I am not a quantum chemist, but I am (starting to be) a user of electronic structure software. In the picture (screenshot) is the electron density of the same molecule. On the left I calculated the density using B3LYP/6-311++G*, on the right I used B3LYP/6-311G*.
I have visualized the densities using Avogadro. In Avogadro, I can visualize a few of the HOMO/LUMO orbitals. The screenshot is of the first LUMO for both calculations.
In the images, red indicates electron rich areas, blue indicates electron poor areas. The molecule (caffeine) was in the presence of point charges which created an electric field, explicitly polarizing the electron density.
My Question: Why does the presence of diffuse function (the plus's in 6-31++G*), make the LUMO orbital opposite in electron density? I understand allowing diffusion would change the electron density, but it looks nearly exactly opposite now (however the total density looks pretty much the same - see last image).
Note that these are screenshots of just two orbitals, the overall density plots shown below, look very similar.
I am not a quantum chemist, so please use small words...