$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                              
    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                     
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.                                   
   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)                                            

generated on 7/7/2017