Discovering Unique, Low-Energy Pure Water Isomers: Memetic Exploration, Optimization, and Landscape Analysis

Abstract

The discovery of low-energy stable and meta-stable molecular structures remains an important and unsolved problem in search and optimization. In this paper, we contribute two stochastic algorithms, the archiving molecular memetic algorithm (AMMA) and the archiving basin hopping algorithm (ABHA) for sampling low-energy isomers on the landscapes of pure water clusters (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O) <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> . We applied our methods to two sophisticated empirical water cluster models, TTM2.1-F and OSS2, and generated archives of low-energy water isomers (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O) <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n n</i> =3-15. Our algorithms not only reproduced previously-found best minima, but also discovered new global minima candidates for sizes 9-15 on OSS2. Further numerical results show that AMMA and ABHA outperformed a baseline stochastic multistart local search algorithm in terms of convergence and isomer archival. Noting a performance differential between TTM2.1-F and OSS2, we analyzed both model landscapes to reveal that the global and local correlation properties of the empirical models differ significantly. In particular, the OSS2 landscape was less correlated and hence, more difficult to explore and optimize. Guided by our landscape analyses, we proposed and demonstrated the effectiveness of a hybrid local search algorithm, which significantly improved the sampling performance of AMMA on the larger OSS2 landscapes. Although applied to pure water clusters in this paper, AMMA and ABHA can be easily modified for subsequent studies in computational chemistry and biology. Moreover, the landscape analyses conducted in this paper can be replicated for other molecular systems to uncover landscape properties and provide insights to both physical chemists and evolutionary algorithmists.