Thermostatic controls in molecular dynamics

Professor Ben Leimkuhler designed new thermostatting algorithms and led a groundbreaking project that aimed to improve the effectiveness of computational mathematics in a number of applications.

Photo of heatmaps showing hot and cold areas
The illustration shows the sampled motions of a small molecular model. Left: an accurate simulation reveals a delicate bridge between the two domains. Right: the error due to a poor thermostat has erased this important feature.

Researchers led by Professor Ben Leimkuhler are expanding the international reputation of the University’s School of Mathematics with a groundbreaking project that aims to improve the effectiveness of computational mathematics in a number of applications.

In a series of papers published from 2009, Professor Leimkuhler’s team at the University of Edinburgh’s School of Mathematics designed new thermostatting algorithms and demonstrated their effectiveness, implementing them in software developed in industry and government laboratories in the UK and the USA.

Thermostats allow accurate molecular study A thermostat plays much the same role in simulation as the thermostat in a home: energizing the system when it is running cold and cooling it down when it becomes overheated. To be effective in simulation, a thermostat must promote heat flow throughout the molecule.

Professor Leimkuhler and his collaborators analysed and implemented ergodic thermostats that minimally perturb the dynamical behaviour of the atoms, thus allowing the accurate study of dynamic mobility using molecular trajectories.

These thermostats have been incorporated into Accelrys Materials Studio, a leading commercial software package, resolving problems identified by their clients.

The project has been hugely successful, with algorithms developed by the Leimkuhler group having been implemented in the world’s leading MD software packages including DL-Poly, AMBER, NAMD and Accelrys’ Material Studio. These packages are used across industrial sectors, in companies such as Sony, Samsung, Pfizer, Novartis, Takeda, Kodak and British Nuclear Fuels.

The work with Accelrys was motivated by the need to address a persistent problem faced by some of its clients, namely the tendency of the thermal control to introduce nonphysical oscillations through a spurious phenomenon known as “ringing”.

This was identified by Leimkuhler and his team as a direct consequence of the thermostat in use in the software. The solution was an improved Nosé- Hoover-Langevin (NHL) thermostat which has a mild effect on measures of dynamic mobility, destroys the ringing behaviour, and restores correct thermally consistent dynamics. The implementation in Materials Studio was carried out by Leimkuhler’s PhD student Charles Matthews after a residency at Accelrys’ Cambridge headquarters.

The project resolved Accelrys’ problem and was highlighted in the subsequent release notes and advertising for Materials Studio. The methods were also incorporated in the DL-Poly suite of software maintained at Daresbury Laboratory

A vital role

Computational molecular science plays a crucial role in applications such as energy, materials science, nanotechnology, and synthetic biology.

Computer simulations of molecular dynamics (MD) provide a modern ‘virtual laboratory’, which allows scientists to glimpse the dynamics of large molecules and atomic nanostructures at sub-microsecond timescales.

Increasingly reliable molecular modelling algorithms and ever faster computers are giving these simulations the upper hand over the traditional experimental make-and-test approach. Because simulations need to explore the behaviour of molecules at defined ambient laboratory conditions, temperature control – thermostatting – is an essential element of any MD algorithm.

In related work, Professor Leimkuhler and his group have designed sophisticated numerical methods with high accuracy and excellent computational efficiency for biomolecular sampling, taming the random components which can otherwise wreak havoc with numerical methods.

They have also examined the control of temperature in the presence of modelling error and external perturbations (such as external heating), resulting in new methods which incorporate quantum mechanics in molecular dynamics.

Still another strand of work is aimed at increasing the timestep in molecular dynamics simulations, using a strategy that accounts for the wide range of time scales of molecular motion.

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