Universal Generalization of Density Functional Theory for Static Correlation

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal $O(N^3)$ generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction’s strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Figure 1

${\mathrm{C}}_2{\mathrm{H}}_4$ rotational barrier potential energy surfaces obtained from CASSCF(12,12)/ACSE, CCSD(T), PBE-RDMFT, SCAN-RDMFT, PBE-DFT, SCAN-DFT, and CASSCF(12,12)/tPBE calculations with the cc-pVDZ basis set.

Figure 2

Relative energies of meta- and para-benzyne with respect to ortho-benzyne from RDMFT and DFT with the SCAN and PBE functionals, MC-PDFT using the tPBE functional, and CCSD(T).