The number of states considered in a CISD C.I. involving *n*
doubly-occupied M.O.s and *m* empty M.O.s is:

No. of States = 1 + 2.n.m + (n.m)^{2} + (n(n-1).m(m-1))/2

This represents:

Ground state

+ (one α electron excited + one β
electron excited)

+ (one α electron and one β
electron excited)

+ (two α electrons excited + two β electrons excited)

The first term represents the ground state, the second term represents number of one-electron excitations, and the third and fourth terms represent the number of two-electron excitations.