In the N-electron basis of Slater determinants, one expects the matrix elements of Ĥ to be integrals over 3N dimensions. However, given the two-electron nature of the Hamiltonian, and because the MOs are orthonormal, Slater determinants that di er by more than two spinorbitals yield a zero matrix element. e remaining elements can be expressed as sums of integrals over one-or two-electron coordinates, which can be computed at a reasonable cost. ese simpli cations are known as Slater-Condon's rules, and reads