Methods¶

Force matching¶

The force matching algorithm with cubic spline basis is implemented in the utility. A list of available options can be found in the reference section of (command –h).

Program input¶

csg_fmatch needs an atomistic reference run to perform coarse-graining. Therefore, the trajectory file must contain forces (note that there is a suitable option in the GROMACS .mdp file), otherwise csg_fmatch will not be able to run.

In addition, a mapping scheme has to be created, which defines the coarse-grained model (see Input files). At last, a control file has to be created, which contains all the information for coarse-graining the interactions and parameters for the force-matching run. This file is specified by the tag –options in the XMLformat. An example might look like the following

<cg>
  <!--fmatch section -->
  <fmatch>
    <!--Number of frames for block averaging -->
    <frames_per_block>6</frames_per_block>
    <!--Constrained least squares?-->
    <constrainedLS>false</constrainedLS>
  </fmatch>
  <!-- example for a non-bonded interaction entry -->
  <non-bonded>
    <!-- name of the interaction -->
    <name>CG-CG</name>
    <type1>A</type1>
    <type2>A</type2>
    <!-- fmatch specific stuff -->
    <fmatch>
      <min>0.27</min>
      <max>1.2</max>
      <step>0.02</step>
      <out_step>0.005</out_step>
    </fmatch>
  </non-bonded>
</cg>

Similarly to the case of spline fitting, the parameters min and max have to be chosen in such a way as to avoid empty bins within the grid. Determining min and max by using csg_stat is recommended (see Setting files). A full description of all available options can be found in csgapps.

Program output¶

csg_fmatch produces a separate .force file for each interaction, specified in the CG-options file (--options). These files have 4 columns containing distance, corresponding force, a table flag and the force error, which is estimated via a block-averaging procedure. If you are working with an angle, then the first column will contain the corresponding angle in radians.

To get table-files for GROMACS, integrate the forces in order to get potentials and do extrapolation and potentially smoothing afterwards.

Output files are not only produced at the end of the program execution, but also after every successful processing of each block. The user is free to have a look at the output files and decide to stop csg_fmatch, provided the force error is small enough.

Three-body Stillinger-Weber interactions¶

As described in the theory section, csg_fmatch is also able to parametrize the angular part of three-body interactions of the Stillinger-Weber type (see subsec. Three-body Stillinger-Weber interactions). The general procedure is the same, as shown in the two-body case (See flowchart in Fig. Flowchart to perform force matching.). It has to be specified in the control file that one wants to parametrize a three-body interaction. An example might look like this:

<cg>
  <!-- fmatch section -->
  <fmatch>
    <!-- Number of frames for block averaging -->
    <frames_per_block>10</frames_per_block>
    <!-- Constrained least squares?-->
    <constrainedLS>true</constrainedLS>
  </fmatch>
  <!-- example for a non-bonded interaction entry with three-body SW interactions -->
  <non-bonded>
    <!-- name of the interaction -->
    <name>CG-CG-CG</name>
    <!-- flag for three-body interactions -->
    <threebody>true</threebody>
    <!-- CG bead types (according to mapping file) -->
    <type1>A</type1>
    <type2>A</type2>
    <type3>A</type3>
    <!-- fmatch section of interaction -->
    <fmatch>
      <!-- short-range cutoff (in nm) -->
      <a>0.37</a>
      <sigma>1.0</sigma>
      <!-- switching range (steepness of exponential switching function) (in nm) -->
      <gamma>0.08</gamma>
      <!-- min for angular interaction (in rad) -->
      <min>0.7194247283</min>
      <!-- max for angular interaction (in rad) -->
      <max>3.1415927</max>
      <!-- step size for internal spline representation (in rad) -->
      <step>0.1</step>
      <!-- output step size for angular interaction (in rad) -->
      <out_step>0.0031415927</out_step>
    </fmatch>
  </non-bonded>
</cg>

As in the case of pair interactions, the parameters min and max have to be chosen in such a way as to avoid empty bins within the grid. Determining min and max by using csg_stat is recommended (see sec. Setting files).

For each three-body interaction as specified in the CG-options file --options, csg_fmatch produces a separate .force file, as well as a .pot file. Due to the functional form of the Stillinger-Weber potential, csg_fmatch outputs the three-body force in angular direction, as well as the angular potential. Therefore, in contrast to the two-body force (see section methods_fm_integration), the angular three-body force does not have to be numerically integrated. The .force, as well as the .pot file have 4 columns containing the angle in radians, the force or potential, the error (which is estimated via a block-averaging procedure) and a table flag.

Coarse-grained simulations with three-body Stillinger-Weber interactions can be done with LAMMPS with the MANYBODY pair_style sw/angle/table (https://docs.lammps.org/pair_sw_angle_table.html). For this, the .pot file has to be converted into a table format according to the LAMMPS angle_style table (https://docs.lammps.org/angle_table.html).