</PRE>

<P><B>Description:</B>

</P>

<P>Perform an energy minimization of the system, by adjusting each atom's

atomic coordinates iteratively until convergence to a low-energy

minimum is achieved.  The algorithm used is set by the

<P>Perform an energy minimization of the system, by iteratively adjusting

atom coordinates.  Iterations are terminated when one of the stopping

criteria is satisfied.  At that point the configuration will hopefully

be in local potential energy minimum.  Mathematically speaking, the

configuration should approximate a critical point for the objective

function (see below), which may or may not be a local minimum.

</P>

<P>The minimization algorithm used is set by the

<A HREF = "min_style.html">min_style</A> command.  Other options are set by the

<A HREF = "min_modify.html">min_modify</A> command.  Minimize commands can be

interspersed with <A HREF = "run.html">run</A> commands to alternate between

relaxation and dynamics.  The minimizers are implemented in a robust

fashion that should allow for systems with highly overlapped atoms

(large energies and forces) to be minimized by pushing the atoms off

of each other.

relaxation and dynamics.  The minimizers bound the distance atoms move

in one iteration, so that you can relax systems with highly overlapped

atoms (large energies and forces) by pushing the atoms off of each

other.

</P>

<P>Alternate means of relaxing a system are to run dynamics with a small

or <A HREF = "fix_nve_limit.html">limited timestep</A>.  Or dynamics can be run

we've tried.  The backtracking method is described in Nocedal and

Wright's Numerical Optimization (Procedure 3.1 on p 41).

</P>

<P>The objective function being minimized is the potential energy of the

system as a function of the N atom coordinates:

<P>The objective function being minimized is the total potential energy

of the system as a function of the N atom coordinates:

</P>

<CENTER><IMG SRC = "Eqs/min_energy.jpg">

</CENTER>

<P>where the first term is the sum of all non-bonded pairwise

interactions including long-range Coulombic interactions, the 2nd thru

5th terms are bond, angle, dihedral, and improper interactions

respectively, and the last term is constraints due to fixes, such as

energy/force interactions with a wall.  See the discussion below about

<P>where the first term is the sum of all non-bonded <A HREF = "pair_style.html">pairwise

interactions</A> including <A HREF = "kspace_style.html">long-range Coulombic

interactions</A>, the 2nd thru 5th terms are

<A HREF = "bond_style.html">bond</A>, <A HREF = "angle_style.html">angle</A>,

<A HREF = "dihedral_style.html">dihedral</A>, and <A HREF = "improper_style.html">improper</A>

interactions respectively, and the last term is energy due to

<A HREF = "fix.html">fixes</A> which can act as constraints or apply force to atoms,

such as thru interaction with a wall.  See the discussion below about

which fix commands affect minimization.

</P>

<P>The starting point for the minimization is the current configuration

of the atoms.  Note that the minimizer only attempts to find a local

energy minimum, not a global minimum.  In a mathematical sense, there

is no guarantee in some cases of even finding a local minimum if the

objective function is ill-behaved.

of the atoms.

</P>

<HR>

[Description:]

Perform an energy minimization of the system, by adjusting each atom's

atomic coordinates iteratively until convergence to a low-energy

minimum is achieved.  The algorithm used is set by the

Perform an energy minimization of the system, by iteratively adjusting

atom coordinates.  Iterations are terminated when one of the stopping

criteria is satisfied.  At that point the configuration will hopefully

be in local potential energy minimum.  Mathematically speaking, the

configuration should approximate a critical point for the objective

function (see below), which may or may not be a local minimum.

The minimization algorithm used is set by the

"min_style"_min_style.html command.  Other options are set by the

"min_modify"_min_modify.html command.  Minimize commands can be

interspersed with "run"_run.html commands to alternate between

relaxation and dynamics.  The minimizers are implemented in a robust

fashion that should allow for systems with highly overlapped atoms

(large energies and forces) to be minimized by pushing the atoms off

of each other.

relaxation and dynamics.  The minimizers bound the distance atoms move

in one iteration, so that you can relax systems with highly overlapped

atoms (large energies and forces) by pushing the atoms off of each

other.

Alternate means of relaxing a system are to run dynamics with a small

or "limited timestep"_fix_nve_limit.html.  Or dynamics can be run

we've tried.  The backtracking method is described in Nocedal and

Wright's Numerical Optimization (Procedure 3.1 on p 41).

The objective function being minimized is the potential energy of the

system as a function of the N atom coordinates:

The objective function being minimized is the total potential energy

of the system as a function of the N atom coordinates:

:c,image(Eqs/min_energy.jpg)

where the first term is the sum of all non-bonded pairwise

interactions including long-range Coulombic interactions, the 2nd thru

5th terms are bond, angle, dihedral, and improper interactions

respectively, and the last term is constraints due to fixes, such as

energy/force interactions with a wall.  See the discussion below about

where the first term is the sum of all non-bonded "pairwise

interactions"_pair_style.html including "long-range Coulombic

interactions"_kspace_style.html, the 2nd thru 5th terms are

"bond"_bond_style.html, "angle"_angle_style.html,

"dihedral"_dihedral_style.html, and "improper"_improper_style.html

interactions respectively, and the last term is energy due to

"fixes"_fix.html which can act as constraints or apply force to atoms,

such as thru interaction with a wall.  See the discussion below about

which fix commands affect minimization.

The starting point for the minimization is the current configuration

of the atoms.  Note that the minimizer only attempts to find a local

energy minimum, not a global minimum.  In a mathematical sense, there

is no guarantee in some cases of even finding a local minimum if the

objective function is ill-behaved.

of the atoms.

:line