Deterministic Tensor Hypercontraction for Memory-efficient Molecular Hybrid DFT Calculations

Abstract

Abstract

Hybrid density-functional calculations with Gaussian orbitals are extensively applied in molecular systems, yet they are often limited by memory requirements, even with the well-established Coulomb-metric resolution-of-the-identity (RI-V) scheme. We introduce ISDF-UDD, a robust tensor-hypercontraction scheme that combines the interpolative separable density fitting (ISDF) algorithm with the uniform density distri- bution (UDD) strategy developed here for a deterministic interpolation-point selection. Across 1,505 GMTKN55 relative energies, the ISDF-UDD method reproduces the RI- V reference with a mean absolute deviation of 0.02 kcal/mol and a root-mean-square deviation of 0.04 kcal/mol at B3LYP. The method exhibits favorable computational scaling, with memory consumption scaling as O(N1.91) and exchange matrix construction as O(N2.84), compared to O(N2.93) and O(N3.81) for the RI-V scheme, respectively. These improvements enable previously intractable large-basis-set calculations, such as clusters containing up to 200 water molecules with HF/cc-pVTZ (11,600 basis functions), on a single node with standard memory configurations. Together with the accuracy validated across 1,505 GMTKN55 reactions, this establishes ISDF-UDD as a robust foundation for large-scale quantum chemical simulations on standard hardware.