Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Abstract

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals. This is done to lower the computational scaling with respect to the number of basis functions ($N$), and $\mathbf{k}$-points ($N_k$). Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e. a set of points, $N_{\text{ISDF}}$) to further reduce computation time and memory usage. This algorithm has linear scaling cost with $\mathbf{k}$-points, no explicit dependence of $N_{\text{ISDF}}$ on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized systems, with additional gains for large systems. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. We perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

References in corpus (11)

• Separable Dual Space Gaussian Pseudo-potentials
• SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters
• Adaptively Compressed Exchange Operator
• Ideal regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: towards chemical accuracy in non-trivial systems
• Gaussian and plane-wave mixed density fitting for periodic systems
• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
• Fast periodic Gaussian density fitting by range separation
• Interpolative separable density fitting decomposition for accelerating Hartree-Fock exchange calculations within numerical atomic orbitals
• Towards Hybrid Density Functional Calculations of Molecular Crystals via Fragment-Based Methods
• Integral-direct Hartree-Fock and Møller-Plesset Perturbation Theory for Periodic Systems with Density Fitting: Application to the Benzene Crystal

Cited by in corpus (2)

• Gaussian-Based Periodic Grand Canonical Density Functional Theory with Implicit Solvation for Computational Electrochemistry
• Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting