Walsh molecular orbitals

Figure 7.31 Walsh molecular orbital diagram for AH2 molecules...

The stability of the trihalogen intermediate is greatest when the least electronegative atom is in the central position. This complex is expected to be bent by examination of the appropriate Walsh molecular orbital diagrams and it is possible that the reaction is constrained to take place only for certain preferred interaction geometries. Trajectory calculations [561] for Cl + Br2, I2 and Br + I2 could not reproduce the experimental results with any surface having a potential well that preferred collinear approach of the reagents. 

There are two classical approaches to bonding in cyclopropane namely the Walsh molecular orbital approach and the bent bonds or banana bonds of the Coulson-Mofiit model. 

In the Walsh description, these very same valence orbitals are used on each CH2 group, but one does not go to the trouble of combining them to make new orbitals pointing approximately along the bond directions.11 One uses directly the three local 2pJ/-type orbitals of the three CH2 groups to build one set of three molecular orbitals, and the three local (2s, 2pj.) out -type hybrids to build a second set of molecular orbitals. The procedure is illustrated in Fig. 26. 

The reader may now wish to compare the three bonding molecular orbitals derived in this manner with the three molecular orbitals shown at the end of the previous section. There is a strong resemblance. This similarity increases if, in the Walsh method, the 2pj/-derived molecular orbitals are allowed to mix with the (2s, 2pz)-... 

Semi-empirical molecular orbital calculations have been carried out on the model phosphorane HaPiCHa. Besides the expected transfer of charge, the inclusion of the phosphorus 2>d orbitals showed a significant hyperconjugative interaction between the CHg orbitals and a 2>d orbital of appropriate symmetry on phosphorus. Calculations on cyclopropylidene-phosphorane revealed a similar interaction between the Walsh orbitals of the ring and an in-plane phosphorus 2>d orbital. 

The reported proposed sequence also offers two additional alternative mechanisms for the cyclodimerization of BCP (3), involving either intermediate 463 or 464 [6a, 13b]. However, they appear less likely, requiring successive three-membered ring fissions and formations. Alternatively, a thermally allowed concerted [jt2s + rt2a -I- pericyclic reaction involving the Walsh type molecular orbital of cyclopropane [124] has been proposed (Fig. 4) [13b]. 

Problem 9-15. Could the same predictions be made from a simple electron repulsion argument If n pairs of electrons must be accommodated in the valence-shell molecular orbitals, then assume simply that they will be as far apart as possible. Up to four electrons will push each other as far apart as possible, to create linear geometry more than four must be distributed more densely, so that the angle between the substituents will be less that 180°. Does this simple hypothesis explain everything that Walsh s rules do Is there any advantage to using Walsh s correlation diagram analysis ... 

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. 

The g tensor for O3 is discussed below on the basis of Walsh s diagram (336) for a 19-electron radical. The O3 ion is expected to be a bent radical with the odd electron occupying the 2b, molecular orbital (MO) (332) which has the form (322)... 

For example, the well known Walsh rules 52 for molecular geometries were first based on simple molecular orbital arguments depending on orbital overlap and the difference between s and p atomic energies. Pearson 51 re-interpreted them from a symmetry point of view as the following example will show. 

Refer to the molecular orbital diagram for NOj in Fig. 5.31. Walsh diagrams, similar to those in Fig. 6.16, predict that the HOMO (oi) becomes more stable as the O—N—Obond... 

Out of each pair of states correlated in this way only one corresponds to an energy minimum. For example, simple molecular orbital theory predicts that CH2 will be linear or nearly linear in its lowest triplet state (Lennard-Jones and Pople, 1951 Walsh, 1953a) the stable state is then 3ZB and the bent configuration then represents the turning-points of vibrational motion in the bending mode of the electronic state. 

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

Fig. 4. Walsh (1953) diagram of the shape of HAAH and the energies of the molecular orbitals (Murrell, el al., 1965). The fifth, sixth, and seventh filled MO s correspond/to H—CssC—H, H—N- =N—H and H—O—O—H, respectively. Two high energy A- -H o orbitals are not shown.

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