Because of the fermionic nature of electrons, a permutation of two contiguous creation operators results in a sign change a † j a † i = -a † i a † j , which makes their ordering relevant, e.g., a † j a † i a † k | = -|I . A determinant can be bro- ken down into two pieces of information: i) a set of creation operators corresponding to the set of occupied spinorbitals in the determinant, and ii) an ordering of the creation operators responsible for the sign of the determinant, known as phase factor. Once an ordering operator Ô is chosen and applied to all determinants, the phase factor may simply be included in the CI coe cient.