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Development of a Tool for Alloy Catalyst Exploration and Analysis Using an Annealing Machine


Waseda University, Graduate School of Advanced Science and Engineering, Applied Chemistry
Hiroshi SAMPEI

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The development of catalysts, materials that accelerate chemical reactions, is one of the crucial research themes for achieving carbon neutrality. In recent years, there has been active research on catalysts composed of multiple elements. However, due to the vast number of possible combinations of these elements, it is extremely difficult to determine each element’s arrangement. In this project, we focused on alloys, materials made up of multiple metal elements, and developed a program to determine the arrangement of metals using an annealing machine. Furthermore, we also developed a program to visualize the alloy structures and their structural information.

Details of the combinatorial optimization problems

This is an optimization problem of the arrangement of metals within a crystal structure. Metals are allocated within the crystal structure to achieve the ratios specified by the user. At the same time, the arrangement is determined to minimize the energy to make the alloy as stable as possible.

Decision variables

Two-dimensional decision variables of metal species × metal position in the alloy (1 if that metal species is present, 0 if not)

Image of decision variable

Metal Species
Metal A Metal B ・・・
Metal Position 0 q (0 or 1) q (0 or 1)
1 q (0 or 1) q (0 or 1)
2 q (0 or 1) q (0 or 1)
Objective function

Minimize energy in metal arrangement (search for the most stable arrangement of metals)

  • The metal species match the ratios specified by the user
  • 1 metal species is assigned to each metal position

When creating the objective function, we quantified the impact of the arrangement of metals and metal pairs within the crystal structure to be used for the coefficients of QUBO and HUBO. By considering the symmetry of the alloy's crystal structure, we could significantly reduce the computational load, but it was necessary to assign the coefficients to all corresponding positions of metal pairs with the same symmetry. It was particularly challenging in the coding to make the lists of metal pairs with the same symmetry and the conversion to QUBO or HUBO.

Future Outlook

We have developed a program to search for the most stable metal arrangements in alloy catalysts using an annealing machine and to visualize the stability and physicochemical information of optimized arrangements. Moving forward, we plan to further improve this program, and we are considering releasing it as open-source software to make it more accessible to researchers in catalytic chemistry. We aim to contribute to the development of high-performance catalysts for achieving carbon neutrality by 2050 by providing tools that assist researchers in understanding catalyst structures in catalyst development.

Achievements / Gratification

Before starting the project, it was unclear how we should formulate the objective function, but we were very delighted when we were able to do it based on the advice from the project manager and other teams as well as referring to the prior paper. Additionally, we were able to gain insights into the problem sizes that the current annealing machine can handle, which should be beneficial for our future projects.

To Viewers

Through the MITOU Target Program, by looking at the themes tackled by the other teams, it was very interesting to realize that a variety of social challenges can be treated as combinatorial optimization problems. We look forward to seeing how problems in fields and areas we hadn't even imagined will be defined and solved as combinatorial optimization problems in the future.

* All information in this article is based on information available at the time of the interview.

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