Block Tensor Decomposition: A dual grid scheme with formal O(N3) for THC decomposition of molecular systems

Abstract

Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals (ERIs). Low-rank approaches such as tensor hyper-contraction (THC) and interpolative separable density fitting (ISDF) have been proposed for Hartree-Fock exchange and correlation's calculations. Their application to molecular systems remains inefficient due to the construction of THC kernel whose time scale increases as quartic with the number of basis functions. In this work, we present an algorithm named block tensor decomposition (BTD) based on a dual grid scheme that combines Hilbert sort and pivoted Cholesky decomposition to generate compact interpolative grids, allowing strict $O(N^3)$ scaling for THC/ISDF kernel construction. The key parameters in BTD are optimized via differential evolution, balancing efficiency and accuracy. Furthermore, we apply BTD in scaled opposite-spin MP2 (SOS-MP2), leveraging sparse mapping in real space to achieve quadratic scaling for electron correlation calculation and linear scaling for exchange calculation. This work advances low-scaling THC/ISDF methodologies for molecular systems, offering a robust framework for efficient and accurate electronic structure computations.

References in corpus (11)

• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Random-phase approximation and its applications in computational chemistry and materials science
• Tensor factorizations of local second-order Møller Plesset theory
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Efficient ab initio auxiliary-field quantum Monte Carlo calculations in Gaussian bases via low-rank tensor decomposition
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting
• Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
• Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange
• Low-Scaling Algorithm for the Random Phase Approximation using Tensor Hypercontraction with k-point Sampling