[Pw_forum] Details on "third order derivatives not implemented with GGA" error

[Paolo Giannozzi]

Brad Malone wrote:

> Is this third derivative the third derivative that is mentioned 
> in the routine PH/raman_mat.f90 (i.e, the third derivative of the 
> energy with respect to the atomic displacements and with respect to
> two electric fields, as described in Lazzeri and Mauri, PRL 90,036401)?

no, it is
$$
{\delta^3 E_{xc}([n]) \over \delta n({\bf r})\delta n({\bf r}')\delta
  n({\bf r}'')} = {\delta^2 V_{xc}(n({\bf r})) \over \delta n({\bf 
r}')\delta n({\bf r}'')}

$$
> I am interested in getting a feel for what would be needed to
> implement the third derivatives with GGA into the code

a sizable amount of algebra and some coding. See PH/setup_dgc.f90
and PH/dgradcorr.f90 for derivatives of the XC functional

P.
-- 
Paolo Giannozzi, Democritos and University of Udine, Italy