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I'm coming from a Physics background and am trying to make sense of the energy level diagram for para-helium and ortho-helium.
From what I've gathered each column shows the different energy levels for different orbitals so that for example the leftmost column with $^1S$ written on top shows the energy levels of 1s, 2s, 3s etc.
What I don't get is what the different denotations on top mean, what does for example $^1P$ and $^3D$ mean?
The index 1 or 3 is used for saying that the spins of the two electrons are parallel or anti-parallel. One spin is up or +1/2, and the other one is down, or -1/2. This is the case in the ground state : the 2 electrons of Helium have two antiparallel spins (one +1/2 and one -1/2). The atom has no total spin, as the two electrons cancel the magnetic effect of their spins. The total spin of the atom is then 1/2 - 1/2 = 0. In such a configuration, the He atom is called para-helium. This remain true if one electron is excited and goes to an upper orbital like 2s, 3s, etc. provided that the two electrons maintain their spins (one up and one down). The total spin is zero, and the atom is an excited state of para-helium.
It is difficult, but not impossible, to change the spin of one electron, so that both electrons have the same spin. In this configuration, the helium is called ortho-helium. The total spin for the whole atom is 1/2 + 1/2 = 1. In that case, there are three possibilities for the projection of the total spin in an external magnetic field. +1 in the sense of the field, -1 in the opposite sens, and zero, if the total spin is perpendicular to the magnetic field. This number 3 is reported in upper index. The differences of the three projections must be an integer.
