Quantum nuclear motion in density functional theory
Creators: name: Ramsey, Sam B.
Publisher: name: The University of Edinburgh
Year: 2024
Subjects: zero-point energy
Density Functional Theory
gigapascal range
DFT predictions
hydrogen molecule vibration
helium defects in beryllium

description: Ab-initio methods such as density functional theory (DFT) can accurately solve the many-body interactions of the electrons of up to hundreds of atoms. This has allowed for the prediction of material properties over a wide range of conditions. As DFT relies on the Born-Oppenheimer approximation, the motion of atomic nuclei must be solved for with additional calculations, as often done in molecular dynamics simulations or the calculation of the phonon spectrum of a crystal structure. In this thesis, we will focus on the effects of quantum nuclear motion; in many systems, it is safe to assume the nuclei behave classically, however, the quantum nature of the nucleus becomes more significant as we look at systems with lower atomic mass, temperatures and pressures. In the extreme, this leads to novel phenomenon such as superfluids, but can also have significant effects even in semi-classical phases. This thesis will detail a systematic study of these highly quantum materials using ab-initio techniques, with a particular focus on systems where quantum nuclear motion significantly affects a material's equation of state (EOS). While it is common to include the zero-point energy calculations where relevant, we find that many ab-initio studies do not take into account the effect the zero-point contributions have on the pressure due to the extra calculations involved. While this effect is insignificant in most situations, under certain conditions, many important properties cannot be accurately calculated without considering it. We first find the limits of the quasi-harmonic density functional perturbation theory (DFPT), in the highly quantum regime of low-pressure, &lt; 1 GPa solid helium. We find that the systematic error due to the choice of functional is the limiting factor in the accuracy of the resulting equation of state. We attempt to account for the known an-harmonic properties of the He-He interaction with the Self-Consistent Ab-initio Lattice Dynamical method (SCAILD), which assumes the system is at a temperature above the Debye limit. We found that this limited the methods accuracy, as under 1 GPa the helium melt line is below the Debye limit PIMD is a fully quantum mechanical approach to modelling nuclear motion, however the computational expensiveness of this technique means a fully converged calculation is not possible. This investigation not only acts as a starting point for future DFT studies in low pressure helium but also serves as a test of these methods in a highly quantum regime. Having established the highly quantum mechanical limit at low pressures, this sets the stage for answering open questions that have, until now, not been addressed in the literature. Typically simulations of H2-He mixtures have focused on high pressures and temperatures due to the interest in planetary dynamics. In experiments at lower pressures, &lt; 15 GPa, the vibrational frequency of hydrogen molecules has been observed to increase strongly with He concentration in H2-He fluid mixtures. This has been associated with H-He interactions, either directly through chemical bonding, or indirectly through increased local pressure. Here we demonstrate, that coupling between hydrogen molecules in the pure hydrogen fluid decreases the frequency of the hydrogen molecule vibron, and that the increase in the Raman frequency seen in the mixture is due to a decrease in the number of H2 molecules participating in the mode. We find no evidence of chemical bonding between He and H atoms, with the helium acting only to separate the hydrogen molecules. The variety of possible environments for H2 gives rise to many Raman active modes, which causes the broadening of the vibron band. As the Raman active modes tend to be the lower frequency vibrons, these effects work together to produce the majority of the shift seen in experiment. DFT also reveals that the pressure in the H2-He mixture is primarily due to quantum nuclear effects. Another area of active research where quantum nuclear motion plays a significant role is in the formation of defects in the beryllium lattice. Beryllium's interaction with both helium and hydrogen is of particular interest due to beryllium's potential use as a key component in fusion reactors. Due to the high neutron flux, these metals are exposed to bubbles often formed by helium, weakening the material. Therefore, it is important to understand the mechanisms behind the nucleation of these bubbles. While the current literature does include the zero-point energy contributions to defect formation, by accounting for the zero-point contributions to the pressure, we are able to analyse how the behaviour of the defects change over a range of pressures up to 20 GPa. We calculate the enthalpy of formation and binding of a number of interstitial defects and vacancy structures. We find substitutional defects transition from binding to each other to repulsing at a pressure of ~18.6 GPa. To our knowledge, this change in behaviour has not been described in the literature and could be relevant to future studies looking to combat the formation of helium defects in beryllium. Recent experimental studies have found evidence of beryllium-hydrogen structures forming on the surface layer of beryllium crystals when they are bombarded with hydrogen isotope ions, but only above an areal density of 2.0x1017 cm2. We performed the first ab-initio study into the interaction of complex beryllium hydride chains with the beryllium surface, showing these chains are unstable with respect to hydrogen atoms bound to the beryllium surface but stable with respect to free hydrogen molecules. Thus, these calculations predict, that while there are hydrogen absorption sites available, the beryllium hydride chains will be absorbed into the beryllium bulk. However, when the beryllium surface is fully saturated with hydrogen, the beryllium chains will spontaneously desorb from the beryllium surface. This provides a theoretical explanation for the formation of beryllium hydride crystals seen in experiments.