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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2023
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| Online-Zugang: | https://arxiv.org/abs/2301.11393 |
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| _version_ | 1866929215035670528 |
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| author | Faulstich, Fabian M. Kristiansen, Håkon E. Csirik, Mihaly A. Kvaal, Simen Pedersen, Thomas Bondo Laestadius, Andre |
| author_facet | Faulstich, Fabian M. Kristiansen, Håkon E. Csirik, Mihaly A. Kvaal, Simen Pedersen, Thomas Bondo Laestadius, Andre |
| contents | We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the $S$-diagnostic. We provide a derivation of the $S$-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the $S$-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$. Throughout the numerical investigations, the $S$-diagnostic is compared to other SRCC diagnostic procedures, that is, the $T_1$, $D_1$, and $D_2$ diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the $S$-diagnostic outperforms the $T_1$, $D_1$, and $D_2$ diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the $S$-diagnostic for geometry optimizations using SRCC reveal that the $S$-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the $S$-diagnostic for electronic correlation simulations show that the $S$-diagnostic correctly predicts strong multi-reference regimes. The $S$-diagnostic moreover correctly detects the successful SRCC computations for [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$, which have been known to be misdiagnosed by $T_1$ and $D_1$ diagnostics in the past. This shows that the $S$-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_11393 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $S$-diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods Faulstich, Fabian M. Kristiansen, Håkon E. Csirik, Mihaly A. Kvaal, Simen Pedersen, Thomas Bondo Laestadius, Andre Chemical Physics Computational Physics Quantum Physics We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the $S$-diagnostic. We provide a derivation of the $S$-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the $S$-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$. Throughout the numerical investigations, the $S$-diagnostic is compared to other SRCC diagnostic procedures, that is, the $T_1$, $D_1$, and $D_2$ diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the $S$-diagnostic outperforms the $T_1$, $D_1$, and $D_2$ diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the $S$-diagnostic for geometry optimizations using SRCC reveal that the $S$-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the $S$-diagnostic for electronic correlation simulations show that the $S$-diagnostic correctly predicts strong multi-reference regimes. The $S$-diagnostic moreover correctly detects the successful SRCC computations for [CuCl$_4$]$^{2-}$, [Cu(NH$_3$)$_4$]$^{2+}$, and [Cu(H$_2$O)$_4$]$^{2+}$, which have been known to be misdiagnosed by $T_1$ and $D_1$ diagnostics in the past. This shows that the $S$-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations. |
| title | The $S$-diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods |
| topic | Chemical Physics Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2301.11393 |