Dimensional Strategies and the Minimization Problem: Barrier-Avoiding Algorithms

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.

Ab initio random structure searching

It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as density-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.

Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II

In the past decade, new theoretical approaches have been developed to determine, predict and understand the struc-ture of chemical compounds. The central element of these methods has been the investigation of the energy landscape of chemical systems. Applications range from extended crystalline and amorphous compounds over clusters and molecular crystals to proteins. In this review, we are going to give an introduction to energy landscapes and methods for their investigation, together with a number of examples. These include structure prediction of extended and mo-lecular crystals, structure prediction and folding of proteins, structure analysis of zeolites, and structure determination of crystals from powder diffraction data.

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.

Exploring the protein folding free energy landscape: coupling replica exchange method with P3ME/RESPA algorithm

A highly parallel replica exchange method (REM) that couples with a newly developed molecular dynamics algorithm particle-particle particle-mesh Ewald (P3ME)/RESPA has been proposed for efficient sampling of protein folding free energy landscape. The algorithm is then applied to two separate protein systems, beta-hairpin and a designed protein Trp-cage. The all-atom OPLSAA force field with an explicit solvent model is used for both protein folding simulations. Up to 64 replicas of solvated protein systems are simulated in parallel over a wide range of temperatures. The combined trajectories in temperature and configurational space allow a replica to overcome free energy barriers present at low temperatures. These large scale simulations reveal detailed results on folding mechanisms, intermediate state structures, thermodynamic properties and the temperature dependences for both protein systems.

Catalytic tempering: A method for sampling rough energy landscapes by Monte Carlo

A new Monte Carlo algorithm is presented for the efficient sampling of the Boltzmann distribution of configurations of systems with rough energy landscapes. The method is based on the introduction of a fictitious coordinate y so that the dimensionality of the system is increased by one. This augmented system has a potential surface and a temperature that is made to depend on the new coordinate y in such a way that for a small strip of the y space, called the "normal region," the temperature is set equal to the temperature desired and the potential is the original rough energy potential. To enhance barrier crossing outside the "normal region," the energy barriers are reduced by truncation (with preservation of the potential minima) and the temperature is made to increase with ||y ||. The method, called catalytic tempering or CAT, is found to greatly improve the rate of convergence of Monte Carlo sampling in model systems and to eliminate the quasi-ergodic behavior often found in the sampling of rough energy landscapes.