# Example: damped second hyperpolarizability: LiH¶

```
#! /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
```