular orbital considerations have shown that the favoured transition state will be that in which there is strongest interaction between the HOMO of the diene and LUMO of the dienophile. In the most common cases the dienophile bears an electron withdrawing substituent and the diene an electron releasing one. Here the interation is between the LUMO of the dienophile and the HOMO of diene. 

However, there are some cases when an unpaired electron is localized not on the n, but on the o orbital of an anion-radical. Of course, in such a case, a simple molecular orbital consideration that is based on the n approach does not coincide with experimental data. Chlorobenzothiadiazole may serve as a representative example (Gul maliev et al. 1975). Although the thiadiazole ring is a weaker acceptor than the nitro group, the elimination of the chloride ion from the 5-chlorobenzothiadiazole anion-radical does not take place (Solodovnikov and Todres 1968). At the same time, the anion-radical of 7-chloroquinoline readily loses the chlorine anion (Fujinaga et al. 1968). Notably, 7-chloroquinoline is very close to 5-chlorobenzothiadiazole in the sense of structure and electrophilicity of the heterocycle. To explain the mentioned difference, calculations are needed to clearly take into account the o electron framework of the molecules compared. It would also be interesting to exploit the concept of an increased valency in the consideration of anion-radical electronic structures, especially of those anion-radicals that contain atoms (fragments) with available d orbitals. This concept is traditionally derived from valence-shell expansion through the use of d orbital, but it is also understandable in terms of simple (and cheaper for calculations) MO theory, without t(-orbital participation. For a comparative analysis refer the paper by ElSolhy et al. (2005). Solvation of intermediary states on the way to a final product should be involved in the calculations as well (Parker 1981). 

Molecular orbital theory may provide an explanation for stereochemical differences between carboxylate-metal ion and phosphate-metal ion interactions. Detailed ab initio calculations demonstrate that the semipo-lar 1 0 double bond of RsP=0 is electronically different from the C=0 double bond, for example, as found in H2C=0 (Kutzelnigg, 1977 Wallmeier and Kutzelnigg, 1979). The P=0 double bond is best described as a partial triple bond, that is, as one full a bond and two mutually perpendicular half-7r bonds (formed by backbonding between the electrons of oxygen and the empty d orbitals of phosphorus). Given this situation, a lone electron pair should be oriented on oxygen nearly opposite the P=0 bond, and these molecular orbital considerations for P=0 may extend to the phosphinyl monoanion 0-P=0. If this extension is valid, then the electronic structure of 0-P=0 should not favor bidentate metal complexation by phosphate this is in accord with the results by Alexander et al. (1990). 

Padwa et al. (44) studied the diazo-decomposition of 119 and found that the cyclic ylide 120 could be trapped by a variety of heterodipolarophiles such as ethyl cyanoacetate (Mander s reagent) to provide aminal 121 or with benzaldehyde to generate the bicyclic acetal 122. In both cases, only a single isomer was formed, with the regiochemistry easily predicted from frontier orbital considerations. Nair et al. (45) were able to employ the highly functionalized o-quinone 125 for the trapping of carbonyl ylide 124 to provide the highly complex cycloadduct 126 in 76% yield. 

The access to different -regions is controlled by the vibration spectra. In particular, it is the anti-symmetric vibration mode that may shift the geometry towards the point of maximal mixing. The other way round, freezing this mode will trap the quantum system at the initial state, cis or trans as the case may be. Now, a vibration excitation along this anti-symmetric mode will be prompting the electronic activity of the system. For example, a perpendicular symmetric attack of carbene can only proceed if non-zero amplitude develops at the diradical states. This concept includes the elementary orbital considerations and overcome them. 

No discussion about strained-ring radical cations would be complete without the valence isomers quadricyclane (15 +) and norbornadiene, (16 +) 15 features two adjacent rigidly held cyclopropane rings, whereas 16 contains two ethene n systems well suited to probe through-space interactions.Molecular orbital considerations suggest the antisymmetric combination of the ethene n orbitals (16) or cyclopropane Walsh orbitals (15) as respective HOMOs of the two parent molecules. The radical ions have different state symmetries and their SOMOs have different orbital symmetries. 

Although mixtures are often obtained, usually one predominates, the one indicated above. This regioselectivity, in which the ortho or para product is favored over the meta, has been explained by molecular-orbital considerations.864 When X = N02, regioselectivity to give the ortho or "para product was very high at room temperature, and this method, combined with subsequent removal of the N02 (see 0-82) has been used to perform regio-selective Diels-Alder reactions.865... 

This reaction is a reverse Diels-Alder Reaction. The orbital considerations controlling the backward reaction are the same as the forward reaction. 

As with the chloropalladation reaction (vide supra)m the rearrangement of >/2-methyl-enecyclopropane to >/4-TMM was shown experimentally to proceed stereoselectively by disrotatory ring cleavage of the distal frontier molecular orbital considerations, which predict that the out-of-phase interaction between the metal orbital in the distal ring-opening of -methylenecyclopropane complexes can be minimized by bending the bond up away from the metal (equation 348)410 ... 

The same principles that we have used for the description of diatomic molecules will now be used in a description of the electronic structures of triatomic molecules. However, let it be clear that in using molecular-orbital theory with any hope of success, we first have to know the molecular geometry. Only in very rare cases is it possible from qualitative molecular-orbital considerations to predict the geometry of a given molecule. Usually this can only be discussed after a thorough calculation has been carried out. 

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