Quantum effects in hydrogen isotopes under extreme conditions
Creators: name: Van De Bund, Sebastiaan
Publisher: name: The University of Edinburgh
Year: 2024
Subjects: Hydrogen
quantum spread
path integral techniques
isotope mass difference
liquid-liquid phase transition
linear quadrupole
hydrides
extreme pressure

description: Hydrogen is the first element in the periodic table, and exhibits a highly unusual phase diagram. Due to its light nuclear mass, hydrogen exhibits significant nuclear quantum effect contributions (NQE). Its closest isotope, deuterium, has double the nuclear mass (and thus weaker NQE), meaning significant isotope effects are observed in various parts of the phase diagram. This thesis assesses the role that NQE plays in hydrogen by employing path-integral techniques to fully account for NQE (neglecting exchange effects), along with an ab-initio treatment of the electrons for a close to full quantum treatment. The hydrogen liquid-liquid transition, an insulator-to-metal transition coinciding with molecular dissociation, is subject to a strong isotope effect well into the kiloKelvin range. Simulations using ab-initio path integral molecular dynamics (PIMD) show that this isotope effect between hydrogen and deuterium is large, on the order of 30 GPa at 1000 K. The choice of xc-functional does not seem to affect the magnitude of the isotopic shift, but does significantly affect the locations of the phase boundaries by as much as 100 GPa due to the difficulty in treating insulating (molecular) and metallic (atomic) fluid phases on the same footing. Next, PIMD runs are performed on the phase I to II transition at lower temperatures for hydrogen and deuterium. To overcome the computational expense of ab-initio simulations, PIMD runs are performed using a classical machine-learned potential (MLP) force field, trained on ab-initio forces. Coloured-noise thermostats are also employed to reduce the required bead count. Phase II for hydrogen is found to be unstable down to 10 K, remaining disordered in phase I due to the high NQE. Deuterium exhibits signs of a re-entrant phase transition due to the delicate balance between thermal and quantum disorder compared to the highly anisotropic quadrupole-quadrupole ordering. To assess the role of quantum effects in the anisotropic quadrupole-quadrupole contribution, path integral Monte Carlo simulations are performed on a lattice of ideal quantum quadrupoles, building on previous work on classical quadrupoles. An isotope effect in the transition temperature between ordered (phase II) and disordered (phase I) is observed when comparing rotational constants corresponding to hydrogen and deuterium. These are also found to agree fairly well with the MLP PIMD simulations, and no stable phase II is obtained at low temperatures which is also in agreement with the PIMD results. However, no re-entrant phase transition is observed for deuterium. Finally, PIMD is employed to study the role of NQE in lanthanum hydride, a superconductor with the highest known critical temperature. The superconducting mechanism is believed to be of the conventional BCS type, with electrons forming Cooper pairs. It is shown that the BCS pairing is in direct competition with covalent bonding. Using PIMD, it is shown that NQE, along with thermal effects, lead to a significant shift in the transition pressure between the low symmetry molecular metallic phase and the high symmetry atomic superconducting phase.