Tensor train compression of molecular orbitals

Abstract

This work systematically investigates the tensor train (TT) compressibility of gridrepresented Hartree-Fock and Density Functional Theory orbitals across a range of molecular systems and TT formats (standard, quantized, and z-permuted quantized). To overcome limitations of current TT solvers, we employ a novel orthogonal tensor train cross approximation (TT-Cross-Orth) to decompose Hartree-Fock and DFT orbitals into TTs, enabling the study of large molecules. We find that the approximation error decreases exponentially with TT-rank for all systems studied and identify QTT as the most efficient TT format. Furthermore, we identify quasi-periodic and symmetric structures-including graphene, graphite layers, and polyalanine helices-as particularly favorable candidates exhibiting sublinear rank growth with system size. The tensor train approach automatically compresses quasi-symmetries and systems with symmetry defects, which makes it an attractive approach for materials science applications. TT-Cross-Orth enforces orthogonality during the decomposition, thereby improving stability and reducing the number of function evaluations compared to standard TT-Cross. These findings establish an empirical foundation for the development of scalable tensor network methods for HF and DFT.

The authors' abstract, as published at the source. The Journal of Chemical Physics, 2026 · DOI ↗