Reducing charge delocalization error of density functional theory

Proper treatment of charge delocalization, besides nondynamic correlation, has been a major challenge to density functional theory. Contemporary functionals are known to undershoot the dissociation of symmetric charged dimer A2, a simple but stringent test, and predict a spurious barrier and improperly delocalize charges for charged molecular clusters. We extend a functional designed to treat nondynamic correlation to treat also the charge delocalization with a modification of the secondary nondynamic correlation for parallel spins. The modified functional is shown to eliminate those problems and reduces the multi-electron self-interaction error. Furthermore, its results are the closest to that of CCSD(T) in the whole range of the dissociation compared with contemporary functionals. It also correctly localizes the net positive charge in (CH4)n clusters and predicts a nearly constant ionization potential as result. Overall, we show the feasibility of treating charge delocalization together with nondynamic correlation. Density Functional Theory (DFT) is the principal method of choice in theoretical chemistry and material science [1, 2]. Contemporary density functional approximations (DFA) perform well when the quantum state is dominated by a single electronic configuration. They are less effective when the nondynamic correlation (NDC) becomes significant and requires a multireference treatment. Multireference quantum effects are associated with degeneracies and near-degeneracies of the ground state and are critical to a large variety of molecular properties, such as transition-metal-ligand interactions, diradicals and molecular magnets. The simple example is the dissociation of H2, where Hartree-Fock (HF) method overshoots the dissociation energy by about 190 kcal/mol and contemporary mainstream DFAs overshoot by over 50 kcal/mol [3, 4]. On the other hand, new methods have emerged that make strides in treating the NDC within the single-determinant framework of Kohn-Sham DFT. In particular, Becke has proposed the Becke’05 (B05) functional for nondynamic correlation designed to compensate the delocalization of the exact exchange, a basic characteristic of systems with nondynamic correlation [5, 6]. B05 was extended by Becke in 2013 [7, 8] to include the strong correlation occurring in the dissociation limit of covalent bonds, resulting in the Becke’13 (B13) method. We have modified B13 by introducing a model for the adiabatic connection for nondynamic correlation and reduced the number of empirical parameters significantly as a result [4]. The method is referred as KongProynov’16/Becke’13 (KP16/B13) here. B13 and KP16/B13 were shown to recover most of the correlation in cases where the correlation is extremely strong. B13 and KP16/B13 reduced the errors for dissociation energies of some covalent-bonds to single digits in kcal/mol [4, 7, 8], and KP16/B13 successfully predicted the Mott metal-insulator transition [9] where other mainstream contemporary functionals failed. Both methods were also shown to be competitive in the prediction of various properties in regular systems [10]. Another major challenge to DFAs is the charge delocalization error, also known as fractional charge error. This error has a broad impact on the accuracy of approximate functionals in various applications: incorrect dissociation limits that involve fractional charge, underestimated reaction barriers and ionization potentials, unrealistic charge distributions, to mention just a few [3, 11-18]. The simplest example of this error is the dissociation of one-electron molecule like H2, where most common DFAs yield errors larger