Structural Constraint Integration in Generative Model for Discovery of Quantum Material Candidates

TL;DR

The results indicate that SCIGEN provides a general framework for generating quantum materials candidates, and it is mathematically proved that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials.

Abstract

Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates.

Figures (4)

• Figure 1: Schematic overview of material generation with geometric patterns as constraints.a. Three primary classes of Archimedean lattices with hexagonal unit cells: triangular, honeycomb, and kagome. b. Guideline for structure initialization for diffusion model, with magnetic atoms at Archimedean lattice vertices. Required components include: (1) lattice types, (2) magnetic atom types, (3) nearest-neighbor distances, and (4) total number of atoms per unit cell. c. Methodology of crystal structure generation via diffusion denoising probabilistic model with geometrical pattern as constraints. The initialized structures are iteratively made noisy ($\sigma$), to prepare predefined pathway of the constrained structure $\boldsymbol{M}_{t}^c$, $t \in [1, T]$. For each denoising step $t$, an unconstrained structure $\boldsymbol{M}_{t}^u$ is combined with constrained structure $\boldsymbol{M}_{t}^c$ to get an integrated structure $\boldsymbol{M}_{t}$. $\boldsymbol{M}_{t}$ is passed to the denoising model $\Phi_{\theta}$ and denoised to become the unconstrained structure $\boldsymbol{M}_{t-1}^u$. By repeating this process, we obtain the final crystal structure $\boldsymbol{M}_{0}$, which is guided by the geometrical pattern constraints $\boldsymbol{M}_{0}^c$ but remains realistic with a fair chance to maintain stability.
• Figure 2: Generated materials with three primary types of archimedean lattices. Archimedean lattice patterns and generated material structures are displayed for a. Triangular, b. Honeycomb, and c. Kagome lattices. d. The sampling profile of the number of atoms per unit cell $N$, generated by measuring the survival ratio from a uniform sampling of $N$. e. The number of materials remaining after pre-screening is presented for the common magnetic atom types in each of the primary geometrical patterns.
• Figure 3: Generated materials with other Archimedean lattice structures. Materials examples covering the rest of Archimedean lattices are presented, with a. Square b. Elongated triangular c. Snub square d. Truncated square e. Small rhombitrihexagonal f. Snub hexagonal g. Truncated hexagonal. In each subplot, the AL pattern and two examples of generated materials are displayed.
• Figure 4: Generated materials of a Lieb-like lattice.a. The Lieb lattice pattern that we integrate into the generated structures. The supercell of the Lieb-like lattice materials and the flat band structures of b.Ce3NaTb4 and c.CeDy3NdYb. We plot the band structures by setting the Fermi level $E_F$ to 0 eV, and the flat bands in both examples are slightly (0.1 -- 0.2 eV) above the Fermi level.