INTRODUCTION

1.1. Introduction

Electron Paramagnetic Resonance (EPR) has been used as a tool to identify

paramagnetic transition metal ions, trapped hole centres and electrons close to the

conduction states in non-linear optical and photorefractive materials [1-3]. The

transition-group, rare earth and actinide ions that are the members of the 3d, 4d, 5d, 4f

and 5f groups have been the subject of EPR investigations. Of the approximately 160

known elements, 55 belong to these series.

Transition metal ion complexes and salts have played a vital role in many aspects

of EPR, including the development of the spin Hamiltonian concept. Their importance

was based on:

1. Availability of a number of unpaired electrons per species (total spin S

ranges from 1/2 to 7/2)

2. Availability of systems with simple local symmetries (e. g., cubic) and

well-characterized neighbors to the central ion

3. Easy preparation, stability and with a variety of oxidation states

4. Availability of reasonably applicable and adequate electronic theory, for

example, the crystal-field model.

Later on, researchers started investigating systems of lower-symmetry, since these

have a tremendous application in chemical catalysis and biomedical. One aspect that

makes transition elements interesting subjects for study by EPR or other techniques is

their variable valence (Table 1.1). This feature is due to their unfilled electron shells.

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For example, the easiness of iron to change between +2 and +3 oxidation states provides

sites for electron transfer in biological oxidation-reduction systems. The observation of

hyperfine splitting will help to identify the central nucleus. The nucleus need not be that

of the host ion; it may instead be a foreign nucleus that is present naturally or is

introduced by doping [4].

The structural simplicity, symmetry, wide range of optical transparency and ease

of preparation of ionic crystals has made them the subject of intensive investigation. In

view of the fact that they are intrinsically insulators with a forbidden gap of ∼8 eV, these

crystals have a wide range of optical transparency. At one end, the UV absorption is due

to electronic excitation and at the other end the lattice vibrations are responsible for IR

absorption. Such crystals are good host media for incorporating various paramagnetic

impurities that can be used as probes for investigating the properties of the host material.

In this process, the influence of the host on the electronic and vibrational properties of the

impurity can also be investigated. This property has been used to extract information

about several important parameters of the materials. A number of experimental

techniques have been used in this process. Some of the physical properties of the crystal

are mainly due to the existence of defects in the crystal, while many others are indirectly

influenced by defects. In the first category, one may mention ionic conductivity,

diffusion, dielectric loss and ionic thermo currents. Properties such as thermal

conductivity, mechanical strength, etc. are strongly influenced by defects. Most of these

defects either created artificially or natural to the crystal, give rise to localized energy

levels between the valence band and the conduction band. Such defects are studied by

optical absorption, luminescence, photoconductivity, etc. Other deliberately introduced

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impurities are paramagnetic in nature and in such cases; the powerful tool of EPR can be

used to identify the surroundings and the location of the impurity.

In some cases, when the impurity defect is a molecular entity, vibrational

spectroscopy of the impurity can be used to investigate the properties of the material. It

will obviously be a great advantage to choose an impurity that will give optical

absorption and is paramagnetic, which has the characteristic vibrational frequencies that

affect the conductivity and dielectric loss. In initial stages of solid state research, the

alkali halides received a lot of attention because of their high symmetry, simple crystal

structure and the ease of preparation of single crystals. A vast amount of work has been

done on the study of various low symmetry materials and an exhaustive review is not

possible in this thesis. However, only some representative examples of various low-

symmetry complexes are presented in their respective chapters. Main influence of the

presence of low symmetry is seen in properties such as lifting of the degeneracy of

electronic energy levels, the splitting of the degenerate modes in the infrared, the high

anisotropy in the g and hyperfine interaction tensors, the unusual sequence of spin-

Hamiltonian parameters, the abnormally low values of hyperfine coupling constants,

mixed ground states, occurrence of spin-forbidden transitions, vibronic mixing, Jahn-

Teller distortions, phase transitions and co-operative magnetic phenomena.

The principle of EPR is based on the possibility of recording unpaired electrons in

atomic, crystalline ionic and molecular structures; in complexes of transition metal ions

such as Cu(II), VO(II), Cr(III), Mo(II), Mn(II), Fe(III), Ni(II), etc.; upon cleavage of

covalent chemical bonds. In the latter case, the unpaired electron(s) appear either at

unoccupied atoms or at molecular and macromolecular fragments, i.e., at free radicals of

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higher activity. Many of the above electronic states have been reported in biological

systems. Over the decades, EPR technique has been constantly improved [5-7]. EPR

spectroscopy enables unpaired electrons to be detected and characterized. This is

possible due to the fact that odd electrons have a magnetic moment caused by spin (S), at

least equal to 1/2.

Molecules with unpaired electrons, like radicals, transition metal complexes, etc.

have a wide range of applications in chemistry, physics, biology and medicine. It may be

used to probe the "static" structure of solid and liquid systems and is also very useful in

investigating dynamic processes.

Structural and spectral investigations on complexes of simple carboxylic acids of

transition metal ions and rare earths, despite a long history, continue to be of current

interest for several reasons. They exist in widely different structures showing the

influence of metal-metal interaction, hydrogen bonding and marked differences in their

thermal decomposition behavior [8-10]. Interest in these salts also stems from the fact

that they lend themselves to a comparative study of salts of the same carboxylic acid with

different metal ions, of different carboxylic acids with the same metal ions and of the

transition metal ions with the rare earths in analogous situations. Published studies on

solids by employing techniques such as X-ray structure determinations, optical spectra,

EPR, Mossbauer spectroscopy and differential thermal and thermo gravimetric studies [9,

10] are numerous.

Coordination compounds containing malonic acid as a ligand have been recently

studied due to their potential application as materials in molecular electronics, catalysts,

biologically active compounds, molecular-based magnetic materials, etc. [11, 12]. On the

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other hand, dicarboxalic acids show additional features such as formation of both normal

and acid complexes, another chemically interesting feature for a comparative study. With

these points of view in mind, EPR studies on single crystals, optical studies, IR behavior

of complexes of simple polycarboxylic acids such as malonic and maleic with transition

metal ions have been undertaken. In the case of malonic acid, detailed crystal structures

have been designed for Cu(II) doped in Diaquamalonatozinc(II) (DAMZ),

Diaquamalanato(1,10-phenanthroline)zinc(II) (DAMPZ) and Fe(III) doped in

Dipotassium diaquabis(malonato-κ2O,O’)zincate(II) dihydrate (PMZD) [13-15]. These

studies show several interesting features. The interest in Cu(II), Fe(III) doped DAMZ,

DAMPZ and PMZD arises from the non isomorphous nature of the metals and zinc

complexes with the difference in the coordination and the interesting options that become

available as a result, regarding the microsymmetry of the guest ion in the host lattice. An

important feature of the malonic bridge is the fact that the magnitude of the exchange

interaction depends on the possible bridging modes that it can adopt. Thus the ferro- or

antiferromagnetic interactions may appear in malonate complexes, governed by the

dimensionality of the structure. In recent years, a vast amount of research has been

devoted to the characterization of dimeric copper(II) complexes. Much of this interest

stems from the fact that copper(II) dimers are excellent model systems for the study of

magnetic interactions [16].

Tutton salts form an isostructural series of hydrated double sulphates which have

been studied by many techniques, because they are easily grown and are interesting for

many subjects. Detailed EPR studies of VO(II)-doped Tutton salts, estimating, among

other things, ligand superhyperfine (SHF) interaction, bonding coefficients, impurity-

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host exchange interaction and host-ion spin-lattice relaxation times. The present thesis

(chapter V and VI) reports an extensive X-band EPR study on a VO(II) doped zinc

sodiumsulphatehexahydrate (ZSSH) and cis-diaquabis(1,10-phenanthroline-N,N')zinc(II)

(1,10-Phenanthroline-N,N') bis(thiosulfato-S)zincate(II) Monohydrate (DPZSZM) single

crystal in the room temperature [17,18].

The motivations for the present studies are: (i) to evaluate accurately the g, A

tensors of the VO(II) ion in ZSSH without the assumption of the coincidences of their

principal axes, using eigen values calculated to the second order perturbation (ii) to

determine correctly the orientations of the VO(II)-O2- bond axes in ZSSH from a

knowledge of the orientations of the principal axes of the g2 tensor (iii) to estimate the

VO(II) impurity ion EPR line width, using the correct expression applicable to the

presence of two different kinds of paramagnetic ions and (iv) to estimate the bonding

coefficients of the [VO(H2O)5]2+ complex in ZSSH using the EPR and optical absorption

data.

1. 2. Electron Paramagnetic Resonance

Electron Paramagnetic Resonance (EPR), often called Electron Spin Resonance

(ESR), is a branch of spectroscopy in which electromagnetic radiation (usually of

microwave frequency) is absorbed by molecules, ions, or atoms possessing electrons with

unpaired spins, i.e., electron spin S > 0. EPR was discovered by Zavoisky in 1945 [19].

EPR spectroscopy is closely related to the probably better known nuclear magnetic

resonance (NMR). The NMR technique deals with nonzero nuclear spins, I > 0. In both

EPR and NMR, the sample material is kept in a strong static magnetic field and subjected

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to an orthogonal low- amplitude high-frequency field. EPR usually requires microwave-

frequency radiation (GHz), while NMR is observed at lower radio frequencies (MHz).

With EPR, energy is absorbed by the sample when the frequency of the radiation is

appropriate to the energy difference between the two states of the electrons in the sample,

but only if the transition satisfies the appropriate selection rules. Some of the

paramagnetic transition metal ions V, Fe, Mn, Co, Cu, Mo, and Ni are biologically

important elements also.

EPR spectra are routinely obtained for paramagnetic transition ions in crystals,

chemical complexes and bio-molecules. Samples may be in the form of crystal, powder,

solution or frozen solution. Most commonly, these systems should have electron spin (S)

and S can be any value from 1/2 to 7/2 in increments of 1/2. When the spin is odd, i.e.,

for example, S = 1/2, 3/2, 5/2 or 7/2, spectra are easily obtained at room temperature.

However if the spin is even, i.e., for example, S = 1, 2 or 3, then the possibility of

obtaining spectra depends upon a number of circumstances that are usually not met; thus

EPR of even spin systems is a very specialized one. EPR spectroscopy is capable of

providing molecular structural details inaccessible by other analytical tools. EPR has

developed into a potent, multipurpose, non-destructive and non-intrusive analytical

method. Hence, EPR has become a powerful tool in the hands of chemists, physicists,

geologists, mineralogists, biologists, etc.

EPR technique detects unpaired electrons, identity of the molecule and

information of the molecular structure (structure, dynamics, bounding), molecular

environment (< 0.8 nm for nuclear spins and up to 50 nm for other electron spins). These

capabilities of EPR are a result of the unpaired electron’s spin magnetic moment being

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very sensitive to local magnetic fields within the sample. These fields often arise from

the nuclear magnetic moments of various nuclei that may be present within the bulk

medium. Examples of such nuclei are interstitial atoms (or ions) within a crystal or glass

matrix, nuclei (such as nitrogen) within the molecular structure that also contains the

unpaired electron, and so on. Thus EPR provides a unique means of studying the internal

structures in great detail.

EPR can provide valuable information on structural and dynamical aspects, even

from current chemical and/or physical processes without influencing the process itself.

Therefore, EPR is considered as an ideal complementary technique for other methods in a

wide range of studies in various branches of science and humanities [20-26].

1. 3. EPR applications

ESR can be used to obtain structural information of molecules together with

details about their electron density distributions. In solutions and solids, the dynamics of

molecules can be determined and the kinetics of chemical reactions can be studied.

Quantitatively, analytical applications such as dosimetry can be mentioned, as well as

characterization of the redox-active centers in proteins. All of these properties can be

observed at room temperature, but often lower temperatures are used.

1.3.1. Biomedical EPR spectroscopy

As the spin of an unpaired electron can sense its nearby environment, each free

radical or transition metal ion will have slightly different properties. Therefore EPR can

be used to identify biological molecules that contain free radicals or transition metal ions

in their structure. EPR is a quantitative technique, i.e., the concentration of unpaired

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electrons present in a sample can be estimated, even if the exact nature of the free radical

being observed is not known. This property is very important to distinguish between

reactive free radicals that are present in high concentrations and may be damaging and

those that may be present in only very low concentrations and may not be. EPR

spectroscopy has also find its application to understand the pathophysiology and

underlying chemical mechanism of a wide range of diseases such as Parkinson's disease,

birth asphyxia, stroke, septic shock, kidney damage and coronary heart disease. Two

major types of EPR signals of biomedical relevance are unpaired electrons in free

radicals and metalloproteins.

In summary, various paramagnetic systems present in different branches of

sciences that can be studied by EPR technique are:

1.3.2. Chemistry

Atoms or ions with partially filled inner electron shells (transition metals)

Measurement of magnetic susceptibility

Molecules with odd number of electrons

Molecules with even number of electrons (triplet states)

Oxidation and reduction processes

Biradicals and triplet state molecules

Electron transfer reaction kinetics

Structure, dynamics and reaction of polymers

Short-time behavior of organic free radicals produced by radiation

Fundamental quantum theory

Organo-metallic, catalysis, molecular magnets etc.,

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1.3.3. Biology

Enzymatic reactions

Photosynthesis

Metallo-proteins

Spin label and spin probe techniques

Control of irradiated food

Saturation transfer and vector EPR techniques for the study of molecular

motions.

1.3.4. Medicine

Radical initiated carcinogenesis

Free radicals in living tissues

Radiation dose assessment

Oxygen concentration measurement

Concentrations and kinetics of short lived radicals by spin trapping

1.3.5. Physics

Conduction electrons in metals, non-metallic conductors and semiconductors

Susceptibility

Quantum dots

Defect centres

Optically detected magnetic resonance

Relaxation properties, phonon densities

1.3.6 Ionization Radiation

Alanin radiation

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Dosimetry

Radiation damage

Irradiated food

1.3.7. Material science

Polymers

Glasses

Superconductors

Corrosion

Fullerenes

1.4. EPR Theory [4, 20, 21, 24-26]

Every electron has a magnetic moment and spin quantum number S = 1/2, with

magnetic components ms = +1/2 and ms = –1/2. In the presence of an external magnetic

field with strength BB0, the electron's magnetic moment aligns itself either parallel

(ms = –1/2) or antiparallel (ms = +1/2) to the field, each alignment having a specific

energy. The parallel alignment corresponds to the lower energy state and the separation

between it and the upper state is

ΔE = geμBBB0 (1)

where ge is the electron's g-factor (also known as Landé g-factor) and μB is the Bohr

magneton. This equation implies that the splitting of the energy levels is directly

proportional to the magnetic field's strength, as shown in Fig 1.1. An unpaired electron

can move between the two energy levels by either absorbing or emitting electromagnetic

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radiation of energy E = hν. This will lead to the resonance condition hν = geμBBB0.

Experimentally, this equation permits a large combination of frequency and magnetic

field values, but majority of EPR measurements are made with microwaves in the 9000 –

10000 MHz (9 – 10 GHz) region, with fields corresponding to about 3500 G (0.35 T).

In principle, EPR spectra can be generated by either varying the photon frequency

incident on a sample while holding the magnetic field constant, or doing the reverse. In

practice, it is usually the frequency that is kept fixed. By varying the external magnetic

field, the gap between the ms = +1/2 and ms = −1/2 energy states is widened until it

matches the energy of the microwaves. At this point, the unpaired electrons can move

between their two spin states. Since there are more electrons in the lower state, due to the

Boltzmann distribution, there is a net absorption of energy, and it is this absorption which

is monitored. Most EPR spectra are recorded only as first derivatives, to get very

accurate magnetic field positions. In few cases, second derivative spectra are also

recorded.

A detailed analysis of the EPR spectrum leads to a very accurate determination of

bonding parameters and the electronic structure of the ground state, which is the unique

characteristic of EPR technique. EPR is sensitive to the changes in symmetry of the

environment. A general consideration of the interaction involved in the case of a

paramagnetic species in a crystal field is formulated in terms of generalized Hamiltonian.

The spin Hamiltonian consists of various terms, which have been arisen due to different

types of interactions between electron spin with either the applied magnetic field or

nuclear spin or another electron spin and the nuclear spin either with the applied magnetic

field or another nuclear spin.

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1.4.1. EPR spectral parameters

In real systems, the unpaired electrons are normally not free, but are generally

associated with one or more atoms. Due to this property, the following information can

be observed. They are

1. An unpaired electron can gain or lose angular momentum, resulting in a change of

its g-factor, causing it to differ from ge. This is more predominant with transition

metal ion systems.

2. If the atom, having the unpaired electron also has a non-zero nuclear spin, then its

nuclear magnetic moment will affect the electron. This results in hyperfine

coupling, i.e., splitting the EPR resonance signal, analogous to J-coupling in

NMR.

3. Interactions of an unpaired electron with its environment influence the EPR

spectral line shape. Line shapes provide a vital information about rates of

chemical reactions, relaxation times etc.

4. The g-factor and hyperfine coupling in an atom or molecule may not be the same

for all orientations of an unpaired electron in an external magnetic field. This

anisotropy depends upon the electronic structure of the atom or molecule and

provides information about the atomic or molecular orbital containing the

unpaired electron.

1.4.2. Spin Hamiltonian

The Spin Hamiltonian (SH) is a phenomenological equation. In other words, SH

is an equation whose sole purpose is to reflect the observed data by means of adjustable

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parameters. In SH, the terms are arranged in such a way that the meaning can be at least

intuitively implied. There is a term which represents the interaction of the electron spin

system S with the externally applied magnetic field B; β B·g·S. In this case, the

adjustable parameters form a (3x3) matrix g which represents the interaction at any given

orientation of B with respect to S. Other terms also exist whereby the adjustable

parameters are contained in (3x3) parameter matrices and represent simple interactions.

Terms with matrices A represent interaction between two spin systems (specifically, the

electron spin system S and some nucleus I; as in the term S·A·I.). Other such terms exist

as well as terms representing higher-order interactions. These terms cannot be

represented properly using (3x3) matrix format parameter and hence they are more

complex to interpret.

In general, EPR data can be fitted to a “Spin-Hamiltonian’ with lesser number of

terms by use of an effective fictitious spin, without knowing the magnitudes of spin-orbit

coupling, crystal field splitting, etc.

In Dyad operator notation, the Spin-Hamiltonian can be expressed as

ℋS = βe B. g. S + I. A. S + S. D. S + I. Q. I + .... (2)

where g, A, D and Q are second rank tensors, whose principal axes need not coincide.

These correspond to the electron g-tensor, hyperfine tensor, zero-field tensor and

quadrupole coupling constant tensor respectively.

A system with a fictitious spin S’ splits into (2S’+1) levels and transitions are

allowed between these according to the selection rules. The only difference between the

true spin S and fictitious spin S' is that the latter defines the effective spin-angular

momentum endowed due to any orbital contribution. Since the spin-only g-factor

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deviates from the free spin value, due to admixture of higher lying states into the ground

state via spin-orbit coupling, it effectively considers the effect of crystal field terms and

spin-orbit term of the generalized Hamiltonian. Since the isotropic g-factor of a free

electron is modified into a tensor when orbital momentum is not completely quenched in

the principal axis system of the g-tensor, the Hamiltonian is written as

ℋ = β (BxgxxSx + BygyySy + BzgzzSz) (3)

If the tensor is cylindrically symmetric, gxx = gyy = gzz = g and Bx = BBy = BzB , then

ℋ = β[BSg] (4)

And in the case of axially symmetric tensor,

ℋ = β[Bzg||Sz + g⊥(BxSx + BySy)] (5)

Likewise, the hyperfine terms, which consist of a dipolar part and isotropic part, are

generally written as:

ℋ = AxxIxSx + AyyIySy +AzzIzSz (6)

If the unpaired electron is purely s-type, then

ℋ = a Iz Sz and a = (8π/3) gβgnβn ⎢ψ(0)⎢2 (7)

where ⎢ψ(0)⎜2 is the squared amplitude of the unpaired s-electron density at the nucleus.

Isotropic hyperfine interaction is due to (a) direct unpaired spin-density in an s-orbital or

in a molecular orbital (M.O.) with s-orbital contribution, (b) spin-polarization, due to

isotropic hyperfine coupling in an isolated paramagnetic atom or ion, where the electron

is in a p or d orbital arises via polarization of core s-electrons and/or (c) configuration

interaction between a ground state M.O. orbital with no s-orbital contribution and states

with finite s-orbital contribution.

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Dipolar coupling arises out of point dipole interaction between p or d orbital with

the nucleus and follows a (3 cos2θ-1) variation given by

ℋd = gβgnβn(3cos2θ-1) (1/⟨r3⟩) (8)

In cases of p3 or d5 high spin configuration, dipolar-coupling vanishes, due to spherical

charge distribution. Also in paramagnetic systems in solutions, where the system tumbles

rapidly, it averages to zero, being represented by a trace–less tensor.

The signs of the experimental principal values of the hyperfine tensor cannot be

obtained from EPR spectra. However a ratio of unpaired p and s densities in simple free–

radicals depends on the hybridization and hence one can estimate the bond angles. From

the hyperfine coupling of a metal nucleus, when the electron occupies a metal orbital, the

covalence of the metal ligand bonds can be estimated.

In systems with more than one unpaired electron, the spin-degeneracy is removed

even in the absence of external magnetic field by second spin-orbital coupling known as

the zero-field interaction. This is also a dipolar type interaction and expressed in the spin

Hamiltonian as

ℋss = D[Sz2-1/3 S(S+1)] + E(Sx

2 – Sy2)

= DxxSxx2

+DyySyy2

+DzzSzz2 (9)

The Dii’s are the principal values of the D-tensor. E is an asymmetry parameter and

represents deviation from axial symmetry. The relative magnitudes of D and gβB are to

be noted in any perturbation treatment of the spin-Hamiltonian.

The quadrupolar term in the spin-Hamiltonian is quite similar to the zero-field

term and is given by

ℋQ = QxxIx2

+ QyyIy2

+ QzzIz 2

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= Q’[Iz2 –1/3 I (I+1)] +Q” [Ix

2 –Iy

2] (10)

where Qii’s are the principal values of the quadrupole coupling constant tensor. Here, Q’

is similar to D and Q” to E. The quadrupolar interaction affects the EPR spectrum in two

different ways. Firstly, the selection rule ΔMS = ±1, ΔmI = 0, breaks down and

‘forbidden’ transitions with ΔmI = ±1, ±2 become allowed. Secondly, quadrupolar

effects cause the intensities of normal transitions and hyperfine spacing to become

unequal, the latter showing progressive increase or decrease from the ends towards the

center. In single crystals, especially when the external field is perpendicular to the

symmetry axis, the analysis becomes difficult due to the presence of intense forbidden

transitions [27].

The choice of spin Hamiltonian based on the symmetry of the paramagnetic

species will help to accurately estimate the parameters such as g, A, D, Q etc. These

parameters can also be calculated theoretically from the knowledge of the ground state

molecular orbital and optical spectroscopic data with the use of perturbation theory. The

methodology of obtaining M.O. coefficients from the observed magnetic resonance

parameters have been described in detail in the literature [28, 29]. It is possible, in

favorable cases, therefore to obtain bonding parameters for transition metal complexes

from EPR data.

1.5. Selection Rules

In EPR, allowed transitions correspond to the change of only ms i.e., Δms = ± 1

and ΔmI = 0. This means that only the electronic spin "flips", whereas the nuclear spin

remains unchanged.

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1.6. Jahn-Teller and Kramers’ theorems

The Jahn-Teller Theorem [30] states that "any non-linear molecular system in a

degenerate electronic state will be unstable and will undergo distortion to form a system

of lower symmetry and lower energy thereby removing the degeneracy". The effect of

Jahn-Teller distortions is best explained for Cu(II) complexes (with 3 electrons in the eg

level) where the result is that most complexes are found to have elongation along the z-

axis.

The Kramers’ [31] degeneracy theorem states that a system containing an odd

number of electrons, so S = 1/2, 3/2, 5/2 etc., even with no symmetry, and with no

magnetic field, must be at least doubly degenerate. A non-Kramers’ center will have S =

1, 2, 3, etc. In other words, systems with odd numbers of electrons relax differently from

systems with even numbers of electrons. Equally, non-Kramers EPR spectroscopy, has

been very important in understanding the EPR of ferrodoxins such as Fe3S4, Fe4S4, and

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Fe8S8, and can be observed for heme proteins, iron-oxo clusters, and inorganic model

complexes of these.

1.7. Magnitude of the crystal field

The magnitude of the crystal field is also important since it controls the extent of

the orbital levels. In order to incorporate the effect of the crystal field into the general

spin Hamiltonian for the ion, three levels of interactions are to be recognized. They are

(i) Smaller effect: The rare earth ions have partially shielded unpaired 4f electrons

by electrons in the outer orbitals. So the electrostatic forces at central metal ion, already

rather weak, are further attenuated. In these ions, L and S remain coupled and precesses

about resultant J, which in turn precesses about the electric field. Thus MJ is a good

quantum number. In calculating the energy value, one must first consider the spin-orbit

coupling term (ℋLS) and then the crystal field (ℋV) as perturbation. The g approximates

to free ion value in many cases.

(ii) Moderate effect: In the iron group transition metal elements, the unpaired

electrons are less well shielded. In such cases, the crystal field is strong enough to

decouple L and S, which then precesses independently (so ML and MS are proper

quantum numbers). The splitting between levels with different ML is of the order of 103

cm-1 so that only the lowest level is occupied at normal temperature and the orbital

angular momentum is largely quenched. Spin-orbit coupling then mixes in contributions

from higher orbital to counteract the quenching. Hence, g would have the value,

deviating from 2.00 in all cases.

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(iii) Stronger effect: In the case of copper complexes such as copper chelates,

iron group cyanides, etc., not only the coupling between the L and S broke down, but

often between l and s for individual electrons. These then tend to pair off as far as

possible leaving a single unpaired electron if the total number is odd. This behaves much

like the unpaired electron in a free radical and g-factor is close to free spin value of 2.00.

1.8. Magnetically and chemically inequivalent sites

A paramagnetic system with anisotropic g and A tensors give rise to EPR

resonance depending on the orientation of the magnetic field B with respect to the tensor

axes. Depending on the space group and the number of molecules per unit cell (Z),

several different spatial orientations of the paramagnetic sites in the single crystals are

possible. Species that are chemically identical (i.e., they are described by identical spin

Hamiltonian parameters) but are spatially oriented differently are referred to as

magnetically distinct sites. It is also possible that due to charge compensation process

[32, 33] in the lattice, depending upon different relative configurations of the ‘radical

vacancy’ directions, there exist many different sets of spin Hamiltonian parameters

(although these may differ only slightly). The species themselves would be expected to

be identical when the charge-compensating vacancies are not considered. Such sites are

termed as chemically distinct sites. These chemically distinct sites are necessarily

magnetically distinct, whereas the converse need not necessarily hold.

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