An efficient implementation of these rules requires

• to find the number of single-particle state substitutions between two determinants
• to find which single-particle states are involved in the substitution
• to compute the phase factor if a reordering of the single-particle states has occured

We can solve this problem using our odometric approach or alternatively using a bit representation as discussed below and in more detail in

• Scemama and Gimer's article (Fortran codes)
• Simen Kvaal's article on how to build an FCI code (C++ code)

We recommend in particular the article by Simen Kvaal. It contains nice general classes for creation and annihilation operators as well as the calculation of the phase (see below).