Orbital-Free Density Functional Theory for Periodic Solids: Construction of the Pauli Potential
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912284080603136 |
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| author | Majumdar, Sangita Shi, Zekun Vignale, Giovanni |
| author_facet | Majumdar, Sangita Shi, Zekun Vignale, Giovanni |
| contents | The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the realization of DFT's full potential awaits the discovery of a direct link between the electron density, $n$, and the non-interacting kinetic energy, $T_{S}[n]$. In this work, we address two key challenges towards this objective. First, we introduce a new algorithm for directly solving the constrained minimization problem yielding $T_{S}[n]$ for periodic densities -- a class of densities that, in spite of its central importance for materials science, has received limited attention in the literature. Second, we present a numerical procedure that allows us to calculate the functional derivative of $T_{S}[n]$ with respect to the density at constant electron number, also known as the Kohn-Sham potential $V_{S}[n](\rv)$. Lastly, the algorithm is augmented with a subroutine that computes the ``derivative discontinuity", i.e., the spatially uniform jump in $V_{S}[n](\rv)$ which occurs upon increasing or decreasing the total number of electrons. This feature allows us to distinguish between ``insulating" and ``conducting" densities for non interacting electrons. The code integrates key methodological innovations, such as the use of an adaptive basis set (``equidensity orbitals") for wave function expansion and the QR decomposition to accelerate the implementation of the orthogonality constraint. Notably, we derive a closed-form expression for the Pauli potential in one dimension, expressed solely in terms of the input density, without relying on Kohn-Sham eigenvalues and eigenfunctions. We validate this method on one-dimensional periodic densities, achieving results within ``chemical accuracy". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbital-Free Density Functional Theory for Periodic Solids: Construction of the Pauli Potential Majumdar, Sangita Shi, Zekun Vignale, Giovanni Computational Physics The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the realization of DFT's full potential awaits the discovery of a direct link between the electron density, $n$, and the non-interacting kinetic energy, $T_{S}[n]$. In this work, we address two key challenges towards this objective. First, we introduce a new algorithm for directly solving the constrained minimization problem yielding $T_{S}[n]$ for periodic densities -- a class of densities that, in spite of its central importance for materials science, has received limited attention in the literature. Second, we present a numerical procedure that allows us to calculate the functional derivative of $T_{S}[n]$ with respect to the density at constant electron number, also known as the Kohn-Sham potential $V_{S}[n](\rv)$. Lastly, the algorithm is augmented with a subroutine that computes the ``derivative discontinuity", i.e., the spatially uniform jump in $V_{S}[n](\rv)$ which occurs upon increasing or decreasing the total number of electrons. This feature allows us to distinguish between ``insulating" and ``conducting" densities for non interacting electrons. The code integrates key methodological innovations, such as the use of an adaptive basis set (``equidensity orbitals") for wave function expansion and the QR decomposition to accelerate the implementation of the orthogonality constraint. Notably, we derive a closed-form expression for the Pauli potential in one dimension, expressed solely in terms of the input density, without relying on Kohn-Sham eigenvalues and eigenfunctions. We validate this method on one-dimensional periodic densities, achieving results within ``chemical accuracy". |
| title | Orbital-Free Density Functional Theory for Periodic Solids: Construction of the Pauli Potential |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2503.15959 |