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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | This is an example in which the Born effective charge for Pb in perovskite
PbTiO3 is calculated.
1) make a self-consistent calculation for a cubic structure of PbTiO3 in
which the Pb atom has been displaced a small distance 0.01*a0 in the z
axis (a0 is the lattice constant, 7.3699 bohr).
(input=chg.in, output=chg.out)
2) make a non-self-consistent calculation to compute the polarization
(lberry=.true. in the input file 'BP.in'). In the ouput file 'BP.out'
we find that the polarization (P) multiplied by the volume of the unit
cell (Omega) is:
Omega * P = 0.2884752 e.bohr
while the distance the Pb atom has been displaced from the perfect cubic cell
structure is
r - r0 = 0.01 * 7.3699 bohr = 0.073699 bohr.
Given that the Born effective charge is defined as
dP
z* = Omega ----
dr
we can use a finite differences approximation to get
0.2884752 e.bohr
z* = ------------------ = 3.91 e
0.073699 bohr
in good agreement with published results. For example, in Zhong, King-Smith
and Vanderbilt, PRL 72, 3618 (1994) the value found is 3.90 e.
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