Exploring New Construction Schemes for Extended-Hierarchy Configuration-Interaction Wave Functions

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Hierarchy CI (hCI) provides a framework for partitioning Hilbert space.
• Understanding electron correlation is crucial for accurate quantum chemical calculations.

Purpose of the Study:

• To propose an extended hierarchy CI (hCI) framework by combining excitation and seniority sectors.
• To systematically examine the influence of different excitation-seniority balances on correlation recovery.
• To evaluate novel determinant ordering strategies for compact configuration interaction (CI) expansions.

Main Methods:

• Defined a generalized hierarchy parameter 'h' = α₁e + α₂s, balancing excitation (e) and seniority (s) contributions.
• Investigated four distinct partitions: positive slope diagonals (PSDs), negative slope diagonals (NSD), vertical chess horse (VCH), and horizontal chess horse (HCH).
• Evaluated partition performance on BeH₂ and H₈ dissociation using the STO-6G basis.

Main Results:

• The efficiency of a partition is contingent on the included excitation-seniority sectors for a given determinant count.
• PSD/hCI (h=2) effectively captures low-seniority configurations for BeH₂, achieving near-CISDT quality with compact expansions.
• NSD and HCH partitions recover static correlation more rapidly for H₈ dissociation compared to VCH, which remained inefficient.

Conclusions:

• The extended hCI (ehCI) framework offers a practical approach to analyze excitation-seniority interactions.
• Novel determinant ordering strategies can lead to more compact and efficient CI expansions.
• The choice of partition significantly impacts the recovery of static and dynamic correlation in quantum chemical calculations.