The FCI Hamiltonian is very sparse and maybe constructed matrix-element by matrix-element for non-zero elements described by the well-known Slater-Condon rules, described in §6.1. These rules exist because physical Hamiltonians at the microscopic-level contain 1-particle (1-body) and 2particle/pair (2-body) interactions. These 1-particle interactions are the kinetic energy or effective potential (interactions with particles that are not electrons, e.g. nuclei), while the 2-particle interactions are the inter-electron interactions. The equations implementing the Slater-Condon rules for explicitly restricted-systems are found in both and .