I was asked by a collaborator if I could calculate the second order susceptibility tensor for a structure. I have been principally using Vasp which includes linear response and hence the first order susceptibility, but does not directly calculate the second order susceptibility. Is anyone aware of an external code that interfaces with Vasp to calculate the 2nd order NLO 𝛘2? If you are not aware of a code that works with Vasp, how about other DFT codes? The structure is periodic and has a total of 64 atoms in the unit cell.

  • $\begingroup$ Take a look at this post at ResearchGate. Is that what you are looking for? $\endgroup$
    – Camps
    Jul 2, 2023 at 16:38

1 Answer 1


The second order susceptibility tensor can be written as the fourier transform of the correlation between the dipole moment (over time) and the polarizability (over time). This is for Sum-Frequency Generation, although SHG is probably similar .

So just calculate those for your system over say 50 ps with a step size of maybe .5 fs.

  • $\begingroup$ analogous to how you can get IR (first order susceptibility) from the fourier transform of the autocorrelation of the dipole moment $\endgroup$
    – Peter Yang
    Jul 12, 2023 at 18:44

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