Who is following who?

A landmark contribution of Linus Pauling was to show the intimate connection between molecular structure and the spatial arrangement of electronic wavefunctions. This is exemplified by the concept of orbital hybridisation. The figure above shows how by taking different linear combinations of s and p orbitals one can produce orbitals with different directionality.

However, as is often the case in quantum chemistry, it turns out not to be quite so simple. I was surprised to learn recently about the notion of imperfect orbital following. Specifically, the direction of the orbitals is not always the same as that of the nuclei, particularly, for non-equilibrium geometries. This can be seen for ammonia as it undergoes the umbrella inversion (the mode associated with the MASER). This phenomenon  of orbital following in ammonia was elucidated by Cohan and Coulson in 1956.  The figures below are from a JACS paper by Foster and Weinhold. [There is also a nice discussion in the book by Weinhold and Landis.]

In Figure 2 the angle associated with the direction of the orbital is plotted versus the HNH angle in the molecule. If the orbitals followed the nuclear geometry the solid line would lie on top of the dashed line. In the tetrahedral geometry, close to the equilibrium geometry, both angles are about 104 degrees, and the orbitals are approximately sp3. Halfway along the umbrella inversion reaction co-ordinate the molecule has D3 symmetry and both angles are 120 degrees. Roughly the orbitals consist of three sp2 orbitals and a lone pair p orbital.