1. Introduction¶
CALYPSO is a swarm-intelligence based structure prediction method and its same-name computer software. The approach requires only chemical compositions of given compounds to predict stable or metastable structures at certain external conditions (e.g., pressure). The method can also be used to inversely design multi-functional materials (e.g., superhard materials, electrides, optical materials, etc). The CALYPSO package is protected by the Copyright Protection Center of China with the Registration No. 2010SR028200 and Classification No. 61000-7500.
1.1. Meaning of CALYPSO¶
CALYPSO is a short name of “Crystal structure AnaLYsis by Particle Swarm Optimization”. It was originally designed to predict 3-dimensional (3D) “crystal structures”. Now, CALYPSO has a more generalized meaning of “structure” prediction, able to deal with structures ranging from 0D to 1D, 2D, and 3D.
“CALYPSO” (with all capitalized letters) is the only name in the field of structure prediction. But the word “Calypso” has diverse meanings. Calypso is the name of one of the Nereids (sea nymphs) in Greek mythology. Calypso also refers to companies, music, places, etc. Have a look at Wikipedia.
CALYPSO structure prediction software takes the advantage of structure evolution via PSO algorithm, one of swarm intelligence schemes. However, many other efficient structure-dealing techniques (e.g., symmetry constraints, bond characterization matrix, introduction of random structures per generation, etc.) were also implemented in CALYPSO. We found that all these techniques implemented are equivalently important for the structure searching efficiency. It is therefore more appropriate to name the developed structure prediction method as a “CALYPSO” method.
1.2. Why PSO?¶
As an unbiased global optimization method, PSO is inspired by the choreography of a bird flock and can be viewed as a distributed behavior algorithm that performs multidimensional search (see, e.g., Kennedy & Eberhart 1995 1). PSO is metaheuristic as it makes few or no assumptions about the solutions and can search very large spaces of candidate solutions (dubbed as particles) by moving them in the search-space based on efficient algorithms over the particle’s position and velocity.
We quote from website of http://www.swarmintelligence.org.
PSO has been successfully applied in many research and application areas. It is demonstrated that PSO can get better results in a faster, cheaper way compared with other methods.
Another reason that PSO is attractive is that there are few parameters to adjust. One version, with slight variations, works well in a wide variety of applications. PSO has been used for approaches across a wide range of applications, as well as for specific applications focused on a specific requirement.
1.3. History of PSO on Structure Prediction¶
Although PSO algorithm has been employed to various optimization problems, the application of PSO in structure prediction started only recently. It was attempted for isolated systems (small clusters and molecules) by Call, Zubarev & Boldyrev in 2007 2. However, this effort did not lead to any practical application.
The CALYPSO team independently initialized the idea of applying PSO algorithm into structure prediction in 2006 (Ma and Wang) before Call et al’s work and made the first application of PSO algorithm into structure prediction of extended systems (e.g., 3D crystals by Wang, Lv, Zhu & Ma in 2010 3, 2D layers by Luo et al, in 2011 4 and Wang et al, in 2012 5, 2D surface reconstruction by Lu et al, in 2014 6, 2D atoms adsorbed on layer materials by Gao et al., in 2015 7). Structure searching efficiencies of isolated systems have been substantially improved by the CALYPSO team (Lv, Wang, Zhu & Ma in 2012 8), where the success of this application has been backed up with the introduction of various efficient techniques (e.g., bond characterization matrix for fingerprinting structures, symmetry constraints on structure generation, etc.).