# Example: damped second hyperpolarizability: LiH¶

Download LiH_DampedGamma.run

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 $$\gamma(-2 \omega;\omega,\omega,0)$$, the third harmonic generation $$\gamma(-3 \omega;\omega,\omega,\omega)$$ use the subkey THG, or the general case $$\gamma(-(\omega_1+\omega_2+\omega_3); \omega_1, \omega_2, \omega_3)$$.

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

\$ADFBIN/adf <<eor
title Damped EFIOR 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 3 0.1000 -0.1000 0.0000 Hartree
gamma
nosymmetry
efior
ALDA
lifetime 0.0034
end
end input
eor


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

aoresponse
scf iterations 50
frequency 3 0.1000 -0.1000 0.0000 Hartree
cubic
nosymmetry
efior
ALDA
lifetime 0.0034
end


In the third example the subkeyword TPA is be used to calculate the $$\gamma$$ 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.

aoresponse
scf iterations 50
frequency 3 0.1000 0.1000 -0.1000 Hartree
gamma
nosymmetry
tpa
ALDA
lifetime 0.0034
end


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

aoresponse
...
frequency 3 0.0000 0.0000 0.0000 Hartree
static
end


For the optical Kerr effect $$\gamma(-\omega;\omega,0,0)$$ use the subkey OKE

aoresponse
...
frequency 3 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
...
frequency 3 0.1000 0.1000 -0.1000 Hartree
idri
end


For the electric field induced second harmonic generation $$\gamma(-2 \omega;\omega,\omega,0)$$ use the subkey EFISHG

aoresponse
...
frequency 3 0.1000 0.1000 0.0000 Hartree
efishg
end


For the third harmonic generation $$\gamma(-3 \omega;\omega,\omega,\omega)$$ use the subkey THG

aoresponse
...
frequency 3 0.1000 0.1000 0.1000 Hartree
thg
end


Or in the general case for $$\gamma(-(\omega_1+\omega_2+\omega_3); \omega_1, \omega_2, \omega_3)$$ choose three input frequencies omega1, omega2, and omega3

aoresponse
...
frequency 3 omega1 omega2 omega3 Hartree
end