mirror of https://github.com/abinit/abinit.git
119 lines
6.1 KiB
Markdown
119 lines
6.1 KiB
Markdown
---
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description: How to calculate electric fields gradients and Mossbauer Fermi contact interaction
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authors: JZ
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to calculate electric fields gradients
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and Mossbauer Fermi contact interaction with the ABINIT package.
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## Introduction
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Because the PAW formalism provides a robust way to reconstruct the
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all-electron wavefunctions in the valence space, it is suitable for
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computing expectation values of observables localized even very close
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to the nuclei. Obtaining equivalent accuracy within the
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norm-conserving pseudopotential framework would require very small
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atomic radii for the pseudization procedure, and concomitantly high
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planewave cutoff energies and lengthy calculations. There remains the
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question of whether even all-electron accuracy in the valence space is
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sufficient for accurate representation of observables close to the
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nuclei, where conventional wisdom would suggest that deep core
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polarizations might be quite significant for properties such as the
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electric field gradient or Fermi contact interaction. Such concerns
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turn out to be unwarranted, however, as our experience and others have
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shown that the PAW formalism together with a typical chemical
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valence/core separation are sufficient for accurate description of
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nuclear point properties such as the electric field gradient
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[[cite:Petrilli1998]], [[cite:Profeta2003]], [[cite:Zwanziger2008]],
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Fermi contact interaction [[cite:Zwanziger2009]] and magnetic chemical
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shielding [[cite:Pickard2001]], [[cite:Zwanziger2023]].
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Both the electric field gradient and Fermi contact interaction are ground-
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state observables, and their computation adds negligible time to a normal
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self-consistent ground state calculation. The total charge density in the PAW
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formalism contains the pseudovalence density, the nuclear ionic charges, and
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the all-electron and pseudo charge densities within the PAW spheres. As done
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in earlier work, the electric field gradient due to the pseudovalence density
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is computed in reciprocal space, and the gradient due to the (fixed) ionic
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charges is computed with an Ewald sum approach. The PAW sphere charge
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densities contribute matrix elements of
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$(3x_\alpha x_\beta -r^2\delta_{\alpha\beta})/r^5$, weighted by the
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charge densities in each channel determined by the self-consistent
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minimization procedure. This treatment [[cite:Zwanziger2008]] is more flexible
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than for example assuming all bands are doubly occupied, and permits the
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current approach to be used with more complex electronic and magnetic states
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than just insulators.
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Within ABINIT, the electric field gradient computation is invoked with
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the key word [[nucefg]] (for NUClear site EFG), optionally together
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with the key word [[quadmom]], at the end of a normal ground state
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calculation. The PAW formalism is required, and the EFG calculation
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adds only a negligible amount of time to the total. The [[nucefg]] key
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word takes the values 1--3. For value 1, the electric field gradient
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in atomic units and SI units (V/m$^2$) is reported, along with the
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eigenvectors showing its orientation in the crystal, and the
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contributions of the planewave density, the PAW on-site terms, and the
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ionic contributions. When [[nucefg]] is input as 2, the electric field
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gradient coupling in MHz and the asymmetry are also reported, where
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the conversion is made for each atom by combining the gradient with
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the nuclear quadrupole moments supplied by [[quadmom]].
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Finally, [[nucefg]] input as 3 allows additional computation of
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a point-charge model of the gradient, for comparison purposes. The
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point charges by atom are supplied through the additional variable
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[[ptcharge]]. Detailed examples of the use of ABINIT to compute EFG's
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can be found in [[cite:Zwanziger2008]], [[cite:Zwanziger2009a]].
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The Fermi contact interaction, which is just the electron density evaluated
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precisely at the nuclear location, is an important component of the isomer
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shift measured in Moessbauer spectroscopy. The isomer shift is directly
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proportional to
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$n_{\mathrm{abs}}(\mathbf{R})-n_{\mathrm{src}}(\mathbf{R})$,
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the difference in electron
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density at the absorber (the sample) and the source. Evaluating the density at a
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nuclear position can be accomplished by treating
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$\delta(\mathbf{r}-\mathbf{R})$ as the
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observable, that is, the three-dimensional Dirac delta function centered on
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the nuclear position $\mathbf{R}$. Because of the short-range nature of the delta
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function, in the PAW-transformed version of the observable only matrix
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elements of the on-site all-electron valence functions are required
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[[cite:Zwanziger2009]], and these are evaluated from a linear fit to the first
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few points of the PAW radial functions.
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Within ABINIT the Fermi contact interaction is invoked by setting the key word
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[[nucfc]] (for NUClear site Fermi Contact) to the value 1. When
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called, the electron density at each nuclear position is reported, in atomic
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units (electrons per cubic Bohr). The isomer shift as measured in Moessbauer
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spectroscopy is typically reported in velocity units and is obtained from the
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formula
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$$\delta = (2\pi cZe^2E_\gamma /3) [n_{\mathrm{abs}}(\mathbf{R})-n_{\mathrm{src}}(\mathbf{R})]\Delta\langle r^2\rangle$$
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where $c$ is the speed of light, $E_\gamma$ the $\gamma$-ray energy,
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$Z$ the atomic number, $e$ the
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electron charge, and $\Delta\langle r^2\rangle$ the change in the
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mean square nuclear radius for
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the transition. The electronic densities
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$n_{\mathrm{abs}}$ and $n_{\mathrm{src}}$ refer to the absorber
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and source respectively. Because of the linearity of this formula in the
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density at the absorber (sample) nucleus, the only unknown
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($\Delta\langle r^2\rangle$) can be
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obtained by comparing the calculated values in several standards to experiment
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and then the computations can be used to interpret the measurements of new
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materials. In [[cite:Zwanziger2009]] it is shown how to perform such studies
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on a variety of compounds.
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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## Tutorials
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* [[tutorial:nuc|The tutorial on the properties of the nuclei]] shows how to compute the electric field gradient and Mossbauer Fermi contact interaction. Prerequisite: PAW1.
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