A CPD-enabled low-scaling environment solver in a coupled cluster based static quantum embedding theory.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The Møller-Plesset Coupled-Cluster (MPCC) embedding framework is a recent advancement in quantum chemistry.
• Accelerating the computational cost of MPCC calculations is crucial for studying larger and more complex chemical systems.
• Efficient handling of large tensors, specifically density-fitting two-electron integral (DF TEI) tensors, is a bottleneck in MPCC methods.

Purpose of the Study:

• To develop a more efficient low-level solver for the MPCC embedding framework.
• To reduce the computational and storage complexity associated with DF TEI tensors.
• To assess the accuracy and performance of the proposed acceleration method on benchmark chemical systems.

Main Methods:

• Incorporation of a canonical polyadic decomposition (CPD)-based low-level solver.
• Factorization of dominant order-three DF TEI tensors using CPD.
• Development of a novel formulation to reduce storage complexity from O(N^3) to O(NR) and computational scaling from O(N^4) to O(NR^2), where R is the CPD rank.

Main Results:

• CPD compression successfully reduced storage and computational scaling for the low-level solver.
• Benchmarks on water clusters and alkane chains demonstrated that CPD-compressed tensors reproduce reference convergence behavior.
• Only small, rank-controlled shifts in absolute energies were observed, preserving chemically relevant energy differences.

Conclusions:

• CPD-based tensor compression is an effective strategy for accelerating MPCC embedding calculations.
• The method maintains high accuracy for energy calculations and differences.
• The linear increase in required CP ranks with system size suggests scalability for larger chemical problems.