# Drude induced dipoles

The thermalized Drude model represents induced dipoles by a pair of
charges (the core atom and the Drude particle) connected by a harmonic
spring. See the [Howto polarizable](Howto_polarizable) doc page for a
discussion of all the polarizable models available in LAMMPS.

The Drude model has a number of features aimed at its use in molecular
systems ([Lamoureux and Roux](howto-Lamoureux)):

-   Thermostatting of the additional degrees of freedom associated with
    the induced dipoles at very low temperature, in terms of the reduced
    coordinates of the Drude particles with respect to their cores. This
    makes the trajectory close to that of relaxed induced dipoles.
-   Consistent definition of 1-2 to 1-4 neighbors. A core-Drude particle
    pair represents a single (polarizable) atom, so the special
    screening factors in a covalent structure should be the same for the
    core and the Drude particle. Drude particles have to inherit the
    1-2, 1-3, 1-4 special neighbor relations from their respective
    cores.
-   Stabilization of the interactions between induced dipoles. Drude
    dipoles on covalently bonded atoms interact too strongly due to the
    short distances, so an atom may capture the Drude particle of a
    neighbor, or the induced dipoles within the same molecule may align
    too much. To avoid this, damping at short range can be done by Thole
    functions (for which there are physical grounds). This Thole damping
    is applied to the point charges composing the induced dipole (the
    charge of the Drude particle and the opposite charge on the core,
    not to the total charge of the core atom).

A detailed tutorial covering the usage of Drude induced dipoles in
LAMMPS is on the [here](Howto_drude2).

As with the core-shell model, the cores and Drude particles should
appear in the data file as standard atoms. The same holds for the
springs between them, which are described by standard harmonic bonds.
The nature of the atoms (core, Drude particle or non-polarizable) is
specified via the [fix drude](fix_drude) command. The special list of
neighbors is automatically refactored to account for the equivalence of
core and Drude particles as regards special 1-2 to 1-4 screening. It may
be necessary to use the *extra/special/per/atom* keyword of the
[read_data](read_data) command. If using [fix shake](fix_shake), make
sure no Drude particle is in this fix group.

There are three ways to thermostat the Drude particles at a low
temperature: use either [fix langevin/drude](fix_langevin_drude) for a
Langevin thermostat, or [fix drude/transform/\*](fix_drude_transform)
for a Nose-Hoover thermostat, or [fix tgnvt/drude](fix_tgnh_drude) for a
temperature-grouped Nose-Hoover thermostat. The first and third require
use of the command [comm_modify vel yes](comm_modify). The second
requires two separate integration fixes like *nvt* or *npt*. The correct
temperatures of the reduced degrees of freedom can be calculated using
the [compute temp/drude](compute_temp_drude). This requires also to use
the command *comm_modify vel yes*.

Short-range damping of the induced dipole interactions can be achieved
using Thole functions through the [pair style thole](pair_thole) in
[pair_style hybrid/overlay](pair_hybrid) with a Coulomb pair style. It
may be useful to use *coul/long/cs* or similar from the CORESHELL
package if the core and Drude particle come too close, which can cause
numerical issues.

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::: {#howto-Lamoureux}
**(Lamoureux and Roux)** G. Lamoureux, B. Roux, J. Chem. Phys 119, 3025
(2003)
:::