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Exploring New Construction Schemes for Extended-Hierarchy Configuration-Interaction Wave Functions
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DOI：10.1021/acs.jpca.5c07650.png)
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Abstract
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Following the work of Kossoski et al. on hierarchy CI (hCI) we propose an extended way of partitioning the Hilbert space by combining the excitation and the seniority sectors in a more general way. We define the hierarchy parameter, h, involving two weights (alpha values), measuring the importance of excitation (e) and seniority (s) contributions to the wave function according to h = alpha(1)e + alpha(2)s. This formulation generates alternative orderings of the excitation-seniority lattice and enables a systematic examination of how different balances between excitation and seniority influence correlation recovery. Four partitions are considered: positive slope diagonals (PSDs), which is equivalent to the original hCI scheme; negative slope diagonals (NSD); vertical chess horse (VCH); and horizontal chess horse (HCH). These partitions are evaluated for the BeH2 and for the cubic and linear H-8 dissociation. These results show that the efficiency of a partition depends on the specific excitation-seniority sectors it includes at a given number of determinants. For BeH2, the PSD/hCI hierarchical ordering (h = 2) incorporates the dominant low-seniority configurations most effectively and reaches near-CISDT quality with compact expansions compared to other partition schemes. For the H-8 systems, NSD and HCH recover static correlation more rapidly in the dissociation regime, whereas VCH remains inefficient across all determinant counts. The present results, obtained in the STO-6G basis for small benchmark systems, are intended as a controlled methodological study of determinant ordering strategies rather than a comprehensive performance assessment. The ehCI framework provides a practical way to analyze how excitation and seniority interact and to design compact CI expansions.
Keywords:
hierarchy CI
excitation
seniority
determinant ordering
configuration interaction
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