Global Optimization of Atomic Clusters via Physically-Constrained Tensor Train Decomposition

TL;DR

This paper presents a novel tensor train-based framework for global optimization of atomic clusters that effectively handles high-dimensional potential energy surfaces by incorporating physical constraints, demonstrated on Lennard-Jones and carbon clusters.

Contribution

It introduces physically-constrained tensor train methods combining algebraic and probabilistic strategies for efficient global optimization of molecular structures.

Findings

Successfully optimized Lennard-Jones clusters up to 45 atoms.

Achieved geometries of 20-atom carbon clusters consistent with quantum simulations.

Established tensor train decomposition as a powerful tool for molecular structure prediction.

Abstract

The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a novel framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through Tensor Train (TT) decomposition. Our approach combines two complementary TT-based strategies: the algebraic TTOpt method, which utilizes maximum volume sampling, and the probabilistic PROTES method, which employs generative sampling. A key innovation is the development of physically-constrained encoding schemes that incorporate molecular constraints directly into the discretization process. We demonstrate the efficacy of our method by identifying global minima of Lennard-Jones clusters containing up to 45 atoms. Furthermore, we establish its practical applicability to real-world systems by optimizing 20-atom carbon clusters using a machine-learned Moment Tensor Potential, achieving geometries consistent with quantum-accurate simulations. This work establishes TT-decomposition as a powerful tool for molecular structure prediction and provides a general framework adaptable to a wide range of high-dimensional optimization problems in computational material science.