Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation...

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical physics

Background:

• Electron repulsion integral (ERI) calculations scale as O(N^4), hindering large molecular simulations.
• Density fitting (DF) is a common approximation but often fails to reduce computational scaling with molecular size.

Purpose of the Study:

• To develop a novel approximation for ERIs that reduces computational scaling.
• To improve the efficiency of electronic structure methods by exploiting sparsity in integrals.

Main Methods:

• Tensor decomposition of three-center overlap integrals to create a low-rank approximation.
• Application of this approximation, termed tensor hypercontraction density fitting (THC-DF), to the ERI tensor.
• Demonstration of scaling reduction for second- and third-order perturbation theory (MP2 and MP3).

Main Results:

• THC-DF reduces the 4th-order ERI tensor to a product of five matrices.
• Storage requirements are simultaneously reduced.
• MP2 and MP3 calculations achieve O(N^4) scaling, down from O(N^5) and O(N^6) respectively.
• The method shows promise for other electronic structure theories like coupled-cluster and configuration interaction.

Conclusions:

• THC-DF offers significant computational efficiency and storage reduction for electronic structure calculations.
• This approximation overcomes limitations of traditional DF methods in reducing computational scaling.
• The technique is broadly applicable to various quantum chemistry methods, enabling larger and more complex simulations.