Self-consistent Hessian-level meta-generalized gradient approximation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910112895991808 |
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| author | Dabbaghi, Pooria Lastra, Juan Maria García de Silva, Piotr |
| author_facet | Dabbaghi, Pooria Lastra, Juan Maria García de Silva, Piotr |
| contents | The $\vartheta$-MGGA class of density functionals is formally reformulated as Hessian-level meta-generalized gradient approximations (HL-MGGAs). In contrast to standard meta-GGAs that rely on the orbital-dependent kinetic-energy density or the density Laplacian, HL-MGGAs utilize the full density Hessian. We introduce a simplified, non-empirical functional, $\vartheta$-PBE, and present a roadmap for its self-consistent implementation within the projector augmented-wave (PAW) method. By utilizing the complete set of spatial second-order density derivatives, the functional's underlying descriptor successfully distinguishes between distinct one-electron density limits, such as single-center atomic densities and two-center bonds, that standard iso-orbital indicators often conflate. Benchmarks across molecular and solid-state datasets reveal that while $\vartheta$-PBE delivers accurate chemisorption energies and molecular properties, challenges remain in predicting bulk lattice constants. Ultimately, this work demonstrates the physical utility and feasibility of designing orbital-independent, Hessian-based exchange-correlation functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07046 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-consistent Hessian-level meta-generalized gradient approximation Dabbaghi, Pooria Lastra, Juan Maria García de Silva, Piotr Chemical Physics Materials Science The $\vartheta$-MGGA class of density functionals is formally reformulated as Hessian-level meta-generalized gradient approximations (HL-MGGAs). In contrast to standard meta-GGAs that rely on the orbital-dependent kinetic-energy density or the density Laplacian, HL-MGGAs utilize the full density Hessian. We introduce a simplified, non-empirical functional, $\vartheta$-PBE, and present a roadmap for its self-consistent implementation within the projector augmented-wave (PAW) method. By utilizing the complete set of spatial second-order density derivatives, the functional's underlying descriptor successfully distinguishes between distinct one-electron density limits, such as single-center atomic densities and two-center bonds, that standard iso-orbital indicators often conflate. Benchmarks across molecular and solid-state datasets reveal that while $\vartheta$-PBE delivers accurate chemisorption energies and molecular properties, challenges remain in predicting bulk lattice constants. Ultimately, this work demonstrates the physical utility and feasibility of designing orbital-independent, Hessian-based exchange-correlation functionals. |
| title | Self-consistent Hessian-level meta-generalized gradient approximation |
| topic | Chemical Physics Materials Science |
| url | https://arxiv.org/abs/2604.07046 |