$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)                                         

generated on 7/7/2017