lammps/doc/pair_eff.txt

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pair_style eff/cut command :h3

[Syntax:]

pair_style eff/cut cutoff eradius_limit_flag pressure_flag

cutoff = global cutoff for Coulombic interactions
eradius_limit_flag = 0 or 1 for whether electron size is restrained (optional)
pressure_flag = 0 or 1 to define the type of pressure calculation (optional) :ul

[Examples:]

pair_style eff/cut 39.7
pair_style eff/cut 40.0 1 1
pair_coeff * *
pair_coeff 2 2 20.0 :pre

[Description:]

This pair style contains a LAMMPS implementation of the electron Force
Field (eFF) potential currently under development at Caltech, as
described in "(Jaramillo-Botero)"_#Jaramillo-Botero.  The eFF was
first introduced by "(Su)"_#Su in 2007.

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
wavefunction 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 wavepackets.  The wavefunction is taken to be a
Hartree product of the wave packets.  To compensate for the lack of
explicit antisymmetry in the resulting wavefunction, a spin-dependent
Pauli potential is included in the Hamiltonian.  Substituting this
wavefunction 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 wavefunction 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
wavefunction, 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,

:c,image(Eqs/eff_energy_expression.jpg)

The individual terms are defined as follows:

:c,image(Eqs/eff_KE.jpg)

:c,image(Eqs/eff_NN.jpg)

:c,image(Eqs/eff_Ne.jpg)

:c,image(Eqs/eff_ee.jpg)

:c,image(Eqs/eff_Pauli.jpg)

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
"(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 "electron_units"_units.html).  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
"kspace_style"_kspace_style.html 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 "atom_style
electron"_atom_style.html 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 "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands, or by mixing as described below:

cutoff (distance units) :ul

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 "pair_coeff"_pair_coeff.html command.
All type pairs use the same global cutoff specified in the pair_style
command.

The {eradius_limit_flag} and {pressure_flag} settings are optional.
Neither or both must be specified.  If not specified they are
both set to 0 by default.

The {eradius_limit_flag} is used to restrain electrons from becoming
unbounded in size at very high temperatures were the Gaussian wave
packet representation breaks down, and from expanding as free
particles to infinite size.  A setting of 0 means do not impose this
restraint.  A setting of 1 imposes the restraint.  The restraining
harmonic potential takes the form E = 1/2k_ss^2 for s > L_box/2, where
k_s = 1 Hartrees/Bohr^2.

The {pressure_flag} is used to control between two types of pressure
computation: if set to 0, the computed pressure does not include the
electronic radial virials contributions to the total pressure (scalar
or tensor).  If set to 1, the computed pressure will include the
electronic radial virial contributions to the total pressure (scalar
and tensor).

IMPORTANT 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).

:line

IMPORTANT NOTE: The currently implemented eFF gives a reasonably
accurate description for systems containing nuclei from Z = 1-6.
Users interested in applying eFF should restrict to systems where
electrons are s-like, or contain p character only insofar as a single
lobe of electron density is shifted away from the nuclear center.  See
further details about some of the virtues and current limitations of
the method in "(Jaramillo-Botero)"_#Jaramillo-Botero.

Work is underway to extend the eFF to higher Z elements with
increasingly non-spherical electrons (p-block and d-block), to provide
explicit terms for electron correlation/exchange, and to improve its
computational efficiency via atom models with fixed 2 s core electrons
and atom models represented as pseudo-cores plus valence electrons.

The current version adds support for models with fixed-core and
effective pseudo-core (i.e. effective core pseudopotentials, 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 p-character effects in
higher Z elements (e.g. Silicon).  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-picosend
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.

:line

[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 "pair_modify"_pair_modify.html shift option is not relevant for
these pair styles.

The {eff/long} (not yet available) style supports the
"pair_modify"_pair_modify.html table option for tabulation of the
short-range portion of the long-range Coulombic interaction.

These pair styles do not support the "pair_modify"_pair_modify.html
tail option for adding long-range tail corrections to energy and
pressure.

These pair styles write their information to "binary restart
files"_restart.html, 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
"run_style respa"_run_style.html command.  They do not support the
{inner}, {middle}, {outer} keywords.

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[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 "Making LAMMPS"_Section_start.html#2_3 section
for more info.

These pair styles require that particles store electron attributes
such as radius, radial velocity, and radital force, as defined by the
"atom_style"_atom_style.html.  The {electron} atom style does all of
this.

Thes pair styles require you to use the "communicate vel
yes"_communicate.html option so that velocites are stored by ghost
atoms.

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:]

If not specified, eradius_limit_flag = 0 and pressure_flag = 0.

:line

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

:link(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).