Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains

Abstract

We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the Hartree-Fock equations (HF) with the density-matrix renormalization group (DMRG) algorithm on Cartesian grids that are iteratively refined. In contrast to the standard way of tackling the mean-field problem by expressing the molecular orbitals as linear combinations of atomic orbitals (LCAO) our method only requires as much basis functions as there are electrons within the system. Benchmark calculations for atoms and molecules with up to ten electrons show excellent agreement with LCAO calculations with large basis sets supporting the validity of the tensor network approach. Our work therefore offers a promising alternative to well-established HF-solvers and could pave the way to define highly accurate, fully numerical, molecule-adaptive basis sets, which, in the future, could lead to benefits for post-HF calculations.

arXiv comment27 pages, 16 figures

References in corpus (16)

• Recent developments in the PySCF program package
• An Area Law for One Dimensional Quantum Systems
• The ITensor Software Library for Tensor Network Calculations
• Time-evolution methods for matrix-product states
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• A Quantum Inspired Approach to Exploit Turbulence Structures
• Learning Feynman Diagrams with Tensor Trains
• Quasioptimality of maximum-volume cross interpolation of tensors
• Parallel cross interpolation for high-precision calculation of high-dimensional integrals
• A review on non-relativistic fully numerical electronic structure calculations on atoms and diatomic molecules
• Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations
• Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
• A quantum-inspired method for solving the Vlasov-Poisson equations
• Tensor networks enable the calculation of turbulence probability distributions
• Grid-based electronic structure calculations: the tensor decomposition approach

Cited by in corpus (3)

• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Inchworm tensor train hybridization expansion quantum impurity solver