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<html>
<head>
<title>Tutorial "Properties at the nuclei"</title>
</head>
<body bgcolor="#ffffff">
<hr>
<h1>ABINIT, lesson "Properties at the nuclei": </h1>
<h2>Observables near the atomic nuclei </h2>
<hr>
<p>The purpose of this lesson is to show how to compute several
observables of interest in Moessbauer, NMR, and NQR spectroscopy,
namely:
<ul>
<li>the electric field gradient,
<li>the isomer shift,
<li>and the electronic density itself.
</ul>
<p>This lesson should take about 1 hour.
<h5>Copyright (C) 2000-2014 ABINIT group (JWZ,XG)
<br> This file is distributed under the terms of the GNU General Public License, see
~abinit/COPYING or <a href="http://www.gnu.org/copyleft/gpl.txt">
http://www.gnu.org/copyleft/gpl.txt </a>.
<br> For the initials of contributors, see ~abinit/doc/developers/contributors.txt .
</h5>
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<br>
<h3><b>Contents</b></h3>
<ul>
<li><a href="lesson_nuc.html#efg">1.</a>
Electric field gradient
<li><a href="lesson_nuc.html#isomer">2.</a>
Moessbauer isomer shift
<li><a href="lesson_nuc.html#density">3.</a>
Electronic density
</ul>
<p><i>Before beginning, you might consider working in a different
subdirectory than the other tutorials, for example "work_nuc".
</i>
<hr>
<a name="efg"> </a>
<h3><b>
1.
Computing the electric field gradient at the
nuclear positions.
</b></h3>
<p>
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.
<p>
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 <it>Principles of Magnetic Resonance, 3rd ed.</it>, C. P.
Slichter (Springer, New York, 1989). ABINIT computes the field gradient at each site,
and then reports the gradient and its coupling based on input values of the nuclear
quadrupole moments.
<p>
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:
<br>
<img src="lesson_nuc/charge.gif" align="left" width=450><br>
<p>
<br>
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:
<ul>
<li>Valence space described by planewaves: expression for gradient is Fourier-transformed
at each nuclear site.
<li>Ion cores: gradient is computed by an Ewald sum method
<li>On-site PAW contributions: moments of densities are integrated in real space around
each atom, weighted by the gradient operator
</ul>
The code reports each contribution separately if requested.
<p>
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 SiO<sub>2</sub>. In addition to typical ground state variables, only
two additional variables are added:
<pre>
prtefg 2
quadmom 0.0 -0.02558
</pre>
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.
<p>
After running the file tnuc_1.in through abinit, you can find the following near the
end of the output file:
<pre>
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
</pre>
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.
<p>
Atom 2 is an oxygen atom, and its entry in the output is:
<pre>
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
</pre>
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.
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