Kinetic energy from a single Kohn-Sham orbital
Mel Levy, Paul W. Ayers
Abstract
Mel Levy, Paul W. Ayers
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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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