\(\renewcommand{\AA}{\text{Å}}\)

# pair_style exp6/rx command

Accelerator Variants: exp6/rx/kk

## Syntax

    pair_style exp6/rx cutoff ...

- cutoff = global cutoff for DPD interactions (distance units)

- weighting = fractional or molecular (optional)

## Examples

    pair_style exp6/rx 10.0
    pair_style exp6/rx 10.0 fractional
    pair_style exp6/rx 10.0 molecular
    pair_coeff * * exp6.params h2o h2o exponent 1.0 1.0 10.0
    pair_coeff * * exp6.params h2o 1fluid exponent 1.0 1.0 10.0
    pair_coeff * * exp6.params 1fluid 1fluid exponent 1.0 1.0 10.0
    pair_coeff * * exp6.params 1fluid 1fluid none 10.0
    pair_coeff * * exp6.params 1fluid 1fluid polynomial filename 10.0

## Description

Style exp6/rx is used in reaction DPD simulations, where the coarse-grained (CG) particles are composed of m species whose reaction rate kinetics are determined from a set of n reaction rate equations through the fix rx command. The species of one CG particle can interact with a species in a neighboring CG particle through a site-site interaction potential model. The exp6/rx style computes an exponential-6 potential given by

\[U_{ij}(r) = \frac{\epsilon}{\alpha-6}\{6\exp[\alpha(1-\frac{r_{ij}}{R_{m}})]-\alpha(\frac{R_{m}}{r_{ij}})^6\}\]

where the \(\epsilon\) parameter determines the depth of the potential minimum located at \(R_m\), and \(\alpha\) determines the softness of the repulsion.

The coefficients must be defined for each species in a given particle type via the pair_coeff command as in the examples above, where the first argument is the filename that includes the exponential-6 parameters for each species. The file includes the species tag followed by the \(\alpha, \epsilon\) and \(R_m\) parameters. The format of the file is described below.

The second and third arguments specify the site-site interaction potential between two species contained within two different particles. The species tags must either correspond to the species defined in the reaction kinetics files specified with the fix rx command or they must correspond to the tag “1fluid”, signifying interaction with a product species mixture determined through a one-fluid approximation. The interaction potential is weighted by the geometric average of either the mole fraction concentrations or the number of molecules associated with the interacting coarse-grained particles (see the fractional or molecular weighting pair style options). The coarse-grained potential is stored before and after the reaction kinetics solver is applied, where the difference is defined to be the internal chemical energy (uChem).

The fourth argument specifies the type of scaling that will be used to scale the EXP-6 parameters as reactions occur. Currently, there are three scaling options: exponent, polynomial and none.

Exponent scaling requires two additional arguments for scaling the \(R_m\) and \(\epsilon\) parameters, respectively. The scaling factor is computed by phi^exponent, where phi is the number of molecules represented by the coarse-grain particle and exponent is specified as a pair coefficient argument for \(R_m\) and \(\epsilon\), respectively. The \(R_m\) and \(\epsilon\) parameters are multiplied by the scaling factor to give the scaled interaction parameters for the CG particle.

Polynomial scaling requires a filename to be specified as a pair coeff argument. The file contains the coefficients to a fifth order polynomial for the \(\alpha\), \(\epsilon\) and \(R_m\) parameters that depend upon phi (the number of molecules represented by the CG particle). The format of a polynomial file is provided below.

The none option to the scaling does not have any additional pair coeff arguments. This is equivalent to specifying the exponent option with \(R_m\) and \(\epsilon\) exponents of 0.0 and 0.0, respectively.

The final argument specifies the interaction cutoff (optional).

The format of a tabulated file is as follows (without the parenthesized comments):

    # exponential-6 parameters for various species      (one or more comment or blank lines)

    h2o  exp6  11.00 0.02 3.50                          (species, exp6, alpha, Rm, epsilon)
    no2  exp6  13.60 0.01 3.70
    ...
    co2  exp6  13.00 0.03 3.20

The format of the polynomial scaling file as follows (without the parenthesized comments):

    # POLYNOMIAL FILE          (one or more comment or blank lines)

    #  General Functional Form:
    #  A*phi^5 + B*phi^4 + C*phi^3 + D*phi^2 + E*phi + F
    #
    #  Parameter  A        B         C        D         E        F
                               (blank)
    alpha        0.0000   0.00000   0.00008  0.04955  -0.73804  13.63201
    epsilon      0.0000   0.00478  -0.06283  0.24486  -0.33737   2.60097
    rm           0.0001  -0.00118  -0.00253  0.05812  -0.00509   1.50106

A section begins with a non-blank line whose first character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections.

Following a blank line, the next N lines list the species and their corresponding parameters. The first argument is the species tag, the second argument is the exp6 tag, the third argument is the \(\alpha\) parameter (energy units), the fourth argument is the \(\epsilon\) parameter (energy-distance^6 units), and the fifth argument is the \(R_m\) parameter (distance units). If a species tag of “1fluid” is listed as a pair coefficient, a one-fluid approximation is specified where a concentration-dependent combination of the parameters is computed through the following equations:

\[\begin{split}R_{m}^{3} = & \sum_{a}\sum_{b} x_{a}x_{b}R_{m,ab}^{3} \\ \epsilon = & \frac{1}{R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\epsilon_{ab}R_{m,ab}^{3} \\ \alpha = & \frac{1}{\epsilon R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\alpha_{ab}\epsilon_{ab}R_{m,ab}^{3}\end{split}\]

where

\[\begin{split}\epsilon_{ab} = & \sqrt{\epsilon_{a}\epsilon_{b}} \\ R_{m,ab} = & \frac{R_{m,a}+R_{m,b}}{2} \\ \alpha_{ab} = & \sqrt{\alpha_{a}\alpha_{b}}\end{split}\]

and \(x_a\) and \(x_b\) are the mole fractions of a and b, respectively, which comprise the gas mixture.

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

This pair style does not support mixing. Thus, coefficients for all I,J pairs must be specified explicitly.

This style does not support the pair_modify shift option for the energy of the exp() and 1/r^6 portion of the pair interaction.

This style does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure for the A,C terms in the pair interaction.

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.

## Restrictions

This command is part of the DPD-REACT 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

fractional weighting