An analytic model for atomic clusters

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Exploring biomolecular energy landscapes

The potential energy landscape perspective provides both a conceptual and a computational framework for predicting, understanding and designing molecular properties. In this Feature Article, we highlight some recent advances that greatly facilitate structure prediction and analysis of global thermodynamics and kinetics in proteins and nucleic acids. The geometry optimisation procedures, on which these calculations are based, can be accelerated significantly using local rigidification of selected degrees of freedom, and through implementations on graphics processing units. Results of progressive local rigidification are first summarised for trpzip1, including a systematic analysis of the heat capacity and rearrangement rates. Benchmarks for all the essential optimisation procedures are then provided for a variety of proteins. Applications are then illustrated from a study of how mutation affects the energy landscape for a coiled-coil protein, and for transitions in helix morphology for a DNA duplex. Both systems exhibit an intrinsically multifunnel landscape, with the potential to act as biomolecular switches.

Energy Landscape and Pathways for Transitions between Watson-Crick and Hoogsteen Base Pairing in DNA

The recent discovery that Hoogsteen (HG) base pairs are widespread in DNA across diverse sequences and positional contexts could have important implications for understanding DNA replication and DNA-protein recognition. While evidence is emerging that the Hoogsteen conformation could be a thermodynamically accessible conformation of the DNA duplex and provide a means to expand its functionality, relatively little is known about the molecular mechanism underlying the Watson-Crick (WC) to HG transition. In this Perspective, we describe pathways and kinetics for this transition at an atomic level of detail, using the energy landscape perspective. We show that competition between the duplex conformations results in a double funnel landscape, which explains some recent experimental observations. The interconversion pathways feature a number of intermediates, with a variable number of WC and HG base pairs. The relatively slow kinetics, with possible deviations from two-state behavior, suggest that this conformational switch is likely to be a challenging target for both simulation and experiment.

Taboo search by successive confinement: surveying a potential energy surface

A taboo search for minima on a potential energy surface (PES) is performed by means of confinement molecular dynamics: the molecular dynamics trajectory of the system is successively confined to various basins on the PES that have not been sampled yet. The approach is illustrated for a 13-atom Lennard-Jones cluster. It is shown that the taboo search radically accelerates the process of surveying the PES, with the probability of finding a new minimum defined by a propagating Fermi-like distribution.

Exact equilibrium statistical mechanics of two particles interacting via Lennard-Jones and Morse potentials

The exact classical statistical phase-space volume is obtained for a finite system consisting of two particles interacting via both Lennard-Jones and Morse potentials and confined in a spherical volume. The case when the center of mass of the system is fixed at the center of the sphere is also considered. It is shown that the microcanonical caloric curve of the system can have properties similar to those of large clusters, and the equation of state of the system can have behavior similar to that of bulk systems. It is also shown that the fixing of the center of mass of the system can appreciably change the properties of the microcanonical caloric curve and the equation of state of the system.

Van der Waals type loop in microcanonical caloric curves of finite systems

The entropy is usually related to the energy density of states. This relation is approximate for the finite systems (clusters) and an exact relation connects the entropy with the phase volume of the system. These relations give the same results only in the thermodynamic limit. We consider the microcanonical caloric curves determined via both the approximate and exact relations. It is proved that if the caloric curve obtained from the exact relation has a van der Waals type loop (or S bend), then the caloric curve obtained from the approximate relation has S-bend, and the reverse statement is not correct. Using properties of the system at low and high energies we have shown that a van der Waals type loop in the caloric curve of the finite system requires a positive value of the second derivative of the logarithm of the canonical total energy distribution function at least at one value of the energy. The latter is the weaker necessary condition for S-bend to occur in the caloric curve than that obtained earlier.