$MEX group                      (relevant if RUNTYP=MEX)
 
   This group governs a search for the lowest energy on the
3N-7 dimensional "seam" of intersection of two different
electronic potential energy surfaces.  Such Minimum Energy
Crossing Points are important for processes such as spin-
orbit coupling that involve transfer from one surface to
another, and thus are analogous to transition states on a
single surface.  The present program requires that the two
surfaces differ in spin quantum number, or space symmetry,
or both.  Analytic gradients are used in the search.
 
   In case the two potential surfaces have identical spin
and space symmetry, this kind of intersection point is
referred to as a Conical Intersection.  See $CONICL using
RUNTYP=CONICAL instead.
 
SCF1, SCF2   = define the molecular wavefunction types,
               possibly in conjunction with the usual
               MPLEVL and DFTTYP keywords.
 
MULT1, MULT2 = give the spin multiplicity of the states.
 
      Permissible combinations of wavefunctions are
           RHF  with ROHF/UHF
           ROHF with ROHF
           UHF  with UHF
      as well as their MP2 and DFT counterparts, and
           GVB  with ROHF/UHF
          MCSCF with MCSCF (CISTEP=ALDET or GUGA only)
 
 
NSTEP  = maximum number of search steps (default=50)
 
STPSZ  = Step size during the search  (default = 0.1D+00)
 
 
NRDMOS = Initial orbitals can be read in
       = 0  No initial orbitals (default)
       = 1  Read in orbitals for first state (in $VEC1)
       = 2  Read in orbitals for second state (in $VEC2)
       = 3  Read in orbitals for both ($VEC1 and $VEC2)
 
NMOS1  = Number of orbitals for first state's $VEC1.
 
NMOS2  = Number of orbitals for second state's $VEC2.
 
NPRT   = Printing orbitals
       = 0  No orbital printed out except at the first
            geometry (default)
       = 1  Orbitals are printed each geometry.  If MCSCF
            is used, CI expansions are also printed.
 
Finer control of the convergence criterion:
 
TDE    = energy difference between two states
         (default = 1.0D-05)
 
TDXMAX = maximum displacement of coordinates
         (default = 2.0D-03)
 
TDXRMS = root mean square displacement
         (default = 1.5D-03)
 
TGMAX  = maximum of effective gradient between the two
         states (default = 5.0D-04)
 
TGRMS  = root mean square effective gradient tolerance
          (default = 3.0D-04)
 
Usage notes:
 
1. Normally $CONTRL will not give SCFTYP or MULT keywords.
SCF1 and SCF2 can be given in any order.  The combinations
permitted ensure roughly equal sophistication in the
treatment of electron correlation.
2. After reading $MEX, SCFTYP and MULT will be set to the
more complex of the two choices, which is considered to be
RHF < ROHF < UHF < GVB < MCSCF.  This permits the $SCF
input defining a GVB wavefunction to be read and tested for
correctness, in a GVB+ROHF run.  Since only one SCFTYP is
stored while reading the input, you might need to provide
some keywords that are normally set by default for the
other (such as ensuring DIIS is selected in $SCF if either
of the states is UHF).
3. It is safest by far to prepare and read $VEC1 and $VEC2
groups so that you know what electronic states you start
with.  It is a good idea to regenerate both states at the
end of the MEX search, to be sure that they remain as you
began.
4. It is your responsibility to make sure that the states
have a different space symmetry, or a different spin
symmetry (or both).  That is why note 3 is so important.
5. $GRAD1 and/or $GRAD2 groups containing gradients may be
given to speed up the first geometry of the MEX search.
6. The search is even trickier than a saddle point search,
for it involves the peaks and valleys of BOTH surfaces
being generated.  Starting geometries may be guessed as
lying between the minima of the two surfaces, but the
lowest energy on the crossing seam may turn out to be
somewhere else.  Be prepared to restart!
7. The procedure is a Newton-Raphson search, conducted in
Cartesian coordinates, with a Lagrange multiplier imposing
the constraint of equal energy upon the two states.  The
hessian matrices in the search are guessed at, and
subjected to BFGS updates.  Internal coordinates will be
printed (for monitoring purposes) if you define $ZMAT, but
the stepper operates in Cartesian coordinates only.  No
geometry constraints can be applied, apart from the point
group in $DATA.
 
  A good paper to read about this kind of search is
A.Farazdel, M.Dupuis  J.Comput.Chem. 12, 276-282(1991)