howto:kg
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- | ====== How to run simulations with Kim-Gordon method ====== | + | This page has been moved to: https://manual.cp2k.org/trunk/methods/kim-gordon.html |
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- | ===== Introduction ===== | + | |
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- | This method is based on density embedding. Let's introduce first the subtraction scheme definition of the density embedding method: | + | |
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- | $\displaystyle E_{tot} = E_{HK}[\rho_{tot}] - \sum_{A}E_{HK}[\rho_{A}] + \sum_{A}E_{KS}[\rho_{A}]$. | + | |
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- | The total electronic density $\rho_{tot} = \sum_{A}\rho_{A}$ is the sum over all the subsystems $A$ of the subsystem densities $\rho_{A}$. The energy functionals $E_{HK}$ and $E_{KS}$ are the Hohenberg–Kohn and the Kohn–Sham functionals, | + | |
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- | $\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' | + | |
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- | where $P$ is the reduced one-particle density matrix of the system. First of all, it's important | + | |
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- | $\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. | + | |
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- | Now, calling the classical Coulomb term $E_{hxc}[\rho]$ and defining the non-additive kinetic energy as $T_{nadd}[\rho, | + | |
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- | $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. | + | |
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- | To avoid the integration of the kinetic energy functional for each subsystem, an atomic potential approximation can be applied. For a local potential: | + | |
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- | $\displaystyle T_{nadd} = T_{S}[\rho]−\sum_{A}T_{S}[\rho_{A}] =$\\ | + | |
- | $\displaystyle \int\rho\mu[\rho]dr - \sum_{a}\int\rho_{A}\mu[\rho_{A}]dr =$\\ | + | |
- | $\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ | + | |
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- | Doing a linearization approximation for the functional $\mu[\rho]$ | + | |
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- | $\displaystyle \mu[\rho]-\mu[\rho_{A}] \sim \sum_{B\neq A} \frac{\partial \mu[\rho_{A}]}{\partial \rho} \rho_{B} = \mu' | + | |
- | $\displaystyle T_{nadd} = \sum_{A}T_{S}\sum_{B\neq A}\int\mu' | + | |
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- | A further approximation of the derivative functional in atomic contributions is: | + | |
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- | $\displaystyle \mu' | + | |
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- | 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: | + | |
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- | $\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/3}$ | + | |
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- | where $\rho_{a}$ is a model atomic density. Such local potential can help to speed up the underlying embedding calculation. | + | |
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- | ===== CP2K tutorial ===== | + | |
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- | 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 ' | + | |
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- | < | + | |
- | & | + | |
- | &CELL | + | |
- | ABC 9.8528 9.8528 9.8528 | + | |
- | &END CELL | + | |
- | & | + | |
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- | ... | + | |
- | &END COORD | + | |
- | & | + | |
- | CONN_FILE_FORMAT USER | + | |
- | &END | + | |
- | </code> | + | |
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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 ' | + | |
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- | < | + | |
- | & | + | |
- | MAX_SCF | + | |
- | EPS_FILTER | + | |
- | EPS_SCF | + | |
- | MU | + | |
- | PURIFICATION_METHOD TRS4 | + | |
- | &END | + | |
- | </code> | + | |
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- | This speeds up the calculation, | + | |
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- | < | + | |
- | &QS | + | |
- | LS_SCF | + | |
- | KG_METHOD | + | |
- | ... | + | |
- | &END QS | + | |
- | </note> | + | |
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- | Once all these passages are done, one has to choose the TNADD_METHOD. For the first type of calculation, | + | |
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- | < | + | |
- | &XC | + | |
- | & | + | |
- | & | + | |
- | FUNCTIONAL T92 # | + | |
- | &END | + | |
- | &END | + | |
- | &END | + | |
- | </ | + | |
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- | 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). Potential templates can be found inside the "tests > QS > regtest-kg" folder of CP2K and they can be generated directly from the code (look at "tests > ATOM > regtest-pseudo > O_KG.inp"). It's important to point out that this method is still in the experimental stage and further investigations are needed. | + | |
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- | < | + | |
- | </ | + |
howto/kg.txt · Last modified: 2024/01/03 13:20 by oschuett