Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to...

Area of Science:

• Computational Quantum Chemistry
• Electronic Structure Theory
• Method Development

Background:

• Accurate electronic structure calculations are crucial for understanding molecular properties.
• Tensor hypercontraction (THC) methods offer a path to reduce computational scaling.
• Existing THC methods require careful parameterization for accuracy and efficiency.

Purpose of the Study:

• To present a systematically improvable tensor hypercontraction (THC) factorization.
• To introduce interpolative separable density fitting (ISDF) as a key component of the THC factorization.
• To develop and evaluate THC algorithms combined with the resolution-of-the-identity (RI) technique for electronic structure calculations.

Main Methods:

• Developed a novel THC factorization based on interpolative separable density fitting (ISDF).
• Integrated ISDF with Becke's atom-centered quadrature grid and the resolution-of-the-identity (RI) technique.
• Applied the developed THC-RI algorithms to cubic-scaling exact exchange (Hartree-Fock, range-separated hybrids) and quartic-scaling Møller-Plesset perturbation theory (MP2, MP3).

Main Results:

• Demonstrated that a single ISDF parameter (c_ISDF) controls the accuracy-cost trade-off.
• Showcased the convergence of THC-RI algorithms to numerically exact RI results across standard Dunning basis sets.
• Validated the utility of THC-RI for larger systems, including water clusters and C20, for exact exchange and MP2 calculations.

Conclusions:

• The developed THC-RI factorization provides a systematically improvable and tunable approach for quantum chemistry.
• Recommendations for optimal c_ISDF parameters are provided for different basis sets and electronic structure methods.
• Future work should focus on stable THC factorization for wave function amplitudes and virtual orbital spaces in large basis sets.