  This review presents a concise, yet comprehensive discussion on the evolution
of theoretical methods employed to determine the ground and excited states of
molecules in weak and strong magnetic fields. The weak-field cases have been
studied previously in the context of NMR, where the shielding tensor was
determined by correcting the Diamagnetic Shielding operator up to the second
order. However, the magnetic fields due to the Neutron Stars are extremely high
and cannot be treated perturbatively. Thus, in the interest of the
astrophysical and astrochemical community, this review aims to elaborate on the
computational advancements in quantum mechanics from Hartree-Fock (HF) to
Density Functional Theory (DFT), in the context of molecules in a high (and
ultrahigh) magnetic field. It is found that the mean-field approximation of
electron-electron correlation, as in the case of Hartree-Fock Theory, yields
inaccurate results. On the contrary, CCSD and DFT are found to overcome these
challenges. However, treating eletron-electron correlations in DFT can be
challenging for heavier ions as transition metals. To circumvent this, we
propose the use of DFT/CCSD along with effective Hamiltonian methods, which are
likely to offer physical insights with reasonable accuracy.
