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--- howto:kg [2018/12/07 13:21] – mpauletti
+++ howto:kg [2024/01/03 13:20] (current) – oschuett
@@ Line 1: / Line 1: @@
-====== 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 would be:
- $\displaystyle E_{tot}[{P_{A}}] =\sum_{A}(T_{S}[P_{A}] + E_{ext}[P_{A}]) + E_{hxc}[\rho] + T_{nadd}[{P_{A}}]$ .
-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
- O   2.28039789       9.14653873       5.08869600       1
- H   1.76201904       9.82042885       5.52845383       1
- H   3.09598708       9.10708809       5.58818579       1
- O   1.25170302       2.40626097       7.76990795       2
- H  0.554129004       2.98263407       8.08202362       2
- H   1.77125704       2.95477891       7.18218088       2
- O   1.59630203       6.92012787      0.656695008       3
- H   2.11214805       6.12632084      0.798135996       3
- H   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>