Commit 3892b517 authored by Yury Lysogorski's avatar Yury Lysogorski
Browse files

add quick potential overview notebook

parent 8316f1d4
%% Cell type:markdown id: tags:
# Day 2 - Parameterization of interatomic potentials
%% Cell type:markdown id: tags:
In this tutorial we will do simple fits for three different interatomic potentials.
* Embedded Atom Method Potential
* Neural Network Potential
* Atomic Cluster Expansion
Some details of these potentials will be summarized in the following.
%% Cell type:markdown id: tags:
## Embedded Atom Method Potential
%% Cell type:markdown id: tags:
* Atomic descriptors: pair functions
$\rho_i = \sum_j \phi(r_{ij})$ (density)
$V_i = \sum_j V(r_{ij})$ (pair repulsion)
* Atomic energy
$E_i = F( \rho_i ) + V_i$
with non-linear embedding function $F$
%% Cell type:markdown id: tags:
## Neural Network Potential
%% Cell type:markdown id: tags:
* Atomic descriptors: pair and three-body symmetry functions
$G_i = \sum_j \phi(r_{ij})$
$G_i = \sum_{jk} \phi(r_{ij},r_{ik}, \cos_{jik})$
* Atomic energy
$E_i = NN(G_i)$
with neural network $NN$. Various different $G_i$ are the inputs to the $NN$.
%% Cell type:markdown id: tags:
## Atomic Cluster Expansion
%% Cell type:markdown id: tags:
* Atomic descriptors: pair, three-body, ... many-body basis functions
$A_i = \sum_j \phi(\pmb{r}_{ij})$ (many different basis functions that depend on direction and length of $r_{ij}$)
$\varphi_i = c_1 A_i + c_2 A_i A_i + c_3 A_i A_i A_i + ...$
* Atomic energy
$E_i = F(\varphi_i)$
with general non-linear function $F$ and several $\varphi_i$. In the tutorial we will use $E_i = \sqrt{\varphi^{(1)}_i} + \varphi^{(2)}_i$ to make contact to the Embedded Atom Method.
%% Cell type:markdown id: tags:
# Reference data
%% Cell type:markdown id: tags:
The potentials are parameterized by fitting to reference data. Here we use DFT data for Cu that we generated with the FHI-aims code. In the following we summarize key properties of the dataset.
%% Cell type:code id: tags:
``` python
```
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment