Scientists from Trinity College Dublin formed new theorems in quantum mechanics that characterize the “energy landscapes” of ensembles of quantum particles that have been demonstrated. The research was published in the journal Physical Review Letters.
Trinity PhD candidate Andrew Burgess (right) and his research mentor Dr. David O’Regan (left) work on an application of their theory. Image Credit: Trinity College Dublin
Their study answers long-standing issues and creates new opportunities for greatly improving the accuracy of computer simulations of materials. Thus, researchers may be able to create a collection of materials that have the potential to transform green technologies completely.
The findings explain how variations in the magnetism and particle count of systems of particles, including atoms, molecules, and more exotic matter, affect their energy. This completes an outstanding problem related to computer-aided matter modeling and builds on several seminal works that started in the early 1980s.
Dr. David O'Regan, Associate Professor of Physics at Trinity, Dr. Edward Linscott from the Paul Scherrer Institute in Switzerland, and PhD Candidate Andrew Burgess completed the collaborative pen-and-paper and computational work.
Computer simulation-based molecular and material investigation and comprehension is a well-established and active field of study. It has a proven track record spanning several decades, and these simulations were used to assist in creating several currently in use materials. Quantum mechanics provides the equations that characterize particles and their interactions in systems studied at the atomic level.
Due to their extreme difficulty, these equations must be approximations in real-world simulations. The challenge of improving these approximations' reliability while minimizing computational costs is approaching its 100th birthday. The small number of known “exact conditions” or precise principles from quantum theory, like the ones found here, are increasingly serving as the foundation for this effort.
Imagine a steep-sided valley, where the ground is not curved but instead made up of angular tiles, as 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 represents 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.
Dr. David O’Regan, Associate Professor, Department of Physics, Trinity College Dublin
Andrew Burgess, Lead Author, said, “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 stopped short of mapping the entire valley.”
I realized 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.
Andrew Burgess, Department of Physics, Trinity College Dublin
Dr. Edward Linscott, from the Laboratory for Materials Simulations at PSI, explains the significance of the team’s findings, adding: “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.”
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 like, including at high magnetization, is already helping us to build better tools for simulating complex materials, even when they are not magnetic.
Dr. David O’Regan, Associate Professor, Department of Physics, Trinity College Dublin
Dr. David O’Regan explained, “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.”
Regan said, “Here we see that we are moving in that same valley landscape and it is 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.”
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 modeling materials based on these theorems and are testing it out on battery cathode materials, so there is plenty of exciting work in the pipeline!”
Journal Reference:
Burgess, A. C., et al. (2024) Tilted-Plane Structure of the Energy of Finite Quantum Systems. Physical Review Letters. doi.org/10.1103/physrevlett.133.026404.