howto:kg
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howto:kg [2018/12/06 10:25] – [How to run simulations with KG method] mpauletti | howto:kg [2020/08/21 10:15] – external edit 127.0.0.1 | ||
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$\displaystyle E_{tot} = E_{HK}[\rho_{tot}] - \sum_{A}E_{HK}[\rho_{A}] + \sum_{A}E_{KS}[\rho_{A}]$. | $\displaystyle E_{tot} = E_{HK}[\rho_{tot}] - \sum_{A}E_{HK}[\rho_{A}] + \sum_{A}E_{KS}[\rho_{A}]$. | ||
- | The total electronic density | + | The total electronic density $\rho_{tot} = \sum_{A}\rho_{A}$ |
$\displaystyle E_{HK}[\rho] = T_{HK}[\rho] + E_{ext}^{HK}[\rho] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r' | $\displaystyle E_{HK}[\rho] = T_{HK}[\rho] + E_{ext}^{HK}[\rho] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r' | ||
$\displaystyle E_{KS}[P] = T_{S}[P] + E_{ext}[P] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r' | $\displaystyle E_{KS}[P] = T_{S}[P] + E_{ext}[P] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r' | ||
- | where $P$ is the reduced one-particle density matrix of the system. | + | where $P$ is the reduced one-particle density matrix of the system. |
$\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. | $\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. | ||
- | Now, if one calls the classical Coulomb term $E_{hxc}[\rho]$ and defines | + | Now, calling |
$\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. | $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. | ||
- | To avoid the integration of the kinetic energy functional for each subsystem, an atomic potential approximation can be applied. For a local potential | + | 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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$\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ | $\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ | ||
- | 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' | $\displaystyle \mu[\rho]-\mu[\rho_{A}] \sim \sum_{B\neq A} \frac{\partial \mu[\rho_{A}]}{\partial \rho} \rho_{B} = \mu' | ||
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$\displaystyle \mu' | $\displaystyle \mu' | ||
- | and the realization that a typical kinetic energy functional is proportional to $\rho^{5/ | + | The realization that a typical kinetic energy functional is proportional to $\rho^{5/ |
$\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/ | $\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/ | ||
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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 ' | + | The division of the total system into subsystems is a critical point, in order to do that properly it is important to specify |
< | < | ||
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</ | </ | ||
- | This strategy is based on the fourth column in the COORD section. At this point the code is able to find the best combination of ' | + | This strategy is based on the fourth column in the COORD section. At this point the code is able to find the best combination of ' |
< | < | ||
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And in the same section others corrections can be added (example: VDW_POTENTIAL).\\ | And in the same section others corrections can be added (example: VDW_POTENTIAL).\\ | ||
- | For the second type of calculation the keyword to select is ATOMIC. This method implies a supplemental atomic potential (create a file which contains all the required potentials). | + | For the second type of calculation the keyword to select is ATOMIC. This method implies a supplemental atomic potential (create a file which contains all the required potentials). |
- | < | + | < |
</ | </ |
howto/kg.txt · Last modified: 2024/01/03 13:20 by oschuett