Electronic energy is retrieved by iFCI using an -body expansion of the form
where each term denotes an increment of correlation energy and refer to bodies of the expansion. Incremental correlation energies are defined as
where terms subtract lower-order increments to avoid double counting. Terms represent -body additions to the correlation energy from electrons in the mean field of the remaining electrons, where each value is computed by solving CAS-CI for electrons in orbitals. For example, performs CAS()-CI to give the value of . Proceeding likewise for higher , CAS()-CI produces each .
Heat-bath CI (HBCI) is utilized to solve each CAS-CI Hamiltonian, performing selected CI computations according to determinants, , coupled to the CI wave function in the form , where is the energy cutoff and are determinants in the HBCI subspace.
Truncation of incremental terms is performed by considering natural orbital (NO) occupancy cutoffs, , where
Doing so reduces the size of the virtual space by only including virtual orbitals with sufficiently large NO eigenvalues. Convergence for each iFCI increment is reached when
with units of E. Further truncation in can be performed by utilizing the parameter and a screening cutoff, , in the form
where is in E and is a scalar. This screening is performed by selecting body correlation energy contributions that are above . See Ref. 916 for more details. is a parameter in the input.
iFCI requires a high-spin perfect pairing (PP) reference, where NOs are localized as local bonding-antibonding pairs, or geminals.