McLean and Liu define the ith order interacting space in
their paper, ``Classification of Configurations and the Determination of
Interacting and Noninteracting Spaces in Configuration Interaction,'' one of
the two primary papers on the subject
:
``The ith-order subspaces, of all levels of orbital occupation,
contain those and only those functions which have a nonzero Hamiltonian matrix
element with some member of the (i-1)th-order subspaces.''
The 0-th order subspace consists of our Hartree-Fock reference(s), and
the first order interacting
space consists of all N-electron basis functions which
have nonzero matrix elements with one or more of the references.