# Mössbauer spectroscopy¶

**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, like, for example, is done in Ref. 1.

One should use all electron basis sets for the Mössbauer active elements. Important is 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 Atomical potential Approximation) MAPA is used by default for ZORA in ADF2017. The MAPA (the Minumium of neutral Atomical potential Approximation) at a point is the minimum of the neutral Atomical potentials at that point. 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 Mösbauer 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 nucleus 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 use the AMSspectrum program: 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.

References

- 1
W.-G. Han, T. Liu, T. Lovell and L. Noodleman,

*DFT calculations of*^{57}Fe*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)