Toward ab initio realizations of Collins's conjecture

An ab initio approach formulated under an entropy-inspired repartitioning of the electronic Hamiltonian is presented. This ansatz produces orbital eigenvalues each shifted by entropic contributions expressed as subsets of scaled pair correlation energy terms present in second-order Møller-Plesset (MP) perturbation theory. Under the auspices of Collins's conjecture, which suggests that the electron correlation energy is approximately proportional to the Jaynes entropy of the one-electron density matrix, we introduce a parameter that controls the accuracy of the resultant one-electron density at the MP2 level. By tuning the density in a somewhat automated way, we achieve one-electron densities on par with those from full configuration interaction for single-bond dissociation. This parameter can then be used to add a Collins's-like static correlation correction to the energy functional, capturing both dynamical and nondynamical correlation effects in many-electron systems. The performance of the proposed method and its related variants approaches the accuracy of generalized valence bond theory for estimating single bond dissociation energies (BDEs) for a set of small, closed-shell molecules composed of first and second row elements. Our results hold implications for reincorporating the missing (static) correlation energy in regularized perturbation theories, which is typically discarded. Finally, we propose generic BDE parameters (accurate to within 7% on average) that could be used for strongly correlated systems in general.