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\section{Geometry Optimization and Vibrational Frequency Analysis} \label{opt}
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\section{Geometry Optimization} \label{opt}
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\PSIthree\ is capable of carrying out geometry optimizations (minimization
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only, at present) for a variety of molecular structures using either analytic
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and numerical energy gradients.
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When analytic gradients are available (see Table \ref{table:methods}),
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\PSIthree\ will automatically generate and use redundant, simple internal
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When present, internal coordinates provided in the INTCO: section of the
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input will be read and used by \PSIthree. If these are missing, \PSIthree\
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will automatically generate and use redundant, simple internal
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coordinates for carrying out the optimization. These simple stretch, bend,
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torsion, and linear bend coordinates may be read from the intco.dat file
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or determined completely by distance criteria using the input geometry.
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torsion, and linear bend coordinates are determined by distance
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criteria using the input geometry.
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By default, optimization is performed in redundant internal coordinates
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regardless of how the geometry was provided in the input. Alternatively,
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the user may specify zmat\_simples=true, in which case the simple internal
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coordinates will be taken from the ZMAT given in the input file. Also,
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the user may specify optimization in delocalized internal coordinates
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the user may specify optimization in non-redundant, delocalized internal coordinates
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with delocalize=true. In this case, the automatically generated simple
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coordinates are delocalized and redandancies are removed. Advanced users
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may wish to specify the simple internal coordinates in the intco.dat file, and
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then allow \PSIthree\ to delocalize them.
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Geometrical constraints may be imposed by the addition of a section
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with nearly the same format as intco.dat. For example, to fix the distance
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Only those coordinates or combinations of coordinates that are specified
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by the "symm =" keyword in the INTCO: section are optimized. Coordinates can
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be approximately frozen by commenting them out within the "symm =" section.
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Geometrical constraints may be precisely imposed by the addition of a section
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with nearly the same format as in INTCO:. For example, to fix the distance
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between atoms 1 and 2, as well as the angle between atoms 2, 1 and 3
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in an optimization, add the following to your input file.
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The constrained simple internals must be ones present (either manually or
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automatically) among the simple internals in intco.dat. Alternatively,
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automatically) among the simple internals in the INTCO: section. Alternatively,
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the z-matrix input format may be used to specify constrained optimizations.
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If zmat\_simples=true, then variables in the z-matrix which end in
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a dollar sign will be taken as simple internals to be optimized, and
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all other variables will be taken as simple internals to keep frozen.
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For methods for which only energies are available, \PSIthree\ will use
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To aid optimizations, force constants may be computed using "jobtype = symm\_fc".
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The determined force constants will be saved in a binary file PSIF\_OPTKING
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(currently file 1). Subsequent optimizations will read and use these force
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constants. In general, \PSIthree\ looks for force constants in the following
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order: in this binary file, in the FCONST: section of the input, and in the fconst.dat
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file. If no force constants are found in any of these, then an empirical
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diagonal force constant matrix is generated.
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For methods for which only energies are available, \PSIthree\ will use non-redundant,
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symmetry-adapted delocalized internal coordinates to generate geometrical
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displacements for computing finite-difference gradients. The simple
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coordinates can be linearly combined by hand or automatically. The goal
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is to form 3N-6(5) symmetry-adapted internal coordinates. The automated
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delocalized coordinates may work for low-symmetry molecules without
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linear angles, but has not been extensively tested. For both analytic-
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linear angles, but have not been extensively tested. For both analytic-
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and finite-difference-gradient optimization methods, Hessian updates are
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performed using the BFGS method.
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The list below shows which coordinates are used by default for different types of jobs. \\
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jobtype=freq dertype=first symmetry-adapted cartesians \\
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jobtype=freq dertype=none symmetry-adapted cartesians \\
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jobtype=fc dertype=first delocalized internals (or user-defined SALCs) \\
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jobtype=symm\_fc dertype=first delocalized internals (or user-defined SALCs) \\
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jobtype=opt dertype=first redundant internals \\
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jobtype=opt dertype=none delocalized internals (or user-defined SALCS) \\
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The following keywords are pertinent for geometry optimizations.
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\item[JOBTYPE = string]\mbox{}\\
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This keyword must be set to {\tt OPT} for geometry optimizations and
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{\tt SYMM\_FC} to compute force constants.
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\item[DERTYPE = string]\mbox{}\\
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This keyword must be set to {\tt NONE} if only energies are available
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for the chosen method and {\tt FIRST} if analytic gradients are available.
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\item[CONV = integer]\mbox{}\\
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The maximum force criteria for optimization is $10^{-conv}$.
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\item[BFGS = boolean]\mbox{}\\
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If true (the default), a BFGS Hessian update is performed.
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\item[BFGS\_USE\_LAST = integer]\mbox{}\\
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This keyword is used to specify the number of gradient step for the BFGS
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update of the Hessian. The default is six.
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\item[SCALE\_CONNECTIVITY = float]\mbox{}\\
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Determines how close atoms must be to be considered bonded in the automatic
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generation of the bonded list. The default is 1.3.
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\item[DELOCALIZE = integer]\mbox{}\\
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Whether to delocalize simple internal coordinates to attempt to produce
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a symmetry-adapted, non-redundant set.
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\item[MIX\_TYPES = boolean]\mbox{}\\
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If set to false, different types of internal coordinates are not allowed
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to mix in the formation of the delocalized coordinates. Although this
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produces cleaner coordinates, often the resulting delocalized coordinates
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form a redundant set.
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\item[ZMAT\_SIMPLES = boolean]\mbox{}\\
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If set to true, the simple internal coordinates are taken from the zmat
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entry in the input file. The default is false.
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\item[POINTS = 3 or 5]\mbox{}\\
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Specifies a 3-point or a 5-point formula for optimization by energy points.
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\item[EDISP = float]\mbox{}\\
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The default displacment size (in au) for finite-difference computations. The
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\item[FRAGMENT\_DISTANCE\_INVERSE = boolean]\mbox{}\\
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For interfragment coordinates. If true, then 1/R(AB) is used, if false,
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then R(AB) is used. The default is true.
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\item[FIX\_INTRAFRAGMENT = boolean]\mbox{}\\
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If true, all intrafragment coordinates are constrained.
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\item[FIX\_INTERFRAGMENT = boolean]\mbox{}\\
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If true, all interfragment coordinates are constrained.
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\item[DUMMY\_AXIS\_1 = 1 or 2 or 3]\mbox{}\\
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Specifies the axis for the location of a dummy atom for the definition
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of a linear bending coordinate. The default is 2.
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\item[DUMMY\_AXIS\_2 = 1 or 2 or 3]\mbox{}\\
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Specifies the axis for the location of a dummy atom for the definition
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of a linear bending coordinate. The default is 3.
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\item[TEST\_B = boolean]\mbox{}\\
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If set to true, a numerical test of the B-matrix is performed.
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\item[PRINT\_FCONST = boolean]\mbox{}\\
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If set to true and jobtype=symm\_fc, then the force constants will
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be written to the fconst.dat file. This allows force constants to be
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reused even if the binary PSIF\_OPTKING file is no longer present.
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\item[Print options]\mbox{}\\
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The following when set to true, print additional information to the
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output file: PRINT\_SIMPLES, PRINT\_PARAMS, PRINT\_DELOCALIZE,
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PRINT\_SYMMETRY, PRINT\_HESSIAN, PRINT\_CARTESIANS.
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\item[DISPLACEMENTS = ( (integer float ...) ...)]\mbox{}\\
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A user may specify displacments along internal coordinates using this
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keyword. For example, displacements = ( (2 0.01 3 0.01) ) will compute
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a new cartesian geometry with the second and third internal coordinates
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\section{Vibrational Frequency Computations} \label{freq}
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\PSIthree\ is also capable of computing harmonic vibrational frequencies
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for a number of different methods using energy points or analytic energy first or
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second derivatives. (At present, only RHF-SCF analytic second derivatives
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are available.) If analytic energy second derivatives are not available,
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\PSIthree\ will generate displaced geometries along symmetry adapted cartesian
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coordinates, compute the appropriate energies or first derivatives, and use finite-difference
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methods to compute the Hessian.
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coordinates, compute the appropriate energies or first derivatives, and use
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finite-difference methods to compute the Hessian.
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The following keywords are pertinent for geometry optimizations and
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vibrational frequency analyses:
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The following keywords are pertinent for vibrational frequency analyses:
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\begin{description}
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\item[JOBTYPE = string]\mbox{}\\
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This keyword (described earlier in this manual) must be set to
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{\tt OPT} for geometry optimizations and {\tt FREQ} for frequency analyses.
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This keyword must be set to {\tt FREQ} for frequency analyses.
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\item[DERTYPE = string]\mbox{}\\
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This keyword (also described earlier) must be set to {\tt NONE} is only
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energies are available for the chosen method and {\tt FIRST} if analytic
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gradients are available.
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\item[BFGS\_USE\_LAST = integer]\mbox{}\\ This keyword is used to specify
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the number of gradient step for the BFGS update of the Hessian. The default
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This keyword may be set to {\tt NONE} if only energies are available
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for the chosen method, or {\tt FIRST} if analytic gradients are available.
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\item[POINTS = 3 or 5]\mbox{}\\
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Specifies whether frequencies are determined by a 3-point or a 5-point
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formula of gradient differences. If only energy points are used, more
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displacements are required, but the effect of this keyword in terms of
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accuracy is the same.
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Note: In some situations, vibrational frequency analysis via finite
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differences may fail if the full point group symmetry is specified via
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the {\tt symmetry} keyword. This happens because the user-given
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{\tt symmetry} value can become incompatible with the actual symmetry
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of the molecule when energies or gradients are evaluated for
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symmetry-lowering displacements. In such situations, the user is
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advised to let the program determine the symmetry automatically, rather
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than specifying {\tt symmetry} manually. Otherwise, an error such as the
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following may result:
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error: problem assigning number of operations per class
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*** stopping execution ***
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The manual pages for the \PSInormco\ and \PSIintder\ modules contain
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information on additional tools useful in vibrational frequency analysis
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and coordinate transformation.
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doc/userman/opt.tex
