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### fix qeq/point command

### fix qeq/shielded command

### fix qeq/slater command

### fix qeq/dynamic command

### fix qeq/fire command

Syntax:

    fix ID group-ID style Nevery cutoff tolerance maxiter qfile keyword ...

- ID, group-ID are documented in fix command
- style = qeq/point or qeq/shielded or qeq/slater or qeq/dynamic or qeq/fire
- Nevery = perform charge equilibration every this many steps
- cutoff = global cutoff for charge-charge interactions (distance unit)
- tolerance = precision to which charges will be equilibrated
- maxiter = maximum iterations to perform charge equilibration
- qfile = a filename with QEq parameters
- zero or more keyword/value pairs may be appended
- keyword = alpha or qdamp or qstep

        alpha value = Slater type orbital exponent (qeq/slater only)
        qdamp value = damping factor for damped dynamics charge solver (qeq/dynamic and qeq/fire only)
        qstep value = time step size for damped dynamics charge solver (qeq/dynamic and qeq/fire only)

Examples:

    fix 1 all qeq/point 1 10 1.0e-6 200 param.qeq1
    fix 1 qeq qeq/shielded 1 8 1.0e-6 100 param.qeq2
    fix 1 all qeq/slater 5 10 1.0e-6 100 params alpha 0.2
    fix 1 qeq qeq/dynamic 1 12 1.0e-3 100 my_qeq
    fix 1 all qeq/fire 1 10 1.0e-3 100 my_qeq qdamp 0.2 qstep 0.1

Description:

Perform the charge equilibration (QEq) method as described in (Rappe and Goddard) and formulated in (Nakano) (also known as the matrix inversion method) and in (Rick and Stuart) (also known as the extended Lagrangian method) based on the electronegativity equilization principle.

These fixes can be used with any pair style in LAMMPS, so long as per-atom charges are defined. The most typical use-case is in conjunction with a pair style that performs charge equilibration periodically (e.g. every timestep), such as the ReaxFF or Streitz-Mintmire potential. But these fixes can also be used with potentials that normally assume per-atom charges are fixed, e.g. a Buckingham or LJ/Coulombic potential.

Because the charge equilibration calculation is effectively independent of the pair style, these fixes can also be used to perform a one-time assignment of charges to atoms. For example, you could define the QEq fix, perform a zero-timestep run via the run command without any pair style defined which would set per-atom charges (based on the current atom configuration), then remove the fix via the unfix command before performing further dynamics.

NOTE: Computing and using charge values different from published values defined for a fixed-charge potential like Buckingham or CHARMM or AMBER, can have a strong effect on energies and forces, and produces a different model than the published versions.

NOTE: The fix qeq/comb command must still be used to perform charge equliibration with the COMB potential. The fix qeq/reax command can be used to perform charge equilibration with the ReaxFF force field, although fix qeq/shielded yields the same results as fix qeq/reax if Nevery, cutoff, and tolerance are the same. Eventually the fix qeq/reax command will be deprecated.

The QEq method minimizes the electrostatic energy of the system (or equalizes the derivative of energy with respect to charge of all the atoms) by adjusting the partial charge on individual atoms based on interactions with their neighbors within cutoff. It reqires a few parameters, in metal units, for each atom type which provided in a file specified by qfile. The file has the following format

    1 chi eta gamma zeta qcore
    2 chi eta gamma zeta qcore
    ...
    Ntype chi eta gamma zeta qcore

There is one line per atom type with the following parameters. Only a subset of the parameters is used by each QEq style as descibed below, thus the others can be set to 0.0 if desired.

- chi = electronegativity in energy units
- eta = self-Coulomb potential in energy units
- gamma = shielded Coulomb constant defined by ReaxFF force field in distance units
- zeta = Slater type orbital exponent defined by the Streitz-Mintmire potential in reverse distance units
- qcore = charge of the nucleus defined by the Streitz-Mintmire potential potential in charge units

The qeq/point style describes partial charges on atoms as point charges. Interaction between a pair of charged particles is 1/r, which is the simplest description of the interaction between charges. Only the chi and eta parameters from the qfile file are used. Note that Coulomb catastrophe can occur if repulsion between the pair of charged particles is too weak. This style solves partial charges on atoms via the matrix inversion method. A tolerance of 1.0e-6 is usually a good number.

The qeq/shielded style describes partial charges on atoms also as point charges, but uses a shielded Coulomb potential to describe the interaction between a pair of charged particles. Interaction through the shielded Coulomb is given by equation (13) of the ReaxFF force field paper. The shielding accounts for charge overlap between charged particles at small separation. This style is the same as fix qeq/reax, and can be used with pair_style reax/c. Only the chi, eta, and gamma parameters from the qfile file are used. This style solves partial charges on atoms via the matrix inversion method. A tolerance of 1.0e-6 is usually a good number.

The qeq/slater style describes partial charges on atoms as spherical charge densities centered around atoms via the Slater 1s orbital, so that the interaction between a pair of charged particles is the product of two Slater 1s orbitals. The expression for the Slater 1s orbital is given under equation (6) of the Streitz-Mintmire paper. Only the chi, eta, zeta, and qcore parameters from the qfile file are used. This style solves partial charges on atoms via the matrix inversion method. A tolerance of 1.0e-6 is usually a good number. Keyword alpha can be used to change the Slater type orbital exponent.

The qeq/dynamic style describes partial charges on atoms as point charges that interact through 1/r, but the extended Lagrangian method is used to solve partial charges on atoms. Only the chi and eta parameters from the qfile file are used. Note that Coulomb catastrophe can occur if repulsion between the pair of charged particles is too weak. A tolerance of 1.0e-3 is usually a good number. Keyword qdamp can be used to change the damping factor, while keyword qstep can be used to change the time step size.

The qeq/fire style describes the same charge model and charge solver as the qeq/dynamic style, but employs a FIRE minimization algorithm to solve for equilibrium charges. Keyword qdamp can be used to change the damping factor, while keyword qstep can be used to change the time step size.

Note that qeq/point, qeq/shielded, and qeq/slater describe different charge models, whereas the matrix inversion method and the extended Lagrangian method (qeq/dynamic and qeq/fire) are different solvers.

Note that qeq/point, qeq/dynamic and qeq/fire styles all describe charges as point charges that interact through 1/r relationship, but solve partial charges on atoms using different solvers. These three styles should yield comparable results if the QEq parameters and Nevery, cutoff, and tolerance are the same. Style qeq/point is typically faster, qeq/dynamic scales better on larger sizes, and qeq/fire is faster than qeq/dynamic.

NOTE: To avoid the evaluation of the derivative of charge with respect to position, which is typically ill-defined, the system should have a zero net charge.

NOTE: Developing QEq parameters (chi, eta, gamma, zeta, and qcore) is non-trivial. Charges on atoms are not guaranteed to equilibrate with arbitrary choices of these parameters. We do not develop these QEq paramters. See the examples/qeq directory for some examples.

Restart, fix_modify, output, run start/stop, minimize info:

No information about these fixes is written to binary restart files. No global scalar or vector or per-atom quantities are stored by these fixes for access by various output commands. No parameter of these fixes can be used with the start/stop keywords of the run command.

Thexe fixes are invoked during energy minimization.

Restrictions:

These fixes are part of the QEQ package. They are only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.

Related commands:

fix qeq/reax, fix qeq/comb

Default: none

(Rappe and Goddard) A. K. Rappe and W. A. Goddard III, J Physical Chemistry, 95, 3358-3363 (1991).

(Nakano) A. Nakano, Computer Physics Communications, 104, 59-69 (1997).

(Rick and Stuart) S. W. Rick, S. J. Stuart, B. J. Berne, J Chemical Physics 101, 16141 (1994).

(Streitz-Mintmire) F. H. Streitz, J. W. Mintmire, Physical Review B, 50, 16, 11996 (1994)

(ReaxFF) A. C. T. van Duin, S. Dasgupta, F. Lorant, W. A. Goddard III, J Physical Chemistry, 105, 9396-9049 (2001)

(QEq/Fire) T.-R. Shan, A. P. Thompson, S. J. Plimpton, in preparation