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. 2022 Dec 31;3(1):113-123.
doi: 10.1021/jacsau.2c00540. eCollection 2023 Jan 23.

Upper-Bound Energy Minimization to Search for Stable Functional Materials with Graph Neural Networks

Jeffrey N Law  1 , Shubham Pandey  2 , Prashun Gorai  2   3 , Peter C St John  1
Affiliations

Upper-Bound Energy Minimization to Search for Stable Functional Materials with Graph Neural Networks

Jeffrey N Law et al. JACS Au. .

Abstract

The discovery of new materials in unexplored chemical spaces necessitates quick and accurate prediction of thermodynamic stability, often assessed using density functional theory (DFT), and efficient search strategies. Here, we develop a new approach to finding stable inorganic functional materials. We start by defining an upper bound to the fully relaxed energy obtained via DFT as the energy resulting from a constrained optimization over only cell volume. Because the fractional atomic coordinates for these calculations are known a priori, this upper bound energy can be quickly and accurately predicted with a scale-invariant graph neural network (GNN). We generate new structures via ionic substitution of known prototypes, and train our GNN on a new database of 128 000 DFT calculations comprising both fully relaxed and volume-only relaxed structures. By minimizing the predicted upper-bound energy, we discover new stable structures with over 99% accuracy (versus DFT). We demonstrate the method by finding promising new candidates for solid-state battery (SSB) electrolytes that not only possess the required stability, but also additional functional properties such as large electrochemical stability windows and high conduction ion fraction. We expect this proposed framework to be directly applicable to a wide range of design challenges in materials science.

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Conflict of interest statement

The authors declare no competing financial interest.

Figures

Figure 1
Figure 1
Initial surrogate model development. (a) Cosine distances between initial and DFT-relaxed structures in the Open Quantum Materials Database (OQMD)., (b) Cosine distances between initial and DFT-relaxed structures for the 53 000 hypothetical decorated structures used in this study (Figure 2). (c) Predicted vs DFT total energy of a GNN trained on ICSD and unrelaxed hypothetical structures and evaluated on the energy of the DFT-relaxed structures. The prediction accuracy for ICSD structures (gray) is high, but low for unrelaxed hypothetical structures (orange).
Figure 2
Figure 2
Overview of approach and data set generation. (a) Starting from an unrelaxed structure, we predict an upper bound for the total energy i.e., energy after a constrained relaxation. We then evaluate the thermodynamic stability relative to competing phases and prioritize structures predicted to be stable, meaning the upper bound of the decomposition energy is <0 eV/atom. If the decomposition energy upper bound is >0 eV/atom, the structure could still be stable after full relaxation. (b) Our element library consists of conducting ions (C), framework cations (F), and anions (A). We build valence-balanced compositions of the general form formula image, where x, yi, and zj are the stoichiometries corresponding to C, F, and A, respectively. Here, i and j are 1–2; i.e., we consider up to 2 framework cations and 2 anions. For a given composition, we decorate the elements in prototype structures (from a prototype library) via ionic substitution. These structures are then relaxed with DFT in two ways: (i) full relaxation and (ii) volume-only relaxation, where the cell shape and atom positions are held constant.
Figure 3
Figure 3
Effect of the volume relaxed data set on energy and surrogate model performance. (a) DFT energy differences between volume relaxed and fully relaxed structures. (b) Predicted vs DFT total energy of the model trained and evaluated on the three data sets. (c) Learning curves of the model’s prediction error by data set size.
Figure 4
Figure 4
DFT confirmation of predicted stable structures. (a) Predicted vs volume-only DFT relaxation total energy. (b) Predicted vs full DFT relaxation total energy. (c) Predicted vs full DFT relaxation decomposition energy. Points in blue indicate structures that remain stable after evaluation of the self-consistent decomposition energy (Section 2.4).
Figure 5
Figure 5
Functional features of the predicted stable structures relevant for battery applications. (a) Histogram showing the distribution of self-consistent decomposition energies for the 2003 structures originally predicted to be stable. (b) UpSet plot of the 285 candidate structures. Combinations of feature cutoffs with less than five members are not visualized. Example compositions are listed for several sets.
Figure 6
Figure 6
Example crystal structures predicted to be stable and exhibit certain features (Figure 5) suitable for application as solid electrolytes. (a) LiSc2F7. (b) LiY2Br7. (c) Li2HfBr6. (d) LiW2Zn4N7. (e) NaLaP4N8. (f) LiSc2HfBr11. (g) Li2HfN2. (h) KScS2. (i) Na2ZrO3.
Figure 7
Figure 7
Reinforcement learning (RL) structure optimization. (a) Crystal building rollout rewards and (b) losses for the policy model vs time as the optimization proceeds. In (a), the r90 line in orange represents the cutoff at which the result was considered a win or loss. (c) Improvement in efficiency of RL compared to a brute-force search. Top candidates are structures with a decomposition energy < −0.1 eV/atom.
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