Abstract
We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Highlights
Accurate and efficient calculation of magnetic properties is an important challenge for quantum-chemical methods
For the LHC and Tao and Vignale (TV) re-parameterizations, which result in everywhere negative functions gLHC(ρ) and gTV(ρ), respectively, this decay behaviour is readily visualized in a log–log plot; see Fig. 2
We have reported an implementation of DFT and current-density functional theory (CDFT) for molecular calculations in magnetic fields
Summary
Accurate and efficient calculation of magnetic properties is an important challenge for quantum-chemical methods. Most applications of DFT to molecular magnetic properties are performed with standard, density-dependent exchange–correlation functionals, often developed primarily for energetics in the absence of magnetic fields. Comparisons of these results with recent benchmark data and those from standard DFT calculations allow us to assess the quality of the different CDFT functionals.
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