Kohn–Sham energy decomposition for molecules in a magnetic field

We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent density-functional theory (CDFT) for molecules in the presence of magnetic fields. For a selection of closed-shell dia- and paramagnetic molecules, we investigate the dependence of the total electronic energy and its Kohn–Sham components on the magnetic field. Results obtained from commonly used density-functional approximations are compared with those obtained from Lieb optimizations based on magnetic-field dependent relaxed coupled-cluster singles-and-doubles (CCSD) and second-order Møller–Plesset (MP2) densities. We show that popular approximate exchange–correlation functionals at the generalized-gradient-approximation (GGA), meta-GGA, and hybrid levels of theory provide a good qualitative description of the electronic energy and its Kohn–Sham components in a magnetic field—in particular, for the diamagnetic molecules. The performance of Hartree–Fock theory, MP2 theory, CCSD theory and BDFT with different exchange–correlation functionals is compared with coupled-cluster singles-doubles-perturbative-triples (CCSD(T)) theory for the perpendicular component of the magnetizability. Generalizations of the TPSS meta-GGA functional to systems in a magnetic field work well—the cTPSS functional, in particular, with a current-corrected kinetic-energy density, performs excellently, providing an accurate and balanced treatment of dia- and paramagnetic systems and outperforming MP2 theory