Dynamics of Charge Separation from Second Excited State and

Subscriber access provided by BRIGHAM YOUNG UNIV

Article

Dynamics of Charge Separation from Second Excited State and Following Charge Recombination in Zinc-Porphyrin-Acceptor Dyads Marina V Rogozina, Vladimir Nikolaevich Ionkin, and Anatoly Ivanovich Ivanov J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp402734h • Publication Date (Web): 16 May 2013 Downloaded from http://pubs.acs.org on May 20, 2013

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Dynamics of Charge Separation from Second Excited State and Following Charge Recombination in Zinc-Porphyrin-Acceptor Dyads Marina V. Rogozina, Vladimir N. Ionkin, and Anatoly I. Ivanov∗ Volgograd State University, University Avenue 100, Volgograd 400062, Russia (Dated: April 29, 2013)

Abstract Intramolecular charge separation from the second singlet excited state of directly linked Zn– porphyrin–imide dyads and following charge recombination into the first singlet excited and the ground states has been investigated in the framework of a model incorporating four electronic states (the first and the second singlet excited, the charge separated and the ground states) as well as their vibrational sublevels. Kinetics of the transitions between these states are described in terms of the stochastic point-transition approach involving reorganization of a number of high frequency vibrational modes. The influence of the model parameters (the number of high frequency vibrational modes, the magnitude of the reorganization energies of the medium and the high frequency intramolecular vibrations, the solvent polarity) on the kinetics of population of the second and the first singlet excited states as well as the charge separated state has been investigated. Simulation of the kinetics of the charge separated state population allows quantitative reproducing the distinctive features of the two-humped kinetic curve observed in the experiment. Keywords: charge transfer, intramolecular reorganization, solvent relaxation, stochastic point-transition model

∗

To whom correspondence should be addressed. E-mail: [email protected]

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

I.

Page 2 of 32

INTRODUCTION

The photoinduced charge transfer reactions are well studied and reviewed in many papers, see, for example, refs 1–7. The charge transfer from the first singlet or triplet excited-states is customarily investigated while the researches of the charge transfer from the second excitedstate, S2 , are limited to a few studies of Zn–porphyrin–imide systems.8–19 Recently it was realized that the molecular triads, acceptor-donor-acceptor, with two excited states of the donor can function as molecular switches and corresponding molecules were synthesized and explored.19 A universal feature of the S2 fluorescence quenching in Zn–porphyrin–acceptor systems by either intermolecular14 or intramolecular electron transfer is high efficient recombination into the S1 state.13,15,16,19,20 This recombination is so efficient that only a minor share of the ionic products survived at the stage of the medium relaxation. Such a behavior is expected because the charge recombination (CR) to the first excited-state in Zn–porphyrin–imide systems resembles the CR in excited donor–acceptor complexes in polar solvents where the CR is also ultrafast21–29 and most probably proceeds in the hot regime.30–32 The scheme of the electronic states involved in photoinduced electron transfer from the second excited state, S2 , in Zn–porphyrin–imide compounds is shown in Figure 1. An excitation of the Soret-band by a short laser pulse leads to population of the S2 state which decays within a few hundreds of femtoseconds predominantly yielding the charge separated (CS) state. Initially, the molecule in the CS state and the surrounding medium are highly nonequilibrium. The free energy of this state is larger than that of the relaxed S1 state even if the energies of the relaxed CS and S2 states are in the inverse order as it is pictured in Figure 1. So, the CR into the S1 state can effectively proceed in parallel with the relaxation of the system in the CS state. The CR at this stage is termed the hot CR. The measurements of the CS state population kinetics in Zn–porphyrin–imide dyads have shown that only 10– 20% of the molecules produced in the CS state can avoid the CR at the hot stage.19 After thermalization, the charge separation from the S1 state can proceed in thermal regime that completes the chain of the transitions S2 → CS → S1 → CS observed in ref 19. For a description of this chain of the transitions the multichannel stochastic model incorporating the hot transitions is the most appropriate.30,33–36 In particular, the kinetics of the population of the S2 and S1 states reported in refs 10–12 were reproduced within the 2


Page 3 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


framework of the multichannel stochastic model involving three electronic states (S2 , CS and S1 ), the medium and intramolecular high frequency vibrational mode reorganization as well as their relaxation.37 Later, in the framework of this model the CS state population kinetics were simulated.31 The model appears to be able to reproduce the kinetic curve of the CS state population with two maxima reported in ref 19 for Zn(II)–porphyrin covalently linked to naphthaleneimide in dimethylformamide (DMF) solution. The main weakness of the model used in refs 31,37 for the description of the charge transfer kinetics is an account of the reorganization of high frequency vibrational modes in terms of single effective mode. In real systems 5–10 high frequency modes are really participate at charge transfer reactions.29,36,38–41 The results of calculations show the charge transfer in both the hot and thermal regimes with real quantum vibration spectrum to be much faster than that with single effective mode.30,36,42 It implies that for quantitative description of the ultrafast charge transfer dynamics the proper high frequency vibrational spectrum is required. The aims of this paper are (i) to reveal how the number of high frequency modes involved in charge transfer influences on the kinetics of the S2 , CS, and S1 state populations in zinc–porphyrin–imide dyads, (ii) to comprehend what is the reason of large distinctions between the kinetics of the CS state population of the same dyad in two solvents, DMF and tetrahydrofuran (THF), with close relaxation properties, and (iii) to fit the CS state population kinetics to that obtained in ref 19 for Zn(II)–porphyrin covalently linked to naphthaleneimide in DMF.

II.

THE MODEL OF ULTRAFAST CHARGE SEPARATION FROM SECOND EX-

CITED STATE AND FOLLOWING CHARGE RECOMBINATION INTO FIRST EXCITED AND GROUND STATES

For the description of ultrafast charge separation from the second excited state and following charge recombination into the first excited and the ground states, a minimal model including four electronic states: the ground state | S0 ⟩, the first and the second singlet excited states, | S1 ⟩, | S2 ⟩, correspondingly, and the charge separated state, | CS⟩, is employed (see Figure 2). The model is an expansion of that described in detail in ref 37. So, we only briefly outline the new elements and introduce the designations used hereafter. 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 32

The real solvents are characterized by several relaxation time scales.43–46 To describe their relaxation, the Markovian approximation is used and the solvent relaxation function, X(t) is written in the form X(t) =

N ∑

xi e−t/τi

(2.1)

i=1

where xi = Eri /Erm , τi , and Eri are the weight, the relaxation time constant, and the reor∑ ganization energy of the ith medium mode, respectively, Erm = Eri , and N is the number of the solvent modes. A reaction coordinate Qi can be associated with each of the solvent modes. Equation 2.1 suggests the diffusional motion of each solvent mode, while an initial part of relaxation is not diffusive but rather inertial.43–46 A possibility of an approximation of the initial relaxation by the exponential function and how this approximation influences on the charge transfer dynamics are discussed in ref 47. Diabatic free energy surfaces for the electronic states in terms of the reaction coordinates Qi is written as follows35,48 US2

N ∑ Q2i = 4Eri i=1

(⃗ n) UCS

N ∑ (Qi − 2Eri )2

=

(m) ⃗

US1 = (⃗l)

US0 =

(2.2)

i=1 N ∑

4Eri Q2i 4Eri

i=1 N ∑

Q2i

i=1

4Eri

+ ∆GCS +

M ∑

nα ~Ωα

(2.3)

α=1

+ ∆GS1S2 +

+ ∆GS0S2 +

M ∑

mα ~Ωα

(2.4)

α=1 M ∑

lα ~Ωα

(2.5)

α=1

where Ωα and nα , mα , lα (nα , mα , lα = 0, 1, 2, ...) are the frequency and quantum numbers of the αth effective intramolecular quantum mode, correspondingly, M – is the number of intramolecular quantum modes, the indexes ⃗n, m, ⃗ ⃗l are abbreviation for the sets of quantum numbers ⃗n = {n1 , n2 , ...nα , ...}, m ⃗ = {m1 , n2 , ...mα , ...}, and ⃗l = {l1 , n2 , ...lα , ...}, ∆GCS is the free energy change of the charge separation from the second excited state S2 , ∆GS1S2 and ∆GS0S2 are the free energy changes of the transitions from the second to the first excited and the ground states, correspondingly. In the framework of the stochastic point–transition approach,33,35 the temporal evolution of the system is described by a set of equations for the probability distribution functions for (m) ⃗

the second excited state ρS2 (Q, t), for the mth ⃗ sublevel of the first excited state ρS1 (Q, t), 4


Page 5 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(⃗ n) for the ⃗nth sublevel of the charge separated state ρCS (Q, t), and the ⃗lth sublevel of the (⃗l)

ground state ρS0 (Q, t) ) ( ∑ ∂ρS2 (⃗ n) ˆ S ρS2 − = L k⃗nCS ρS2 − ρCS − kIC ρS2 ∂t n (⃗ n) ) ∑ ( ) ( ∂ρCS (⃗ n) (⃗ n) (⃗ n) (m) ⃗ CR CS ˆ k⃗nm ρCS − ρS1 − = LCS ρCS + k⃗n ρS2 − ρCS − ⃗ ∂t m ∑ (0) ∑ 1 ∑ 1 (⃗n) (⃗ n′α ) δ⃗n0 k⃗lρCS + ρ − ρ CS (nα +1) (nα ) CS τ τ vα vα α α l (m) ⃗ ( ) ∑ ∂ρS1 ⃗ (m) ⃗ (⃗ n) ˆ S ρ(m) k⃗nCR ρS1 − ρCS + δm = L ⃗m ⃗ ∗ kIC ρS2 + m ⃗ S1 − ∂t m ∑ ∑ 1 (m) 1 (m ⃗ ′α ) ⃗ ρ − ρ (mα +1) S1 (mα ) S1 α τvα α τvα ∑ 1 (⃗l) ∑ (0) ∑ 1 ′ ) ∂ρS0 (⃗lα ˆ S ρ(⃗l) + ρ − ρ = L k ρ + ⃗l CS S0 (lα +1) S0 (lα ) S0 ∂t τ τ vα vα α α l

(2.6) (2.7)

(2.8)

(⃗l)

(2.9)

where Q stands for the vector with components Q1 , Q2 , ..., QN , the vectors ⃗n′α , m ⃗ ′α , ⃗lα′ are defined as follows ⃗n′ = {n1 , n2 , ...nα + 1, ...}, m ⃗ ′ = {m1 , n2 , ...mα + 1, ...}, ⃗l′ = {l1 , n2 , ...lα + α

α

α

ˆ S and L ˆ CS are the Smoluchowski operators describing diffusion on the free energy 1, ...}. L surfaces US2 , US1 , US0 , and UCS , correspondingly [ ] N 2 ∑ ∂ ∂ 1 2 ˆS = 1 + Qi + ⟨Qi ⟩ 2 , L τ ∂Q ∂Qi i i i=1 [ ] N 2 ∑ 1 ∂ ∂ 2 ˆ CS = L 1 + (Qi − 2Eri ) + ⟨Qi ⟩ 2 , τ ∂Q ∂Qi i i i=1

(2.10)

(2.11)

with ⟨Q2i ⟩ = 2Eri kB T being the dispersion of the equilibrium distribution along the ith coordinate. Here kB is the Boltzmann constant and T is the temperature, kIC is the rate constant of the internal conversion | S2 ⟩ → | S1 ⟩. CR The coupling parameters k⃗nCS = k⃗nCS (Q), k⃗nCR m ⃗ = k⃗ nm ⃗ (Q) and k⃗l = k⃗l(Q) are the Zusman (⃗ n)

(⃗ n)

(m) ⃗

(0)

(⃗l)

rates of the charge transfer between US2 and UCS , UCS and US1 , UCS and US0 , respectively. In the case of the charge separation from S2 state and the CR into the S0 state, the Zusman

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 32

rates are: ) 2πV⃗n2 ( (⃗ n) 2 δ US2 − UCS , V⃗n2 = VCS F⃗nCS , ~ (CS) ∏ (Sα(CS) )nα e−Sα(CS) Ervα CS (CS) F⃗n = , Sα = nα ! ~Ωα α ) 2πV⃗l2 ( (⃗l) (0) 2 F⃗lCR0 , k⃗l = δ US0 − UCS , V⃗l2 = VCR0 ~ (CR0) ∏ (Sα(CR0) )lα e−Sα(CR0) Ervα CR0 (CR0) F⃗l = = , Sα lα ! ~Ωα α k⃗nCS =

For the charge transfer between the CS and S1 states, the Zusman rates have more common form k⃗nCR m ⃗

( ) 2πV⃗n2m (⃗ n) (m) ⃗ ⃗ = δ UCS − US1 , ~

F⃗nCR m ⃗ =

∏

CR 2 V⃗n2m nm ⃗ , ⃗ = VCR F⃗



{ } exp −Sα(CR) nα !mα ! 

α

∑

min(nα ,mα )

r=0

√ 2 (CR) nα +mα −2r (CR) (−1) ( Sα )  , Sα(CR) = Ervα , r!(nα − r)!(mα − r)! ~Ωα nα −r

where VCS , VCR , VCR0 are electronic couplings for | S2 ⟩ → | CS⟩, | CS⟩ → | S1 ⟩, | CS⟩ → | S0 ⟩; F⃗nm ⃗ , Sα , and Ervα are the Franck–Condon, the Huang–Rhys factors, and the reorganization energy of the αth high frequency vibrational mode, respectively. The indexes (CS) and (CR) stand for the parameters relating to the charge separation or the CR processes, correspondingly. A single–quantum mechanism of high frequency mode relaxation is adopted and the (n )

transitions nα → nα − 1 are supposed to proceed with the rate constant 1/τvαα where (n )

(1)

τvαα = τvα /nα .49 It should be emphasized that the model accounts for the local reversibility of electron transfer that can be properly described only if the intramolecular vibrational relaxation (IVR) is also taken into account.34 It is known that the IVR is multiphasic and can have several components, on the timescale from hundreds fs to few ps.50,51 Because an intramolecular vibrational redistribution is the fastest phase it determines the lifetime of the excited vibrational states. The intramolecular vibrational redistribution is known to proceed on the time scale of ∼ 100 fs.50,51 Unfortunately, there is no detail information on the lifetimes of the excited states of the intramolecular normal vibrational modes so, this estimation is used in what follows. After the intramolecular vibrational redistribution in S1 , the molecule is vibrationally hot and remains so for a few picoseconds, the time needed for vibrational cooling to take place. Because the energy accepted by the intramolecular 6


Page 7 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


vibrational modes in the process S2 → CS → S1 is smaller than 0.8 eV (a part is accepted by the surrounding medium during its relaxation in CS state) and the number of vibrational degrees of freedom is about 200, the increase of the temperature is not large and is neglected in this paper. The system being initially in the ground state with a thermal distribution of the nuclear coordinates is assumed to be transferred to the second excited state | S0 ⟩ → | S2 ⟩ by a short pump pulse. Since the excitation does not include a considerable charge redistribution, the equilibrium state of the polar medium immediately after excitation may be accepted as a good approximation. The excitation wavelength used in the experiments is near to the red edge of the absorption band of the transition | S0 ⟩ → | S2 ⟩ therefore the intramolecular high frequency modes are supposed to be in the ground state. This allows specifying the initial conditions in the form ρS2 (Q, t = 0) =

∏ i

[

] Q2i √ exp − , 2⟨Q2i ⟩ 2π⟨Q2i ⟩ 1

(⃗ n)

(2.12)

(m) ⃗

ρCS (Q, t = 0) = 0,

ρS1 (Q, t = 0) = 0,

(⃗l)

ρS0 (Q, t = 0) = 0. The set of eqs 2.6 – 2.8 with the initial conditions eqs 2.12 is solved numerically using the Brownian simulation method.36,52,53 The time-dependent populations of all states of interest are calculated with the equation ∑ ∫ (⃗n) Pi (t) = ρi (Q1 , Q2 , ..., QN , t)dQ1 dQ2 ...dQN (2.13) n

where the index runs i = S2 , S1 , S0 , and CS. The influence of the reorganization of the quantum vibrational modes on electron transfer kinetics is customarily described in terms of a single effective mode. Because the models with single mode and with real spectrum of the quantum vibrational modes predict essentially different kinetics of both the thermal42 and the hot charge transfer,30,36 the more realistic model exploiting a real high frequency spectral density is used in this paper. Unfortunately, the spectrum (frequencies and Huang–Rhys factors) is known only for a few molecular systems.29,36,38–41 So, a problem arises how to imitate such a spectrum. A possible solution of this problem was suggested in ref 37. The charge transfer rate was shown to depend weakly on the vibrational spectral density provided the total reorganization energy, 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 32

Erv , is constant. Hence, a universal spectral density with variable total reorganization energy may be exploited as a possible approximation for any donor–acceptor system. This conclusion is confirmed here once again by the example of charge transfer from second excited state in porphyrin–imide systems. Two spectral densities of donor–acceptor complexes consisting of hexamethylbenzene as electron donor and tetracyanoethylene as electron acceptor (HMB/TCNE) and phenylcyclopropane/tetracyanoethylene (PhCP/TCNE) are exploited.54 The intramolecular reorganization of these complexes involve 10 and 5 active vibrational modes. The values of the spectral parameters (frequencies and partial reorganization energies) are given in Table I.29,36 The total reorganization energy is connected with ∑ partial reorganization energies, Ervα , by equation Erv = c α Ervα , where the quantity c is determined by the magnitude of Erv . At the end of this section we outline the physical processes incorporating into the model. The excitation of the system to the state S2 is visualized as an appearance of a wave packet in the vicinity of the S2 term bottom (see Figure 2). Further two competing processes proceed. The first is the internal conversion | S2 ⟩ → | S1 ⟩ with the rate constant, kIC , that can be imaged as system transfer to the isoenergy excited vibrational states and the second is the (⃗ n)

charge separation at the points of the term crossings US2 = UCS populating the vibrational repetitions of the CS state (thin dashed lines in Figure 2). Next, the systems created in the (⃗ n)

CS state at term crossing points move to the UCS term bottom due to the medium relaxation. In the course of the medium relaxation, the systems pass the crossing points of the terms (m) ⃗

(⃗ n)

US1 and UCS that results in hot transitions to the first excited state S1 . In parallel with the hot CR the intramolecular vibrational relaxation occurs that may be imagined as vertical (⃗ n′ )

(⃗ n)

transitions between neighbor states, UCS → UCSα . The intramolecular vibrational relaxation (m) ⃗

(m ⃗′ )

in the S1 state, US1 → US1 α , also plays an important role because it can pronouncedly increase the effectiveness of the hot CR.34 Upon completion of fast S2 state decay, the relaxation of the medium and intramolecular vibrations, the populations of the S1 and CS states can be far from the thermal equilibrium. At next stage, the populations approach their equilibrium values nearly in the thermal regime. The charge recombination into the ground state | CS⟩ → | S0 ⟩ occurring in the Marcus inverted region proceeds rather slow and, hence, mainly in the thermal regime. This is also the reason why this recombination is supposed to occur from the ground state of the high frequency vibrational modes (see fourth term in the right-hand side of eq 2.7). 8


Page 9 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


III.

INFLUENCE OF THE NUMBER OF HIGH FREQUENCY VIBRATIONAL

MODES ON THE CHARGE SEPARATION AND RECOMBINATION KINETICS

To apprehend how the number of high frequency modes influence on the charge transfer kinetics a series of calculations for the models with different vibrational spectra involving 1, 5 and 10 modes has been performed. All simulations are executed at the room temperature, kB T = 0.025 eV. The typical parameters for Zn–porphyrin derivatives are accepted: ∆GS0S2 = −2.9 eV, ∆GS1S2 = −0.8 eV,19 the internal conversion (S2 → S1 ) rate kIC = 0.5 ps−1 ,19 the electronic couplings VCS = 0.0235 eV, VCR = 0.045 eV, VCR0 = 0.0029 eV.31 The effective frequency for the model with single quantum vibrational mode is set Ωv = 0.1 eV and for the models with 5 and 10 modes the spectra listed in Table I are used. The relaxation times for the single mode model and for multimode models are set the same for (1)

all quantum vibrational modes and are equal to τv = 50 fs. Figures 3 and 4 demonstrate the influence of the number of high frequency modes on charge separation kinetics for a few values of Erm and Erv in DMF solution (the solvent relaxation parameters are55 x1 = 0.508, x2 = 0.453, x3 = 0.039, τ1 = 0.217 ps, τ2 = 1.70 ps, τ3 = 29.1 ps). The free energy level of the the equilibrated system in the CS state depends on the molecular structure of the diad and the solvent polarity and may be placed either higher or lower than the S1 level. For example, the charge separation free energy for Zn(II) porphyrin covalently linked to naphthaleneimide in DMF is ∆GCS = −1.025 eV19 and this value is used in this section. The kinetics of populations for the models with five and ten high frequency vibrational modes are nearly identical but considerably differ from that for the model with single vibrational mode. This is one more evidence for the possibility of exploiting a universal spectral density of high frequency vibrations involving 5–10 modes in the description of charge transfer kinetics in both the hot and thermal regimes.54 The CS state population kinetics display two maxima for majority of the parameter values adopted in the calculations. The physical mechanism of this phenomenon is discussed in detail in ref 31. The largest impact of the number of high frequency modes is predicted for the CS state population kinetics. It is large on both the short and long time scales. A moderate impact is expected for the S1 state population and for S2 it is the smallest. For all parameters used the model with single high frequency vibrational mode predicts on short time scale larger 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 32

population of the CS state than those with 5 or 10 modes. This is one more manifestation of the general trend: the effectiveness of hot charge recombination rises with the number of active high frequency modes reaching a saturation for the models with approximately 5 modes provided that the total reorganization energy Erv is kept constant.54 Analysis of the results for the model with 5–10 vibrational modes reveals the following trends: (i) both maxima of the CS state population decreases with increasing the magnitude of both Erm and Erv ; (ii) the fraction of particles in the CS state escaped the hot recombination (the population of the CS state at time t ≈ 1 ps) decreases from 0.3 to 0.1 with increase of Erm from 0.5 to 0.9 eV and this quantity weakly depends on Erv ; (iii) the maximum of S1 state population increases with increasing Erm and weakly depends on Erv ; (iv) only 1–30% of the relaxed CS state population are produced by direct transition from the S2 state and the rest are created by the charge separation from the S1 state. This regularities are relevant only for the internal conversion rate kIC = 0.5 ps−1 and the region of the parameters shown in Figures 3 and 4, 0.5 ≤ Erm ≤ 0.9 eV and 0.2 ≤ Erv ≤ 0.6 eV. The variation of kinetics of the S1 and the CS state populations presented in Figures 3 and 4 can be appreciated if one notices that the charge separation from the S1 state proceeds in the Marcus normal region for all parameters used, hence, its rate constant decreases with increasing either Erm or Erv . At the same time, the charge recombination into the S0 state proceeds in the Marcus inverted region and inverse dependence of the rate on the reorganization energies is expected. Possibly, the variations of the CS state kinetics displayed in Figure 4 requires a more detailed explanation. For the smallest Erv (top row) the time constant of the charge recombination into the ground state, τCR0 is considerably lager than the time constant of the charge separation from the first excited state, τCS1 , hence, the CS state population decays with the time constant τCR0 while S1 decays with τCS1 . For larger Erv (middle row) the ratio of the time scales inverts, τCR0 < τCS1 , so that the CS and the S1 state populations decay with the same rate equal to 1/τCS1 . For the largest Erv (bottom row) the strong inequality τCR0 ≪ τCS1 is fulfilled but for the single mode model the CS state population decays again with the time constant τCR0 . To understand such a behavior let us assume that the kinetics of the charge separation from the S1 state and the charge recombination to the ground state are exponential and irreversible. Supposing that at the moment t = 3 ps the charge separation from the S2 10


Page 11 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


state is completed and the population of the CS state is PCS (t = 3 ps) and of S1 is equal to PS1 (t = 3 ps) = 1 − PCS (t = 3 ps), one can obtain for the population of the CS state at t > 3 ps an estimation PCS (t′ ) = [1 − PCS (t = 3 ps)]

[ ′ ] τCR0 ′ ′ e−t /τCS1 − e−t /τCR0 + PCS (t = 3 ps)e−t /τCR0 τCS1 − τCR0 (3.1)

Here t′ = t − 3 ps and PCS (t = 3 ps) is the fraction of the particles in the CS state escaped the hot recombination. For Erv = 0.2 and 0.4 eV the second term in right-hand side of eq 3.1 plays a minor role and the standard kinetics for an intermediate is observed. For the largest Erv = 0.6 eV the single mode model leads to τCR0 = 26 ps and τCS1 = 896 ps so that the second term dominates, (1 − PCS (t = 3 ps))

τCR0 ≪ PCS (t = 3 ps) τCS1 − τCR0

(3.2)

and the CS state population decays with the time constant τCR0 . The first term in eq 3.1 is visualized as a low plateau (well seen for black line in Figure 4) that slowly goes down with the time constant τCS1 . In this case the kinetic curve has a single maximum. For the model with 10 high frequency vibrational modes we get τCR0 = 27 ps and τCS1 = 210 ps and the inequality 3.2 is not met. As a result, the CS state population decays with the time constant τCS1 .

IV.

INFLUENCE OF THE SOLVENT POLARITY ON CHARGE SEPARATION

AND RECOMBINATION KINETICS

Figures 5 and 6 also show the influence of the number of high frequency modes on charge separation kinetics for a few values of Erm and Erv but in another solvent, THF, with the relaxation parameters:55 x1 = 0.443, x2 = 0.557, τ1 = 0.226 ps, τ2 = 1.52 ps, and charge separation free energy is ∆GCS = −0.78 eV.19 The dynamical properties of DMF and THF solvents are close to each other but the THF is much less polar (dielectric constants are ε0 = 36.7 and 7.58, correspondingly). As a result, the free energy level of the CS state in THF is higher by 0.245 eV than that in DMF.19 The rest of the parameters are the same as in the previous section. The variation of the solvent polarity does not change the qualitative behavior of the kinetic curves. Therefore, the trends stated in the previous section are essentially valid in 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 32

this solvent too. However the quantitative alterations are rather large. The main differences concern the magnitude of the CS state population and the rate of S1 state decay. In THF this population is considerably smaller than that in DMF on the whole time interval. The fraction of the particles in the CS state escaped the hot recombination is of the order of 1% for large reorganization energies. At the next stage the charge separation from the S1 state does not increase considerably the CS state population because of its small rate constant. This prediction is in full accordance with the experimental data that show the CS state population in THF at long time scale (tens of ps) to be unobservable due to its smallness.19 There are two main reasons leading to such large distinctions between the population kinetics in these two solvents. Firstly, a higher position of the CS state term in THF strongly increases the efficiency of the hot charge recombination into the S1 state56 that results in decreasing the fraction of particles in the CS state that have escaped the hot recombination. Secondly, the activation energy for charge separation from the S1 state in THF is larger by 0.11 eV than that in DMF that decreases its rate constant by a factor of ≈ 100. As a result, the charge separation from the S1 state proceeds slower than the CR into the ground state and the CS state population does not rises noticeably at the time scale of S1 state decay. It should be also mentioned that in THF solution the rate of thermal reverse reaction (CS → S1 ) is much larger than that in DMF. This also reduces the CS state population but plays a smaller role than decreasing the charge separation rate. The rate constant of the charge separation from the S1 state in the THF solution appeared to be so small that the fluorescence and internal conversion from this state may effectively compete with the charge separation. These processes are omitted in the present model but they should be accounted for in the quantitative description of the charge separation and CR kinetics in THF because they additionally suppress the CS state population.

V.

FITTING OF KINETICS OF CHARGE SEPARATED STATE POPULATION

The fitting is aimed to reproduce the following experimental data obtained for Zn(II) porphyrin covalently linked to naphthaleneimide in DMF solution:19 (i) the population of the CS state at three key points in time (PCS (tmax ) = 0.16 at the time of the first maximum, PCS (t = 3ps) = 0.07, corresponding to the minimum between two maxima, and PCS (t = 12


Page 13 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


100ps) = 0.19 in the vicinity of the second maximum), (ii) the time scale of the S2 state decay, τCS2 = 0.4 ps, the time scale of the charge separation from the first excited state τCS1 = 170 ps, and the charge recombination to the ground state τCR0 = 38 ps. We use the invariable parameters borrowed from independent measurements and estimations: ∆GS0S2 = −2.9 eV, ∆GS1S2 = −0.8 eV, ∆GCS = −1.025 eV, the dynamic parameters of the DMF solvent (see −1 section III), the time scale of the internal conversion τIC = kIC = 2.0 ps, the time constant of (1)

vibrational relaxation τv = 100 fs. The variable parameters are the reorganization energies Erm , Erv , and the electronic couplings VCS , VCR1 , and VCR0 . The best fit pictured in Figure 7 is obtained with the parameters: Erm =0.91 eV, Erv = 0.30 eV, VCS =0.023 eV, VCR1 = 0.056 eV, and VCR0 = 0.00415 eV. These parameters are quit reasonable except for the magnitudes of VCR0 and Erm . The quantity VCR0 turned out to be on an order of magnitude smaller than VCS and VCR1 . Because the electronic coupling is determined by the overlapping of the corresponding orbitals on the donor and the acceptor, the smallness of VCR0 can indicate the orbital of the ground electronic state to be more compact than those of the excited states. The magnitude of Erm seems to be a little bit too large for the intramolecular electron transfer. However, all our attempts to fit the experimental data with smaller Erm failed. There is one more evidence in favor of large value of Erm for this reaction. If a considerably smaller value of Erm were obtained in DMF, the model would predict much larger population of the CS state in THF contrary to the experimental data because in THF Erm is expected to be even smaller than that in DMF. This fitting allows excellent reproducing the magnitudes of the key experimental parameters: PCS (tmax ) = 0.16, PCS (t ≈ 1ps) = 0.07, and PCS (t = 100ps) = 0.19. The S2 state decay is nearly exponential and its time scale is equal to τCS2 = 0.22 ps. This value differs essentially from experimental 0.4 ps. However, it cannot be increased because its magnitude for given medium relaxation time scale is rigidly determined by the height of the first maximum and the height of the plateau in the area approximately from 1 ps to 3 ps (see Figure 7). In other words the values PCS (tmax ) = 0.16 and PCS (t ≈ 1ps) = 0.07 can be obtained with different sets of the model parameters but τCS2 is invariably equal to 0.22 ps. The discrepancy may be caused by either the roughness of the model or the experimental errors. The fact is that the decay of measured optical signal at the given frequency is treated as the decay of the state population. However, the relaxation of the medium and the intramolecular reorganization can considerably affect the decay of the signal on such a 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

short time scale. The time scales of the charge separation from the first excited state, τCS1 , and the CR into the ground state, τCR0 , in the experiment were determined by using the excitation to the S1 state.19 We did the same theoretically. The kinetics of the charge separation and recombination are calculated in the framework of the same model but with the initial conditions corresponding to the excitation of Zn–porphyrin–imide to the S1 state. The time constants τCS1 and τCR0 can be uniquely determined only if the kinetics are exponential. However, the simulated kinetics deviate noticeably from exponential. To avoid the uncertainties of the calculation of τCS1 and τCR0 , two approaches are exploited. Supposing that the charge separation and the CR are irreversible, the CS state population after excitation to the S1 state is described by well-known eq 5.1 for an intermediate population being produced with time constant τCS1 and decaying with time constant τCR0 PCS (t) =

τCR0 [e−t/τCS1 − e−t/τCR0 ] τCS1 − τCR0

(5.1)

The fitting of this equation to PCS (t) simulated brings to the following values: τCS1 = 135 ps and τCR0 = 48 ps (experimental data τCS1 = 170 ps and τCR0 = 38 ps). The effective time scales can be also determined with alternative eqs 5.2 and 5.3 ∫ ∞ τCS1 = PS1 (t)dt ∫

(5.2)

0 ∞

τCR0 =

PCS (t)dt

(5.3)

0

These equations unexpectedly result in the time scales nearly identical to the previous estimations: τCS1 = 134 ps and τCR0 = 48 ps. Both estimations of τCS1 and τCR0 are rather close to but different from the experimental values. In order to gain some insight into the reason of distinctions between the theoretical and experimental estimations of these two time constant, we derive the population PCS (t = 100 ps) using eq 3.1. With PCS (t = 3 ps) = 0.07, τCS1 = 150 ps, and τCR0 = 50 ps we get PCS (t = 100 ps) = 0.185 while with experimental times τCS1 ps and τCR0 ps we obtain PCS (t = 100 ps) = 0.14, which considerably smaller than the measured value at this moment. These simple computations show that the theoretical estimation is in better agreement with the magnitudes of the population in two key points. Moreover, this means that a better agreement between the theoretical and experimental estimations of τCS1 and τCR0 cannot be achieved. 14


Page 15 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


VI.

CONCLUDING REMARKS

For the description of the kinetics of the charge separation and charge recombination in Zn–porphyrin derivatives excited to the S2 state the multichannel stochastic model involving four electronic states (the first and the second singlet excited, the charge separated and the ground states) has been elaborated. The influence of the parameters (the number of the high frequency vibrational modes involving in the charge transfer, the medium reorganization energy, the total reorganization energy of high frequency modes, and the solvent polarity) on the charge separation and recombination kinetics in Zn–porphyrin–imide dyads has been investigated. The main conclusions can be summarized as follows. • The CS state population kinetics display two maxima for a wide region of the parameters. So, the two-humped kinetic curve in Zn–porphyrin derivatives seems to be rather universal provided that the relaxed CS state lies below S1 and that hot recombination occurs to S1 following CS from the S2 state. • The fraction of molecules in the CS state that has escaped the hot recombination varies in the interval from 0.01 to 0.3 in the region of reasonable parameters. In other words, only 1–30% of the CS state population are produced by direct transitions from S2 state and the rest are created by the S1 state. • The models with single and many active high frequency vibrational modes predict quantitatively different kinetics of the CS state population. This indicates that the model with real spectrum of high frequency modes should be exploited to get quantitative description of the experimental data. The model elaborated has been applied for fitting to experimental kinetics observed for Zn(II)–porphyrin covalently linked to naphthaleneimide in the DMF solution. The twohumped kinetic curve has been quantitatively reproduced. Three time scales of the S2 state decay, τCS2 , charge separation from the first excited state, τCS1 , and charge recombination to the ground state, τCR0 , calculated are also in a good accord with the experimental data. These results allows us to conclude that the multichannel stochastic model can quantitatively describe the kinetics of the electron transfer from the second excited state including effective hot reverse electron transfer to the first excited state. 15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (Grant No. 11-03-00736).

16


Page 17 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References and Notes

1

Kuznetsov, A.M. Charge Transfer in Physics, Chemistry and Biology; Gordon & Breach: Amsterdam, 1995; p 622.

2

Domcke, W.; Stock, G. Theory of Ultrafast Nonadiabatic Excited State Processes and Their Spectroscopic Detection in Real Time. Adv. Chem. Phys. 1997, 100, 1–168.

3

Electron Transfer: From isolated Molecules to Biomolecules. Advances in Chemical Physics; Jortner, J., Bixon, M., Eds.; Wiley: New York, 1999; Vol. 106, p 734; Vol. 107, p 735.

4

Barzykin, A.V.; Frantsuzov, P.A.; Seki, K.; Tachiya, M. Solvent Effects in Nonadiabatic Electron–Transfer Reactions: Theoretical Aspects. Adv. Chem. Phys. 2002, 123, 511–616.

5

Burshtein, A.I. Non-Markovian Theories of Transfer Reactions in Luminescence and Chemiluminescence and Photo- and Electrochemistry. Adv. Chem. Phys. 2004, 129, 105–418.

6

Vauthey, E. Investigations of Bimolecular Photoinduced Electron Transfer Reactions in Polar Solvents Using Ultrafast Spectroscopy. J. Photochem. Photobiol. A 2006, 179, 1–12.

7

Ivanov, A.I.; Mikhailova, V.A. Kinetics of Fast Photochemical Charge Separation and Charge Recombination Reactions. Russ. Chem. Rev. 2010, 79, 1047–1070.

8

LeGourriérec, D.; Andersson, M.; Davidsson, J.; Mukhtar, E.; Sun, S.; Hammarström, L. Photoinduced Electron Transfer from a Higher Excited State of a Porphyrin in a Zinc Porphyrin– Ruthenium(II) tris-Bipyridine Dyad. J. Phys. Chem. A 1999, 103, 557–559.

9

Andersson, M.; Davidsson, J.; Hammarström, L.; Korppi-Tommola, J.; Peltola, T. Photoinduced Electron Transfer Reactions in a Porphyrin–Viologen Complex: Observation of S2 to S1 Relaxation and Electron Transfer from the S2 State. J. Phys. Chem. B 1999, 103, 3258–3262.

10

Mataga, N.; Shibata, Y.; Chosrowjan, H.; Yoshida, N.; Osuka, A. Internal Conversion and Vibronic Relaxation from Higher Excited Electronic State of Porphyrins: Femtosecond Fluorescence Dynamics Studies. J. Phys. Chem. B 2000, 104, 4001–4004.

11

Mataga, N.; Chosrowjan, H.; Shibata, Y.; Yoshida, N.; Osuka, A.; Kikuzawa, T.; Okada, T. First Unequivocal Observation of the Whole Bell-Shaped Energy Gap Law in Intramolecular Charge Separation from S2 Excited State of Directly Linked Porphyrin–Imide Dyads and Its Solvent-Polarity Dependencies. J. Am. Chem. Soc. 2001, 123, 12422–12423.

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

12

Page 18 of 32

Mataga, N.; Chosrowjan, H.; Taniguchi, S.; Shibata, Y.; Yoshida, N.; Osuka, A.; Kikuzawa, T.; Okada, T. Ultrafast Charge Separation from the S2 Excited State of Directly Linked PorphyrinImide Dyads: First Unequivocal Observation of the Whole Bell-Shaped Energy-Gap Law and Its Solvent Dependencies. J. Phys. Chem. A 2002, 106, 12191–12201.

13

Mataga, N.; Taniguchi, S.; Chosrowjan, H.; Osuka, A.; Yoshida, N. Ultrafast Charge Transfer and Radiationless Rrelaxation from Higher Excited State (S2 ) of Directly Linked Zn-Porphyrin (ZP)-Acceptor Dyads: Investigations into Fundamental Problems of Exciplex Chemistry. Chem. Phys. 2003, 295, 215–228.

14

Morandeira, A.; Engeli, L.; Vauthey, E. Ultrafast Charge Recombination of Photogenerated Ion Pairs to an Electronic Excited State. J. Phys. Chem. A 2002, 106, 4833–4837.

15

Kubo, M.; Mori, Y.; Otani, M.; Murakami, M.; Ishibashi, Y.; Yasuda, M.; Hosomizu, K.; Miyasaka, H.; Imahori, H.; Nakashima, S. Ultrafast Photoinduced Electron Transfer in Directly Linked Porphyrin–Ferrocene Dyads. J. Phys. Chem. A 2007, 111, 5136–5143.

16

Fujitsuka, M.; Cho, D. W.; Tojo, S.; Inoue, A.; Shiragami, T.; Yasuda, M.; Majima, T. Electron Transfer from Axial Ligand to S1 - and S2 -Excited Phosphorus Tetraphenylporphyrin. J. Phys. Chem. A 2007, 111, 10574–10579.

17

Petersson, J.; Eklund,M.; Davidsson, J.; Hammarström, L. Variation of Excitation Energy Influences the Product Distribution of a Two-Step Electron Transfer: S2 vs S1 Electron Transfer in a Zn(II)porphyrin-Viologen Complex. J. Am. Chem. Soc. 2009, 131, 7940–7941

18

Petersson, J.; Eklund,M.; Davidsson, J.; Hammarström, L. Ultrafast Electron Transfer Dynamics of a Zn(II)porphyrin-Viologen Complex Revisited: S2 vs S1 Reactions and Survival of Excess Excitation Energy. J. Phys. Chem. B 2010, 114, 14329–14338.

19

Wallin, S.; Monnereau, C.; Blart, E.; Gankou, J.-R.; Odobel, F.; Hammarström, L. StateSelective Electron Transfer in an Unsymmetric Acceptor–Zn(II)porphyrin–Acceptor Triad: Toward a Controlled Directionality of Electron Transfer from the Porphyrin S2 and S1 States as a Basis for a Molecular Switch. J. Phys. Chem. A 2010, 114, 1709–1721.

20

Robotham, B.; Lastman, K.; Langford, S.J.; Ghiggino, K.P. Ultrafast Electron Transfer in a Porphyrin-Amino Naphthalene Diimide Dyad. J. Photochem. Photobiol. A 2013, 251, 167–174.

21

Asahi, T.; Mataga, N. Charge Recombination Process of Ion Pair State Produced by Excitation of Charge-Transfer Complex in Acetonitrile Solution. Essentially Different Character of Its Energy Gap Dependence from that of Geminate Ion Pair Formed by Encounter between Fluorescer

18


Page 19 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and Quencher. J. Phys. Chem. 1989, 93, 6575–6578. 22

Asahi, T.; Mataga, N. Femtosecond-Picosecond Laser Photolysis Studies on the Dynamics of Excited Charge-Transfer Complexes: Aromatic Hydrocarbon-Acid Anhydride, Tetracyanoethylene, and -Tetracyanoquinodimethane Systems in Acetonitrile Solutions. J. Phys. Chem. 1991, 95, 1956–1963.

23

Segawa, H.; Takehara, C.; Honda, K.; Shimidzu, T.; Asahi, T.; Mataga, N. Photoinduced Electron-Transfer Reactions of Porphyrin Heteroaggregates: Energy Gap Dependence of an Intradimer Charge Recombination Process. J. Phys. Chem. 1992, 96, 503–506.

24

Benniston, A.C.; Harriman, A.; Philp, D.; Stoddart, J.F. Charge Recombination in CyclophaneDerived, Intimate Radical Ion Pairs. J. Am. Chem. Soc. 1993, 115, 5298–5299.

25

Gould, I.R.; Noukakis, D.; Gomez-Jahn, L.; Goodman, J.L.; Farid, S. Explanation of the Driving-Force Dependence of Return Electron Transfer in Contact Radical-Ion Pairs. J. Am. Chem. Soc. 1993, 115, 4405–4406.

26

Wynne, K.; Reid, G.D.; Hochstrasser, R.M. Vibrational Coherence in Electron Transfer: The Tetracyanoethylene–Pyrene Complex. J. Chem. Phys. 1996, 105, 2287–2297.

27

Hubig, S.M.; Bockman, T.M.; Kochi, J.K. Optimized Electron Transfer in Charge-Transfer Ion Pairs. Pronounced Inner-Sphere Behavior of Olefin Donors. J. Am. Chem. Soc. 1996, 118, 3842–3851.

28

Nicolet, O.; Vauthey, E. Ultrafast Nonequilibrium Charge Recombination Dynamics of Excited Donor-Acceptor Complexes. J. Phys. Chem. A 2002, 106, 5553–5562.

29

Wynne, K.; Galli, C.; Hochstrasser, R. M. Ultrafast Charge Transfer in an Electron DonorAcceptor Complex. J. Chem. Phys. 1994, 100, 4797–4510.

30

Yudanov, V.V.; Mikhailova, V.A.; Ivanov, A.I. Nonequilibrium Phenomena in Charge Recombination of Excited Donor-Acceptor Complexes and Free Energy Gap Law. J. Phys. Chem. A 2010, 114, 12998–13004.

31

Rogozina, M. V.; Ionkin, V. N.; Ivanov, A. I. What Factors Control Product Yield in Charge Separation Reaction from Second Excited State in Zinc-Porphyrin Derivatives? J. Phys. Chem. A 2012, 116, 1159–1167.

32

Ionkin, V.N.; Ivanov, A.I.; Vauthey, E. Charge Recombination in Excited Donor-Acceptor Complexes with Two Absorption Bands. Russ. J. Phys. Chem. A 2009, 83, 683–688.

33

Zusman, L.D. Outer-Sphere Electron Transfer in Polar Solvents. Chem. Phys. 1980, 49, 295–

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

304. 34

Mikhailova, V.A.; Ivanov, A.I. Effect of Relaxation of Intramolecular High-Frequency Vibrational Mode on Nonthermal Electron Transfer Probability. Stochastic Point-Transition Approach. J. Phys. Chem. C 2007, 111, 4445–4451.

35

Feskov, S.V.; Ionkin, V.N.; Ivanov, A.I. Effect of High-Frequency Modes and Hot Transitions on Free Energy Gap Dependence of Charge Recombination. J. Phys. Chem. A 2006, 110, 11919–11925.

36

Feskov, S.V.; Ionkin, V.N.; Ivanov, A.I.; Hagemann, H.; Vauthey, E. Solvent and Spectral Effects in the Ultrafast Charge Recombination Dynamics of Excited Donor-Acceptor Complexes. J. Phys. Chem. A 2008, 112, 594–601.

37

Ionkin, V.N.; Ivanov, A.I. Numerical Simulations of Ultrafast Charge Separation Dynamics from Second Excited State of Directly Linked Zn-Porphyrin-Imide Dyads and Ensuing Hot Charge Recombination into First Excited State. J. Phys. Chem. A 2009, 113, 103–107.

38

Heller, E. J.; Sundberg, R. L.; Tannor, D. Simple Aspects of Raman Scattering. J. Phys. Chem. 1982, 86, 1822–1833.

39

Markel, F.; Ferris, N. S.; Gould, I. R.; Myers, A. B. Mode-Specific Vibrational Reorganization Energies Accompanying Photoinduced Electron Transfer in the Hexamethylbenzene/Tetracyanoethylene Charge-Transfer Complex. J. Am. Chem. Soc. 1992, 114, 6208–6219.

40

Kulinowski, K.; Gould, I. R.; Myers, A. B. Absorption, Fluorescence, and Resonance Raman Spectroscopy of the Hexamethylbenzene/Tetracyanoethylene Charge-Transfer Complex: Toward a Self-Consistent Model. J. Phys. Chem. 1995, 99, 9017–9026.

41

Myers Kelly, A. Resonance Raman Intensity Analysis of Vibrational and Solvent Reorganization in Photoinduced Charge Transfer. J. Phys. Chem. A 1999, 103, 6891–6903.

42

Yudanov, V.V.; Mikhailova, V.A.; Ivanov, A.I. Mikhailova, V.A.; Ivanov, A.I. Reorganization of Intramolecular High Frequency Vibrational Modes and Dynamic Solvent Effect in Electron Transfer Reactions. J. Phys. Chem. A 2012, 116, 4010–4019.

43

Rosenthal, S.J.; Xie, X.; Du, M.; Fleming, G.R. Femtosecond Solvation Dynamics in Acetonitrile: Observation of the Inertial Contribution to the Solvent Response. J. Chem. Phys. 1991, 95, 4715–4718.

44

Maroncelli, M.; Kumar, V.P.; Papazyan, A. A Simple Interpretation of Polar Solvation Dynamics. J. Phys. Chem. 1993, 97, 13–17.

20


Page 21 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


45

Jimenez, R.; Fleming, G.R.; Kumar, P.V.; Maroncelli, M. Femtosecond Solvation Dynamics of Water. Nature 1994, 369, 471–473.

46

Gumy, J.C.; Nicolet, O.; Vauthey, E. Investigation of the Solvation Dynamics of an Organic Dye in Polar Solvents Using the Femtosecond Transient Grating Technique. J. Phys. Chem. A 1999, 103, 10737–10743.

47

Kichigina, A.O.; Ivanov A.I. The Influence of the Inertial Medium Relaxation Component on the Kinetics of ”Hot” Transitions. Rus. J. Phys. Chem. B 2012, 6, 175–180.

48

Bagchi, B.; Gayathri, N. Interplay Between Ultrafast Polar Solvation and Vibrational Dynamics in Electron Transfer Reactions: Role of High–Frequency Vibrational Modes. Adv. Chem. Phys. 1999, 107, 1–80.

49

Ivanov, A.I.; Ionkin, V.N.; Feskov, S.V. Acceleration of the Recombination of Photoexcited Donor-Acceptor Complexes with a High-Frequency Vibrational Mode. Russ. J. Phys. Chem. A 2008, 82, 303–309.

50

Kovalenko, S. A.; Schanz, R.; Hennig, H.; Ernsting, N. P. Cooling Dynamics of an Optically Excited Molecular Probe in Solution from Femtosecond Broadband Transient Absorption Spectroscopy. J. Chem. Phys. 2001, 115, 3256–3273.

51

Elsaesser, T.; Kaiser, W. Vibrational and Vibronic Relaxation of Large Polyatomic Molecules in Liquids. Annu. Rev. Phys. Chem. 1991, 42, 83–107.

52

Fedunov, R.G.; Feskov, S.V.; Ivanov, A.I.; Nicolet, O.; Pagès, S.; Vauthey, E. Effect of the Excitation Pulse Carrier Frequency on the Ultrafast Charge Recombination Dynamics of DonorAcceptor Complexes: Stochastic Simulations and Experiments. J. Chem. Phys. 2004, 121, 3643–3656.

53

Gladkikh, V.; Burshtein, A.I.; Feskov, S.V.; Ivanov, A.I.; Vauthey, E. Hot Recombination of Photogenerated Ion Pairs. J. Chem. Phys. 2005, 123, 244510-1–11.

54

Ionkin, V. N.; Ivanov, A. I. Independence of the Rate of the Hot Charge Recombination in Excited Donor-Acceptor Complexes from the Spectral Density of High-Frequency Vibrations. Chem. Phys. 2009, 360, 137–140.

55

Horng, M.L.; Gardecki, J.A.; Papazyan, A.; Maroncelli, M. Subpicosecond Measurements of Polar Solvation Dynamics: Coumarin 153 Revisited. J. Phys. Chem. 1995, 99, 17311–17337.

56

Ivanov, A.I.; Potovoi, V.V. Theory of Non-Thermal Electron Transfer. Chem. Phys. 1999, 247, 245–259.

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

Figure captions Figure 1. The scheme of the electronic states involved in photoinduced electron transfer from the second excited state in Zn-porphyrin-imide compounds. The horizontal arrows indicate the electronic transitions and the vertical wavy lines visualize the medium and intramolecular vibrational relaxation Figure 2. Cuts in the free energy surface of the ground and the first and second excited states, and the CS state. The dashed lines are the vibrational sublevels of the CS and the S1 electronic states. The transitions between vibrational sublevels of the high frequency mode involved in the model are not shown. Figure 3. Population kinetics of the S2 (first column), CS (second and third columns), and the S1 (last column) states in a solvent with the dynamic parameters of DMF. The results of calculation are presented for models with a single vibrational mode (black lines), five vibrational modes (red lines), and ten vibrational modes (blue lines). The values of Erm are the same in the rows and are indicated in the first column, Erv = 0.4 eV. Figure 4. Population kinetics of the S2 (first column), CS (second and third columns), and the S1 (last column) states in a solvent with the dynamic parameters of DMF. The results of calculation are presented for models with a single vibrational mode (black lines), five vibrational modes (red lines), and ten vibrational modes (blue lines). The values of Erv are the same in the rows and are indicated in the first column, Erm = 0.9 eV. Figure 5. Population kinetics of the S2 (first column), CS (second and third columns), and the S1 (last column) states in a solvent with the dynamic parameters of THF. The results of calculation are presented for models with a single vibrational mode (black lines), five vibrational modes (red lines), and ten vibrational modes (blue lines). The values of Erm are the same in the rows and are indicated in the first column, Erv = 0.4 eV. Figure 6. Population kinetics of the S2 (first column), CS (second and third columns), and the S1 (last column) states in a solvent with the dynamic parameters of THF. The results of calculation are presented for models with a single vibrational mode (black lines), five vibrational modes (red lines), and ten vibrational modes (blue lines). The values of Erv are the same in the rows and are indicated in the first column, Erm = 0.9 eV. Figure 7. Kinetics of the CS state population of Zn(II)-porphyrin covalently linked to naphthaleneimide in DMF solution. The left half of the Figure shows data for the first 3 picoseconds, and the right half shows data for 3–200 ps. The values of the parameters are 22


Page 23 of 32

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


listed in the text.

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 32

TABLE I: Frequencies and partial reorganization energies of high frequency vibrational modes for charge transfer in HMB/TCNE and PhCP/TCNE complexes

HMB/TCNEa

PhCP/TCNEb

No ~Ωα , eV Ervα , eV ~Ωα , eV Ervα , eV

a

1

0.0558

0.0084

0.1272

0.0317

2

0.0672

0.0011

0.1469

0.0356

3

0.0744

0.0023

0.1823

0.0416

4

0.1188

0.0108

0.1935

0.1994

5

0.1602

0.0449

0.1993

0.0918

6

0.1722

0.0189

7

0.1782

0.0253

8

0.1922

0.1702

9

0.1947

0.0175

10 0.2755

0.1006

Reference 40, b Reference 41

24


Page 25 of 32

S

hot CS state

CS

2

IC

CS

S

1

CS state

IC

C R

fluorescence

Soret-band excitation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


S

0

FIG. 1: Rogozina, Ionkin, Ivanov

25



S2

Free energy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

CS

S1

S0

Solvation coordinate


26


Page 27 of 32

DMF S

0.6

E

S

CS

2

1.0

1

1.0

0.70

0.5

0.35

=0.5 eV

rm

0.4 0.5 0.2

0.0

0.0

0.0

0.4

0.8

1.0

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E

0.0 0

1

2

3

0.00 0

500

1000

0

0.4

0.8

0.8

0.2

0.4

0.4

20

40

0

100

200

0

500

1000

=0.7 eV

rm

0.5

0.0

0.0 0.0

0.4

1.0

E

0.0 0

0.8

1

2

3

0.0 0

500

1000

0.2

0.24

1.0

0.1

0.12

0.5

=0.9 eV

rm

0.5

0.0

0.00

0.0 0

1

2

0

1

2

3

0.0 0

time, ps


27


500

1000


DMF S

CS

2

1.0

S

1

0.3

E =0.2 eV

0.70

1.0

0.35

0.5

rv

0.2 0.5 0.1

0.0

0.0

0.0

0.5

1.0

1.0

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 32

0.00 0

1

2

3

0.0 0

500

1000

0.2

0.24

1.0

0.1

0.12

0.5

0

250

500

0

500

1000

0

500

1000

E =0.4 eV rv

0.5

0.0

0.0 0.0

0.5

1.0

0.00 0

1.5

1

2

3

0.0 0

500

1000

1.0

0.90

E =0.6 eV rv

0.2

0.2

0.1

0.1

0.5

0.45

0.0

0.0

0.0 0

1

2

3

0

1

2

3

0.00 0

time, ps


28


400

800

Page 29 of 32

THF S

CS

2 0.3

1.0

E

S

1

1.0

0.3

=0.5 eV

rm

0.2

0.2

0.1

0.1

0.5

0.5

0.0

0.0

0.0

0.5

1.0

1.0

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


E

0.0 0

1

2

3

0.0 0

500

1000

0.2

0.2

1.0

0.1

0.1

0.5

0

500

1000

0

500

1000

0

500

1000

=0.7 eV

rm

0.5

0.0

0.0 0

1

1.0

E

0.0 0

2

1

2

3

0.0 0

500

1000

0.08

0.08

1.0

0.04

0.04

0.5

=0.9 eV

rm

0.5

0.0

0.00

0.00 0

2

4

0

1

2

3

0.0 0

time, ps


29


500

1000


THF CS

S

2

S

1

1.0

0.16

0.16

1.0

0.08

0.08

0.5

E =0.2 eV rv

0.5

0.0

0.00 0

1

2

3

1.0

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 32

0.00 0

1

2

3

0.0 0

500

1000

0.08

0.08

1.0

0.04

0.04

0.5

0

500

1000

0

500

1000

0

500

1000

E =0.4 eV rv

0.5

0.00

0.0 0

2

1.0

0.00 0

4

1

2

3

0.0 0

500

1000

0.06

0.06

1.0

0.03

0.03

0.5

E =0.6 eV rv

0.5

0.0

0.00

0.00 0

2

4

6

0

1

2

3

0.0 0

time, ps


30


200

400

Page 31 of 32

0,2

0.2 0.19

population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.16

0,1

0.1 0.08

0.07

0,0 0

1

2

3

100

time, ps


31


200


hot ET

thermal ET

CS

thermal ET

FIG. 8: TOC

32


relaxation

S1

hot CS relaxation

S2

relaxation

thermal ET

soret-band excitation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 32

S0

Dynamics of Charge Separation from Second Excited State and

Recommend Documents