HPC Case Study: Linear Scaling Materials Modelling

Classical modelling of a protein (left) vs the more accurate approach using the quantum theory to model the electronic density (right).

My research interests are in the development of methods for electronic structure calculations at the atomic level”, explains Chris Skylaris, Professor of Computational Chemistry at the University of Southampton. “I use quantum theory to describe the electrons within atoms, molecules, and materials”.

Before we continue, it may be prudent to familiarise ourselves with some of these terms.


Quantum theory is the study of atoms and subatomic particles. These particles are invisible, even with instruments, so their movements and positions exist within a range of probabilities called a wave function, a mathematical model that produces reliable predictions despite famously allowing a hypothetical cat to be both alive and dead at the same time. 

Electronic structure calculations, meanwhile, are calculations that harness quantum mechanics – more specifically, a quantum mechanical modelling method called density functional theory – to determine these wave functions.

The real and potential applications of electronic structure calculations and density functional theory are far-reaching, enabling researchers to understand everything from biochemical processes to the nature of impurities in graphene. 

Professor Skylaris and his colleagues have assisted with research into these subjects and many more, using density functional theory to model the movements and interactions of particles through computer simulations.

“From batteries to proteins to drug design to catalysts for fuel cells and the production of new chemicals, we make methods for the simulation of materials”.

Their work would have been impossible without HPC clusters like Iridis. 

However, even the most powerful supercomputer would have been inadequate for their purposes without an ingenious code called ONETEP, developed by Professor Skylaris and others.

How ONETEP works

The time required for conventional electronic structure calculations increases with the third power as atoms are added to the simulation. This has the unfortunate effect of increasing the computational burden of a simulation by a factor of eight every time the number of atoms increases by a factor of two.

Imagine, says Professor Skylaris, that a single CPU processor node can simulate 100 atoms. “If you go from 100 atoms to 200 atoms then this is double, but it’s in the power of three, so it needs eight times the resource.  If I wanted to model 200 atoms I would not need two nodes, but eight nodes”.

For this reason, a high performance computing cluster like Iridis isn’t significantly better than a desktop PC when it comes to running large simulations involving thousands of atoms. It doesn’t take many additional atoms for the computational burden of the simulation to become overwhelming, even for the most powerful supercomputers.  

“You can do bigger calculations on an HPC than on a desktop, but not much bigger”.

ONETEP – which stands for Order-N Electronic Total Energy Package – overcomes this problem using an approach called linear scaling. In the simplest possible terms, linear scaling allows researchers to widen the scope of an electronic structure calculation without drastically increasing the computational cost.

Liner scaling calculations: Reformulating the quantum theory used in electronic structure calculations allows ONETEP to scale linearly with system size and model much larger systems.

If you go to twice the CPU with ONETEP, you will be able to do twice the number of atoms. As a result, we can run our calculations on complex models with tens of thousands of atoms.

In this regard, a linear scaling method like ONETEP is able to exploit the power of HPC clusters like Iridis – and vice versa.

Professor Chris Skylaris

“Only on HPC can you actually unleash the potential of a method like ONETEP”.

Professor Chris Skylaris

It’s worth stressing that ONETEP is more than simply a clever piece of software. “The linear scaling is due to a reformulation of the quantum theory that takes advantage of wave function localisation”, Professor Skylaris explains.

On top of this there has been a large amount of software engineering work to develop this theory into an efficient code for supercomputers. The software engineering of the code is a continuous effort in order to keep it up to date with computer hardware developments”. 

He and his colleagues are also engaged with creating bespoke models for different types of materials. For instance, the team has developed solvent, electrolyte, and voltage control models in order to study the growth of dendrite clusters on graphite anodes within Li-ion batteries. 

While theirs wasn’t the first research project investigating the mechanisms underlying capacity-loss in the batteries that power electric cars, smartphones, and countless other modern devices, their research yielded new insights into the phenomenon. 

The team at Southampton has contributed towards the development of safer and more durable batteries, which has implications for a safer and more durable planet. 

Elsewhere, Professor Skylaris and his colleagues have used their linear scaling approach to carry out electronic structure calculations on a 2,600-atom protein ligand system, a feat once considered too computationally expensive to attempt. 

Among other things, this breakthrough has implications for drug optimisation.

Accessing HPC

Professor Skylaris has made extensive use of HPC in his research, and his expertise with this advanced technology is significant. 

As Chair of the HPC Academic Governance Board at the University of Southampton, Professor Skylaris is concerned with ensuring that other academics are similarly empowered to harness the potential of HPC in their research – including those from fields not traditionally associated with supercomputing.

According to Professor Skylaris, the goal of the HPC Academic Governance Board, which has representatives from all schools, is to “enlarge the community of users of HPC at the university and bring in new users”.

He goes on. “We have a tradition of users in chemistry, physics. And then we have other departments such as medicine, the humanities, and so on, that could benefit from HPC. We aim to educate them about the possible benefits of using HPC”. 

There has never been a better time to explore those benefits. In 2023 the University of Southampton created a team of HPC Research Software Engineers (RSEs) whose sole purpose is to help academics from all disciplines to exploit the revolutionary research potential of high-performance computing. 

For more information, including details on how to get help from the HPC
RSEs free of charge, see: https://rsg.southampton.ac.uk/hpc