Friday, April 2, 2010

Double bonds - banana and otherwise



Figure 4.12. (a) B3LYP/6-31G(d) optimized geometry of ethene; (b) and (c) 0.045 au isosurfaces of the two localized banana MOs corresponding to the double bond.
Click on the picture for an interactive version
From Molecular Modeling Basics CRC Press, 2010

VSEPR theory can be used to explain structures of molecules with double and triple bonds, though this is rarely done in textbooks. Figure 4.12 shows some localized MOs for ethene, where the double bond is shown to consist of two curved MOs (sometimes called banana bonds), rather than the usual sigma and pi MOs. The banana LMOs are less spread out than single-bond LMOs, leading to less repulsion and an H–C–C angle larger than 109.5°, namely 116.3° [at the B3LYP/6-31G(d) level of theory].



Figure 4.13. 0.045 au isosurfaces of a localized pi MO [(a) top view and (b) side view] and two localized sigma bond MOs in benzene. The level of theory is B3LYP/6-31G(d).
Click on the picture for an interactive version
From Molecular Modeling Basics CRC Press, 2010

In the case of benzene the LMOs actually look like sigma and pi orbitals (Figure 4.13). Figure 4.13a and b are two views of the pi-bond LMO primarily between C4 and C5. Notice, however, that there is significant delocalization onto C3 and C6. There are identical pi-bond LMOs between C3 and C2 as well as C1 and C6, and the net result is an identical C–C bond length of 1.397 Å, roughly halfway between the CC bond length in ethane (1.531 Å) and ethene (1.331 Å).

I have discussed how to make these plots in a previous post.
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