On the rank-reduced relativistic coupled cluster method.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Relativistic coupled cluster (RCC) methods are crucial for accurate electronic structure calculations, especially for heavy elements.
• Amplitude tensors in RCC methods can become computationally expensive due to their size.
• Efficient tensor decomposition techniques are needed to reduce computational cost without sacrificing accuracy.

Purpose of the Study:

• To investigate the efficiency of Tucker decomposition for amplitude tensors in single-reference relativistic coupled cluster with single and double excitations (SR-RCCSD).
• To assess the feasibility of rank reduction for improving the computational scaling of SR-RCCSD.
• To evaluate the accuracy of correlation energy estimates using compressed amplitude tensors.

Main Methods:

• Benchmark calculations on (AuCl)n chains, Aun clusters, and a YbCl2 cluster model.
• Application of Tucker decomposition to amplitude tensors in SR-RCCSD.
• Analysis of compression rates and accuracy of correlation energy estimates by rejecting small singular values.
• Comparison of Goldstone diagrammatic technique with the antisymmetrized Brandow approach.

Main Results:

• Achieved 1 kJ/mol accuracy for correlation energy estimates in moderate-size systems and reaction energies.
• Demonstrated high compression rates for amplitude tensors, with significant reduction in tensor size (e.g., ~3% for YbCl7 double amplitudes).
• Confirmed the feasibility of rank reduction for SR-RCCSD, leading to improved computational scaling.
• Highlighted the advantage of the Goldstone diagrammatic technique.

Conclusions:

• Tucker decomposition is an effective method for compressing amplitude tensors in SR-RCCSD.
• Rank reduction via Tucker decomposition significantly improves computational efficiency for heavy element systems.
• The proposed approach enables high-precision modeling of larger, complex systems containing heavy atoms.