@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 Theory and Calculation of the Reorganization Energy of Electron Transfer at Liquid/Liquid Interface Hadi Jabbar Al-Agealy Adil Ali Al-Saadi Dept. of Physics/ College of Education Pure Science (Ibn Al-Haitham) University of Baghdad Received in: 13 May 2012 Accepted in:24 September 2012 Abstract A description of the theoretical of the reorganization energies have been described according to the outer-sphere Marcus model .It is a given expression according this model unable to evaluate the reorganization energy for electron transfer at liquid /liquid interface. The spherical model approach have been used to evaluate the radius of donor and acceptor liquid alternatively .Theoretical results of the reorganization free energy for electron transfer at liquid/liquid interface system was carried out . Matlap program is then used to calculate 𝐸0 for electron transfer reaction between water donor stated and many liquid acceptor state. This shows a good agreement with the experiment. The results calculation shows that 𝐸0 is a function of dielectric constant and refractive index and polarity of acceptor . Key word: Reorganization energy, Electron transfer, liquid/liquid interface. 104 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 Introduction Electron transfer (ET) reaction is one of the most fundamental processes in chemistry and biology. Both experiment and theory calculation of electron transfer (ET) have made tremendous progress [1] .The transfer of a single electron from an atom or a molecule to another is considered to be the most elementary chemical and biological reaction[2] . In simple terms, an electron transfer (ET) reaction involves the transfer of an electron from a 'donor' to an 'acceptor'[3].Since no chemical bonds are broken or formed in the transfer and further more the changes in the bond lengths and angles are rather small[4] . Electron transfer (ET) reaction involves an oxidation of donor |𝐷 > state and reduction of an acceptor |𝐴 > state are among the most significant and universal processes[5]. The electron donor acceptor molecules play a key role in understanding the charge transfer processes[6].The effect of a solvent on the kinetics of (ET) reaction is controlled by coupling of the electric charge of the transferred electron to the nuclear component of the electric potential created by the partial charges on the overall natural solvent molecules [7].One of the most important factor on electron transfer reaction is the reorganization energy 𝐸0(𝑒𝑉) that is defined as the charge in energy if the reactant state |𝐷 > −|𝐴 > were to distort to equilibrium configuration of the product state |𝐷+ > −|𝐴− > without transfer of the electron [8].Despite the importance of 𝐸0(𝑒𝑉) in the electron transfer kinetics precise measurement of this quantity are rather rare as it is difficult to measure the reorganization energy directly [9]. The charging path is use to produce a system with a non equilibrium dielectric polarization to obtain statistical mechanical expression for the free energy of a system [10].In this paper, we will study the reorganization energy one of the most important parameters of the charge transfer in liquid/liquid interface with outer-sphere model according the electrostatic potential. Many acceptor liquids are used with water donor to calculate the value of reorganization energies. Theory The Marcus description of outer-sphere electron transfer reaction has been extensively studied for electron transfer between molecular electron acceptor|𝐴 > and donor |𝐷 > species in solution [11].We assume the electron transfer processes that are obtained between a reactant one liquid donor |𝐷 >state and a reactant immiscible liquid acceptor |𝐴 >state system as illustrated in scheme 1. |𝐷 > (𝑙𝑖𝑞1) + |𝐴 > (𝑙𝑖𝑞2) 𝐸𝑇 �� |𝐴− > (𝑙𝑖𝑞1) + |𝐷+ > (𝑙𝑖𝑞2) Under anon equilibrium of the two reactant system in a fixed position with a charge distribution 𝜌 and a distance R between their center. Frist assumes that two dielectric liquid as a plane interface at Z=0,and electron is a fixed at d form interface [10]. The electrostatic potential is generated at any point distant r from the center of the ion is given by . 𝛷(𝑟) = 𝑒 4𝜋∈0∈𝑠𝑟 ……………….. (1) The work required to charge the ion in dielectric solvent from ( 0 to 𝑒0) is 𝑊 = −∫ 𝛷(𝑟)𝑑𝑒 𝑒0 0 = −𝑒0 2 8𝜋∈0∈𝑠𝑟 ……………….. (2) For linearity medium to a charge in electric field and static treatment low frequency of electronic polarization in the system .When a solvent nuclear coordinates are fixed , but allowing the electronic polarization of solvent a adapted , then the charge that determines the distribution of coordinates in the transition state 𝑒𝐸𝑇 is to be given [13]. 𝑒𝐸𝑇 = 𝑒0 + 𝜆(𝑒 − 𝑒0) ……………….. (3) Where 𝜆 is the lagrangian coefficient ,then the potential in Eq.(1) can be written as. 𝛷(𝑟) = 𝑒0 4𝜋𝜖0𝜖𝑠𝑟 + 𝜆 (𝑒−𝑒0) 4𝜋𝜖0𝜖𝑜𝑝𝑟 ……………….. (4) 105 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 Where 𝜖𝑠and 𝜖𝑜𝑝 are the static and optical dielectric constant. The change in charge is the electronic polarization of the solvent and optical dielectric constant then the work required to change the ion in dielectric solvent is to be written as [13] . 𝑊𝑇 = ∫ 𝛷(𝑟)𝑑𝑒𝐸𝑇 = ∫� 𝑒 4𝜋𝜖0𝜖𝑠𝑟 + 𝜆 (𝑒−𝑒0) 4𝜋𝜖0𝜖𝑜𝑝𝑟 �𝑑𝑒𝐸𝑇 1 𝜆=0 = 𝑒(𝑒_𝑒0) 4𝜋𝜖0𝜖𝑠𝑟 + (𝑒−𝑒0) 2 8𝜋𝜖0𝜖𝑜𝑝𝑟 ……………….. (5) The work done to the change of the a actuation solvent is 𝑊𝑎𝑐𝑡 = 𝑒0 2 8𝜋𝜖𝑠𝜖𝑜𝑝𝑟 ……………….. (6) Then the energy of solvent that describe the non equilibrium dielectric polarization in the liquid /liquid system is given by adding Eq. (5) and Eq. (6) with Eq. (2), results. ∆𝐸 = 𝑒0 2 8𝜋𝜖𝑠𝜖0𝑟 + 𝑒 (𝑒−𝑒0) 4𝜋𝜖0𝜖𝑠𝑟 + (𝑒−𝑒0) 2 8𝜋𝜖0𝜖𝑜𝑝𝑟 − 𝑒0 2 8𝜋𝜖𝑠𝜖0𝑟 ……………….. (7) Simply to ∆𝐸 = (𝑒−𝑒0) 2 8𝜋𝜖0𝑟 � 1 𝜖𝑜𝑝 − 1 𝜖𝑠 � ……………….. (8) For a non equilibrium liquid-liquid interface the actual charge can be given as [14]. 𝑒0,1 = 𝑒1 + 𝑚�𝑒1 − 𝑒1 𝑝� = 𝑒1 − 𝑚∆𝑒 ……………….. (9) 𝑒0,2 = 𝑒2 + 𝑚�𝑒2 − 𝑒2 𝑝� = 𝑒2 + 𝑚∆𝑒 ……………….. (10) With Eq.(8),the energy of solvation for two ions is given by ∆𝐸𝑛𝑜𝑛𝑒𝑞 = 1 4𝜋𝜖0 �(𝑒1−𝑒01) 2 2𝑎1 + (𝑒2−𝑒02) 2 2𝑎2 − (𝑒1−𝑒01)(𝑒2−𝑒02) 𝑎1+𝑎2 �� 1 𝜖𝑜𝑝 − 1 𝜖𝑠 � ……………….. (11) We then obtain at a fixed position the reactant [15]. ∆𝐸𝑛𝑜𝑛𝑒𝑞 = 𝜆2𝐸0……………………………. .... ..(12) Where 𝐸0 is the contribution of the solvent reorganization energy due to reaction by comparing Eq. (11), and Eq. (12) ,𝐸0 can be written as. 𝐸0 = (Δ𝑒0)2 4𝜋𝜖0 � 1 2𝑎1 + 1 2𝑎2 − 1 𝑎1+𝑎2 �� 1 𝜖𝑜𝑝 − 1 𝜖𝑠 � ……………….. (13) Where 𝑅 = 𝑎1 + 𝑎2 is the separation distance between the two reactants and 𝑎1, 𝑎2 are the radii of ions,𝜖𝑜𝑝 𝑎𝑛𝑑 𝜖𝑠 refers to the optical and static dielectric constant of two liquids and given by [15]. 𝜖𝑜𝑝 = 𝜖𝑜𝑝1 + 𝜖𝑜𝑝2 ……………….. (14) 𝜖𝑠 = 𝜖𝑠1 + 𝜖𝑠2 ……………….. (15) Substituting Eq. (14) and Eq.(15) in Eq. (13) results. 𝐸0 = (Δ𝑒)2 4𝜋𝜖0 � 1 2𝑎1 + 1 2𝑎2 − 1 𝑅 �� 1 𝜖1 𝑜𝑝+𝜖2 𝑜𝑝 − 1 𝜖1 𝑆+𝜖2 𝑆� ……………….. (16) The radii of donor and acceptor can be estimated from the apparent molar volume using spherical approach [ 16]. 𝑎𝑖 = � 3𝑀𝑊 4𝜋𝑁𝐴𝜌 � 1 3 ……………….. (17) Where 𝑎𝑖is the radius of donor or acceptor , 𝑁𝐴 Avogadro's number constant, MW is the molecular weight ,and 𝜌 is the density of liquid masses. Results For the liquid/liquid interface systems ,one of the most important parameter for charge transfer is the reorganization free energies 𝐸0(𝑒𝑉).This can be calculation of theoretically by using the expression(15 ).The calculate the values of the reorganization energies𝐸0(𝑒𝑉) for water/liquid system, one can find the values of radius for donor (water) and acceptor (liquid) using Eq.(16),substation the values of Avogadro's construes 𝑁𝐴 = 6.02 × 1023 𝑀𝑜𝑙𝑒𝑐𝑢𝑙𝑒 𝑚𝑜𝑙 , molecular weight MW ,and Density mass 𝜌 for all liquids from table ( 1) in Eq. (16) we 106 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 can evaluate the theoretical values of radii for water and variety of liquid , values of this calculation one are listed in the table (2 ) . Next we can calculate the reorganization free energy for water / liquid system by inserting in expression ( 15) the values of radii of donor and accepter , dielectric constant 𝜖 optical dielectric constant𝜖𝑜𝑝 from table (1 ) and assume the distance 𝑅 = 𝑎𝐷 + 𝑎𝐴 between center to center for donor and acceptor knowing that 𝑒 2 4𝜋𝜖0 = 14.4 𝑒𝑉 the results of reorganization free energy have been summarized in table (3). Discussion In our research ,we have been applied the semi classical treatment to calculate the reorganization free energies for charge transfer at liquid/liquid interface system using a two spherical model based on the Marcus theory of electron transfer (ET) .The results of the reorganization energy for liquid/liquid system indicate that is in general whenever there is an increase in the dielectric constant for acceptor, there is an increase in the reorganization energies,similary whenever, there is an increase in the interface index for acceptor liquid leads to decrease in the reorganization energies for system with the same refractive index and dielectric constant for the donor .This can be explained from the physical meaning of the reorganization energy that is usually assumed comprise two contributions from the inner molecule and the oriented molecule dipoles lead to say the change transfer interaction for donor with acceptor molecule which results from the reorganization energy. The more range dielectric constant for acceptor reduce the reorientation of the donor molecule about acceptor needed more energy.It has been observed from table (3) that when the refractive index of acceptor molecule is large leads to small energy to reorganizefor system. Also one of the most effect on the reorganization energy is the polarity function 𝑓(𝑛, 𝜖) = � 1 𝜖𝑜𝑝 − 1 𝜖𝑠 � for system, the small polarity function results to decrease the reorganization energy. Table (3 ) shows that when the acceptor liquid oil more polar leads to have large value of the reorganization energy this because of the type of oil has large dielectric constant that shows for Dodecanese(𝜖𝑠≈2.5) has range value of (𝐸0 = 0.778 𝑒𝑉),while the Decalin oil has small dielectric constant 𝜖𝑠 = 2.196 that leads to small value of 𝐸0 ≈ 0.700 𝑒𝑉.On the other hand the reorganization energy for the system contains oil has large refractive index leads to small value for reorganization energy such that Idobenzene 𝑛 = 1.62 event has large dielectric constant 𝜖𝑠 = 4.5 this indicates that the effect of total polarity term .In summary the results of calculation of the reorganization energy 𝐸0 in table ( 3),indicate that the charge transfer is more probable in liquid-liquid system has more polarity parameter for example water/formic acid have 𝑓(𝑛, 𝜖) ≅ 0.2657 lead to large reorganization energy 𝐸0 ≈ 0.898 𝑒𝑉.Not ably the charge transfer in system has large dielectric constant are stronger than system have small dielectric constant. Our results show agreement with experimental value for 𝐸𝑂 [12 ]. Conclusions It can be summarized depending the our results of calculation that the charge transfer is more probable happen and stronger depends on the three parameters dielectric constant, optical properties (refractive index )and polarity .It has shown that all donor molecular have large dielectric constant ,has large reorganization energies for charge transfer ,indicate that the transitions involve more energy to happen .On the other hand the increase of refractive index leads to small depending on the optical properties of molecule. Consequently the system has large 𝐸0 refers that type of oil has more reaction media than other oil types with same donor. 107 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 References 1-Jing, M.C; TongIng, H.and Chung,-Y.M (1990) , Experimental Investigation of Excited- State Electron-Transfer Reaction: Effects of Free Energy and Solvent on Rates, J. Phys. Chem,94 : 2889-2896 2-AL-Agealy, H.J.M and Hassooni, M.A. (2011) ,Calculate of the Rate constant of Electron Transfer in[TiO]_(2-)Safranine Dye system".Ibn-AL-Haitham for pure&appl.Sci, 24(3): 64- 77. 3-Kavarnos,J.G. (1993), fundamental photoinduced electron transfer, Book . ISBN 0-89573- 751-5 VCH Publishers, Inc. New York. 4-Hussein,K.M. (2011), Study of the electron transfer at metal/semiconductor interface by using quantum mechanical theories, M.Sc. Thesis, university of Baghdad. 5-Hassooni,M.A. (2009) ,A quantum mechanical model for electron transfer at semiconductor /Dye system in solvent system" M.Sc. Thesis, Baghdad University College of education Ibn – AL-Haitham. 6-Anunays, A. (2003), Electron donor/acceptor molecular, proc.Indian.Natu.Scil.Acad., 69A( 1): 95-107. 7-Lickeko,LM. and Matyushov, D.V. (2003) ,Reorganization energy of inter molecular electron transfer in solvent near isotropic nematic transition,J.chem.phys. 119 ( 3): 1559. 8-Malin,L.A. (2001) ,Electron transfer in Ruthenium manganese complexes for Artificial photo synthesis, Ph.D. Thesis, uppsala university. 9-Sharp, K.A. (1998) ,Calculation of electron transfer reorganization energies using the finite difference poisson-Boltzman model " Bio, phys. J. 73: 1241-1250. 10-Marcus,R.A. (1990) Reorganization energy for electron transfer at liquid –liquid and dielectric semiconductor –liquid interface"J.phys.chem. 94: 1050-1055. 11-Florian,G. (2004) electron transfer processes at semiconductor /liquid and metal Nano gab junction ,Ph.D. Thesis ,California institute of technology.pasdena,California. 12 -Thu, B.T. (1984) Charge Transfer to a Solvent state,J.Phys.chem. (88): 3906-3913.L.A.75 Laboratories physico-chimie des Rayonnements.Bat.350,universite paris-sud,91405 Orsay,France. 13-Marcus,R.A.(2000) Tutorial on a rate constant and reorganization energies,J.Electroanlytical chem.983, 2. 14-Marcus, R.A. ( 1960),Discussion comment on mixed reaction-diffusion controlled rates, Discuss Faraday Soc. 29,21-31. 15-Marcus,R.A. (1991) ,Theory of electron transfer rate a cross liquid-liquid interface, J.phys.chem,95 :2010-2013. 16-Al-Agealy, H.J. and Hassoni, M.A. (2010) ,A theoretical study of the effect of the solvent tyoe on the reorganization energies of dye /semiconductor system interface" Ibn Al-Haitham J. For Pure & Appl. Sci, 23(3): 51-57. 17-Greenwood, N. N.and Earnshaw, A.(1997) Chemistry of the Elements, 2nd edition .Butterworth-Heinemann, Oxford, UK. 18- Wells, A. F. (1984) ,Structural Inorganic Chemistry" 5th edition., Oxford University Press, Oxford, UK, 1984. 19-Silberberg, M. S. (2009), Chemistry, Book, 5th edition, McGraw-Hill. acidity values from. 20-West, R.C (1995) ,Handbook of chemistry and physics" 76thed.CRC.press:BocaRaton.FL. 21-Paul,W.; Derek,M.D;David,J.G.C. and Donald,G.T. (2010) ,Minnesota Solvent Descriptor Database, Department of Chemistry and Supercomputer Institute, University of Minnesota ,Minneapoils.MN 55455-0431. 108 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 Table(1):Characteristic of Liquid Material Liquid Type Molecule weight (MW) (𝒈. 𝒎𝒐𝒍−𝟏) [17,19] Density(𝛒𝛒) ( 𝒈. 𝒄𝒎−𝟑) [17,19] Dielectric constant (𝝐𝒔) [20,21] Refractive index(n) [20,21] water 18 1 80 1.333 Acetone 58.08 0.791 20.493 1.3588 Dodecane 170.33 0.750 2 1.421 Decalin 138.25 0.896 2.196 1.47553 Formic acid 46.03 1.22 51.1 1.3714 Bromoform 252.73 2.889 4.2488 1.6005 Chloroform 119.38 1.483 4.7113 1.4459 Cyclohexane 84.16 0.779 2.0165 1.4266 Perfluorobenzene 186.05 1.6120 2.029 1.3777 N-methylformamide 59.07 1.003 181.59 1.4319 N,N dimethylformamide 73.09 0.944 37.219 1.4305 Ethanol 46.0414 0.790 24.852 1.3611 n-hexadecane 226.44 0.733 2.0402 1.4345 Idobenzene 204.01 1.831 4.5470 1.6200 Cumene 120.19 0.862 2.3712 1.4912 Mesitylene 120.19 0.8637 2.2650 1.4994 Haxanic acid 116.16 0.93 2.6 1.4163 1,2 ethanediol 63 1.1151 40.245 1.4318 m-xylene 106.16 0.86 2.3478 1.4972 Table (2):The theoretical calculation values of radii 𝒂𝒊(𝑨°) for donor and acceptor liquids Liquid Type Molecule weight (MW) (𝒈. 𝒎𝒐𝒍−𝟏) [17,19] Density (𝛒𝛒) ( 𝒈. 𝒄𝒎−𝟑) [𝟏𝟕, 𝟏𝟗] Radii 𝑎𝑖(𝑨𝟎) water 18 1 1.92520792 Acetone 58.08 0.791 3.076121696 Dodecane 170.33 0.750 4.481913106 Decalin 138.25 0.896 3.940087332 Formic acid 46.03 1.22 2.463847665 Bromoform 252.73 2.889 3.261043233 Chloroform 119.38 1.483 3.171881441 Cyclohexane 84.16 0.779 3.498723009 Perfluorobenzene 186.05 1.6120 3.576638252 N-methylformamide 59.07 1.003 2.858087259 N,N dimethylformamide 73.09 0.944 3.13099322 Ethanol 46.0414 0.790 2.848135287 n-hexadecane 226.44 0.733 4.96595975 Idobenzene 204.01 1.831 3.534878643 Cumene 120.19 0.862 3.809258931 Mesitylene 120.19 0.8637 3.806758065 Haxanic acid 116.16 0.93 3.672073423 1,2 ethanediol 63 1.1151 2.818787796 m-xylene 106.16 0.86 3.657696142 109 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 Table(3):Our calculation results of reorganization free energy 𝑬𝟎 (𝒆𝑽) for charge transfer at water/liquid interface system. System Type Dielectric constant 𝝐𝒔 for acceptor [19-20] Optical dielectric constant 𝝐𝒐𝒑 for acceptor Reorganization free energy 𝑬𝟎( 𝒆𝑽) Water/Acetone 20.493 1.84633744 0.8516752339 Water/Dodecanese 2 2.019241 0.778518135 Water/decalin 2.196 2.177188781 0.7002127746 Water/formic acid 51.1 1.88073796 0.8986405084 Water/bromoform 4.2488 2.56160025 0.6932973949 Water/chloroform 4.7113 2.09062681 0.7858438989 Water/cyclohexane 2.0165 2.03518756 0.7861255431 Water/perfluorobenzene 2.029 1.89805729 0.8150156249 Water/N,Methylformamide 181.59 2.05033761 0.8363805396 Water/N,Ndimeethylformamide 37.219 2.04633025 0.8075301745 Water/ethanol 24.852 1.85259321 0.8635918533 Water/n-hexadecane 2.0402 2.05779025 0.8246426859 Water/Idobenzene 4.5470 2.6244 0.6761547218 Water/Cumene 2.3712 2.22367744 0.7415657842 Water/Mesitylene 2.2650 2.24820036 0.7369760191 Water/hexanic acid 2.6 2.00590569 0.8118435171 Water/1,2 ethanediol 40.245 2.05005124 0.8244227082 Water/m-xylene 2.3478 2.24160784 0.7406532221 Fig.(1): Solute-solvent cage charge transfer complex model for an electron-transfer reaction between a redox reactant pair. Donor D and acceptor A. Initial state Intermediate CT state Final state 110 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I2@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (2) 2013 الحسابات النظریة لطاقة اعادة الترتیب لالنتقال االلكتروني لسطح سائل/سائل ھادي جبار مجبل العكیلي عادل علي منصور السعدي جامعة بغداد /) ابن الھیثم( للعلوم الصرفة الفیزیاء/كلیة التربیةعلوم قسم 2012ایلول 24قبل البحث في ، 2012ایار 13 :فياستلم البحث الخالصة وص�������فت طاق�������ة اع�������ادة الترتی�������ب تبع�������ا النم�������وذج م�������اركوس الكروي.اس�������تخدمت عالق�������ة تبع�������آ لھ�������ذا االنم�����وذج تمكن�����ا بھ�����ا م�����ن حس�����اب طاق�����ة اع�����ادة الترتی�����ب لالنتق�����ال االلكترون�����ي لس�����طح سائل/س�����ائل . اس�����تعمل ر للس������ائل الواھ������ب والقاب������ل عل������ى التتابع.النت������ائج النظری������ة انم������وذج التقری������ب الك������روي لحس������اب نص������ف القط������ للطاق�����ة الح�����رة الع�����ادة الترتی�����ب لالنتق�����ال االلكترون�����ي لس�����طح نظ�����ام سائل/س�����ائل اجری�����ت. ببرن�����امج الم�����اتالب لتفاع������ل االنتق������ال االلكترون������ي م������ابین حال������ة الواھ������ب ا 𝐸0) ادة الترتی������ب(ال������ذي اس������تعمل لحس������اب طاق������ة اع������ المس������تقبل للس������وائل المختلف������ة، نت������ائج الحس������ابات اظھ������رت توافق������اً جی������داَ م������ع العملي،النت������ائج (الم������اء) وحال������ة دالة ثابت العزل الكھربائي ومعامل االنكسار واالستقطابیة للقابل. 𝐸0) ( المحسوبة بینت ان :طاقة اعادة الترتیب، االنتقال االلكتروني،سطح سائل/سائل.الكلمات المفتاحیة 111 | Physics