Gauge-invariant real-space method for density functional calculations in an external magnetic field

This paper describes a configuration-space method for ab initio electronic structure calculations in an arbitrarily strong external magnetic field. Special attention is paid to a manifestly gauge-invariant formulation of the problem that is independent of the discretization. We will show that rigorous gauge invariance can be implemented quite efficiently in real-space methods. To be able to reproduce empirical data for realistic systems, we also formulate our real-space algorithm in magnetic fields for nonlocal ionic pseudopotentials. Here, gauge invariance is again an issue, but has to be maintained by construction of such potentials. Numerical applications focus on two points. The first one is a careful assessment of the convergence properties of our algorithm and in particular the implications of our gauge-invariant formulation. We then calculate the magnetic susceptibilities and nuclear magnetic resonance shifts for a number of typical molecules of physical interest and compare with previous work.