“A local tensor that unifies kinetic energy density and vorticity in density functional theory” S. Sen and E.I. Tellgren, J. Chem. Phys. 149, 144109 (2018): Editor’s Choice 2018 (72 articles out of all published in 2018), Featured article, also selected for publication as popular science article in SciLight (AIP)
(Clockwise from left) Fig. 1: C atom in a uniform magnetic field;
Fig. 2: H2O in a non-uniform magnetic field.
A new ingredient for designing exchange-correlation functionals for use of DFT in magnetic fields was proposed. Instead of kinetic energy density as a scalar, a tensor , Q, was suggested which contains the usual kinetic energy density as its trace and vorticity on the off-diagonals. The natural inclusion of vorticity into the tensor form of the kinetic energy density such that functionals with Q or quantities derived from Q as ingredients would smoothly transition between computations with a field to one without suggests that the minimum level of complexity for functionals that can handle computations in magnetic fields is where the kinetic energy density is considered, ie. the so-called meta-GGA functionals. This finding fits well with our observation that TPSS, a meta-GGA functional, works very well for computing both magnetic properties as well as PES in magnetic fields. Quantities analogous to the electron localisation function (ELF) can also be derived from Q which are necessary to for designing functionals with suitable short and long rage behaviour.
Fig 3.1 Spin and Orbital Effects: Errors in anapole susceptibility, A, computed by various methods in Luaug-cc-pCVTZ basis relative to MP2.
Fig 3.2 Effect of Correlation
Fig 3.3 DFT functionals and relatively cheaper wavefunction methods like Hartree-Fock and MP2 were benchmarked against coupled-cluster for properties like magnetisability and anapole susceptibilities. TPSS and KT3 functionals were found to be the best suited for describing magnetic properties.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement 745336.