Error Control and Automatic Detection of Reference Active Spaces in Many-Body Expanded Full Configuration Interaction

Abstract: We present a wide-reaching revamp of the generalized many-body expanded full configuration interaction (MBE-FCI) method. First, we outline how to automatize the selection of reference active spaces whereby the inherent bias introduced through a manual identification is reduced, also within the context of traditional complete active space methods. Second, we allow for the use of compact orbital clusters as expansion objects, which works to circumvent the unfavorable scaling with the number of orbitals included in the space complementary to the reference orbitals. Finally, we present a new algorithm for ensuring that many-body expansions can be efficiently terminated while conservatively accounting for resulting errors. These developments are all tested on a variety of molecular systems and different orbital representations to illustrate the abilities of our algorithm to produce correlation energies within predetermined error bounds, significantly broadening the overall applicability of the MBE-FCI method.