Application and Performance Assessment of Annealing Methods for Electrostatic-Energy-Based Configuration Search in Mixed Crystals
Abstract
In first-principles design of solid solutions and disordered materials, exhaustive evaluation of all possible substitutional configurations is often impractical because the number of site occupations increases exponentially. Here, we develop a framework for pre-screening mixed-crystal configurations using annealing methods, where the Ewald electrostatic energy is used as the objective function. Substitutional occupations are represented by binary variables, allowing the Ewald energy to be mapped onto an Ising-type Hamiltonian and the search for low-energy configurations to be formulated as a combinatorial optimization problem. We implement this formulation using simulated annealing (SA) and quantum annealing (QA), and benchmark their performance against exhaustive search. For the small-scale system CaYAlO4, SA achieved a speed-up of about 30 times, while QA achieved a speed-up of more than 100 times; both methods identified all lowest-energy configurations. For the medium-scale system β-KSbF4 and the large-scale Ba-doped SiAlON system, SA achieved speed-ups of about 200--300 times while stably identifying the lowest-energy structures. In contrast, QA showed limited speed-up for the medium-scale β-KSbF4 system and missed some low-energy configurations, likely due to chain breaks. These results indicate that, among the approaches examined here, SA showed comparatively robust performance for Ewald-energy-based configuration search in mixed crystals. The proposed formulation can be implemented using publicly available libraries and provides a practical route for accelerating candidate-structure generation before first-principles calculations.
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BibTeX
@misc{saquai2026application,
title = {{Application and Performance Assessment of Annealing Methods for Electrostatic-Energy-Based Configuration Search in Mixed Crystals}},
author = {Tack Saquai and Kenta Hongo and Ryo Maezono and Tom Ichibha},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.24557},
eprint = {2605.24557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24557},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Application and Performance Assessment of Annealing Methods for Electrostatic-Energy-Based Configuration Search in Mixed Crystals
AU - Tack Saquai
AU - Kenta Hongo
AU - Ryo Maezono
AU - Tom Ichibha
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2605.24557
UR - https://arxiv.org/abs/2605.24557
AB - In first-principles design of solid solutions and disordered materials, exhaustive evaluation of all possible substitutional configurations is often impractical because the number of site occupations increases exponentially. Here, we develop a framework for pre-screening mixed-crystal configurations using annealing methods, where the Ewald electrostatic energy is used as the objective function. Substitutional occupations are represented by binary variables, allowing the Ewald energy to be mapped onto an Ising-type Hamiltonian and the search for low-energy configurations to be formulated as a combinatorial optimization problem. We implement this formulation using simulated annealing (SA) and quantum annealing (QA), and benchmark their performance against exhaustive search. For the small-scale system CaYAlO_4, SA achieved a speed-up of about 30 times, while QA achieved a speed-up of more than 100 times; both methods identified all lowest-energy configurations. For the medium-scale system β-KSbF_4 and the large-scale Ba-doped SiAlON system, SA achieved speed-ups of about 200--300 times while stably identifying the lowest-energy structures. In contrast, QA showed limited speed-up for the medium-scale β-KSbF_4 system and missed some low-energy configurations, likely due to chain breaks. These results indicate that, among the approaches examined here, SA showed comparatively robust performance for Ewald-energy-based configuration search in mixed crystals. The proposed formulation can be implemented using publicly available libraries and provides a practical route for accelerating candidate-structure generation before first-principles calculations.
ER -