Excitation energies can be found by taking the difference between the ground state energy of systems with different numbers of electrons. For example, a gap energy can be written as
where is the energy to add an electron (the electron affinity) and is the energy to remove an electron (the ionization potential).
To obtain an estimate of the electron(hole) energies, , within a QMC calculation, all that is required is to include (remove) the corresponding conduction (valence) orbital in the Slater Determinant part of the trial wavefunction given in Eq.(). The -point at which the electron(hole) energy is calculated, is determined by the -value of this conduction (valence) orbital.