• Quadrupole splitting (in the case of nuclei with nuclear spin I > ½, the distribution of positive charge in the nucleus is not spherically symmetrical resulting
in quadrupole moment Q, which in turn results in the split of the nuclear energy
levels and hence the split of the corresponding absorption bands in the
Mössbauer spectrum);
• Magnetic hyperfine Zeeman splitting (when the atomic nucleus with spin I will
be subjected to the magnetic field, then each nuclear energy level splits into
2I + 1 levels).
The source of radiation in this method is a highly monochromatic gamma-ray
beam whose energy is changed using the Doppler effect: The sample is fixed and
the radiation source moves at a constant velocity toward or away from the sample,
and as a result, the energy of radiation incident on the sample increases or decreases
with respect to the primary energy of radiation. In this way, an absorption spectrum
of gamma radiation is created, the analysis of which allows obtaining information
about the local structure (oxidation state, coordination number, nature of binding,
etc.) and precisely measuring—due to a high energy and extremely narrow line
widths of c-rays—small energy changes in nuclei, atoms, and crystals induced by
electrical, magnetic, or gravitational field. The studies of hyperfine splitting,
especially as a function of temperature, allow additionally obtaining information on
the ordering of magnetic materials.
Theoretical studies on the above-mentioned spectroscopic methods are currently conducted in practice only with the help of methods based on the formalism of quantum mechanics. In practice, only in the case of vibrational
spectroscopy, it is possible to use classical methods (both stationary-molecular
mechanics and dynamical—molecular dynamics), in which atoms are treated as
charged particles, and their interactions are described by means of analytic two
and more center functions, the so-called interatomic potentials. It is then possible
to calculate the total potential energy of such a classical system, hence the forces
acting on individual atoms and their minimization (relaxation of the structure),
and then calculating (for the relaxed structure) the frequencies of normal modes
of vibrations and simulation of vibrational spectra. However, due to the lack of a
correct description of the electron density, such an approach does not allow to
analyze the processes dealt with by other spectroscopic methods mentioned
above, and therefore, in remaining parts of this chapter, classical methods will not
be further discussed.
1.2 Theoretical Foundations for Modeling of Real Systems
and Processes Studied by Spectroscopic Methods
The physical reality that surrounds us is extremely complex and impossible to be
accurately described using available physical theories. This applies in particular to
the micro-world and the structure and properties of materials of various sizes and
1 Computational Methods in Spectroscopy
5
in quadrupole moment Q, which in turn results in the split of the nuclear energy
levels and hence the split of the corresponding absorption bands in the
Mössbauer spectrum);
• Magnetic hyperfine Zeeman splitting (when the atomic nucleus with spin I will
be subjected to the magnetic field, then each nuclear energy level splits into
2I + 1 levels).
The source of radiation in this method is a highly monochromatic gamma-ray
beam whose energy is changed using the Doppler effect: The sample is fixed and
the radiation source moves at a constant velocity toward or away from the sample,
and as a result, the energy of radiation incident on the sample increases or decreases
with respect to the primary energy of radiation. In this way, an absorption spectrum
of gamma radiation is created, the analysis of which allows obtaining information
about the local structure (oxidation state, coordination number, nature of binding,
etc.) and precisely measuring—due to a high energy and extremely narrow line
widths of c-rays—small energy changes in nuclei, atoms, and crystals induced by
electrical, magnetic, or gravitational field. The studies of hyperfine splitting,
especially as a function of temperature, allow additionally obtaining information on
the ordering of magnetic materials.
Theoretical studies on the above-mentioned spectroscopic methods are currently conducted in practice only with the help of methods based on the formalism of quantum mechanics. In practice, only in the case of vibrational
spectroscopy, it is possible to use classical methods (both stationary-molecular
mechanics and dynamical—molecular dynamics), in which atoms are treated as
charged particles, and their interactions are described by means of analytic two
and more center functions, the so-called interatomic potentials. It is then possible
to calculate the total potential energy of such a classical system, hence the forces
acting on individual atoms and their minimization (relaxation of the structure),
and then calculating (for the relaxed structure) the frequencies of normal modes
of vibrations and simulation of vibrational spectra. However, due to the lack of a
correct description of the electron density, such an approach does not allow to
analyze the processes dealt with by other spectroscopic methods mentioned
above, and therefore, in remaining parts of this chapter, classical methods will not
be further discussed.
1.2 Theoretical Foundations for Modeling of Real Systems
and Processes Studied by Spectroscopic Methods
The physical reality that surrounds us is extremely complex and impossible to be
accurately described using available physical theories. This applies in particular to
the micro-world and the structure and properties of materials of various sizes and
1 Computational Methods in Spectroscopy
5