$FFCALC group             (relevant for RUNTYP=FFIELD)
 
    This group permits the study of the influence of an
applied electric field on the wavefunction.  The most
common finite field calculation applies a sequence of
fields to extract the linear polarizability and the first
and second order hyperpolarizabilities (static alpha, beta,
and gamma tensors).  The method is general, because it
relies on finite differencing of the energy values, and so
works for all ab initio wavefunctions.  If the dipole
moments are available (true for SCF or CI functions, and
see MPPROP in $MP2), the same tensors are formed by
differencing the dipoles, which is more accurate.  Some
idea of the error in the numerical differentiations can be
gleaned by comparing energy based and dipole based
quantities.
 
    For analytic computation of static polarizabilities
alpha, beta, and gamma (as well as frequency dependent NLO
properties), for closed shell cases, see $TDHF and $TDHFX.
For analytic computation of the static polarizability
alpha, see POLAR in $CPHF.
 
    The standard computation obtains the polarizabilities,
by double numerical differentiation.  See ONEFLD to apply a
single electric field, but for a more general approach to
applied static fields, see $EFIELD.
 
 
OFFDIA = .TRUE. computes the entire polarizability tensors,
                which requires a total of 49 wavefunction
                evaluations (some of gamma is not formed).
       = .FALSE. forms only diagonal components of the
                polarizabilities, using 19 wavefunctions.
                The default is .TRUE.
 
ESTEP         = step size for the applied electric field
                strength, 0.01 to 0.001 is reasonable.
                (default=0.001 a.u.)
 
The next parameters pertain to applying a field in only one
direction:
 
ONEFLD = flag to apply one field (default=.FALSE.)
 
SYM    = a flag to specify when the field to be applied
         does not break the molecular symmetry.  Since most
         fields do break the nuclear point group symmetry,
         the default is .FALSE.
 
EFIELD = an array of the three x,y,z components of the
         single applied field.
 
 
                         * * *
 
LOCHYP = a flag to perform a localized orbital analysis of
         the alpha, beta, and gamma polarizabilities.
         See $LOCAL for similar analyses of the energy,
         multipole moments, or alpha polarizability.
         References for this keyword are given below.
 
 
    Finite field calculations require large basis sets, and
extraordinary accuracy in the wavefunction.  To converge
the SCF to many digits is sometimes problematic, but we
suggest you use the input to increase integral accuracy and
wavefunction convergence, for example
 
   $CONTRL ICUT=20 ITOL=30 $END
   $SCF    CONV=1d-7 FDIFF=.FALSE. $END
 
    Examples of fields that do not break symmetry are a Z-
axis field for an axial point group which is not
centrosymmetric (i.e. C2v).  However, a field in the X or Y
direction does break the C2v symmetry. Application of a Z-
axis field for benzene breaks D6h symmetry.  However, you
could enter the group as C6v in $DATA while using D6h
coordinates, and regain the prospect of using SYM=.TRUE.
If you wanted to go on to apply a second field for benzene
in the X direction, you might want to enter Cs in $DATA,
which will necessitate the input of two more carbon and
hydrogen atom, but recovers use of SYM=.TRUE.
 
 
References:
   J.E.Gready, G.B.Bacskay, N.S.Hush
     Chem.Phys.  22, 141-150(1977)
   H.A.Kurtz, J.J.P.Stewart, K.M.Dieter
     J.Comput.Chem.  11, 82-87(1990).
 
polarizability analysis:
   S.Suehara, P.Thomas, A.P.Mirgorodsky, T.Merle-Mejean,
   J.C.Champarnaud-Mesjard, T.Aizawa, S.Hishita,
   S.Todoroki, T.Konishi, S.Inoue
     Phys.Rev.B 70, 205121/1-7(2004)
   S.Suehara, T.Konishi, S.Inoue
     Phys.Rev.B 73, 092203/1-4(2006)
 
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