Restricted reference stability and correlated calculations

A real closed-shell RHF or RKS stationary point has distinct internal and external real orbital-rotation channels. Equal alpha and beta rotations remain within the restricted singlet space. Opposite rotations break the spin restriction and probe the real UHF or UKS space. The normalized maps are (kappa, +kappa)/sqrt(2) and (kappa, -kappa)/sqrt(2).

This is the transformation in Seeger and Pople, J. Chem. Phys. 66, 3045 (1977), DOI 10.1063/1.434318, Section III, Eqs. (34)-(36). The KS analogue is Bauernschmitt and Ahlrichs, J. Chem. Phys. 104, 9047 (1996), DOI 10.1063/1.471637. The current implementation tests these real channels only. It does not certify stability to complex orbital rotations.

Both channels have independent eigenvalue, convergence and stop records. The default aggregate verdict remains conservative: a detected instability or a missing convergence verdict makes usable false. A real external instability is labelled as external; it does not establish an internal restricted saddle or an excited electronic state. Historical archives without channel records cannot be reclassified automatically.

For a closed-shell CCSD, CCSD(T), DLPNO-CCSD or DLPNO-CCSD(T) single point, run_job(reference_contract="real_restricted_cc", ...) requests a separate constrained-reference assessment. It requires converged SCF, converged tests for both real channels, and a stable internal channel. reference_usable then describes admission of that real restricted reference. The external verdict and the conservative usable field remain unchanged. This option does not follow the unstable mode, change the orbitals, suppress a test or claim an unrestricted ground-state minimum. It is refused for geometry or Hessian work and for methods outside the listed closed-shell CC family.

Reference admission does not certify the correlated answer. Check amplitude convergence, the triples definition, frozen core, basis and local truncation errors separately. Coupled-cluster energies are not variational HF energies; an external HF instability is a reason to examine reference dependence and possible strong correlation, not proof of an internally unstable RHF solution or an accuracy guarantee for its correlated energy. An independent matched-method comparison and appropriate reference diagnostics remain necessary for a quantitative application. Never silently substitute the constrained-reference assessment for a general SCF stability requirement.