Electron Spin Polarization of Radical Pairs in Simple Molecular Wires

Mar 15, 2007 - The density vector approach as developed for chemically induced dynamic electron polarization (CIDEP) has been extended to transient ...
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J. Phys. Chem. C 2007, 111, 5203-5210

5203

Electron Spin Polarization of Radical Pairs in Simple Molecular Wires Petersen L. Hasjim† and James R. Norris, Jr.*,‡ Department of Chemistry and Institute for Biophysical Dynamics, The UniVersity of Chicago, Chicago, Illinois 60637 ReceiVed: September 26, 2006; In Final Form: January 16, 2007

The density vector approach as developed for chemically induced dynamic electron polarization (CIDEP) has been extended to transient radicals produced by flash photolysis in molecular wire polymers that exhibit reversible electron transfer. Unique electron spin polarization (ESP) arising from the hyperfine structure is predicted for reversible electron transfer in molecular wires. A radical pair consisting of one stationary radical and one radical reversibly migrating in a polymer is used to explain the difference in CIDEP in normal solution versus CIDEP in reversible molecular wires. Balanced anti-phase ESP is predicted as electron spins transfer forward, where forward refers to increasing the distance between the members of the radical pair. However, unbalanced antiphase ESP is predicted when electrons transfer back to certain previous positions. The unusual, unbalanced antiphase spectral lines originate because the electron spin migration is confined to a single polymer molecule. If electron spins were to migrate among different polymers, i.e., among a collection of polymers, then the unusual, unbalanced antiphase electron spin polarization would vanish. These considerations suggest that hyperfine driven CIDEP can provide a novel tool for investigating molecular wires.

Introduction The discovery of chemical induced dynamic electron polarization (CIDEP) has provided a unique way to explore and understand free radical chemistry, especially photochemistry.1 Many experiments have been conducted as well as theories proposed to explain the various CIDEP phenomena.2 Numerous experimental and theoretical investigations have focused on radical pairs in liquids where diffusion plays an important role in developing the spin polarizations.3-12 More complicated systems where diffusion, electron transfer, radical recombination, and termination occur have also been explored and solved. Experimental studies independent of CIDEP or EPR show that certain polymers exhibit photoconductive properties.13,14 Only a few experimental studies using CIDEP to investigate polymer free radicals have been reported.15-20 The extension of the simple vector diagram6,7,21 picture of CIDEP is based on reversible electron transfer occurring within a polymer Pn that forms one-half of a photoinduced radical pair D+Pn- as in hυ

DPn 98 D+Pnwhere D is the electron donor to the acceptor Pn. A significant difference is predicted between the CIDEP of radical pairs in normal solution and radical pairs associated with conducting polymers. Radical pairs of simple molecules in liquids experience standard three-dimensional diffusion while they undergo electron transfer, recombination, and termination. For example, after creation the acceptor molecule may undergo electrontransfer reactions with other unreduced acceptor molecules as shown in Figure 1. In the illustration of Figure 1 by electron* Address correspondence to this author. E-mail: [email protected]. Phone: (773) 702-7864. Fax: (773) 702-0805. † Department of Chemistry. ‡ Institute for Biophysical Dynamics.

Figure 1. Example of reversible electron transfer in liquid solution and within the acceptor system before radical-radical recombination. Fifteen arbitrary electron-transfer reaction states are shown. This figure shows the distance between the radical pair changing because of electron transfer. The distance between the two members of the radical pair can also increase by liquid solution diffusion. In the example illustrated in this figure, if the concentration of the unreduced acceptor is low, then the radical pair separates primarily by diffusion. If the concentration of the unreduced acceptor is high, then the radical pair can also separate by electron transfer.

transfer step 14, the reduced acceptor has “re-encountered” the oxidized donor and at that time can either separate as seen in step 15 or terminate by returning to the ground state (not shown in Figure 1). The radical pair D+A14- is different from the initial radical pair D+A1-, not just because the spatial location of A14is different from A1-, but because the molecule A14 is a different molecule from the molecule A1 and consequently the local magnetic field of A14- that arises primarily from its magnetic nuclei is almost always different from that of A1-. At step 14, the radical either quenches back to the ground state or additional electron transfer occurs resulting in A15-. Radicals in polymers also experience similar factors, but because their electron spins can transfer from one monomer to the next within the same polymer molecule in a reversible

10.1021/jp066322s CCC: $37.00 © 2007 American Chemical Society Published on Web 03/15/2007

5204 J. Phys. Chem. C, Vol. 111, No. 13, 2007 manner, a “memory” effect can occur that is effectively impossible without a reversibly conducting polymer or “wire”. If D denotes the electron donor molecules and Pi denotes the monomeric units of the polymer, confined one-dimensional electron transfer in polymers can be depicted as

D + P1P2P3... T D+ + P1-P2P3... T D+ + P1P2-P3... T D+ + P1P2P3-...T... D+ + P1P2-P3... T D+ + P1P2P3-, etc. Neglecting interchain electron transfer, backward electron transfer in a polymer must return the electron to the same, prior monomer while electron transfer in liquid solutions is less likely to return the electron spin back to its original molecule. In a context meaningful to CIDEP, the monomers are magnetically distinguishable because the net local magnetic field arising from nuclei is different on the different members of the polymer. This difference in electron transfer can be exploited to distinguish between spins reversibly hopping in polymers versus spins reversibly migrating via liquid solution electron transfer or spins separating irreversibly as in natural and artificial photosynthesis. The CIDEP associated with radical pairs of simple molecules in liquid solution disappears with electron transfer because the radical pair is almost always different after each electron transfer.8,20 This is also true for forward electron transfers in a polymer, which makes new radical pairs and scrambles the CIDEP of the previous radical pairs. However, backward electron transfer in a polymer restores the previous radical pair and the ESP of radical pair CIDEP returns as long as the nuclear and electron spin lattice relaxation times are long compared to the electron-transfer times. Thus, the distinguishing feature of radical pairs in polymers is preservation of the magnetic environment of the electron spin when the spins return to previous monomer sites which restore electron spin polarization (ESP). Radical pairs formed with polymers do not experience the normal diffusion associated with molecular translational movement as long as the electron spin is confined within the 1-D polymer. In the limit where nuclear and electronic spinlattice relaxation times are long relative to electron-transfer time, a “memory” effect of the previous spin environment of a prior polymer site exists, which leads to special ESP in the EPR spectrum. The CIDEP of a conducting polymer is sensitive to the electron-transfer rate and to the length of the polymer over which the electron-transfer process occurs. Consequently, the CIDEP of conducting polymers is also dependent on energy heterogeneity and the motion of the solvent and system matrix. In this report, we present a simple theoretical explanation of CIDEP at early times in polymers or molecular wires after the creation of the radical pairs by a light pulse. The model is an extension of the vector diagram approach used previously for photosynthesis.7 The density vector diagram is used to simulate the EPR spectra in the frequency domain and depicts the physics and chemistry behind the novel CIDEP phenomena in reversibly conducting polymers. Besides the interesting ESP that occurs, the conducting polymer system is of interest because of its potential applications for molecular electronics. Characterization and understanding of electron transfer in polymers is a valuable pursuit since the fundamental event in molecular electronics is the electron-transfer process. These considerations suggest that CIDEP can provide new data for insight into the electron-transfer dynamics in polymers.

Hasjim and Norris Theoretical Model Using the vector diagram method,7 a description of the time dependence of a simple radical pair in a large externally applied magnetic field can be formulated with the wave functions of four states, |S〉, |T0〉, |T+〉, and |T-〉, which under some circumstances represent the singlet and triplet eigenstates of the spin system. Due to a large Zeeman splitting between |T+〉, |T-〉 and |S〉, |T0〉, the populations of |T+〉 and |T-〉 can be assumed to be invariant and thus electron spin-spin interactions are restricted to S-T0 mixing such that the two corresponding wave functions are sufficient to characterize the time evolution of the system. This simplification of a four state system to a two level system is essential to the utilization of the precessing density vector to explore the CIDEP. For classification of the ESP we use the previous nomenclature,7 namely equal antiphase doublets are referred to as correlated radical pair polarization (CRPP) while unequal antiphase doublets are defined as hyperfine induced CIDEP. The general Hamiltonian of the twolevel system is

( )

∆ω H ) ∆ω 2 ET 2 Es

(1)

Without loss of generalization, ET is set equal zero and thus ∆E becomes the standard isotropic singlet-triplet splitting with ES ) 2J. For simplicity the g values of the radical pairs are assumed to be equal, a good approximation for the samples of the proposed studies. In such cases, CIDEP is driven by the hyperfine interaction, ai. Inclusion of ∆g terms can easily be used in simulations of actual experimental data but is not necessary for a description of the CIDEP “memory” effect occurring in reversibly conducting polymers. Also, a single 1/2 nuclear spin per monomer is all that is needed to capture the essence of the CIDEP since the typical hyperfine dominated radical pair CIDEP spectrum of typical π-radicals has one-half of its spectrum in absorption and one-half in emission. The isotropic electron spin-spin interaction 2J between the radical pairs is an exponentially decreasing function of distance r between radicals given by22-25

J(r) ) J0e-βr ) 1013e-λr

(2)

where J(r)/p is in rad‚s-1 and λ and β are in Å-1. Also neglected is the dipolar interaction between spins since its effective contribution to the CIDEP is minimal.24 Even if the rotational correlation time of the radical pair is large, the effect of the dipolar contribution to CIDEP is negligible because of cancellations associated with the static, powder average.24 The spectroscopic description and the physical explanation of CIDEP are intertwined. On the basis of the well-accepted assumption that only two states evolve in time, the EPR spectroscopy and photochemistry of electron spin pairs can be described by the four wave functions (|T0〉, |S〉, |Φa〉, |Φb〉), where |Φa〉 and |Φb〉 are the eigenfunctions useful for determination of the EPR transitions and |T0〉 and |S〉 are the wave functions useful for the chemical separation and recombination reactions. The time evolution of the density vector is easily determined by solving its equation of motion about the Hamiltonian vector that defines the EPR spectroscopic axis system as previously presented:6,7,21,26

dF b(t) )b F (t) × Ω B dt

(3)

Electron Spin Polarization of Radical Pairs

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Figure 2. (a) All possible combinations of hyperfine values in the polymer model, i.e., 32 ) 25 different polymers as defined by the single local magnetic nuclei of each member of the polymer of chain length five. At all five positions for radicals on the polymer, 16 polymers have the electron spin interacting with a hyperfine field of +a and 16 with a hyperfine field of -a. The branching is drawn to illustrate that forward electron transfers always jump to both positive and negative hyperfine fields while backward electron transfers always return to whatever hyperfine field the electron experienced before at the return site. (b) The nine steps of electron transfer used to illustrate CIDEP for molecular wires or conducting polymers Pi. The donor is considered stationary. For each step 32 polymers are used to represent 32 different hyperfine fields that may be found considering one spin one-half nucleus on each Pi.

where the Hamiltonian is represented by the vectorΩ B )B J+ b a.6,7,21,26 The EPR spectral intensity, M, is determined by the projection of the density vector along the Ω B direction multiplied by the transition probability to the upper or lower triplet states.7 The height of the absorption and emission spectrum for the nth step is calculated by7

[31 + F(t)‚Ω ]/4 1 ) (1 - z‚Ω )[ - F(t)‚Ω ]/4 3

Mb+,n ) -Mb-,n ) (1 + z‚Ωn)

n

(4a)

Ma+,n ) -Ma-,n

n

(4b)

n

As a vehicle for illustrating the ESP or CIDEP “memory” effect associated with bidirectional electron spin migration in molecular wires, a short polymer consisting of five monomers is presented as a pedagogical model. The length was chosen because of the exponential nature of spin-spin interaction. A five-monomer polymer is the optimum system that captures the strong-to-weak spin-spin interactions that characterize the development of CIDEP. Having more than five monomers in the polymers does not alter the essence of the physical explanation of the system while having less than five would not capture the whole CIDEP picture. In real experiments, where

the number of monomers per polymer is large, the number of polymers with different hyperfine interactions is enormous because all combinations of hyperfine interactions must be considered for each polymer to simulate the EPR spectrum. To simplify the calculations while still mimicking the real system and still capturing the spin dynamics controlling the EPR spectrum, no hyperfine is considered on D and only a single hyperfine interaction (+a or -a) is assumed for radical A. With oligomers that only have five monomers and two hyperfine values, groups of thirty-two (25) such polymers are enough to simulate the system. The general hyperfine configurations of a group of thirty-two polymers are shown in Figure 2a. The distance between the Pi molecules is assumed to be static at 9.75 Å. In simulating actual experimental data, these restrictions used in Figure 2 can easily be lifted. We assume that after a photolysis process, the electron spin is transferred from a donor D to an acceptor P1P2P3P4P5 (polymer) and radical-pair evolution begins with the anion at P1-P2P3P4P5. As is often the case, the initial electron transfer from donor to polymer is assumed to arise from an excited triplet state precursor and consequently initially the radical pair is a pure triplet state. Each polymer receives one electron from a single donor that resides near the end monomer P1. Each

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subsequent electron transfer constitutes a single instantaneous step in the time evolution of the ESP. The donor radical D is assumed to be stationary. No solution diffusion, recombination, and termination terms are included in the system used for calculation. Long nuclear and electron spin-lattice relaxation times are assumed in order to preserve the ESP and to prevent hyperfine switching on individual polymer members. This assumption is consistent with our pulsed EPR T1 measurement of migrating bacteriochlorophyll free radicals in the light harvesting complex of Rhodobacter sphaeroides of about 12 µs. The calculated CIDEP spectra will be presented after each electron-transfer step and the effect of electron-transfer rates on spectral line width will be neglected. Results and Discussions The nine electron-transfer steps of Figure 2b for 32 polymers as distinguished by their hyperfine fields are used to illustrate the CIDEP expected in short polymers in the limit of long spinlattice relaxation times for both electrons and nuclei. Because of the small ensemble size, the electron transfer in each of the 32 polymers goes in the same direction at each step to give maximum signal intensities. Electron-transfer times of 10-8, 10-7, or 10-6 s are employed in each step of the calculations to demonstrate the effect of transfer rates on CIDEP intensity. These are the typical electron-transfer times relevant to the EPR time scale of CIDEP in liquid solutions. For each (electron transfer) step, a calculated ESP spectrum using eq 4 and the corresponding vector diagram are presented. In each diagram showing the ESP spectrum, a Boltzmann equilibrium spectrum for the same separation distance is also inserted for comparison. The relative intensities of the EPR spectra are at scale but the vector diagrams are not drawn to scale. The initial chemistry is viewed to take place when donor molecules are ionized by flash photolysis such that an electron is transferred to a nearby polymer at monomer position one, i.e., P1. Since the initial distance of separation between spins is close, at this point the spin-spin interaction is very strong. The simulated EPR spectra and its vector diagram are shown in Figure 3. Note that balanced, symmetrical antiphase doublets occur. The strong electron spin-spin interaction causes a wide splitting of the emission and absorption spectrum. The absolute values of the magnitudes of the emission and absorption spectra are equal and very small. This initially observed ESP is classified as CRPP. For the first electron-transfer step, the density vector for each of the 32 different polymers starts at the same position and precesses around the same Hamiltonian (Ω1) and therefore the projections of density vectors along the Hamiltonian, i.e., the population differences, are all the same. In the second step, electrons transfer from monomer P1 to monomer P2. The spin pair separation distance is greater and hence the interaction between the spins is not very strong. Its magnitude is comparable to the hyperfine values. The calculated EPR spectrum is depicted in Figure 4. The splitting between emission and absorption lines is small due to a moderate spinspin interaction. The absolute heights of the spectral lines are essentially equal for emission and absorption. In this second step, a spin population difference exists for hopping to positive versus negative hyperfine lines as shown in Figure 4b. However, since in the previous step Ω1 was almost aligned with J1, the position of the density vector was barely tilted from the z-axis. Consequently, the transition probability and population differences are still about the same magnitudes as in the prior step. Thus, the difference between absorption and emission is negligible and the electron transfer has not induced any noticeable imbalance that would define the presence of CIDEP.

Figure 3. (a) First step: Calculated EPR spectrum of the radical pair immediately after initial donor to acceptor electron transfer. The inset figure is the Boltzmann equilibrium spectrum calculated for this radical pair distance. The intensity of the calculated CIDEP spectra is very small compared to Boltzmann and therefore will not be observed experimentally. (b) First step: Density vector diagram illustrating the initial radical pair (electron transfer from D to P1). The density vector precesses about a positive hyperfine field. A complementary diagram would be for the negative hyperfine field, i.e., a mirror image of this diagram. In this case where the J value is much larger than the hyperfine value, the Hamiltonian (Ω1) is almost aligned along the J direction. The spectroscopic eigenvectors Φa and Φb are always aligned with the Hamiltonian. The J1 and Ω1 are the J and Ω resulting from electron transfer to monomer 1 while the Φa+ and Φb+ indicate Φa and Φb formed because of the electron hop to a monomer that has a positive hyperfine field. Subscripts i and f denotes initial and final position of the density vector.

In the third step as the electrons transfer forward to the third monomer, the spin pair interaction becomes negligible compared to hyperfine values. In this case, the absorption and emission line, i.e., the antiphase doublet, of each radical species collapses to a single magnetic field value and no antiphase doublets are seen. The computed spectra in Figure 5 show the summed difference in absorption and emission of the 32 radicals due to

Electron Spin Polarization of Radical Pairs

Figure 4. (a) Second step: Calculated EPR spectra of the second radical pair showing a first visit. On the first visit, which is a forward electron transfer, the absolute sizes of the emission and absorption are equal such that the emission and the enhanced absorption cancel each other on the low field half of the spectrum and on the high field half of the spectrum. Electron-transfer rates have no effect on this step. This type of ESP is also defined as CRPP.7,21 (b) Second step: Vector diagram after electron transfer from P1 to P2 for jumps to positive and negative hyperfine fields. A slight difference in the projection of the density vector along the Φ2 spectroscopic axis is shown by the precession angles.

the electron hopping to either a positive or negative value of the hyperfine interactions. The absolute values of the overlapping absorption and emission intensities are essentially equal so that the net CIDEP is diminishingly small (see the intensity in Figure 5). At this point, the very small net CIDEP is because Hamiltonian spectroscopic axis Ω3 is just slightly misaligned with the x-axis. Tracking the movement of density vectors in Figure 5b, the density vectors associated with hopping to positive and negative hyperfine fields precess almost at the same angle and path, but in reverse directions. If the spin-spin interaction is effectively zero such that the Hamiltonian is given only by the hyperfine values, the net CIDEP for electron-transfer jumping to positive hyperfine is exactly cancelled by jumping to negative hyperfine. Complete cancellation is observed in the radical pair CIDEP of simple molecules where liquid solution diffusion causes the distance of donor and acceptor to be very

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Figure 5. (a) Third step: Calculated EPR spectrum showing the ESP for the radical pair with one of the electron spins on monomer 3. Because of the large distance between the radical pairs, the low field lines have collapsed to a single magnetic field position. Likewise for the high field lines. On the first visit to monomer 3, only a small imbalance between the emission and absorption is observed on the low field side as a small net absorption. On the high field side on the first visit only a small net emission is seen. This imbalance is known as radical pair CIDEP. In this instance the intensity of this imbalance is about 100 times smaller than the intensity for the Boltzmann spin population of the inset. (b) Third step: Vector diagram after electron transfer from the positive hyperfine in P2 to both positive and negative hyperfines in P3. Very weak spin-spin interaction causes Ω3 to almost align with the x-axis. Two initial density vectors exist in this graph but they coincide with each other. Electron hopping to positive and negative hyperfine fields in this step reveals that the density vectors precess around Ω3 at almost the same angle but in reverse directions.

far apart. Consequently, additional electron transfer between acceptors distant from the donor member of the radical pair diminishes the CIDEP. Since in this polymer step J is not completely zero, the Hamiltonian is slightly tilted from the x-axis such that a very small net CIDEP exists. The distinguishing phenomenon occurs in the fourth step when electrons transfer back to monomer P2 from monomer P3. Because of the long nuclear and electron T1s, the spin environments from the nuclei have not changed. When electrons transfer back to their previous position, spins return to whatever

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Figure 6. (a) Fourth step: On the second visit to monomer 2, a backward electron transfer, net emission is on the low field half and net absorption on the high field half of the spectrum. This type of ESP is known as radical pair CIDEP. The dotted, solid, and dashed lines are CIDEP intensity calculated with electron transfer times of 10-8, 10-7, and 10-6 s, respectively. Here the spectral intensities are significantly larger than the Boltzmann spectral intensities of the inset. (b) Fourth step: Continuation from previous diagram as electron transfer back from P3 to P2. Electrons have to transfer to the original hyperfine fields in P2, which was a positive hyperfine field (depicted here only to the positive hyperfine while the negative is just the mirror image).

Figure 7. (a) Fifth and ninth steps: On the second visit to P3 the CIDEP is much larger. Thus, in the case of electron transfer in polymers, significant CIDEP is produced while electron transfer in liquid solution destroys CIDEP. The dotted, solid, and dashed lines are CIDEP intensity calculated with electron-transfer times of 10-8, 10-7, and 10-6 s, respectively. (b) Fifth step: Electron transfer from P2 to P3 for the second time. Initial positions for transferring to positive and negative hyperfines are different from those in Figure 5b. The precession angles of the density vectors around the Hamiltonians are different.

hyperfine value they experienced previously on P2. As a consequence, the absorption and emission spectral intensity for each radical pair is no longer balanced, leading to a pronounced CIDEP spectrum as presented in Figure 6. Unsymmetrical, unbalanced, antiphase doublets are realized. The intensity of the hyperfine radical pair CIDEP depends on the transition probability to the triplet state multiplied by the population difference. The transition probability to the triplet state is fixed at each step by the Hamiltonian, but the population difference varies with the angle between density vector and the Hamiltonian. The magnitude of the net CIDEP depends on the electrontransfer rate since the final positions of the density vectors from previous precession would vary the population difference upon returning to P2. This phenomenon is in contrast to the electron transfer observed in simple molecules such as when durosemiquinone radical anions transfer spin to other duroquinone

molecules. In simple molecules experiencing separation by diffusion only, i.e., not acceptor-to-acceptor or donor-to-donor electron transfer, then the CIDEP occurs as explained by Monchick and Adrian6 where the distance of separation goes sequentially from close, far, close, and finally far at which point in time a large CIDEP EPR signal is observed. For this solution diffusion case, the hyperfine is constant while the separation distance of the pair changes. In a conducting polymer, both distance of separation and hyperfine are changing. If acceptorto-acceptor or donor-to-donor electron transfer occurs for simple molecules undergoing solution diffusion, the process of additional electron transfer changes hyperfine as well as distance of separation. Once such solution electron transfer occurs, a greatly diminished chance exists for a spin to return to the original molecule that formed the geminate radical pair. Consequently electron transfer in liquid solutions rapidly

Electron Spin Polarization of Radical Pairs

Figure 8. (a) Sixth, seventh, and eighth steps: Negligible CIDEP as electron transfer away from the donor. No CIDEP signal dependence on electron-transfer rates. (b) Sixth, seventh, and eighth steps: Vector diagram of radical pairs as the distance between them becomes very large.

destroys CIDEP. The confinement of spin to a single polymer provides the increased opportunity for electron transfer to recreate the same hyperfine interaction at the same distance of separation and distinguishes reversible electron transfer in polymers from electron transfer in ordinary liquid solution with simple molecules. In polymers, another electron transfer from P2 to P3, i.e., the fifth step, would likely produce an imbalanced emission and absorption spectra. Figure 7 shows the magnitude and phase of the CIDEP for this fifth step (or the second P2 to P3) at different electron-transfer rates (for all steps). The main distinctions between the fifth step and the third step are the positions of the initial density vectors. In the third step, the initial position of density vector before jumping to positive and negative hyperfine fields are the same while they are different in this second P2to-P3 step. The differences in CIDEP magnitude and phase are caused by the different precession angles of the density vectors jumping to positive and negative hyperfine fields around Ω3 as

J. Phys. Chem. C, Vol. 111, No. 13, 2007 5209 shown in Figure 7b. For one of the electron-transfer rates, the precession angle of the density vector resulting from electron transfer to positive hyperfine is bigger than that of transfer to negative hyperfine. At another electron transfer, the reverse is true. Hence, the phase of the net CIDEP changes depending on electron-transfer rates and for actual spectral simulations a more detailed treatment must be applied. As electrons transfer farther away (sixth and seventh steps), i.e., from P3 to P4 and P4 to P5, the spin-spin interaction approaches zero. The Hamiltonian is almost perfectly aligned with the hyperfine field on the x-axis. The net CIDEP after hopping to positive and negative hyperfine fields cancel each other; consequently, no signal is detected as depicted in Figure 8. The same spectra are predicted in the eighth step for electron transfer from P5 back to P4. Although the spins have to transfer back to their original hyperfine fields due to the assumed long T1 values, the Hamiltonian axis is still aligned with the x-axis. The net CIDEP of positive and negative hyperfine pair in P5 returning to positive hyperfine in P4 is cancelled by the net CIDEP of positive and negative hyperfine pair in P5 returning to negative hyperfine in P4. At this far distance of separation, the CIDEP of polymers is the same as that of simple molecules in liquid. However, in the ninth step when the spins return to P3, the net CIDEP in that position is recovered as shown in Figure 7. The large CIDEP of this ninth step illustrates the unique difference between electron transfer in liquid solution and electron transfer in polymers. In liquid solutions, nine electron-transfer steps would completely destroy any CIDEP. On the basis of these nine steps of electron transfer, unique electron spin polarization of radical pairs in a short polymer system is predicted. Other situations where the first electrontransfer step goes into the middle of the polymer strand can also be considered. The donor spin can migrate in a polymer where the distance of separation involves the movement of both halves of the radical pair. These different sequences of electrontransfer steps have also been considered and give similar results. In summary, electron transfer in the first visit results in a balanced absorption and emission spectra while second-time electron transfer produces an imbalance in the region where the spin-spin interaction is comparable to the hyperfine values. This special spin polarized spectrum is explained by (1) reversible electron transfer between monomers in polymers where the density vector is confined primarily to the xz plane and (2) long nuclear and electron spin-lattice relaxation time compared to the electron transfer or measurement time in experiment, which leads to memory of previous spin environments. Work is underway to exploit these predictions experimentally. Acknowledgment. Support from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences Contract DE-FG02-96ER14675 is gratefully acknowledged. References and Notes (1) Fessenden, R. W.; Schuler, R. H. J. Chem. Phys. 1963, 39, 2147. (2) McLauchlan, K. A. J. Chem. Soc., Perkin Trans. 1997, 2465. (3) Pedersen, J. B.; Freed, J. H. J. Chem. Phys. 1973, 58, 2746. (4) Pedersen, J. B.; Freed, J. H. J. Chem. Phys. 1973, 59, 2869. (5) Pedersen, J. B.; Freed, J. H. J. Chem. Phys. 1975, 62, 1706. (6) Monchick, L.; Adrian, F. J. J. Chem. Phys. 1978, 68, 4376. (7) Norris, J. R.; Morris, A. L.; Thurnauer, M. C.; Tang, J. J. Chem. Phys. 1990, 92, 4239. (8) Hore, P. J.; McLauchlan, K. A. Chem. Phys. Lett. 1980, 75, 582. (9) Hore, P. J.; McLauchlan, K. A. Mol. Phys. 1981, 42, 533. (10) Jager, M.; Norris, J. R. J. Magn. Reson. 2001, 150, 26. (11) Jager, M.; Norris, J. R. J. Phys. Chem. A 2002, 106, 3659.

5210 J. Phys. Chem. C, Vol. 111, No. 13, 2007 (12) Jager, M.; Yu, B. C.; Norris, J. R. Mol. Phys. 2002, 100, 1323. (13) Jastrzebska, M.; Kocot, A.; Tajber, L. J. Photochem. Photobiol., B 2002, 66, 201. (14) Crippa, P. R.; Cristofoletti, V.; Romeo, N. Biochim. Biophys. Acta 1978, 538, 164. (15) Krinichnyi, V. I.; Chemerisov, S. D.; Lebedev, Y. S. Phys. ReV. B: Condens. Matter Mater. Phys. 1997, 55, 16233. (16) Maliakal, A.; Weber, M.; Turro, N. J.; Green, M. M.; Yang, S. Y.; Pearsall, S.; Lee, M. J. Macromolecules 2002, 35, 9151. (17) Ikoma, T.; Akiyama, K.; Tero-Kubota, S. Phys. ReV. B: Condens. Matter Mater. Phys. 2005, 71, art. no. 195206. (18) Ito, F.; Ikoma, T.; Akiyama, K.; Watanabe, A.; Tero-Kubota, S. J. Phys. Chem. B 2005, 109, 8707.

Hasjim and Norris (19) Ito, F.; Ikoma, T.; Akiyama, K.; Watanabe, A.; Tero-Kubota, S. J. Phys. Chem. B 2006, 110, 5161. (20) Pedersen, J. B. FEBS Lett. 1979, 97, 305. (21) Wang, Z. Y.; Jau, T.; Norris, J. R. J. Magn. Reson. 1992, 97, 322. (22) Kobori, Y.; Sekiguchi, S.; Akiyama, K.; Tero-Kubota, S. J. Phys. Chem. A 1999, 103, 5416. (23) Kobori, Y.; Yago, T.; Akiyama, K.; Tero-Kubota, S.; Sato, H.; Hirata, F.; Norris, J. R. J. Phys. Chem. B 2004, 108, 10226. (24) Kobori, Y.; Yamauchi, S.; Akiyama, K.; Tero-Kubota, S.; Imahori, H.; Fukuzumi, S.; Norris, J. R. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10017. (25) Kobori, Y.; Akiyama, K.; Tero-Kubota, S. J. Chem. Phys. 2000, 113, 465. (26) Adrian, F. J. J. Chem. Phys. 1971, 54, 3918.