forked from lijiext/lammps
74 lines
3.9 KiB
ReStructuredText
74 lines
3.9 KiB
ReStructuredText
Polarizable models
|
|
==================
|
|
|
|
In polarizable force fields the charge distributions in molecules and
|
|
materials respond to their electrostatic environments. Polarizable
|
|
systems can be simulated in LAMMPS using three methods:
|
|
|
|
* the fluctuating charge method, implemented in the :doc:`QEQ <fix_qeq>`
|
|
package,
|
|
* the adiabatic core-shell method, implemented in the
|
|
:doc:`CORESHELL <Howto_coreshell>` package,
|
|
* the thermalized Drude dipole method, implemented in the
|
|
:doc:`USER-DRUDE <Howto_drude>` package.
|
|
|
|
The fluctuating charge method calculates instantaneous charges on
|
|
interacting atoms based on the electronegativity equalization
|
|
principle. It is implemented in the :doc:`fix qeq <fix_qeq>` which is
|
|
available in several variants. It is a relatively efficient technique
|
|
since no additional particles are introduced. This method allows for
|
|
charge transfer between molecules or atom groups. However, because the
|
|
charges are located at the interaction sites, off-plane components of
|
|
polarization cannot be represented in planar molecules or atom groups.
|
|
|
|
The two other methods share the same basic idea: polarizable atoms are
|
|
split into one core atom and one satellite particle (called shell or
|
|
Drude particle) attached to it by a harmonic spring. Both atoms bear
|
|
a charge and they represent collectively an induced electric dipole.
|
|
These techniques are computationally more expensive than the QEq
|
|
method because of additional particles and bonds. These two
|
|
charge-on-spring methods differ in certain features, with the
|
|
core-shell model being normally used for ionic/crystalline materials,
|
|
whereas the so-called Drude model is normally used for molecular
|
|
systems and fluid states.
|
|
|
|
The core-shell model is applicable to crystalline materials where the
|
|
high symmetry around each site leads to stable trajectories of the
|
|
core-shell pairs. However, bonded atoms in molecules can be so close
|
|
that a core would interact too strongly or even capture the Drude
|
|
particle of a neighbor. The Drude dipole model is relatively more
|
|
complex in order to remedy this and other issues. Specifically, the
|
|
Drude model includes specific thermostatting of the core-Drude pairs
|
|
and short-range damping of the induced dipoles.
|
|
|
|
The three polarization methods can be implemented through a
|
|
self-consistent calculation of charges or induced dipoles at each
|
|
timestep. In the fluctuating charge scheme this is done by the matrix
|
|
inversion method in :doc:`fix qeq/point <fix_qeq>`, but for core-shell
|
|
or Drude-dipoles the relaxed-dipoles technique would require an slow
|
|
iterative procedure. These self-consistent solutions yield accurate
|
|
trajectories since the additional degrees of freedom representing
|
|
polarization are massless. An alternative is to attribute a mass to
|
|
the additional degrees of freedom and perform time integration using
|
|
an extended Lagrangian technique. For the fluctuating charge scheme
|
|
this is done by :doc:`fix qeq/dynamic <fix_qeq>`, and for the
|
|
charge-on-spring models by the methods outlined in the next two
|
|
sections. The assignment of masses to the additional degrees of
|
|
freedom can lead to unphysical trajectories if care is not exerted in
|
|
choosing the parameters of the polarizable models and the simulation
|
|
conditions.
|
|
|
|
In the core-shell model the vibration of the shells is kept faster
|
|
than the ionic vibrations to mimic the fast response of the
|
|
polarizable electrons. But in molecular systems thermalizing the
|
|
core-Drude pairs at temperatures comparable to the rest of the
|
|
simulation leads to several problems (kinetic energy transfer, too
|
|
short a timestep, etc.) In order to avoid these problems the relative
|
|
motion of the Drude particles with respect to their cores is kept
|
|
"cold" so the vibration of the core-Drude pairs is very slow,
|
|
approaching the self-consistent regime. In both models the
|
|
temperature is regulated using the velocities of the center of mass of
|
|
core+shell (or Drude) pairs, but in the Drude model the actual
|
|
relative core-Drude particle motion is thermostatted separately as
|
|
well.
|