‘Orbital molecules’ are made up of coupled orbital states on several metal ions within an orbitally-ordered (and sometimes also charge-ordered) solid such as a transition metal oxide. Spin-singlet dimers (a weak metal-metal bond) are known in several materials, but recent discoveries of more exotic species such as 18-electron heptamers in AlV2O4 and 3-atom trimerons in magnetite (Fe3O4) have shown that a general new class of quantum electronic states that we call ‘orbital molecules’ awaits exploration.The discovery of trimerons is particularly important as it provides the solution to the important and long-running problem of the low temperature Verwey phase of magnetite. This was discovered in 1939 but remained contentious as the complex superstructure was unknown. The applicant and co-workers recently used a synchrotron microcrystal technique to solve the structure. This showed that the Verwey transition is driven by Fe2+/3+ charge ordering in a first approximation, but with the formation of a self-organised network of trimeron orbital molecules that had not been predicted in over 70 years of previous study.To expand the magnetite discovery into a general breakthrough in understanding quantum matter, this project will explore chemical tuning of orbital molecule self-organisation, discovery of novel orbital molecule orders in frustrated networks, and investigations of trimeron glass and liquid phases in magnetite. Evidence for liquid phases is key to possible applications. The project will develop high resolution diffraction and total scattering methods to determine long range and local orbital molecule orders, with further characterisation from magnetisation and conductivity measurements. Samples will be synthesised at ambient and high pressures.This study will pioneer a new area of research in the electronic properties of solids, and may help to underpin future post-silicon orbitronic technologies based on the creation and manipulation of orbital states.