Tensor Hypercontraction Form of the Perturbative Triples Energy in Coupled-Cluster Theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster theory is a powerful quantum chemical method for accurate electronic structure calculations.
• The perturbative triples (T) correction is crucial for high accuracy but computationally expensive, scaling as O(N^7).
• Reduced-scaling methods are needed to make accurate coupled-cluster calculations feasible for larger systems.

Purpose of the Study:

• To develop and present working equations for a reduced-scaling method to evaluate the perturbative triples (T) energy.
• To reduce the computational scaling of the (T) energy calculation.
• To provide implementation details for future research and software development.

Main Methods:

• Utilizing tensor hypercontraction (THC) of the triples amplitudes (t).
• Developing working equations for the reduced-scaling (T) energy evaluation.
• Analyzing the convergence properties and error growth with respect to system size.

Main Results:

• The method reduces the scaling of the (T) energy from O(N^7) to O(N^6).
• Achieved sub-millihartree (mEh) differences for absolute energies and sub-0.1 kcal/mol for relative energies compared to standard CCSD(T).
• Demonstrated convergence to the exact CCSD(T) energy with increasing rank or eigenvalue tolerance.

Conclusions:

• The proposed THC-based reduced-scaling method offers a computationally efficient alternative for calculating the perturbative triples energy.
• The method maintains high accuracy, making it suitable for larger molecular systems.
• This work lays the foundation for practical implementation in quantum chemistry software.