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
 lifetime 0.0034
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
 quadratic
 nosymmetry
 eope
 ALDA
 lifetime 0.0034
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