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# 10.5.7. 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 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):

- 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.

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 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 command. If using 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 for a Langevin thermostat, or fix drude/transform/* for a Nose-Hoover thermostat, or fix tgnvt/drude for a temperature-grouped Nose-Hoover thermostat. The first and third require use of the command comm_modify vel yes. 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. 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 in pair_style hybrid/overlay 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.

(Lamoureux and Roux) G. Lamoureux, B. Roux, J. Chem. Phys 119, 3025 (2003)