2010-09-02 03:53:20 +08:00
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<HTML>
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>pair_style eff/cut command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<P>pair_style eff/cut cutoff eradius_limit_flag pressure_flag
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</P>
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2010-09-02 04:17:25 +08:00
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<UL><LI>cutoff = global cutoff for Coulombic interactions
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<LI>eradius_limit_flag = 0 or 1 for whether electron size is restrained (optional)
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<LI>pressure_flag = 0 or 1 to define the type of pressure calculation (optional)
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</UL>
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2010-09-02 03:53:20 +08:00
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<P><B>Examples:</B>
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</P>
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<PRE>pair_style eff/cut 39.7
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pair_style eff/cut 40.0 1 1
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pair_coeff * *
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pair_coeff 2 2 20.0
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</PRE>
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<P><B>Description:</B>
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</P>
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2011-06-14 07:18:49 +08:00
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<P>This pair style contains a LAMMPS implementation of the electron Force
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Field (eFF) potential currently under development at Caltech, as
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described in <A HREF = "#Jaramillo-Botero">(Jaramillo-Botero)</A>. The eFF was
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first introduced by <A HREF = "#Su">(Su)</A> in 2007.
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2010-09-02 03:53:20 +08:00
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</P>
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<P>eFF can be viewed as an approximation to QM wave packet dynamics and
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Fermionic molecular dynamics, combining the ability of electronic
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structure methods to describe atomic structure, bonding, and chemistry
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in materials, and of plasma methods to describe nonequilibrium
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dynamics of large systems with a large number of highly excited
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electrons. Yet, eFF relies on a simplification of the electronic
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wavefunction in which electrons are described as floating Gaussian
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wave packets whose position and size respond to the various dynamic
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forces between interacting classical nuclear particles and spherical
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Gaussian electron wavepackets. The wavefunction is taken to be a
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Hartree product of the wave packets. To compensate for the lack of
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explicit antisymmetry in the resulting wavefunction, a spin-dependent
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Pauli potential is included in the Hamiltonian. Substituting this
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wavefunction into the time-dependent Schrodinger equation produces
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equations of motion that correspond - to second order - to classical
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Hamiltonian relations between electron position and size, and their
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conjugate momenta. The N-electron wavefunction is described as a
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product of one-electron Gaussian functions, whose size is a dynamical
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variable and whose position is not constrained to a nuclear
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center. This form allows for straightforward propagation of the
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wavefunction, with time, using a simple formulation from which the
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equations of motion are then integrated with conventional MD
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algorithms. In addition to this spin-dependent Pauli repulsion
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potential term between Gaussians, eFF includes the electron kinetic
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energy from the Gaussians. These two terms are based on
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first-principles quantum mechanics. On the other hand, nuclei are
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described as point charges, which interact with other nuclei and
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electrons through standard electrostatic potential forms.
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</P>
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<P>The full Hamiltonian (shown below), contains then a standard
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description for electrostatic interactions between a set of
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delocalized point and Gaussian charges which include, nuclei-nuclei
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(NN), electron-electron (ee), and nuclei-electron (Ne). Thus, eFF is a
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mixed QM-classical mechanics method rather than a conventional force
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field method (in which electron motions are averaged out into ground
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state nuclear motions, i.e a single electronic state, and particle
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interactions are described via empirically parameterized interatomic
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potential functions). This makes eFF uniquely suited to simulate
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materials over a wide range of temperatures and pressures where
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electronically excited and ionized states of matter can occur and
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coexist. Furthermore, the interactions between particles -nuclei and
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electrons- reduce to the sum of a set of effective pairwise potentials
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in the eFF formulation. The <I>eff/cut</I> style computes the pairwise
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Coulomb interactions between nuclei and electrons (E_NN,E_Ne,E_ee),
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and the quantum-derived Pauli (E_PR) and Kinetic energy interactions
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potentials between electrons (E_KE) for a total energy expression
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given as,
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</P>
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<CENTER><IMG SRC = "Eqs/eff_energy_expression.jpg">
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</CENTER>
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<P>The individual terms are defined as follows:
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</P>
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<CENTER><IMG SRC = "Eqs/eff_KE.jpg">
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</CENTER>
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<CENTER><IMG SRC = "Eqs/eff_NN.jpg">
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</CENTER>
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<CENTER><IMG SRC = "Eqs/eff_Ne.jpg">
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</CENTER>
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<CENTER><IMG SRC = "Eqs/eff_ee.jpg">
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</CENTER>
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<CENTER><IMG SRC = "Eqs/eff_Pauli.jpg">
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</CENTER>
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<P>where, s_i correspond to the electron sizes, the sigmas i's to the
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fixed spins of the electrons, Z_i to the charges on the nuclei, R_ij
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to the distances between the nuclei or the nuclei and electrons, and
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r_ij to the distances between electrons. For additional details see
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<A HREF = "#Jaramillo-Botero">(Jaramillo-Botero)</A>.
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</P>
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<P>The overall electrostatics energy is given in Hartree units of energy
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by default and can be modified by an energy-conversion constant,
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according to the units chosen (see <A HREF = "units.html">electron_units</A>). The
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cutoff Rc, given in Bohrs (by default), truncates the interaction
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distance. The recommended cutoff for this pair style should follow
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the minimum image criterion, i.e. half of the minimum unit cell
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length.
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</P>
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<P>Style <I>eff/long</I> (not yet available) computes the same interactions as
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style <I>eff/cut</I> except that an additional damping factor is applied so
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it can be used in conjunction with the
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<A HREF = "kspace_style.html">kspace_style</A> command and its <I>ewald</I> or <I>pppm</I>
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option. The Coulombic cutoff specified for this style means that
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pairwise interactions within this distance are computed directly;
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interactions outside that distance are computed in reciprocal space.
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</P>
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2011-06-14 07:18:49 +08:00
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<P>This potential is designed to be used with <A HREF = "atom_style.html">atom_style
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2010-09-02 03:53:20 +08:00
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electron</A> definitions, in order to handle the
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description of systems with interacting nuclei and explicit electrons.
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</P>
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<P>The following coefficients must be defined for each pair of atoms
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types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
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above, or in the data file or restart files read by the
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<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
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commands, or by mixing as described below:
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</P>
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<UL><LI>cutoff (distance units)
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</UL>
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<P>For <I>eff/cut</I>, the cutoff coefficient is optional. If it is not used
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(as in some of the examples above), the default global value specified
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in the pair_style command is used.
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</P>
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<P>For <I>eff/long</I> (not yet available) no cutoff will be specified for an
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individual I,J type pair via the <A HREF = "pair_coeff.html">pair_coeff</A> command.
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All type pairs use the same global cutoff specified in the pair_style
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command.
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</P>
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<P>The <I>eradius_limit_flag</I> and <I>pressure_flag</I> settings are optional.
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Neither or both must be specified. If not specified they are
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both set to 0 by default.
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</P>
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<P>The <I>eradius_limit_flag</I> is used to restrain electrons from becoming
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unbounded in size at very high temperatures were the Gaussian wave
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packet representation breaks down, and from expanding as free
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particles to infinite size. A setting of 0 means do not impose this
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restraint. A setting of 1 imposes the restraint. The restraining
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harmonic potential takes the form E = 1/2k_ss^2 for s > L_box/2, where
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k_s = 1 Hartrees/Bohr^2.
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</P>
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<P>The <I>pressure_flag</I> is used to control between two types of pressure
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computation: if set to 0, the computed pressure does not include the
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electronic radial virials contributions to the total pressure (scalar
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or tensor). If set to 1, the computed pressure will include the
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electronic radial virial contributions to the total pressure (scalar
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and tensor).
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</P>
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<P>IMPORTANT NOTE: there are two different pressures that can be reported
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for eFF when defining this pair_style, one (default) that considers
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electrons do not contribute radial virial components (i.e. electrons
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treated as incompressible 'rigid' spheres) and one that does. The
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radial electronic contributions to the virials are only tallied if the
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flexible pressure option is set, and this will affect both global and
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per-atom quantities. In principle, the true pressure of a system is
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somewhere in between the rigid and the flexible eFF pressures, but,
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for most cases, the difference between these two pressures will not be
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significant over long-term averaged runs (i.e. even though the energy
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partitioning changes, the total energy remains similar).
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</P>
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<HR>
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<P>IMPORTANT NOTE: The currently implemented eFF gives a reasonably
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accurate description for systems containing nuclei from Z = 1-6.
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Users interested in applying eFF should restrict to systems where
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electrons are s-like, or contain p character only insofar as a single
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lobe of electron density is shifted away from the nuclear center. See
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further details about some of the virtues and current limitations of
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the method in <A HREF = "#Jaramillo-Botero">(Jaramillo-Botero)</A>.
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</P>
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<P>Work is underway to extend the eFF to higher Z elements with
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increasingly non-spherical electrons (p-block and d-block), to provide
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explicit terms for electron correlation/exchange, and to improve its
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2011-02-23 06:29:54 +08:00
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computational efficiency via atom models with fixed 2 s core electrons
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and atom models represented as pseudo-cores plus valence electrons.
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</P>
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<P>The current version adds support for models with fixed-core and
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effective pseudo-core (i.e. effective core pseudopotentials, ECP)
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definitions. to enable larger timesteps (i.e. by avoiding the high
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frequency vibrational modes -translational and radial- of the 2 s
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electrons), and in the ECP case to reduce the p-character effects in
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higher Z elements (e.g. Silicon). A fixed-core should be defined with
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a mass that includes the corresponding nuclear mass plus the 2 s
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electrons in atomic mass units (2x5.4857990943e-4), and a radius
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equivalent to that of minimized 1s electrons (see examples under
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/examples/USER/eff/fixed-core). An pseudo-core should be described
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with a mass that includes the corresponding nuclear mass, plus all the
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core electrons (i.e no outer shell electrons), and a radius equivalent
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to that of a corresponding minimized full-electron system. The charge
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for a pseudo-core atom should be given by the number of outer shell
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electrons.
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2010-09-02 03:53:20 +08:00
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</P>
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<P>In general, eFF excels at computing the properties of materials in
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extreme conditions and tracing the system dynamics over multi-picosend
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timescales; this is particularly relevant where electron excitations
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can change significantly the nature of bonding in the system. It can
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capture with surprising accuracy the behavior of such systems because
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it describes consistently and in an unbiased manner many different
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kinds of bonds, including covalent, ionic, multicenter, ionic, and
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plasma, and how they interconvert and/or change when they become
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excited. eFF also excels in computing the relative thermochemistry of
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isodemic reactions and conformational changes, where the bonds of the
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reactants are of the same type as the bonds of the products. eFF
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assumes that kinetic energy differences dominate the overall exchange
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energy, which is true when the electrons present are nearly spherical
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and nodeless and valid for covalent compounds such as dense hydrogen,
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hydrocarbons, and diamond; alkali metals (e.g. lithium), alkali earth
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metals (e.g. beryllium) and semimetals such as boron; and various
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compounds containing ionic and/or multicenter bonds, such as boron
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dihydride.
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</P>
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<HR>
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<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
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</P>
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<P>For atom type pairs I,J and I != J, the cutoff distance for the
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<I>eff/cut</I> style can be mixed. The default mix value is <I>geometric</I>.
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See the "pair_modify" command for details.
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</P>
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<P>The <A HREF = "pair_modify.html">pair_modify</A> shift option is not relevant for
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these pair styles.
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</P>
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<P>The <I>eff/long</I> (not yet available) style supports the
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<A HREF = "pair_modify.html">pair_modify</A> table option for tabulation of the
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short-range portion of the long-range Coulombic interaction.
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</P>
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<P>These pair styles do not support the <A HREF = "pair_modify.html">pair_modify</A>
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tail option for adding long-range tail corrections to energy and
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pressure.
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</P>
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<P>These pair styles write their information to <A HREF = "restart.html">binary restart
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files</A>, so pair_style and pair_coeff commands do not need
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to be specified in an input script that reads a restart file.
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</P>
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<P>These pair styles can only be used via the <I>pair</I> keyword of the
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<A HREF = "run_style.html">run_style respa</A> command. They do not support the
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<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>These pair styles will only be enabled if LAMMPS is built with the
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"user-eff" package. It will only be enabled if LAMMPS was built with
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2011-08-26 00:46:23 +08:00
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that package. See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
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section for more info.
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2010-09-02 03:53:20 +08:00
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</P>
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<P>These pair styles require that particles store electron attributes
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such as radius, radial velocity, and radital force, as defined by the
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<A HREF = "atom_style.html">atom_style</A>. The <I>electron</I> atom style does all of
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this.
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</P>
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<P>Thes pair styles require you to use the <A HREF = "communicate.html">communicate vel
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yes</A> option so that velocites are stored by ghost
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atoms.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "pair_coeff.html">pair_coeff</A>
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</P>
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<P><B>Default:</B>
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</P>
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<P>If not specified, eradius_limit_flag = 0 and pressure_flag = 0.
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</P>
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<HR>
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<A NAME = "Jaramillo-Botero"></A>
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