Professor John Murrell FRS (1932–2016) was a theoretical chemist whose research continues to have a major influence on molecular science. He studied for his PhD with Christopher Longuet-Higgins FRS first at King's College London and then at the University of Cambridge. This gave him a deep grounding in how theory can be used to interpret molecular spectra. Then, in the last 40 years of the twentieth century, first at the University of Sheffield and subsequently at the University of Sussex, he directed research working in the field of theoretical chemistry. This was at a time when computers were starting to become available so that realistic quantum mechanical calculations could be carried out to help explain experimental results. In particular, John Murrell was one of the first theoretical chemists to realize that general potential energy surfaces for molecules could be constructed that enabled calculations to be carried out on both molecular spectra and chemical reaction dynamics. This has proved to be a very powerful and general procedure for performing simulations in molecular science. He was an inspiring teacher and book writer and many of his students started their own research groups working in this field. A Royal Society Biographical Memoir contains full details of John Murrell's outstanding career [1].

This theme issue of the *Philosophical Transactions of the Royal Society* contains original research papers written by students and colleagues of John Murrell. A central theme running through the collection is the Murrell hallmark of using potential energy surfaces to give new insight into the structure and dynamics of molecules. A paper by Varandas & Rocha [2] offers strategies for modelling the potential energy surfaces of small carbon clusters, and the authors show how current theory can yield accurate surfaces from systems made complex by the presence of conical intersections. Accuracy is also central to calculations presented in work by Mizus *et al*. [3] where a new potential energy surface for the water molecule is used to generate a set of improved transition intensities for selected ro-vibrational transitions—work that reflects the significance of the water molecule in the search of life on other planets. The chemical role played by water molecules in the Earth's upper atmosphere is illustrated in the contribution by Linton *et al.* [4], where *ab initio* methods have been used to study the reaction between NO^{+} and small numbers of water molecules. One of the products, a protonated water cluster, has long been proposed as a precursor to cloud formation at very high altitudes. Clusters of water molecules as models for ion solvation are the subject of a paper by Hey *et al.* [5]. Empirical potential energy surfaces have been constructed to compare the sulfite and chlorate ions in solution, and the calculations show that the former ion preferentially favours hydrogen bond formation. A further series of contributed papers investigate the link between potential energy surfaces and reactive and non-reactive collisions—a theme that Murrell also explored in many of his papers. In a study that includes experiment and theory, Xie *et al.* [6] show how a surface constructed from a combination of *ab initio* data points and electrostatic terms is necessary for a complete account of measured rate coefficients for an elementary ion–molecule reaction. Shan & Clary [7] use *ab initio* data to calculate the parameters needed for a semi-classical transition state calculation of rate coefficients for the reaction between methanol and a hydrogen atom. This approach has made it possible to evaluate the contribution from hindered rotor states in reactant geometries that lead to product formation.

For unimolecular reactions, a paper by Farantos [8] investigates the possibility that a complete understanding of non-statistical behaviour requires a detailed knowledge of the phase space explored by molecules following excitation. It is argued that a dynamic description of phase space rather than stationary points on a potential energy surface provides for a better interpretation of rate processes. Two papers on the topic of non-reactive collisions investigate ion transport and energy transfer. Tuttle *et al.* [9] use accurate interatomic potentials to study the interaction between C^{+} and a series of rare gas atoms, and provide evidence for a small chemical component to the interaction that arises from electron transfer between the constituents. Calculated transport coefficients point to the presence of a single spin-orbit component in the complementary experiments. Moving from single collision events to ensembles of molecules, McCaffery [10] shows how an angular momentum model can effectively compute the evolution of quantum state populations in gaseous mixture under non-equilibrium conditions. The results demonstrate how near-resonant vibrational energy transfer has a profound influence on the time scale over which equilibrium can be achieved. If state-resolved kinetics and collision dynamics are to be realized, it will be necessary to orientate molecules in order to identify any stereo-chemical constraints. A contribution by Reid [11] discusses how the degree of molecular alignment by, for example, an electric field, might be quantified in order to best characterize the molecular frame which will act as a reference point for such experiments. A precise description of an energy surface for any collection of reactive or bound atoms necessitates a knowledge of electron correlation. In their paper, King *et al.* [12] give details of calculations undertaken on a sequence of two-electron systems, H^{−}–Ar^{16+}, where they show that an analytical solution to the correlation problem can yield accurate total energies.

As systems increase in complexity, for example, mixtures of gases, the ability to treat individual atomic or molecular interactions rapidly becomes untenable and alternative methods, such statistical mechanics, have to be adopted. In their paper on gas adsorption in metal–organic frameworks, Dunne & Manos [13] successfully use statistical mechanics to account for the behaviour of CO_{2} and CH_{4} adsorption isotherms with respect to composition and mechanical pressure. The final contribution by Lindgren *et al*. [14] retains the theme of energy surfaces, but departs from their use to describe interactions between atoms and molecules. A many-body description of electrostatic interactions is used to model the dynamics of self-assembly processes involving nano- and micro-sized charged particles. The calculations show how particle polarizability can influence assembly into larger structures.

## Footnotes

One contribution of 14 to a theme issue ‘Modern theoretical chemistry’.

- Accepted December 13, 2017.

- © 2018 The Author(s)

Published by the Royal Society. All rights reserved.