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howto:kg [2019/05/08 17:26] mpaulettihowto:kg [2024/01/03 13:20] (current) oschuett
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-====== How to run simulations with Kim-Gordon method ====== +This page has been moved to: https://manual.cp2k.org/trunk/methods/embedding/kim-gordon.html
- +
-===== Introduction ===== +
- +
-This method is based on density embedding. Let's introduce first the subtraction scheme definition of the density embedding method: +
- +
-$\displaystyle E_{tot} = E_{HK}[\rho_{tot}] - \sum_{A}E_{HK}[\rho_{A}] + \sum_{A}E_{KS}[\rho_{A}]$. +
- +
-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, respectively. +
- +
-$\displaystyle E_{HK}[\rho] = T_{HK}[\rho] + E_{ext}^{HK}[\rho] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r')}{r-r'}drdr' + E_{XC}[\rho]$.\\ +
-$\displaystyle E_{KS}[P] = T_{S}[P] + E_{ext}[P] + \frac{1}{2} \int\int \frac{\rho(r)\rho(r')}{r-r'}drdr' + E_{XC}[\rho]$. +
- +
-where $P$ is the reduced one-particle density matrix of the system. 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. +
- +
-$\displaystyle E_{ext}^{HK}[\rho_{tot}] = \sum_{A}E_{ext}^{HK}[\rho_{A}]$. +
- +
-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: +
- +
-$\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$. +
- +
-To avoid the integration of the kinetic energy functional for each subsystem, an atomic potential approximation can be applied. For a local potential: +
- +
-$\displaystyle T_{nadd} = T_{S}[\rho]−\sum_{A}T_{S}[\rho_{A}] =$\\ +
-$\displaystyle \int\rho\mu[\rho]dr - \sum_{a}\int\rho_{A}\mu[\rho_{A}]dr =$\\ +
-$\displaystyle \sum_{a}\int\rho_{A}(\mu[\rho]-\mu[\rho_{A}])dr$ +
- +
-Doing a linearization approximation for the functional $\mu[\rho]$ +
- +
-$\displaystyle \mu[\rho]-\mu[\rho_{A}] \sim \sum_{B\neq A} \frac{\partial \mu[\rho_{A}]}{\partial \rho} \rho_{B} = \mu'[\rho_{A}]$\\ +
-$\displaystyle T_{nadd} = \sum_{A}T_{S}\sum_{B\neq A}\int\mu'[\rho_{A}]\rho_{A}\rho_{B}dr$ +
- +
-A further approximation of the derivative functional in atomic contributions is: +
- +
-$\displaystyle \mu'[\rho_{A}]\rho_{A} = V^{K}[\rho_{A}] \sim \sum_{a \in A}V_{a}^{K}(R_{a})$ +
- +
-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: +
- +
-$\displaystyle V_{a}^{K}(R_{a}) = N_{a}\rho_{a}^{2/3}$ +
- +
-where $\rho_{a}$ is a model atomic density. Such local potential can help to speed up the underlying embedding calculation. +
- +
-===== CP2K tutorial ===== +
- +
-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: +
- +
-<code> +
-  &SUBSYS +
-    &CELL +
-      ABC 9.8528 9.8528 9.8528 +
-    &END CELL +
-    &COORD +
-   2.28039789       9.14653873       5.08869600       1 +
-   1.76201904       9.82042885       5.52845383       1 +
-   3.09598708       9.10708809       5.58818579       1 +
-   1.25170302       2.40626097       7.76990795       2 +
-  0.554129004       2.98263407       8.08202362       2 +
-   1.77125704       2.95477891       7.18218088       2 +
-   1.59630203       6.92012787      0.656695008       3 +
-   2.11214805       6.12632084      0.798135996       3 +
-   1.77638900       7.46326399       1.42402995       3 +
- ... +
-    &END COORD +
-    &TOPOLOGY +
-      CONN_FILE_FORMAT USER +
-    &END +
-</code> +
- +
-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 'minimum units' through the COLORING_METHOD in order to simplify the calculation. Another suggestion is to run KG calculations using LS_SCF, replacing the SCF section with the keyword LS_SCF: +
- +
-<code> +
-    &LS_SCF +
-      MAX_SCF     40 +
-      EPS_FILTER  1.0E-6 +
-      EPS_SCF     1.0E-7 +
-      MU         -0.1 +
-      PURIFICATION_METHOD TRS4 +
-    &END +
-</code> +
- +
-This speeds up the calculation, especially increasing the dimension of the system. +
- +
-<note>Keep in mind: all the keywords have to be activated in the QS section as well\\ +
-    &QS +
-      LS_SCF +
-      KG_METHOD +
-      ... +
-    &END QS +
-</note> +
- +
-Once all these passages are done, one has to choose the TNADD_METHOD. For the first type of calculation, discussed in the previous section, the keyword to select is EMBEDDING (default). Inside the KG_METHOD the XC functional can be selected: +
- +
-<code> +
-      &XC +
-        &XC_FUNCTIONAL +
-          &KE_GGA +
-            FUNCTIONAL T92   #example +
-          &END +
-        &END +
-      &END +
-</code> +
- +
-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. +
- +
-<note>Keep in mind: there is also the possibility to completely avoid the $T_{nadd}$ selecting NONE as TNADD_METHOD, but in this way the result of the calculation is going to be wrong, since one term is missing.  +
-</note>+
howto/kg.1557336375.txt.gz · Last modified: 2020/08/21 10:15 (external edit)