forked from lijiext/lammps
249 lines
11 KiB
Plaintext
249 lines
11 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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minimize command :h3
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[Syntax:]
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minimize etol ftol maxiter maxeval :pre
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etol = stopping tolerance for energy (unitless)
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ftol = stopping tolerance for force (force units)
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maxiter = max iterations of minimizer
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maxeval = max number of force/energy evaluations :ul
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[Examples:]
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minimize 1.0e-4 1.0e-6 100 1000
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minimize 0.0 1.0e-8 1000 100000 :pre
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[Description:]
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Perform an energy minimization of the system, by iteratively adjusting
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atom coordinates. Iterations are terminated when one of the stopping
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criteria is satisfied. At that point the configuration will hopefully
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be in local potential energy minimum. More precisely, the
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configuration should approximate a critical point for the objective
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function (see below), which may or may not be a local minimum.
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The minimization algorithm used is set by the
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"min_style"_min_style.html command. Other options are set by the
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"min_modify"_min_modify.html command. Minimize commands can be
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interspersed with "run"_run.html commands to alternate between
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relaxation and dynamics. The minimizers bound the distance atoms move
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in one iteration, so that you can relax systems with highly overlapped
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atoms (large energies and forces) by pushing the atoms off of each
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other.
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Alternate means of relaxing a system are to run dynamics with a small
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or "limited timestep"_fix_nve_limit.html. Or dynamics can be run
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using "fix viscous"_fix_viscous.html to impose a damping force that
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slowly drains all kinetic energy from the system. The "pair_style
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soft"_pair_soft.html potential can be used to un-overlap atoms while
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running dynamics.
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The "minimization styles"_min_style.html {cg}, {sd}, and {hftn}
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involves an outer iteration loop which sets the search direction along
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which atom coordinates are changed. An inner iteration is then
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performed using a line search algorithm. The line search typically
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evaluates forces and energies several times to set new coordinates.
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Currently, a backtracking algorithm is used which may not be optimal
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in terms of the number of force evaulations performed, but appears to
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be more robust than previous line searches we've tried. The
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backtracking method is described in Nocedal and Wright's Numerical
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Optimization (Procedure 3.1 on p 41).
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The "minimization styles"_min_style.html {quickmin} and {fire} perform
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damped dynamics using an Euler integration step. Thus they require a
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"timestep"_timestep.html be defined, typically the same value used for
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"running dynamics"_run.html with the system, though it may be more
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efficient to use a larger timestep.
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The objective function being minimized is the total potential energy
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of the system as a function of the N atom coordinates:
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:c,image(Eqs/min_energy.jpg)
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where the first term is the sum of all non-bonded "pairwise
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interactions"_pair_style.html including "long-range Coulombic
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interactions"_kspace_style.html, the 2nd thru 5th terms are
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"bond"_bond_style.html, "angle"_angle_style.html,
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"dihedral"_dihedral_style.html, and "improper"_improper_style.html
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interactions respectively, and the last term is energy due to
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"fixes"_fix.html which can act as constraints or apply force to atoms,
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such as thru interaction with a wall. See the discussion below about
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how fix commands affect minimization.
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The starting point for the minimization is the current configuration
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of the atoms.
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:line
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The minimization procedure stops if any of several criteria are met:
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the change in energy between outer iterations is less than {etol}
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the 2-norm (length) of the global force vector is less than the {ftol}
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the line search fails because the step distance backtracks to 0.0
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the number of outer iterations or timesteps exceeds {maxiter}
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the number of total force evaluations exceeds {maxeval} :ul
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For the first criterion, the specified energy tolerance {etol} is
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unitless; it is met when the energy change between successive
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iterations divided by the energy magnitude is less than or equal to
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the tolerance. For example, a setting of 1.0e-4 for {etol} means an
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energy tolerance of one part in 10^4. For the damped dynamics
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minimizers this check is not performed for a few steps after
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velocities are reset to 0, otherwise the minimizer would prematurely
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converge.
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For the second criterion, the specified force tolerance {ftol} is in
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force units, since it is the length of the global force vector for all
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atoms, e.g. a vector of size 3N for N atoms. Since many of the
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components will be near zero after minimization, you can think of
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{ftol} as an upper bound on the final force on any component of any
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atom. For example, a setting of 1.0e-4 for {ftol} means no x, y, or z
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component of force on any atom will be larger than 1.0e-4 (in force
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units) after minimization.
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Either or both of the {etol} and {ftol} values can be set to 0.0, in
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which case some other criterion will terminate the minimization.
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During a minimization, the outer iteration count is treated as a
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timestep. Output is triggered by this timestep, e.g. thermodynamic
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output or dump and restart files.
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Using the "thermo_style custom"_thermo_style.html command with the
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{fmax} or {fnorm} keywords can be useful for monitoring the progress
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of the minimization. Note that these outputs will be calculated only
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from forces on the atoms, and will not include any extra degrees of
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freedom, such as from the "fix box/relax"_fix_box_relax.html command.
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Following minimization, a statistical summary is printed that lists
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which convergence criterion caused the minimizer to stop, as well as
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information about the energy, force, final line search, and
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iteration counts. An example is as follows:
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Minimization stats:
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Stopping criterion = max iterations
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Energy initial, next-to-last, final =
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-0.626828169302 -2.82642039062 -2.82643549739
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Force two-norm initial, final = 2052.1 91.9642
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Force max component initial, final = 346.048 9.78056
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Final line search alpha, max atom move = 2.23899e-06 2.18986e-05
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Iterations, force evaluations = 2000 12724 :pre
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The 3 energy values are for before and after the minimization and on
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the next-to-last iteration. This is what the {etol} parameter checks.
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The two-norm force values are the length of the global force vector
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before and after minimization. This is what the {ftol} parameter
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checks.
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The max-component force values are the absolute value of the largest
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component (x,y,z) in the global force vector, i.e. the infinity-norm
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of the force vector.
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The alpha parameter for the line-search, when multiplied by the max
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force component (on the last iteration), gives the max distance any
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atom moved during the last iteration. Alpha will be 0.0 if the line
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search could not reduce the energy. Even if alpha is non-zero, if the
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"max atom move" distance is tiny compared to typical atom coordinates,
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then it is possible the last iteration effectively caused no atom
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movement and thus the evaluated energy did not change and the
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minimizer terminated. Said another way, even with non-zero forces,
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it's possible the effect of those forces is to move atoms a distance
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less than machine precision, so that the energy cannot be further
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reduced.
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The iterations and force evaluation values are what is checked by the
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{maxiter} and {maxeval} parameters.
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:line
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IMPORTANT NOTE: There are several force fields in LAMMPS which have
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discontinuities or other approximations which may prevent you from
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performing an energy minimization to high tolerances. For example,
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you should use a "pair style"_pair_style.html that goes to 0.0 at the
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cutoff distance when performing minimization (even if you later change
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it when running dynamics). If you do not do this, the total energy of
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the system will have discontinuities when the relative distance
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between any pair of atoms changes from cutoff+epsilon to
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cutoff-epsilon and the minimizer may behave poorly. Some of the
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manybody potentials use splines and other internal cutoffs that
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inherently have this problem. The "long-range Coulombic
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styles"_kspace_style.html (PPPM, Ewald) are approximate to within the
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user-specified tolerance, which means their energy and forces may not
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agree to a higher precision than the Kspace-specified tolerance. In
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all these cases, the minimizer may give up and stop before finding a
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minimum to the specified energy or force tolerance.
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Note that a cutoff Lennard-Jones potential (and others) can be shifted
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so that its energy is 0.0 at the cutoff via the
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"pair_modify"_pair_modify.html command. See the doc pages for
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inidividual "pair styles"_pair_style.html for details. Note that
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Coulombic potentials always have a cutoff, unless versions with a
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long-range component are used (e.g. "pair_style
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lj/cut/coul/long"_pair_lj.html). The CHARMM potentials go to 0.0 at
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the cutoff (e.g. "pair_style lj/charmm/coul/charmm"_pair_charmm.html),
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as do the GROMACS potentials (e.g. "pair_style
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lj/gromacs"_pair_gromacs.html).
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If a soft potential ("pair_style soft"_pair_soft.html) is used the
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Astop value is used for the prefactor (no time dependence).
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The "fix box/relax"_fix_box_relax.html command can be used to apply an
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external pressure to the simulation box and allow it to shrink/expand
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during the minimization.
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Only a few other fixes (typically those that apply force constraints)
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are invoked during minimization. See the doc pages for individual
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"fix"_fix.html commands to see which ones are relevant.
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IMPORTANT NOTE: Some fixes which are invoked during minimization have
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an associated potential energy. For that energy to be included in the
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total potential energy of the system (the quantity being minimized),
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you MUST enable the "fix_modify"_fix_modify.html {energy} option for
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that fix. The doc pages for individual "fix"_fix.html commands
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specify if this should be done.
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:line
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[Restrictions:]
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Features that are not yet implemented are listed here, in case someone
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knows how they could be coded:
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It is an error to use "fix shake"_fix_shake.html with minimization
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because it turns off bonds that should be included in the potential
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energy of the system. The effect of a fix shake can be approximated
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during a minimization by using stiff spring constants for the bonds
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and/or angles that would normally be constrained by the SHAKE
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algorithm.
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"Fix rigid"_fix_rigid.html is also not supported by minimization. It
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is not an error to have it defined, but the energy minimization will
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not keep the defined body(s) rigid during the minimization. Note that
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if bonds, angles, etc internal to a rigid body have been turned off
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(e.g. via "neigh_modify exclude"_neigh_modify.html), they will not
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contribute to the potential energy which is probably not what is
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desired.
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Pair potentials that produce torque on a particle (e.g. "granular
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potentials"_pair_gran.html or the "GayBerne
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potential"_pair_gayberne.html for ellipsoidal particles) are not
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relaxed by a minimization. More specifically, radial relaxations are
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induced, but no rotations are induced by a minimization, so such a
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system will not fully relax.
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[Related commands:]
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"min_modify"_min_modify.html, "min_style"_min_style.html,
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"run_style"_run_style.html
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[Default:] none
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