Supporting Text Analysis of Time Traces of the Fluorescence and the Transient Absorptions in Fig.

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1 upporting Text Analysis of Time Traces of the Fluorescence an the Transient Absorptions in Fig. 3. Fig. 6 shows the energy iagram an reaction scheme of the tria in PhCN. The total quantum yiel (Φ total ) for the final C generation is reporte (1) to be.4. In this section, kinetic parameters for the C processes ( 4 an 4 6 in Fig. 6) are etermine by using the fluorescence ecay measurement along with the previously reporte transient absorption ata (1). From the schematic representation of the energy an electron transfer processes in Fig. 6, the following couple ifferential equations are obtaine: [ 1] [ 3] [ 4] [ 5] [ 6] ( k k )[] 1, [ 1] = + 1 [] 1 ( ), = k k + k + k ( )[ 3], [ 3] = k k + k [ 3] ( )[ 4], [ 4] = k + k k + k = k 4 34 C CR1 35 Z [ 3], [ 5] [ 4] [ 6], [ 6] = k k C CR H where the k ij enote the rate constants for the process from [i] to [j] in Fig. 6. The k Z (= s 1 ) an the k H ( = s 1 ) are fluorescence eactivation rate constants of 1 ZnP* an 1 H P*, respectively in the absence of the energy an electron transfer processes as reporte in ref. 1. When these couple ifferential equations are represente by a matrix form as, X(t)/ = P X(t), time evolution of the [1] [6] states can be solve as X(t) = Q exp(λt) Q 1 X(t = ), where Q an λ are the matrices of eigenvectors an eigenvalues, respectively, so that PQ = Qλ. The initial conition, X(t = ) was set to be [1] t = = [] t = =.5 an [3] t = = [4] t = = [5] t = = [6] t = = estimate from the absorbance values in ZnP, H P, an C 6 moieties at 53-nm light as reporte in ref. 1. The time traces of [1] [6] obtaine from Eqs. 1 6 were convolute as in ref. by the

2 response functions etermine by the laser pulse wih (18 ps) to obtain the calculate time traces in Fig. 3. Fig. 7 shows the time-profiles of the populations in the [1] [6] states. The fluorescence intensity in Fig. 3A was set to be proportional to the calculate trace of [] in Fig. 7. Absorbance intensities were reprouce by summations of the sixabsorbance values (for 1 6), which were set to be proportional to the populations (in Fig. 7) multiplie by molar extinction coefficients (ε). The ε values for 1 6 were chosen to fit the absolute intensities in Fig. 3B an were comparable with the reporte values of the transient species of 1 ZnP*, 1 H P*, 1 C 6 *, H P +, 3 C 6 * an ZnP +, respectively (3 6). The 65-nm rise in Fig. 3B is attribute to the builup in ZnP + an in 3 C 6 * by processes 4 6 an by 3 5, respectively. The kinetic parameters were etermine an revise from previous work (1) as follows: k 3 = s 1, k C1 = s 1 ( 4), k 35 = s 1 (1) an k C = s 1 (4 6). The rate of k C1 = s 1 is close to the C rate of s 1 in the ZnP C 6 ya (ZnP 1 C 6 * ZnP + C - 6 ) in Fig. 1B (7). The ifference in these C rates can be explaine by the ifference in FCWD because G C =.37 ev reporte in the ya is slightly larger than G C ( 4) =.3 ev in this tria (7), supporting the valiities of the present analysis. Quantitative Analysis of EP. In Eq., off-iagonal terms of ρ,t an ρ T, are evelope by the coherent T mixing in ρ 1 an memorize by Eq. 3 into ρ, contributing to the sequential ET polarization. From Eqs. an 4 in the main text, the ensity matrix ρ 1 (s) is escribe in the T system as follows: s+ kc ( i/ h) Q1 ( i/ h) Q1 ( / h) C ( / h)( ) ( / h) ( / h) + C ( / h)( + ) ( / h) ( i/ h) Q ( i/ h) Q s+ k ( t = ) ( t ) ( t ) ( t = ) ρ ρ 1, 1, i Q1 s+ k + i J1 + 1 i Q1 ρ1, T ρ1, T = =, i Q1 s k i J1 1 i Q 1 ρ 1, T ρ 1, T = ρ ρ 1 1 C 1, TT 1, TT [ 7] where k = D k (cos θ k 1/3)/ is the ipolar interaction epening on the D value (D k ) an on the ipolar axis angle (θ k ) with respect to the B. Q is expresse as

3 1 Q k = gc eff gp β B + A k C mmc m AP k nmpk n m n ( 6, ) 6, 6,,,, [ 8] with C6, eff C6x C6y C6z g = g sin θ cos φ + g sin θ sin φ + g cos θ, 9 where θ an φ are the polar angles of the B with respect to the z an x principal axes, respectively, in the g-tensor (g x, g y, g z ) of C 6.ρ 1 (s) can be obtaine by setting the initial population in ρ 1 (t = ) to be singlet: ρ 1, (t = ) = 1 an ρ 1,T (t = ) = ρ 1,T (t = ) = ρ 1,TT (t = ) = in Eq. 7. To obtain the EPR positions an their transition intensities in the seconary C state, the four eigenstates are obtaine as, a = T +, b = cosµ + sinµ T, c = -sinµ + cosµ T an = T -, where the Hamiltonian H in Eq. 4 is iagonalize uner the high B limit (8). If k C process is much faster than the time resolution of the EPR spectrometer, the initial conitions of the seconary C state (ρ abc ) in, a, b c an can be compute as ρ -1 ( t = ) = lim sk Uρ U, [ 1] abc C 1 s with 1 cosµ sinµ U=, 11 sinµ cosµ 1 ρ 1 1,T ( s ρ ρ ) = ρ1,t ( ) ( ) s ρ1,t T s 1,. 1

4 The angle µ is represente as follows (9): Q J + + ω ω ω ( J + + ω ) [ ] cos µ=, sin µ=, 13 where ω = {(J + ) +4Q } 1/. The unitary transformation an the subsequent inverse Laplace transformation of Eq. 3 provies the time-ifferential equation of the ensity matrix ρ(t) in this spin system. In the limit of the fast spin spin relaxation in the zero-quantum coherences for the offiagonal terms (ρ bc an ρ cb ), the time-evolution of the CRP populations (ρ kk ) simplifies to a set of couple time-ifferential equations in ρ abc (1), & ρaa wab wac wba wca ρaa & ρbb wab wba wbc wb kcr cos µ wcb wb ρbb =, 14 & ρ cc w sin µ ac wbc wca wcb wc kcr wc ρcc & ρ w w w w ρ b c b c [ ] where w ij enotes the spin-lattice relaxation rate constant between the i an j states in, a follows:. The relaxation rate constants can be relate as c an, b w = w hν w = w hν w = w hν w = w hν MW MW MW MW ac ca exp, b b exp, ab ba exp, c c exp, 15 kt B kt B kt B kt B where υ MW enotes the microwave frequency (= 9. GHz in the present work). In the weak-coupling limit (µ π/4) in the CRP (11), where Q >> J + is applicable in this system, the spin-lattice relaxation times can be simplifie as follows: T = 1, T = 1, 16 1, C6 1, ZnP wac + wca wab + wba

5 with w ac = w b, w ca = w b, w ab = w c, an w ba = w c. The relaxation times (1/w bc an 1/w cb ) between the b an c states correspon to the ephasing time between the an T states inuce by fluctuations of the J an (1). These bc an cb relaxation times shoul be much longer than the T 1 values because of the long istance between the ZnP an C 6 in the tria an thus can be neglecte. Because the molecular size of this tria is large enough, its rotational correlation time ( ns obtaine by the Debye formula by using raii Å an solvent viscosity = 1. cp of PhCN) is estimate to be slower than the inverse value (78 ns) of the frequency of D, inicating that the rotational motion oes not average the ipolar interaction in this system. The anisotropic Zeeman interaction also was reporte in the N-methylfulleropyrroliine anion raical in a liqui solution (13). Time evolution of ρ abc was calculate by solving Eq. 14 as ρ abc (t) = exp(ηt) 1 ρ abc (t = ), where an η are the matrices of eigenvectors an eigenvalues of the relaxation matrix in Eq. 14, an was convolute with the response time of the TREPR signal (). For the EPR transitions among the four levels, the transition intensities are represente as in ref. 8, I ab = (ρ bb ρ aa )sin µ, I ac = (ρ cc ρ aa )cos µ, I b = (ρ ρ bb )sin µ, an I c = (ρ ρ cc )cos µ. The ρ abc (t) was use for the computations of the TREPR spectrum an the time profile shown in Fig. 4. The time-epenent spectra were compute by summing the above four-line spectra obtaine at all possible equally istribute Ω with respect to the irection of B (1). For C 6 three lines from a nitrogen HF-coupling constant (a N =. mt) were taken into account with Lorentzian peak-functions (13), while nine lines by a N =.196 mt (four equivalent nitrogen atoms) were consiere for the porphyrin π cation raicals with Gaussian line-shapes (14). Quantitative Analysis of J. From Fig. 8, in the absence of the electronic coupling interactions, the C an the CR states are represente as ( ) = λ + hν+ ECR X 17, X j Ei i j

6 an ( ) = λ ( 1 ), [ 18] E X X G C CR where a single high-frequency intramolecular vibrational moe (υ > 1 cm 1 ) is consiere in the CR state. E i is the excite state energy in the ith CR state. In the C state, we can assume that only the lowest vibrational levels are populate at room temperature. In the presence of the V CR interaction, when the spin multiplicities are ientical between the C an the CR states, the following secular equation is obtaine: ( ) ε( ) E X X V FC CR i, j i, j CR, i j ( ) ε( ) V FC E X X CR, i j C i, j [ ] =, 19 where FC j = FC j = exp( λ v /ħυ) (λ v /ħυ) j (j!) 1 is the Franck Conon factor in the vibrational moe. From Eq. 19, the potentials (ε + an ε ) of the electronic states (soli lines in Fig. 8) are obtaine as follows: ε ± ( ) ( ) ( ) ( ) ( ) { } 4,, 1 X = E, CR X + E i j i, j C X ± ECR X E i, j C X + VCR i FCj The singlet-triplet energy gap ( e) in the C state is efine from Fig. 8 as follows: { + ij C } ( ) { ε ij C } ( ) ( ) ( ) ε ( ) ( ) ε X = 1 X E X, for X χ 1 ij. i, ( ) ( ) ( ) ( ) ε X = 1 X E X, for X χ ij. i, where i enotes the electron spin quantum number in the CR states: i = when the CR i in Fig. 8 is the singlet state while i = 1 if the CR i is the triplet state. The term (1 i ) correspons the sign (+ or ) of the singlet triplet energy gap, because the singlet or

7 triplet C state s energy stabilization or estabilization epens on the spin multiplicity of the CR state (). As examples, at X = 1 in Fig. 8, if CR i is the singlet state, the singlet C state is selectively stabilize leaing to negative value (1 i = 1) in e(x = 1), while, if CR i is the triplet state the triplet C state is selectively stabilize leaing to positive value (1 i = +1) in e(x = 1). The χ in Fig. 8 is obtaine as λ GCR jhυ Ei χ i, j=. 3 λ [ ] At X = χ in Fig. 8, both of the upper an the lower electronic states in the soli lines are the 5%/5% mixings between the C an CR states. Contributions from the upper an the lower states cancel the singlet-triplet energy gap, i.e., e(χ) =. We consier the liqui environment in which the solvent relaxation (along with the X coorinate) is much faster than the Q 1 interaction in Eq. 8. In the time scale (>1 9 s) of the coherent singlet-triplet mixing by Q 1, the C state cannot recognize its position in the X coorinate. In this case, the J is efine as a single value average by P(X) = (λ /πk B T) 1/ exp{ λ (X 1) /k B T} as escribe in Eq. 6 in the main text. ε ( ) ( ) i, j J = X P X X. 6 i j The J values were compute by the numerical integrations of Eq. 6 with substituting Eqs. 17, 18, an 3 for Eq. 6. We have consiere nine CR states (for i states) in the tria to simulate the J 1 value: the, T 1, T, 1, an states in H P an C 6, where E T1 (H P) = 1.4 ev, E T (H P) = 1.8 ev, E 1 (H P) = 1.89 ev, E (H P) =.3 ev, E T1 (C 6 ) = 1.5 ev, E T (C 6 ) = 1.6 ev, E 1 (C 6 ) = 1.75 ev, an E (C 6 ) = 1.9 ev (1, 3, 15, 16). E ox E re = 1.59 ev is known as the C state energy in PhCN (7). Configuration Interaction in the 1 state of the H P moiety. It is well-known that 1 (b 1u, b 3g ) an 1 (a u, b g ) are mixe thoroughly through the configuration interaction (CI), giving

8 the very strong B ban an weak Q ban absorptions in the porphyrins. Methos for the semiquantitative estimation of the mixing coefficients in A 1 (b 1u, b 3g ) + B 1 (a u, b g ) were previously reporte in ref. 17. By using this metho, from the absorption intensities of the Q X (,) (at 65 nm), the Q Y (,) (at 56 nm), an the B bans (at 4 nm) obtaine from ref. 16, the coefficients are estimate as 1 H P* ~.9 1 (b 1u, b 3g ).4 1 (a u, b g ) in the tria. The 1 (b 1u, b 3g ) coefficient (A =.9) in this wavefunction is larger than that (A =.8) for magnesium tetraphenylporphyrin (MgTPP) reporte in ref. 17. This result is consistent with the results that the (,) fluorescence ban intensity is about three times stronger than the vibronic (,1) fluorescence intensity in the tria (18), whereas the (,) fluorescence intensity is comparable with the (,1) intensity in MgTPP (17), because the (,1) ban intensity borrows the 1 (a u, b g ) coefficient of B through the vibronic coupling (15). 1. Luo, C., Guli, D. M., Imahori, H., Tamaki, K. & akata, K. () J. Am. Chem. oc. 1, Kobori, Y., ekiguchi,., Akiyama, K. & Tero-Kubota,. (1999) J. Phys. Chem. A 13, Guli, D. M. & Prato, M. () Acc. Chem. Res. 33, Fajer, J., Borg, D. C., Forman, A., Dolphin, D. & Felton, R. H. (197) J. Am. Chem. oc. 9, Roriguez, J., Kirmaier, C. & Holten, D. (1989) J. Am. Chem. oc. 111, Gasyna, Z., Browett, W. R. & tillman, M. J. (1985) Inorg. Chem. 4, Imahori, H., Tamaki, K., Guli, D. M., Luo, C. P., Fujitsuka, M., Ito, O., akata, Y. & Fukuzumi,. (1) J. Am. Chem. oc. 13, Closs, G. L., Forbes, M. D. E. & Norris, J. R. (1987) J. Phys. Chem. 91, Morris, A. L., nyer,. W., Zhang, Y. N., Tang, J., Thurnauer, M. C., Dutton, P. L., Robertson, D. E. & Gunner, M. R. (1995) J. Phys. Chem. 99, Fukuju, T., Yashiro, H., Maea, K., Murai, H. & Azumi, T. (1997) J. Phys. Chem. A 11, Timmel, C. R., Fursman, C. E., Hoff, A. J. & Hore, P. J. (1998) Chem. Phys. 6,

9 1. Hore, P. J., Hunter, D. A., McKie, C. D. & Hoff, A. J. (1987) Chem. Phys. Lett. 137, Zoleo, A., Maniero, A. L., Prato, M., everin, M. G., Brunel, L. C., Koratos, K. & Brustolon, M. () J. Phys. Chem. A 14, Fukuzumi,., Eno, Y. & Imahori, H. () J. Am. Chem. oc. 14, pellane, P. J., Gouterman, M., Antipas, A., Kim,. & Liu, Y. C. (198) Inorg. Chem. 19, Tkachenko, N. V., Vehmanen, V., Nikkanen, J. P., Yamaa, H., Imahori, H., Fukuzumi,. & Lemmetyinen, H. () Chem. Phys. Lett. 366, Yamauchi,., Matsukawa, Y., Ohba, Y. & Iwaizumi, M. (1996) Inorg. Chem. 35, Tamaki, K., Imahori, H., Nishimura, Y., Yamazaki, I. & akata, Y. (1999) 7,