2009Physical Review ARequires access

Kinetic energy from a single Kohn-Sham orbital

Mel Levy, Paul W. Ayers

Open publisher page 12 citations

Abstract

We observe that the noninteracting kinetic energy, as a functional of the electron density $\ensuremath{\rho}$, may be obtained from a formula that contains only a single Kohn-Sham orbital, ${\ensuremath{\varphi}}_{i}(\mathbf{r})$, where $i$ is arbitrary. Specifically, ${T}_{s}[\ensuremath{\rho}]=(\ensuremath{-}1/4)\ensuremath{\int}{{\ensuremath{\nabla}}^{2}{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]/{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]}[3\ensuremath{\rho}(\mathbf{r})+\mathbf{r}\ensuremath{\cdot}\ensuremath{\nabla}\ensuremath{\rho}(\mathbf{r})]d\mathbf{r}$.

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What this paper is about

We observe that the noninteracting kinetic energy, as a functional of the electron density $\ensuremath{\rho}$, may be obtained from a formula that contains only a single Kohn-Sham orbital, ${\ensuremath{\varphi}}_{i}(\mathbf{r})$, where $i$ is arbitrary. Specifically, ${T}_{s}[\ensuremath{\rho}]=(\ensuremath{-}1/4)\ensuremath{\int}{{\ensuremath{\nabla}}^{2}{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]/{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]}[3\ensuremath{\rho}(\mathbf{r})+\mathbf{r}\ensuremath{\cdot}\ensuremath{\nabla}\ensuremath{\rho}(\mathbf{r})]d\mathbf{r}$.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We observe that the noninteracting kinetic energy, as a functional of the electron density $\ensuremath{\rho}$, may be obtained from a formula that contains only a single Kohn-Sham orbital, ${\ensuremath{\varphi}}_{i}(\mathbf{r})$, where $i$ is arbitrary. Specifically, ${T}_{s}[\ensuremath{\rho}]=(\ensuremath{-}1/4)\ensuremath{\int}{{\ensuremath{\nabla}}^{2}{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]/{\ensuremath{\phi}}_{i}[\ensuremath{\rho};\mathbf{r}]}[3\ensuremath{\rho}(\mathbf{r})+\mathbf{r}\ensuremath{\cdot}\ensuremath{\nabla}\ensuremath{\rho}(\mathbf{r})]d\mathbf{r}$.

Key concepts: Physics, Nabla symbol, Kinetic energy, Energy (signal processing), Kohn–Sham equations, Mathematical physics, Atomic physics, Density functional theory

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