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### fix drude/transform/direct command

### fix drude/transform/inverse command

Syntax:

    fix ID group-ID style keyword value ...

- ID, group-ID are documented in fix command
- style = drude/transform/direct or drude/transform/inverse

Examples:

    fix 3 all drude/transform/direct
    fix 1 all drude/transform/inverse

Description:

Transform the coordinates of Drude oscillators from real to reduced and back for thermalizing the Drude oscillators as described in (Lamoureux) using a Nose-Hoover thermostat. This fix is designed to be used with the thermalized Drude oscillator model. Polarizable models in LAMMPS are described in this Section.

Drude oscillators are a pair of atoms representing a single polarizable atom. Ideally, the mass of Drude particles would vanish and their positions would be determined self-consistently by iterative minimization of the energy, the cores' positions being fixed. It is however more efficient and it yields comparable results, if the Drude oscillators (the motion of the Drude particle relative to the core) are thermalized at a low temperature. In that case, the Drude particles need a small mass.

The thermostats act on the reduced degrees of freedom, which are defined by the following equations. Note that in these equations upper case denotes atomic or center of mass values and lower case denotes Drude particle or dipole values. Primes denote the transformed (reduced) values, while bare letters denote the original values.

Masses: \begin{equation} M' = M + m \end{equation} \begin{equation} m' = \frac {M\, m } {M'} \end{equation} Positions: \begin{equation} X' = \frac {M\, X + m\, x} {M'} \end{equation} \begin{equation} x' = x - X \end{equation} Velocities: \begin{equation} V' = \frac {M\, V + m\, v} {M'} \end{equation} \begin{equation} v' = v - V \end{equation} Forces: \begin{equation} F' = F + f \end{equation} \begin{equation} f' = \frac { M\, f - m\, F} {M'} \end{equation}

This transform conserves the total kinetic energy \begin{equation} \frac 1 2 \, (M\, V^2\ + m\, v^2) = \frac 1 2 \, (M'\, V'^2\ + m'\, v'^2) \end{equation} and the virial defined with absolute positions \begin{equation} X\, F + x\, f = X'\, F' + x'\, f' \end{equation}

This fix requires each atom know whether it is a Drude particle or not. You must therefore use the fix drude command to specify the Drude status of each atom type.

NOTE: only the Drude core atoms need to be in the group specified for this fix. A Drude electron will be transformed together with its core even if it is not itself in the group. It is safe to include Drude electrons or non-polarizable atoms in the group. The non-polarizable atoms will simply not be transformed.

This fix does NOT perform time integration. It only transform masses, coordinates, velocities and forces. Thus you must use separate time integration fixes, like fix nve or fix npt to actually update the velocities and positions of atoms. In order to thermalize the reduced degrees of freedom at different temperatures, two Nose-Hoover thermostats must be defined, acting on two distinct groups.

NOTE: The fix drude/transform/direct command must appear before any Nose-Hoover thermostating fixes. The fix drude/transform/inverse command must appear after any Nose-Hoover thermostating fixes.

Example:

    fix fDIRECT all drude/transform/direct
    fix fNVT gCORES nvt temp 300.0 300.0 100
    fix fNVT gDRUDES nvt temp 1.0 1.0 100
    fix fINVERSE all drude/transform/inverse
    compute TDRUDE all temp/drude
    thermo_style custom step cpu etotal ke pe ebond ecoul elong press vol temp c_TDRUDE[1] c_TDRUDE[2]

In this example, gCORES is the group of the atom cores and gDRUDES is the group of the Drude particles (electrons). The centers of mass of the Drude oscillators will be thermostated at 300.0 and the internal degrees of freedom will be thermostated at 1.0. The temperatures of cores and Drude particles, in center-of-mass and relative coordinates, are calculated using compute temp/drude

In addition, if you want to use a barostat to simulate a system at constant pressure, only one of the Nose-Hoover fixes must be npt, the other one should be nvt. You must add a compute temp/com and a fix_modify command so that the temperature of the npt fix be just that of its group (the Drude cores) but the pressure be the overall pressure thermo_press.

Example:

    compute cTEMP_CORE gCORES temp/com
    fix fDIRECT all drude/transform/direct
    fix fNPT gCORES npt temp 298.0 298.0 100 iso 1.0 1.0 500
    fix_modify fNPT temp cTEMP_CORE press thermo_press
    fix fNVT gDRUDES nvt temp 5.0 5.0 100
    fix fINVERSE all drude/transform/inverse

In this example, gCORES is the group of the atom cores and gDRUDES is the group of the Drude particles. The centers of mass of the Drude oscillators will be thermostated at 298.0 and the internal degrees of freedom will be thermostated at 5.0. The whole system will be barostated at 1.0.

In order to avoid the flying ice cube problem (irreversible transfer of linear momentum to the center of mass of the system), you may need to add a fix momentum command:

    fix fMOMENTUM all momentum 100 linear 1 1 1

Restart, fix_modify, output, run start/stop, minimize info:

No information about this fix is written to binary restart files.

Restrictions: none

Related commands:

fix drude, fix langevin/drude, compute temp/drude, pair_style thole

Default: none

(Lamoureux) Lamoureux and Roux, J Chem Phys, 119, 3025-3039 (2003).