ENVIRONMENTSIMILARITY

This is part of the envsim module | |

It is only available if you configure PLUMED with ./configure –enable-modules=envsim . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Measure how similar the environment around atoms is to that found in some reference crystal structure.

This CV was introduced in this article [87]. The starting point for the definition of the CV is the local atomic density around an atom. We consider an environment \(\chi\) around this atom and we define the density by

\[ \rho_{\chi}(\mathbf{r})=\sum\limits_{i\in\chi} \exp\left(- \frac{|\mathbf{r}_i-\mathbf{r}|^2} {2\sigma^2} \right), \]

where \(i\) runs over the neighbors in the environment \(\chi\), \(\sigma\) is a broadening parameter, and \(\mathbf{r}_i\) are the coordinates of the neighbors relative to the central atom. We now define a reference environment or template \(\chi_0\) that contains \(n\) reference positions \(\{\mathbf{r}^0_1,...,\mathbf{r}^0_n\}\) that describe, for instance, the nearest neighbors in a given lattice. \(\sigma\) is set using the SIGMA keyword and \(\chi_0\) is chosen with the CRYSTAL_STRUCTURE keyword. If only the SPECIES keyword is given then the atoms defined there will be the central and neighboring atoms. If instead the SPECIESA and SPECIESB keywords are given then SPECIESA determines the central atoms and SPECIESB the neighbors.

The environments \(\chi\) and \(\chi_0\) are compared using the kernel,

\[ k_{\chi_0}(\chi)= \int d\mathbf{r} \rho_{\chi}(\mathbf{r}) \rho_{\chi_0}(\mathbf{r}) . \]

Combining the two equations above and performing the integration analytically we obtain,

\[ k_{\chi_0}(\chi)= \sum\limits_{i\in\chi} \sum\limits_{j\in\chi_0} \pi^{3/2} \sigma^3 \exp\left(- \frac{|\mathbf{r}_i-\mathbf{r}^0_j|^2} {4\sigma^2} \right). \]

The kernel is finally normalized,

\[ \tilde{k}_{\chi_0}(\chi) = \frac{1}{n} \sum\limits_{i\in\chi} \sum\limits_{j\in\chi_0} \exp\left( - \frac{|\mathbf{r}_i-\mathbf{r}^0_j|^2} {4\sigma^2} \right), \]

such that \(\tilde{k}_{\chi_0}(\chi_0) = 1\). The above kernel is computed for each atom in the SPECIES or SPECIESA keywords. This quantity is a multicolvar so you can compute it for multiple atoms using a single PLUMED action and then compute the average value for the atoms in your system, the number of atoms that have an \(\tilde{k}_{\chi_0}\) value that is more that some target and so on.

The kernel can be generalized to crystal structures described as a lattice with a basis of more than one atom. In this case there is more than one type of environment. We consider the case of \(M\) environments \(X = \chi_1,\chi_2,...,\chi_M\) and we define the kernel through a best match strategy:

\[ \tilde{k}_X(\chi)= \frac{1}{\lambda} \log \left ( \sum\limits_{l=1}^{M}\exp \left (\lambda \: \tilde{k}_{\chi_l}(\chi) \right ) \right ). \]

For a large enough \(\lambda\) this expression will select the largest \(\tilde{k}_{\chi_l}(\chi)\) with \(\chi_l \in X\). This approach can be used, for instance, to target the hexagonal closed packed (HCP keyword) or the diamond structure (DIAMOND keyword).

The CRYSTAL_STRUCTURE keyword can take the values SC (simple cubic), BCC (body centered cubic), FCC (face centered cubic), HCP (hexagonal closed pack), DIAMOND (cubic diamond), and CUSTOM (user defined). All options follow the same conventions as in the lattice command of LAMMPS. If a CRYSTAL_STRUCTURE other than CUSTOM is used, then the lattice constants have to be specified using the keyword LATTICE_CONSTANTS. One value has to be specified for SC, BCC, FCC, and DIAMOND and two values have to be set for HCP (a and c lattice constants in that order).

If the CUSTOM option is used then the reference environments have to be specified by the user. The reference environments are specified in pdb files containing the distance vectors from the central atom to the neighbors. Make sure your PDB file is correctly formatted as explained in this page If only one reference environment is specified then the filename should be given as argument of the keyword REFERENCE. If instead several reference environments are given, then they have to be provided in separate pdb files and given as arguments of the keywords REFERENCE_1, REFERENCE_2, etc. If you have a reference crystal structure configuration you can use the Environment Finder app to determine the reference environments that you should use.

If multiple chemical species are involved in the calculation, it is possible to provide the atom types (names) both for atoms in the reference environments and in the simulation box. This information is provided in pdb files using the atom name field. The comparison between environments is performed taking into account whether the atom names match.

- Examples

The following input calculates the ENVIRONMENTSIMILARITY kernel for 250 atoms in the system using the BCC atomic environment as target, and then calculates and prints the average value for this quantity.

Click on the labels of the actions for more information on what each action computes