	2013
	Hasanuddin University

Presented By

Group 9

Hikmawati (H311 11 290)

paper of kinetics Pysical Chemistry

The paper is organized so that readers can add insight or expand existing knowledge about electron transfer

PREFACE

Praise to Allah SWT who has given taufik, guidance, and inayah so that we all can still move as usual as well as the author so we can complete the this paper that contains electron transfer in physical chemistry.

The paper is organized so that readers can add insight or expand existing knowledge about electron transfer that we present in this paper an arrangement of a concise, easy to read and easy to understand.

The authors also wish to express many thanks to his teammates and the father / mother of teachers who have guided the author in order to make authors of scientific papers in accordance with the provisions in force so that it becomes a scientific paper is good and right.

Hopefully, this paper can be useful for readers and expanding horizons about electron transfer. And don’t forget also the author apologizes for any shortcomings here and there of the paper's authors do.Please critique and suggestions.Thank you.

December 8, 2013

The authors

CHAPTER I

INTRODUCTION

Electron transfer occurs when an electron moves from an atom or a chemical species (e.g. a molecule) to another atom or chemical species. ET is a mechanistic description of the thermodynamic concept of redox, wherein the oxidation states of both reaction partners change.

The Marcus theory states that the probability that an electron will transfer from a donor to an acceptor during a transition state will decrease with increasing distance between the donor and acceptor. Factors that control the rate constant of electron transfer involved in a unimolecular electron transfer, where the probability of transfer from a donor to an acceptor is identified by the term are distance between donor-acceptor complex; the Gibbs energy of activation; and the reorganization of energy.

CHAPTER II

BIBLIOGRAPHY

Numerous biological processes involve ET reactions. These processes include oxygen binding, photosynthesis, respiration, and detoxification. Additionally, the process of energy transfer can be formalized as a two-electron exchange (two concurrent ET events in opposite directions) in case of small distances between the transferring molecules. ET reactions commonly involve transition metal complexes but there are now many examples of ET in organic chemistry.

The electron transfer processes of photosynthesis and carbohydrate metabolism drive the flow of protons across the membranes of specialized cellular compartments. A radical is a very reactive species containing one or more unpaired electrons. To emphasize the presence of an unpaired electron in a radical, it is common to use a dot (.) when writing the chemical formula. For example, the chemical formula of the hydroxyl radical may be written as ^.OH. Hydroxyl radicals and other reactive species containing oxygen can be produced in organisms as undesirable by-products of electron transfer reactions and have been implicated in the development of cardiovascular disease, cancer, stroke, inflammatory disease, and other conditions.

2.1 Classes of electron transfer

There are several classes of electron transfer, defined by the state of the two redox centers and their connectivity

2.1.1 Inner-sphere electron transfer

In inner-sphere ET, the two redox centers are covalently linked during the ET. This bridge can be permanent, in which case the electron transfer event is termed intramolecular electron transfer. More commonly, however, the covalent linkage is transitory, forming just prior to the ET and then disconnecting following the ET event. In such cases, the electron transfer is termed intermolecular electron transfer. A famous example of an inner sphere ET process that proceeds via a transitory bridged intermediate is the reduction of [CoCl(NH₃)₅]²⁺by [Cr(H₂O)₆]²⁺. In this case the chloride ligand is the bridging ligand that covalently connects the redox partners.

2.1.2 Outer-sphere electron transfer

In outer-sphere ET reactions, the participating redox centers are not linked via any bridge during the ET event. Instead, the electron "hops" through space from the reducing center to the acceptor. Outer sphere electron transfer can occur between different chemical species or between identical chemical species that differ only in their oxidation state. The later process is termed self-exchange. As an example, self-exchange describes the degenerate reaction between permanganate and its one-electron reduced relative manganate:

[MnO₄]^- + [Mn*O₄]^2- → [MnO₄]^2- + [Mn*O₄]^-

In general, if electron transfer is faster than ligand substitution, the reaction will follow the outer-sphere electron transfer. Often occurs when one/both reactants are inert or if there is no suitable bridging ligand. A key concept of Marcus theory is that the rates of such self-exchange reactions are mathematically related to the rates of "cross reactions". Cross reactions entail partners that differ by more than their oxidation states. One example (of many thousands) is the reduction of permanganate by iodide to form iodine and, again, manganate. Five steps of an outer sphere reaction :

1. reactants diffuse together out of their solvent shells => precursor complex (requires work =w_r)

2. changing bond lengths, reorganize solvent => activated complex

3. Electron transfer

4. Relaxation of bond lengths, solvent molecules => successor complex

5. Diffusion of products (requires work=w_p)

2.2 Marcus Theory of Electron Transfer

The first generally accepted theory of ET was developed by Rudolph A. Marcus to address outer-sphere electron transfer and was based on a transition-state theory approach. The Marcus theory of electron transfer was then extended to include inner-sphere electron transfer by Noel Hush and Marcus. The resultant theory, called Marcus-Hush theory, has guided most discussions of electron transfer ever since. Both theories are, however, semiclassical in nature, although they have been extended to fully quantum mechanicaltreatments by Joshua Jortner, Alexender M. Kuznetsov, and others proceeding from Fermi's Golden Rule and following earlier work innon-radiative transitions. Furthermore, theories have been put forward to take into account the effects of vibronic coupling on electron transfer; in particular, the PKS theory of electron transfer.

Before 1991, ET in metalloproteins was thought to affect primarily the diffuse, averaged properties of the non-metal atoms forming an insulated barrier between the metals, but Beratan, Betts and Onuchic subsequently showed that the ET rates are governed by the bond structures of the proteins -- that the electrons, in effect, tunnel through the bonds comprising the chain structure of the proteins.

Marcus Theory is a theory originally developed by Rudolph A. Marcus, starting in 1956, to explain the rates of electron transferreactions–the rate at which an electron can move or jump from one chemical species (called the electron donor) to another (called the electron acceptor). It was originally formulated to address outer sphere electron transfer reactions, in which the two chemical species only change in their charge with an electron jumping (e.g. the oxidation of an ion like Fe²⁺/Fe³⁺), but do not undergo large structural changes. It was extended to include inner sphere electron transfer contributions, in which a change of distances or geometry in the solvation or coordination shells of the two chemical species is taken into account (the Fe-O distances in Fe(H₂O)²⁺ and Fe(H₂O)³⁺ are different).

For redox reactions without making or breaking bonds Marcus theory takes the place of Eyring's transition state theory which has been derived for reactions with structural changes. Both theories lead to rate equations of the same exponential form. However, whereas in Eyring theory the reaction partners become strongly coupled in the course of the reaction to form a structurally defined activated complex, in Marcus theory they are weakly coupled and retain their individuality. It is the thermally induced reorganization of the surroundings, the solvent (outer sphere) and the solvent sheath or the ligands (inner sphere) which create the geometrically favourable situation prior to and independent of the electron jump.

The original classical Marcus theory for outer sphere electron transfer reactions demonstrates the importance of the solvent and leads the way to the calculation of the Gibbs free energy of activation, using the polarization properties of the solvent, the size of the reactants, the transfer distance and the Gibbs free energy $\Delta$ G⁰ of the redox reaction. The most startling result of Marcus' theory was the "inverted region": whereas the reaction rates usually become higher with increasing exergonicity of the reaction, electron transfer should, according to Marcus theory, become slower in the very negative $\Delta$ G⁰ domain. The inverted region was searched for 30 years until it was unequivocally verified experimentally in 1984.

According to the Marcus theory of electron transfer, which was proposed by R.A. Marcus in 1965, the rates of electron transfer (from ground or excited states) depend on:

1. The distance between the donor and acceptor, with electron transfer becoming more efficient as the distance between donor and acceptor decreases.

2. The reaction Gibbs energy, ΔrG, with electron transfer becoming more efficient as the reaction becomes more exergonic. For example, efficient photooxidation of S requires that the reduction potential of S* be lower than the reduction potential of Q.

3. The reorganization energy, the energy cost incurred by molecular rearrangements of donor, acceptor, and medium during electron transfer. The electron transfer rate is predicted to increase as this reorganization energy is matched closely by the reaction Gibbs energy.

Electron transfer can also be studied by time-resolved spectroscopy.The oxidized and reduced products often have electronic absorption spectra distinct from those of their neutral parent compounds. Therefore, the rapid appearance of such known features in the absorption spectrum after excitation by a laser pulse may be taken as indication of quenching by electron transfer.

R.A. Marcus received the Nobel Prize in Chemistry in 1992 for this theory. Marcus theory is used to describe a number of important processes in chemistry and biology, including photosynthesis, corrosion, certain types of chemiluminescence, charge separation in some types of solar cell and more. Besides the inner and outer sphere applications, Marcus theory has been extended to address heterogeneous electron transfer.

2.3 Electron transfer in homogeneous systems

We end the chapter by applying the concepts of transition state theory and quantum theory to the study of a deceptively simple process, electron transfer between molecules in homogeneous systems. We begin by examining the features of a theory that describes the factors governing the rates of electron transfer. Then, we discuss the theory in the light of experimental results on a variety of systems, including protein complexes. We shall see that relatively simple expressions may be used to predict the rates of electron transfer with reasonable accuracy.

2.3.1 The rates of electron transfer processes

Consider electron transfer from a donor species D to an acceptor species A in solution. The net reaction is

In the first step of the mechanism, D and A must diffuse through the solution and collide to form a complex DA, in which the donor and acceptor are separated by a distance comparable to r, the distance between the edges of each species. We assume that D, A, and DA are in equilibrium:

where ka and ka ′ are, respectively, the rate constants for the association and dissociation of the DA complex.

Our discussion concentrates on the following two key aspects of the theory, which was developed independently by R.A. Marcus, N.S. Hush, V.G. Levich, and R.R. Dogonadze:

1. Electrons are transferred by tunnelling through a potential energy barrier, the height of which is partly determined by the ionization energies of the DA and D+A− complexes. Electron tunnelling influences the magnitude of κν.

2. The complex DA and the solvent molecules surrounding it undergo structural rearrangements prior to electron transfer. The energy associated with these rearrangements and the standard reaction Gibbs energy determine Δ‡G.

According to the Franck–Condon principle, electronic transitions are so fast that they can be regarded as taking place in a stationary nuclear framework. This principle also applies to an electron transfer process in which an electron migrates from one energy surface, representing the dependence of the energy of DA on its geometry, to another representing the energy of D+A−. We can represent the potential energy (and the Gibbs energy) surfaces of the two complexes (the reactant complex, DA, and the product complex, D+A−) by the parabolas characteristic of harmonic oscillators, with the displacement coordinate corresponding to the changing geometries (Fig. 24.27). This coordinate represents a collective mode of the donor, acceptor, and solvent.

According to the Franck–Condon principle, the nuclei do not have time to move when the system passes from the reactant to the product surface as a result of the transfer of an electron. Therefore, electron transfer can occur only after thermal fluctuations bring the geometry of DA to q* in Fig. 24.27, the value of the nuclear coordinate at which the two parabolas intersect. The factor κν is a measure of the probability that the system will convert from reactants (DA) to products (D+A−) at q* by electron transfer within the thermally excited DA complex. To

understand the process, we must turn our attention to the effect that the rearrangement of nuclear coordinates has on electronic energy levels of DA and D+A− for a given distance r between D and A (Fig. 24.28). Initially, the electron to be transferred occupies the HOMO of D, and the overall energy of DA is lower than that of D+A− (Fig. 24.28a). As the nuclei rearrange to a configuration represented by q* in Fig. 24.28b, the highest occupied electronic level of DA and the lowest unoccupied electronic level of D+A− become degenerate and electron transfer becomes energetically feasible.

Over reasonably short distances r, the main mechanism of electron transfer is tunnelling through the potential energy barrier depicted in Fig. 24.28b. The height of the barrier increases with the ionization energies of the DA and D+A− complexes. After an electron moves from the HOMO of D to the LUMO of A, the system relaxes to the configuration represented by q0 P in Fig. 24.28c. As shown in the illustration, now the energy of D+A− is lower than that of DA, reflecting the thermodynamic tendency for A to remain reduced and for D to remain oxidized.

2.4 Heterogeneous electron transfer

In heterogeneous electron transfer, an electron moves between a chemical species and a solid-state electrode. Theories addressing heterogeneous electron transfer have applications in electrochemistry and the design of solar cells.

The strength of the electronic coupling of the donor and acceptor decides whether the electron transfer reaction is adiabatic or non-adiabatic. In the non-adiabatic case the coupling is weak, i.e. H_AB in Fig. 3 is small compared to the reorganization energy and donor and acceptor retain their identity. The system has a certain probability to jump from the initial to the final potential energy curves. In the adiabatic case the coupling is considerable, the gap of 2 H_AB is larger and the system stays on the lower potential energy curve.

Marcus theory as laid out above, represents the non-adiabatic case. Consequently the semi-classical Landau-Zener theory can be applied, which gives the probability of interconversion of donor and acceptor for a single passage of the system through the region of the intersection of the potential energy curves

$P_{if} = 1-\exp[-\frac{4\pi^2 {H_{if}^2}}{hv \mid(s_i - s_f)\mid}]$

where H_if is the interaction energy at the intersection, v the velocity of the system through the intersection region, s_i and s_f the slopes there.

Fig. 3 Energy diagram for Electron Transfer including inner and outer sphere reorganization and electronic coupling: The vertical axis is the free energy, and the horizontal axis is the "reaction coordinate" – a simplified axis representing the motion of all the atomic nuclei (inclusive solvent reorganization)

Working this out one arrives at the basic equation of Marcus theory

$k_{et} = \frac{2\pi}{\hbar}|H_{AB}|^2 \frac{1}{\sqrt{4\pi \lambda k_bT}}\exp \left ( -\frac{(\lambda +\Delta G^\circ)^2}{4\lambda k_bT} \right )$

where $k_{et}$ is the rate constant for electron transfer, $|H_{AB}|$ is the electronic coupling between the initial and final states, $\lambda$ is the reorganization energy (both inner and outer-sphere), and $\Delta G^\circ$ is the total Gibbs free energy change for the electron transfer reaction (

is the Boltzmann constant and

is the absolute temperature).

Thus Marcus's theory builds on the traditional Arrhenius equation for the rates of chemical reactions in two ways: 1. It provides a formula for the activation energy, based on a parameter called the reorganization energy, as well as the Gibbs free energy. The reorganization energy is defined as the energy required to “reorganize” the system structure from initial to final coordinates, without making the charge transfer. 2. It provides a formula for the pre-exponential factor in the Arrhenius equation, based on the electronic coupling between the initial and final state of the electron transfer reaction (i.e., the overlap of the electronic wave functions of the two states).

CHAPTER III

CONCLUSION

There are several classes of electron transfer, defined by the state of the two redox centers and their connectivity they are Inner-sphere electron transfer and Outer-sphere electron transfer

Marcus theory is used to describe a number of important processes in chemistry and biology, including photosynthesis, corrosion, certain types of chemiluminescence, charge separation in some types of solar cell and more. Besides the inner and outer sphere applications, Marcus theory has been extended to address heterogeneous electron transfer.

REFERENCES

Anonim, 2013, Electron Transfer (Online), (http://en.wikipedia.org/Electron transfer)

Atkins, P., dan Paula, J.D; 2005, Physical Chemistry for the Life Sciences, Freeman Publishers, Oxford.

Atkins, P., dan Paula, J., 2006, Atkins’ Physical Chemistry, Eighth Edition, W. H. Freeman And Company, New York.

Corral, S., 2013, Marcus Theory of Electron Transfer (Online), (http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics)

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2.2 Marcus Theory of Electron Transfer

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