  [Abridged] The extension of conceptual DFT to include external fields in
chemical systems is utilised to investigate the effects of strong magnetic
fields on the electronic charge distribution and its consequences on the
reactivity of $\pi$-systems. Formaldehyde, H$_2$CO, is considered as a
prototypical example and current-DFT calculations are used to evaluate the
electric dipole moment together with the electron density and the Fukui
functions, which provide insight into how H$_2$CO behaves chemically in a
magnetic field. In particular, the symmetries of these quantities are analysed
based on group, representation, and corepresentation theories using QSym$^2$.
This allows us to leverage the simple symmetry constraints on the macroscopic
electric dipole moments to make profound predictions on the more nuanced
symmetry transformation properties of the microscopic frontier MOs, electron
densities, and Fukui functions. This is especially useful for complex-valued
MOs in magnetic fields whose detailed symmetry analyses lead us to define the
new concepts of modular and phasal symmetry breaking. Through these, the
connection between the vanishing constraints on the electric dipole moments and
the symmetry of electron densities and Fukui functions can be formalised, and
the inability of the magnetic field in all three orientations considered to
induce asymmetry with respect to the molecular plane can be understood from a
molecular perspective. Furthermore, the detailed forms of the Fukui functions
reveal remarkable reversals in the direction of the C=O dipole moment in the
presence of a parallel or perpendicular magnetic field, which can be attributed
to the mixing between frontier MOs due to their subduced symmetries in magnetic
fields. The findings in this work are also discussed in the wider context of a
long-standing debate on the possibility to create enantioselectivity by
external fields.
