Abstract
ABSTRACTWe 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 optimisations 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 generalised-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 magnetisability. Generalisations 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.
Highlights
When the Schrodinger equation was solved for the hydrogen molecule and the helium atom in the 1920s, it was made clear that any molecular system could be accurately described with quantum mechanics [2, 3, 4]
Quantum chemistry relies on manybody quantum mechanics, which has proven to be a resilient adversary for a century
It was found that while the KT2 functional outperformed all other functionals at reproducing NMR shielding constants, it did so for the wrong reason: The error in diamagnetic term was an order of magnitude larger than for the other functionals
Summary
When the Schrodinger equation was solved for the hydrogen molecule and the helium atom in the 1920s, it was made clear that any molecular system could be accurately described with quantum mechanics [2, 3, 4]. The strong field regime 0.1B0 < B < B0 is interesting as the direct magnetic effects and electrostatic forces in small molecules are on the same order of magnitude, leading to novel and complicated bonding mechanisms. This regime corresponds to the upper range of magnetic field strengths encountered in magnetic white dwarf (MWD) stars. It was found that the correlation energy was mostly unaffected by the field, except for the beryllium atom
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