Example: damped second hyperpolarizability: LiH
***********************************************

"Download LiH_DampedGamma.run"

   #! /bin/sh


   # If the subkey lifetime and GAMMA or CUBIC is included in the key AORESPONSE,
   # the damped (frequency dependent) second hyperpolarizability is calculated.
   # This test example consists of three calculations calculations: two with GAMMA
   # and one with CUBIC.

   # The the first two examples subkey EFIOR is used, which means the electric
   # field induced optical rectification gamma(0;omega,-omega,0). In the third
   # example two-photon absorption (TPA) cross sections are calculated, the reduced
   # form of gamma(-omega;omega,omega,-omega). Examples can easily be modified to
   # calculate the static case gamma(0;0,0,0), the optical Kerr effect
   # gamma(-omega;omega,0,0), the intensity dependent refractive index
   # gamma(-omega;omega,omega,-omega), the electric field induced second harmonic
   # generation gamma(-2omega;omega,omega,0), the third harmonic generation
   # gamma(-3omega;omega,omega,omega) use the subkey THG, or the general case
   # gamma(-(omega1+omega2+omega3);omega1,omega2,omega3).

   # Note: results will be physically meaningless due to small basis set. Purpose
   # of this job is to provide a test case for the second hyperpolarizability
   # implementation

   # In the first example the second hyperpolarizability is calculated with the
   # subkey GAMMA, for EFIOR, the electric field induced optical rectification
   # gamma(0;omega,-omega,0).


   ####################
   # Damped EFIOR, 2n+1
   ####################

   AMS_JOBNAME=EFIOR_gamma $AMSBIN/ams <<eor
   System
     atoms
        Li    0.00000000    0.00000000    3.49467000
        H     0.00000000    0.00000000    1.89402300
     end
   end

   Task SinglePoint

   Engine ADF
     title Damped EFIOR of LiH, 2n+1
     allpoints
     aoresponse
       alda
       efior
       frequencies 0.1000 -0.1000 0.0000 [Hartree]
       gamma
       lifetime 0.0034
       scf iterations 50
     end
     basis
       core None
       type SZ
     end
     numericalquality good
     symmetry nosym
   EndEngine
   eor


   # In the second example the second hyperpolarizability is calculated with the
   # subkey CUBIC, again for EFIOR, the electric field induced optical
   # rectification gamma(0;omega,-omega,0).

   #####################
   # Damped EFIOR, Cubic
   #####################

   AMS_JOBNAME=EFOR_cubic $AMSBIN/ams <<eor
   System
     atoms
        Li    0.00000000    0.00000000    3.49467000
        H     0.00000000    0.00000000    1.89402300
     end
   end

   Task SinglePoint

   Engine ADF
     title Damped EFIOR of LiH, Cubic
     allpoints
     aoresponse
       alda
       cubic
       efior
       frequencies 0.1000 -0.1000 0.0000 [Hartree]
       lifetime 0.0034
       scf iterations 50
     end
     basis
       core None
       type SZ
     end
     numericalquality good
     symmetry nosym
   EndEngine
   eor


   # In the third example the subkeyword TPA is be used to calculate the gammagamma
   # corresponding to the two photon absorption process (i.e., the reduced form of
   # gamma(-omega;omega,omega,-omega)), however, TPA can ONLY be used with keyword
   # GAMMA.

   ##################
   # Damped TPA, 2n+1
   ##################

   AMS_JOBNAME=TPA_gamma $AMSBIN/ams <<eor
   System
     atoms
        Li    0.00000000    0.00000000    3.49467000
        H     0.00000000    0.00000000    1.89402300
     end
   end

   Task SinglePoint

   Engine ADF
     title Damped TPA of LiH, 2n+1
     allpoints
     aoresponse
       alda
       frequencies 0.1000 0.1000 -0.1000 [Hartree]
       gamma
       lifetime 0.0034
       scf iterations 50
       tpa
     end
     basis
       core None
       type SZ
     end
     numericalquality good
     symmetry nosym
   EndEngine
   eor


   # For the static case gamma(0;0,0,0) use the subkey STATIC
   #   aoresponse
   #    ...
   #    frequencies 0.0000 0.0000 0.0000 [Hartree]
   #    static
   #   end

   # For the optical Kerr effect gamma(-omega;omega,0,0) use the subkey OKE
   #   aoresponse
   #    ...
   #    frequencies 0.1000 0.0000 0.0000 [Hartree]
   #    oke
   #   end

   # For the intensity dependent refractive index gamma(-omega;omega,omega,-omega)
   # use the subkey IDRI
   #   aoresponse
   #    ...
   #    frequencies 0.1000 0.1000 -0.1000 [Hartree]
   #    idri
   #   end

   # For the electric field induced second harmonic generation
   # gamma(-2omega;omega,omega,0) use the subkey EFISHG
   #   aoresponse
   #    ...
   #    frequencies 0.1000 0.1000 0.0000 [Hartree]
   #    efishg
   #   end

   # For the third harmonic generation gamma(-3omega;omega,omega,omega) use the
   # subkey THG
   #   aoresponse
   #    ...
   #    frequencies 0.1000 0.1000 0.1000 [Hartree]
   #    thg
   #   end

   # Or in the general case for gamma(-(omega1+omega2+omega3);omega1,omega2,omega3)
   # choose three input frequencies omega1, omega2, and omega3
   #   aoresponse
   #    ...
   #    frequencies omega1 omega2 omega3 [Hartree]
   #   end

