Derivation of the Configuration Interaction Singles (CIS) Method for Various Single Determinant References and Extensions to Include Selected Double Substitutions (XCIS)

|Φ0〉 is the so-called “reference,” typically obtained from a Hartree-Fock self-consistent-field (SCF) procedure as the best single Slater determinant (or configuration state function, CSF) which describes the electronic state of interest. |Φi 〉 is the determinant formed by replacing spin-orbital i in |Φ0〉 with spin orbital a, etc. These notes follow the convention that i, j, k denote orbitals occupied in the reference, a, b, c denote orbitals unoccupied in the reference, and p, q, r are general indices. The widely-employed CI singles and doubles (CISD) wavefunction includes only those N -electron basis functions which represent single or double substitutions relative to the reference state and typically accounts for about 95% of the correlation energy for small molecules near their equilibrium geometries.