Implementation of the Coupled-Cluster Method with Single, Double, and Triple Excitations using Tensor Decompositions

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster theory is a powerful method for accurate electronic structure calculations.
• The standard coupled-cluster with single, double, and triple excitations (CCSDT) method scales computationally as N^8, limiting its application to larger systems.
• Reducing the computational cost of CCSDT is crucial for advancing quantum chemistry.

Purpose of the Study:

• To implement a computationally efficient version of the coupled-cluster with single, double, and triple excitations (CCSDT) method.
• To reduce the computational scaling of the CCSDT method through the use of tensor decompositions.
• To maintain high accuracy in electronic structure calculations while decreasing computational cost.

Main Methods:

• Implementation of the coupled-cluster with single, double, and triple excitations (CCSDT) method.
• Utilized tensor decompositions, specifically Tucker-3 compression and singular value decomposition (SVD), for the triple amplitudes tensor.
• Employed density fitting for the decomposition of electron repulsion integrals.
• Factorized coupled-cluster equations to achieve reduced computational scaling.

Main Results:

• Achieved a practical computational scaling of N^6 for the implemented CCSDT method, a significant improvement over the conventional N^8 scaling.
• Demonstrated that the dimension of the compressed tensor grows linearly with system size (N), ensuring efficiency.
• Verified the accuracy of the method through benchmark calculations, achieving accuracy levels of 1 kJ/mol with reasonable SVD subspace sizes.
• Showcased numerical efficiency using linear alkanes as model systems.

Conclusions:

• The developed tensor-decomposition-based CCSDT method offers a significant reduction in computational cost while maintaining high accuracy.
• This approach enables more feasible and accurate quantum chemistry calculations for larger molecular systems.
• The method shows potential for extension to higher excitation levels and further error reduction strategies.