XtalOpt Version 14: Variable-Composition Crystal Structure Search for Functional Materials Through Pareto Optimization

Version 14 of XtalOpt, an evolutionary multi-objective global optimization algorithm for crystal structure prediction, is now available for download from its official website https://xtalopt.github.io, and the Computer Physics Communications Library. The new version of the code is designed to perform a ground state search for crystal structures with variable compositions by integrating a suite of ab initio methods alongside classical and machine-learning potentials for structural relaxation. The multi-objective search framework has been enhanced through the introduction of Pareto optimization, enabling efficient discovery of functional materials. Herein, we describe the newly implemented methodologies, provide detailed instructions for their use, and present an overview of additional improvements included in the latest version of the code.

💡 Research Summary

XtalOpt version 14 represents a substantial upgrade to the open‑source evolutionary crystal structure prediction (CSP) code, extending its capabilities from fixed‑composition searches to fully variable‑composition (VC) explorations while integrating multi‑objective (Pareto) optimization. The authors describe the implementation of a Pareto‑based selection scheme that simultaneously evaluates the thermodynamic stability of candidate structures (via their distance above the convex hull of the entire population) and any number of user‑defined material properties (e.g., band gap, dielectric constant, hardness). Structures that lie on or near the Pareto front are preferentially chosen as parents for the next generation, ensuring a balanced trade‑off between low energy and functional performance.

A central novelty is the native support for VC searches. Users now specify the chemical system with a single “chemicalFormulas” flag, which can contain explicit formulas, comma‑separated lists, or hyphen‑separated ranges (e.g., “Ti1O2‑Ti4O8”). When the Boolean flag “vcSearch = true” is activated, the algorithm is allowed to generate offspring whose compositions differ from those of their parents and may even fall outside the initially listed formulas. This is achieved by computing a convex hull for the whole population using the Qhull library; the hull distance provides an energetic fitness measure that is composition‑agnostic, enabling the algorithm to explore the entire compositional space of the chosen elements.

The genetic operators have been significantly expanded. In addition to the classic crossover, stripple, and permustrain mutations, version 14 introduces:

1. Multi‑cut crossover: the parent cells can be sliced at multiple points (controlled by “crossoverCuts”), producing alternating “ribbons” that are recombined, thereby increasing structural diversity.
2. Permutomic mutation: randomly adds or removes a single atom from a parent structure, followed by a small lattice distortion, to sample stoichiometry more uniformly.
3. Permucomp mutation: creates a completely new composition with a random total atom count (bounded by “maxAtoms”), useful for long‑term diversification across multiple elements.

The probability of applying each operator is now expressed as a “relative weight” rather than a fixed percent, allowing the sum of weights to be arbitrary and enabling dynamic adjustment during a run. Default weight values are provided for both VC and fixed‑composition (FC/MC) modes, and users can fine‑tune them to bias the search toward particular operations.

Computational cost is managed through “maxAtoms” and “minAtoms” parameters. “maxAtoms” caps the total number of atoms in any generated cell (default 20) and is automatically raised if any input formula exceeds this limit. “minAtoms” (default 1) prevents the generation of unrealistically small cells in VC mode. The code also supports both command‑line (CLI) and graphical (GUI) interfaces, and it can invoke a variety of relaxation engines, including density‑functional theory (DFT) packages, classical force fields, and modern machine‑learning interatomic potentials such as the Universal Interatomic Potentials (UIPs). Scripts for seamless integration with UIPs are supplied, facilitating high‑throughput screening.

The overall workflow proceeds as follows: (i) generate an initial population from the user‑defined formulas (optionally using the randSpg library for symmetry‑constrained cells); (ii) locally relax each structure with the chosen engine; (iii) compute user‑specified objectives; (iv) build the convex hull of the population and evaluate each structure’s distance above the hull; (v) select parents via Pareto ranking or a scalar fitness function; (vi) apply the weighted genetic operators to produce offspring; (vii) submit offspring for relaxation; and repeat until a predefined number of structures have been evaluated or convergence criteria are met.

Version 14.1 adds the multi‑cut crossover as a default feature, while version 14.2 introduces the “minAtoms” flag for tighter control over cell size. The authors provide detailed usage instructions, default parameter tables, and illustrative examples demonstrating how the new capabilities accelerate the discovery of functional materials across a broad compositional landscape.

In summary, XtalOpt 14 delivers a powerful, flexible platform for crystal structure prediction that couples variable‑composition exploration with Pareto‑based multi‑objective optimization and an expanded suite of genetic operators. By allowing simultaneous optimization of thermodynamic stability and functional properties, and by supporting modern machine‑learning potentials for rapid relaxation, the code markedly improves the efficiency of high‑throughput materials discovery, particularly for systems where optimal performance requires a delicate balance of competing attributes.