Three Lagrangians for the complete-active space coupled-cluster method.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster (CC) methods are powerful tools in quantum chemistry for describing electron correlation.
• Complete-active space (CAS) methods are essential for systems with strong static correlation.
• Combining CAS and CC methods (CASCC) is computationally demanding due to the exponential scaling of model spaces.

Purpose of the Study:

• To develop novel variational formulations for the complete-active space coupled-cluster (CASCC) method.
• To enable efficient and accurate treatment of electron correlation in challenging quantum chemical systems.
• To overcome the computational scaling limitations of traditional CASCC approaches.

Main Methods:

• Derivation of three fully variational formulations for CASCC.
• Approximation of model vectors using smooth manifolds, specifically matrix-product states.
• Extension of variational formulations to the time domain, deriving abstract evolution equations.

Main Results:

• The proposed variational formulations allow for favorably scaling multireference coupled-cluster calculations.
• The methods enable systematic correction of tailored coupled-cluster calculations.
• The approach provides a pathway for improving quantum chemical density-matrix renormalization group (DMRG) methods by resolving dynamical correlation at chemical accuracy.

Conclusions:

• The developed variational CASCC formulations offer a significant advancement in computational quantum chemistry.
• These methods provide a scalable and accurate approach for studying complex electronic structures.
• The work opens new avenues for accurate and efficient quantum chemical calculations, particularly for systems with strong electron correlation.