Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The adiabatic connection (AC) formula provides a theoretical framework for calculating electron correlation energy.
• Multireference wave functions are essential for describing complex electronic systems.
• Efficiently recovering electron correlation in these systems remains a computational challenge.

Purpose of the Study:

• To apply the AC formula with extended random phase approximation (ERPA) to complete active space (CAS) wave functions.
• To develop and evaluate a computationally efficient method for capturing remaining electron correlation.
• To investigate the performance of a simplified AC0 approach.

Main Methods:

• Application of the AC formula in conjunction with the extended random phase approximation (ERPA).
• Development of the AC-CAS method, avoiding higher-than-two-electron reduced density matrices.
• Implementation and analysis of the AC0 approach, based on a first-order expansion of the AC integrand.

Main Results:

• The AC-CAS method efficiently recovers electron correlation for CAS wave functions with significant computational savings.
• AC-CAS systematically reduces errors in absolute energies and energy differences as active spaces are enlarged.
• The AC0 approach retains good accuracy while avoiding the full ERPA eigenequation, offering a more efficient alternative.

Conclusions:

• The AC-CAS method provides an accurate and computationally feasible approach for electron correlation in multireference systems.
• The AC0 method represents a highly efficient ab initio strategy for capturing electron correlation within CAS wave functions.
• These methods offer significant advantages over traditional perturbation theory approaches.