The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4))...

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• The parametric 2-electron reduced density matrix (p2RDM) algorithm is a powerful tool for electronic structure calculations.
• High-rank tensors, such as electron repulsion integrals and excitation amplitudes, pose a computational challenge.
• Efficient tensor decomposition methods are crucial for reducing the computational cost of quantum chemical calculations.

Purpose of the Study:

• To apply tensor hypercontraction to approximate electron repulsion integral tensors and two-particle excitation amplitudes.
• To develop a computationally efficient algorithm for the p2RDM method.
• To assess the accuracy and scalability of the proposed tensor hypercontraction approach.

Main Methods:

• Tensor hypercontraction was employed to represent high-rank tensors as products of lower-rank tensors.
• The method was applied to electron repulsion integral tensors and two-particle excitation amplitudes within the p2RDM framework.
• The computational scaling of the algorithm was analyzed, showing a dependence of O(r^4) on the number of single-particle basis functions (r).

Main Results:

• The tensor hypercontraction approach successfully approximated the electron repulsion integral tensor and two-particle excitation amplitudes.
• The developed algorithm demonstrated a favorable O(r^4) computational scaling.
• Applications to small molecules, hydrogen chains, and alkanes confirmed the practical utility and low formal scaling.
• The accuracy achieved was comparable to the standard p2RDM algorithm, falling between CCSD and CCSD(T) levels of theory.

Conclusions:

• Tensor hypercontraction offers an efficient strategy for approximating key components in the p2RDM algorithm.
• The method significantly reduces computational cost while maintaining high accuracy.
• This approach holds promise for enabling more accurate and feasible electronic structure calculations for larger systems.