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 ـــي المســـتحث فوتوئبــــا اللكترو نتقـــال االدراســـة النظریــــة لال M نو مثیـــل الفــــالوجی23)(bpyRuیــــوم بـــین الروتون" نـ V 2+ . 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 حســبت بطریقـــة شـــبه G‡وطاقـــة التنشـــیط ،G،والطاقـــة الحــرة ام هـــذا التطبیــق ، طاقـــة اعـــادة االلتحــ فــي هـش ومعـدل –اخـذت مـن طریقـة ملیكـان التـي VDA االلكترونـيلالنتقـال ة عناصـر مصـفوفة االزدواج االلكترونـي یكالسـیك لنظام KET االنتقال االلكتروني  223)( MVbpyRu نموذج كمي أ وفق على حسبتوالتي. نتقال االلكتروني لنظام نتائج حساباتنا لال 223)( 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 Departme nt of Physics , College of Education I bn- Al-Haitham , Unive rsity of Baghdad Abstract Electron transfer (ET) reactions represent an elementary chemical p rocess which occurs in a large variety of molecules, ranging from small ion p airs up to large biological sy st em. A theoretical st udy of p hoto – induced electron transfer between Ruthenium (II) tirs -( 2,2  - bipy rdine ) Ru(bp y ) 2 3 and M ethy l Viologen M V 2+ in a variety of Solvents at room temp erature is p resented . This st udy is based on an op tical activation by the absorp tion of light .The Solvent is described by a dielectric continuum model, and the transferring is represented by a quantum mechanical wave function . In this app lication, 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 M ulliken –Hush method, and the rate of electron transfer KET in  22 3)( MVbpyRu sy st em are calculated with a quantum mechanical model. Our calculation results for the electron transfer in  22 3)( MVbpyRu sy st em show a good agreement with the exp erimentally observed results . Introduction Electctron t ransfer (ET) on a molecular level is a very imp ortant class of chemical reactions ranging from simple bimolecular reduction oxidation reactions to comp lex electron transp ort chains in protein (1). The (ET) p rocess is like any other chemical reaction , a transition from a metastable initial to a stable final st ate (2). ET can be optically or/and thermally activated and triggers p hotosy n thesis , metabolism, polymerization reactions, electrochemical reactions(3). A molecular (ET) reaction involves an oxidation of a Donor (D) molecule and reduction of an Accep tor molecule (A). If the donor and accep tor are freely diffusing in a solvent , then p rior to ET a bimolecular diffusion creats an encounter comp lex . In the encounter comp lex , electron transfer reaction occurs at a certain distance and arrangement. The encounter comp lex can either be in close contact, or in a solvent sep arated configuration , and ET may occur at a distribution of different donor- accep tor con- figureations . If the donor and accep tor are att ached to each other, no diffusion p rocesses are needed p rior to ET , and unimolecular ET reaction kinetic is observed . The theory describing ET p rocesses was developed from the transition state theory by M arcus. For this development M arcus was awarded the 1992 Nobel Prize in Chemistry (4,5,6) . The rate of p hoto induced ET are evaluated depending on the quantum mechanical theory and non adiabatic limit RDA =10A o . The value of ET rate const ants 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 st udy the p hoto induced ET from 2 3)(bpyRu acting as an electron donor to NN  dimethy l- 44  bipy ridine (M ethy l Viologen) acting as an electron accep tor . The structures of t he 2 3)(bpyRu and M V 2+ that are used in this work are shown in figure (1) The System Ruthenium (II) – trisbipy ridine 2 3)(bpyRu was used in numerous invest igations as a p hotosensitizer during the last 30 y ears due to the very favorable p hotochemical p rop erties (7). The absorbance in both t he 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 st able towards degrading reactions ( 7,8). One way of inducing ET is to exp ose aphotosensitizer 2 3)(bpyRu to light of a wave length that is absorbed by 2 3)(bpyRu , thus transferring it to an excited st ate  2 3)(bpyRu eq.[1] (9) ]1.[....................)(*)( 2 3 2 3   bpyRuhbpyRu  Here, the frequency of the sp ectral absorp tion maximum m ax is given by : ]2.......[........................................max  Gh  Where h, is p lanck constant, m ax is frequency of light ,  reorganization energy and G is free energy . If a quencher (M V 2+ ) is added to the sy st em, this molecule is able to quench the excited st ate of 2 3)(* bpyRu .i.e. it is able to remove the excitation energy (10). The quenching mechanism can be ET from the sy st em 2 3)(* bpyRu to M thy le Viologen M V 2+ , Fig.(2) gives a reduced M ethy le Viologen radicl and oxidized ruthenium 3 3)(bpyRu equation [3] (9,10). ]3[..............................)()(* 23 3 2 3 2      MVbpyRuMVbpyRu ET Theory of Electron Transfe r In quantum mechanical models the golden rule exp ression for the transition p robability between different electronic st ates (Donor- Accep tor), is often used to treat nonadiabatic electron transfer . In the high temp erature 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 p arameters: the electronic couplong matrix element VDA , the free energy chan ge of the reaction G , and the reorganization ener gy  , 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 exp ression for KET (14). 1 4 2 TKK BET     ]4.[..........). ........exp(2 TK G V B DA   Where  is p lanck,s const ant divided by BK,2 which is t he Boltzman constant, and G ‡ is the Gibbs free energy of activation . The p otential energy surfaces of the reactant and p roduct 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 t o the crossing p oint is t he 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 accep tor together and the difference between the reduction p otentials of t he acceptor and donor. The reorganization energy  is the sum of the inner  in, and outer,  out , reorganization(15)  =  in+  out ………………………[6] The inner reorganization comp onent is the energy required to alter bond distances and bond angles that would change with the change in oxidation st ate. The outer reorganization energy is required for the reorientation of the solvent around the changed comp lexes (15) . In many comp lexes 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 p olar 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 p ermitt ivity , p and s is the op tical and static dielectric constants , (rD, rA,) are the donor and accep tor radii and RDA is the donor – accep tor center to center distance . Re sults The rate of ET is determined by many p arameters . The effective free energy G for the reaction , the value of the reorganization energy of the electron donor (D) and accep tor (A) required up on ET , activation free energy G ‡ , and coupling coefficient matrix element of ET,VDA A more genral exp ression equation eq.[7] was app lied to evaluate the reorganization energy  ,for a donoer 23)(bpyRu and acceptor M V2+ sy st em 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 accep tor and rD=3.5  A for donor (17), p and s are the op tical 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 p resent sy st em are 0.952eV and 0.908 eV in acetonetriale and water solvent resp ectively. So the other variable in the rate ET exp ression is the driving force G ( effective free energy ) that is p rovided by the absorp tion of light in 2 3)(bpyRu -M V 2+ sy st em that is very clear from eq.[2] and figure (2) . The driving force is defined as t he part of the work it t akes to bring the donor and accep tor together , and the difference between the reduction p otentials 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 absorp tion energy taken from absorp tion sp ectral of 2 3)(bpyRu . These results of G ( eV ) in acetonitrial and water solution are sumarized in table (1). Now, by substitut ing 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). Anot her imp ortant factor for ET are the electronic coupling coefficients, VDA, which is the most difficult p arameter to obtain exp erimentally. However, according to the theory by Hush (19), and the assump tion that the reaction is activationless , the electronic coupling,VDA ,can be est imated to be (0.01,0.03,0.2) eV Finally we can calculate the rate of the p hoto induced ET values K between 2 3)(bpyRu and M ethy le Viologen M V 2+ 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 list ed in tables (3-4). Discussion when the  22 3)( MVbpyRu solution sy st ems are p romoted to electronically excited st ates by the absorp tion of light, some of this absorp tion energy of light is used to distort the nuclear configuration from and its equilibrium donor st ate to the accep tor st ate 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 st ructural rearrangements are necessary when V 2+ is oxidized . The calculation result of reorganization energies are fitting with theoretical and exp erimental 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 -M V 2+ solution sy st em, which corresp ond 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 exp erimental values , that are clear for awave length 460A o , 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 exp lained p hy sically 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 t he exp erimental values (1,11). Conclusion In our research, theoretical st udies to calculate the rate of electron transfer for the  22 3)( MVbpyRu solution molecules sy st em in a variety solvent, are p romoted to electronically excited st ates by the absorp tion of light . Up on light absorp tion , an electron is formally transferred from the Ru(II) metal center across one of the bipy ridine ligands to the M V 2+ . The reorganization energies are calculated with dielectric continuum model and are found~ eVeV 908.0952.0  for a sy st em in water and acetonitrile solution resp ectively . This result show large reorganization energy in more p olar solvent, that means  is p rop ortional to op/1 It turned out that the mode of reaction p ath way st rongly depends on the solvent p olarity whereas ET is favored in p olar solvents. Also the rate of ET for sy st em is a function of the height barrier G ‡ . When a treated quantum mechanically as vibrational wave functions of the reactant nuclear coordinates to coordinate sp ace that overlaps with p roduct coordinates sp ace (also referred to as "nuclear tunnellig"). The p robability to bridge the gab between the reactant and the p roduct G ‡ is the largest. From the present results t hat are concluded , the p hoto induced ET in  22 3)( MVbpyRu sy st em is activated in the inverted region. The calculation results for the rate of ET in  22 3)( MVbpyRu solvent sy st em show a good agreement with the exp erimentally observed results. Re ferences 1. Hammarest rom,L. (2001).Labrabory exp eriment for the course ,Laser sp ektroskop i NV 1, Dep . Of p hy sical chemistry , University of Up p sala 2. Wachsmann,H.(2001). Vibronic coupling and ultrafast ET Studied by p icosecond time – resolved resonance, thesis ,p h.D Berlin Univesity . 3.Chen,P.Y.M eyer,T.(1998).J.Chem.Rev, 98,1439. 4.Barbara,P.F.;M eyer,T.J.and Ratner,M .,(1996),J.p hy s.chem,100: 1348. 5.Bixon,M .Jort ner,J.(1997).j.Chem.phy s,107,5154 6.Jort ner,J.and Bixon,M .(1999).Adv.chem.p hy s. 106:35. 7.Juris,A.; Balzani,V.; Bargellett i, F.; Canp agna,S. and Belser,P. (1988). Vonzelewsky , APL.Coord Chem. Rev. 84,85. 8. Kalyanasundaram, K.(1992). Book,Academics p ress London. IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 9. De Armond,M .K. and M y rich,M .L.(1989). 22:364. 10. M eyer,T.J.(1986). Pure and APPL. Chem. 58:1193. 11. Helena,B.(2001),Electvon and Energy transfer in sup amolecular comp lexes designed for arficial p hotosy nthesis thesis, Acta University , up salla. 12. Jort ner, J.(1976).J.Chem.phy s.64,4860. 13.M arcus,R.A.and Sutin,N.(1985).Biochim.Biophy s.Acta. 14. Hadi,J.M .(2004) . thesis,Ph.D. Quantum mechanical model for electron transfer-swiched dy e using in solid st ate laser , Baghdad University . 15.Brunschwig,B.S.;Ehrensons,S.and Sutin,N.(1986). J.p hy s.Chem,90:3657. 16. M ikael,A.(2000). T hesis ,Ph.D.Tuning electron transfer reaction by selectivo excitation in p orp hy rine accee ptor assemblies ,Acta University ,Up sala. 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.p hy s. chem. B. 105(2): 400. 19.Chen,P.and M eyer,T.J.(1996).Inoeg.Chem. 35:5520. Table (1):The free ene rgy )(eVG for acceptor MV2+ and donor 2 3)(bpyRu Wave len gth( 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 ene rgy G ‡ )(eV for acceptor MV2+ and donor 2 3)(bpyRu Wave len gth  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 sol vent for different VDA Wave len gth  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 1.21308x10 11 2729448305 303272033.9 460 1.068855 x10 12 2.404914 x10 10 2672127376 480 5.96902 x10 12 1.343031 x10 11 1.49225 x10 10 500 2.2887 x10 13 5.1496 x10 11 5.7218 x10 10 520 6.5012 x10 13 1.4627 x10 12 1.6253 x10 11 540 1.4468 x10 14 3.2554 x10 12 3.6172 x10 11 560 2.6258 x10 14 5.9682 x10 12 6.546x10 11 580 4.02385 x10 14 9.0643 x10 12 1.0071 x10 12 600 5.3731 x10 14 1.2089 x10 13 1.3432 x10 12 IBN AL- HAITHAM J. FO R PURE & APPL. SC I VO L.22 (3) 2009 Table (4): Rate of ET between 2 3)(bpyRu and MV 2+ in acetoni tril e sol uti on (CH3CN) Wave len gth  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 x10 10 1192743400 132527044.4 460 5.2186 x10 11 1.1741 x10 10 1304665511 480 3.2207 x10 12 7.2466 x10 10 8051873912 500 1.3613 x10 13 3.06300 x10 11 3.4033 x10 10 520 4.22487 x10 13 9.5059 x10 12 1.0562 x10 11 540 1.0173 x10 14 2.2890 x10 12 2.5433 x10 11 560 1.9879 x10 14 4.4728 x10 12 4.9697x10 11 580 3.2685 x10 14 7.3543 x10 12 8.1714 x10 11 600 4.6572x10 14 1.04789 x10 13 1.16432 x10 12 Table(5):Our resul t for reorgani zation ene rgie s compared with the oreti cal and experime ntal Value s Solvent Our result  ev Exp erimental  ev Theoretical  ev Water (H2O) o.952 1.00(11) 1(16) Acetonitrile 0.908 ~1.0[11]