CP2K Open Source Molecular Dynamics

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