Extending conceptual DFT to include external variables: the influence of magnetic fields

An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity. The two simplest global reactivity descriptors, the electronic chemical potential (μ) and the hardness (η), are considered for the main group atoms H-Kr using current density-functional theory. The magnetic field strength, |B|, is varied between 0.0 and 1.0 B ₀ = ħe ^-1 a ₀ ^-2 ≈ 2.3505 × 10⁵ T, encompassing the Coulomb and intermediate regimes. The carbon atom is studied as an exemplar system to gain insight into the behaviour of the neutral, cationic and anionic species under these conditions. Their electronic configurations change with increasing |B|, leading to a piecewise behaviour of the ionization energy (I) and electron affinity (A) values as a function of |B|. This results in complex behaviour of properties such as the electronegativity χ = -1/2(I + A) = -μ and hardness η = 1/2(I - A). This raises an interesting question: to what extent are atomic properties periodic in the presence of a magnetic field? In the Coulomb regime, close to |B| = 0, we find the familiar periodicity of the atomic properties, and make the connections to response functions central to conceptual DFT. However, as the field increases in the intermediate regime configurational changes of the atomic species lead to discontinuous changes in their properties; fundamentally changing their behaviour, which is illustrated by constructing a periodic table of χ and η values at |B| = 0.5 B ₀. These values tend to increase for groups 1-2 and decrease for groups 16-18, leading to a narrower range overall and suggesting substantial changes in the chemistry of the main group elements. Changes within each group are also examined as a function of |B|. These are more complex to interpret due to the larger number of configurations accessible to heavier elements at high field. This is illustrated for group 17 where Cl and Br have qualitatively different configurations to their lighter cogener at |B| = 0.5 B ₀. The insight into periodic trends in strong magnetic fields may provide a crucial starting point for predicting chemical reactivity under these exotic conditions.