</PRE>

</PRE>

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

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

</P>

</P>

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

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

atomic coordinates iteratively until convergence to a low-energy

atom coordinates.  Iterations are terminated when one of the stopping

minimum is achieved.  The algorithm used is set by the

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_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

<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

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

relaxation and dynamics.  The minimizers are implemented in a robust

relaxation and dynamics.  The minimizers bound the distance atoms move

fashion that should allow for systems with highly overlapped atoms

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

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

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

of each other.

other.

</P>

</P>

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

<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

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

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

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

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

</P>

</P>

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

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

system as a function of the N atom coordinates:

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

</P>

</P>

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

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

</CENTER>

</CENTER>

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

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

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

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

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

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

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

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

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

<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.

which fix commands affect minimization.

</P>

</P>

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

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

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

of the atoms.

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.

</P>

</P>

<HR>

<HR>

[Description:]

[Description:]

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

Perform an energy minimization of the system, by iteratively adjusting

atomic coordinates iteratively until convergence to a low-energy

atom coordinates.  Iterations are terminated when one of the stopping

minimum is achieved.  The algorithm used is set by the

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

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

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

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

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

relaxation and dynamics.  The minimizers are implemented in a robust

relaxation and dynamics.  The minimizers bound the distance atoms move

fashion that should allow for systems with highly overlapped atoms

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

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

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

of each other.

other.

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

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

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

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

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

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

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

The objective function being minimized is the potential energy of the

The objective function being minimized is the total potential energy

system as a function of the N atom coordinates:

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

:c,image(Eqs/min_energy.jpg)

:c,image(Eqs/min_energy.jpg)

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

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

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

interactions"_pair_style.html including "long-range Coulombic

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

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

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

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

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

"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.

which fix commands affect minimization.

The starting point for the minimization is the current configuration

The starting point for the minimization is the current configuration

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

of the atoms.

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.

:line

:line