\(\renewcommand{\AA}{\text{Å}}\)

# compute efield/wolf/atom command

## Syntax

    compute ID group-ID efield/wolf/atom alpha keyword val

- ID, group-ID are documented in compute command

- efield/atom/wolf = style name of this compute command

- alpha = damping parameter (inverse distance units)

- zero or more keyword/value pairs may be appended

- keyword = limit or cutoff

      limit group2-ID = limit computing the electric field contributions to a group (default: all)
      cutoff value = set cutoff for computing contributions to this value (default: maximum cutoff of pair style)

## Examples

    compute 1 all efield/wolf/atom 0.2
    compute 1 mols efield/wolf/atom 0.25 limit water cutoff 10.0

## Description

Added in version 8Feb2023.

Define a computation that approximates the electric field at each atom in a group.

\[\vec{E}_i = \frac{\vec{F}coul_i}{q_i} = \sum_{j \neq i} \frac{q_j}{r_{ij}^2} \qquad r < r_c\]

The electric field at the position of the atom i is the coulomb force on a unit charge at that point, which is equivalent to dividing the Coulomb force by the charge of the individual atom.

In this compute the electric field is approximated as the derivative of the potential energy using the Wolf summation method, described in Wolf, given by:

\[E_i = \frac{1}{2} \sum_{j \neq i} \frac{q_i q_j \mathrm{erfc}(\alpha r_{ij})}{r_{ij}} + \frac{1}{2} \sum_{j \neq i} \frac{q_i q_j \mathrm{erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c\]

where \(\alpha\) is the damping parameter, and erf() and erfc() are error-function and complementary error-function terms. This potential is essentially a short-range, spherically-truncated, charge-neutralized, force-shifted, pairwise 1/r summation. With a manipulation of adding and subtracting a self term (for i = j) to the first and second term on the right-hand-side, respectively, and a small enough \(\alpha\) damping parameter, the second term shrinks and the potential becomes a rapidly-converging real-space summation. With a long enough cutoff and small enough \(\alpha\) parameter, the electric field calculated by the Wolf summation method approaches that computed using the Ewald sum.

The value of the electric field components will be 0.0 for atoms not in the specified compute group.

When the limit keyword is used, only contributions from atoms in the selected group will be considered, otherwise contributions from all atoms within the cutoff are included.

When the cutoff keyword is used, the cutoff used for the electric field approximation can be set explicitly. By default it is the largest cutoff of any pair style force computation.

Computational Efficiency

This compute will loop over a full neighbor list just like a pair style does when computing forces, thus it can be quite time-consuming and slow down a calculation significantly when its data is used in every time step. The compute efield/atom command of the DIELECTRIC package is more efficient in comparison, since the electric field data is collected and stored as part of the force computation at next to no extra computational cost.

## Output info

This compute calculates a per-atom vector, which can be accessed by any command that uses per-atom values from a compute as input. See the Howto output page for an overview of LAMMPS output options.

The vector contains 3 values per atom which are the x-, y-, and z-direction electric field components in force units.

## Restrictions

This compute is part of the EXTRA-COMPUTE package. It is only enabled if LAMMPS was built with that package.

This compute requires neighbor styles ‘bin’ or ‘nsq’.

## Related commands

pair_style coul/wolf, compute efield/atom

## Default

The option defaults are limit = all and cutoff = largest cutoff for pair styles.

(Wolf) D. Wolf, P. Keblinski, S. R. Phillpot, J. Eggebrecht, J Chem Phys, 110, 8254 (1999).