Time-dependent nuclear-electronic orbital Hartree–Fock theory in a strong uniform magnetic field

Abstract

In an ultrastrong magnetic field, with field strength B ≈ B0 = 2.35 × 105 T, molecular structure and dynamics differ strongly from that observed on the Earth. Within the Born–Oppenheimer (BO) approximation, for example, frequent (near) crossings of electronic energy surfaces are induced by the field, suggesting that nonadiabatic phenomena and processes may play a more important role in this mixed-field regime than in the weak-field regime on Earth. To understand the chemistry in the mixed regime, it therefore becomes important to explore non-BO methods. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. The NEO generalized Hartree–Fock theory and time-dependent Hartree–Fock (TDHF) theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF− with clamped heavy nuclei are compared against the quadratic eigenvalue problem. Each molecule has three semi-classical modes owing to the hydrogen—two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well; in particular, it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.