# Introduction

Versatile Object-oriented Toolkit for Coarse-graining Applications, or VOTCA, is a package which helps to systematically coarse-grain various systems [Ruehle:2009.a]. This includes deriving the coarse-grained potentials, assessing their quality, preparing input files required for coarse-grained simulations, and analyzing the latter.

A typical coarse-graining workflow includes sampling of the system of interest, analysis of the trajectory using a specific mapping and a coarse-graining method to derive coarse-grained potentials and, in case of iterative methods, running coarse-grained simulations and iteratively refining the coarse-grained potentials.

In most cases, coarse-graining requires canonical sampling of a reference (high resolution) system. In addition, iterative methods require canonical sampling of the coarse-grained system. The sampling can be done using either molecular dynamics (MD), stochastic dynamics (SD), or Monte Carlo (MC) techniques. The latter are implemented in many standard simulation packages. Rather than implementing its own MD/SD/MC modules, VOTCA allows swift and flexible integration of existing programs in such a way that sampling is performed by the program of choice. At the moment, an interface to GROMACS [gromacs4] and LAMMPS [lammps] simulation packages is provided. The rest of the analysis needed for systematic coarse-graining is done using the package tools.

Fig. 1 Three-bead coarse-grained model of propane.

The workflow can be exemplified on coarse-graining of a propane liquid. A single molecule of propane contains three carbon and eight hydrogen atoms. A united atom coarse-grained representation of a propane molecule has three beads and two bead types, A and B, with three and two hydrogens combined with the corresponding atom, as shown in the figure above. This representation defines the , as well as the bonded coarse-grained degrees of freedom, such as the bond \(b\) and the bond angle \(\theta\). Apart from the bonded interactions, \(u_b\) and \(u_\theta\), beads belonging to different molecules have non-bonded interactions, \(u_\text{AA}\), \(u_\text{AB}\), \(u_\text{BB}\). The task of coarse-graining is then to derive a potential energy surface \(u\) which is a function of all coarse-grained degrees of freedom. Note that, while the atomistic bond and angle potentials are often chosen to be simple harmonic functions, the coarse-grained potentials cannot be expressed in terms of simple analytic functions. Instead, tabulated functions are normally used.

The coarse-graining method defines criteria according to which the potential energy surface is constructed. For example, for the bond \(b\) and the angle \(\theta\) can be used. In this case a coarse-grained potential will be a potential of mean force. For the non-bonded degrees of freedom, the package provides or methods. In this case the radial distribution functions of the coarse-grained model will match those of the atomistic model. Alternatively, (or multiscale coarse-graining) can be used, in which case the coarse-grained potential will approximate the many-body potential of mean force. The choice of a particular method is system-specific and requires a thorough consistency check. It is important to keep in mind that coarse-graining should be used with understanding and caution, methods should be crossed-checked with each other as well as with respect to the reference system.

The package consists of two parts: a C++ kernel and a scripting engine. The kernel is capable of processing atomistic topologies and trajectories and offers a flexible framework for reading, manipulating and analyzing topologies and generated by MD/SD/MC sampling trajectories. It is modular: new file formats can be integrated without changing the existing code. Currently, an interface for GROMACS [gromacs4] and LAMMPS [lammps] topologies and trajectories is provided. The kernel also includes various coarse-graining tools, for example calculations of probability distributions of bonded and non-bonded interactions, correlation and autocorrelation functions, and updates for the coarse-grained pair potential.

The scripting engine is used to steer the iterative procedures. Here the analysis tools of the package used for sampling (e.g. GROMACS tools) can be integrated into the coarse-graining workflow, if needed. The coarse-graining workflow itself is controlled by several Extensible Markup Language (XML) input files, which contain mapping and other options required for the workflow control. In what follows, these input files are described.

Before using the package, do not forget to initalize the variables in the bash

    source <csg-installation>/bin/VOTCARC.bash

More details as well as several examples can be found in ref. [Ruehle:2009.a]. Please cite this paper if you are using the package.