# Example: damped first hyperpolarizability: LiH¶

```
#! /bin/sh
# If the subkey lifetime and BETA or QUADRATIC is included in the key
# AORESPONSE, the damped (frequency dependent) first hyperpolarizability is
# calculated. This test example consists of two calculations calculations: one
# with BETA and the other with QUADRATIC.
# The subkey EOPE is used, which means the electro-optical Pockels effect
# beta(-omega;omega,0). This example can easily be modified to calculate the
# static beta(0;0,0), the optical rectification beta(0;omega,-omega), the second
# harmonic generation beta(-2omega;omega,omega), or the general case
# beta(-(omega1+omega2);omega1,omega2).
# Note: results will be physically meaningless due to small basis set. Purpose
# of this job is to provide a test case for the first hyperpolarizability
# implementation
# In the first example the first hyperpolarizability is calculated with the
# subkey BETA, for EOPE, the electro-optical Pockels effect
# beta(-omega;omega,0).
###########################
# Damped EOPE, 2n+1
###########################
AMS_JOBNAME=EOPE_beta $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 EOPE of LiH, 2n+1
allpoints
aoresponse
alda
beta
eope
frequencies 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 second example the first hyperpolarizability is calculated with the
# subkey QUADRATIC, again for EOPE, the electro-optical Pockels effect
# beta(-omega;omega,0).
################################
# Damped EOPE, Quadratic
################################
AMS_JOBNAME=EOPE_quadratic $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 EOPE of LiH, Quadratic
allpoints
aoresponse
alda
eope
frequencies 0.1000 0.0000 [Hartree]
lifetime 0.0034
quadratic
scf iterations 50
end
basis
core None
type SZ
end
numericalquality good
symmetry nosym
EndEngine
eor
# For the static case beta(0;0,0) use the subkey STATIC
# aoresponse
# ...
# frequencies 0.0000 0.0000 [Hartree]
# static
# end
# For optical rectification beta(0;omega,-omega) use the subkey OPTICALR.
# aoresponse
# ...
# frequencies 0.1000 -0.1000 [Hartree]
# opticalr
# end
# For the second harmonic generation beta(-2omega;omega,omega) use the subkey SHG
# aoresponse
# ...
# frequencies 0.1000 0.1000 [Hartree]
# shg
# end
# Or in the general case for beta(-(omega1+omega2);omega1,omega2) choose two
# input frequencies omega1 and omega2
# aoresponse
# ...
# frequencies omega1 omega2 [Hartree]
# end
```