Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster (CC) methods are essential for accurate electronic structure calculations.
• Unrestricted CC methods suffer from spin-contamination, affecting results.
• Spin-extended CC (ECC) aims to resolve spin-contamination but faces challenges.

Purpose of the Study:

• To present an approximate treatment of spin-extended coupled-cluster (ECC) theory.
• To address and resolve the inherent problems in ECC, namely non-terminating amplitude equations and underdetermined nonlinear equations.
• To provide a computationally efficient and accurate method for electronic structure calculations.

Main Methods:

• Developed an approximate ECC by truncating the Taylor series of the exponential ansatz.
• Introduced an orthogonal projection manifold to remove linear dependencies in the excitation manifold.
• Proposed an efficient solver for the resulting sparse, non-diagonal-dominant equations.

Main Results:

• The approximate ECC method rigorously eliminates spin-contamination.
• The method successfully addresses non-terminating amplitude equations and solution redundancies.
• The approach is orbital-invariant and yields more accurate results than configuration interaction and linearized CC methods.

Conclusions:

• The presented approximate ECC method offers a robust and accurate treatment of electron correlation.
• This work provides a practical approach to overcoming limitations in existing ECC formulations.
• The method demonstrates significant potential for improving the description of chemical systems in quantum chemistry.