Mössbauer spectroscopy
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**Isomer shifts**

By default the electron density at the nuclei is calculated; no input
key is required. In the implementation in ADF, the electron density is
not calculated exactly at the center of the nucleus, however, at
points on a small sphere around the center of a nucleus. The printed
electron density in the output of ADF is the average electron density
on these points. The radius of the sphere is an approximated finite
nuclear radius. The electron density at the nuclei could be used for
the interpretation of isomer shifts in Mössbauer spectroscopy.
Typically one needs to perform a fit of the experimentally measured
isomer shifts and calculated electron densities, for example as done
in Ref. [1].

One should use all-electron basis sets for the Mössbauer active
elements. It is important to use the same basis set, same exchange-
correlation functional, same integration accuracy, and same nuclear
model (see key NUCLEARMODEL) if electron densities at nuclei in
different molecules are compared. Note that the absolute electron
density at a nucleus heavily depends on the accuracy of the basis set
in the core region of this nucleus, especially if relativistic effects
are included.

In case of ZORA the electron density at the nuclei is calculated with
the ZORA-4 method, which includes a small component density.
Previously it was using the ZORA density, which does not include a
small component density. If you also want to calculate this ZORA
density at the nuclei, include the keywords:

   PRINT FWPICTURE

Instead of SAPA (the Sum of neutral Atomic potential Approximation)
MAPA is used by default for ZORA in ADF2017. The MAPA (the Minimum of
neutral Atomic potential Approximation) at a point is the minimum of
the neutral atomic potentials at that point. The advantage of MAPA
over SAPA is that the gauge dependence of ZORA is reduced. The ZORA
gauge dependency is small for almost all properties, except for the
electron density very close to a heavy nucleus.

A ZORA calculation gives a too large density at the nucleus compared
to a relativistic Dirac calculation, mostly due to the 1s-orbital. If
one performs a fit of the experimentally measured isomer shifts
against calculated electron densities, the fact that the ZORA electron
density is too large is not so important. If an absolute value of the
electron density at the nucleus is important one may use the
relativistic X2C method; see key RELATIVITY. Note that one then needs
large basis sets with tight STO 1s-functions to get accurate results
(for example the basis sets in the TZ2P-J or QZ4P-J directory).

**Quadrupole splittings**

For the calculation of Mössbauer quadrupole splittings see the key
QTENS.

**Nuclear resonance vibrational spectroscopy (NRVS)**

The nuclear resonance vibrational spectroscopy (NRVS) experiment can
be thought of as Mössbauer spectroscopy with vibrational sidebands.
The NRVS experiment provides the complete set of bands corresponding
to modes that involve motion of the Mössbauer active atoms. In order
to calculate this with the ADF program a partial vibrational density
of states (PVDOS) has been implemented. A PVDOS factor for a given
atom is the ratio of this atom's nuclear kinetic (vibrational) energy
to the total vibrational energy of all nuclei, for a given mode. PVDOS
factors for every atom and every mode are written to adf.rkf if IR
Frequencies are calculated. To visualize the calculated PVDOS with the
AMS-GUI use AMSspectra: select the PVDOS spectrum type. Next select
one or more atoms to get the PVDOS spectrum generated by the selected
atoms. This is useful for analysis of NRVS spectra in bioinorganic
chemistry for NRVS-active nuclei.

[1] W.-G. Han, T. Liu, T. Lovell and L. Noodleman, *DFT calculations
    of* ^57Fe *Mössbauer isomer shifts and quadrupole splittings for
    iron complexes in polar dielectric media: Applications to methane
    monooxygenase and ribonucleotide reductase*, Journal of
    Computational Chemistry 27, 1292 (2006)
