Beyond Kohn-Sham DFT by including explicit orbital density dependence

Many shortcomings of practical implementations of Kohn-Sham DFT can be traced to self-interaction error that is introduced when the classical Coulomb interaction is estimated from total electron density. A more accurate estimate includes only the interaction of an orbital density with the density of other orbitals, thereby introducing explicit orbital density dependence (ODD). While shortcomings of KS-DFT functional calculations are often ascribed to 'high-correlation', the root of the problem can in some cases be due this single-electron self-interaction. One example of such a system is the manganese dimer, Mn2. Calculations at the generalized gradient approximation (GGA) and meta-GGA level give qualitatively incorrect results with the bond energy overestimated by nearly 1 eV and bond length underestimated by about 1 A in a ferromagnetic ground state. However, calculations including Perdew-Zunger self-interaction correction, which brings in an ODD functional form, give antiferromagnetic ground state and the results are in close agreement with both experimental observations and high level quantum chemistry calculations [1]. The shortcoming of the GGA and meta-GGA functionals can be understood from analysis of the atomic and molecular orbitals. Similarly, the balance between localized and delocalized electronic states in diamine molecular cations [2] and electronic holes in oxides (such as Al substituted SiO2 and Li substituted MgO) [3] are well represented with an ODD functional while GGA and meta-GGA functionals as well as commonly used hybrid functionals (with less than 50% exact exchange) fail to produce the localized states. The energy of excited electronic states of molecules is also better reproduced with ODD form [4]. By extending the functional form beyond that of KS-DFT and allowing for explicit ODD in the energy functional, self-interaction can be avoided and the accuracy of calculated results improved significantly.