Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: Theory, implementation, and...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• The accurate evaluation of electronic structure is crucial for understanding chemical and physical properties.
• Standard methods often struggle with computational cost for large systems or suffer from reference dependence.
• Self-consistent Green's function methods offer a rigorous approach but require efficient implementations.

Purpose of the Study:

• To present an efficient MPI-parallel algorithm for the self-consistent correlated second-order exchange term (SOX) within the scGWSOX scheme.
• To reduce the computational scaling of scGWSOX calculations using tensor hypercontraction (THC).
• To evaluate intermolecular interaction energies and analyze the behavior of different Green's function methods.

Main Methods:

• Implementation of an MPI-parallel algorithm for scGWSOX.
• Application of tensor hypercontraction (THC) to reduce computational scaling from O(nτnAO5) to O(nτN2nAO2).
• Evaluation of intermolecular interaction energies using THC-adapted scGW, scGF2, and scGWSOX.

Main Results:

• The developed approach enables the largest fully self-consistent scGWSOX calculations with over 1100 atomic orbitals and negligible THC fitting errors.
• scGW shows overbinding for large systems, while scGWSOX exhibits a slight underbinding, attributed to exclusion-principle violating diagrams.
• All perturbative fully self-consistent Green's function methods are demonstrated to be size-extensive and size-consistent.

Conclusions:

• The efficient THC-adapted scGWSOX method provides a robust and accurate approach for large-scale electronic structure calculations.
• Understanding the role of specific diagrams is essential for developing systematic and accurate theoretical methods.
• Fully self-consistent Green's function methods offer reliable and systematic energy evaluations, overcoming limitations of non-self-consistent approaches.