Ideally, the mass of the Drude particle should be small, and the
stiffness of the harmonic bond should be large, so that the Drude
particle remains close ot the core. The values of Drude mass, Drude
charge, and force constant can be chosen following different
strategies, as in the following examples of polarizable force
fields:
* :ref:`Lamoureux and Roux <Lamoureux>` suggest adopting a global half-stiffness, :math:`K_D` = 500 kcal/(mol Ang :math:`{}^2`) - which corresponds to a force constant :math:`k_D` = 4184 kJ/(mol Ang :math:`{}^2`) - for all types of core-Drude bond, a global mass :math:`m_D` = 0.4 g/mol (or u) for all types of Drude particles, and to calculate the Drude charges for individual atom types from the atom polarizabilities using equation (1). This choice is followed in the polarizable CHARMM force field.
* Alternately :ref:`Schroeder and Steinhauser <Schroeder>` suggest adopting a global charge :math:`q_D` = -1.0e and a global mass :math:`m_D` = 0.1 g/mol (or u) for all Drude particles, and to calculate the force constant for each type of core-Drude bond from equation (1). The timesteps used by these authors are between 0.5 and 2 fs, with the degrees of freedom of the Drude oscillators kept cold at 1 K.
* In both these force fields hydrogen atoms are treated as non-polarizable.
The motion of of the Drude particles can be calculated by minimizing
the energy of the induced dipoles at each timestep, by an interative,
self-consistent procedure. The Drude particles can be massless and
therefore do not contribute to the kinetic energy. However, the
relaxed method is computationall slow. An extended-lagrangian method
can be used to calculate the positions of the Drude particles, but
this requires them to have mass. It is important in this case to
decouple the degrees of freedom associated with the Drude oscillators
from those of the normal atoms. Thermalizing the Drude dipoles at
temperatures comparable to the rest of the simulation leads to several
problems (kinetic energy transfer, very short timestep, etc.), which
can be remediated by the "cold Drude" technique (:ref:`Lamoureux and Roux <Lamoureux>`).
Two closely related models are used to represent polarization through
"charges on a spring": the core-shell model and the Drude
model. Although the basic idea is the same, the core-shell model is
normally used for ionic/crystalline materials, whereas the Drude model
is normally used for molecular systems and fluid states. In ionic
crystals the symmetry around each ion and the distance between them
are such that the core-shell model is sufficiently stable. But to be
applicable to molecular/covalent systems the Drude model includes two
important features:
#. The possibility to thermostat 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.
#. The Drude dipoles on covalently bonded atoms interact too strongly due to the short distances, so an atom may capture the Drude particle (shell) of a neighbor, or the induced dipoles within the same molecule may align too much. To avoid this, damping at short of the interactions between the point charges composing the induced dipole can be done by :ref:`Thole <Thole>` functions.
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**Preparation of the data file**
The data file is similar to a standard LAMMPS data file for
*atom_style full*\ . The DPs and the *harmonic bonds* connecting them
to their DC should appear in the data file as normal atoms and bonds.
You can use the *polarizer* tool (Python script distributed with the
USER-DRUDE package) to convert a non-polarizable data file (here
*data.102494.lmp*\ ) to a polarizable data file (\ *data-p.lmp*\ )