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839 lines
34 KiB
TeX
839 lines
34 KiB
TeX
%
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% $Id$
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%
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\label{sec:geom}
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The \verb+GEOMETRY+ directive is a compound directive that allows the
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user to define the geometry to be used for a given calculation. The
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directive allows the user to specify the geometry with a relatively
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small amount of input, but there are a large number of optional
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keywords and additional subordinate directives that the user can
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specify, if needed. The directive therefore appears to be rather long
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and complicated when presented in its general form, as follows:
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\begin{verbatim}
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GEOMETRY [<string name default geometry>] \
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[units <string units default angstroms>] \
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[(angstrom_to_au || ang2au) \
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<real angstrom_to_au default 1.8897265>] \
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[print [xyz] || noprint] \
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[center || nocenter] \
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[bqbq] \
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[autosym [real tol default 1d-2]] \
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[autoz || noautoz] \
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[adjust] \
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[(nuc || nucl || nucleus) <string nucmodel>]
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[SYMMETRY [group] <string group_name> [print] \
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[tol <real tol default 1d-2>]]
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<string tag> <real x y z> [vx vy vz] [charge <real charge>] \
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[mass <real mass>] \
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[(nuc || nucl || nucleus) <string nucmodel>]
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... ]
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[ZMATRIX || ZMT || ZMAT
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<string tagn> <list_of_zmatrix_variables>
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...
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[VARIABLES
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<string symbol> <real value>
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... ]
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[CONSTANTS
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<string symbol> <real value>
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... ]
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(END || ZEND)]
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[ZCOORD
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CVR_SCALING <real value>
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BOND <integer i> <integer j> \
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[<real value>] [<string name>] [constant]
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ANGLE <integer i> <integer j> \
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[<real value>] [<string name>] [constant]
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TORSION <integer i> <integer j> <integer k> <integer l> \
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[<real value>] [<string name>] [constant]
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END]
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[SYSTEM surface <molecule polymer surface crystal default molecule>
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lat_a <real lat_a> lat_b <real lat_b> lat_c <real lat_c>
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alpha <real alpha> beta <real beta> gamma <real gamma>
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END]
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END
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\end{verbatim}
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The three main parts of the \verb+GEOMETRY+ directive
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are:
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\begin{itemize}
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\item keywords on the first line of the directive (to specify such optional
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input as the geometry name, input units, and print level for the output)
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\item symmetry information
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\item Cartesian coordinates or Z-matrix input to specify the locations
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of the atoms and centers
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\item lattice parameters (needed only for periodic systems)
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\end{itemize}
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The following sections present the input for this compound directive in
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detail, describing the options available and the usages of the various
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keywords in each of the three main parts.
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\section{Keywords on the {\tt GEOMETRY} directive}
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\label{sec:geomkeys}
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This section presents the options that can be specified using the keywords
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and optional input on the main line of the {\tt GEOMETRY} directive.
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As described above, the first line of the directive has the general form,
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\begin{verbatim}
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GEOMETRY [<string name default geometry>] \
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[units <string units default angstroms>] \
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[bqbq] \
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[print [xyz] || noprint] \
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[center || nocenter] \
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[autosym [real tol default 1d-2]] \
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[autoz || noautoz] \
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[adjust] \
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[(nuc || nucl || nucleus) <string nucmodel>]
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\end{verbatim}
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All of the keywords and input on this line are optional. The following
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list describes all options and their defaults.
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\begin{itemize}
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\item \verb+<name>+ -- user-supplied name for the geometry; the
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default name is \verb+geometry+, and all NWChem modules look for a
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geometry with this name. However, multiple geometries may
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be specified by using a different name for each. Subsequently,
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the user can direct a module to a named geometry by
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using the \verb+SET+ directive (see
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the example in Section \ref{sec:set}) to associate the default
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name of \verb+geometry+ with the alternate name.
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% \subsection*{{\tt UNITS}}
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\item \verb+units+ -- keyword specifying that a value will be entered
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by the user for the string variable \verb+<units>+. The default
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units for the geometry input are \angstroms\ (Note: atomic units or
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Bohr are used within the code, regardless of the option specified
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for the input units. The default conversion factor used in the code
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to convert from {\angstroms} to Bohr is $1.8897265$ which may be
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overidden with the \verb+angstrom_to_au+ keyword described below.). The code
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recognizes the following possible values for the string variable
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\verb+<units>+:
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\begin{itemize}
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\item \verb+angstroms+ or \verb+an+ --- Angstroms (\AA), the default
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(converts to A.U. using the \AA to A.U. conversion factor)
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\item \verb+au+ or \verb+atomic+ or \verb+bohr+ --- Atomic units (A.U.)
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\item \verb+nm+ or \verb+nanometers+ --- nanometers (converts to
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A.U. using a conversion factor computed as $10.0$ times the
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\AA\ to A.U. conversion factor)
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\item \verb+pm+ or \verb+picometers+ --- picometers (converts to
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A.U. using a conversion factor computed as $0.01$ times the
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\AA\ to A.U. conversion factor)
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\end{itemize}
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\item \verb+angstrom_to_au+ -- may also be specified as
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\verb+ang2au+. This enables the user to modify the conversion
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factors used to convert between \AA\ and A.U.. The default value is
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$1.8897265$.
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\item \verb+bqbq+ -- keyword to specify the treatment of interactions
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between dummy centers. The default in NWChem is to ignore such
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interactions when computing energies or energy derivatives. These
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interactions will be included if the keyword \verb+bqbq+ is
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specified.
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\item \verb+print+ and \verb+noprint+ -- complementary keyword pair to
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enable or disable printing of the geometry. The default is to print
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the output associated with the geometry. In addition, the keyword
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\verb+print+ may be qualified by the additional keyword \verb+xyz+,
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which specifies that the coordinates should be printed in the XYZ
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format of molecular graphics program XMol.
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\item \verb+center+ and \verb+nocenter+ -- complementary keyword pair
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to enable or disable translation of the center of nuclear charge to
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the origin. With the origin at this position, all three components
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of the nuclear dipole are zero. The default is to move the center
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of nuclear charge to the origin.
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\item \verb+autosym+ -- keyword to specify that the symmetry of the
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geometric system should be automatically determined. This option is on
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by default. Only groups up to and including $O_{h}$ are recognized.
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Occasionally NWChem will be unable to determine the full symmetry
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of a molecular system, but will find a proper subgroup of the full
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symmetry. The default tolerance is set to work for most cases, but may
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need to be decreased to find the full symmetry of a geometry. Note that
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autosym will be turned off if the \verb+SYMMETRY+ group input is given
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(See section \ref{sec:symgrp}).
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\item \verb+noautoz+ -- by default NWChem (release 3.3 and later)
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will generate redundant internal coordinates from user input
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Cartesian coordinates. The internal coordinates will be used in
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geometry optimizations. The \verb+noautoz+ keyword disables use of
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internal coordinates. The \verb+autoz+ keyword is provided only for
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backward compatibility. See Section \ref{sec:zcoord} for a more
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detailed description of redundant internal coordinates, including
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how to force the definition of specific internal variables in
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combination with automatically generated variables.
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\item \verb+adjust+ -- This indicates that an existing geometry is
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to be adjusted. Only new input for the redundant internal
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coordinates may be provided (Section \ref{sec:zcoord}). It is
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not possible to define new centers or to modify the point
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group using this keyword. See Section \ref{sec:zcoord} for
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an example of its usage.
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\item \verb+nucleus+ -- keyword to specify the default model for the nuclear
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charge distribution. The following values are recognized:
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\begin{itemize}
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\item \verb+point+ or \verb+pt+ --- point nuclear charge distribution. This
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is the default.
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\item \verb+finite+ or \verb+fi+ --- finite nuclear charge distribution
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with a Gaussian shape. The RMS radius of the Gaussian is determined from
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the nuclear mass number $A$ by the expression
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$r_{\rm RMS} = 0.836*A^{1/3}+0.57$ fm.
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\end{itemize}
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NOTE: If you specify a finite nuclear size, you should ensure that the basis
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set you use is contracted for a finite nuclear size. See the Section
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\ref{sec:basis} for more information.
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\end{itemize}
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The following examples illustrate some of the various options that the
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user can specify on the first input line of the \verb+GEOMETRY+
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directive, using the keywords and input options described above.
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The following directives all specify the same geometry for $H_2$ (a
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bond length of 0.732556\ \AA):
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\begin{verbatim}
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geometry geometry units nm
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h 0 0 0 h 0 0 0
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h 0 0 0.732556 h 0 0 0.0732556
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end end
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geometry units pm geometry units atomic
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h 0 0 0 h 0 0 0
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h 0 0 73.2556 h 0 0 1.3843305
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end end
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\end{verbatim}
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\section{{\tt SYMMETRY} --- Symmetry Group Input}
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\label{sec:symgrp}
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The \verb+SYMMETRY+ directive is used (optionally) within the compound
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\verb+GEOMETRY+ directive to specify the point group for the molecular
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geometry.
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The general form of the directive, as described above within the general
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form of the \verb+GEOMETRY+ directive, is as follows:
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\begin{verbatim}
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[SYMMETRY [group] <string group_name> [print] \
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[tol <real tol default 1d-2>]]
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\end{verbatim}
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The keyword \verb+group+ is optional, and can be omitted without
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affecting how the input for this directive is processed\footnote{For
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periodic systems, there are additional keywords within this
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directive (not yet documented), so having a keyword for the group
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name is useful.}. However, if the \verb+SYMMETRY+ directive is
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used, a group name must be specified by supplying an entry for the
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string variable \verb+<group_name>+. The group name should be
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specified as the standard Sch\"{o}flies symbol. Examples of expected
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input for the variable \verb+group_name+ include such entries as:
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\begin{itemize}
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\item \verb+c2v+ -- for molecular symmetry $C_{2{\it v}}$
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\item \verb+d2h+ -- for molecular symmetry $D_{2h}$
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\item \verb+Td+ -- for molecular symmetry $T_d$
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\item \verb+d6h+ -- for molecular symmetry $D_{6h}$
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\end{itemize}
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The \verb+SYMMETRY+ directive is optional. The default is no symmetry
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(i.e., $C_1$ point group). Automatic detection of point
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group symmetry is available through the use of \verb+autosym+ in the
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\verb+GEOMETRY+ directive main line (discussed in Section \ref{sec:geomkeys}).
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Note: if the \verb+SYMMETRY+ directive is present the \verb+autosym+
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keyword is ignored.
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If only symmetry-unique atoms are specified, the others will be
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generated through the action of the point group operators, but the
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user if free to specify all atoms. The user must know the symmetry of
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the molecule being modeled, and be able to specify the coordinates of
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the atoms in a suitable orientation relative to the rotation axes and
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planes of symmetry. Appendix \ref{symexamples} lists a number of
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examples of the
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\verb+GEOMETRY+ directive input for specific molecules having symmetry
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patterns recognized by NWChem. The exact point group symmetry will be
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forced upon the molecule, and atoms within $10^{-3}$ A.U. of a
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symmetry element (e.g., a mirror plane or rotation axis) will be
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forced onto that element. Thus, it is not necessary to specify to a
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high precision those coordinates that are determined solely by
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symmetry.
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The keyword \verb+print+ gives information concerning the point group
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generation, including the group generators, a character table, the
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mapping of centers, and the group operations.
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The keyword \verb+tol+ relates to the accuracy with which the symmetry-unique
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atoms should be specified. When the atoms are generated, those that are
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within the tolerance, \verb+tol+, are considered the same.
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\section{Cartesian coordinate input}
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\label{sec:cart}
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The default in NWChem is to specify the geometry information entirely
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in Cartesian coordinates, and examples of this format have
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appeared above (e.g, Section \ref{sec:realsample}). Each center
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(usually an atom) is identified on a line of the following form:
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\begin{verbatim}
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<string tag> <real x y z> [vx vy vz] \
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[charge <real charge>] [mass <real mass>] \
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[(nuc || nucl || nucleus) <string nucmodel>]
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\end{verbatim}
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The string \verb+<tag>+ is the name of the atom or center, and its case
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(upper or lower) is important. The tag is limited to 16 characters
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and is interpreted as follows:
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\begin{itemize}
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\item If the entry for \verb+<tag>+ begins with either the symbol or
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name of an element (regardless of case), then the center is treated
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as an atom of that type. The default charge is the atomic number
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(adjusted for the presence of ECPs by the ECP \verb+NELEC+ directive
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; see Section \ref{sec:ecp}). Additional characters can be added to
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the string, to distinguish between atoms of the same element (For
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example, the tags \verb+oxygen+, \verb+O+, \verb+o34+,
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\verb+olonepair+, and \verb+Oxygen-ether+, will all be interpreted
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as oxygen atoms.).
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\item If the entry for \verb+<tag>+ begins with the characters
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\verb+bq+ or \verb+x+ (regardless of case), then the center is
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treated as a dummy center with a default zero charge (Note: a tag
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beginning with the characters \verb+xe+ will be interpreted as a
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xenon atom rather than as a dummy center.). Dummy centers may
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optionally have basis functions or non-zero charge. See Section
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\ref{sec:sample2} for a sample input using dummy centers with
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charges.
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\end{itemize}
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It is {\em important} to be aware of the following points regarding
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the definitions and usage of the values specified for the variable
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\verb+<tag>+ to describe the centers in a system:
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\begin{itemize}
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\item If the tag begins with characters that cannot be matched against
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an atom, and those characters are not \verb+BQ+ or \verb+X+, then a
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fatal error is generated.
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\item The tag of a center is used in the \verb+BASIS+ (Section
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\ref{sec:basis}) and \verb+ECP+ (Section \ref{sec:ecp}) directives
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to associate functions with centers.
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\item All centers with the same tag will have the same basis
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functions.
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\item When using automatic symmetry detection,
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only centers with the same tag will be candidates for testing for
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symmetry equivalence.
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\item The user-specified charges (of all centers, atomic and dummy)
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and any net total charge of the system (Section \ref{sec:charge})
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are used to determine the number of electrons in the system.
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\end{itemize}
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The Cartesian coordinates of the atom in the molecule are specified as
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real numbers supplied for the variables \verb+x+, \verb+y+, and
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\verb+z+ following the characters entered for the tag. The values
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supplied for the coordinates must be in the units specified by the
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value of the variable \verb+<units>+ on the first line of the
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\verb+GEOMETRY+ directive input.
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After the Cartesian coordinate input, optional velocities may be
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entered as real numbers for the variables \verb+vx+, \verb+vy+, and
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\verb+vz+. The velocities should be given in atomic units and are
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used in QMD and PSPW calculations.
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The Cartesian coordinate input line also contains the optional keywords
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\verb+charge+, \verb+mass+ and \verb+nucleus+, which allow the user to
|
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specify the charge of the atom (or center) and its mass (in atomic mass
|
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units), and the nuclear model. The default charge for an atom is
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its atomic number, adjusted for the presence of ECPs (see Section
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\ref{sec:ecp}). In order to specify a different value for the charge on a
|
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particular atom, the user must enter the keyword \verb+charge+, followed by
|
|
the desired value for the variable \verb+<charge>+.
|
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The default mass for an atom is taken to be the mass of its most abundant
|
|
naturally occurring isotope or of the isotope with the longest half-life.
|
|
To model some other isotope of the element, its mass must be defined
|
|
explicitly by specifying the keyword \verb+mass+, followed by the value (in
|
|
atomic mass units) for the variable \verb+<mass>+.
|
|
|
|
The default nuclear model is a point nucleus. The keyword \verb+nucleus+ (or
|
|
\verb+nucl+ or \verb+nuc+) followed by the model name \verb+<nucmodel>+
|
|
overrides this default. Allowed values of \verb+<nucmodel>+ are \verb+point+ or
|
|
\verb+pt+ and \verb+finite+ or \verb+fi+. The \verb+finite+ option is
|
|
a nuclear model with a Gaussian shape. The RMS radius of the Gaussian is
|
|
determined by the atomic mass number via the formula $r_{\rm RMS} = 0.836*
|
|
A^{1/3} + 0.57$ fm. The mass number $A$ is derived from the variable
|
|
\verb+<mass>+.
|
|
|
|
The geometry of the system can be specified entirely in Cartesian
|
|
coordinates by supplying a \verb+<tag>+ line of the type described
|
|
above for each atom or center. The user has the option, however, of
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|
supplying the geometry of some or all of the atoms or centers using a
|
|
Z-matrix description. In such a case, the user supplies the input tag
|
|
line described above for any centers to be described by Cartesian
|
|
coordinates, and then specifies the remainder of the system using the
|
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optional \verb+ZMATRIX+ directive described below in Section
|
|
\ref{sec:Z-matrix}.
|
|
|
|
\section{{\tt ZMATRIX} --- Z-matrix input}
|
|
\label{sec:Z-matrix}
|
|
|
|
The \verb+ZMATRIX+ directive is an optional directive that can be used
|
|
within the compound \verb+GEOMETRY+ directive to specify the structure
|
|
of the system with a Z-matrix, which can include both internal and
|
|
Cartesian coordinates. The \verb+ZMATRIX+ directive is itself a
|
|
compound directive that can include the \verb+VARIABLES+ and
|
|
\verb+CONSTANTS+ directives, depending on the options selected. The
|
|
general form of the compound \verb+ZMATRIX+ directive is as follows:
|
|
\begin{verbatim}
|
|
[ZMATRIX || ZMT || ZMAT
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|
<string tagn> <list_of_zmatrix_variables>
|
|
...
|
|
|
|
[VARIABLES
|
|
<string symbol> <real value>
|
|
... ]
|
|
|
|
[CONSTANTS
|
|
<string symbol> <real value>
|
|
... ]
|
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|
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(END || ZEND)]
|
|
\end{verbatim}
|
|
|
|
The input module recognizes three possible spellings of this directive
|
|
name. It can be invoked with \verb+ZMATRIX+, \verb+ZMT+, or
|
|
\verb+ZMAT+. The user can specify the molecular structure using
|
|
either Cartesian coordinates or
|
|
internal coordinates (bond lengths, bond angles and dihedral angles.
|
|
The Z-matrix input for a center defines connectivity, bond length, and
|
|
bond or torsion angles. Cartesian coordinate input for a center
|
|
consists of three real numbers defining the x,y,z coordinates of the
|
|
atom.
|
|
|
|
Within the Z-matrix input, bond lengths and Cartesian coordinates must
|
|
be input in the user-specified units, as defined by the value specified
|
|
for the variable \verb+<units>+ on the first line of the \verb+GEOMETRY+
|
|
directive. All angles are specified in
|
|
degrees.
|
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|
|
The individual centers (denoted as \verb+i+, \verb+j+, and \verb+k+
|
|
below) used to specify Z-matrix connectivity may be designated either
|
|
as integers (identifying each center by number) or as tags ({\em If
|
|
tags are used, the tag must be unique for each center.}) The use of
|
|
``dummy'' atoms is possible, by using \verb+X+ or \verb+BQ+ at the
|
|
start of the tag.
|
|
|
|
Bond lengths, bond angles and dihedral angles (denoted below as {\tt
|
|
R}, {\tt alpha}, and {\tt beta}, respectively) may be specified
|
|
either as numerical values or as symbolic strings that must be
|
|
subsequently defined using the \verb+VARIABLES+ or \verb+CONSTANTS+
|
|
directives. The numerical values of the symbolic strings labeled
|
|
\verb+VARIABLES+ may be subject to changes during a geometry
|
|
optimization say, while the numerical values of the symbolic strings
|
|
labeled \verb+CONSTANTS+ will stay frozen to the value given in the
|
|
input. The same symbolic string can be used more than once, and
|
|
any mixture of numeric data and symbols is acceptable. Bond angles
|
|
($\alpha$) must be in the range $0 < \alpha < 180$.
|
|
|
|
The Z-matrix input is specified sequentially as follows:
|
|
\begin{verbatim}
|
|
tag1
|
|
tag2 i R
|
|
tag3 i R j alpha
|
|
tag4 i R j alpha k beta [orient]
|
|
...
|
|
\end{verbatim}
|
|
|
|
The structure of this input is described in more detail below. In the
|
|
following discussion, the tag or number of the center being currently
|
|
defined is labeled as \verb+C+ (``C'' for current). The values
|
|
entered for these tags for centers defined in the Z-matrix input are
|
|
interpreted in the same way as the \verb+<tag>+ entries for Cartesian
|
|
coordinates described above (see Section \ref{sec:cart}). Figures
|
|
\ref{fig:zmat1}, \ref{fig:zmat2} and \ref{fig:zmat3} display the
|
|
relationships between the input data and the definitions of centers
|
|
and angles.
|
|
|
|
\begin{figure}[htbp]
|
|
\centering
|
|
\begin{latexonly}
|
|
\ifx\pdfoutput\undefined
|
|
\includegraphics[angle=270,width=6in]{zmat1.eps}
|
|
\else
|
|
\includegraphics[angle=0,width=6in]{zmat1.pdf}
|
|
\fi
|
|
\end{latexonly}
|
|
\begin{htmlonly}
|
|
\psfig{figure=zmat1.eps,angle=270,width=6in}
|
|
\end{htmlonly}
|
|
\caption{\label{fig:zmat1} Relationships between the centers, bond angle
|
|
and dihedral angle in Z-matrix input.}
|
|
\end{figure}
|
|
|
|
\begin{figure}[htbp]
|
|
\centering
|
|
\begin{latexonly}
|
|
\ifx\pdfoutput\undefined
|
|
\includegraphics[angle=270,width=6in]{zmat2.eps}
|
|
\else
|
|
\includegraphics[angle=270,width=6in]{zmat2.pdf}
|
|
\fi
|
|
\end{latexonly}
|
|
\begin{htmlonly}
|
|
\psfig{figure=zmat2.eps,angle=270,width=6in}
|
|
\end{htmlonly}
|
|
|
|
\caption{\label{fig:zmat2} Relationships between the centers and two
|
|
bond angles in Z-matrix input with optional parameter specified as $+1$.}
|
|
\end{figure}
|
|
|
|
\begin{figure}[htbp]
|
|
\centering
|
|
\begin{latexonly}
|
|
\ifx\pdfoutput\undefined
|
|
\includegraphics[angle=270,width=6in]{zmat3.eps}
|
|
\else
|
|
\includegraphics[angle=270,width=6in]{zmat3.pdf}
|
|
\fi
|
|
\end{latexonly}
|
|
\begin{htmlonly}
|
|
\psfig{figure=zmat3.eps,angle=270,width=6in}
|
|
\end{htmlonly}
|
|
\caption{\label{fig:zmat3} Relationships between the centers and two
|
|
bond angles in Z-matrix input with optional parameter specified as $-1$.}
|
|
\end{figure}
|
|
|
|
The Z-matrix input shown above is interpreted as follows:
|
|
\begin{enumerate}
|
|
|
|
\item \verb+tag1+
|
|
|
|
Only a tag is required for the first center.
|
|
|
|
\item \verb+tag2 i R+
|
|
|
|
The second center requires specification of its tag and the
|
|
bond length ($R_{Ci}$) distance to a previous atom, which is identified by
|
|
\verb+i+.
|
|
|
|
\item \verb+tag3 i R j alpha+
|
|
|
|
The third center requires specification of its tag, its bond length distance
|
|
($R_{Ci}$) to one of the two previous centers (identified by the
|
|
value of \verb+i+), and the bond angle $\alpha = \widehat{Cij}$.
|
|
|
|
\item \verb+tag i R j alpha k beta [<integer orient default 0>]+
|
|
|
|
The fourth, and all subsequent centers, require the tag, a bond
|
|
length ($R_{Ci}$) relative to center \verb+i+, the bond angle with
|
|
centers \verb+i+ and \verb+j+ ($\alpha = \widehat{Cij}$), and {\em either}
|
|
\begin{enumerate}
|
|
\item the dihedral angle ($\beta$) between the current center and centers
|
|
\verb+i+, \verb+j+, and \verb+k+ (Figure \ref{fig:zmat1}), or
|
|
\item a second bond angle $\beta = \widehat{Cik}$ and an orientation to
|
|
the plane containing the other three centers (Figure
|
|
\ref{fig:zmat2} and \ref{fig:zmat3}).
|
|
\end{enumerate}
|
|
|
|
By default, $\beta$ is interpreted as a dihedral angle (see Figure
|
|
\ref{fig:zmat1}), but if the optional final parameter (\verb+<orient>+) is
|
|
specified with the value $\pm 1$, then $\beta$ is interpreted as
|
|
the angle $\widehat{Cik}$. The sign of \verb+<orient>+ specifies the
|
|
direction of the bond angle relative to the plane containing the
|
|
three reference atoms. If \verb+<orient>+ is $+1$, then the new center
|
|
(\verb+C+) is above the plane (Figure \ref{fig:zmat2}); and if
|
|
\verb+<orient>+ is $-1$, then \verb+C+ is below the plane (Figure
|
|
\ref{fig:zmat3}).
|
|
\end{enumerate}
|
|
|
|
Following the Z-matrix center definitions described above, the user can
|
|
specify initial values for any symbolic variables used to define the
|
|
Z-matrix tags. This is done using the optional \verb+VARIABLES+ directive,
|
|
which has the general form:
|
|
|
|
% <string symbol> <real value> <real value>
|
|
\begin{verbatim}
|
|
VARIABLES
|
|
<string symbol> <real value>
|
|
...
|
|
\end{verbatim}
|
|
Each line contains the name of a variable followed by its value.
|
|
Optionally, an equals sign (\verb+=+) can be included between the
|
|
symbol and its value, for clarity in reading the input file.
|
|
|
|
%If a second value follows the first value, a second structure gets
|
|
%created, built from all the second valued internal coordinates and
|
|
%the lone valued internal coordinates for those which are attributed
|
|
%only a single vale. the program will define
|
|
%a Linear Synchronous Transit (LST) path between the first structure
|
|
%and the second structure ( the initial and final structures respectively).
|
|
%A number of structures (11 in total) get created in equal increments
|
|
%of the internal coordinates. The set of coordinates get written
|
|
%to the file ./xxxx.lst.coord. In an 'LST' task , specified by
|
|
%'task <theory> lst', the program calculates the energy of the
|
|
%system for all these structures in sequence.
|
|
|
|
Following the \verb+VARIABLES+ directive, the \verb+CONSTANTS+
|
|
directive may be used to define any Z-matrix symbolic variables that remain
|
|
unchanged during geometry optimizations.
|
|
To freeze the Cartesian coordinates of an atom, refer
|
|
to Section \ref{sec:activeatoms}. The general form of this directive
|
|
is as follows:
|
|
\begin{verbatim}
|
|
CONSTANTS
|
|
<string symbol> <real value>
|
|
...
|
|
\end{verbatim}
|
|
Each line contains the name of a variable followed by its value. As
|
|
with the \verb+VARIABLES+ directive, an equals sign (\verb+=+) can be
|
|
included between the symbol and its value.
|
|
|
|
The end of the Z-matrix input using the compound \verb+ZMATRIX+
|
|
directive is signaled by a line containing either \verb+END+ or
|
|
\verb+ZEND+, following all input for the directive itself and its
|
|
associated optional directives.
|
|
|
|
A simple example is presented for water. All Z-matrix parameters are
|
|
specified numerically, and symbolic tags are used to specify
|
|
connectivity information. This requires that all tags be unique, and
|
|
therefore different tags are used for the two hydrogen atoms, which may
|
|
or may not be identical.
|
|
\begin{verbatim}
|
|
geometry
|
|
zmatrix
|
|
O
|
|
H1 O 0.95
|
|
H2 O 0.95 H1 108.0
|
|
end
|
|
end
|
|
\end{verbatim}
|
|
|
|
The following example illustrates the Z-matrix input for the molecule
|
|
$CH_3CF_3$. This input uses the numbers of centers to specify
|
|
the connectivity information (\verb+i+, \verb+j+, and \verb+k+), and
|
|
uses symbolic variables for the Z-matrix parameters {\tt R}, {\tt
|
|
alpha}, and {\tt beta}, which are defined in the inputs for the
|
|
\verb+VARIABLES+ and
|
|
\verb+CONSTANTS+ directives.
|
|
|
|
\begin{verbatim}
|
|
geometry
|
|
zmatrix
|
|
C
|
|
C 1 CC
|
|
H 1 CH1 2 HCH1
|
|
H 1 CH2 2 HCH2 3 TOR1
|
|
H 1 CH3 2 HCH3 3 -TOR2
|
|
F 2 CF1 1 CCF1 3 TOR3
|
|
F 2 CF2 1 CCF2 6 FCH1
|
|
F 2 CF3 1 CCF3 6 -FCH1
|
|
variables
|
|
CC 1.4888
|
|
CH1 1.0790
|
|
CH2 1.0789
|
|
CH3 1.0789
|
|
CF1 1.3667
|
|
CF2 1.3669
|
|
CF3 1.3669
|
|
constants
|
|
HCH1 104.28
|
|
HCH2 104.74
|
|
HCH3 104.7
|
|
CCF1 112.0713
|
|
CCF2 112.0341
|
|
CCF3 112.0340
|
|
TOR1 109.3996
|
|
TOR2 109.3997
|
|
TOR3 180.0000
|
|
FCH1 106.7846
|
|
end
|
|
end
|
|
\end{verbatim}
|
|
|
|
The input for any centers specified with Cartesian coordinates must
|
|
be specified using the format of the \verb+<tag>+ lines described
|
|
in Section \ref{sec:cart} above. However, in
|
|
order to correctly specify these Cartesian coordinates
|
|
within the Z-matrix, the user must
|
|
understand the orientation of centers specified using
|
|
internal coordinates. These are arranged as follows:
|
|
\begin{itemize}
|
|
\item The first center is placed at the origin.
|
|
\item The second center is placed along the positive z-axis.
|
|
\item The third center is placed in the z-x plane.
|
|
\end{itemize}
|
|
|
|
\section{{\tt ZCOORD} --- Forcing internal coordinates}
|
|
\label{sec:zcoord}
|
|
|
|
By default redundant internal coordinates are generated for use in
|
|
geometry optimizations. Connectivity is inferred by comparing
|
|
inter-atomic distances with the sum of the van der Waals radii of the
|
|
two atoms involved in a possible bond, times a scaling factor. The
|
|
scaling factor is an input parameter of \verb+ZCOORD+ which maybe
|
|
changed from its default value of 1.3. Under some circumstances
|
|
(unusual bonding, bond dissociation, \ldots) it will be necessary to
|
|
augment the automatically generated list of internal coordinates to
|
|
force some specific internal coordinates to be included in among the
|
|
internal coordinates. This is accomplished by including the optional
|
|
directive {\tt ZCOORD} within the geometry directive. The general
|
|
form of the \verb+ZCOORD+ directive is as follows:
|
|
\begin{verbatim}
|
|
ZCOORD
|
|
CVR_SCALING <real value>
|
|
BOND <integer i> <integer j> \
|
|
[<real value>] [<string name>] [constant]
|
|
ANGLE <integer i> <integer j> <integer k> \
|
|
[<real value>] [<string name>] [constant]
|
|
TORSION <integer i> <integer j> <integer k> <integer l> \
|
|
[<real value>] [<string name>] [constant]
|
|
END
|
|
\end{verbatim}
|
|
|
|
The centers \verb+i+, \verb+j+, \verb+k+ and \verb+l+ {\em must} be
|
|
specified using the numbers of the centers, as supplied in the input
|
|
for the Cartesian coordinates. The \verb+ZCOORD+ input parameters are
|
|
defined as follows:
|
|
|
|
\begin{itemize}
|
|
\item {\tt cvr\_scaling} --- scaling factor applied to van der Waals radii.
|
|
\item {\tt bond} --- a bond between the two centers.
|
|
\item {\tt angle} --- a bond angle $\widehat{ijk}$.
|
|
\item {\tt torsion} --- a torsion (or dihedral) angle. The
|
|
angle between the planes \verb+i-j-k+ and \verb+j-k-l+.
|
|
\end{itemize}
|
|
|
|
A value may be specified for a user-defined internal coordinate, in
|
|
which case it is forced upon the input Cartesian coordinates while
|
|
attempting to make only small changes in the other internal
|
|
coordinates. If no value is provided the value implicit in the input
|
|
coordinates is kept. If the keyword \verb+constant+ is specified, then
|
|
that internal variable is not modified during a geometry optimization
|
|
with DRIVER (Section \ref{sec:driver}). Each internal coordinate may
|
|
also be named either for easy identification in the output, or
|
|
for the application of constraints (Section \ref{sec:constraints}).
|
|
|
|
If the keyword \verb+adjust+ is specified on the main \verb+GEOMETRY+
|
|
directive, only \verb+ZCOORD+ data may be specified and it can
|
|
be used to change the user-defined internal coordinates, including
|
|
adding/removing constraints and changing their values.
|
|
|
|
\section{Applying constraints in geometry optimizations}
|
|
\label{sec:activeatoms}
|
|
\label{sec:constraints}
|
|
|
|
Internal coordinates specified as constant in a \verb+ZCOORD+ directive
|
|
or in the constants section of a \verb+ZMATRIX+ directive, will be
|
|
frozen at their initial values if a geometry optimization is
|
|
performed with DRIVER (Section \ref{sec:driver}).
|
|
|
|
If internal coordinates have the same name (give or take
|
|
an optional sign for torsions) then they are forced to have
|
|
the same value. This may be used to force bonds or angles to
|
|
be equal even if they are not related by symmetry.
|
|
|
|
When atoms have been specified by their Cartesian coordinates, {\em
|
|
and} internal coordinates are not being used, it is possible to freeze
|
|
the cartesian position of selected atoms. This is useful for such
|
|
purposes as optimizing a molecule absorbed on the surface of a cluster
|
|
with fixed geometry. Only the gradients associated with the active
|
|
atoms are computed. This can result in a big computational saving,
|
|
since gradients associated with frozen atoms are forced to zero (Note,
|
|
however, that this destroys the translational and rotational
|
|
invariance of the gradient. This is not yet fully accommodated by the
|
|
STEPPER geometry optimization software, and can sometimes result in
|
|
slower convergence of the optimization. The DRIVER optimization
|
|
package does not suffer from this problem).
|
|
|
|
The \verb+SET+ directive (Section \ref{sec:set}) is used to freeze
|
|
atoms, by specifying a directive of the form:
|
|
\begin{verbatim}
|
|
set geometry:actlist <integer list_of_center_numbers>
|
|
\end{verbatim}
|
|
This defines only the centers in the list as active. All other
|
|
centers will have zero force assigned to them, and will remain frozen
|
|
at their starting coordinates during a geometry optimization.
|
|
|
|
For example, the following directive specifies that atoms numbered 1,
|
|
5, 6, 7, 8, and 15 are active and all other atoms are frozen:
|
|
\begin{verbatim}
|
|
set geometry:actlist 1 5:8 15
|
|
\end{verbatim}
|
|
or equivalently,
|
|
\begin{verbatim}
|
|
set geometry:actlist 1 5 6 7 8 15
|
|
\end{verbatim}
|
|
|
|
If this option is not specified by entering a \verb+SET+ directive,
|
|
the default behavior in the code is to treat all atoms as active. To
|
|
revert to this default behavior after the option to define frozen
|
|
atoms has been invoked, the \verb+UNSET+ directive must be used (since
|
|
the database is persistent, see Section \ref{sec:persist}). The form
|
|
of the \verb+UNSET+ directive is as follows:
|
|
\begin{verbatim}
|
|
unset geometry:actlist
|
|
\end{verbatim}
|
|
|
|
\section{{\tt SYSTEM} --- Lattice parameters for periodic systems}
|
|
\label{sec:latticeparam}
|
|
|
|
This keyword is needed only for for 1-, 2-, and 3-dimensional
|
|
periodic systems.
|
|
|
|
The {\tt system} keyword can assume the following values
|
|
|
|
\begin{itemize}
|
|
\item {\tt polymer} --- system with 1-d translational symmetry.
|
|
\item {\tt surface} --- system with 2-d translational symmetry.
|
|
\item {\tt crystal} --- system with 3-d translational symmetry.
|
|
\item {\tt molecule} --- no translational symmetry (this is the default)
|
|
\end{itemize}
|
|
|
|
When the system possess translational symmetry, {\bf fractional} coordinates
|
|
are used in the directions where translational symmetry exists.
|
|
This means that for crystals $x$, $y$ and $z$ are fractional, for
|
|
surfaces $x$ and $y$ are fractional, whereas for polymers only $z$ is
|
|
fractional.
|
|
For example, in the following H$_2$O layer input (a 2-d periodic
|
|
system), $x$ and $y$ coordinates are fractional, whereas $z$
|
|
is expressed in \AA .
|
|
\begin{verbatim}
|
|
geometry units angstrom
|
|
O 0.353553 0.353553 2.100000000
|
|
H 0.263094 0.353553 2.663590000
|
|
H 0.444007 0.353553 2.663590000
|
|
\end{verbatim}
|
|
|
|
Since no space group symmetry is available yet other than $P1$, input
|
|
of cell parameters is relative to the primitive cell. For example,
|
|
this is the input required for the cubic face-centered type structure
|
|
of bulk MgO.
|
|
|
|
\begin{verbatim}
|
|
|
|
system crystal
|
|
lat_a 2.97692 lat_b 2.97692 lat_c 2.97692
|
|
alpha 60.00 beta 60.00 gamma 60.00
|
|
end
|
|
\end{verbatim}
|
|
|
|
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: "user"
|
|
%%% End:
|