Rationale for the Extrapolation Procedure in Selected Configuration Interaction
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909222391775232 |
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| author | Burton, Hugh G. A. Loos, Pierre-François |
| author_facet | Burton, Hugh G. A. Loos, Pierre-François |
| contents | Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12530 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rationale for the Extrapolation Procedure in Selected Configuration Interaction Burton, Hugh G. A. Loos, Pierre-François Chemical Physics Materials Science Nuclear Theory Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies. |
| title | Rationale for the Extrapolation Procedure in Selected Configuration Interaction |
| topic | Chemical Physics Materials Science Nuclear Theory |
| url | https://arxiv.org/abs/2312.12530 |