2009) 3( 22مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد اي یردین ب 2-2ترز) II(یوم ونبین الروث" یانالنتقال االلكتروني المستحث فوتو ا ومثیل الفایلوجین هادي جبار مجبل العكیلي ابن الهیثم ، جامعة بغداد - قسم الفیزیاء ، كلیة التربیة الخالصة الجزیئـات ، تتـراوح ث في أي تشكیلة كبیرة من دیمثل التفاعل االبتدائي للعملیات الكیمیائیة التي تح االنتقال االلكتروني .الى النظام الحیوي الكبیر " یة الصغیرة وصوالاالزواج االیون ـا اللكترو نتقـــال االدراســـة النظریــــة لال ـــي المســـتحث فوتوئبـــ 2یــــوم بـــین الروتون" نـ 3)(bpyRuــالوجی +MV2 نو مثیـــل الفــ . حققت هنا معینة لمذیبات مختلفة وعند درجة الحرارة نمــوذج أ الضــوء المــذیب وصـف مــن خــاللهـذه الدراســة معتمــدة علــى اسـاس التنشــیط البصــري مــن خـالل امتصــاص . دالة الموجة لمن خال" االستمراریة للعوازل ، واالنتقال كمیا ــادة االلتحــ فــي ــیط ،G،والطاقـــة الحــرة ام هـــذا التطبیــق ، طاقـــة اعـ ــة التنشـ وطاقـ ‡ G ة شـــبه حســبت بطریقـــ هـش ومعـدل –اخـذت مـن طریقـة ملیكـان التـي VDA االلكترونـيلالنتقـال ة عناصـر مصـفوفة االزدواج االلكترونـي یكالسـیك لنظام KET االنتقال االلكتروني 22 3)( MVbpyRu نموذج كمي أ وفق على حسبتوالتي. نتقال االلكتروني لنظام نتائج حساباتنا لال 22 3)( MVbpyRu مع النتائج التجریبیة المالحظة " اظهرت تطابقا . IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 Photo -induced Electron Transfer Between Ruthenium (II) tris –( 2,2  - bipyrdine ) and Methyl Viologen H.J.M.Al-Agealy Department of Physics , College of Education Ibn- Al-Haitham , University of Baghdad Abstract Electron transfer (ET) reactions represent an elementary chemical process which occurs in a large variety of molecules, ranging from small ion pairs up to large biological system. A theoretical study of photo – induced electron transfer between Ruthenium (II) tirs -( 2,2  - bipyrdine ) Ru(bpy) 2 3 and Methyl Viologen MV2+ in a variety of Solvents at room temperature is presented . This study is based on an optical activation by the absorption of light .The Solvent is described by a dielectric continuum model, and the transferring is represented by a quantum mechanical wave function . In this application, the reorganization energy  , the driving free energy G , and the activation free energy G ‡ are calculated with semi classical model . The electronic coupling for the electron transfer DAV reaction is taken from Mulliken –Hush method, and the rate of electron transfer KET in  22 3)( MVbpyRu system are calculated with a quantum mechanical model. Our calculation results for the electron transfer in  22 3)( MVbpyRu system show a good agreement with the experimentally observed results . Introduction Electctron transfer (ET) on a molecular level is a very important class of chemical reactions ranging from simple bimolecular reduction oxidation reactions to complex electron transport chains in protein (1). The (ET) process is like any other chemical reaction , a transition from a metastable initial to a stable final state (2). ET can be optically or/and thermally activated and triggers photosyn thesis , metabolism, polymerization reactions, electrochemical reactions(3). A molecular (ET) reaction involves an oxidation of a Donor (D) molecule and reduction of an Acceptor molecule (A). If the donor and acceptor are freely diffusing in a solvent , then prior to ET a bimolecular diffusion creats an encounter complex . In the encounter complex , electron transfer reaction occurs at a certain distance and arrangement. The encounter complex can either be in close contact, or in a solvent separated configuration , and ET may occur at a distribution of different donor- acceptor con- figureations . If the donor and acceptor are attached to each other, no diffusion processes are needed prior to ET , and unimolecular ET reaction kinetic is observed . The theory describing ET processes was developed from the transition state theory by Marcus. For this development Marcus was awarded the 1992 Nobel Prize in Chemistry (4,5,6) . The rate of photo induced ET are evaluated depending on the quantum mechanical theory and non adiabatic limit RDA =10Ao. The value of ET rate constants K are controlled by : IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 reorganization energy  , driving free energy G ; activation free energy G ‡, and electronic coupling matrix element VDA. In this research we will study the photo induced ET from 2 3)(bpyRu acting as an electron donor to NN  dimethyl- 44  bipyridine (Methyl Viologen) acting as an electron acceptor . The structures of the 2 3)(bpyRu and MV2+ that are used in this work are shown in figure (1) The System Ruthenium (II) – trisbipyridine 2 3)(bpyRu was used in numerous investigations as a photosensitizer during the last 30 years due to the very favorable photochemical properties (7). The absorbance in both the visible and UV regions is high (1,11) . In the excited state , 2 3)(bpyRu is both a good reductant and oxidant , and the life time is long enough to be used in bimolecular electron or energy transfer reactions . In addition both the reduced and oxidized forms are relatively stable towards degrading reactions ( 7,8). One way of inducing ET is to expose aphotosensitizer 2 3)(bpyRu to light of a wave length that is absorbed by 2 3)(bpyRu , thus transferring it to an excited state  2 3)(bpyRu eq.[1] (9) ]1.[....................)(*)( 2 3 2 3   bpyRuhbpyRu  Here, the frequency of the spectral absorption maximum max is given by: ]2.......[........................................max  Gh  Where h, is planck constant, max is frequency of light ,  reorganization energy and G is free energy . If a quencher (MV2+) is added to the system, this molecule is able to quench the excited state of 2 3)(* bpyRu .i.e. it is able to remove the excitation energy (10). The quenching mechanism can be ET from the system 2 3)(* bpyRu to Mthyle Viologen MV 2+ , Fig.(2) gives a reduced Methyle Viologen radicl and oxidized ruthenium 3 3)(bpyRu equation [3] (9,10). ]3[..............................)()(* 23 3 2 3 2      MVbpyRuMVbpyRu ET Theory of Electron Transfer In quantum mechanical models the golden rule expression for the transition probability between different electronic states (Donor- Acceptor), is often used to treat nonadiabatic electron transfer . In the high temperature limit , when the energy of each vibration is considerably less than the thermal energy , TKh B (12,13), the ET rate constant KET between the reactants at a fixed distance is determined by three parameters: the electronic couplong matrix element VDA , the free energy change of the reaction G , and the reorganization energy  , which IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 includes both intra molecular  in; and solvent s out coordinates, the expression for KET (14). 1 4 2 TKK BET     ]4.[..........).........exp(2 TK G V B DA   Where  is planck , s constant divided by BK,2 which is the Boltzman constant, and G ‡ is the Gibbs free energy of activation . The potential energy surfaces of the reactant and product states can be described as free energy surfaces, and ET occurs at the crossing of the reactant and product surfaces . The amount of free energy required to bring the reactant to the crossing point is the free energy of activation, G ‡ , defined as (13). G ‡=   ]5.......[.................... 4 2   G Where G is the free energy change for any chemical reaction which is the difference in the energy of the products and the reactants. For ET reactions, this can be broken into the work it takes to bring the donor and acceptor together and the difference between the reduction potentials of the acceptor and donor. The reorganization energy  is the sum of the inner  in, and outer,  out , reorganization(15)  =  in+  out ………………………[6] The inner reorganization component is the energy required to alter bond distances and bond angles that would change with the change in oxidation state. The outer reorganization energy is required for the reorientation of the solvent around the changed complexes (15) . In many complexes or big molecules that have asmall inner reorganization, such that , we can assume  out out. can be estimated from a dielectric continuum model for the solvent, and give the largest contribution to  in many ET reactions in polar media (16). The solvent reorganization energy in this model is given by (16) ]7.....[.............................. 111 2 1 2 1 4 2                      spoDAAD Rrr e   Where e is the charge involved (usually one electron ),  is the vacuum permittivity , p  and s is the optical and static dielectric constants , (rD, rA,) are the donor and acceptor radii and RDA is the donor – acceptor center to center distance . Results The rate of ET is determined by many parameters . The effective free energy G for the reaction , the value of the reorganization energy of the electron donor (D) and acceptor (A) required upon ET , activation free energy G ‡ , and coupling coefficient matrix element of ET,VDA A more genral expression equation eq.[7] was applied to evaluate the reorganization energy  ,for a donoer 2 3)(bpyRu and acceptor MV 2+ system in a variety solvent , where IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 radii rA=6.5 A for acceptor and rD=3.5 A for donor (17), p  and s are the optical and static dielectric constants of the solvent[ p   1.344 and s =37.5for acetonitriale (16) , p  =1.77 and s =78.5 for water ](16,18 ) . The values of reorganization energies , in the present system are 0.952eV and 0.908 eV in acetonetriale and water solvent respectively. So the other variable in the rate ET expression is the driving force G ( effective free energy ) that is p rovided by the absorp tion of light in 2 3)(bpyRu -MV 2+ system that is very clear from eq.[2] and figure (2) . The driving force is defined as the part of the work it takes to bring the donor and acceptor together , and the difference between the reduction potentials of the acceptor and donor. The theoretical calculation values of the free energy can be evaluated by using eq.[2] , where E= h is the absorption energy taken from absorption spectral of 2 3)(bpyRu . These results of G ( eV ) in acetonitrial and water solution are sumarized in table (1). Now, by substituting the values of the driving force G ( eV ) and the solvent reorganization energy )(eV for both solvents in eq.[5] we can calculate the ET activation barrier G ‡ )(eV .These calculated values are summarized in table (2). Another important factor for ET are the electronic coupling coefficients, VDA, which is the most difficult parameter to obtain experimentally. However, according to the theory by Hush (19), and the assumption that the reaction is activationless , the electronic coupling,VDA ,can be estimated to be (0.01,0.03,0.2) eV Finally we can calculate the rate of the photo induced ET values K between 2 3)(bpyRu and Methyle Viologen MV2+ in a different solvent by inserting the values of the coefficients )(eV , G ( eV ), G ‡ )(eV , and VDA )(eV in equation eq.[4] , the results of rate ET are listed in tables (3-4). Discussion when the  22 3)( MVbpyRu solution systems are promoted to electronically excited states by the absorption of light, some of this absorption energy of light is used to distort the nuclear configuration from and its equilibrium donor state to the acceptor state without transfer of an electron . The resulting values of the reorganization energies were unusually high [0.952 eV in acetonitrile and 0.908eV in water] , which could indicate that large structural rearrangements are necessary when V2+ is oxidized . The calculation result of reorganization energies are fitting with theoretical and experimental values in the same solution that is shown in table(5). Table (1) shows the overall driving force free energy changes , G , that can be calculated for the 2 3)(bpyRu -MV2+ solution system, which correspond to the inverted region . The Inverted region may be observed when the driving force for reaction is greater than the reorganization energy,  G .Consequently inverted region effects are most easily discerned for those reactions with small reorganizatioin energies in both solution and IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 large driving force ,which is very clear from table (1). The values of the driving free energy that are calculated theoretically fit with experimental values , that are clear for awave length 460Ao, G =-1,7eV , 1.73eV (1,11). Tables (4-5) and (1) indicate that -  G increasing , the rate of ET, K decrease with increasing - G . This view is for two solvents , because the barrier for ET increases as also in table(2). The effect of decreasing KET in the inverted region can be explained physically as follows: increasing the driving force - G to values learger than the reorganization energy  leads to the increasing of the free energy of activation G ‡ , i.e. barrier of the reaction . The calculation results of KET fit well with the experimental values (1,11). Conclusion In our research, theoretical studies to calculate the rate of electron transfer for the  22 3)( MVbpyRu solution molecules system in a variety solvent, are promoted to electronically excited states by the absorp tion of light . Upon light absorption , an electron is formally transferred from the Ru(II) metal center across one of the bipyridine ligands to the MV 2+ . The reorganization energies are calculated with dielectric continuum model and are found~ eVeV 908.0952.0  for a system in water and acetonitrile solution respectively . This result show large reorganization energy in more polar solvent, that means  is proportional to op/1 It turned out that the mode of reaction path way strongly depends on the solvent polarity whereas ET is favored in polar solvents. Also the rate of ET for system is a function of the height barrier G ‡. When a treated quantum mechanically as vibrational wave functions of the reactant nuclear coordinates to coordinate space that overlaps with product coordinates space (also referred to as "nuclear tunnellig"). The probability to bridge the gab between the reactant and the product G ‡ is the largest. From the present results that are concluded , the photo induced ET in  22 3)( MVbpyRu system is activated in the inverted region. The calculation results for the rate of ET in  22 3)( MVbpyRu solvent system show a good agreement with the experimentally observed results. References 1. Hammarestrom,L. (2001).Labrabory experiment for the course ,Laser spektroskopi NV 1, Dep. Of physical chemistry, University of Uppsala 2. Wachsmann,H.(2001). Vibronic coupling and ultrafast ET Studied by picosecond time – resolved resonance, thesis ,ph.D Berlin Univesity . 3.Chen,P.Y.Meyer,T.(1998).J.Chem.Rev, 98,1439. 4.Barbara,P.F.;Meyer,T.J.and Ratner,M.,(1996),J.phys.chem,100: 1348. 5.Bixon,M.Jortner,J.(1997).j.Chem.phys,107,5154 6.Jortner,J.and Bixon,M.(1999).Adv.chem.phys. 106:35. 7.Juris,A.; Balzani,V.; Bargelletti, F.; Canpagna,S. and Belser,P. (1988). Vonzelewsky, APL.Coord Chem. Rev. 84,85. 8. Kalyanasundaram, K.(1992). Book,Academics press London. IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 9. De Armond,M.K. and Myrich,M.L.(1989). 22:364. 10. Meyer,T.J.(1986). Pure and APPL. Chem. 58:1193. 11. Helena,B.(2001),Electvon and Energy transfer in supamolecular complexes designed for arficial photosynthesis thesis, Acta University, upsalla. 12. Jortner, J.(1976).J.Chem.phys.64,4860. 13.Marcus,R.A.and Sutin,N.(1985).Biochim.Biophys.Acta. 14. Hadi,J.M.(2004) . thesis,Ph.D. Quantum mechanical model for electron transfer-swiched dye using in solid state laser , Baghdad University . 15.Brunschwig,B.S.;Ehrensons,S.and Sutin,N.(1986). J.phys.Chem,90:3657. 16. Mikael,A.(2000). Thesis ,Ph.D.Tuning electron transfer reaction by selectivo excitation in porphyrine accee ptor assemblies ,Acta University ,Upsala. 17.Glaudi.T.J.;Jeffrey,M.Z.;Yanna,M.K.and Daniel,G.(1996).J.Am.soc. 118: 6060-6062. 18. Kucnuskas,et.al, (2001). J.phys. chem. B. 105(2): 400. 19.Chen,P.and Meyer,T.J.(1996).Inoeg.Chem. 35:5520. Table (1):The free energy )(eVG for acceptor MV 2+ and donor 2 3)(bpyRu Wave length( nm) eVG water eVG acet. 300 -3.173 -3.216 320 -2.915 -2.958 340 -2.687 -2.737 360 -2.485 -2.528 380 -2.304 -2.347 400 -2.141 -2.185 420 -1.994 -2.537 440 -1.860 -1.903 460 -1.737 -1.781 480 -1625 -1.669 500 -1.522 -1.566 520 -1.427 -1.471 540 -1.339 -1.382 560 -1.257 -1.301 580 -1.181 -1.224 600 -1.110 -1.153 IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 Table (2):The activation free energy G ‡ )(eV for acceptor MV 2+ and donor 2 3)(bpyRu Wave length  nm G ‡ eVwater G ‡ eVacet. 300 1.294 1.345 320 1.010 1.056 340 0.790 0.830 360 0.616 0.652 380 0.479 0.511 400 0.371 0.398 420 0.284 0.309 440 0.216 0.237 460 0.162 0.180 480 0.119 0.135 500 0.085 0.098 520 0.059 0.070 540 0.039 0.048 560 0.024 0.031 580 0.013 0.019 600 0.006 0.010 Table(3): Rate of ET between 2 3)(bpyRu and MV 2+ in water solvent for different VDA Wave length  nm KETs -1 VDA=0.02 eV VDA=0.03eV VDA=0.01 eV 300 2.285x10-8 5.140 x10-10 5.712 x10-11 320 1.914 x10-3 4.307 x10-5 4.785 x10-6 340 13.009 0.292 0.032 360 13381.190 301.076 33.452 380 3222297.941 72501.703 8055.744 400 248165224.3 5583717.547 620413.060 420 7832952172 176241423.9 19582380.43 440 1.21308x1011 2729448305 303272033.9 460 1.068855 x10 12 2.404914 x10 10 2672127376 480 5.96902 x1012 1.343031 x1011 1.49225 x1010 500 2.2887 x1013 5.1496 x1011 5.7218 x1010 520 6.5012 x1013 1.4627 x1012 1.6253 x1011 540 1.4468 x10 14 3.2554 x10 12 3.6172 x10 11 560 2.6258 x1014 5.9682 x1012 6.546x1011 580 4.02385 x1014 9.0643 x1012 1.0071 x1012 600 5.3731 x1014 1.2089 x1013 1.3432 x1012 IBN AL- HAITHAM J. 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SC I VO L.22 (3) 2009 Table (4): Rate of ET between 2 3)(bpyRu and MV2+ in acetonitrile solution (CH3CN) Wave length  nm KET(sec) -1 VDA=0.02eV VDA=0.03eV VDA=0.01eV 300 3.0020x10 -9 6.754 x10 -11 7.505 x10 -12 320 3.173 x10 -4 7.1404 x10 -6 7.933 x10 -7 340 2.6593 0.0598 6.64 x10-3 360 3301.100 74.274 8.252 380 935735.115 21054.040 2339.337 400 837017.730 1883289.894 209254.432 420 3022181989 67999094.64 7555454.96 440 5.3010 x1010 1192743400 132527044.4 460 5.2186 x1011 1.1741 x1010 1304665511 480 3.2207 x10 12 7.2466 x10 10 8051873912 500 1.3613 x1013 3.06300 x1011 3.4033 x1010 520 4.22487 x1013 9.5059 x1012 1.0562 x1011 540 1.0173 x1014 2.2890 x1012 2.5433 x1011 560 1.9879 x10 14 4.4728 x10 12 4.9697x10 11 580 3.2685 x1014 7.3543 x1012 8.1714 x1011 600 4.6572x1014 1.04789 x1013 1.16432 x1012 Table(5):Our result for reorganization energies compared with theoretical and experimental Values Solvent Our result  ev Experimental  ev Theoretical  ev Water (H2O) o.952 1.00(11) 1(16) Acetonitrile 0.908 ~1.0[11]