Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to...

Area of Science:

• Computational Chemistry
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Accurate prediction of electronic properties and magnetic couplings in molecules and solids is crucial.
• Existing methods often face limitations in computational cost and accuracy for complex systems.
• The second-order exchange (SOX) term offers a more rigorous treatment of electron correlation.

Purpose of the Study:

• To develop and implement efficient algorithms for evaluating the SOX term within self-consistent GW (scGW) frameworks.
• To investigate the impact of the SOX term on electronic properties, magnetic exchange couplings, and Néel temperatures.
• To explore the theoretical underpinnings of electron correlation effects modulated by SOX.

Main Methods:

• Development of MPI-parallel algorithms for SOX term evaluation with various screening types.
• Integration of SOX into self-consistent GW calculations, forming new theoretical schemes (scGWSOX, scGWSOSEX, etc.).
• Application of tensor hypercontraction for computational scaling reduction.
• Broken-symmetry approach to study magnetic exchange couplings.
• High-temperature expansion for Néel temperature evaluation.

Main Results:

• Successful implementation of efficient, scalable algorithms for SOX calculations, enabling unprecedentedly large system sizes.
• Demonstrated reliable evaluation of small energy differences and significant impact of SOX on effective magnetic exchange couplings.
• Quantified superexchange and explained its modulation by weak electron correlation.
• Accurate prediction of Néel temperatures for solids, showing good agreement with experimental data.
• Proved the lack of Φ-derivability for the considered theories.

Conclusions:

• The developed SOX-inclusive scGW methods provide a significant advancement in accurately describing electronic and magnetic properties of molecules and solids.
• SOX term plays a critical role in understanding and quantifying superexchange interactions and their modulation.
• The computational framework allows for reliable predictions of material properties, including magnetic ordering temperatures.