MARICI

Mathematical Architecture for Realizing Inorganic Crystalline materials using mixed-Integer nonlinear programming

Future works

You will find out mathematical crystal chemistry (MCC) is incomplete if you use MARICI several times. However, I believe that we share my curiosity and future prospect on mathematical crystal chemistry. Although the current MARICI has some difficulty to predict new materials, future reseach will solve all of them. I am looking foward to the collaboration with you to build the science for discovering new functional materials with small computations.

Mathematical crystal chemistry
Threading of structural optimization (technical problem)

MARICI demands small memory resources; in fact, the data to search crystal structures is lattice parameters, several kinds of atomic radii, atomic positions, and Boolean variables assigning the types of interatomic distance constraints to each pair of atoms. That is why MARICI can execute a structural optimization by using one CPU to design one crystal structure if the number of atoms per unit cell is small enough (less than about 30). However, since the simplest threading results in lacking the memory resoures for large chemical systems, the developer should implement parallel structural optimization for saving the consumption.

Symmetry-oriented search for crystal structures

While MARICI can search complex crystal structures consisting of more than three kinds of chemical elements with small computation, the computational resource is lacked for eahaustive search for crystal structures consisting of more than 30 atoms of several kinds of chemical elements due to too large number of the compilation of chemical compositions. For such large chemical systems, initial structure generation based on space group constraints may be helpful, because it constrains not only spatial order of atoms but also chemical compositions.

Default atomic radii

As inorganic structural chemistry points out, chemical bonding distance can be estimated by the sum of empirically determined atomic radii corresponding to the type of interatomic forces. However, since the conventional tables of atomic radii assign one value for each chemical element, those values are insufficient to design crystal structures by mathematical crystal chemistry (MCC). That is why the latest MARICI does not have any table on atomic radii, which make all users fill in the values for each ionic chemical element. It is important to note that MCC need both the minimum and maximum atomic radii for each chemical element. In fact, most of chemical elements have the flexibilities of their atomic radii. The developer must update the conventional tables on atomic radii by analyzing crystal structures registerd in Inorganic Crystal Structure Database for usability of MARICI.

Computational discovery of quaternary oxides

MARICI can search complex crystal structures consisting of more than three kinds of chemical elements with small computation. Now the developer try to collaborate with Okamoto and Yamaura laboratory in The Institute for Solid State Physics, The University of Tokyo, to discover unknown crystal structures of quaternary oxides.

Which prototypes of crystal structures are synthesizable?

Since MARICI just designs prpototypes of crystal structures given in each chemical composition, MARICI cannot identify which crystal structures can be realized. It means you must select the promising crystal prototypes among the optimal solutions, assign chemical elements to each atom site, and apply ab initio calculation for evaluating the stability of crystal structures. However, how to execute the first two parts? You can remove most of (maybe) unstable structures by such as upper limits of the number of atomic environments, but it is very arbitrary decision. Besides, since the computational cost of ab initio simulation is not small, the exhaustive assignment of chemical elements to each atom site is infeasible due to finite computational resources.

Which crystal structures make functional materials?

Crystal structures determine their functionality through electronic structure. For example, if cations constitute the kagome lattice, magnetic flustration is caused. The developer keens to formulate the rule to select promising crystal structures having functionality by mixed-integer nonlinear programming, but there is no idea now.

Can MARICI contribute to Climate Techs?

If you have no ideas on macro economics, you should learn it before criticizing the carbon-neutral society. I believe that we can realize Green Transformation (GX) accompanied by economic growth if scientists make success to discover high-performance materials which are necessary for GX such as ferroelectric materials, photovoltaic materials, catalysts for sunlight water splitting, and solid-state battery. Note that these innovative materials will be realized by oxides, nitrides, halides, chalcogenides, mixed-anion compounds, and so on, which MARICI is suitable to predict. Since it may be necessary for "green economic growth" to collaborate with entrepreneurs and angel investors, the developer keens to receive message from them.