• Understanding the exact shape of energy landscapes of quantum particles can potentially make computer simulations of materials far more accurate.
  • Such simulations are helping to design next-gen materials for use in physics, chemistry, and green technologies.
  • This work addresses questions that have been incompletely answered since the 1980s, opening the door to scientific progress in a host of related fields.

Trinity PhD candidate Andrew Burgess (right) and his research mentor Dr David O’Regan (left) work on an application of their theory.

The exploration and understanding of molecules and materials using computer simulation is a mature and thriving research area. It has a long track record of success over several decades, and several materials in current use were developed with the help of such simulations. When studying systems at the atomic level, the equations that describe the particles and their interactions are those of quantum mechanics.

These equations are very demanding, and must be approximated for practical simulations. The art of making such approximations more reliable, while keeping the computational costs manageable, is approaching its 100th year. This work is increasingly guided by the handful of known “exact conditions”, i.e., definite rules from quantum theory, such as those found here.

Explaining how to visualise what the team discovered, Dr David O’Regan says “Imagine a steep-sided valley, where the ground is not curved but instead made up of angular tiles, like you might see in an old arcade game where the images were made using polygons.

“We have found that the height profile in fractured valleys like this represent the exact energy of isolated collections of particles, like molecules. Heading straight up the valley corresponds to changing the number of electrons that hold together the molecule, while moving to each side increases its magnetism. This work completes the mapping of this valley up to high magnetic states, finding that the valley walls are steep and tilted.”

 

An illustration of the exact energy landscape of the oxygen atom, which takes the form of a tiled valley, as described by the quantum mechanical theory.

Andrew Burgess, lead author, describes in more detail how the discovery came about, saying “While working on a different problem, I needed to know the shape of this energy valley for simple systems. Hunting through published research, I could find lots of nice graphs but to my surprise they stoped short of mapping the entire valley. I realised that existing quantum mechanical theorems could be used for systems with one electron such as the hydrogen atom. However, for systems with two electrons such as the helium atom, these theorems could tell me little about the sides of the valley. Specifically, a quantum mechanical theorem known as the spin constancy condition was incomplete.”

Dr Edward Linscott, from the Laboratory for Materials Simulations at PSI, explains the significance of the team’s findings: “Understanding the geography of this energy landscape may seem quite abstract and esoteric – but actually, this knowledge can help solve all sorts of real-world problems. When colleagues of ours use computer simulations to try to find next-generation materials for more efficient solar panels, or catalysts for more energy efficient industrial chemistry, our knowledge of the energy landscape can be baked into the calculations that they perform, making their predictions more accurate and reliable.”

Dr O’Regan added: “The energy differences and slopes of this valley landscape underpin the stability of matter, interactions between materials and light, chemical reactions, and magnetic effects. Knowing what the entire valley surface looks, including at high magnetisation, is already helping us to build better tools for simulating complex materials, even when they are not magnetic.

“Motivating this work is the need to provide improved simulation theory and methods for developing materials for renewable energy and chemistry applications. When a battery is discharging, for example, there are metal atoms that change their particle count and magnetism. Here we see that we’re moving in that same valley landscape and it’s the drop in height, so to speak, that gives the energy that the battery provides. This is an example of applied simulation and abstract quantum theory being practiced side by side, each motivating and improving the other.”

Reflecting on the nature of this kind of research, Mr Burgess added: “This interplay between theory and practical simulation is what I love most about this area of research. We have already developed a new method for modelling materials based on these theorems and are testing it out on battery cathode materials, so there is plenty of exciting work in the pipeline!”

Read more: You can access the paper ‘The tilted-plane structure of the energy of finite quantum systems’ in the journal Physical Review Letters, at this link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.026404 , or for the manuscript pre-print see: https://arxiv.org/abs/2307.16003 .

The research conducted in the described publication was funded by the Irish Research Council, and by the Swiss National Science Foundation.