Standard Electronic Orientation

The previous two sections show how to `standardize' the DFT energy of a molecule. However, it ignores the effect of a rotation of a degenerate orbital. For example, the occupied p-orbital of the Boron atom. In HF theory rotation of this orbital does not effect the energy. In DFT rotation will introduce grid effects, introducing an error dependent on the size of the grid. Obviously, with an infinite grid this problem does not exist.

This can be overcome by removal of degeneracy, forcing the orbital into a particular orientation. In Q-CHEM this is achieved by introducing a small quadrupole field [147], with the components
$$\begin{align}x^{2} &= +1 \mathrm{x} 10^{-10} \\ y^{2} &= +2 \mathrm{x} 10^{-10} \\ z^{2} &= -3 \mathrm{x} 10^{-10} \end{align}$$
The effect of the field on the total energy is negligible, but `standardizes' the DFT energy for degenerate molecules.