$EFIELD group   (not required)
 
    This group permits the study of the influence of an
external electric field on the molecule.  The method is
general, and so works for all wavefunctions, and for both
energies and nuclear gradients.
 
EVEC        = an array of the three x,y,z components of
              the applied electric field, in a.u., where
              1 Hartree/e*bohr = 5.1422082(15)D+11 V/m
              A typical size for the EVEC components is
              therefore about 0.001 a.u.
 
SYM         = a flag to specify when the field breaks the
              the molecular symmetry. Since most fields
              break symmetry, the default is .FALSE.
 
Restrictions: analytic hessians are not available, but
numerical hessians are.  Because an external field causes a
molecule with a dipole to experience a torque, geometry
optimizations must be done in Cartesian coordinates only.
Internal coordinates eliminate the rotational degrees of
freedom, which are no longer free.
 
A nuclear hessian calculation will have two rotational
modes with non-zero "frequency", caused by the torque.  A
gas phase molecule will rotate so that the dipole moment is
anti-parallel to the applied field.  To carry out this
rotation during geometry optimization will take many steps,
and you can help save much time by inputting a field
opposite the molecular dipole.  There is also a stationary
point at higher energy with the dipole parallel to the
field, which will have two imaginary frequencies in the
hessian.  These will appear as the first two modes in a
hessian run, but will not have the i for imaginary included
on the printout since they are rotational modes.
 
sign conventions:
Dipole vectors are considered to point from the negative
end of the molecule to the positive end.  Thus HCl at the
MP2/aug-cc-pVDZ level's geometry of R=1.2831714 has a
positive dipole, if we place Cl at the origin and H along
the positive z-axis.  The sign convention on applied fields
is such that a +1 charge particle feels a force in the
positive direction under a positive field, namely, as if
there was a negative plate at large +Z and a positive plate
at large -Z.  Hence positive fields enhance HCl's dipole:
      EVEC(z)      E(MP2)       mu(MP2)
      -0.001  -460.2567905970  1.112875
      -0.0001 -460.2571917846  1.153172
       0.0    -460.2572372416  1.157646
      +0.0001 -460.2572828745  1.162119
      +0.001  -460.2577014871  1.202350
and the higher energy for each negative EVEC means HCl
would prefer to turn around in the field.
 
Thus, one use for this group is calculation of the electric
dipole by finite difference, for wavefunctions that cannot
yield molecular properties due to not having a relaxed
density matrix.  Perform two RUNTYP=ENERGY jobs per
component, with fields 0.001 and -0.001 a.u.  The central
difference formula for each component of the dipole is
   mu = 2.541766*(E(+0.001)-E(-0.001)/0.002, in Debye.
The differentiation using data from HCl gives 1.157635.
 
For an application to molecular ionization in intense
fields generated by lasers, see
    H.Kono, S.Koseki, M.Shiota, Y.Fujimura
    J.Phys.Chem.A  105, 5627-5636(2001)