University of Groningen
First principles theoretical modeling of the isomer shift of Mossbauer spectraKurian, Reshmi
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Chapter 1
Introduction and Objective
Synopsis
The basic ideas behind Mossbauer Spectroscopic technique is outlined in the
present chapter. The recoilless emission and absorption of γ-rays, which is
the key feature of this spectroscopy is explained with illustrations. The un-
derstanding of the electronic structure of the compounds under study, from
the Mossbauer spectra parameters are discussed in detail. The chapter also
includes the objective and scope of this dissertation.
1.1 Introduction
Fifty years ago Rudolf L. Mossbauer discovered the recoilless nu-
clear resonance absorption of γ-rays while working on his doc-
toral thesis. This phenomenon, which rapidly developed into a new
spectroscopic technique is known as Mossbauer effect [1–4]. Over
the last couple of decades, Mossbauer spectroscopy has become one
of the most captivating tools in chemical physics providing informa-
tion about the chemical environment of the resonating nucleus on an
atomic scale [1–4]. The most well-known application is the determi-
nation of iron 57Fe in crystalline and in disordered solid samples. Be-
sides iron, there are many elements in the periodic table which have
4 1. Introduction and Objective
Mossbauer active nuclei [5–8]. The Mossbauer effect has been ob-
served for the elements which are dotted in the periodic table shown
(Figure 1.1).
Figure 1.1: The periodic table showing the Mossbauer active nuclei, thedotted elements.
The phenomenon of recoilless resonance absorption/emission of
γ-rays by nuclei is the basic characteristic of Mossbauer Spectoscopy
[5, 9]. When a nucleus in an excited state of energy Ee undergoes a
transition to the ground state with energy Eg by emitting a γ quan-
tum, E0 = Ee - Eg, the γ quantum energy E0 may be totally absorbed
by a nucleus of the same kind in its ground state. This phenomenon is
called nuclear resonance absorption of γ-rays and is shown schemati-
cally in Figure 1.2. The resonance absorption is observable only if the
emission and absorption lines overlap sufficiently. The mean lifetime
of the excited state τN , determines the width of the resonance lines
(Γ) according to time-energy uncertainity relation, Γ.τN ≥ ~. There-
1.1. Introduction 5
fore, longer lifetimes produce too narrow transition lines and shorter
lifetimes produce too broad transition lines, and the resonance over-
lap between the emission and absorber lines is not possible. The suit-
able lifetimes of the excited nuclear states for the resonance absorption
range from 10−6 to 10−11s. The spectral line shape may be described
by the Lorentzian or Breit-Wigner form [5,9]. For the 14.4 keV level of57Fe, the natural line width Γ is determined using the mean life time τ
= t1/2ln2
= 1.43×10−7 s , which is Γ = ~/2π = 4.55 × 10−9eV.
Figure 1.2: Schematic representation of nuclear resonance absorption of γ-rays.
When a γ-ray is emitted from an excited nucleus of mass M, there
occurs a recoil of the nucleus according to which the nucleus moves
with velocity v in the opposite direction of γ-ray emission. According
to the conservation of momentum, the linear momenta of the nucleus
and the γ quantum are equal and the energy of the emitted γ quantum
are reduced as, Eγ = E0 - ER. The recoil energy can be written as,
ER =p2
2M=
E2γ
2Mc2(1.1)
The range of transition energies Eγ for the occurrence of resonance
absorption is 5-180 keV. However, the difficulties of high-energy nu-
clear transitions can get around by the use of synchrotron radiation
1.2. Applications of Mossbauer Spectroscopy 15
Figure 1.8: The Magnetic Splitting of the nuclear energy levels and corre-sponding Mossbauer spectrum.
in a molecule, study the magnetic ordering, etc.
1.2 Applications of Mossbauer Spectroscopy
The fields of applications of Mossbauer spectroscopy includes solid-
state physics / chemistry, bio-chemistry / physics, catalysis, nano-
science, materials science, metallurgy etc. This technique has even
become established for the planetary exploration on the surface of
Mars, the presence of water on Mars is confirmed by Mossbauer spec-
troscopy [15]. Even though there are numerous studies on Mossbauer
active nuclei like Sn, Au, Hg, I, etc., the best studied Mossbauer active
nucleus is 57Fe and we will survey a few applications of Mossbauer
spectroscopy to this element. For a complete review of applications of
6 1. Introduction and Objective
sources [10]. For the Mossbauer transition of 57Fe from the excited to
the ground state (E0 = Ee - Eg = 14.4 keV), the recoil energy ER is eval-
uated to be 1.95 × 10−3 eV according to Eqn. 1.1. This value is about
six orders of magnitude larger than the natural width of the spectral
transition under consideration (Γ = 4.55 × 10−9 eV). Figure 1.3 shows
intensity I(E) as a function of the transition energy for emission and
absorption of γ transition. The recoil effect reduces the transition en-
ergy by ER for the emission process and increases the transition en-
ergy by ER for the absorption process. Therefore, the transition lines
for the emission and absorption are separated by a distance 2ER on the
energy scale as shown in Figure 1.3, which is about 10−6 times larger
than the natural line width Γ. Hence, the overlap between two transi-
tion lines and nuclear resonance absorption is not possible in isolated
atoms or molecules in the gaseous or liquid state.
If the γ-ray emission takes place while both the emitter and absorber
Figure 1.3: The transition lines for emission and absorption in an isolatednuclei, which is separated by 2ER.
nucleus are moving relative to each other, then the γ-photon of energy
Eγ receives a Doppler energy ED, ie, Eγ = E0 - ER + ED. For 57Fe, mov-
1.1. Introduction 7
ing the source at a velocity of 1mm/s towards the sample increases the
energy of the emitted photons by about ten natural line widths. Thus,
the Doppler shift of the emission and absorption lines allows for the
fine tuning of the resonances in Mossbauer experiments [5,9]. The rel-
ativistic Doppler formula for an emitter and absorber with a relative
velocity of υ is,
v = v0
√
1− υ/c
1 + υ/c(1.2)
where c is the speed of light. Expanding Eqn 1.2 into Taylor series
gives the velocity shift, i.e.,
v = v0
(
1− υ/c+1
2υ2/c2 − .......
)
(1.3)
where the first order part vanishes because of the random nuclear dis-
placements and the second order term remains. However, the second
order Doppler shift is quite small, as an example, 0.07 mm/s for 57Fe
for a decrease of 100 K [11].
Figure 1.4: Recoil-free emission or absorption of γ-rays when the nuclei arein solid matrix.
Rudolf L. Mossbauer observed that the recoilless emission and ab-
sorption of γ rays is possible if nuclei are embedded into a solid envi-
ronment (like shown in Figure 1.4) and the transition lines can over-
lap, thus resulting in the resonance absorption. This can be explained
from the classical point of view, when the γ-ray is emitted by a nu-
cleus bound in a lattice, the entire crystal lattice will absorb the recoil.
8 1. Introduction and Objective
In this case, the mass M in the denominator of Eqn. 1.1 should be the
mass of the whole crystal, not the individual nucleus. This reduces
the recoil energy to a negligible amount. Therefore, Eγ = E0 and the
entire process becomes a recoilless resonant absorption [5, 9].
Figure 1.5: Energy levels separated by ~ω of a Debye solid.
The quantum mechanical description of the recoil effect is some-
what more complicated. Of course, the lattice vibrations are quan-
tised and the energy can be absorbed or emitted by the crystal lattice
in quanta of certain energy (phonons). For a Debye solid with one vi-
brational frequency ω, the lattice can only receive or release energies
in integral multiples of ~ω. The energy distribution defined by the
population of the levels spaced by ~ω is shown schematically in Fig-
ure 1.5. If ER <~ω, the lattice cannot absorb the recoil energy, i.e., the
zero phonon process occurs, and the γ-ray is emitted without a recoil.
It suggests that there must be zero-phonon transitions ie, emission
process without excitation of phonons in the lattice. There is a cer-
tain probability f (known as Debye-Waller factor or Lamb-Mossbauer
factor) that no lattice excitation (zero-phonon processes) takes place
during γ-emission or absorption whereas f denotes the fraction of nu-
clear transitions which occur without recoil and only for this fraction
1.1. Introduction 9
is the Mossbauer effect observable. This recoil-free fraction can be ex-
pressed as, f = exp (-ER/~ω). Within the Debye model for solids, f
increases with the decreasing transition energy Eγ , with decreasing
temperature, and with increasing Debye temperature θ. Thus, θ is a
measure of the strength of the bond between the Mossbauer atom and
the lattice.
Figure 1.6: The partial overlap of emission and absorption lines due to thedifferent electron-nuclear interactions in the source and absorber.
The recoilless resonant absorption is necessary for the maximum
overlap of the emission line and absorption line. In-order to make the
nuclear resonance absorption of γ-rays successful, the emission and
absorption lines should coincide or at least partially overlap. How-
ever, the complete overlap between the emission and absorption lines
is possible only if identical materials are used as source and absorber.
If the source and the absorber nuclei are in different chemical environ-
ment, which is usually the case, they have slightly different absorp-
tion/emission frequencies due to the interactions with the surround-
ing electrons [5, 9]. This is schematically shown in Figure 1.6, where
the partial overlap of the absorption and emission lines is because of
the different electron nuclear interactions in the absorber and emit-
ter. Because the Mossbauer lines are very sharp, even small energy
10 1. Introduction and Objective
differences will destroy the resonance. However, with the use of the
Doppler effect, ie, by moving the source and absorber relative to each
other, the perfect overlap can be obtained. For 57Fe, Doppler veloci-
ties up to a few mm/s are sufficient to achieve good overlap between
the emission and absorption lines. A Mossbauer spectrum, which is a
plot of the relative transmission of the gamma radiation as a function
of the Doppler velocity, reflects the nature and strength of the hyper-
fine interactions between the Mossbauer nucleus and the surrounding
electrons. The Mossbauer effect makes it possible to resolve the hyper-
fine interactions and provide information on the electronic structure.
The three main hyperfine interactions corresponding to the nuclear
moments are,
1) Isomer Shift
2) Quadrupole Splitting
3) Magnetic Hyperfine Splitting
1.1.1 Isomer Shift
Mossbauer Isomer Shift (MIS) is defined as a displacement of the fre-
quency of the nuclear γ-transition in the target (absorber) nucleus ∆Eaγ
with respect to the reference (source) nucleus ∆Esγ [5,6,12]. The varia-
tion of the nuclear volume, ie, the nuclear charge radius, during the γ
transition is responsible for the occurrence of Mossbauer isomer shift,
because the atomic nucleus is not a point-like object but an object of
a finite spatial extent. The different nuclear charge radius in the ex-
cited and ground state induce different electron-nuclear interactions
therein, hence the frequency of the γ transition in the nucleus im-
mersed in a specific electronic environment is different than in the
bare nucleus. In a Mossbauer experiment one measures the change
1.1. Introduction 11
of the energy of the resonance γ quantum between the source (s) and
the absorber (a) nuclei, thus there appears a dependence of the en-
ergy of resonance γ quantum on the electronic environment in which
the given nucleus is immersed. The MIS, δ measured in terms of the
Doppler velocity necessary to achieve resonance is given in Eqn. 1.4,
δ =c
Eγ
(∆Eaγ −∆Es
γ) (1.4)
where c is the velocity of light and Eγ is the energy of the γ quantum.
Figure 1.7: The isomer Shift and Quadrupole Splitting of the nuclear energylevels and corresponding Mossbauer spectra.
This shift appears in the spectrum as the difference between the
position of the baricenter of the resonance signal and zero Doppler
velocity as shown in Figure 1.7 [5, 6, 12]. Traditionally, the energy dif-
ferences ∆Ea/sγ are calculated within the framework of perturbation
12 1. Introduction and Objective
theory, whereby the variation of the electron-nuclear interaction po-
tential during the γ-transition is treated as a weak perturbation of the
nuclear energy levels [5, 6, 12–14]. This approach leads to the well
known expression for the isomer shift of Mossbauer spectra as a lin-
ear function of the so-called contact electron density (electron density
at the nucleus) in the absorber ρae and source ρse compounds, see Eqn.
1.5,
δ = α(ρ(a) − ρ(s)) (1.5)
where α is a calibration constant, which depends on the parameters
of the nuclear γ-transition. The most valuable information derived
from isomer shift data refers to the oxidation state and spin state of a
Mossbauer-active atom, its bond properties etc.
1.1.2 Quadrupole splitting
Quadrupole splitting in the Mossbauer spectrum occurs when a nu-
cleus with an electric quadrupole moment experiences a non-uniform
electric field [5, 9]. The nuclear charge distribution deviates from the
spherical symmetry for a nucleus that has spin quantum number I >
1/2 and thus has a non zero electric quadrupole moment. The mag-
nitude of the quadrupole moment may change in going from one
state of excitation to another. The sign of the electric quadrupole
moment, Q indicates the shape of the deformation. Q is negative
for a flattened (pancake-shaped) nucleus and positive for an elon-
gated nucleus (cigar-shaped). Q is constant for a given Mossbauer
nucleus, ie, changes in the quadrupole interaction energy observed
in different compounds of a given Mossbauer nuclide under constant
experimental conditions can only arise from the changes in the elec-
tric field gradient (EFG) generated by the surrounding electrons and
1.1. Introduction 13
other nuclei. Therefore, the interpretation of quadrupole splittings
requires the knowledge of the EFG. The interaction between the elec-
tric quadrupole moment of the nucleus and EFG at the nuclear po-
sition give rise to a splitting in the nuclear energy levels into sub
states, which are characterised by the absolute magnitude of the nu-
clear magnetic spin quantum number |mI |.
As the Mossbauer spectroscopy involves the absorption of the γ-
rays to promote a nucleus from the ground state to an excited state,
the quadrupole Hamiltonian has to be solved for each energy level if
both levels have nuclear spin greater than 1/2. For 57Fe, the ground
state has nuclear spin I = 1/2 and the lowest excited state has I = 3/2.
The second part of Figure 1.7 shows the quadrupole splitting of the
nuclear energy levels of 57Fe, where the absorption line is split due to
the interaction of the nuclear quadrupole moment with non-zero EFG
at the nucleus. The separation between the lines , ∆EQ, is known as
the quadrupole splitting and is written as,
∆EQ =1
2qQVzz
(
1 + η2
3
)1/2
(1.6)
where e is the electrical charge, Q is the nuclear quadrupole moment,
and V is the electric field gradient due to the total electron density
plus all nuclear charges. V can be decomposed into three principal
components, Vzz, Vyy, and Vxx, in descending order of magnitude, and
η is the asymmetry parameter defined as (Vxx - Vyy)/Vzz. For the
substates with axially symmetric EFG (η = 0), the energy separation
∆EQ is,
∆EQ =1
2qQVzz (1.7)
The quadrupole splitting provides information on the symmetry of
the coordination sphere of the resonating atom.
14 1. Introduction and Objective
1.1.3 Magnetic Hyperfine Splitting
The dipole interaction between the nuclear spin moment and the mag-
netic field is called the Magnetic Hyperfine Splitting (Nuclear Zeeman
effect) [5, 9]. A nuclear state with spin I > 1/2 possesses a magnetic
dipole moment µ. The magnetic field splits the nuclear level of spin
I into (2I + 1) equispaced non-degenerate substates characterised by
the magnetic spin quantum numbers mI . Therefore for 57Fe, the ex-
cited state with I = 3/2 is split into four, and the ground state with I
= 1/2 into two substates as shown in Figure 1.8. The energies of the
sublevels are given from first-order perturbation theory by,
EM (mI) = −µHmI/I = −gNβNHmI (1.8)
where βN is the nuclear Bohr magneton, µ is the nuclear magnetic mo-
ment, mI is the magnetic spin quantum number and gN is the nuclear
g-factor.
The magnetic hyperfine splitting enables one to determine the ef-
fective magnetic field acting at the nucleus. The total effective mag-
netic field is the vector sum of externally applied magnetic filed and
the internal magnetic field, ~Heff = ~Hext + ~Hint. The latter consist of
three parts, ~Hint = ~HL + ~HD + ~HC . ~HL is the contribution from the
orbital motion of the electrons, ~HD is the contribution of the magnetic
moment of the spin of the electrons outside the nucleus (spin-dipolar
term) and ~HC is the contribution of the spin-density at the nucleus
(Fermi contact term).
The magnetic hyperfine interaction gives a clear understanding of
the magnetic properties of materials. In compounds with unpaired
electrons the Mossbauer spectroscopy enables one to distinguish be-
tween the high-spin and low-spin states, spin density at various nuclei
16 1. Introduction and Objective
Mossbauer spectroscopy, see Refs. [16–18].
Soon after its discovery, Mossbauer spectroscopy was used to solve
problems in solid state research. Fluck et. al [19] successfully used
this technique is to distinguish between Prussian Blue (PB) and Turn-
bull’s Blue (TB). Both these are compounds with the general molecular
formula AxMa[Mb(CN)6]zH2O (where, A = alkali cation and Ma/Mb
= metal ion). PB is prepared by adding FeIII salt to a solution of
[FeII(CN)6]4−, and TB by adding FeII salt to a solution of [FeIII(CN)6]
3−.
It was believed for a long time that these were chemically different
compounds, Prussian Blue with [FeII(CN)6]4− anions and Turnbulls
Blue with [FeIII(CN)6]3− anions. However, the Mossbauer spectra reco-
rded by Fluck et. al [19] were nearly identical for both PB and TB
showing only the presence of [FeII(CN)6]4− and FeIII in the high spin
state. The explanation is that during the preparation of TB, imme-
diately after adding a solution of FeII to a solution of [FeIII(CN)6]3−, a
rapid electron transfer takes place from FeII to the anion [FeIII(CN)6]3−
with subsequent precipitation of the same material as of PB. It is now
agreed that TB and PB are the same because of the rapidity of electron
exchange through a Fe-CN-Fe linkage.
Thermal spin transition (spin crossover) and electron transfer re-
sulting in valence tautomerism are another aspects which attracted
increasing attention by chemists and physicists because of the promis-
ing potential for practical applications in sensors and display devices
[20]. Prussian Blue Analogues are demanding among those compounds
which show pressure and temperature induced electron transfer [21].
For instance, the CoII- FeIII cyano complex when doped with potas-
sium ions, K0.1Co4[Fe(CN)6]2.718 H2O, may undergo a thermally in-
duced electron transfer around 20 K from the CoII with spin S=3/2 to
the FeIII with spin S=1/2, turning the CoII-HS to CoIII-LS and the FeIII-
1.2. Applications of Mossbauer Spectroscopy 17
LS to FeII- LS [21]. The diamagnetic pair CoIII-FeII (total spin S = 0) can
be converted back to the paramagnetic pair with the application of
light. It has been observed that the formation of the diamagnetic pairs
can be enhanced by increasing the potassium concentration or doping
with the alkali ions like rubidium or caesium and with the application
of pressure. Ksenofontov et. al. [21] proved this by measuring the
Mossbauer spectra under applied pressure on a sample which con-
tained a small fraction of potassium. There is no thermally induced
electron transfer at ambient pressure, at 4.2 K, and the spectrum is
magnetically split into a sextet with a local magnetic field of 165 kOe
arising from the S=1/2 Fermi contact field. At a pressure of 3 kbar,
most of the sextet intensity disappears and a singlet arising from the
FeII-LS sites emerges. At 4 kbar, the pressure-induced electron trans-
fer from CoII-HS to FeIII-LS is complete and the spectrum shows only
the typical FeII-LS singlet [21].
Recent discovery of high-temperature superconductivity (HTSC)
in iron-based compounds has initiated a considerable research activ-
ity comparable or even in excess to the discovery of HTCS in cuprates
[22]. Iron-based superconductors belong to pnictide (compounds of
group V elements) [23–25] or chalcogenide (compounds of group VI
elements) type of compounds [26]. In resolving the origin of supercon-
ductivity in these compounds, the knowledge of their local geometry
and local electronic structure is extremely important. Although the
X-ray diffraction methods can provide the reliable crystalline struc-
tures and the long range magnetic order can be studied by the neu-
tron diffraction method, the local geometric and electronic structure is
accessible via the use of Mossbauer spectroscopy, which is capable of
providing information on an atomic scale [5, 27].
Mossbauer spectroscopy technique finds numerous applications in
18 1. Introduction and Objective
biological systems. For example, Schunemann et. al [28] have stud-
ied the spin distribution and iron oxidation states of the intermediate
states in the reaction cycle of cytochrome P450. The enzyme super-
family cytochrome P450 are found in many living organisms, and play
an important role in many physiological processes for example in the
biotransformation of xenobiotics and synthesis of steroid hormones.
The active site of cytochrome P450 contains a substrate binding site
next to the heme iron centre. They catalyse a variety of reactions by
the transfer of an active oxygen from its heme unit to the substrates.
When a substrate binds to the active site of the enzyme, intermediate
states are formed, however little is known about these intermediate
states. Mossbauer spectroscopy can give clear evidence about the iron
oxidation states of these intermediate states [28].
The advent of third-generation synchrotron radiation sources ex-
tends the applicability of the Mossbauer technique. The use of syn-
chrotron source is an alternative to the conventional Mossbauer tech-
nique [1, 2]. The radiation from the synchrotron source is intense,
tuneable in energy, and is available in the form of short pulses. There
are several ways of Mossbauer filtration of synchrotron radiation (MFSR),
such as pure nuclear reflection, total external reflection (TER), forward
scattering (nuclear resonant forward scattering (NFS) and nuclear in-
elastic scattering (NIS)) etc. The use of synchrotron radiation over-
comes some of the limitations of the conventional technique. For in-
stance, NFS allows the direct determination of the Lamb-Mossbauer
factor [10]. In addition, the high brilliance and the extremely colli-
mated beam lead to a large flux of photons through the very small
size of the sample (0.1-1 mm2), makes possible to measure extremely
small samples, and also samples under unusual conditions like high
pressure [1, 2].
1.3. Significance of the present work 19
1.3 Significance of the present work
The parameters of Mossbauer spectra, such as the isomer shift, quadru-
pole splitting, magnetic hyperfine splitting, are sensitive characteris-
tics of the electronic structure and carry important information on the
spin- and oxidation-state of the resonating atom as well as on its lo-
cal chemical environment. The theoretical estimation of Mossbauer
isomer shifts and the evaluation of the nuclear structure parameters
therein, is the main goal of this thesis.
The Mossbauer isomer shift is the measure of the energy differ-
ence between the energies of γ-transitions occurring in the absorber
and source. Because the electronic environments in which the sample
and the reference nuclei are immersed are different, the isomer shift
probes this difference. However, the relationship between the isomer
shift and the local electronic structure is not straightforward. The iso-
mer shift depends on the nuclear structure parameters, such as the
charge radius variation during the γ-transition, as well as on the lo-
cal electronic structure parameters, such as the electron density ρa/se
in the vicinity of nucleus [6, 12]. Although measurable in principle,
these characteristics are not directly accessible from the experiment.
In such a situation, the first principles quantum chemical calculations
of the local electronic structure and of the isomer shift are of the ut-
most importance. Thus, the theoretical calculation of the electron con-
tact density at the target nucleus in chemical compounds, and calibra-
tion against the experimental isomer shifts remains the most reliable
way of determining the nuclear structure parameters. In these calcu-
lations, all relevant effects, such as the effects of relativity, the effects
of electron correlation and of the solid-state environment, have to be
included, which makes such calculations very demanding.
20 1. Introduction and Objective
The success of the traditional approach for MIS calculation relies
on the availability of the contact densities from the theoretical cal-
culations. The contact density is easily available from the calcula-
tions in which the theoretical methods fulfilling Hellmann-Feynman
theorem, such as the self-consistent field (SCF) method or the Kohn-
Sham (KS) method of density functional theory (DFT), are employed
[29–31]. However, the use of the most sophisticated methods of the
ab initio wave function theory, the coupled-cluster method or single-
reference and multi-reference Møller-Plesset perturbation theory, re-
quires the calculation of the so-called relaxed density matrix which
considerably increases the amount of computational work necessary
to obtain the density. Hence relatively low-level computational meth-
ods are commonly employed in the calibration of the Mossbauer iso-
mer shift.
The standard model of MIS calculations is based on certain as-
sumptions, such as constant density inside the nucleus and point char-
ge nuclear model [6, 12]. The former is valid only within the non-
relativistic formalism, where ρ is replaced with the electron density at
the nuclear position ρ(0). However, the electronic wavefunction in the
vicinity of the nucleus is considerably modified by relativity [12, 32],
hence the relativistic density is divergent near the nucleus and cannot
be defined as ρ(0). Within the standard approach, the non relativistic
contact densities ρ(0) calculated are scaled using an element specific
constant S(Z), in order to account for the effect of relativity. Gen-
erally, this scaling factor is obtained through the comparison of the
four-component relativistic electron density for a one-electron atom
with the corresponding non relativistic density [6]. From the values
of the scaling factor for various elements it is clear that the effect of
relativity is significant in the contact density [6]. Another limitation
1.4. Scope of the thesis 21
is the assumption of point-charge nuclear model. The effect of the
finite size of the nucleus is considered as a perturbation and the per-
turbation Hamiltonian is obtained as the difference between the po-
tential of a uniformly charged sphere and the usual Coulomb poten-
tial [6, 12–14, 18].
Taking all these limitations into consideration, it is desirable there-
fore to employ a more direct theoretical approach for the calculation
of MIS, which allows the straightforward inclusion of the most impor-
tant effects such as relativity and electron correlation. This thesis ex-
plains the development and calculations based on such an approach,
which is based on the non-perturbative inclusion of the finite size nu-
cleus into theoretical calculations. Within this new approach, the most
accurate ab initio methods can be employed, which offers a possibility
for a systematic improvement of the results of theoretical modelling
of the Mossbauer isomer shift.
1.4 Scope of the thesis
In chapter 2, all the quantum chemical formalisms within the scope of
this thesis are introduced. The inclusion of relativity via Normalized
Elimination of Small the Component method in the calculations are
explained. In this chapter, the traditional approach for the MIS calcu-
lations and its limitations are explained, describing the necessity of a
more accurate theoretical framework. The new approach, according
to which the isomer shift is treated as the linear response of the elec-
tronic density with respect to the nuclear radius is described in detail.
Chapter 3 validates density functional theory for the calculation
of MIS within the context of the new theoretical formalism. The val-
22 1. Introduction and Objective
idation of pure and hybrid density functionals for the modelling of
Mossbauer Isomer shift is illustrated. The investigation of the effect
of basis set truncation on the calculated values of isomer shifts are
carried out and described in detail.
In Chapter 4, the importance of the proper account of relativity and
electron correlation is demonstrated in a series of atomic calculations
for various oxidation states of iron atom. From the Mossbauer exper-
iments the parameters of the nuclear γ-transition are not known with
sufficiently high accuracy, hence the calibration of the theoretically ob-
tained contact densities with the experimental isomer shifts is impor-
tant (see Eqn. 1.5). The calibration constant α in Eqn. 1.5 gives infor-
mation on the internal parameters of the nuclear γ-transition, such as
the variation of the nuclear charge radius. Chapter 4 describes the cal-
ibration of 119Sn contact densities with the experimental isomer shifts
to obtain a reliable value of the calibration constant α. The obtained
value of calibration constant α is validated by the comparison of cal-
culated vs. experimental isomer shifts. An independent test of the
calibration constant is carried out by studying the isomer shift varia-
tion under pressure for CaSnO3 perovskite.
Chapter 5 details the calculation of 57Fe calibration constant α us-
ing a series of iron compounds. The reliability of the obtained cali-
bration constant, α is tested via calculating the relative isomer shifts
∆δx = δx − δref , choosing various reference compounds.
Chapter 6 describes the investigation on the possible origin of two
different signals in the Mossbauer spectra of Prussian blue analogue
RbMnFe(CN)6H2O, in which a switching of magnetism occurs with
light and temperature. The analysis is based on two parameters, i)
the distribution of Rb+ around iron and ii) the difference in oxidation
states of iron.
1.4. Scope of the thesis 23
Chapter 7 details the study on the recently discovered iron based
superconductors [22–26]. The aim is to analyse the influence of the
structural variation near the 57Fe nucleus and chemical substitutions
in the coordination sphere of 57Fe, on the isomer shift and magnetic
hyperfine coupling constants in these compounds. This will give us an
idea on the applicability of Mossbauer parameters to understand the
structure of these iron based superconductors under phase transitions
and upon chemical substitutions.
Chapter 8 give a conclusion and outlook of the dissertation.