# Selected non-orthogonal configuration interaction with compressed single and double excitations

**Authors:** Chong Sun, Fei Gao, Gustavo E. Scuseria  
**arXiv:** [2403.02350](https://arxiv.org/abs/2403.02350)  
**Date:** 2024-03-01  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.02350v1/

## Key points

- Electronic structure theory aims to address both dynamic and static correlation
- Non-orthogonal configuration interaction (NOCI) is a versatile tool for treating static correlation by combining diverse reference states
- A novel framework compresses orthogonal single and double excitations into a smaller NOCI dimension, recovering missing dynamic correlations
- Compressed NOCISD is refined into SNOCISD through selection processes using metric and energy tests
- Effectiveness of SNOCISD validated in applications such as dissociation of the nitrogen molecule and hole-doped two-dimensional Hubbard model

## Summary

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In electronic structure theory, accurately addressing both dynamic and static correlation is a primary goal. Non-orthogonal configuration interaction (NOCI) is a versatile tool for treating static correlation by combining diverse reference states to offer valuable chemical insights. However, achieving quantitative accuracy requires the inclusion of missing dynamic correlation. This study introduces a novel framework for compressing orthogonal single and double excitations into an NOCI of significantly smaller dimension. This compression process is iterated with each Slater determinant in a reference NOCI, resulting in another NOCI that includes all its single and double excitations (NOCISD). By doing so, the missing dynamic correlations from the reference are effectively recovered. Furthermore, this compressed NOCISD is refined through a selection process using metric and energy tests to create SNOCISD. The effectiveness of SNOCISD is validated through its application to the dissociation of the nitrogen molecule and the hole-doped two-dimensional Hubbard model at various interaction strengths. The data supporting the findings of this study are openly available on GitHub at https://github.com/sunchong137/data_for_nocisd_paper. Additionally, relevant literature references include works by prominent researchers such as Roos et al., Thom and Head-Gordon, Jiménez-Hoyos et al., Barca et al., Jensen et al., Mahler and Thompson, Smeyers and Doreste-Suarez, among others. Moreover, additional references provide insights into quantum theory of many-particle systems, nonunitary Bogoliubov transformations, robust formulations of Wick's theorem for computing matrix elements between Hartree–Fock–Bogoliubov wavefunctions, construction of linearly independent non-orthogonal AGP states, efficient selected configuration interaction algorithms inspired by heat-bath sampling, semistochastic heat-bath configuration interaction methods with perturbation theory, fast semistochastic heat-bath configuration interaction techniques, stochastic optimization methods like Adam by Kingma and Ba. Overall, this study presents a comprehensive approach to incorporating dynamic correlations into NOCI calculations through compression techniques and selection processes while providing open access to data for further research and validation.