The purpose of this lesson is to show how to compute several observables of interest in Moessbauer, NMR, and NQR spectroscopy, namely:
This lesson should take about 1 hour.
Before beginning, you might consider working in a different subdirectory than the other tutorials, for example "work_nuc".
Various spectroscopies, including nuclear magnetic resonance and nuclear quadrupole resonance (NMR and NQR), as well as Moessbauer spectroscopy, show spectral features arising from the electric field gradient at the nuclear sites. Note that the electric field gradient (EFG) considered here arises from the distribution of charge within the solid, not due to any external electric fields.
The way that the EFG is observed in spectroscopic experiments is through its coupling
to the nuclear electric quadrupole moment. The physics of this coupling is described in
various texts, for example
The electric field and its gradient at each nuclear site arises from the distribution of
charge, both electronic and ionic, in the solid. The gradient especially is quite sensitive
to the details of the distribution at short range, and so it is necessary to use the PAW
formalism to compute the gradient accurately. The various sources of charge in the
PAW decomposition are summarized in the following equation:

Here the "v" subscript indicates valence, "c" indicates core, and "Z" indicates the ions.
Essentially the gradient must be computed for each source of charge, which is
done in the code as follows:
The electric field gradient computation is performed at the end of a ground-state calculation, and takes almost no additional time. The tutorial file is for stishovite, a polymorph of SiO2. In addition to typical ground state variables, only two additional variables are added:
prtefg 2
quadmom 0.0 -0.02558
The first variable instructs Abinit to compute and print the electric field gradient, and
the second gives the quadrupole moments of the nuclei, one for each type of atom. Here we
are considering silicon and oxygen, and in particular Si-29, which as zero quadrupole moment,
and O-17, the only stable isotope of oxygen with a non-zero quadrupole moment.
After running the file tnuc_1.in through abinit, you can find the following near the end of the output file:
Electric Field Gradient Calculation
Atom 1, typat 1: Cq = 0.000000 MHz eta = 0.000000
efg eigval : -0.165960
- eigvec : -0.000001 -0.000001 -1.000000
efg eigval : -0.042510
- eigvec : 0.707107 -0.707107 0.000000
efg eigval : 0.208470
- eigvec : 0.707107 0.707107 -0.000002
total efg : 0.082980 0.125490 -0.000000
total efg : 0.125490 0.082980 -0.000000
total efg : -0.000000 -0.000000 -0.165960
This fragment gives the gradient at the first atom, which was silicon. Note that
the gradient is not zero, but the coupling is---that's because the quadrupole moment
of Si-29 is zero, so although there's a gradient there's nothing in the nucleus for
it to couple to.
Atom 2 is an oxygen atom, and its entry in the output is:
Atom 2, typat 2: Cq = 6.603688 MHz eta = 0.140953
efg eigval : -1.098710
- eigvec : -0.707107 0.707107 0.000000
efg eigval : 0.471922
- eigvec : -0.000270 -0.000270 1.000000
efg eigval : 0.626789
- eigvec : 0.707107 0.707107 0.000382
total efg : -0.235961 0.862750 0.000042
total efg : 0.862750 -0.235961 0.000042
total efg : 0.000042 0.000042 0.471922
efg_el : -0.044260 -0.065290 0.000042
efg_el : -0.065290 -0.044260 0.000042
efg_el : 0.000042 0.000042 0.088520
efg_ion : -0.017255 0.306132 -0.000000
efg_ion : 0.306132 -0.017255 -0.000000
efg_ion : -0.000000 -0.000000 0.034509
efg_paw : -0.174446 0.621908 0.000000
efg_paw : 0.621908 -0.174446 0.000000
efg_paw : 0.000000 0.000000 0.348892
Now we see the electric field gradient coupling, in frequency
units, along with the asymmetry of the coupling tensor, and,
finally, the three contributions to the total. Note that the
valence part, efg_el, is quite small, while the ionic part and
the on-site PAW part are larger. In fact, the PAW part is largest--this
is why these calculations give very poor results with norm-conserving
pseudopotentials, and need the full accuracy of PAW.