Singlet and Triplet States

In a hydrogenic (one electron) species, the frequencies of the lines in the atomic absorption or emission spectra corresponds to transitions between different energy levels.

In atoms with more than one electron, interaction between the electrons means that the transition energies are not simply related to differences between the energies of the different energy levels.

The electrons in different orbitals can interact with each other in a range of possible ways, depending on the relative orientations on the electrons spins, and also the nature of the orbitals occupied. In a two electron system, the are two possible types of pairing of the electrons, when in different orbitals, and these are known as singlet and triplet states.

Let us consider Helium:

The ground state electronic configuration is 1s2, and the first excited state is 1s12s1. However, whilst the electrons must have paired spins when both occupy the 1s orbital, they need not be when one occupies the 1s orbital and the other occupies the 2s orbital.

Hund’s rule states that the configuration with the electron spins parallel is at a lower energy than the configuration with paired spins. When the electron spins are paired, their individual spin momenta cancel each other out, and there is no overall spin.

There is only one orientation in which this may be achieved, and hence this configuration is known as a singlet state. When the electron spins are parallel, their individual spin momenta add together to give non-zero total spin, and this can be achieved in three ways. Thus, the state is known as a triplet state.

Hund’s rule therefore means that the triplet excited state of He is lower in energy than the singlet excited state of He.

The degree of electron-electron repulsion depends greatly upon the state the two electrons occupy, and the difference between the triplet and singlet states in He is 0.8 eV.

Whilst the spectrum of helium might be more complicated than that of hydrogen due to the splitting of the levels into singlet and triplet states, there are two important simplifications in interpreting the spectrum: the first is that only one electron may be promoted from the ground state, and the second is that no transitions occur from a triplet state to a singlet state, or vice versa.

This is because the relative orientations of the electron spin cannot change during a transition.