Behavior of the active–active propagation constraint for non‑Valdemoro 3‑RDM reconstructions in ACSE

Investigate the behavior of restricting active–active propagation in the anti‑Hermitian contracted Schrödinger equation—i.e., setting to zero residual elements whose indices all lie in the active orbital space—when employing three‑electron reduced density matrix reconstruction functionals other than the Valdemoro reconstruction, in order to determine the effect of this constraint on ACSE performance.

Background

In practical ACSE calculations, the residual depends on the 3-RDM and is typically approximated via reconstruction functionals such as the Valdemoro (V) or Nakatsuji–Yasuda (NY) forms. For multireference wavefunctions the 3-cumulant can be large when all indices are within the active space, which can degrade the V reconstruction that neglects the 3-cumulant.

A common mitigation is to restrict active–active propagation by setting residual elements with all-active indices to zero. The authors note that this restriction is essential for the V reconstruction but explicitly state that the behavior of this constraint has not been explored for other reconstructions, leaving its impact on non‑V functionals unresolved.