Ortho-para mixtures of hydrogen

Hydrogen is the simplest atom, and it forms the simplest molecule. Its importance on a fundamental scientific level can not be overstated, but it is also of practical importance, given that it is a candidate for a future energy source. Research on hydrogen is performed in a variety of fields, physics, chemistry, and even astrophysics. An aspect of hydrogen that has received limited attention until now is the set of phenomena associated with the rotational properties of individual molecules. Molecular hydrogen and isotopes exist in two varieties, ortho and para, due to the coupling of the nuclear spins of each atom. Para hydrogen can only be in an even angular momentum state, ortho can only be in an odd one. The low temperature properties of para clusters and liquids are well known, mixtures of arbitrary proportions of ortho para hydrogen have received very little attention. It is indeed possible to prepare ortho para mixtures of a desired proportion, since the interconversion times of the two species are on the order of days at ambient pressures. In the solid phase it is known that the anomalous reentrant phase transition can be attributed to the characteristics of the distribution of ortho-para species in hydrogen. It is proposed here to investigate the properties of mixtures of ortho and para hydrogen via computer simulation methods. The methods to be used are variational quantum Monte Carlo to obtain approximate results, and to understand the nature of the ground state wavefunctions describing such systems, and also path-integral and diffusion Monte Carlo to obtain quantitative information. Special attention will be paid to all possible phases that may occur, such as the superfluid phase (thought to occur in para hydrogen clusters), the structural ordering known in ortho hydrogen at low temperature, phase separation between the two different species, and possibly nucleation of the ortho species. The equilibrium methods will enable the study of structural properties, but also the study of quantities like superfluid fraction. One approximate (classical) method would allow the study of nucleation.

There are a number of results from this project which have been published, and their significance affects not only the narrow field of the project itself but also other fields. The proposed project was an investigation of ortho-para hydrogen through many-body methods. A result strictly related is a study of hydrogen containing crystals. In this work the orientational phase diagram of these materials was determined. A theoretical framework was developed in which an important question of principle was settled, namely, how to model in a simple way materials in which the nuclear spin relaxation time of the hydrogens happens on intermediate time-scales between the time-scale of molecular rotation and the time scale of the experiment. The theoretical framework developed in this article was then used to determine the phase diagram of certain hydrogen-containing molecular solids, and an unusual reentrant phase diagram was predicted. The unusual aspect of this phase diagram, which only occurs in highly quantum systems, was that in some pressure regions the orientational ordering is destroyed by quantum fluctuations at low temperatures (the system reenters the disordered state). In another work related to this project, a many-body technique was developed to model the Mott metal-insulator transition. Hydrogen is thought to become metallic at very high pressures, and since it constitutes a half-filled system this metal-insulator transition could possibly be of the Mott type. Up to this day the Mott transition lacks a comprehensive description, since it usually occurs together with magnetic order. An early approach due to Brinkman- Rice describes the Mott transition without any magnetic order, such that charge fluctuations on the insulating side are non-existent. In recent results from this project a formalism was developed in which a first- order metal-insulator transition occurs, the insulating state displays charge fluctuations due to the binding of electrons and holes, but the transition does not show long-range magnetic order. This may be an important step in modelling the Mott transition. In studying metal-insulator transitions (in hydrogen or elsewhere) one cannot avoid the calculation of the con- ductivity. However, the conductivity is an extremely difficult quantity to calculate. Formally, DC conductivity in electronic models is given by their Drude weight, which involves excited electronic states, in many calculations inac- cessible (for example variational theories). Under this project a mathematical approach was developed which allows the casting of the DC conductivity in terms of ground state momentum densities, hence no excited states are necessary. The central outcome of this research was the unification of two disparate views on conductivity. One view rooted in many-body physics relates conductivity to discontinuities in the momentum density, which if present, renders the system conducting. A number of fundamental theories are based on this picture, for example the Landau theory of Fermi liquids. The other view relates conductivity to the extent of localization of the center of mass of all the charge carriers. This idea was suggested by Walter Kohn, was up until now considered a hypothesis, and is in general thought of as unconnected to the idea regarding the discontinuity of the momentum density. A recent paper from this project presents the mathematical proof of Kohn`s theory of localization, and places the two seemingly disparate views of conductivity on the same theoretical basis, in other words a unified picture of the conductivity emerges. In a collaboration, the phase diagram of a magnetically frustrated system was also calculated. In this study a variational Monte Carlo program for a magnetic system was implemented, and the complete phase diagram of the spin - Heisenberg model with third nearest neighbor couplings was determined. The Monte Carlo calculation was compared to other ones, a cluster mean-field calculation and exact diagonalization. The phase diagram determined turned out to be extremely rich, with a number of genuinely ordered magnetic phases, but also phases displaying magnetic frustration. A yet unpublished project involves a detailed model for solid hydrogen, involving molecular rotations, vibrations, and rotation-vibration coupling. With this model we can calculate the lattice distortion of solid hydrogen as a function of pressure, temperature, and ortho-para mixing.