Electron Transfer At Metal/Molecule Interface Hadi J. M. Al-Agealy Mohammed Z. Fadhil Dept. of Physics/College of Education for pure science (Ibn-ALHaitham)/ University of Baghdad Received in: 24 June 2012, Accepted in: 15 October 2012 Abstract Theoretically description of the electron transfer of the electron transfer of met/mol has been investigated in this work according to the quantum theory. By using a model that is derived depending on the first order perturbation theory, the rate constant at met/mol interface can be calculated with the calculated reorganization energy. The reorganization energy that is evaluated according to the outer sphere model is based on the electstatistics potential of the molecular donor and acceptor. The molecular parameters introduced in this model are the molecular weight, mass, density, and radius of molecule have been evaluated according to the apparent molar volume using spherical approach. The theoretical results are obtained according to our model of rate constant for electron transfer, a corresponding with the experimental data for some qualilative metal/molecule interface some qualitative of the experimental studies . Key word : Electron transfer, Metal/Molecule interface 86 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Introduction Electron transfer (ET) from a metal donor to an acceptor molecule state is one of the simplest conceivable reactions, as chemical bonds are neither formed nor broken. Such charge transfer reactions are of vital importance to a variety of processes in physics, chemistry and biology. For example, homogeneous ET is the primary step in photosynthesis, and various chemical reactions. Electron transfer at molecule–solid interfaces, on the other hand, plays an important role in technologically highly relevant fields [1]. Electronic transport has been a central issue of physical research during the last century. Tremendous amounts of materials have been investigated, for instance metals [2]. Electron transfer processes through molecular systems have attracted much attention over the past fifty years [3]. Now a days , the field of organic electronics has reached the point where several applications are routinely available for use.Others are close to be commerce lilted , while others are in a design or testing phase for unique application including nano scale technologies [4]. Electron transfer at the metal/ molecule interface is important for technological application such as bio catalysis, electrochemistry, photodiodes, solar energy conversion, and more recently, molecular electronics [5] .The traditional experimental approach for studying these processes is based on measuring the electron transfer in D – A super molecular systems between electron donor and acceptor A unit that are covalently liked through molecular. In many instances electron transfer reaction takes place near interface are part of the interface being the solvent and the other part being a more or less solid such as a metal [6]. Electron transfer processes have been studied extensively in donor – acceptor system and in the last decade at an electrode interface through an electrochemical approach. Rudolph Marcus described electron transfer between two stats, a model which was the basis for his 1992 Nobel prize [7]. Latter, this model was extended to describe Electron transfer from a single donating state to a continuum of accepting state. Understanding transport across the interface between the active organic molecule and the metallic electrode has proved particular challenging, especially in the single molecule limit [8]. In this paper, a theoretical calculation of rate constant for electron transfer in Metal/Molecule interface system is given depending on the reorganization energy ,and the coupling matrix element coefficient. Theory A theoretical model formulation for charge transfer in metal /molecule interface utilized is based on the first order perturbation theory and quantum mechanic theory. The state of donor and acceptor system is given by the time dependent wave function [9]. φ(r,t)=∑ CK(t) < φn(r) > ∞0 e _iEn T ħ ……………….. (1) The Hamiltonian model for our system consists of three parts [10]. Ĥmet−mol= Ĥmet + Ĥmol + Ûmet/mol ……………………..….….... (2) The Hamiltonian operator of the metal/molecules system Ĥmet−mol satisfies the Schrodinger equation iħ ∂ ∂t �φ(r,t) >= Ĥmet−mol�φ(r,t) > [11]. The probability of the rate electron transfer from donor state to acceptor state per unit time is the rate constant that is given by [12]. KET = WDA t = 2π ħ │HDA(E)│2 δ(EA − ED)………………….……… (3) Then the probability of electron transfer rate constant equation [3], also can be expressed in term of density of state ρ(E − EA − ED) . KET = 2π ħ │HDA(E)│2ρ(E)……………………………………….…. (4) Where the integral delta function is ∫ ρ (E − Eo)δ(E − Eo)dE = ρ(Eo) ∞ −∞ [13]. 87 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 The system density operator ρ by the definition can be expressed in the form [14]. ρ(E) = e −(E°+∆G) 4E°kBT (4Emol metkBT) 1 2� …………………………………………………. (5) Where ∆G is the free energy difference between the acceptor and the donor and E° is the energy of reorganization .The rate constant for electron transfer from a metal to a reactant at the interface is given by [15]. KET = 2π ħ ∫ │HDA(t)│2 ∞ 0 1 (4Emol metkBT) 1 2� F(E) e −(E°+∆G) 2 4Emol met kBT dE …………..... (6) Where F(E) is the Fermi-Dirac distribution with E measured relative to the chemical potential of the electrons F(E) = 1 1+exp E−EF kBT [16]. The expansion of HDA(∈) is given by. HDA(∈) = a0V0 + a ∈ + ⋯ ≈ |V0|2(1 + a ∈ +b ∈2+ ⋯ … ………....… (7) The integration of equation [6], with expansion in equation [7], can be written as. KET = 2π ħ e −Emol met 4kBT �4πEmol metkBT ∫ |HDA(∈) +∞ −∞ | 2 (1+∈ 2+∈4+⋯ ) 2(e ∈ 2kBT+e −∈ 2kBT e −∈2+F(∈,η) 4Emol metkBT dE ……..….. (8) Where F(∈, η) = 2(Emol met−∈)eη − e2η2, the result of solvent integral equation[8] KET = 2π ħ e −Emol met 4kBT �4πkBT |HDA|2 �πkBT − π3kB 3T3 16Emol met + 5π5kB 3T3 522(Emol met)2 − ⋯ . �....................... (9) Using the first and second term that. KET ≅ 2π ħ e −λ 4kBT �4πkBT |HDA|2 �πkBT − π3kB 3T3 16Emol met�………………………………..… (10) Where ħ is the planks constant,kB is the Boltzmann' sconstant,T the temperature ,|HDA|is the coupling coefficient between two state system and Emol met is the free energy. The reorganization energy for charge transfer at metal /molecule system a notification of Marcus theory exist which takes into account the electrostatic interaction between the metal and molecule is given by [17]. Emol met = q 2 8πεo �1 D − 1 2R � ( 1 n2 − 1 ε )……………………………………….….. (11) Where εois the vacuum permittivity , ε is the static dielectric constant of the solvent ,n is the refrective index of the solvent ,R is the distance between center to center ,and D is the radius of the molecules. The radii of molecules can be estimated from the apparent molar volume using spherical approach [18]. D = � 3M 4πNAρ � 1 3…………………………………………………….……….. (12) Where M is the molecular weight, NA is the Avogadro's number, and ρ is the mass density. Results First-order perturbation theory and quantum theory treatment have been used to study the transitions of electron at metal/molecule system. One of the important parameters for calculation and study of the rate constant of electron transfer at metal/molecule interface is the reorganization energies Emol. met.(eV). It can be evaluated theoretically using equation [11], the first steps to calculate the reorganization energies Emol. met.(eV) involved which estimated the radii for donor metals and acceptor molecules using spherical approach equation [12],inserting the values of Avogadro's 88 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 construes N = 6.02 × 1023 Molecule mol ,molecular weight M ,and density mass 𝜌 for all metals and molecules from tables (1) to (2)in equation [12], we can estimate the values of radii for metals and variety of molecules , results of calculation are listed in the table (2) . Next we can calculated the reorganization energy for metal / molecule system for Au metals donor ,and (4-aminothiophenol) ,(3,4,10-preylenetetracurboxyleicdiimide) ,Pentacene, and naphthalene an acceptor molecules by substituting in equation[11], the values of accepter radius D, dielectric constant 𝜀 optical dielectric constant𝜖𝑜𝑝 for solvents from table (2) and assume the distance R = DD + DA between center to center for donor and acceptor, knowing that e 2 8πϵ = 7.2 eV , results of reorganization energy have been summarized in table (3). Next, we calculated the rate constant of electron transfer at metal / molecule depending on Eq. [10], Inserting the results of the reorganization energy from table (3), and take the coupling coefficient (91) cm-1 [20]. Results are summarized in table (4) Discussion As depending on quantum theory, a first-order perturbation theory and quantum theory treatment have been used to study the transitions of electron at metal/molecule system. The most important factor that limited the values of rate constant at metal/molecule system is the reorganization energy of electron transfer. It is calculated according to continuum classical theory .These theoretical approaches are modeled in the sense that their physical concepts such as a refractive index, and static dielectric constant for donor acceptor system are determined. Table (3) shows that the reorganization energy values for metal / molecule system increase with the increase of the dielectric constant for the solvent lead to decrease in rate compared with system having small reorganization energy ,because the system has small value of reorganization energy more orient to transfer of electron. On the other hand there is an increase in the refractive index for solvent leads to decrease in the reorganization energies for all metal / molecule systems. The interactions of electron transfer should be affected by properties of organic solvent molecules, since these molecules have polarity parameter [ 1 ∈op − 1 ∈s ] which gives a less defined, the small polarity function results to decrease the reorganization energy and increase in rate of charge for system that shows a comparsion between table(3), and table(4) for rate constant. The more range dielectric constant for acceptor reduces the reorientation of the donor metal about acceptor molecule 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 reorganizae for system and large rate of transfer see table (4).Also, then in spite of these facts, the results showed in table (4) are depending on the active radii for both donor and acceptor respectively this meane the rate dependence on distant. Also,table (4) shows that when the solvent is more polar leads to have large value of the reorganization energy and small rate transfer, this is because of the type of solvents has large dielectric constant and small refractive index that is shown for 2,2,2-trifluoroethano solvent have (ε≈ 26.726) and refractive index n= 1.2907 have polarity range value of (0.5628 ) ,and the reorganization energy are ranged Emol. met.(eV) = 0.77748 , 0.565626, 0.583684 ,and 0.770667eVfor theAu/naphthalene,Au/3,4,10,perylenetetracarboxyleicdiimide, Au/pentacene, and Au/4,aminothiophenol interface system and rate KET =1.92 × 10 11 ,2.25×1011 ,2.22×1011 ,1.93×1011 On the other hand the xylene liquid has small polarity ≈ 0.0259 , this indicats that xylene have small dielectric constant 2.3879 and large refractive index 1.4995,results to small 89 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 reorganization energy and large rate constant(8.88 × 1011 , 1.04 × 1012 , 1.02 × 1012 , 8.92×1011) that are shown in table(4). That leads to opinion the reorganization energies are the key of the probability of electron transfer at metal / molecule interface. Our results show a good agreement with experimental data (7× 1011 − 4 × 1012 𝑠𝑒𝑐−1) [21]. Conclusions In this study, we have investigated the electron transfer at metal/molecule interface system depending on quantum theory. The reorganization energy has been calculated depending on the semi classical continuum dielectric model based on classical electron transfer theory. It can be concluded that electron transfer at metal/molecules interface system depends on the polarity from depending on both dielectric constant, and optical properties (refractive index). Our results of the reorganization energy calculation indicate that electron transfer is more probable happen in the metal/molecules system havy large polarity. It can be concluded that the metal/molecule with solvent system has large dielectric constant, leads to large reorganization energies for electron transfer, and the transitions involve more energy to happen. Also the increases of refractive index lead to small reorganization energy depending on the optical properties of solvent. Consequently the system has large E0 refers that system has less electron reaction media than other system has small reorganization energy. References 1-Stähler, J.; Meyer, M.; Zhu1, X .Y.;Bovensiepen, U. and Wolf2, M. (2007) Dynamics of electron transfer at polar molecule–metal interfaces: the role of thermally activated tunneling New Journal of Physics.Rev.9, 394. 2-Simon, V. (2006), Fabrication of Metal-Molecule Contacts, Group Prof. Dr. E. Scheer Department of Physics University of Konstanz. 3- Mendez, H.; thurzo,I. and zahn, R.T.(1997)Experimental study of charge transport mechanisms in a hybrid metal organic l inorganic device, Phys . Rev .8,(75), 45321 4–Elizabeth, T.; Marco, D.; Ferri, V.; Klaus, M. and Michael, Z.(2006)Approaches for controlling current Flowing through metal / Molecule sunctions , Adv. Mater .189: 1323 – 1328 5–Wei, C.; Wang, L.; Hang, C.;Ting, T.L.; Gao X.Y., Kian P.L., chen Z.K., and Andrew T.S.W. (2006) Effect of functional group of Arowatic thiols on electron transfer at molecule / Metal interface J.A chem. Soc. 71 6-Christoph H., and Marc.T.M.K.(2003)solvent Reorganization In electron and ion transfer reaction near a smoth Electrified Surface :a molecular dynamics study, J.an. Chem. Soc.125:9840-9845. 7-Maria ,A.R. (2003)electron transfer through molecular system in A metal /sameconductor Junction, PhD Thesis,Harvard University. 8-Kevin ,T.;pavel ,A.F.,and prashant, V.K.(2011)photoInduced electron transfer from quantum dot to metal oxide nano particles ,PNAS. 108 , (1). 9-ITZHAK B.(2005) QUANTUM MECHANICS,book . ,willy sonc publishing. 10-Al-Agealy H.J.M.,and Hassooni, M.A.(2011),calculate of the rate constant of electron transfer in TiO2-safranine dye system"IBN Al-HATHAM J.FOR PURE &APPL.SCI.24, (3) 11-Garrison ,J. C. and Chiao,R. Y. (2008)Quantum Optic,book, Oxford University Press Published in the United States by Oxford University Press Inc., New York 12-Jan,G.K. and Andreas,Gr.(2002)Semiconductors for micro and Nanotechnology—An Introduction for Engineers, WILEY-VCH Verlag GmbH, Weinheim 90 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 13-John,W.N.(2000)QUANTUM MECHANICS, book,Physics Department University of Wisconsin-MilwaukeeP.O.Box 413Milwaukee, WI 53201November 20 14-Shigeji, F.and Salvador, G.(2002)Quantum Statistical Theory of Superconductivity, Book,Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow 15- Mohsin Aneed Hassooni (2009) A Theoretical Model for Electron Transfer in Dye/ Semiconductor System Interface with Verity Solvents” Ph.D, Thesis, IBN Al-HATHAM of University of Baghdad 16-Charles, k.(2005) Introduction to solid state physics ,book 8th edition, Wiley and Sonc pub. 17- Kuciauskas, H. and Micheal .S. (2001)Electron transfer in Tio2 solar cells , J. Phys .Chem. B. 105. (2):394 – 402 18–AL_Agealy H.J., and Hassooni M.(2010) A theoretic study of the effect of the solvent type on the reorganization energies of Dye – semiconductor system interface, Ibn AL_Haitham G.hor pure of appl. Sci. 23(3): 51 – 57. 19-Paul, W.; Derek, M.; Dolney, David, J.; Giesen, Christopher J., Cramer (2010) Minnesota Solvent Descriptor Data base ,Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455-0431. 20-Nienh, H.; chung, M. and Charles, H.(2000) Portrait of the potential femtosecond studies of electron dynamics at interface .ACC.Chm.Res. 33:111-118. 21- Zhu, X.Y. (2004) Electron structure and electron dynamics at molecule/metal interface surface science reports, 56: 1-83. Table No.(1):Properties and calculated radii of molecule[11] Molecule Molecule weight 𝐠. 𝐦𝐨𝐥−𝟏 [11] density 𝐠. 𝐜𝐦−𝟑 [11] Radii calculated (A) Pentacene 278.36 1.3 4.39534 Nphthalene 128.17 1.14 3.54594 3,4,10,perylenetetracarboxyl eicdiimide 390.35 1.68 4.51668 4-aminothiophenol 125.19 1.2 3.4586 Table No.(2):Properties of organic solvent[19] Solvent type Refraction index (n) Dielectric constant (ε) 1,1,1-trichloroethane 1.4379 7.0826 Dichloroethane 1.4448 10.125 Hexanol 1.4178 12.51 Pentanol 1.4101 15.13 Butanol 1.3993 17.332 Nitropropane 1.4018 23.73 Trifluoroethanol 1.2907 26.726 Acetonitrile 1.3442 35.688 Dimethylsulfoxide 1.4170 46.826 formic acid 1.3714 51.1 N-methylformamide(E/Z mixture) 1.4319 181.56 Formamide 1.4472 108.94 Water 1.3328 78.355 xylene (mixture) 1.4995 2.3879 Dibromoethane 1.5387 4.9313 91 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 Table No.(3): Theoretical results of the reorganization energy for electron transfer at metal/ molecule interface system. Solvent Au/ nphthalene Au/3,4,10,peryl enetetracarbox yleicdiimide Au/pentacene Au/4,aminothiop henol xylene(mixture) 0.035863 0.026091 0.026924 0.035549 Dibromoethane 0.303312 0.220663 0.227708 0.300654 1,1,1-trichloroethane 0.47306 0.344157 0.355144 0.468914 1,2- dichloroethane 0.525296 0.38216 0.39436 0.520694 1- hexanol 0.576749 0.419592 0.432987 0.571695 Pentanol 0.603394 0.438977 0.452991 0.598107 1- butanol 0.625758 0.455247 0.46978 0.620275 1- nitropropane 0.644732 0.46905 0.484024 0.639082 2,2,2- trifluoroethanol 0.77748 0.565626 0.583684 0.770667 Acetonitrile 0.72577 0.528007 0.544863 0.71941 Dimethylsulfoxide 0.658443 0.479025 0.494318 0.652673 formic acid 0.70742 0.514657 0.531086 0.701221 Water 0.75998 0.552895 0.570546 0.753321 Formamide 0.64685 0.470591 0.485614 0.641182 N-methylformamide (E/Z mixture) 0.666091 0.484589 0.500059 0.660254 Table No.(4) : Our theoretical results of electron transfer rate constant for metal/ mo0lecul interface system with variety solvent at the coupling coefficient H= 91 cm-1 Rate of electron transfer KET (sec -1) Au/4- aminothiop henol Au/pentacen e Au/3,4,10,pe rylenetetrac arboxyleicdi imide Au/nephthalen Solvent 8.92ˣ1011 1.02ˣ1012 1.04ˣ1012 8.88 ˣ1011 xylene(mixture) 3.09ˣ1011 3.55ˣ1011 3.61ˣ1011 3.08 ˣ1011 Dibromoethane 2.47ˣ1011 2.84ˣ1011 2.89ˣ1011 2.46 ˣ1011 1,1,1-trichloroethane 2.35ˣ1011 2.7ˣ1011 2.74ˣ1011 2.34 ˣ1011 1,2- dichloroethane 2.24ˣ1011 2.57ˣ1011 2.61ˣ1011 2.23ˣ1011 1- hexanol 2.19ˣ1011 2.52ˣ1011 2.56ˣ1011 2.18 ˣ1011 Pentanol 2.15ˣ1011 2.47ˣ1011 2.51ˣ1011 2.14 ˣ1011 1- butanol 2.12ˣ1011 2.43ˣ1011 2.47ˣ1011 2.11 ˣ1011 1- nitropropane 1.93ˣ1011 2.22ˣ1011 2.25ˣ1011 1.92 ˣ1011 2,2,2- trifluoroethanol 1.99ˣ1011 2.29ˣ1011 2.33ˣ1011 1.99 ˣ1011 Acetonitrile 2.09ˣ1011 2.41ˣ1011 2.45ˣ1011 2.09 ˣ1011 Dimethylsulfoxide 2.02ˣ1011 2.32ˣ1011 2.36ˣ1011 2.01 ˣ1011 formic acid 1.95ˣ1011 2.24ˣ1011 2.28ˣ1011 1.94 ˣ1011 Water 2.11ˣ1011 2.43ˣ1011 2.47ˣ1011 2.1 ˣ1011 Formamide 2.08ˣ1011 2.39ˣ1011 2.43ˣ1011 2.07ˣ1011 N-methylformamide 92 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013 / جزیئةالنتقال الاللكتروني لسطح معدن ا ھادي جبار مجبل العكیلي محمد زھیر فاضل /جامعة بغداد)ابن الھیثم(قسم الفیزیاء/كلیة التربیة للعلوم الصرفة 2012تشرین االول 15: قبل البحث في ، 2012حزیران 24 : في استلم البحث الخالصة لنظریة الكم. االنموذج المشتق باالعتماد على التقریب "انظریا تبع فة وصاإللكترون في سطح معدن / جزیئ انتقال ة مع حساب الطاقة إلعادة التنظیم.طاقة اعادة یئاالول لنظریة االضطراب استعمل لحساب ثابت المعدل لسطح المعدن / جز ت المالة. المعالتنظیم حسبت تبعا النموذج الكروي الخارجي على اساس الجھد الكھروستاتیكي للجزیئات المانحة والمستقب الجزیئیة التي أدخلت في ھذا االنموذج ھي الوزن الجزیئي والكثافة الكتلیة، ونصف قطرھا الجزئي الذي حسب تبعا لحجم وني كانت متوافقھ رمعدل االنتقال االلكت ثابت الموالري باستخدام التقریب كروي. النتائج النظریة المستحصلة وفقا النموذج عملیة لبعض سطوح معدن/ جزیئة لدراسات تجریبیة.مقارنة مع النتائج ال :االنتقال االلكتروني ،سطح معدن / جزیئةالكلمات المفتاحیة 93 | Physics @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹1a26@@ÖÜ»€a@I3@‚b«@H2013 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 26 (3) 2013