Rationale for the extrapolation procedure in selected configuration interaction

Area of Science:

• Quantum chemistry
• Computational chemistry
• Theoretical chemistry

Background:

• Selected configuration interaction (SCI) methods are advanced techniques for high-accuracy calculations of molecular electronic states.
• Current SCI methods depend on extrapolation procedures to obtain precise energy estimates.
• Understanding the factors influencing extrapolation is crucial for improving computational accuracy.

Purpose of the Study:

• To provide a theoretical basis for the linear extrapolation commonly used in SCI methods.
• To identify key factors that govern the convergence to the linear regime.
• To develop a novel non-linear extrapolation formula for enhanced data post-processing.

Main Methods:

• Analysis of the exact electronic energy landscape.
• Derivation of extrapolation formulas from first principles.
• Investigation of the role of energy gaps and internal-external space coupling.

Main Results:

• A theoretical rationale for linear extrapolation based on variational energy and perturbative corrections is established.
• The energy gap and coupling between internal/external spaces are identified as critical for reaching the linear regime.
• A new non-linear extrapolation formula is derived, improving upon existing methods.

Conclusions:

• The study clarifies the underlying principles of SCI extrapolation techniques.
• The newly derived non-linear formula offers improved accuracy for both ground and excited states.
• This work advances the precision of computational chemistry for molecular systems.