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. is the determinant formed by replacing spin-orbital

Head-Gordon, Pople, and others have advocated the use of configuration interaction with only single substitutions (CIS) as the starting point for investigations of excited electronic states. In their 1992 paper, Foresman, Head-Gordon, Pople, and Frisch [1] list the following desirable properties of CIS: well defined (and differentiable), applicable to large systems, size-consistent, variational, and providing directly comparable (i.e. orthogonal) electronic state solutions. They go on to present equations for the CIS energy and gradient when the reference is a single determinant obtained from an SCF procedure. These notes present a derivation of the CIS energy for general and several specific types of single-determinant references. Later, we discuss some extensions which are necessary for reliable treatments of open-shell systems.