The maximum overlap method (Sec. 4.5.11) is successful in many cases, but when optimizing excited state orbitals it can be prone to variational collapse (falling from the target configuration to the ground state). This behavior was improved with the “initial” MOM (IMOM) procedure, which uses the initial guess molecular orbital coefficients as the reference for the overlap criterion (see Sec. 7.6 for details). While IMOM lends a significant improvement to the MOM, it occasionally also falls victim to variational collapse, incentivizing the pursuit of alternatives to these methods.
One such alternative, proposed by Kevin Carter-Fenk and John Herbert, is the
state-targeted energy projection (STEP) procedure, which applies a simple level-shift
formalism to converge to the target state.
J. Chem. Theory Comput.
(2020), 16, pp. 5067. The STEP algorithm retains the cost-effectiveness of the MOM procedures (about the same cost per cycle as a normal SCF), while simultaneously being far more robust in converging to the target state. Further details on the STEP procedure can be found in Sec. 7.8.3, and for a complete account of the STEP algorithm the reader is referred to Ref. 158.
The STEP-related $rem variables are the following: