Validity and scope of the correlation conjecture

Determine the scope of molecular deformations and electronic-structure changes for which the cumulant correlation energy is approximately a linear function of the particle-hole symmetrized entropy, as asserted by the correlation conjecture underlying i-DMFT.

Background

The paper considers coarse-grained RDMFT correlation functionals of the form $\tilde F(\zeta)$, with the simplest approximation being linear in a correlation measure. For the particle-hole symmetrized entropy $ph$, this gives a constant correlation temperature and underlies i-DMFT. Prior observations for diatomic dissociation processes suggest an approximately linear relation between the correlation functional and $ph$, but the paper emphasizes that this observation is restricted to ground-state 1RDMs along particular dissociation curves and does not establish a general functional relation.

The numerical study of planar $\mathrm{H}_4^{2+}$ further shows that the relation can hold for deformations preserving minimal orbital pairing but fail for deformations that change orbital character or involve multiple correlated orbital pairs. Establishing the precise validity domain of the conjecture is therefore an explicit unresolved issue relevant to systematically extending i-DMFT beyond its lowest approximation rung.