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# pair_style lj/relres command

Accelerator Variants: lj/relres/omp

## Syntax

    pair_style lj/relres Rsi Rso Rci Rco

- Rsi = inner switching cutoff between the fine-grained and coarse-grained potentials (distance units)

- Rso = outer switching cutoff between the fine-grained and coarse-grained potentials (distance units)

- Rci = inner cutoff beyond which the force smoothing for all interactions is applied (distance units)

- Rco = outer cutoff for all interactions (distance units)

## Examples

    pair_style lj/relres 4.0 5.0 8.0 10.0
    pair_coeff 1 1 0.5 1.0 1.5 1.1
    pair_coeff 2 2 0.5 1.0 0.0 0.0 3.0 3.5 6.0 7.0

## Description

Pair style lj/relres computes a LJ interaction using the Relative Resolution (RelRes) framework which applies a fine-grained (FG) potential between near neighbors and a coarse-grained (CG) potential between far neighbors (Chaimovich1). This approach can improve the computational efficiency by almost an order of magnitude, while maintaining the correct static and dynamic behavior of a reference system (Chaimovich2).

\[\begin{split}E = \left\{\begin{array}{lr} 4 \epsilon^{\scriptscriptstyle FG} \left[ \left(\frac{\sigma^{FG}}{r}\right)^{12} - \left(\frac{\sigma^{FG}}{r}\right)^6 \right]-\Gamma_{si}, & \quad\mathrm{if}\quad r< r_{si}, \\ \sum_{m=0}^{4} \gamma_{sm}\left(r-r_{si}\right)^m-\Gamma_{so} , & \quad\mathrm{if}\quad r_{si}\leq r< r_{so}, \\ 4 \epsilon^{\scriptscriptstyle CG} \left[ \left(\frac{\sigma^{CG}}{r}\right)^{12} - \left(\frac{\sigma^{CG}}{r}\right)^6 \right]-\Gamma_c, & \quad\mathrm{if}\quad r_{so}\leq r<r_{ci}, \\ \sum_{m=0}^{4} \gamma_{cm}\left(r-r_{ci}\right)^m -\Gamma_c, & \quad\mathrm{if}\quad r_{ci}\leq r< r_{co}, \\ 0, & \quad\mathrm{if}\quad r\geq r_{co}.\end{array}\right.\end{split}\]

The FG parameters of the LJ potential (\(\epsilon^{FG}\) and \(\sigma^{FG}\)) are applied up to the inner switching cutoff, \(r_{si}\), while the CG parameters of the LJ potential (\(\epsilon^{CG}\) and \(\sigma^{CG}\)) are applied beyond the outer switching cutoff, \(r_{so}\). Between \(r_{si}\) and \(r_{so}\) a polynomial smoothing function is applied so that the force and its derivative are continuous between the FG and CG potentials. An analogous smoothing function is applied between the inner and outer cutoffs (\(r_{ci}\) and \(r_{co}\)). The offsets \(\Gamma_{si}\), \(\Gamma_{so}\) and \(\Gamma_{c}\) ensure the continuity of the energy over the entire domain. The corresponding polynomial coefficients \(\gamma_{sm}\) and \(\gamma_{cm}\), as well as the offsets are automatically computed by LAMMPS.

Note

Energy and force resulting from this methodology can be plotted via the pair_write command.

The following coefficients must be defined for each pair of atom types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, or by mixing as will be described below:

- \(\epsilon^{FG}\) (energy units)

- \(\sigma^{FG}\) (distance units)

- \(\epsilon^{CG}\) (energy units)

- \(\sigma^{CG}\) (distance units)

Additional parameters can be defined to specify different \(r_{si}\), \(r_{so}\), \(r_{ci}\), \(r_{co}\) for a particular set of atom types:

- \(r_{si}\) (distance units)

- \(r_{so}\) (distance units)

- \(r_{ci}\) (distance units)

- \(r_{co}\) (distance units)

These parameters are optional, and they are used to override the global cutoffs as defined in the pair_style command. If not specified, the global values for \(r_{si}\), \(r_{so}\), \(r_{ci}\), and \(r_{co}\) are used. If this override option is employed, all four arguments must be specified.

Here are some guidelines for using the pair_style lj/relres command.

In general, RelRes focuses on the speedup of pairwise interactions between all LJ sites. Importantly, it works with any settings and flags (e.g., special_bonds settings and newton flags) that can be used in a molecular simulation with the conventional LJ potential. In particular, all intramolecular topology with its energetics (i.e., bonds, angles, etc.) remains unaltered.

At the most basic level in the RelRes framework, all sites are mapped into clusters. Each cluster is just a collection of sites bonded together (the bonds themselves are not part of the cluster). In general, a molecule may be comprised of several clusters, and preferably, no two sites in a cluster are separated by more than two bonds. There are two categories of sites in RelRes: “hybrid” sites embody both FG and CG models, while “ordinary” sites embody just FG characteristics with no CG features. A given cluster has a single hybrid site (typically its central site) and several ordinary sites (typically its peripheral sites). Notice that while clusters are necessary for the RelRes parameterization (discussed below), they are not actually defined in LAMMPS. Besides, the total number of sites in the cluster are called the “mapping ratio”, and this substantially impacts the computational efficiency of RelRes: For a mapping ratio of 3, the efficiency factor is around 4, and for a mapping ratio of 5, the efficiency factor is around 5 (Chaimovich2).

The flexibility of LAMMPS allows placing any values for the LJ parameters in the input script. However, here are the optimal recommendations for the RelRes parameters, which yield the correct structural and thermal behavior in a system of interest (Chaimovich1). One must first assign a complete set of parameters for the FG interactions that are applicable to all atom types. Regarding the parameters for the CG interactions, the rules rely on the site category (if it is a hybrid or an ordinary site). For atom types of ordinary sites, \(\epsilon^{CG}\) must be set to 0 (zero) while the specific value of \(\sigma^{CG}\) is irrelevant. For atom types of hybrid sites, the CG parameters should be generally calculated using the following equations:

\[\sigma_I^{CG}=\frac{\left((\sum_{\alpha\in A}\sqrt{\epsilon_\alpha^{FG}\left(\sigma_\alpha^{FG}\right)^{12}}\right)^{1/2}}{\left((\sum_{\alpha\in A}\sqrt{\epsilon_\alpha^{FG}\left(\sigma_\alpha^{FG}\right)^6}\right)^{1/3}} \quad\mathrm{and}\quad \epsilon_I^{CG}=\frac{\left((\sum_{\alpha\in A}\sqrt{\epsilon_\alpha^{FG}\left(\sigma_\alpha^{FG}\right)^6}\right)^4}{\left((\sum_{\alpha\in A}\sqrt{\epsilon_\alpha^{FG}\left(\sigma_\alpha^{FG}\right)^{12}}\right)^2}\]

where \(I\) is an atom type of a hybrid site of a particular cluster \(A\), and corresponding with this cluster, the summation proceeds over all of its sites \(\alpha\). These equations are derived from the monopole term in the underlying Taylor series, and they are indeed relevant only if geometric mixing is applicable for the FG model; if this is not the case, Ref. (Chaimovich2) discusses the alternative formula, and in such a situation, the pair_coeff command should be explicitly used for all combinations of atom types \(I\;!=J\).

The switching distance (the midpoint between inner and outer switching cutoffs) is another crucial factor in RelRes: decreasing it improves the computational efficiency, yet if it is too small, the molecular simulations may not capture the system behavior correctly. As a rule of thumb, the switching distance should be approximately \(\,\sim\! 1.5\sigma\) (Chaimovich1); recommendations can be found in Ref. (Chaimovich2). Regarding the switching smoothing zone, \(\,\sim\!0.1\sigma\) is recommended; if desired, smoothing can be eliminated by setting the inner switching cutoff, \(r_{si}\), equal to the outer switching cutoff, \(r_{so}\) (the same is true for the other cutoffs \(r_{ci}\) and \(r_{co}\)).

As an example, imagine that in your system, a molecule is comprised just of one cluster such that one atom type (#1) is associated with its hybrid site, and another atom type (#2) is associated with its ordinary sites (in total, there are 2 atom types). If geometric mixing is applicable, the following commands should be used:

    pair_style lj/relres Rsi Rso Rci Rco
    pair_coeff 1 1 epsilon_FG1 sigma_FG1 epsilon_CG1 sigma_CG1
    pair_coeff 2 2 epsilon_FG2 sigma_FG2 0.0         0.0
    pair_modify shift yes

In a more complex situation, there may be two distinct clusters in a system (these two clusters may be on same molecule or on different molecules), each with its own switching cutoffs. If there are still two atom types in each cluster as in the earlier example, the commands should be:

    pair_style lj/relres Rsi Rso Rci Rco
    pair_coeff 1 1 epsilon_FG1 sigma_FG1 epsilon_CG1 sigma_CG1 Rsi1 Rso1 Rci Rco
    pair_coeff 2 2 epsilon_FG2 sigma_FG2 0.0         0.0       Rsi1 Rso1 Rci Rco
    pair_coeff 3 3 epsilon_FG3 sigma_FG3 epsilon_CG3 sigma_CG3
    pair_coeff 4 4 epsilon_FG4 sigma_FG4 0.0         0.0
    pair_modify shift yes

In this example, the switching cutoffs for the first cluster (atom types 1 and 2) is defined explicitly in the pair_coeff command which overrides the global values, while the second cluster (atom types 3 and 4) uses the global definition from the pair_style command. The emphasis here is that the atom types that belong to a specific cluster should have the same switching/cutoff arguments.

In the case that geometric mixing is not applicable, for simulating the system from the previous example, we recommend using the following commands:

    pair_style lj/relres Rsi Rso Rci Rco
    pair_coeff 1 1 epsilon_FG1  sigma_FG1  epsilon_CG1  sigma_CG1  Rsi1  Rso1  Rci Rco
    pair_coeff 1 2 epsilon_FG12 sigma_FG12 0.0          0.0        Rsi1  Rso1  Rci Rco
    pair_coeff 1 3 epsilon_FG13 sigma_FG13 epsilon_CG13 sigma_CG13 Rsi13 Rso13 Rci Rco
    pair_coeff 1 4 epsilon_FG14 sigma_FG14 0.0          0.0        Rsi13 Rso13 Rci Rco
    pair_coeff 2 2 epsilon_FG2  sigma_FG2  0.0          0.0        Rsi1  Rso1  Rci Rco
    pair_coeff 2 3 epsilon_FG23 sigma_FG23 0.0          0.0        Rsi13 Rso13 Rci Rco
    pair_coeff 2 4 epsilon_FG24 sigma_FG24 0.0          0.0        Rsi13 Rso13 Rci Rco
    pair_coeff 3 3 epsilon_FG3  sigma_FG3  epsilon_CG3  sigma_CG3
    pair_coeff 3 4 epsilon_FG34 sigma_FG34 0.0          0.0
    pair_coeff 4 4 epsilon_FG4  sigma_FG4  0.0          0.0
    pair_modify shift yes

Notice that the CG parameters are mixed only for interactions between atom types associated with hybrid sites, and that the cutoffs are mixed on the cluster basis.

More examples can be found in the examples/relres folder.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Mixing, shift, table, tail correction, restart, rRESPA info

For atom type pairs \(I,\:J\) with \(I\;!=J\), the \(\epsilon^{FG}\), \(\sigma^{FG}\), \(\epsilon^{CG}\), \(\sigma^{CG}\), \(r_{si}\), \(r_{so}\), \(r_{ci}\), and \(r_{co}\) parameters for this pair style can be mixed, if not defined explicitly. All parameters are mixed according to the pair_modify mix option. The default mix value is geometric, and it is recommended to use with this lj/relres style. See the “pair_modify” command for details.

This pair style supports the pair_modify shift option for the energy of the pair interaction. It is recommended to set this option to yes. Otherwise, the offset \(\Gamma_{c}\) is set to zero. Constants \(\Gamma_{si}\) and \(\Gamma_{so}\) are not impacted by this option.

The pair_modify table option is not relevant for this pair style.

This pair style does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure, since the energy of the pair interaction is smoothed to 0.0 at the cutoff.

This pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file.

This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.

## Restrictions

This pair style is part of the EXTRA-PAIR package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

pair_coeff

## Default

none

(Chaimovich1) A. Chaimovich, C. Peter and K. Kremer, J. Chem. Phys. 143, 243107 (2015).

(Chaimovich2) M. Chaimovich and A. Chaimovich, J. Chem. Theory Comput. 17, 1045-1059 (2021).