[Pw_forum] Method of computing static dielectric constant of materials

[Rajan Pandey]

Dear Quantum Espresso community,

I am trying to compute the static dielectric constant of materials using the
methodology
as implemented in CP code (part of the Quantum Espresso). The method is
explained
in the example30 of Quantum Espresso distribution. The system discussed is
MgO,
Ref: P.Umari and A.Pasquarello, Physical Review Letters, 89, p.157602
(2002).

The example30 mentioned above has following note:

"NOTE: the electronic dipole is defined modulo a factor (2*L=31.824i a.u.,
during the MD simulation the term "ln det S" changes the Riemann
plane, this must be taken into account when addressing the
electronic dipole."

The above statement is given in the context of a cubic supercell with length
L containing 64 atoms of MgO.

I am studying a well known system, SiO2 (alpha quartz) for sanity check. I
am simulating SiO2 in a 1x1x2
trigonal supercell (18 atoms) as well as in an orthorhombic (in alpha quartz
case it will be tetragonal because a = b )
supercell. The ambiguity is that when I use the formula along with the
"NOTE" of example30 in Quantum Espresso,
mentioned above, I get wrong results for static dielectric constant.
However, when I do not use the
"NOTE" mentioned above, and by using the formula described in example30, I
get the simulated value close
to the experimental static dielectric constant of SiO2. This means that the
method works for non-cubic unit cells too.
I am not able to understand the role of the point mentioned in the NOTE
(above) in general, when the formula described
in example30 (reiterated below), seems to work.

The difference d_Eps  between static and high-frequency dielectric constant
is given by:

d_Eps=4*pi*(D2_el + D2_ion - D1_el - d1_ion)/(0.001 a.u. * Omega)

D1(2)_el = electronic contribution of the dipole at the beginning (end) of
the relaxation.
D1(2)_ion = ionic contribution of the dipole at the beginning (end) of the
relaxation.
Omega = supercell volume

I shall appreciate any comments from community members.

Thanks, and regards,

Rajan
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