Structure prediction for multicomponent materials using biminima.

The potential energy surface of a heteroparticle system will contain points that are local minima in both coordinate space and permutation space for the different species. We introduce the term biminima to describe these special points, and we formulate a deterministic scheme for finding them. Our search algorithm generates a converging sequence of particle-identity swaps, each accompanied by a number of local geometry relaxations. For selected binary atomic clusters of size N = N(A) + N(B) ≤ 98, convergence to a biminimum on average takes 3 N(A)N(B) relaxations, and the number of biminima grows with the preference for mixing. The new framework unifies continuous and combinatorial optimization, providing a powerful tool for structure prediction and rational design of multicomponent materials.This work was nancially supported by EPSRC grant EP/J010847/1 and the ERC.This is the accepted manuscript. The final version's available from APS at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.156102

Quasi-combinatorial energy landscapes for nanoalloy structure optimisation.

We formulate nanoalloy structure prediction as a mixed-variable optimisation problem, where the homotops can be associated with an effective, quasi-combinatorial energy landscape in permutation space. We survey this effective landscape for a representative set of binary systems modelled by the Gupta potential. In segregating systems with small lattice mismatch, we find that homotops have a relatively straightforward landscape with few local optima - a scenario well-suited for local (combinatorial) optimisation techniques that scale quadratically with system size. Combining these techniques with multiple local-neighbourhood structures yields a search for multiminima, and we demonstrate that generalised basin-hopping with a metropolis acceptance criterion in the space of multiminima can then be effective for global optimisation of binary and ternary nanoalloys.This work was financially supported by EPSRC Grant No. EP/J010847/1 and the ERC.This is the final version of the article. It first appeared from the Royal Society of Chemistry via http://dx.doi.org/10.1039/C5CP01198

Communication: a new paradigm for structure prediction in multicomponent systems.

We analyse the combinatorial aspect of global optimisation for multicomponent systems, which involves searching for the optimal chemical ordering by permuting particles corresponding to different species. The overall composition is presumed fixed, and the geometry is relaxed after each permutation in order to relieve local strain. From ideas used to solve graph partitioning problems we devise a deterministic search scheme that outperforms (by orders of magnitude) conventional and self-guided basin-hopping global optimisation. The search is guided by the energy gain from either swapping particles i and j (ΔEij) or changing the identity of particles i (ΔEi). These quantities are derived from the underlying (arbitrary) energy function, hence not constituting external bias, and for site-separable force fields each ΔEi can be approximated simply and efficiently. In our self-guided variant of basin-hopping, particles are weighted by an approximate ΔEi when randomly selected for an exchange, yielding a significant improvement for segregated multicomponent systems with modest particle size mismatch.This work was nancially supported by the EPSRC grant EP/J010847/1.This is the accepted manuscript. The final version's available from AIP at http://scitation.aip.org/content/aip/journal/jcp/139/22/10.1063/1.4843956?track=twee

Improving double-ended transition state searches for soft-matter systems.

Transitions between different stable configurations of biomolecules are important in understanding disease mechanisms, structure-function relations, and novel molecular-scale engineering. The corresponding pathways can be characterized efficiently using geometry optimization schemes based on double-ended transition state searches. An interpolation is first constructed between the known states and then refined, yielding a band that contains transition state candidates. Here, we analyze an example where various interpolation schemes lead to bands with a single step transition, but the correct pathway actually proceeds via an intervening, low-energy minimum. We compare a number of different interpolation schemes for this problem. We systematically alter the number of discrete images in the interpolations and the spring constants used in the optimization and test two schemes for adjusting the spring constants and image distribution, resulting in a total of 2760 different connection attempts. Our results confirm that optimized bands are not necessarily a good description of the transition pathways in themselves, and further refinement to actually converge transition states and establish their connectivity is required. We see an improvement in the optimized bands if we employ the adjustment of spring constants with doubly-nudged elastic band and a smaller improvement from the image redistribution. The example we consider is representative of numerous cases we have encountered in a wide variety of molecular and condensed matter systems

Probing helical transitions in a DNA duplex†

The complex conformational change from B-DNA to Z-DNA requires inversion of helix-handedness. Multiple degrees of freedom are intricately coupled during this transition, and formulating an appropriate reaction coordinate that captures the underlying complexity would be problematic. In this contribution, we adopt an alternative approach, based on the potential energy landscape perspective, to construct a kinetic transition network. Microscopic insight into the $\mathbf{B \rightarrow Z}$ transition is provided in terms of geometrically defined discrete paths consisting of local minima and the transition states that connect them. We find that the inversion of handedness can occur via two competing mechanisms, either involving stretched intermediates, or a B-Z junction, in agreement with previous predictions. The organisation of the free energy landscape further suggests that this process is likely to be slow under physiological conditions. Our results represent a key step towards decoding the more intriguing features of the $\mathbf{B \rightarrow Z}$ transition, such as the role of ionic strength and negative supercoiling in reshaping the landscape

Machine learning prediction for classification of outcomes in local minimisation

Machine learning schemes are employed to predict which local minimum will result from local energy minimisation of random starting configurations for a triatomic cluster. The input data consists of structural information at one or more of the configurations in optimisation sequences that converge to one of four distinct local minima. The ability to make reliable predictions, in terms of the energy or other properties of interest, could save significant computational resources in sampling procedures that involve systematic geometry optimisation. Results are compared for two energy minimisation schemes, and for neural network and quadratic functions of the inputs

The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein

The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.Comment: 19 page

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Crystallisation pathways are explored by direct analysis of the potential energy landscape for a system of Lennard-Jones particles with periodic boundary conditions. A database of minima and transition states linking liquid and crystalline states is constructed using discrete path sampling and the entire potential energy landscape from liquid to crystal is visualised. We demonstrate that there is a strong negative correlation between the number of atoms in the largest crystalline cluster and the potential energy. In common with previous results we find a strong bias towards the growth of FCC rather than HCP clusters, despite a very small potential energy difference. We characterise three types of perfect crystals with very similar energies: pure FCC, pure HCP, and combinations of FCC and HCP layers. There are also many slightly defective crystalline structures. The effect of the simulation box is analysed for a supercell containing 864 atoms. There are low barriers between some of the different crystalline structures via pathways involving sliding layers, and many different defective structures with FCC layers stacked at an angle to the periodic box. Finally, we compare a binary Lennard-Jones system and visualise the potential energy landscape from supercooled liquid to crystal.We acknowledge the Engineering and Physical Sciences Research Council, UK (EPSRC) for funding under Programme Grant EP/I001352/1 ... VKD is grateful to Darwin College, Cambridge for a Research Fellowship.This is the author accepted manuscript. The final version is available from the Institute of Physics via http://dx.doi.org/10.1088/1742-5468/2016/07/07400

Kinetic Analysis of Discrete Path Sampling Stationary Point Databases

Analysing stationary point databases to extract phenomenological rate constants can become time-consuming for systems with large potential energy barriers. In the present contribution we analyse several different approaches to this problem. First, we show how the original rate constant prescription within the discrete path sampling approach can be rewritten in terms of committor probabilities. Two alternative formulations are then derived in which the steady-state assumption for intervening minima is removed, providing both a more accurate kinetic analysis, and a measure of whether a two-state description is appropriate. The first approach involves running additional short kinetic Monte Carlo (KMC) trajectories, which are used to calculate waiting times. Here we introduce `leapfrog' moves to second-neighbour minima, which prevent the KMC trajectory oscillating between structures separated by low barriers. In the second approach we successively remove minima from the intervening set, renormalising the branching probabilities and waiting times to preserve the mean first-passage times of interest. Regrouping the local minima appropriately is also shown to speed up the kinetic analysis dramatically at low temperatures. Applications are described where rates are extracted for databases containing tens of thousands of stationary points, with effective barriers that are several hundred times kT.Comment: 28 pages, 1 figure, 4 table