Walsh model

Later there was an attempt by ab initio calculation to fit the electron structure of diazirine into the Walsh model of cyclopropane (69MI50800). According to these SCF-LCAO-MO calculations three MOs add to the description of the lone electron pairs, all of which also contribute to some extent to ring bonding. As to strain, 7r-character and conjugative effect, the term pseudo-rr-character was used. 

The problems of why certain theoretical models seem to work, henceforth designated the justification problem, is a constant preoccupation of theoretical chemists. The papers written on justification are numerous. We note here the most recent attempt by Buenker and Peyerimhoff to summarize arguments and data relevant to the justification of the old Mulliken-Walsh model of molecular structure which proved particularly successful in the interpretation of the dependence of bond angle and bond length distortions on the number of electrons (i.e. MO occupancy) in small molecules26S ... 

The effectiveness of the second type of overlap presumably determines the extent of oMnic character of tho epoxide. That ethylene oxides are less unaaturated in character than the corresponding cyclopropane derivatives is then attributable to a less favorable oxygen atomic-orbital orientation. The Walsh model is a satisfactory one in that it predicts accurately the C—H bond force constants... 

Fig. 3. The highest occupied molecular orbital capable of 7r-bonding in the Walsh model (73) for cyclopropane.

D A barrier height of 0.8 kcal/mole is obtained in the absence of silicon d orbitals, i) Such a picture is reminiscent of the Walsh model of aziridine -where the nitrogen atom is sp2 hybridized as in methylene imine 171.172),... 

A. The Coulson-Moffit and Walsh Models of the Molecular Orbitals of Cyclopropane 220... 

The Coulson-Moffit and Walsh models of the cyclopropane orbitals have been used since the 1940s but there has been some argument about which, if either, provides an adequate description of the facts. Walsh s model has been the more popular because it is perhaps easier in concept and also because it was believed that the models are equivalents, although it was pointed out that they were not at the very outset more recent studies have particularized the differencesS S. ... 

FIGURE 3. Alternative hybridization schemes in the Coulson-Mofiit model the hybridization state is between sp and sp and the maxima of the orbitals in the plane of the ring are directed at 22° to the C-C bonds. In the Walsh model there are sp hybrid bisecting the C-C-C angles and, perpendicular to these, unhybridized C(2p) orbitals all these orbitals being in-plane... 

FIGURE 4. Showing how molecular orbitals of the Coulson-Moffit and the Walsh models are made up by the linear combination of atomic orbitals of Figure 3. For each model the upper trio of symmetry d and a l is antibonding and the lower is bonding... 

The underlying reason could be that the Walsh model of cyclopropane has a quasi-cyclopropenyl ring system which could be more effective at accepting an electron pair than the external p system, which is so adept at electron pair donation. Delocalization into the former one would require the planar conformation observed for the radical anions 127 and 128 . 

The bent bond picture, later restated in terms of localized molecular orbitals, extends the model presented by Pauling and Slater for ethylene to a stem with three centers. Walsh s model parallels that of Mulliken for the a, w model of the double bond widely used in Hiickel theory. Since the canonical orbitals are good models for the interpretation of photoelectron spectra (see Introduction) we will discuss the Walsh model briefly. 

According to the Walsh model discussed before, one linear combination of the 3e orbital of cyclopropane is capable of interaction with a tt system in the so called bisected conformation a, the most stable conformation (s-trans) of vinylcyclo-propane The same model predicts for the perpendicular conformation b no interaction between the three-membered ring and the double bond. 

To interprete the PE spectra of these bicyclopropyl derivatives the Walsh model is suitable. It has been diown recently that for compounds with 6 values of zero degree the consideration of the tangential p orbitals only (see below) in the three-membered rings is sufficient. For those compounds, however, in which B also deviates considerable from zero the radially oriented 2p orbitals (see below) have to be con-... 

To use the Walsh model for quantitative description the mixing of HOMO and LUMO, both of the same symmetry, has to be considered This amounts essentially to an admixture of radially oriented components into the HOMOs. As will be shown below this type of mixing plays an important role in reproducing the orbital pattern of bicyclopropyls and higher homologues. The mixing can be expressed as follows ... 

The research on bicydopropylderivatives has led to two corollarys (1) The purely tangential Walsh model works only if the dihedral angle, 6, between both cyclopropane rings does not deviate much from zero degree. (2) The interaction integral Pvvw is found to be —1.73 eV, a value close to tliat found for vinylcyclopropane. 

The main outcome of the PE studies on tricyclopropylderivatives is similar to that derived in the previous chapters (1) For twist angles 6 which deviate considerably from 0 the simple tangential Walsh model has to be extended and the radial contributions have to be considered. (2) For twist angles d around 0° the resonance integral is a maximum, (Jvvw = — 1.73 eV. 

As mentioned earlier, oxidative complexation (pattern 3) and reductive decomplexa-tion (pattern 13) are nothing but alternate representations of 7r-complexation (pattern 2) and TT-decomplexation (pattern 12), respectively. It might be useful to note that the -TT-complex formalism and palladacyclopropane formalism correspond to the Walsh model and more commonly used bent o--bond representation of cyclopropanes, respectively. The palladacyclopropane formalism is useful in discussing the formation of larger palladacycles in terms of carbopalladation of palladacyclopropanes and paUadcyclo-propenes (Part IV). 

The observed interbond angles of PH2 in its two valence states X (92 ) and A A (123 ) were in turn discussed in terms of the Walsh model [43 to 45], the electrostatic force theory [46], and the valence shell electron pair repulsion (VSEPR) theory [47]. 

Of the two, the Walsh model (scheme 74) has become by far the preferred one, especially if one wants to explain the conjugative properties of the cyclopropyl group in terms of overlap, e.g. between and a neighbouring p-type AO or group orbital, attached to the cyclopropane ring in position 1. For such a purpose, the model shown... 

Furthermore, both of them have been used to describe bonding in cyclopropane (sp hybrids in the Moffitt-Coulson model and spVp pair in the Walsh model). 

In summary, we can say that the effect of the Ax perturbation has been well understood for some time while the effect of the A6 perturbation has eluded detection partly because we have been lulled to acceptance of the Walsh model and partly because SD MO theory, the major conceptual vehicle of the chemistry in the second half of this century, is incapable of handling this problem. 

The electron effects of substituents on the structure of the cyclopropane ring have received considerable attention during the year. Microwave studies on 1-cyano- and 1,1-dicyano-cyclopropane have shown that the remote C-2—C-3 bonds are reduced in length (1.500 and 1.485 A, respectively) when compared with cyclopropane (1.510 A). These observations are in accord with the simple Walsh model for electron-accepting substituents. The prediction of a lengthened C-1—C-2 bond was borne out by 1-cyanocyclopropane (1.529 A), but this bond length was not determined for... 

---