A new wavefunction hierarchy for interacting geminals.

Area of Science:

• Quantum chemistry
• Computational physics
• Many-body theory

Background:

• Accurate electronic structure calculations are crucial for understanding molecular properties.
• Existing methods often face challenges with computational cost for larger systems.
• The development of size-consistent and accurate wavefunction ansatze is an active research area.

Purpose of the Study:

• To introduce a novel truncation scheme for non-orthogonal antisymmetrized products of interacting geminals (APIG).
• To establish a wavefunction hierarchy that allows for systematic improvement of accuracy in electronic structure calculations.
• To provide a computationally efficient method for estimating ground-state properties of quantum systems.

Main Methods:

• Development of a truncation scheme for APIG based on antisymmetrized products of strongly orthogonal geminals (APSG).
• Derivation of mathematical expressions for the first four orders of the interacting geminal (IG) hierarchy (IG0, IG1, IG2, IG3).
• Analysis of the computational scaling for evaluating the transition density matrix, demonstrating cubic complexity with system size.

Main Results:

• The proposed IG wavefunction hierarchy enables a gradual increase in accuracy from APSG to full APIG.
• Explicit mathematical formulations for IG0, IG1, IG2, and IG3 are presented.
• Computational cost for transition density matrix evaluation scales cubically with system size, indicating good scalability.
• Numerical results show that early truncation levels (e.g., IG2 or IG3) yield results nearly identical to the full APIG.

Conclusions:

• The new truncation scheme provides a practical and accurate approach for electronic structure calculations.
• The IG hierarchy offers a tunable balance between accuracy and computational cost.
• This method is particularly promising for studying systems where high accuracy is required without prohibitive computational expense.