Pragmatic Improvement of Magnetic Exchange Couplings from Subsystem Density-Functional Theory through Orthogonalization of Subsystem Orbitals

We explore a pragmatic way of correcting magnetic exchange coupling constants from subsystem density-functional theory (sDFT). Our previous work [Faraday Discuss. 2020, 224, 201-226] showed that sDFT yields robust spin densities for broken-symmetry-like states, but severely underestimates the magnitude of exchange couplings when using approximate, density-dependent nonadditive kinetic-energy functionals. Evaluating the nonadditive kinetic energy nonselfconsistently by means of potential reconstruction and the exact single-particle kinetic-energy expression improved the results tremendously, but this rendered the approach computationally unattractive. Here, we follow the idea of evaluating the total-system kinetic energy (as needed for the nonadditive kinetic energy) from a set of approximate supersystem orbitals, which are simply obtained from orthogonalizing the sDFT subsystem orbitals. We demonstrate that this leads to a significant correction of the exchange-coupling constants at low computational cost. Moreover, the coupling constants calculated in this way are more robust to a change of the exchange-correlation functional than the corresponding broken-symmetry (Kohn-Sham-) DFT values. However, we also identify a significant basis-set dependence in the results from orthogonalized sDFT.