howto:kg
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howto:kg [2018/12/07 13:20] – mpauletti | howto:kg [2019/05/08 17:26] – mpauletti | ||
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$\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. | $\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. | ||
- | Now, calling the classical Coulomb term $E_{hxc}[\rho]$ and defining the non-additive kinetic energy as $T_{nadd}[\rho, | + | Now, calling the classical Coulomb term $E_{hxc}[\rho]$ and defining the non-additive kinetic energy as $T_{nadd}[\rho, |
$\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. | $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. | ||
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$\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ | $\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ | ||
- | Making | + | Doing a linearization approximation for the functional $\mu[\rho]$ |
$\displaystyle \mu[\rho]-\mu[\rho_{A}] \sim \sum_{B\neq A} \frac{\partial \mu[\rho_{A}]}{\partial \rho} \rho_{B} = \mu' | $\displaystyle \mu[\rho]-\mu[\rho_{A}] \sim \sum_{B\neq A} \frac{\partial \mu[\rho_{A}]}{\partial \rho} \rho_{B} = \mu' |
howto/kg.txt · Last modified: 2024/01/03 13:20 by oschuett