# [Pw_forum] about the feasibility of second order coefficient of Nonlinear Optical within PWSCF

Paolo Giannozzi giannozz at nest.sns.it
Mon Feb 18 23:02:08 CET 2008

On Feb 18, 2008, at 14:08 , xu yuehua wrote:

> i am writing to enquire that is there a way to get the second order
> coefficient of Nonlinear Optical within PWSCF, directly or indirectly.

second-order nonlinear optical coefficients, i.e. \gamma in the
following formula, where P is the induced polarization and E the
electric field: P=\alpha E + \beta E^2 + \gamma E^3 ? this is
the fourth-order derivative of the energy wrt electric field and
can be calculated using the second-order response to an
applied electric field. The latter is calculated by the phonon
code for the Raman calculation. The code already calculates
the nonlinear optical coefficient \beta (called "electro-optical
coefficients": I do not think this is correct, by the way). Static
calculations, though (\omega=0), and no ultrasoft PP. So all
ingredients are there, but require some programming. It is
something that I wanted to do (and still want to do: it is useful
to estimate how nonlinear optical properties change in phtalocyanines
when deposited on some surfaces and doped), but it requires an
amount of patience that I am afraid I no longer have. Anybody
interested?

Paolo
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Paolo Giannozzi, Dept of Physics, University of Udine
via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222