Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller–Plesset Perturbation Theory

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 ISDF controls the tradeoff between accuracy and cost. In particular, c ISDF sets the number of interpolation points used in THC, N IP = c ISDF × N X with N 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 rangeseparated hybrids (e.g., ωB97X-V) and quartic-scaling second-and third-order Møller-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 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 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.

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…energy and size of the pruned grids were found to be similar or superior to hand-optimized 429 or other automatically-generated 430,431 grids. We are now turning to the THC factorization of the double excitation amplitudes 432 and the efficient implementation of a reduced-scaling THC-CCSD method.…”

Exploring Avenues beyond Revised DSD Functionals: II. Random-Phase Approximation and Scaled MP3 Corrections

“…Thus, the estimated speed-up of MP3 over CCSD would be 10–20 times (i.e., the typical number of CCSD iterations). Therefore, in terms of computational cost, this advantage makes the results obtained for DSD3 and ωDSD3 functionals interesting enough without the need for using any further acceleration techniques, such as tensor hypercontraction density fitting (THC-DF-MP3) 76 or the interpolative separable density fitting (ISDF) 77 for the MP3 step.…”

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

“…From the unified analysis of finite-size errors of the periodic HF theory and the MP2 theory, an immediate question is whether the finite-size errors of higher order Møller-Plesset perturbation theories (MPn) for periodic systems can be analyzed in a similar fashion. This is also a timely question, given the recent resurgence of interests on the third and fourth order perturbation theories in quantum chemistry [2,3,21,34,9]. We expect that the quadrature based analysis of finitesize errors can be carried out to all finite-order perturbation theories, where each energy term in the TDL is a multi-layer integral over Ω * , and its numerical calculation corresponds to a trapezoidal quadrature rule.…”