Understanding the core limitations of second-order correlation-based functionals through: functional, orbital, and eigenvalue-driven analysis
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917947695431680 |
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| author | Singh, Aditi Fabiano, Eduardo Śmiga, Szymon |
| author_facet | Singh, Aditi Fabiano, Eduardo Śmiga, Szymon |
| contents | Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves numerous methodologies, which has a greater possibility for error accumulation if the functionals are poorly formulated. This study aims to investigate the performance and limitations of second-order correlation functionals within the framework of density functional theory. Specifically, we focus on three major classes of density functional approximations that incorporate second-order energy expressions: \textit{ab initio} (primarily Görling-Levy) functionals, adiabatic connection models, and double-hybrid functionals. The principal objectives of this research are to evaluate the accuracy of second-order correlation functionals, to understand how the choice of reference orbitals and eigenvalues affects the performance of these functionals, to identify the intrinsic limitations of second-order energy expressions, especially when using arbitrary orbitals or non-canonical configurations, and propose strategies for improving their accuracy. By addressing these questions, we aim to provide deeper insights into the factors governing the accuracy of second-order correlation functionals, thereby guiding future functional development. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Understanding the core limitations of second-order correlation-based functionals through: functional, orbital, and eigenvalue-driven analysis Singh, Aditi Fabiano, Eduardo Śmiga, Szymon Chemical Physics Atomic Physics Density Functional Theory has long struggled to obtain the exact exchange-correlational (XC) functional. Numerous approximations have been designed with the hope of achieving chemical accuracy. However, designing a functional involves numerous methodologies, which has a greater possibility for error accumulation if the functionals are poorly formulated. This study aims to investigate the performance and limitations of second-order correlation functionals within the framework of density functional theory. Specifically, we focus on three major classes of density functional approximations that incorporate second-order energy expressions: \textit{ab initio} (primarily Görling-Levy) functionals, adiabatic connection models, and double-hybrid functionals. The principal objectives of this research are to evaluate the accuracy of second-order correlation functionals, to understand how the choice of reference orbitals and eigenvalues affects the performance of these functionals, to identify the intrinsic limitations of second-order energy expressions, especially when using arbitrary orbitals or non-canonical configurations, and propose strategies for improving their accuracy. By addressing these questions, we aim to provide deeper insights into the factors governing the accuracy of second-order correlation functionals, thereby guiding future functional development. |
| title | Understanding the core limitations of second-order correlation-based functionals through: functional, orbital, and eigenvalue-driven analysis |
| topic | Chemical Physics Atomic Physics |
| url | https://arxiv.org/abs/2503.05292 |