Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Previous work accelerated tensor-hypercontracted (THC) scaled opposite spin MP2 (SOS-MP2) energy calculations to cubic scaling using sparsity and GPUs.
• The primary bottleneck for THC-SOS-MP2 was the cubic scaling of the THC metric matrix inversion.

Purpose of the Study:

• To develop a local THC approximation to reduce the computational cost of THC metric matrix inversion.
• To enable efficient SOS-MP2 calculations for large molecules.

Main Methods:

• Proposed a local tensor-hypercontracted (THC) approximation for metric matrix inversion.
• Combined with graphical processing unit (GPU) techniques and locality-exploiting approaches.

Main Results:

• Achieved linear scaling for THC metric matrix inversion with respect to molecular size.
• Errors introduced by the local THC approximation are < 0.6 kcal/mol for molecules up to 200 atoms.
• Demonstrated O(N^2.5) scaling for SOS-MP2 calculations up to 10,000 basis functions.

Conclusions:

• The new algorithms remove the primary bottleneck for THC-SOS-MP2 calculations on large molecules.
• Feasible SOS-MP2 calculations for proteins like ubiquitin (1231 atoms) in under a day on a single node.