AI-Driven Accelerated Discovery of Intercalation-type Cathode Materials for Magnesium Batteries

We introduce CGCNN model and modify it to match the prediction of electrode voltage. The model of CGCNN in our work is illustrated as Fig. 2. In this model, a crystal is represented as a multigraph where atoms are embedded into the nodes and the connection between atoms are embedded into edges. Then, three layers of graph convolution are introduced to update the atom feature vectors based on its surrounding environment. Unlike the typical CGCNN that pools all nodes to represent the entire crystal, our modified network specifically pools the vectors of the working ions, followed by an output layer that predicts the cathode voltage. This approach allows us to utilize datasets from all intercalation-type cathodes as input, since the open cell voltage of a cathode material is determined by the change in free energy during deintercalation:

where E refers to electrode voltage, $\mathit{\Delta G}$ denotes the change of Gibbs free energy when an ion is transferred from cathode to metal anode, n is the charge of the transferred ion, and F is the Faraday constant. It’s noteworthy that the change in the Gibbs free energy mainly depends on the local environment of the working ion, which is well represented through the process of graph convolution in the model that aggregate the surrounding information into the atom vector of the working ion. This approach in Fig. 2 captures the common characteristics of various ionic intercalation-type cathodes and enables us to use fully discharged electrode structures to construct our dataset. This provides a more comprehensive understanding compared to previous studies that dealt with cathodes for different working ions separately. By applying graph convolution, the working ions acquire detailed information about their electrochemical environment, which is essential for accurate voltage prediction.

A total of 4,045 samples of different working ions from the Battery Explorer of Materials Project are used for the training of our modified CGCNN[12]. Samples are randomly split into training, validation, and test sets with the ratio of 0.8:0.1:0.1, while maintaining the same proportion for each working ion. Mean Absolute Error (MAE) is employed as the loss function and the evaluation metric. After fully training, the MAE of our models for Li, Mg, Na, Al, K, Ca, and Zn cathodes are 0.32 V, 0.29 V, 0.32 V, 0.33 V, 0.30 V, 0.29 V and 0.25 V, respectively, which outperform previous reports on predictions for LIBs and multivalent metal-ion batteries, as depicted in Fig. 3(a)[6, 13, 14]. The model shows a consistent prediction MAE for all ionic electrodes, independent of their respective dataset size, highlighting its ability to effectively harness the similarities inherent in intercalation-type materials. The predicted voltages plotted against target voltages of the test set are distributed around dashed line y=x, as shown in Fig. 3(b) and Supplementary Fig. 2, indicating a high accuracy of our model for all types of batteries.

To further verify the model’s capability, we applied it to a combination of two datasets: stable Mg compounds sourced from the Materials Project (2,202 structures with an energy above hull lower than 150 meV/atom) and the GNoME AI database (13,106 structures with negative formation energy, see Supplementary Table 1). It is evident that the introduction of the GNoME AI dataset has significantly broadened the scope of material screening. Voltage distribution of these two datasets is shown in Fig. 4(a) and 4(b), respectively. We find it intriguing that the MP database exhibited a bimodal voltage distribution around 0 V and 4 V, whereas the predicted voltages for GNoME database cluster around 0V. This difference may originate from the different criteria for choosing stable structures in the two databases. A total of 160 structures with predicted voltages higher than 3.0 V and volumetric capacities above 800 Ah/L are selected, and the first-principles calculations were performed to verify their predicted voltages. The comparison of predicted voltage against first-principles calculated voltage is illustrated in Fig. 4(c), showing the high accuracy (MAE of 0.51V) of our model for voltage prediction.

The impressive performance of our CGCNN model in predicting voltages of various electrode materials stems from its powerful capability to extract and comprehend atomic-level information[15]. A general feature of CGCNN model is its capability for hierarchical visualization, which enables us to visualize the compositional and structural similarities between materials in an arbitrary material space with representations learned from different layers of the networks[15]. To further demonstrate this feature, here, we adjust the initial atom feature vectors into random binary vectors of length 640 to ensure no element information is passed to the model (Supplementary Fig. 3). In the embedding layers, the atom features learned by our model are set to vectors of length 64, where principal component analysis (PCA) is introduced to project these vectors to 2-dimensional space[16]. As depicted in Fig. 5(a), all elements are randomly scattered on x-y plane, indicating that the positional information of elements in the periodic table has not been learned due to random input of atomic features. However, after applying three layers of GCN to aggregate local chemical environments, the t-SNE [17] dimensionality-reduced data shows these atoms in specific chemical environments are effectively grouped together according to their element classes, such as halogen, metalloid and transition metal (TM) elements, as shown in Fig. 5(b). Additionally, working ions (Li, Mg, Al, etc.) from various types of batteries cluster together in the local environment layer. This indicates that the model can extract atomic features from random encodings during the training process, making the effective training of various ionic types of electrodes possible.

Ionic conductivity is a key parameter for cathode materials as it significantly influences the overall efficiency and performance of a battery[18, 19]. However, screening ionic conductivity of cathode materials using high precision ab-initio MD method can be challenging due to the computational capability and cost limitations. MD simulation with machine learning force field is a way to address this problem without sacrificing too much precision. Herein, we utilize NequIP model and the structural relaxation data from Materials Project to construct robust, precise and universal force fields for Mg cathode materials, and employ it to screen ionic conductivity for high-voltage cathodes materials selected in the previous section[11]. To enable fast and stable training of NequIP model, only the first three and the final steps of the structural relaxations for 151,336 crystals in the Materials Project are utilized. This sampling method is proved to be effective, because most intermediate steps are similar to each other and involve small forces, not useful for efficient training[10]. After a full training, our model can accurately predict the energy and force with MAE of 40.8 meV/atom and 61.8 meV/Å, respectively, which is comparable to existing models (Supplementary Fig. 4)[10, 20].

To calculate ionic conductivity of the selected high-voltage Mg cathode materials, we create a supercell for each structure that initially contains at least 512 atoms, but with one-fifth of the Mg atoms deleted randomly to create ionic migration interstices. We then perform 10ps of NPT ensemble NequIP-based MLMD simulations at 1200K to equilibrate lattice vectors, followed by 50 ps of NVT ensemble simulations at 1200K to achieve Mg ionic conductivity. All structures successfully pass this simulation sequence without any crash, demonstrating the excellent stability of our model. The diffusivity of Mg ions is calculated through:

where d=3 represents the dimension of the supercell, $\mathit{\Delta t}$ is the time interval and $r_{i}(t)$ represent the position of ion $i$ out of N ions at time $t$. We can then obtain the ionic conductivity $\sigma$ through Einstein Relation:

where N is the total number of ions, $Z=2$ for magnesium ions, V is volume and T is temperature.

The MLMD results for the selected high-voltage Mg cathode materials at 1200K are shown in Fig. 6(a), where the x-axis shows the CGCNN-predicted cathode voltage, y-axis represents the calculated volumetric capacities, and the size of the scattered points corresponds to the relative ionic conductivity calculated using MLMD. The materials with an ionic conductivity greater than 100 $\mathit{mS}{\cdot}cm^{-1}$ are screened out and highlighted in red in Fig. 6(a). To validate the accuracy of this MLMD model, we select a high-voltage, high-mobility material, $\mathit{Mg}_{2}\mathit{SeCl}_{2}O_{3}$, for ab-initio MD validations. Considering the high computational cost of ab-initio MD calculations, we construct a supercell of $4\times 2\times 2$ and randomly delete one-fifth of the Mg atoms, and perform NVT ab-initio MD at 800K and 1500K for 10 ps. For MLMD, we use the same supercell created in the previous section and perform 50 ps NVT simulations at 800K, 1000K, 1200K and 1500K, respectively. The comparison of mean square displacement (MSD) of Mg ions between the MLMD and ab-initio MD trajectories is shown in Fig. 6(b), indicating very similar ion migration behaviors using these simulation methods. Fig. 6(c) presents the Arrhenius plots of Mg diffusion coefficients at various temperatures simulated by MLMD and ab-initio MD. The diffusion barriers derived from ab-initio MD (0.40 eV) and MLMD (0.36 eV) are remarkably close, demonstrating the NequIP-based MLMD model’s high accuracy. So far,we have screened thousands of Mg structures and identified 23 materials with a voltage higher than 3.0V, a volumetric capacity greater than 800Ah/L, and ionic conductivity over 100 $\mathit{mS}{\cdot}cm^{-1}$ at 1200K. Examples of these structures are shown in Fig. 6(d) and Supplementary Table 3. These selected high-voltage Mg cathode structures hold great promise in future research of high-energy-density Mg batteries.