Time-reversal symmetry in RDMFT and pCCD with complex-valued orbitals

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Reduced density matrix functional theory (RDMFT) and paired cluster theory (pCCD) are effective for non-dynamic electronic correlation.
• Current applications use real-valued orbitals, limiting scalability to extended systems.
• Extended systems often require complex-valued orbitals and Bloch states.

Purpose of the Study:

• To investigate the theoretical and practical implications of using complex-valued orbitals with time-reversal symmetry in RDMFT and pCCD.
• To understand how complex orbitals affect optimization algorithms and solution stability.
• To explore the impact on calculations for extended systems.

Main Methods:

• Theoretical analysis of time-reversal symmetry in RDMFT and pCCD with complex-valued orbitals.
• Development and application of optimization algorithms accommodating complex coefficients.
• Numerical simulations to demonstrate energy lowering and stability issues.

Main Results:

• Complex-valued orbitals can lower the energy, particularly when non-dynamic electronic correlation is significant.
• Theoretical changes primarily impact optimization algorithms.
• Practical implications include potential instabilities and N-representability violations.

Conclusions:

• Adopting time-reversal symmetry with complex-valued orbitals in RDMFT and pCCD presents both opportunities for energy reduction and challenges in solution stability.
• Further research is needed to address instabilities and N-representability issues for reliable application to extended systems.
• This work highlights critical considerations for advancing these quantum chemical methods.