CP2K Open Source Molecular Dynamics

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howto:kg [2018/12/07 13:11] – 130.60.136.203howto:kg [2018/12/07 13:17] – mpauletti
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 $\displaystyle E_{KS}[P] = T_{S}[P] + E_{ext}[P] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r')}{r-r'}drdr' + E_{XC}[\rho]$. $\displaystyle E_{KS}[P] = T_{S}[P] + E_{ext}[P] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r')}{r-r'}drdr' + E_{XC}[\rho]$.
  
-where $P$ is the reduced one-particle density matrix of the system. In order to arrive at the working equations, one has to introduce the restriction that the external energy functional in the Hohenberg–Kohn energy is linear in the density.+where $P$ is the reduced one-particle density matrix of the system. First of all, it's important to introduce the restriction that the external energy functional in the Hohenberg–Kohn energy is linear in the density.
  
 $\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. $\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$.
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 $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$.
  
-To avoid the integration of the kinetic energy functional for each subsystem, an atomic potential approximation can be applied. For a local potential one can write:+To avoid the integration of the kinetic energy functional for each subsystem, an atomic potential approximation can be applied. For a local potential:
  
 $\displaystyle T_{nadd} = T_{S}[\rho]−\sum_{A}T_{S}[\rho_{A}] =$\\ $\displaystyle T_{nadd} = T_{S}[\rho]−\sum_{A}T_{S}[\rho_{A}] =$\\
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 $\displaystyle \mu'[\rho_{A}]\rho_{A} = V^{K}[\rho_{A}] \sim \sum_{a \in A}V_{a}^{K}(R_{a})$ $\displaystyle \mu'[\rho_{A}]\rho_{A} = V^{K}[\rho_{A}] \sim \sum_{a \in A}V_{a}^{K}(R_{a})$
  
-and the realization that a typical kinetic energy functional is proportional to $\rho^{5/3}$ leads to a model for the final atomic local potential of the form:+The realization that a typical kinetic energy functional is proportional to $\rho^{5/3}$ leads to a model for the final atomic local potential of the form:
  
 $\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/3}$ $\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/3}$
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 ===== CP2K tutorial ===== ===== CP2K tutorial =====
  
-The division of the total system into subsystems is a critical point, in order to do that properly it is important to tell the CP2K which is the 'minimum unit'. One can use the section TOPOLOGY to define the minimum subsystem:+The division of the total system into subsystems is a critical point, in order to do that properly it is important to specify which is the 'minimum unit', that can be defined in the TOPOLOGY section:
  
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howto/kg.txt · Last modified: 2024/01/03 13:20 by oschuett