It is relatively easy to implement CIPSI as an alternative to GKCI and HCI. (It is especially easy since the key equations already exist inside Epstein-Nesbet pertubation theory correction to selected-CI methods.)
The main motivation is that helps the hierarchy of methods. GKCI is very fast for selecting determinants (and noniterative) but tends to select too many determinants. HCI is slower and iterative, but gives a better selection of the minimal set of determinants. CIPSI is still slower than HCI (and is still iterative) but gives probably "as good as possible" a set of determinants as one can attain in any semi-computationally-efficient way.
It would be interesting to do a systematic comparison, which is something @JamesSMAnderson has expressed interest in.
It is relatively easy to implement CIPSI as an alternative to GKCI and HCI. (It is especially easy since the key equations already exist inside Epstein-Nesbet pertubation theory correction to selected-CI methods.)
The main motivation is that helps the hierarchy of methods. GKCI is very fast for selecting determinants (and noniterative) but tends to select too many determinants. HCI is slower and iterative, but gives a better selection of the minimal set of determinants. CIPSI is still slower than HCI (and is still iterative) but gives probably "as good as possible" a set of determinants as one can attain in any semi-computationally-efficient way.
It would be interesting to do a systematic comparison, which is something @JamesSMAnderson has expressed interest in.