Mechanism and Dynamics of Charge Transfer in Donor-Bridge-Acceptor Systems

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Mechanism and Dynamics of Charge Transfer

in Donor-Bridge-Acceptor Systems

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Mechanism and Dynamics of Charge Transfer

in Donor-Bridge-Acceptor Systems

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 2 mei 2016 om 15:00 uur

door

Natalie GORCZAK-VOS

Diplom-Ingenieur in Materials Science, Technische Universität Darmstadt, Duitsland,

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. L.D.A. Siebbeles copromotor: Dr. F.C. Grozema

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. L.D.A. Siebbeles Technische Universiteit Delft Dr. F.C. Grozema Technische Universiteit Delft

Onafhankelijke leden:

Prof. dr. H.S.J. van der Zant Technische Universiteit Delft Prof. dr. J. van Esch Technische Universiteit Delft

Prof. dr. D.M. Guldi Friedrich-Alexander-Universität Erlangen-Nürnberg Prof. dr. A.M. Brouwer Universiteit van Amsterdam

Overige leden:

Prof. dr. F.D. Lewis Northwestern University

Prof. dr. F.D. Lewis heeft in belangrijke mate aan de totstandkoming van het proef-schrift bijgedragen.

This work was supported by the Netherlands Organization for Scientific Research (NWO).

Printed by: GVO drukkers & vormgevers B.V. | Ponsen & Looijen

Front & Back: designed by the author

An electronic version of this dissertation is available at

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6.5 Conclusions . . . 101 References. . . 103 Summary 109 Samenvatting 113 Acknowledgements 117 A Appendix to Chapter 2 119 B Appendix to Chapter 3 127 C Appendix to Chapter 4 139 D Appendix to Chapter 6 145 Curriculum Vitæ 155 List of Publications 157

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Donor-bridge-acceptor molecules as model

systems to study photoinduced charge

transfer

.

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1

2 1.Donor-Bridge-Acceptor Molecules as Model Systems

Whenever life becomes too complex, model systems are used to break the com-plexity down and to systematically study an observed phenomenon. The motivation usually goes beyond the pure understanding of the underlying mechanism. The ul-timate goal is to mimic or even optimise nature for technological applications. Photoinduced charge transfer is such a real life phenomenon that plays an impor-tant role for instance in photosynthesis [1–3], and DNA damage and repair [4–8]. Applications can be found in organic solar cells [9,10], water splitting devices [11], and molecular computation [12,13]. The model systems are so-called donor-bridge-acceptor (DBA) molecules comprising a donor, bridge, and donor-bridge-acceptor moiety that are covalently bound to each other. The name itself suggests that the three fragment molecules are, although covalently bound, separate units that only weakly interact with each other.

Charge transfer in DBA molecules has been extensively studied, both experi-mentally and theoretically for over half a century. Coherent tunnelling and incoher-ent hopping have been idincoher-entified as the two major mechanisms for charge transfer through molecular bridges [14–18]. The DBA systems investigated in this thesis exhibit charge transfer largely in the coherent tunnelling regime, which is therefore elaborated below.

The early theoretical work has focussed on demonstrating the main parameters of charge tunnelling and how to find approximate expressions for these, namely the effective electronic coupling Jeffbetween the donor and acceptor and the activation

barrier ∆Ga_{for the charge transfer reaction. Marcus provided an expression for the}

activation barrier in terms of driving force ∆GCT and reorganisation energy λ and

predicted three regions of charge transfer depending on the relation of ∆GCT and λ [19]. McConnell related the electronic coupling to the bridge length and energy barrier on the basis of a simplified one-state-per-fragment model, which entailed an exponential decay of the charge transfer rate constant with bridge length [20]. Since then, experiments have been devoted to individually manipulate these parameters by smart variations of the donor, bridge, or acceptor moieties in order to prove the theoretical predictions [21–26]. Although the one-state-per-fragment picture seem-ingly explains experimental results in many instances [27–30], it is surprising that in times of readily available computing power and computational chemistry software, this simplistic model is still largely used to support experimental data. In partic-ular, parameters such as the effective electronic coupling taking full account of the electronic structure of the entire DBA molecule are usually not calculated.

This thesis, demonstrates in a combined computational and experimental effort a few examples of DBA systems containing widely studied donor, bridge, and acceptor moieties that require including multiple states in the description of the fragment molecules. Moreover, a holistic approach for the interpretation and the prediction of experimental data is advocated, in which the fragment molecules cannot be seen as entirely individual units. This approach includes the determination of the initial and final states for charge transfer and calculations of the effective electronic couplings on

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1.1.Basic theory of non-adiabatic electron and hole transfer

1

3 the basis of electronic structure calculations of the fragment molecules as well as the entire DBA systems using (time-dependent) density functional theory. Furthermore, the effects of using linear vs. cross-conjugated bridges are discussed. Finally, a step away from charge tunnelling is taken to study direct charge injection into the bridging base pairs of DNA hairpins.

1.1. Basic theory of non-adiabatic electron and hole transfer

Based on the assumption of weakly interacting donor, bridge, and acceptor units, energy level diagrams can be drawn such as in Fig.1.1displaying the energy level alignment of the frontier orbitals of the fragment molecules. Charge transfer in

D

onor

Bridge

Acceptor

Donor

Bridge

Acceptor

E

(a)

(b)

Figure 1.1: Energy level alignment of the frontier fragment orbitals of the donor and acceptor with a schematic illustration of photoinduced (a) electron and (b) hole transfer. The shaded area represents the manifold of bridge fragment orbitals as the transfer medium.

such a molecular system can be triggered by selective light absorption of either the electron donor or the electron acceptor fragment. In this way it is possible to separately study electron and hole transfer as depicted in Fig.1.1. In electron transfer, an electron is promoted from the highest occupied fragment molecular or-bital (HOFO) to the lowest unoccupied fragment molecular oror-bital (LUFO) of the electron donor. This electron can subsequently transfer to the LUFO of the electron acceptor. Therefore, the interaction between the LUFOs of the donor and acceptor determines the rate of electron transfer. In hole transfer, the electron acceptor is excited, which generates a hole in the HOFO of the acceptor fragment that can transfer to the HOFO of the electron donor. In contrast to electron transfer, the interaction between the HOFOs of the donor and acceptor dictates the hole transfer rate.

The bridge fragment orbitals are not specified in Fig.1.1. Roughly speaking, the position of the bridge levels determines the mechanism of charge transfer. If the frontier orbitals of the bridge can be occupied, i.e. they are thermally accessible,

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the charge can transfer via a multi-step hopping mechanism. Although each hop can be regarded as a coherent tunnelling process from one fragment to the neighbouring one, the overall transfer process is considered incoherent since all coherences are lost after each hop is completed. If the frontier orbitals of the bridge are energetically inaccessible, charge transfer can occur via a one-step coherent tunnelling mecha-nism. Rather than directly tunnelling through space, the bridge orbitals are used as a medium that facilitates the donor-acceptor interaction. This thesis focuses, except for the last chapter, on DBA molecules that exhibit charge transfer in the coherent tunnelling regime.

Irrespective of the specific orbitals that are involved, charge transfer in the weak interaction regime can be viewed as a transition between the potential energy sur-face of the excited state and of the charge separated state as depicted in Fig. 1.2. According to the Franck-Condon condition and to satisfy the conservation of energy,

q

E

D

*

-B-A

D

+

-B-A

-q

₁

q

_c

q

₂

λ

ΔG

CT

Figure 1.2: Potential energy surfaces of the initial and final state shown as parabolas with equal curvature in the context of Marcus theory. Charge transfer occurs at the crossing point qc. The

relevant parameters are explained in the text.

the transition occurs at the crossing point of the two potential energy surfaces. The rate constant for this non-adiabatic charge transfer can be described by a Fermi “golden rule” expression:

kCT =

2π ℏ J

2

effFC, (1.1)

where the charge transfer rate constant kCT is proportional to the square of the

effective electronic coupling Jeff and to the Franck-Condon factor FC. Once again,

this description is only appropriate for DBA systems with weak electronic interaction between the fragments, which entails that the initial and final states are localised

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1.1.Basic theory of non-adiabatic electron and hole transfer

1

5 on the donor and acceptor, respectively. A delocalised initial state can have strong effects on the charge transfer properties, such as a rate constant that is almost independent of the distance between donor and acceptor [31]. The character of the initial state is one subject of this thesis, particularly treated in Chapter2.

1.1.1. Franck-Condon factor

In its general quantum chemical form, the Franck-Condon factor contains the overlap of the vibrational wavefunctions (including both internal and solvent degrees of freedom) of the initial and final states. In classical Marcus theory, FC describes the probability of reaching the crossing point when the two potential energy surfaces are approximated by two identical parabolas that are shifted with respect to each other as shown in Fig.1.2[19]. This leads to a compact expression of FC:

FC = √ 1 4πλkBT exp ( − (∆GCT + λ)2 4λkBT ) , (1.2)

where the Boltzmann term embodies the activation energy in terms of the reorgan-isation energy λ , and the Gibbs free energy of the charge transfer reaction ∆GCT.

The reorganisation energy accounts for the fact that the equilibrium nuclear coordi-nates of the initial and final state are different from each other. As shown in Fig.1.2,

λ is the Gibbs free energy needed to rearrange the nuclear coordinates of the final

state to the equilibrium coordinates of the initial state. It contains an inner and an outer contribution, related to the nuclear coordinates of the DBA molecule and the solvent molecules, respectively. Depending on the relation between λ and ∆GCT,

three regions can be distinguished. In the Marcus normal region (−∆GCT < λ), the

charge transfer rate constant increases with increasing ∆GCT; in the inverted region

(−∆GCT > λ), the rate constant decreases with increasing ∆GCT; in the optimal

region, where−∆GCT = λ, charge transfer occurs barrier-less. The dependence of

λ on the distance between the donor and acceptor is primarily determined by the

outer contribution that increases with a larger distance. The distance dependence of ∆GCT stems from the distance dependence of the stabilisation energy of the charge

separated state, which contains two terms: the electrostatic interaction between the charged donor and acceptor and the change in solvation energy upon charge separa-tion. Given that both λ and ∆GCT depend on the distance between the donor and

acceptor, FC does too. However, the electronic coupling is generally considered to dominate the distance dependence of the charge transfer rate constant [22]. Except for Chapter 6, this thesis largely compares DBA systems with similar FC factors with each other, which is why the focus here is on the electronic contribution to charge transfer.

1.1.2. Effective electronic coupling

In analogy to FC, the electronic coupling in Eq. (1.1) associated with the overlap of the electronic wavefunctions of the initial and final state. Without an intervening bridge, this electronic coupling would simply be the direct coupling between the

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1

initial and final state, i.e. between the relevant donor and acceptor frontier fragment orbitals. In the presence of a bridging medium, the fragment orbitals of the bridge can mediate charge transfer resulting in an effective electronic coupling Jeff. The

fragment orbitals of the bridge can be viewed as virtual pathways from the donor to the acceptor. Mcconnell [20] treated a scenario where the bridge is composed of n identical repeat units with only one relevant fragment orbital per unit, i.e. the LUFO of the bridge in the case of electron transfer; the HOFO in the case of hole transfer. By employing perturbation theory, he developed already in the 1960s a compact expression for Jeffthat is known as the McConnell superexchange

model [20]: Jeff=VDBVBA ∆E ( VBB ∆E )n−1 . (1.3)

VDBdenotes the direct electronic coupling between the donor and bridge units, VBA

between the acceptor and bridge units, and VBBbetween adjacent bridge units. The

energy difference between the donor/acceptor and bridge units is denoted as ∆E. From Eq. (1.1) and Eq. (1.3) follows thus that kCT falls off exponentially with the

bridge length r

kCT ∝ e−β(r−r0)_, _(1.4)

where r0 is the length of one bridge unit. The decay parameter β is then given by

β = 2 r0 ln ( ∆E VBB ) . (1.5)

Therefore, the larger ∆E and the smaller VBB, the steeper is the distance

depen-dence of the charge transfer rate constant. This correlation has been demonstrated in a number of publications, thus validating the McConnell model [27–29,32, 33]. However, as mentioned before, this simplification excludes the possibility of other bridging orbitals to mediate charge transfer, which turns out to be especially impor-tant when studying cross-conjugated bridges, as discussed in the following section. A more accurate expression for Jeffaccounting for the entire electronic structure of

the bridge has been formulated in the early 1990s [34]:

Jeff= VIF− ∑ i VIB_iVB_iF HBiBi− E , (1.6)

In this notation, the Hamiltonian submatrix HBB describing the bridge is

diago-nalized. VIF represents the direct through-space coupling between the initial and

final state, which is often negligible when a bridge resides between the donor and acceptor. The second term of Eq. (1.6) sums up all indirect couplings between ini-tial and final state mediated via the individual bridge fragment orbitals. It contains the direct coupling between the initial (final) state and the i-th fragment orbital of the bridge VIBi (VBiF) and its energy HBiBi. E is the energy of the transferring charge in the DBA system at the crossing point of the two non-adiabatic states. Two implications of the summation in Eq. (1.6) are worth mentioning at this point.

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1.2.Controlling charge transfer by quantum interference

1

7 (i) Performing the summation over all bridge fragment orbitals, all pathways laid out by the bridge can be taken into account. At the same time, the summation over only a subset of bridge orbitals provides insight into which pathways are most relevant for charge transfer in a given DBA system. This option is especially helpful in Chapter3and Chapter5. (ii) The summation preserves the sign of each effective electronic coupling, thereby allowing for cumulative enhancement or reduction of the individual pathways. This can lead in certain cases to a complete cancellation of Jeff, which is referred to as destructive quantum interference and discussed below.

1.2. Controlling charge transfer by quantum interference

The concept of quantum interference on the molecular scale has been introduced by Sautet and Joachim [35] in the 1980s in the context of single molecule junctions. In single molecule junctions a molecular bridge is connected to two metal electrodes instead of a donor and acceptor moiety. Charge transport along the molecular bridge is triggered upon applying a bias voltage by contrast to the photoinduced charge

transfer in DBA systems. In a sense, single molecule junctions present an alternative

to DBA molecules and are extensively studied in the context of single molecule electronics. In analogy to the effective electronic coupling for charge transfer Jeff,

the probability of a charge to cross the bridge from one electrode to the other is characterised by the transmission coefficient T (E). Using the non-equilibrium Green’s function approach, T (E) can be written as [36]:

T (E) = ∑ i VLiVRi E− ϵi+ iγi 2 (1.7)

where VLi(VRi) is the coupling between the left (right) electrode and the i-th

trans-mission channel of the bridge, which roughly corresponds to the molecular orbital of the bridge. Its energy is given by ϵi. The broadening of the molecular orbitals

due to the coupling to the electrodes is described by γi. Without going into

de-tail, the similarity between Eq. (1.7) and Eq. (1.6) is quite obvious. Consequently, charge transfer and transport have been related to each other many times [16,36–

40]. Therefore, it is not surprising, that also the concept of quantum interference has been brought to charge transfer in DBA systems [41]. A comparison of charge transfer in DBA systems to transport through a molecular bridge in between elec-trodes is subject of Chapter3.

The origin of quantum interference is illustrated in Fig. 1.3 using the example of a biphenyl molecule, which is particularly relevant in Chapter3. A more detailed description of quantum interference can be found for instance in [36,42]. The three highest occupied and the three lowest unoccupied orbitals of biphenyl are shown, with HOMO-1 and HOMO-2, and LUMO+1 and LUMO+2 being degenerate. We consider two cases: (i) connecting a donor and acceptor (or two electrodes) both at the para positions of the phenyl rings (linear conjugation), and (ii) connecting one at the para and the other at the meta position (cross-conjugation). In both

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1

D A A D HOMO HOMO-1 HOMO-2 LUMO LUMO+1 LUMO+2

-V

_Ip

V

_Im

-V

_Ip

-V

_Im

-V

_pF

V

_pF

E

₁

E

₂

-E

₂

-E

₁

linear

cross

(a)

(b)

Figure 1.3: (a) The chemical structures of the linearly and cross-conjugated biphenyl bridge. The acceptor is connected to both bridges at the para position. The donor is connected at either the para or the meta position. (b) The three highest occupied and three lowest unoccupied orbitals of the biphenyl bridge. The direct couplings between initial (final) state and HOMO and LUMO of the bridge are shown for the linearly (solid line) and the cross-conjugated (dashed line) bridge.

cases, the energy of the donor/acceptor or the electrodes is in the middle of the HOMO-LUMO gap. In case (i), the contribution to Jeff (or T (E)) by the HOMO

of biphenyl (−VIBi)VBiF(−E1)−1 is equal in sign and magnitude to the contribu-tion by the LUMO (−VIBi)(−VBiF)(E1)−1 because of the symmetry of the two orbitals. Thus, the HOMO and LUMO pathways constructively interfere with each other. The same holds for the pairwise contributions of HOMO-1 and LUMO+1 and HOMO-2 and LUMO+2, and all remaining orbitals. This behaviour gives rise to the so called constructive HOMO-LUMO interference. In case (ii), the contribution of the HOMO is exactly opposite the one of the LUMO. The exactly pairwise can-cellation of pathways results in a vanishing Jeff (or T (E)), the so called destructive

HOMO-LUMO interference. The presence of constructive HOMO-LUMO inter-ference in the linearly conjugated biphenyl bridge and destructive HOMO-LUMO interference in the cross-conjugated biphenyl bridge can be extrapolated in general to all linearly and cross-conjugated molecular bridges [43,44].

The example of biphenyl also demonstrates a different type of interference origi-nating from the contribution of degenerate orbitals [45, 46]. Because of the sym-metry of the degenerate orbitals HOMO-1 and HOMO-2, the respective contribu-tions VIBiVBiF(−E2)−1 and VIBi(−VBiF)(−E2)−1 cancel, which leads to destruc-tive interference. Likewise, the degenerate LUMO+1 and LUMO+2 destrucdestruc-tively

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1.3.Outline of the thesis

1

9 interfere. By contrast to the HOMO-LUMO interference, this type of destructive interference is present in both the linear and cross-conjugated biphenyl. As a conse-quence, the linearly conjugated biphenyl can exhibit destructive interference if other pathways play a subordinate role or are entirely switched off. The latter situation is presented in Chapter3.

The design of single molecule switches based on the control of quantum in-terference has been proposed as large ON/OFF ratios are expected when switching between constructive and destructive interference [35,36,42,45,47–50]. As demon-strated both theoretically [51] and recently also experimentally [52], such a switching mechanism could be realised by electrochemically reducing a cross-conjugated an-thraquinone bridge to a linearly conjugated form. While the effects of quantum interference in single molecule junctions have been experimentally demonstrated a number of times [46, 53–56], experimental evidence in DBA systems are less abun-dant [41, 57, 58]. This could be due to the difficulty in designing suitable DBA systems, a subject that is addressed in Chapter5.

1.3. Outline of the thesis

This thesis presents a combined experimental and computational approach to study photoinduced charge transfer in a series of DBA molecules. The mechanism of charge transfer and the relevant rate constants are obtained from careful analysis of femtosecond transient absorption spectroscopy data. (Time-dependent) density functional theory is employed to interpret the experimental results.

In Chapter 2, the distance dependence of electron vs. hole transfer in linearly conjugated DBA systems containing n = 1− 3 phenyl bridges is compared. The

experimentally observed difference between the shallow distance dependence for electron transfer and the relatively strong dependence for hole transfer is explained in terms of a delocalised initial state for electron transfer in contrast to a localised initial state for hole transfer. This delocalisation was not foreseen on the basis of the experimental steady-state and transient absorption spectra, demonstrating the necessity of computational methods for the assessment of the initial state.

The series of linearly conjugated DBA molecules is expanded by two cross-conju-gated biphenyl bridges in Chapter 3 to examine the occurrence of quantum inter-ference. In particular, a comparison between charge transfer and transport along the investigated molecular bridges is drawn. This comparison demonstrates the in-equality of Eq. (1.6) and Eq. (3.1) (when connecting only the bridge to electrodes), that can be traced back to the specific symmetry of the initial and final states de-fined by the donor and acceptor moieties. The symmetry of the initial and final state in relation to the bridge fragment orbitals further causes destructive instead of

constructive interference in the linearly conjugated DBA system with the biphenyl

bridge.

The role of orbital symmetry of the donor, bridge, and acceptor fragments is further addressed in Chapter 4, where two DBA systems are studied containing the same

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donor and acceptor as before but a different linearly and cross-conjugated bridge. Based on the conclusions of Chapter2 and Chapter3, a computational design of a linearly and cross-conjugated DBA molecule exhibiting pronounced quantum inter-ference effects is presented in Chapter5. Using the biphenyl bridges from Chapter3, appropriate donor and acceptor moieties are screened. This chapter emphasises the challenges to realise localised initial and final states while coupling to all bridge fragment orbitals at the same time.

Finally, in Chapter6 electron injection into base pairs of DNA hairpins is studied, where the sequence of base pairs is varied and thereby supposedly their energetics. The aim is to gain insight into the dynamics of electron injection in order to find a sequence of base pairs that efficiently promotes long range electron transfer. This chapter also addresses the question whether electron migration along the hairpins occurs via consecutive hops between the base pairs or delocalisation along the bases.

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References

1

11

References

[1] A. V. Vooren, V. Lemaur, A. Ye, D. Beljonne, and J. Cornil, Impact of bridging

units on the dynamics of photoinduced charge generation and charge recombi-nation in donor-acceptor dyads,ChemPhysChem 8, 1240 (2007).

[2] M. R. Wasielewski, Photoinduced Electron-Transfer in Supramolecular Systems

for Artificial Photosynthesis, Chem Rev 92, 435 (1992).

[3] G. D. Scholes, G. R. Fleming, A. Olaya-Castro, and R. van Grondelle, Lessons

from nature about solar light harvesting,Nat Chem 3, 763 (2011).

[4] D. B. Hall, R. E. Holmlin, and J. K. Barton, Oxidative DNA damage through

long-range electron transfer, Nature 382, 731 (1996).

[5] S. Kanvah, J. Joseph, G. B. Schuster, R. N. Barnett, C. L. Cleveland, and U. Landman, Oxidation of DNA: damage to nucleobases, Acc Chem Res 43, 280 (2010).

[6] Z. Liu, C. Tan, X. Guo, Y. T. Kao, J. Li, L. Wang, A. Sancar, and D. Zhong,

Dynamics and mechanism of cyclobutane pyrimidine dimer repair by DNA photolyase,Proc Natl Acad Sci U S A 108, 14831 (2011).

[7] J. C. Genereux and J. K. Barton, Mechanisms for DNA charge transport,Chem Rev 110, 1642 (2010).

[8] F. D. Lewis, H. Zhu, P. Daublain, B. Cohen, and M. R. Wasielewski, Hole

mobility in DNA a tracts,Angew Chem Int Ed 45, 7982 (2006).

[9] S. Günes, H. Neugebauer, and N. S. Sariciftci, Conjugated Polymer-Based

Organic Solar Cells,Chem Rev 107, 1324 (2007).

[10] C. Bauer, J. Teuscher, J. C. Brauer, A. Punzi, A. Marchioro, E. Ghadiri, J. D. Jonghe, M. Wielopolski, N. Banerji, and J. E. Moser, Dynamics and

Mecha-nisms of Interfacial Photoinduced Electron Transfer Processes of Third Gener-ation Photovoltaics and Photocatalysis,Chimia 65, 704 (2011).

[11] J. D. Megiatto Jr, D. D. Méndez-Hernández, M. E. Tejeda-Ferrari, A.-L. Teill-out, M. J. Llansola-Portolés, G. Kodis, O. G. Poluektov, T. Rajh, V. Mujica, T. L. Groy, D. Gust, T. A. Moore, and A. L. Moore, A bioinspired redox relay

that mimics radical interactions of the Tyr–His pairs of photosystem II, Nat Chem 6, 423 (2014).

[12] A. P. de Silva and S. Uchiyama, Molecular logic and computing,Nat Nanotech-nol 2, 399 (2007).

[13] A. P. de Silva, Luminescent Photoinduced Electron Transfer (PET) Molecules

(18)

1

12 References

[14] Y. A. Berlin, A. L. Burin, and M. A. Ratner, Elementary steps for charge

transport in DNA: thermal activation vs. tunneling,Chem Phys 275, 61 (2002). [15] F. C. Grozema, Y. A. Berlin, and L. D. A. Siebbeles, Mechanism of charge

migration through DNA: Molecular wire behavior, single-step tunneling or hop-ping? J Am Chem Soc 122, 10903 (2000).

[16] D. M. Adams, L. Brus, C. E. D. Chidsey, S. Creager, C. Creutz, C. R. Kagan, P. V. Kamat, M. Lieberman, S. Lindsay, R. A. Marcus, R. M. Metzger, M. E. Michel-Beyerle, J. R. Miller, M. D. Newton, D. R. Rolison, O. Sankey, K. S. Schanze, J. Yardley, and X. Y. Zhu, Charge transfer on the nanoscale: Current

status,J Phys Chem B 107, 6668 (2003).

[17] E. A. Weiss, M. R. Wasielewski, and M. A. Ratner, Molecules as wires:

Molecule-assisted movement of charge and energy, Top Curr Chem 257, 103 (2005).

[18] M. Gilbert and B. Albinsson, Photoinduced charge and energy transfer in

molec-ular wires,Chem Soc Rev 44, 845 (2015).

[19] R. A. Marcus and N. Sutin, Electron Transfers in Chemistry and Biology,

Biochim Biophys Acta 811, 265 (1985).

[20] H. Mcconnell, Intramolecular Charge Transfer in Aromatic Free Radicals, J Chem Phys 35, 508 (1961).

[21] G. L. Closs, G. L. and J. R. Miller, J. R., Intramolecular Long-Distance Electron

Transfer in Organic Molecules,Science 240, 440 (1988).

[22] M. N. Paddon-Row, Investigating Long-Range Electron-Transfer Processes with

Rigid, Covalently-Linked Donor-(Norbornylogous Bridge)-Acceptor Systems, Acc Chem Res 27, 18 (1994).

[23] W. B. Davis, W. A. Svec, M. A. Ratner, and M. R. Wasielewski, Molecular-wire

behaviour in p-phenylenevinylene oligomers,Nature 396, 60 (1998).

[24] R. A. Malak, Z. N. Gao, J. F. Wishart, and S. S. Isied, Long-range electron

transfer across peptide bridges: The transition from electron superexchange to hopping,J Am Chem Soc 126, 13888 (2004).

[25] R. H. Goldsmith, L. E. Sinks, R. F. Kelley, L. J. Betzen, W. H. Liu, E. A. Weiss, M. A. Ratner, and M. R. Wasielewski, Wire-like charge transport at

near constant bridge energy through fluorene oligomers,Proc Natl Acad Sci U S A 102, 3540 (2005).

[26] E. A. Weiss, M. J. Tauber, R. F. Kelley, M. J. Ahrens, M. A. Ratner, and M. R. Wasielewski, Conformationally gated switching between superexchange

and hopping within oligo-p-phenylene-based molecular wires, J Am Chem Soc

(19)

References

1

13 [27] D. Hanss and O. S. Wenger, Tunneling barrier effects on photoinduced charge

transfer through covalent rigid rod-like bridges,Inorg Chem 48, 671 (2009). [28] F. D. Lewis, J. Liu, W. Weigel, W. Rettig, I. V. Kurnikov, and D. N. Beratan,

Donor-bridge-acceptor energetics determine the distance dependence of electron tunneling in DNA,Proc Natl Acad Sci U S A 99, 12536 (2002).

[29] O. S. Wenger, Barrier heights in long-range electron tunneling, Inorg Chim Acta 374, 3 (2011).

[30] E. A. Weiss, M. J. Ahrens, L. E. Sinks, A. V. Gusev, M. A. Ratner, and M. R. Wasielewski, Making a molecular wire: Charge and spin transport through

para-phenylene oligomers,J Am Chem Soc 126, 5577 (2004).

[31] S. Skourtis and A. Nitzan, Effects of initial state preparation on the distance

dependence of electron transfer through molecular bridges and wires, J Chem Phys 119, 6271 (2003).

[32] J. Wiberg, L. J. Guo, K. Pettersson, D. Nilsson, T. Ljungdahl, J. Martensson, and B. Albinsson, Charge recombination versus charge separation in

donor-bridge-acceptor systems, J Am Chem Soc 129, 155 (2007).

[33] D. Hanss and O. S. Wenger, Electron tunneling through oligo-p-xylene bridges,

Inorg Chem 47, 9081 (2008).

[34] J. W. Evenson and M. Karplus, Effective Coupling in Bridged Electron-Transfer

Molecules - Computational Formulation and Examples,J Chem Phys 96, 5272 (1992).

[35] P. Sautet and C. Joachim, Electronic Interference Produced by a Benzene

Em-bedded in a Polyacetylene Chain, Chem Phys Lett 153, 511 (1988).

[36] G. C. Solomon, D. Q. Andrews, T. Hansen, R. H. Goldsmith, M. R. Wasielewski, R. P. V. Duyne, and M. A. Ratner, Understanding quantum

in-terference in coherent molecular conduction,J Chem Phys 129, 054701 (2008). [37] D. Segal, A. Nitzan, W. B. Davis, M. R. Wasielewski, and M. A. Ratner,

Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions,J Phys Chem B 104, 3817 (2000). [38] A. Nitzan and M. A. Ratner, Electron transport in molecular wire junctions,

Science 300, 1384 (2003).

[39] Y. A. Berlin and M. A. Ratner, Intra-molecular electron transfer and electric

conductance via sequential hopping: Unified theoretical description,Radiat Phys Chem 74, 124 (2005).

[40] A. Nitzan, A relationship between electron-transfer rates and molecular

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1

14 References

[41] A. B. Ricks, G. C. Solomon, M. T. Colvin, A. M. Scott, K. Chen, M. A. Rat-ner, and M. R. Wasielewski, Controlling Electron Transfer in

Donor-Bridge-Acceptor Molecules Using Cross-Conjugated Bridges, J Am Chem Soc 132, 15427 (2010).

[42] T. Hansen, G. C. Solomon, D. Q. Andrews, and M. A. Ratner, Interfering

pathways in benzene: an analytical treatment,J Chem Phys 131, 194704 (2009). [43] D. Q. Andrews, G. C. Solomon, R. P. V. Duyne, and M. A. Ratner, Single

Molecule Electronics: Increasing Dynamic Range and Switching Speed Using Cross-Conjugated Species,J Am Chem Soc 130, 17309 (2008).

[44] G. C. Solomon, D. Q. Andrews, R. H. Goldsmith, T. Hansen, M. R. Wasielewski, R. P. V. Duyne, and M. A. Ratner, Quantum Interference in

Acyclic Systems: Conductance of Cross-Conjugated Molecules, J Am Chem Soc 130, 17301 (2008).

[45] R. Härtle, M. Butzin, O. Rubio-Pons, and M. Thoss, Quantum Interference and

Decoherence in Single-Molecule Junctions: How Vibrations Induce Electrical Current,Phys Rev Lett 107, 046802 (2011).

[46] S. Ballmann, R. Hartle, P. B. Coto, M. Elbing, M. Mayor, M. R. Bryce, M. Thoss, and H. B. Weber, Experimental Evidence for Quantum Interference

and Vibrationally Induced Decoherence in Single-Molecule Junctions,Phys Rev Lett 109, 056801 (2012).

[47] S. Chen, Y. Zhang, S. Koo, H. Tian, C. Yam, G. Chen, and M. A. Ratner,

Interference and Molecular Transport - A Dynamical View: Time-Dependent Analysis of Disubstituted Benzenes,J Phys Chem Lett 5, 2748 (2014).

[48] N. Renaud, M. A. Ratner, and C. Joachim, A Time-Dependent Approach to

Electronic Transmission in Model Molecular Junctions,J Phys Chem B 115, 5582 (2011).

[49] T. Markussen, R. Stadler, and K. S. Thygesen, The relation between structure

and quantum interference in single molecule junctions, Nano Lett 10, 4260 (2010).

[50] A. A. Kocherzhenko, F. C. Grozema, and L. D. A. Siebbeles, Charge Transfer

Through Molecules with Multiple Pathways: Quantum Interference and De-phasing,J Phys Chem C 114, 7973 (2010).

[51] E. H. van Dijk, D. J. T. Myles, M. H. van der Veen, and J. C. Hummelen,

Synthesis and properties of an anthraquinone-based redox switch for molecular electronics,Org Lett 8, 2333 (2006).

[52] M. Baghernejad, X. T. Zhao, K. B. Ornso, M. Fueg, P. Moreno-Garcia, A. V. Rudnev, V. Kaliginedi, S. Vesztergom, C. C. Huang, W. J. Hong, P. Broek-mann, T. Wandlowski, K. S. Thygesen, and M. R. Bryce, Electrochemical

(21)

References

1

15

Control of Single-Molecule Conductance by FermiLevel Tuning and Conjuga-tion Switching,J Am Chem Soc 136, 17922 (2014).

[53] M. Mayor, H. B. Weber, J. Reichert, M. Elbing, C. V. Hanisch, D. Beckmann, and M. Fischer, Electric current through a molecular rod-relevance of the

posi-tion of the anchor groups,Angew Chem Int Ed Engl 42, 5834 (2003).

[54] C. R. Arroyo, S. Tarkuc, R. Frisenda, J. S. Seldenthuis, C. H. Woerde, R. Eelkema, F. C. Grozema, and H. S. van der Zant, Signatures of quantum

interference effects on charge transport through a single benzene ring, Angew Chem Int Ed Engl 52, 3152 (2013).

[55] C. M. Guedon, H. Valkenier, T. Markussen, K. S. Thygesen, J. C. Hummelen, and S. J. van der Molen, Observation of quantum interference in molecular

charge transport,Nat Nanotechnol 7, 304 (2012).

[56] S. V. Aradhya, J. S. Meisner, M. Krikorian, S. Ahn, R. Parameswaran, M. L. Steigerwald, C. Nuckolls, and L. Venkataraman, Dissecting Contact Mechanics

from Quantum Interference in Single-Molecule Junctions of Stilbene Deriva-tives,Nano Lett 12, 1643 (2012).

[57] C. Patoux, C. Coudret, J. P. Launay, C. Joachim, and A. Gourdon, Topological

effects on intramolecular electron transfer via quantum interference,Inorg Chem

36, 5037 (1997).

[58] M. L. Kirk, D. A. Shultz, D. E. Stasiw, D. Habel-Rodriguez, B. Stein, and P. D. Boyle, Electronic and Exchange Coupling in a Cross-Conjugated D-B-A

Biradical: Mechanistic Implications for Quantum Interference Effects, J Am Chem Soc 135, 14713 (2013).

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Different mechanisms for hole and electron

transfer along identical molecular bridges:

The importance of the initial state

delocalisation

We report measurements of hole and electron transfer along identical oligo-p-phenylene molecular bridges of increasing length. Although the injection barriers for hole and elec-tron transfer are similar, we observed striking differences in the distance dependence and absolute magnitude of the rates of these two processes. Electron transfer is charac-terised by an almost distance-independent, fast charge transfer rate. On the other hand, hole transfer presents a much slower rate that decreases significantly with the length of the bridge. Time-dependent density functional calculations show that the observed differences can be explained by the delocalisation of the respective initial excitation. The evaluation of the initial state is therefore essential when comparing charge transfer rates between different donor-bridge-acceptor systems.

This chapter is based on N. Gorczak, S. Tarkuç, N. Renaud, A.J. Houtepen, R. Eelkema, L.D.A. Siebbeles, and F.C. Grozema, J Phys Chem A 118, 3891 (2014) [1].

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18 2.Importance of Initial State Delocalisation

2.1. Introduction

Understanding charge transfer through molecular bridges is of fundamental inter-est: not only as this mechanism is at the centre of perspective technologies, such as molecular electronics [2, 3] or artificial solar energy conversion [4, 5], but also due to the importance of charge transfer processes in biochemical reactions [6,7]. Donor-bridge-acceptor (DBA) molecules offer an interesting platform to systemati-cally study photoinduced electron and hole transfer through molecular bridges and to understand the key parameters that govern these processes. Transient absorp-tion spectroscopy is widely applied in such studies, where either the electron-donor is excited, initiating electron transfer, or the electron acceptor is excited, initiating hole transfer.

Although charge separation involving both hole and electron transfer have been investigated independently in separate DBA systems, only a few measurements of these two distinct processes through the same molecular bridge and under the same experimental conditions have been reported. Following the seminal work of Johnson

et al. [8] on charge shift along saturated molecular bridges, it is generally assumed that both electron and hole transfer through the same bridge occur via identi-cal mechanisms, and thus exhibit a similar distance dependence of their respective transfer rates. In this chapter, we report measurements of photoinduced hole and electron transfer along a series of well defined conjugated molecular bridges. A key difference with the previous studies is that we deal with a charge separation reaction rather than a charge shift reaction in the work of Johnson et al. [8]. This means that the energetics of the transfer reaction are strongly determined by Coulomb interactions between electron and hole in this case. These measurements allow a direct comparison of charge and electron transfer in a charge separation reaction and yield a conclusion that is strikingly different from the one obtained for charge shift [8].

Several fields would greatly benefit from a direct comparison of photoinduced electron and hole transfer through the same molecular bridge. One example is charge transfer in DNA. Motivated by the relevance of hole transfer for the DNA damage [9,10] and electron transfer for the DNA repair [11] mechanism, both elec-tron and hole transfer have been independently measured along various DNA hair-pins [12–15]. While striking differences between the two types of charge carriers were observed, the different experimental conditions during the measurements make a di-rect comparison between hole and electron transfer difficult.

Another example where a direct comparison would be beneficial is the investiga-tion of effects of cross-conjugainvestiga-tion on rates of charge transfer. Ricks et al. [16] have recently reported electron transfer rate constants that are one order of mag-nitude lower through a cross-conjugated than through a linearly conjugated bridge. This large difference was attributed to quantum interference effects that occur in cross-conjugated bridges [17,18] although other potentially differing factors between the linearly and cross-conjugated bridges, e.g. bridge energetics, molecular confor-mation, or initial state delocalisation, were not taken into consideration. Because

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2.1.Introduction

2

19 quantum interference effects should be identical for the two types of charge carriers, measurements of both hole and electron transfer rates through the same bridges could clarify the role of quantum interference in these systems.

The distance dependence of electron or hole transfer along a variety of molecular bridges have been previously measured experimentally using transient absorption spectroscopy. These studies have revealed, in some cases, a crossover from a strong to a weak distance dependence upon lengthening the bridge. This abrupt change in distance dependence is typically interpreted in terms of two distinct charge trans-port regimes: (1) the superexchange mechanism, where the charge tunnels from the donor to the acceptor through the energy barrier constituted by the bridge molecule, and (2) a thermally activated hopping mechanism where the charge hops between neighbouring units of the bridge to reach the acceptor [19–22]. The crossover from superexchange to hopping can be attributed in many cases to a lowering of the energy barrier with increasing number of bridge units caused by the extended con-jugation of the bridge [19, 23]. A particular focus has therefore been put on the impact of this energy barrier on the overall charge transfer rates [24–28].

When dominated by the superexchange mechanism, the charge transfer rate con-stant kCT shows a strong exponential decay with the distance between the donor

and acceptor d [29]:

kCT ∝ e−βd. (2.1)

The decay is characterised by the fall-off parameter β with a value larger than 0.2 Å−1 [30]; while lower values might hint at a hopping mechanism. Because β is largely determined by the energy difference between the donor/acceptor and bridge units, a larger energy difference results in a stronger distance dependence of kCT.

The energy difference is generally approximated by the Gibbs free energy barrier for electron or hole injection ∆Ge/h that is calculated from the oxidation and

re-duction potentials of the isolated donor, bridge, and acceptor units [23,24, 26]. It is important here to distinguish the situation of actual injection of a charge into the bridge and the situation where the bridge acts as a tunnelling barrier. These two situations are characterised by a different (dielectric) response of the environment, as is discussed in more detail below. The approach of using experimental oxidation and reduction potentials for the individual non-connected subsystems neglects pos-sible shifts of energy levels due to the covalent bond between neighbouring units and assumes that the initial excitation is fully localised on the donor or acceptor. These approximations are rather crude and may not be valid in all cases. Never-theless, a correlation between ∆Ge/hand β is usually experimentally observed. For

example, Hanss and Wenger [31] showed that using a different donor moiety with the exact same molecular bridge can significantly reduce ∆Ge/h and consequently

yields a weaker distance dependence of the charge transfer rate. A systematic study of such energy barrier alteration was particularly successful using DNA hairpins as molecular bridges for hole transfer [12].

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the same molecular bridges depicted in Fig. 2.1and under the same experimental conditions. This study offers the first direct comparison between photo-induced electron and hole transfer mechanisms and provides important information about their respective rates. The DBA molecules are composed of a pyrrole derivative (SNS) as electron donor and a perylene derivative (PDI) as acceptor connected by p-oligophenylene bridges (p-Phn) where n = 1− 3. The charge transfer rate

constants were determined upon selective pulsed laser excitation of the donor or the acceptor by femtosecond transient absorption spectroscopy using global and target analysis. We observe a striking difference between hole and electron transfer in these systems, both in terms of the absolute rate constants and the distance dependence. The distance dependence of hole transfer falls in the superexchange regime while the electron transfer rate constants are one to two orders of magnitude faster and almost independent of distance. An analysis of the Gibbs injection barriers ∆Ge/hindicates

that the weak distance dependence of electron transfer cannot be attributed to a hopping mechanism. Instead, we identify a substantial delocalisation of the initial excited state onto the bridge as the origin for the small β by performing time-dependent density functional theory (TD-DFT) electronic structure calculations. Moreover, due to considerable shifts of the bridge energy levels when connecting the bridge to the donor and acceptor we question the validity of the common approach to estimate ∆Ge/h using energetic parameters for the non-connected subunits.

S N S N O O N O O C6H13 C6H13 n S NH S N O O N O O C6H13 C6H13 C6H13 C6H13 1-3 SNSref PDIref

Figure 2.1: Chemical structures of the DBA systems 1-3 where the compound name stands for the number of phenyl units n, and the donor and acceptor reference compounds SNSref and PDIref.

2.2. Results and discussion

2.2.1. Absorbance spectra

The absorbance spectra of 1-3 and of the donor and acceptor reference compounds

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2.2.Results and discussion

2

21

PDIref is substituted with two branched alkyl chains for solubility reasons. It is

known that the electronic properties are not significantly affected by substitution on the imide nitrogen [32]. The spectra of 1-3 overlap with the spectrum of PDIref in the range of 450-550 nm indicating that the electronic coupling between PDI and Phn or SNS is very small. The similarity of the spectra around 350 nm between

1-3 and SNSref also suggests that there is no significant coupling between SNS

and Phn or PDI. However, 1 shows a stronger absorption compared to 2 and 3,

which is likely due to interaction between SNS and Ph or PDI for the shortest bridge. The phenylene bridges absorb below 300 nm with a red-shift in absorption with increasing n resulting from the linear conjugation of the phenyl units. The absorption appears at the blue edge of the spectra for 2 and 3.

0.15 0.10 0.05 0.00 absorbance 600 500 400 300 wavelength (nm) 1 2 3 PDIref SNSref

Figure 2.2: Ground-state absorbance spectra of 1-3 and of the donor and acceptor reference compounds PDIref and SNSref.

Fig. 2.2 demonstrates that the absorption of SNS, Phn, and PDI are sufficiently

separated to allow for selective excitation of acceptor and donor. This enables the study of both hole and electron transfer along the same bridge. The excitation of PDI at 527 nm generates a hole in the highest occupied fragment molecular orbital (HOFO) of PDI that can subsequently transfer to the HOFO of SNS. Excitation at 350 nm leads to excitation of an electron from the SNS HOFO to its lowest unoccupied fragment molecular orbital (LUFO) . Subsequently, this electron can transfer to the LUFO of PDI, resulting in the same charge-separated state but via a different route. It is important to note that light of 350 nm is also partly absorbed by PDI. Therefore, parallel to the process of electron transfer, hole transfer is also observed after excitation at 350 nm.

2.2.2. Hole and electron transfer rates

Hole transfer rate constants were determined from target analysis of transient ab-sorption data following excitation of PDI at 527 nm, as described in the experimental section. Fig.2.3a shows the evolution of the difference absorbance (∆OD) spectra observed during hole transfer in 3. Immediately after excitation of PDI (Fig.2.3a), the spectrum is identical to the ∆OD spectrum of PDIref (see Fig. 2.3b) with

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-10 -5 0 5 DmOD 900 800 700 600 500 wavelength (nm) (a) 0 ps 600 ps 3000 ps _-10 -5 0 5 DmOD 900 800 700 600 500 wavelength (nm) (b) hot PDI* PDI* PDIref* population 10 2 4 6100 2 4 610002 time (ps) 4 3 2 1 0 DmOD (c) hot PDI* PDI* 710 nm

Figure 2.3: (a) Difference absorbance spectra of 3 after excitation of PDI at 0, 600, and 3000 ps. (b) Target analysis reveals the difference absorbance spectra corresponding to hot PDI∗, PDI∗, and PDI– ·_{. The spectrum of PDIref is displayed for comparison. (c) The population profiles}

visualise the formation of PDI– ·_{that cannot be deducted directly from the kinetic trace at 710 nm}

due to the overlapping photoinduced absorption bands of PDI– ·_{and PDI}∗_.

a typical bleach at 490 nm and 530 nm, stimulated emission around 580 nm, and two broad absorption bands at 690 nm and 850 nm. After 600 ps the spectrum exhibits additional sharp absorption features at 710 nm and 800 nm that are typical for PDI– · [33]. After 3 ns, the spectrum corresponds entirely to that of PDI– ·. Because of the overlapping photoinduced absorption of PDI∗ and PDI– ·, charge transfer rates could not be determined from the transient absorption at a single wavelength but had to be determined by target analysis (see Fig.2.3c). The datasets of 1-3 were analysed by fitting to a sequential kinetic model in which the initial PDI∗ (hot PDI∗) relaxes within the first picoseconds due to solvent reorganisation and/or interactions between the charge and molecular vibration modes. PDI∗ sub-sequently undergoes hole transfer leading to the formation of SNS+·−Phn−PDI– ·_.

This fast initial relaxation effect has been shown previously for PDI even for an al-most non-dipolar solvent such as toluene [34]. The corresponding species associated spectra (SAS) are shown in Fig. 2.3b with their respective population profiles in Fig.2.3c for 3. No signatures of SNS+· were observed as these are out of the spec-tral range of the probe light. We exclude formation of Ph+

n since no photoinduced

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23 [23].

Electron transfer rates were obtained by the change in absorbance after ex-citation of SNS at 350 nm. Fig. 2.4a shows the transient absorption spectra of

3. Immediately after excitation, the spectrum contains features of two species: a

-1 0 1 DmOD 900 800 700 600 500 wavelength (nm) (a) 0 ps 10 ps 3000 ps -1 0 1 DmOD 900 800 700 600 500 wavelength (nm) (b) SNS* PDI* SNSref* 0.8 0.6 0.4 0.2 0.0 DmOD 10 2 4 6100 2 4 610002 time (ps) population (c) SNS* PDI* 710 nm

Figure 2.4: Difference absorbance spectra of 3 following excitation at 350 nm at 0, 10, and 3000 ps (a), the fitted SAS (b), and population profiles (c). The kinetic trace at 710 nm is also shown in (c).

broad absorption band from 490 to 580 nm resembling the SNS singlet (compare to

SNSref in Fig.2.4b), and the ∆OD spectrum of PDI∗. The presence of PDI∗ is due to absorption by PDI that accounts for approximately 30 % of the total absorp-tion at 350 nm. Therefore, both initial states and the subsequent electron and hole transfer processes were included in the target analysis of the transient absorption data for excitation at 350 nm. Hot PDI∗ is omitted in the hole transfer scheme for simplicity; this does not lead to significantly worse global fits. In the parallel electron transfer process, SNS∗ undergoes electron transfer leading to formation of SNS+·−Phn−PDI– ·_{. As a consequence of the parallel electron and hole transfer}

processes, the population of PDI– · rises in two stages: initially by electron trans-fer from SNS∗ and subsequently by hole transfer from PDI∗. This can be seen in the kinetic trace at 710 nm (Fig.2.4c) that exhibits a fast increase during the first 10 ps as a result of electron transfer. Thereafter it continues to rise as a result of hole transfer on the nanosecond timescale similar to that following PDI excitation.

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2

The SAS of PDI∗ and PDI– · resulting from data analysis for excitation at 350 nm (Fig.2.4b) agree with the SAS resulting from PDI excitation. Although the SAS of SNS∗could not be disentangled completely from the contribution of PDI∗, it resem-bles the ∆OD spectrum of SNSref. The strength of the applied analysis is shown by the fact that the rate constants of hole transfer determined from excitation at 527 nm and 350 nm are similar for each sample (Table2.1).

Table 2.1: Electron kETand hole kHT transfer rate constants (ps−1) determined by target analysis

of transient absorption following excitation at 350 nm or 527 nm.

ex. at 350 nm ex. at 527 nm

kET kHT kHT

1 0.35 0.028 0.042

2 0.25 0.0025 0.0024

3 0.17 0.0010 0.0010

The hole and electron transfer rate constants are listed in Table2.1and plotted on a logarithmic scale vs. the through-space donor-acceptor distance in Fig. 2.5. There are two clear distinctions between electron and hole transfer. The electron

0.001 0.01 0.1 1 kCT (ps -1 ) 22 20 18 16 14 12 10 through-space distance () hole (b = 0.42 -1) electron (b = 0.09 -1)

Figure 2.5: Logarithmic plots of the electron (blue squares) and hole (black squares) transfer rate constants vs. the donor-acceptor distance for 1-3. The error bars fall within the size of the symbols. The solid lines correspond to an exponential distance dependence with decay parameter

β (Eq. (2.1)).

transfer rates are at least one order of magnitude larger than hole transfer rates, which could be due to a larger driving force for electron than for hole transfer. Even more interesting, is the strikingly differing distance dependence of the rates. The strong distance dependence with β = 0.42 Å−1 of hole transfer is characteris-tic for a superexchange mechanism through phenylene bridges [35]. On the other hand, the much weaker distance dependence of electron transfer is surprising for two reasons. Firstly, the small β of 0.09 Å−1is not consistent with a superexchange

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25 mechanism [30] and may indicate that electron transfer occurs via of a hopping mechanism. However, a hopping mechanism is usually not observed for such short phenylene bridges [23,25, 36]. Secondly, the large difference between electron and hole transfer suggests different transfer mechanisms. A possible origin for this dis-tinct behaviour could be that the energy of the electron originating from the SNS is substantially closer to the LUFO of Phn than the energy of the hole in PDI to

the HOFO of Phn. Therefore, we examine in the following section the height of the

injection barriers for hole and electron transfer.

2.2.3. Energetics

As discussed in the introduction, the distance dependence of charge transfer is largely determined by the injection barrier. Therefore, we consider whether the large difference in distance dependence for hole and electron transfer can be ex-plained by a significantly smaller injection barrier for electron compared with hole transfer. Electron injection barriers were estimated for the three compounds ac-cording to the equation for the Gibbs energy of photoinduced charge transfer1_[₃₈_]

for the radical ion pairs SNS+·-Phn– · with respect to the excitation energy Eex:

∆G = Eox− Ered− e2 dϵ+ e 2 ( 1 2rox ( 1 ϵ − 1 ϵox ) + 1 2rred ( 1 ϵ − 1 ϵred )) − Eex, (2.2)

with the elementary charge e. Barriers for hole injection were calculated using Eq. (2.2) for the radical ion pairs PDI– ·-Ph_n+·. The oxidation and reduction po-tential of the electron donating and accepting unit Eoxand Eredwere obtained from

cyclic voltammetry and are listed in Table2.2along with the radii of the radical ions

rox and rred that were taken from literature. It should be noted that in Eq. (2.2)

the assumption is made that the donor and acceptor are spherical. Since this is usually not the case, the values obtained using Eq. (2.2) should be considered as a rough estimate, not a precise calculation.

Table 2.2: Oxidation and reduction potentials and radical ions radii of SNS, PDI, and Phn.

Eox (V vs. SCE) Ered(V vs. SCE) rox/red (Å)a

SNS 0.96b _3.8

PDI -0.70c _7.6

Ph 2.40cd _-3.35ed _1.6

Ph2 1.85cd -2.68ed 3.8

Ph3 1.60cd -2.40ed 5.8

a _{Taken from ref [}₃₉_{] where the radius of SNS is approximated by the radius of phenothiazine.} b_{ACN as solvent.} c_{DCM as solvent.} d_{Taken from ref [}₄₀_]. e_{DMA as solvent.}

The centre-to-centre distance between the radical ions dD−B and dA−B was

deter-mined from the DFT structure calculations (Table 2.3). ϵ is the static dielectric

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2

constant of the solvent that was used in the transient absorption spectroscopy mea-surements (toluene with ϵ = 2.38). ϵoxand ϵreddenote the solvent used in the cyclic

voltammetry measurements of the respective electron donating and accepting unit (DCM with ϵ = 8.9, ACN with ϵ = 37.5, and DMA with ϵ = 37.8). The energies of the excited states Eex were obtained from the maxima of the absorbance spectra: Eex = 3.54 eV for donor excitation and Eex= 2.35 eV for acceptor excitation.

Table 2.3: Distance between the radical ions of donor and bridge, acceptor and bridge, and donor and acceptor

dD−B (Å) dA−B (Å) dD−A (Å)

1 4.0 8.5 12.5

2 6.1 10.7 16.8

3 8.3 12.8 21.1

The injection barrier and driving force for hole and electron transfer are repre-sented in Fig.2.6a and Fig.2.6b respectively. As seen in these figures, the driving force for electron transfer is ten times larger than the one for hole transfer. This could explain why electron transfer is much faster than hole transfer in 1-3. How-ever, as mentioned in the introduction, the distance dependence of kCT is dominated

by the injection barrier. Using Eq. (2.2) we obtained hole injection barriers of 1.7, 0.5, and 0.2 eV for 1-3. Surprisingly, the injection barriers for electron transfer are of the same order of magnitude, namely 1.8, 0.6, and 0.3 eV. All of these values correspond to the situation where a charge is actually injected into the bridge and were calculated using the full (static) dielectric constant of the solvent (toluene). Since toluene is an almost non-dipolar solvent, the difference between the static and optical dielectric constant is very small (2.38 vs. 2.24). When using the optical dielectric constant, corresponding to the bridge acting as a virtual intermediate, the injection barrier for hole injection in 1 changes from 1.7 eV to 1.8 eV.

The most important conclusion from these calculations is the fact that the injection barriers for electron and hole transfer are very similar, suggesting that both trans-fer processes are likely to follow the same mechanism. In particular, the similar injection barriers imply similar decay parameters β for both processes. This how-ever contradicts the experimental observation of β = 0.09 Å−1 for electron transfer suggesting a hopping mechanism and β = 0.42 Å−1 for hole transfer suggesting a superexchange mechanism. The differences found experimentally between electron and hole transfer thus can not be explained by the injection barriers calculated using Eq. (2.2).

2.2.4. Charge distribution of the initial state

In order to understand the difference between hole and electron transfer measured for compounds 1-3 we have computed the excitation spectra of 1-3 using TD-DFT (M06-2X/DZP) in the gas phase. According to the TD-DFT calculations the first

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27 2 1 0 -1 DG (eV) D-B-A* D-B+-A- D+-B-A -(a) 1 2 3 2 1 0 -1 DG (eV) D*-B-A D+-B--A D+-B-A -(b) 1 2 3

Figure 2.6: Gibbs energies for the states relevant to the hole (a) and electron (b) transfer pathways with respect to the excited states.

two excited states with significant oscillator strength (0.9 and 0.5) are located at 2.73 eV and 4.16 eV for 1-3. These values are systematically larger than the ex-perimentally observed ones (2.35 eV and 3.54 eV). We attribute this discrepancy to stabilisation by the solvent that is not taken into account in the calculations. The lower energy excited state corresponds to the HOFO-LUFO transition (weight of >0.95) on the PDI fragment. The calculated energy of the lowest excited state of

1-3 match the one of an isolated PDI molecule (2.74 eV). This agreement is also in

line with the overlapping experimental absorbance spectra of 1-3 and PDIref in Fig.2.2. The higher energy excited state corresponds to SNS excitation. In contrast to PDI excitation, this excited state in 1-3 is 0.09 eV lower than the excitation of the isolated SNS molecule. Moreover, the SNS excitation in 1-3 consists of mainly two transitions (both with weight of around 0.5): the HOFO-LUFO transition on the SNS fragment and a transition from the HOFO on the SNS fragment to the LUFO on the Phn fragment. The subtle red-shift of about 6 nm in the calculated energy

of the SNS excitation in 1-3 with respect to the isolated SNS molecule cannot be clearly observed in the experimental absorbance spectra.

The change in charge distribution upon excitation to the second allowed excited state is shown in Fig.2.7. The difference of multipole derived atomic charges [41] in the excited state with respect to the ground-state were summed for the donor, acceptor, and the individual phenyl units. A clear charge transfer character with approximately uniform charge delocalisation over SNS and Phnis observed for 1-3.

The degree of bridge population decreases only slightly with increasing number of phenyl units. The charge transfer state extends on the PDI for 1. However, the population on the PDI is negligible for 2 and 3. This can explain the discrepancy observed experimentally between the absorbance spectra of 1 and of 2-3 between 300 and 400 nm in Fig.2.2. The finding that the charge is initially evenly distributed over the SNS and the entire Phn provides an intuitive explanation for the observed

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cal-2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 charge distribution SNS Ph1 Ph2 Ph3 PDI 1 2 3

Figure 2.7: Charge distribution over the SNS, the individual phenyl units, and the PDI of the excited state that corresponds to excitation of the SNS unit as compared to the ground-state for

1-3.

culations show that the real through-space distance between the radical ion pairs needs to be redefined. More importantly, the electron transfer process cannot be described by the superexchange mechanism as the electron transfer is not mediated by the bridge but originates from it to some extent.

The substantial charge transfer character for SNS excitation was not expected, espe-cially not for 1 where the estimated electron injection barrier is almost 2 eV. However as demonstrated earlier by Senthilkumar et al. [42], fragment energies are strongly affected by their local environment. Our calculations show that in the present case the energies of the LUFO of Phn shift down by approximately 1 eV. Therefore, the

energy difference between the LUFO of Phnand the LUFO of SNS decreases, which

gives rise to the observed delocalisation of the SNS excitation. Such a modification of site energies is not considered by common approaches that might consequently miss the initial state delocalisation that has a large effect on charge transfer. The effect of initial delocalisation on the charge transfer dynamics has been previously discussed by Skourtis and Nitzan [43]. The present results experimentally confirm their theoretical prediction.

2.3. Conclusions

We have shown that hole transfer through the widely studied p-oligophenylene bridges occurs via the superexchange mechanism of hole tunnelling for n≤ 3 conform with widespread literature [23,25,36]. Electron transfer through the same bridges on the contrary exhibits barely any distance dependence, despite the equally high injection barriers. This is inconsistent with a tunnelling process. We attribute this behaviour to a modification of the electronic structure of the bridge induced by the covalent bonding to the donor and acceptor moieties. As a consequence, the bridge energy levels shift down in energy, whereby the LUFO is most strongly affected. The shift of the LUFO diminishes the electron injection barrier; the shift of the HOFO increases the hole injection barrier. Our results thus disclose the failure of

Mechanism and Dynamics of Charge Transfer in Donor-Bridge-Acceptor Systems

Mechanism and Dynamics of Charge Transfer

in Donor-Bridge-Acceptor Systems

Mechanism and Dynamics of Charge Transfer

in Donor-Bridge-Acceptor Systems

Proefschrift

Natalie GORCZAK-VOS

Contents

1

Donor-bridge-acceptor molecules as model

systems to study photoinduced charge

transfer

1

1

1.1.

Basic theory of non-adiabatic electron and hole transfer

D

onor

Bridge

Acceptor

Donor

Bridge

Acceptor

E

(a)

(b)

1

q

E

D

-B-A

D

-B-A

-q

q

q

λ

ΔG

1

1.1.1.

Franck-Condon factor

1.1.2.

Effective electronic coupling

1

1

1.2.

Controlling charge transfer by quantum interference

1

-V

V

-V

-V

-V

V

E

E

E

-E

-E

linear

cross

(a)

(b)

1

1.3.

Outline of the thesis

1

1

References

1

1

1

1

2

Different mechanisms for hole and electron

transfer along identical molecular bridges:

The importance of the initial state

delocalisation

2

2.1.