$VSCF group         (optional, relevant to RUNTYP=VSCF)
 
    This group governs the computation of vibrational
frequencies including anharmonic effects.  Besides the
keywords shown below, the input file must contain a $HESS
input (and perhaps a $DIPDR input), to start with
previously obtained harmonic vibrational information.  The
VSCF method requires only energies, so any energy type in
GAMESS may be used, perhaps with fully numerical harmonic
vibrational information.  Energies are sampled along the
directions of the harmonic normal modes, and usually along
pairs of harmonic normal modes, after which the nuclear
vibrational wavefunctions are obtained.  The dipole on the
grid points may be used to give improved IR intensities.
 
    The most accurate calculation computes the potential
surface directly, on all grid points, but this involves
many energy evaluations.  An attractive alternative is the
Quartic Force Field approximation of Yagi et al., which
computes a fit to the derivatives up to fourth order by
computing a specialized set of points, after which this fit
is used to generate the full grid of points for the solver.
 
    Since there are a great many independent energy
evaluations, no matter which type of surface is computed,
the VSCF method allows for computations in subgroups (much
like the FMO method).  Thus any $GDDI input group will be
read and acted upon, if found.
 
    Vibrational wavefunctions are obtained at an SCF-like
level, termed VSCF, using product nuclear wavefunctions,
along with an MP2-like correction to the vibrational
energy, which is termed correlation corrected (cc-VSCF).
In addition, vibrational energy levels based on second
order degenerate pertubation theory (see VDPT) or a CI
analog (see VCI) may be obtained.
 
    Most VSCF applications have been carried out with an
electronic structure level of MP2 with triple zeta basis
sets.  This is thought to give accuracy to 50 wavenumbers
for the larger fundamentals.  Use of internal coordinates
is known to give improved accuracy for lower frequencies,
particularly in weakly bound clusters.
 
    Restarts involve the $VIBSCF input (which has different
formats for each PETYP), and the READV keyword.  Restarts
are safest on the same machine, where normal mode phases
are reproducible.
 
    References for the VSCF method, the QFF approximation,
and the solvers are given in Chapter 4 of this manual,
along with a number of sample applications.
 
 
                       * * * * *
 
The first input variables control the generation of the
potential surface on which the nuclear vibrations occur:
 
PETYP  = DIRECT computes the full potential energy surface,
                according to NCOUP/NGRID.  The total number
                of energy/dipole calculations for NCOUP=2
                will be M*NGRID + (M*(M-1)/2)*NGRID*NGRID,
                where M is the number of normal modes.
                This is the default.
       = QFF    the Quartic Force Field approximation to
                the potential surface is obtained.  This is
                usually only slightly less accurate, but
                has a greatly reduced computational burden,
                namely 6*M + 12*M*(M-1)/2 energy/dipoles.
 
INTCRD = flag setting the coordinate system used for the
         grids.  Any internal coordinates to be used must
         be defined in $ZMAT, using 3N-6 simple, DLC, or
         natural internal coordinates.  Of course, you must
         enter NZVAR in $CONTRL as well.
         The default is to use Cartesians (default .FALSE.)
 
INTTYP = 0 default if INTCRD=.FALSE. (ignore this keyword)
       = 1 implies that the $ZMAT contains only stretches,
           bends, and torsions.  It also selects an
           approximate transformation between Cartesian
           and internal coords.
       = 2 the other $ZMAT coordinates may be used, and
           the coordinate transformation will be iterated
           to convergence.  (default if INTCRD=.TRUE.)
 
NCOUP  = the order of mode couplings included.
       = 1 computes 1-D grids along each harmonic mode
       = 2 adds additionally, 2-D grids along each pair
           of normal modes. (default=2)
       = 3 adds additionally, 3-D grids for mode triples,
           for PETYP=DIRECT only.
 
NGRID  = number of grid points to be used in solving for
         the anharmonic vibrational levels.  In the case
         of PETYP=DIRECT, each of these grid points must be
         explicitly computed.  For PETYP=QFF these grid
         points are obtained from a fitted quartic force
         field.  Reasonable values are 8 or 16 for DIRECT,
         with 16 considered significantly more accurate.
         For PETYP=QFF, the generation of the solver grid
         is very fast, so use 16 always. (default=16)
 
AMP    = step size for PETYP=DIRECT displacements.  The
         maximum distance along each mode is a function of
         its frequency,
            amplitude(i)=sqrt(2*(AMP+1/2)/freq(i))
         so that AMP resembles a vibrational quantum
         number.  The default goes far enough past the
         classical turning points of the fundamentals to
         capture the relevant part of the surface.
         (default = 7.0)
 
STPSZ  = step size for PETYP=QFF displacements.  The
         step along each mode depends on the harmonic
         frequency, as well as this parameter, whose
         default is usually satisfactory (default=0.5)
 
In case the user wants to control each normal mode with a
separate parameter, arrays of values may be given, using
the keywords AMPX(1)=xx,yy,... or STPSZX(1)=xx,yy,zz...
 
IMODE  = array of modes for which anharmonic effects will
         be computed.  IMODE(1)=10,19 computes anharmonic
         energies and wavefunctions for modes 10 and 19,
         only.  In the current implementation, pairs of
         modes cannot be coupled, so NCOUP is forced to 1
         if this option is specified.  This approximation
         is intended for larger molecules, where the whole
         VSCF calculation is prohibitive.
 
                       * * * * *
 
The next set of keywords relates to the solver step which
finds the vibrational states.  The results always include
VSCF and cc-VSCF (SCF and non-degenerate MP2-like
solutions).  Use of the restart option makes comparing the
solvers very fast, compared to the time to generate the
electronic potential energy surface's points.
 
VDPT   = option to use 2nd order degenerate perturbation
         theory, based on the ground and singly excited
         vibrational levels.  Results for virtual CI within
         the same singly excited space will also be given.
         Selection of VDPT turns VCI on, as well.
         (default=.FALSE.)
 
VCI    = option to use the virtual CI solver within a space
         of the ground and both singly and doubly excited
         vibrational levels.
         Selection of VCI turns VDPT off.
         (default=.FALSE.)
 
The solver always finds the ground vibrational state (v=0)
by default, and defaults to finding the fundamentals (v=1
in every mode).  It can rapidly find excited levels (such
as all v=2) if restarted (see READV) from $VIBSCF, using
the following to control the excitation levels:
 
IEXC   = 1 obtain fundamental frequencies (default)
       = 2 instead, obtain first overtones
       = 3 instead, obtain second overtones
 
IEXC2  = 0 skip combination bands (default)
       = 1 add one additional quanta in other modes
       = 2 add two other quanta in one mode at a time.
 
     IEXC  IEXC2   for H2O, which has only three modes:
       0     0        only 000 ground state, no transitions
       1     0     000, and 100, 010, 001  (fundamentals)
       2     0     000, and 200, 020, 002  (1st overtones)
       3     0     000, and 300, 030, 003  (2nd overtones)
       1     1     000, and 100, 010, 001, 110, 101, 110
                      (1st overtones and combinations)
       1     2     000, and 100, 010, 001, 210, 201, 021
       2     1     000, and 200, 020, 002, 120, 102, 012
                      between them, 1st and 2nd overtones,
                      and all 2-1-0 combinations.
 
ICAS1, ICAS2 = starting and ending vibrations whose quanta
         are included.  The default is all modes, ICAS1=1
         and ICAS2=3N-6 (or 3N-5).
 
SFACT  = a numerical cutoff for small contributions in
         the solver.  The default is 1d-4: 5d-3 or 1d-3 may
         affect accuracy of results, 1d-4 is safer, and
         1d-5 might not converge.
 
VCFCT  = scaling factor for pair-coupling potential.
         Sometimes when pair-coupling potential values
         are larger than the corresponding single mode
         values, they must be scaled down.  It is seldom
         necessary to select a scaling other than unity.
         (Default=1.0)
 
                       * * * * *
 
The next two relate to simplified intensity computation.
These simplifications are aimed at speeding up MP2 runs, if
one does not care so much about intensities, and would like
to eliminate the considerable extra time to compute MP2-
level dipoles.  DMDR must not be used if overtones are
being computed.
 
DMDR   = if true, indicates that the harmonic dipole
         derivative tensor $DIPDR will be read and used,
         rather than computing dipoles.  (default=.FALSE.)
 
MPDIP  = If .TRUE. the run will compute MP2 level dipoles
         for the IR intensity evaluation.
         Entering .FALSE. uses SCF level dipoles instead.
         Default=.TRUE. for MP2 runs, except when using the
         RI-MP2 program, which cannot compute MP2 dipoles,
         and so chooses .FALSE. here.
         It is more accurate to use the DMDR flag instead
         instead of turning off MPDIP, if an MP2 level
         $DIPDR is available from the MP2 hessian run.
 
* * * *
 
   These relate to the initial harmonic mode generation.
   Normally, a $HESS is provided, from which harmonic
   modes are obtained.  It is possible to give the
   harmonic data explicitly with the first two:
 
RDFRQ  = array of harmonic frequencies, starting from the
         smallest.
 
CMODE  = array of normal mode displacements given in the
         same order as the frequencies read in RDFRQ.  The
         data should be the x,y,z displacement of the first
         atom of the first mode, then x,y,z for the second
         atom, then going on to give each additional mode.
 
PROJCT = controls the projection of the hessian matrix
         (same meaning as in $FORCE).  Default is .TRUE.
         which removes small mixings between rotations
         or translations and the harmonic modes.
 
                      * * * *
 
READV  = flag to indicate restart data $VIBSCF should be
         read in to resume an interrupted calculation, or
         to obtain overtones in follow-on runs.
         (default is .FALSE.)
 
GEONLY = option to generate all points on the potential
         energy surface needed by the VSCF routine, without
         energy evaluations.  The purpose of this is to
         prepare a set of geometries at which the energy
         is needed.  A possible use for this is to obtain
         energies from a different program package, which
         might have an energy unavailable in GAMESS, but
         which lacks its own VSCF program.
         (default=.false.)