… and there is no description.
Periodic boundary conditions (PBC) are ubiquitous in molecular simulations. However, when visualizing results, one often prefers to see whole molecules rather than fragments cut by the simulation box. If the molecule percolates through the box, minimizing artificial cuts becomes essential. Below are two methods for reconstructing intact structures under PBC:
Problem: given a series molecules $i=1,\dots,N$, connected with junction atoms $\mathbf{x}_i^k$, for $k=1,2,…m$ if there are $m_i$ atoms from molecule $i$ that are bonded with other molecules. The connection bonds are defined as $\mathbf{b}_i := \lbrace\mathbf{x}_j^{k_1}-\mathbf{x}_i^{k_2}|\forall k_1, k_2\, \mathrm{and}\, \forall j\in \mathrm{neighbor\, of}\, i\rbrace$, assume that the center-of-mass of the molecules are fixed, but are […]
The structure factor, commonly denoted as $S(\mathbf{q})$, is an essential characterization quantity in molecular simulations. Its calculation is straightforward based on its definition. Since periodic boundary conditions are typically used in these simulations, we have $$S(\mathbf{q}) := \mathcal{FT}\lbrace\langle\rho(\mathbf{r})\rho(\mathbf{0})\rangle\rbrace(\mathbf{q})$$ which actually represents a circular convolution. This means that using the Fast Fourier Transform (FFT) can dramatically […]
A path on energy landscape is like: and this post is a guide to generate such animations. Step 1: Generate the Energy Landscape An energy landscape is essentially an energy function $U(\mathbf{x})$. This function can be created in various ways. For example, you might generate a series of Gaussian functions with random parameters $\mu_i$, $\sigma_i$, […]
Mapping coarse-grained models back to all-atom models is a tricky problem. E.g., for polymeric systems, CG models are often used to polymerize monomers to cross-linked polymer networks. Mapping back these systems to all-atom models need to handle reactions amongst monomers. Dealing back-mapping case by case is dumb: for one specific kind of reactions, there are […]