$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                       
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)                          

generated on 7/7/2017