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