One more quantum number, that relating to the inversion (i) symmetry operator can be used in atomic cases because the total potential energy $$V$$ is unchanged when all of the electrons have their position vectors subjected to inversion (i.e., $$i\textbf{r} = \textbf{-r}$$). This quantum number is straightforward to determine. Because each $$L, S, M_L, M_S, H$$ state discussed previously consists of a few (or, in the case of configuration interaction several) symmetry adapted combinations of Slater determinant functions, the effect of the inversion operator on such a wavefunction $$\Psi$$ can be determined by:
1. applying i to each orbital occupied in $$\Psi$$ thereby generating a ± 1 factor for each orbital (+1 for s, d, g, i, etc orbitals; -1 for p, f, h, j, etc orbitals),
2. multiplying these $$\pm 1$$ factors to produce an overall sign for the character of $$\Psi$$ under $$\hat{i}$$.
When this overall sign is positive, the function $$\Psi$$ is termed "even" and its term symbol is appended with an "e" superscript (e.g., the $$^3P$$ level of the $$O$$ atom, which has $$1s^22s^22p^4$$ occupancy is labeled $$^3P^e$$); if the sign is negative $$\Psi$$ is called "odd" and the term symbol is so amended (e.g., the $$^3P$$ level of $$1s^22s^12p^1$$ $$B^+$$ ion is labeled $$^3P_o$$).