Materials informatics based on evolutionary algorithms: Application to search for superconducting hydrogen compounds

We present a materials informatics approach to search for superconducting hydrogen compounds, which is based on a genetic algorithm and a genetic programing. This method consists of five stages: (i) collection of physical and chemical property data, (ii) development of superconductivity predictor based on the collected data by a genetic programing, (iii) prediction of potential candidates for high temperature superconductivity by regression analysis, (iv) crystal structure search of the candidates by a genetic algorithm, and (v) validation of the superconductivity by first-principles calculations. By repeatedly performing the process as (i) $\to$ (ii) $\to$ (iii) $\to$ (iv) $\to$ (v) $\to$ (i) $\to \cdots$, the database and predictor are further improved, which leads to an efficient search for superconducting materials. Using the first-principles data of binary hydrogen compounds, many of which have not been experimentally realized yet, we applied this method to hypothetical ternary ones and predicted ${\mathrm{KScH}}_{12}$ with a modulated hydrogen cage showing the superconducting critical temperature of 122 K at 300 GPa and ${\mathrm{GaAsH}}_6$ showing 98 K at 180 GPa.

Figure 1

Materials informatics approach to search for new functional materials, which is based on the genetic algorithm (GA) and the genetic programing (GP).

Figure 2

Schematic view of evolutionary algorithm. $I$ represents an individual and $N$ is the number of individuals in the population.

Figure 3

Flowchart at each generation with respect to functionality predictor development by GP. The case of the superconductivity is shown as an example of the functionality (see Sec. 3b).

Figure 4

Schematic view of mathematical function development by evolutionary operations: (a) mating and (b) mutation.

Figure 5

Flowchart at each generation with respect to crystal structure prediction by GA.

Figure 6

Schematic view of crystal structure search by the evolutionary operations: (a) mating and (b) mutation.

Figure 7

Elements forming the binary hydrogen compounds included in the database and all the $T_{\text{c}}$ data. The elements are divided into nine groups using different colors: Alkali metal (AM), alkaline earth metal (AEM), lanthanide (Lan.), actinide (Act.), transition metal (TM), post-transition metal (PTM), metalloid (Met.), reactive nonmetal (RNM), and noble gas (NG).

Figure 8

Relationships between the superconducting $T_{\text{c}}$ and hydrogen concentration (top left), $T_{\text{c}}$ and mass per atom (top right), $T_{\text{c}}$ and pressure (bottom left), and $T_{\text{c}}$ and space-group number (bottom right) for superconducting binary hydrogen compounds predicted by first-principles calculations.

Figure 9

Correlation between $T_{\text{c}}$ and the superconductivity evaluation value $x$ calculated by the predictor. The training and testing data are represented as circle and triangle, respectively.

Figure 10

(Left) Crystal structure of ${\mathrm{KScH}}_{12}$, predicted by GA. The space group is a monoclinic $C2/m$ (No. 12) with $a=5.3726\AA$, $b/a=1.7795$, $c/a=0.5131$, $\beta =106.6^{\circ }$, K: $4i$ (0.77998, 0, 0.47704), Sc: $4g$ (0, 0.26336, 0), H1: $8j$ (0.74515, 0.37079, 0.01997), H2: $8j$ ($-0.05716$, 0.43888, 0.14288), H3: $8j$ (0.57041, 0.41013, $-0.05075$), H4: $8j$ (0.81603, 0.18680, 0.40624), H5: $8j$ (0.68641, 0.18066, 0.59388), H6: $4h$ (0, 0.38665, 0.5), and H7: $4h$ (0, 0.84338, 0.5) at 300 GPa. (Right) Crystal structure of $Im\text{−}3m{\mathrm{CaH}}_6$ reported earlier [84]. Crystal structures were drawn with vesta [88].

Figure 11

Crystal structure of ${\mathrm{GaAsH}}_6$, predicted by GA. The space group is a cubic $Pm$-3 (No. 200) with $a=3.1050\AA$, Ga: $1b$ (0.5, 0.5, 0.5), As: $1a$ (0, 0, 0), and H: $6g$ (0.74736, 0.5, 0). Crystal structure was drawn with vesta [88].