# Example: damped first hyperpolarizability: LiH¶

Download LiH_DampedBeta.run

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 $$\beta(-2\omega;\omega,\omega)$$, or the general case $$\beta (-(\omega_1+\omega_2); \omega_1, \omega_2)$$.

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 $$\beta(-\omega;\omega,0)$$.

\$ADFBIN/adf <<eor
title Damped EOPE of LiH, 2n+1
basis
Type SZ
core None
end
atoms
Li    0.00000000    0.00000000    3.49467000
H     0.00000000    0.00000000    1.89402300
end
symmetry nosym
allpoints
numericalquality good
aoresponse
scf  iterations 50
frequency 2 0.1000 0.0000 Hartree
beta
nosymmetry
eope
ALDA
end
end input
eor


In the second example the first hyperpolarizability is calculated with the subkey QUADRATIC, again for EOPE, the electro-optical Pockels effect $$\beta(-\omega;\omega,0)$$.

aoresponse
scf  iterations 50
frequency 2 0.1000 0.0000 Hartree
nosymmetry
eope
ALDA
end


For the static case $$\beta(0;0,0)$$ use the subkey STATIC

aoresponse
...
frequency 2 0.0000 0.0000 Hartree
static
end


For optical rectification $$\beta(0;\omega,-\omega)$$ use the subkey OPTICALR.

aoresponse
...
frequency 2 0.1000 -0.1000 Hartree
opticalr
end


For the second harmonic generation $$\beta(-2\omega;\omega,\omega)$$ use the subkey SHG

aoresponse
...
frequency 2 0.1000 0.1000 Hartree
shg
end


Or in the general case for $$\beta (-(\omega_1+\omega_2); \omega_1, \omega_2)$$ choose two input frequencies omega1 and omega2

aoresponse
...
frequency 2 omega1 omega2 Hartree
end