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<H1><A NAME="SECTION002400000000000000000">
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22. Constraints for Geometry Optimization</A>
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</H1>
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<A NAME="sec:constraintsnew"></A>
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<P>
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The constraints directive allows the user to specify which constraints
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should be imposed on the system during the geometry optimization. Currently
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such constraints are limited to fixed atom positions and
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harmonic restraints (springs) on the distance between the two atoms. The
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general form of constraints block is presented below:
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<PRE>
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CONSTRAINTS [string name ] \
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[clear] \
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[enable||disable] \
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[fix atom <integer list>] \
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[spring bond <integer atom1> <integer atom2> <real k> <real r0> ]
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END
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</PRE>
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The keywords are described below
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<UL>
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<LI><I>name</I> - optional keyword that associates a name with a given set of
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constraints. Any unnamed set of constraints will be given a name ''default''
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and will be automatically loaded prior to a calculation. Any constraints
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with the name other than ''default'' will have to be loaded manually using
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SET directive. For example,
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</LI>
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</UL>
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<P>
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<PRE>
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CONSTRAINTS one
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spring bond 1 3 5.0 1.3
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fix atom 1
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END
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#the above constraints can be loaded using set directive
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set constraints one
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....
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task ....
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</PRE>
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<P>
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<UL>
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<LI><I>clear</I> - destroys any prior constraint information. This may be
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useful when the same constraints have to be redefined or completely removed from
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the runtime database.
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<P>
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</LI>
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<LI><I>enable||disable</I> - enables or
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disables particular set of constraints without actually removing the
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information from the runtime database.
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<P>
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</LI>
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<LI><I>fix atom</I> - fixes atom positions during geometry optimization. This
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directive requires an integer list that specifies which atoms are to be
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fixed. This directive can be repeated within a given constraints block.
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To illustrate the use "<I>fix atom</I>" directive let us
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consider a situation where we would like to fix atoms 1, 3, 4, 5, 6 while performing an optimization on some hypothetical system.
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There are actually several
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ways to enter this particular constraint.
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There is a straightforward option which requires the most typing
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<P>
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<PRE>
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constraints
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fix atom 1 3 4 5 6
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end
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</PRE>
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<P>
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Second method uses list input
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<PRE>
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constraints
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fix atom 1 3:6
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end
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</PRE>
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<P>
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Third approach illustrates the use of multiple fix atom directives
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<PRE>
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constraints
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fix atom 1
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fix atom 3:6
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end
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</PRE>
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<P>
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</LI>
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<LI><I>spring</I> bond <<IMG
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WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
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SRC="img161.gif"
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ALT="$i j k r_0$">> - places a spring with a spring constant <IMG
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WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img162.gif"
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ALT="$k$"> and equilibrium length <IMG
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WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img163.gif"
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ALT="$r_0$">
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between atoms <IMG
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WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img164.gif"
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ALT="$i$"> and <IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img66.gif"
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ALT="$j$"> (all in atomic units). Please note that this type of constraint adds an additional term to
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the total energy expression
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<BR><P></P>
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<DIV>
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<!-- MATH
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\begin{displaymath}
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E=E_{total}+\frac{1}{2}k(r_{ij}-r_0)^2
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\end{displaymath}
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-->
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<IMG
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WIDTH="184" HEIGHT="78" BORDER="0"
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SRC="img165.gif"
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ALT="\begin{displaymath}
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E=E_{total}+\frac{1}{2}k(r_{ij}-r_0)^2
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\end{displaymath}">
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</DIV>
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<BR CLEAR="ALL">
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<P></P>
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This additional term forces the distance between atoms <IMG
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WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img164.gif"
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ALT="$i$"> and <IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img66.gif"
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ALT="$j$"> to be in the vicinity of <IMG
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WIDTH="18" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img163.gif"
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ALT="$r_0$"> but never exactly that. In general
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the spring energy term will always have some nonzero residual value, and this has to be accounted for when comparing total
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energies. The "<I>spring bond</I>" directive can be repeated within a given constraints block. If the spring between the same pair of atoms
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is defined more than once, it will be replaced by the latest specification in the order it appears in the input block.
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</LI>
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</UL>
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<P>
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<ADDRESS>
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Edoardo Apra
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2004-05-25
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