Tensor train compression of molecular orbitals.

Abstract

This work systematically investigates the tensor train (TT) compressibility of grid-represented Hartree-Fock (HF) and Density Functional Theory (DFT) 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 quantized tensor train 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.