RECORD
Compactification of Determinant Expansions via Transcorrelation
Chemical Physics · Submitted 4 May 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. | background 0.98 | 0.06 | 0.03 | asserted 1.00 |
| s1 | Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. | background 0.98 | 0.07 | 0.02 | asserted 1.00 |
| s2 | To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. | contribution 0.71 | 0.95 | 0.84 | asserted 1.00 |
| s3 | Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. | result 1.00 | 0.91 | 0.15 | asserted 1.00 |
| s4 | The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. | interpretation 0.72 | 0.77 | 0.16 | asserted 1.00 |
| s5 | Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects. | contribution 0.56 | 0.93 | 0.05 | asserted 0.92 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Although selected configuration interaction (SCI) algorithms can tackle much larger Hilbert spaces than the conventional full CI (FCI) method, the scaling of their computational cost with respect to the system size remains inherently exponential. Additionally, inaccuracies in describing the correlation hole at small interelectronic distances lead to the slow convergence of the electronic energy relative to the size of the one-electron basis set. To alleviate these effects, we show that the non-Hermitian, transcorrelated (TC) version of SCI significantly compactifies the determinant space, allowing to reach a given accuracy with a much smaller number of determinants. Furthermore, we note a significant acceleration in the convergence of the TC-SCI energy as the basis set size increases. The extent of this compression and the energy convergence rate are closely linked to the accuracy of the correlation factor used for the similarity transformation of the Coulombic Hamiltonian. Our systematic investigation of small molecular systems in increasingly large basis sets illustrates the magnitude of these effects.
Human review
How the literature uses it
1 arXiv paper cite this in 2 sentences
What it cites · 2 sentences without a confident label
Uses the method or tool of 1 paper
-
[ref] In the present implementation, the left and right eigenvectors are computed separately, leading to an overall increase of the computational time by a factor of 2.
An efficient implementation of Slater-Condon rules · Computational cost · 0.84
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.