.. index:: pair_style eff/cut

pair_style eff/cut command
==========================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style eff/cut cutoff keyword args ...

* cutoff = global cutoff for Coulombic interactions
* zero or more keyword/value pairs may be appended

  .. parsed-literal::

     keyword = *limit/eradius* or *pressure/evirials* or *ecp*
       *limit/eradius* args = none
       *pressure/evirials* args = none
       *ecp* args = type element type element ...
         type = LAMMPS atom type (1 to Ntypes)
         element = element symbol (e.g. H, Si)

Examples
""""""""

.. code-block:: LAMMPS

   pair_style eff/cut 39.7
   pair_style eff/cut 40.0 limit/eradius
   pair_style eff/cut 40.0 limit/eradius pressure/evirials
   pair_style eff/cut 40.0 ecp 1 Si 3 C
   pair_coeff * *
   pair_coeff 2 2 20.0
   pair_coeff 1 s 0.320852 2.283269 0.814857
   pair_coeff 3 p 22.721015 0.728733 1.103199 17.695345 6.693621

Description
"""""""""""

This pair style contains a LAMMPS implementation of the electron Force
Field (eFF) potential currently under development at Caltech, as
described in :ref:`(Jaramillo-Botero) <Jaramillo-Botero>`.  The eFF for Z<6
was first introduced by :ref:`(Su) <Su>` in 2007. It has been extended to
higher Zs by using effective core potentials (ECPs) that now cover up
to second and third row p-block elements of the periodic table.

eFF can be viewed as an approximation to QM wave packet dynamics and
Fermionic molecular dynamics, combining the ability of electronic
structure methods to describe atomic structure, bonding, and chemistry
in materials, and of plasma methods to describe nonequilibrium
dynamics of large systems with a large number of highly excited
electrons.  Yet, eFF relies on a simplification of the electronic
wave function in which electrons are described as floating Gaussian
wave packets whose position and size respond to the various dynamic
forces between interacting classical nuclear particles and spherical
Gaussian electron wave packets.  The wave function is taken to be a
Hartree product of the wave packets.  To compensate for the lack of
explicit antisymmetry in the resulting wave function, a spin-dependent
Pauli potential is included in the Hamiltonian.  Substituting this
wave function into the time-dependent Schrodinger equation produces
equations of motion that correspond - to second order - to classical
Hamiltonian relations between electron position and size, and their
conjugate momenta.  The N-electron wave function is described as a
product of one-electron Gaussian functions, whose size is a dynamical
variable and whose position is not constrained to a nuclear
center. This form allows for straightforward propagation of the
wave function, with time, using a simple formulation from which the
equations of motion are then integrated with conventional MD
algorithms. In addition to this spin-dependent Pauli repulsion
potential term between Gaussians, eFF includes the electron kinetic
energy from the Gaussians.  These two terms are based on
first-principles quantum mechanics.  On the other hand, nuclei are
described as point charges, which interact with other nuclei and
electrons through standard electrostatic potential forms.

The full Hamiltonian (shown below), contains then a standard
description for electrostatic interactions between a set of
delocalized point and Gaussian charges which include, nuclei-nuclei
(NN), electron-electron (ee), and nuclei-electron (Ne). Thus, eFF is a
mixed QM-classical mechanics method rather than a conventional force
field method (in which electron motions are averaged out into ground
state nuclear motions, i.e a single electronic state, and particle
interactions are described via empirically parameterized interatomic
potential functions). This makes eFF uniquely suited to simulate
materials over a wide range of temperatures and pressures where
electronically excited and ionized states of matter can occur and
coexist.  Furthermore, the interactions between particles -nuclei and
electrons- reduce to the sum of a set of effective pairwise potentials
in the eFF formulation.  The *eff/cut* style computes the pairwise
Coulomb interactions between nuclei and electrons (E_NN,E_Ne,E_ee),
and the quantum-derived Pauli (E_PR) and Kinetic energy interactions
potentials between electrons (E_KE) for a total energy expression
given as,

.. math::

   U\left(R,r,s\right) =  E_{NN} \left( R \right) + E_{Ne} \left( {R,r,s} \right) + E_{ee} \left( {r,s} \right) + E_{KE} \left( {r,s} \right) + E_{PR} \left( { \uparrow  \downarrow ,S} \right)

The individual terms are defined as follows:

.. math::

   E_{KE}  = & \frac{\hbar^2 }{{m_{e} }}\sum\limits_i {\frac{3}{{2s_i^2 }}} \\
   E_{NN}  = & \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{{Z_i Z_j }}{{R_{ij} }}} \\
   E_{Ne}  = & - \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i,j} {\frac{{Z_i }}{{R_{ij} }}Erf\left( {\frac{{\sqrt 2 R_{ij} }}{{s_j }}} \right)} \\
   E_{ee}  = & \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{1}{{r_{ij} }}Erf\left( {\frac{{\sqrt 2 r_{ij} }}{{\sqrt {s_i^2  + s_j^2 } }}} \right)} \\
   E_{Pauli}  = & \sum\limits_{\sigma _i  = \sigma _j } {E\left( { \uparrow  \uparrow } \right)_{ij}}  + \sum\limits_{\sigma _i  \ne \sigma _j } {E\left( { \uparrow  \downarrow } \right)_{ij}} \\

where, s_i correspond to the electron sizes, the sigmas i's to the
fixed spins of the electrons, Z_i to the charges on the nuclei, R_ij
to the distances between the nuclei or the nuclei and electrons, and
r_ij to the distances between electrons.  For additional details see
:ref:`(Jaramillo-Botero) <Jaramillo-Botero>`.

The overall electrostatics energy is given in Hartree units of energy
by default and can be modified by an energy-conversion constant,
according to the units chosen (see :doc:`electron_units <units>`).  The
cutoff Rc, given in Bohrs (by default), truncates the interaction
distance.  The recommended cutoff for this pair style should follow
the minimum image criterion, i.e. half of the minimum unit cell
length.

Style *eff/long* (not yet available) computes the same interactions as
style *eff/cut* except that an additional damping factor is applied so
it can be used in conjunction with the
:doc:`kspace_style <kspace_style>` command and its *ewald* or *pppm*
option.  The Coulombic cutoff specified for this style means that
pairwise interactions within this distance are computed directly;
interactions outside that distance are computed in reciprocal space.

This potential is designed to be used with :doc:`atom_style electron <atom_style>` definitions, in order to handle the
description of systems with interacting nuclei and explicit electrons.

The following coefficients must be defined for each pair of atoms
types via the :doc:`pair_coeff <pair_coeff>` command as in the examples
above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands, or by mixing as described below:

* cutoff (distance units)

For *eff/cut*\ , the cutoff coefficient is optional.  If it is not used
(as in some of the examples above), the default global value specified
in the pair_style command is used.

For *eff/long* (not yet available) no cutoff will be specified for an
individual I,J type pair via the :doc:`pair_coeff <pair_coeff>` command.
All type pairs use the same global cutoff specified in the pair_style
command.

----------

The *limit/eradius* and *pressure/evirials* keywords are optional.
Neither or both must be specified.  If not specified they are unset.

The *limit/eradius* keyword is used to restrain electron size from
becoming excessively diffuse at very high temperatures were the
Gaussian wave packet representation breaks down, and from expanding as
free particles to infinite size.  If unset, electron radius is free to
increase without bounds.  If set, a restraining harmonic potential of
the form E = 1/2k_ss\^2 for s > L_box/2, where k_s = 1 Hartrees/Bohr\^2,
is applied on the electron radius.

The *pressure/evirials* keyword is used to control between two types
of pressure computation: if unset, the computed pressure does not
include the electronic radial virials contributions to the total
pressure (scalar or tensor).  If set, the computed pressure will
include the electronic radial virial contributions to the total
pressure (scalar and tensor).

The *ecp* keyword is used to associate an ECP representation for a
particular atom type.  The ECP captures the orbital overlap between a
core pseudo particle and valence electrons within the Pauli repulsion.
A list of type:element-symbol pairs may be provided for all ECP
representations, after the "ecp" keyword.

.. note::

   Default ECP parameters are provided for C, N, O, Al, and Si.
   Users can modify these using the pair_coeff command as exemplified
   above.  For this, the User must distinguish between two different
   functional forms supported, one that captures the orbital overlap
   assuming the s-type core interacts with an s-like valence electron
   (s-s) and another that assumes the interaction is s-p.  For systems
   that exhibit significant p-character (e.g. C, N, O) the s-p form is
   recommended. The "s" ECP form requires 3 parameters and the "p" 5
   parameters.

.. note::

   there are two different pressures that can be reported for eFF
   when defining this pair_style, one (default) that considers electrons
   do not contribute radial virial components (i.e. electrons treated as
   incompressible 'rigid' spheres) and one that does.  The radial
   electronic contributions to the virials are only tallied if the
   flexible pressure option is set, and this will affect both global and
   per-atom quantities.  In principle, the true pressure of a system is
   somewhere in between the rigid and the flexible eFF pressures, but,
   for most cases, the difference between these two pressures will not be
   significant over long-term averaged runs (i.e. even though the energy
   partitioning changes, the total energy remains similar).

----------

.. note::

   This implementation of eFF gives a reasonably accurate description
   for systems containing nuclei from Z = 1-6 in "all electron"
   representations.  For systems with increasingly non-spherical
   electrons, Users should use the ECP representations.  ECPs are now
   supported and validated for most of the second and third row elements of
   the p-block.  Predefined parameters are provided for C, N, O, Al, and
   Si.  The ECP captures the orbital overlap between the core and valence
   electrons (i.e. Pauli repulsion) with one of the functional forms:

.. math::

   E_{Pauli(ECP_s)} = & p_1\exp\left(-\frac{p_2r^2}{p_3+s^2} \right) \\
   E_{Pauli(ECP_p)} = & p_1\left( \frac{2}{p_2/s+s/p_2} \right)\left( r-p_3s\right)^2\exp \left[ -\frac{p_4\left( r-p_3s \right)^2}{p_5+s^2} \right]

Where the first form correspond to core interactions with s-type valence
electrons and the second to core interactions with p-type valence
electrons.

The current version adds full support for models with fixed-core and
ECP definitions.  to enable larger timesteps (i.e. by avoiding the
high frequency vibrational modes -translational and radial- of the 2 s
electrons), and in the ECP case to reduce the increased orbital
complexity in higher Z elements (up to Z<18).  A fixed-core should be
defined with a mass that includes the corresponding nuclear mass plus
the 2 s electrons in atomic mass units (2x5.4857990943e-4), and a
radius equivalent to that of minimized 1s electrons (see examples
under /examples/USER/eff/fixed-core).  An pseudo-core should be
described with a mass that includes the corresponding nuclear mass,
plus all the core electrons (i.e no outer shell electrons), and a
radius equivalent to that of a corresponding minimized full-electron
system.  The charge for a pseudo-core atom should be given by the
number of outer shell electrons.

In general, eFF excels at computing the properties of materials in
extreme conditions and tracing the system dynamics over multi-picosecond
timescales; this is particularly relevant where electron excitations
can change significantly the nature of bonding in the system. It can
capture with surprising accuracy the behavior of such systems because
it describes consistently and in an unbiased manner many different
kinds of bonds, including covalent, ionic, multicenter, ionic, and
plasma, and how they interconvert and/or change when they become
excited.  eFF also excels in computing the relative thermochemistry of
isodemic reactions and conformational changes, where the bonds of the
reactants are of the same type as the bonds of the products.  eFF
assumes that kinetic energy differences dominate the overall exchange
energy, which is true when the electrons present are nearly spherical
and nodeless and valid for covalent compounds such as dense hydrogen,
hydrocarbons, and diamond; alkali metals (e.g. lithium), alkali earth
metals (e.g. beryllium) and semimetals such as boron; and various
compounds containing ionic and/or multicenter bonds, such as boron
dihydride.

----------

**Mixing, shift, table, tail correction, restart, rRESPA info**\ :

For atom type pairs I,J and I != J, the cutoff distance for the
*eff/cut* style can be mixed.  The default mix value is *geometric*\ .
See the "pair_modify" command for details.

The :doc:`pair_modify <pair_modify>` shift option is not relevant for
these pair styles.

The *eff/long* (not yet available) style supports the
:doc:`pair_modify <pair_modify>` table option for tabulation of the
short-range portion of the long-range Coulombic interaction.

These pair styles do not support the :doc:`pair_modify <pair_modify>`
tail option for adding long-range tail corrections to energy and
pressure.

These pair styles write their information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.

These pair styles can only be used via the *pair* keyword of the
:doc:`run_style respa <run_style>` command.  They do not support the
*inner*\ , *middle*\ , *outer* keywords.

----------

Restrictions
""""""""""""

These pair styles will only be enabled if LAMMPS is built with the
USER-EFF package.  It will only be enabled if LAMMPS was built with
that package.  See the :doc:`Build package <Build_package>` doc page for
more info.

These pair styles require that particles store electron attributes
such as radius, radial velocity, and radial force, as defined by the
:doc:`atom_style <atom_style>`.  The *electron* atom style does all of
this.

Thes pair styles require you to use the :doc:`comm_modify vel yes <comm_modify>` command so that velocities are stored by ghost
atoms.

Related commands
""""""""""""""""

:doc:`pair_coeff <pair_coeff>`

Default
"""""""

If not specified, limit_eradius = 0 and pressure_with_evirials = 0.

----------

.. _Su:

**(Su)** Su and Goddard, Excited Electron Dynamics Modeling of Warm
Dense Matter, Phys Rev Lett, 99:185003 (2007).

.. _Jaramillo-Botero:

**(Jaramillo-Botero)** Jaramillo-Botero, Su, Qi, Goddard, Large-scale,
Long-term Non-adiabatic Electron Molecular Dynamics for Describing
Material Properties and Phenomena in Extreme Environments, J Comp
Chem, 32, 497-512 (2011).
