Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order M{\o}ller-Plesset Perturbation Theory

TL;DR

This paper introduces a systematically improvable tensor hypercontraction (THC) method based on interpolative separable density fitting (ISDF) for molecules, enabling efficient and accurate calculations of exact exchange and MP2/MP3 energies with controlled tradeoffs.

Contribution

It develops a new THC-ISDF approach with a single parameter to balance accuracy and cost, and demonstrates its effectiveness for large molecular systems and benchmark sets.

Findings

Converges to exact RI results with proper ISDF points

Achieves cubic and quartic scaling for exchange and MP2/MP3

Provides practical guidelines for parameter selection

Abstract

We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter $c_\text{ISDF}$ controls the tradeoff between accuracy and cost. In particular, $c_\text{ISDF}$ sets the number of interpolation points used in THC, $N_\text{IP} = c_\text{ISDF}\times N_\text{X}$ with $N_\text{X}$ being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., $\omega$B97X-V) and quartic-scaling second- and third-order M{\o}ller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 non-covalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on $c_\text{ISDF}$ for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and $\text{C}_{20}$. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wavefunction amplitudes as well as the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.