The ammonia VSEPR

The H-N-H angle in NH₃ is 107^o while the H-C-H angle in CH₄ is 109.5^o. The simplest explanation for both is the Valence Shell Electron Pair Repulsion (VSEPR) theory. Methane adopts a tetrahedral geometry to minimize repulsion between the four electron pairs in the C-H bonds. Similarly for ammonia, but it has a lone pair, which is fatter near the nucleus, so the lone pair-bond repulsion is slightly larger than the bond-bond repulsion. This results in a H-N-H angle that is slightly smaller than 109.5^o.

Here is a Jmol application I wrote to illustrate just that. I use GAMESS and B3LYP/6-31G(d) to compute the geometry (H-N-H angle = 106^o) and molecular orbitals. Molecular orbitals are not unique and most quantum programs do not produce VSEPR orbitals by default. Instead you have to tell the programs to localize the orbitals after they have been computed. There are several criteria for what localized orbitals are, and one of them is to minimize electron pair repulsion as VSEPR theory suggests. In GAMESS (the only program I know of which this option) such localized molecular orbitals are called Ruedenberg orbitals after Klaus Ruedenberg who first devised an algorithm to compute them with modern theoretical methods.

Jmol allows you to load several files at once and display orbitals for each simultaneously. So I simply computed orbitals for three different ammonia orientations (get the output files here, here, and here). Then it was simply a matter of writing a small script to go from one geometry to the other. It's very simple and the entire script can be found here:

load files "nh3b.log" "nh3c.log" "nh3d.log"
background white
rotate x -90
frame 1.1;isosurface mo26 mo 26 fill translucent 0.4
delay 4
frame 1.1;isosurface mo24a mo 24 fill translucent 0.9;delay 0.2
frame 1.1;isosurface mo24a mo 24 fill translucent 0.8;delay 0.2
frame 1.1;isosurface mo24a mo 24 fill translucent 0.7;delay 0.2
frame 1.1;isosurface mo24a mo 24 fill translucent 0.6;delay 0.2
frame 1.1;isosurface mo24a mo 24 fill translucent 0.5
delay 3
frame 1.1;isosurface mo24a mo 24 fill translucent 1.0
frame 3.1;isosurface mo24d mo 24 fill translucent 0.5;
select 3.1; spacefill off; wireframe off;
select 2.1; spacefill off; wireframe off;
frame all
delay 1
frame 3.1;isosurface mo24d mo 24 fill translucent 1.0;
frame 2.1;isosurface mo24 mo 24 fill translucent 0.5
frame all
spin on