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A molecule is made up of bound charged particles. Apply a strong enough electric field and it will be torn apart. What will happen if a magnetic field is applied? This question has to be answered in several layers spanning effects on electronic structure, electronic potential energy surface (PES) and nuclear motion while keeping in mind possible caveats in applying the zero-field methodologies directly such as the validity of the Born–Oppenheimer approximation, maintenance of gauge invariance, choice of basis sets, symmetry of the system in the presence of the field, etc. This thesis builds on the work done in the last two decades, adding to the existing methodologies by formulating, implementing, benchmarking and applying a fully quantum and non-perturbative method for solving the nuclear Schrödinger equation in the presence of a magnetic field of arbitrary strength.
The central contribution is to adapt the Wilson Hamiltonian formalism, originally rooted in lattice gauge theory, to molecular systems via a reduced-mass and mass-weighted charge approach, enabling the first fully quantum mechanical calculations of the rovibrational spectra of diatomic molecules, such as H2, under arbitrary magnetic field strengths and orientations. The work has uncovered coupled electron–nuclear dynamics, revealed nonlinear spectral shifts, symmetry breaking, and field-induced state mixing in the rovibrational spectra of H2.
In parallel, a real-space Wilson Hamiltonian is combined with imaginary-time propagation (WH- ITP) for the first time and applied to two-dimensional quantum dots, achieving high accuracy across weak to ultrastrong fields and capturing key phenomena such as energy shifts, wavefunction localization, and anisotropy in materials like GaAs and phosphorene.
Finally, the response of atoms and molecules to non-uniform magnetic fields is explored using gauge-origin-invariant Hartree–Fock methods, uncovering novel mechanisms of orbital degeneracy lifting, strong directional dependence, and the critical role of reference points in determining energy shifts and equilibrium configurations.
This work provides a plausible, unified, and versatile framework for understanding matter in extreme magnetic environments, with implications for spectroscopy, astrochemistry, and quantum materials. |