Dynamical Simulation of Electron Transfer Processes in Alkanethiolate

Article pubs.acs.org/JPCC

Dynamical Simulation of Electron Transfer Processes in Alkanethiolate Self-Assembled Monolayers at the Au(111) Surface Veronika Prucker,† Oscar Rubio-Pons,† Michel Bockstedte,‡ Haobin Wang,§ Pedro B. Coto,*,† and Michael Thoss*,†,‡ †

Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien (ICMM), Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7/B2 91058, Erlangen, Germany ‡ Lehrstuhl für Theoretische Festkörperphysik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7/B2 91058, Erlangen, Germany § Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003, United States S Supporting Information *

ABSTRACT: Electron transfer is investigated in a series of self-assembled monolayers (SAMs) consisting of nitrile-substituted short chain alkanethiolate molecules adsorbed at the Au(111) surface. Using first-principles methods and a model electron transfer Hamiltonian, we analyze the main factors controlling, at the molecular level, the electron injection times from donor states localized at the tail group of the SAM into the Au(111) substrate. We show that the donor−acceptor electronic couplings depend significantly on the orbital symmetry of the donor state and the length of the aliphatic spacer chain of the SAM. The dependence on the donor state symmetry and on the molecular structure of the linker can be used to control the electron injection times even in situations where the energy separation between the donor states is smaller than their width.

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INTRODUCTION

Charge transfer or transport is an ubiquitous phenomenon in many processes in physics, chemistry, biology and technology.1−3 Examples range from intramolecular charge transfer in donor−acceptor complexes in solution4−12 over electron transfer in sensory proteins or photosynthesis13 to charge transport processes in solar cells.14,15 Among the variety of electron transfer (ET) processes, heterogeneous ET in molecular systems at semiconductor or metal surfaces has been of great interest recently. Important applications of this fundamental process include photonic energy conversion in dye-sensitized solar cells, in which photoexcitation triggers the injection of an electron from an excited electronic state of a dye molecule into the conduction band of a semiconductor,14−18 or charge transport in nanoscale molecular junctions.19−28 In this work, we consider the related process of heterogeneous ET in self-assembled monolayers (SAMs) of organic molecules at metal surfaces. The understanding of ET at the molecule− metal interface is a prerequisite for the development of nanoscale molecular devices.29 From the molecular structure point of view, one of the simplest SAM motifs that can be used in the study of heterogeneous ET at molecule−metal interfaces consists of (see Figure 1) (i) a tail group, which provides donor states appropriate for the charge injection process, (ii) a chain-like molecular spacer (the wire), which can exhibit different sizes, degrees of conformational flexibility (rigidity) and virtual states, © 2013 American Chemical Society

Figure 1. Alkanethiolate SAM with a CN tail group at a Au(111) surface.

and which may serve as a tool for controlling the ET process, and (iii) an anchor group (the headgroup), which binds the molecule to the substrate and modulates the donor−acceptor couplings. Using this generic architecture, there are two primary characteristics of the adsorbed molecule that affect Received: September 13, 2013 Revised: October 31, 2013 Published: November 21, 2013 25334

dx.doi.org/10.1021/jp4091848 | J. Phys. Chem. C 2013, 117, 25334−25342

The Journal of Physical Chemistry C

Article

Figure 2. Different cluster models of the nitrile-substituted alkanethiolate/Au(111) self-assembled monolayers investigated in this work.

the efficiency and the time-scale of the ET. The first is the nature of the donor state, in particular its energy and symmetry properties. The energy of the donor state affects the ET process via the alignment with the energies of acceptor states. Particularly, in the presence of nearly degenerate donor states, their symmetry may influence the electron injection process profoundly through the distinct donor−acceptor couplings.30 The second characteristic is the structure and length of the bridge. The electronic and molecular structures of the bridge offer a straightforward way to control the ET through mechanisms such as the modulation of the relative energies of the virtual states located on the bridge or facilitating constructive interference effects between different ET paths. The length of the bridge can also be used to control ET injection times, as the distance between the donor and acceptor moieties modulates the ET couplings.20,31−37 Understanding how these factors affect the dynamics and efficiency of the ET process is of fundamental importance for the rational design of new electronic devices with improved characteristics and controlled range of operation. From the theoretical perspective, modeling heterogeneous ET at molecule−substrate interfaces requires a fully quantum mechanical description both in the characterization of the electronic structure of the system and in the simulation of the electron injection dynamics. In particular, the methodology employed has to be able to simultaneously describe a usually small set of discrete states, the donor states, located in a molecular adsorbate, and a quasi-continuum set of acceptor states in the metal or semiconductor substrate. It has long been recognized that the description of the kinetics and dynamics of

ET processes may benefit from the use of charge localized diabatic states34 that provide a natural basis to interpret the ET process and to calculate the donor−acceptor ET couplings. As is well-known, the definition of diabatic states is not unique.38 In addition to general diabatization procedures,39,40 a variety of specific diabatization schemes have been devised for the description of ET processes including the Mulliken−Hush approach,6,41 the Generalized Mulliken−Hush method,42,43 or the fragment charge difference method.44 The flexibility in the definition of the diabatic basis has also been used in recent work carried out by our group,45−47 where it has been shown that a diabatization scheme inspired by the projection operator approach to resonant electron-molecule scattering48 provides charge localized states and donor−acceptor couplings that can appropriately describe the quantum dynamics of ET reactions in dye-semiconductor systems. In this contribution, we consider, specifically, ET in nitrilesubstituted alkanethiolate SAMs at the Au(111) surface depicted in Figure 2. Recent experimental works using the core-hole clock spectroscopy technique49 have analyzed in detail the time scale and the characteristics of the electron injection dynamics in these systems.30,50,51 In a recent communication considering systems with one methylene unit,30 it was shown that the donor π1* and π2* states corresponding to the two π*-like quasi-degenerate resonances of the CN chromophore exhibit different electron injection times. The origin of this difference was found to be a consequence of the specific symmetry of the donor states that determines the magnitude of the donor−acceptor ET couplings.30 In this contribution, we extend these investigations 25335



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work we use the mean-field single-electron picture. Thus, we identify the ET model Hamiltonian with the Kohn−Sham matrix and use the orbitals and orbital energies to represent the corresponding electronic states and energies within the partitioning method. We have checked that the partitioning method does not lead to erroneously localized donor and acceptor states by comparison with the experimental characterization of the donor states30 and with the Kohn−Sham orbitals obtained for smaller models. Following previous work,45,46,52 and to keep the electronic structure calculations practical from a computational point of view, we have applied the partitioning technique to cluster models built using the optimized geometries obtained in the periodic DFT calculations. The sizes of the different clusters were selected to minimize boundary effects. The electronic structure calculations for the cluster models, required to obtain the donor and acceptor energies and orbitals and the coupling terms, were performed using TURBOMOLE57 at the DFT level of theory employing the PBE functional and the defSV(P) basis set.58 The core electrons of the Au atoms were described using an ECP.59 In the first step of the procedure, a localized basis set allowing for the separation of the donor and the acceptor spaces has to be selected. In the present application, we have used the atomic orbitals employed in the DFT calculations (|ϕj⟩) for this purpose, which can straightforwardly be separated into two groups, one centered on the donor moiety, |ϕdj ⟩, and the other on the acceptor part, |ϕaj ⟩. Since it has been shown that working with orthogonal orbitals is advantageous,60 the basis set |ϕj⟩ is orthogonalized according to Löwdin’s symmetric orthogonalization method61

and present a theoretical study of the ET process in a series of nitrile-substituted alkanethiolate SAMs with different alkyl spacer chain lengths adsorbed at the Au(111) surface (see Figure 2). Specifically, we investigate the effect of the increase of the spacer chain length on the ET injection times by analyzing the impact of such a modification on two of the main factors determining the efficiency of the ET, namely, the energy and symmetry of the donor states and the donor−acceptor ET couplings.

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METHODS In this section, we briefly outline the theoretical protocol used in the simulation of heterogeneous ET processes at molecule− metal interfaces. Further details can be found in refs 45, 46, and 52 and in the Supporting Information. Molecular Structure. The geometries of the different systems investigated in this work were modeled employing density functional theory (DFT) calculations with periodic boundary conditions within the super cell approach in the low coverage limit. Specifically, the systems were optimized using slab models consisting of five layers of Au atoms (comprising 125 atoms) and the respective organic molecule. To prevent artificial interactions between successive slabs in the nonperiodic dimension, a vacuum layer with a minimum width of 20 Å was enforced. In all optimizations, the organic molecules, the Au atoms of the surface layer and the next two Au layers were relaxed. The DFT computations were carried out using the Perdew−Burke−Emzerhof (PBE) exchange-correlation functional,53 periodic boundary conditions, and the projected augmented wave method.54 A k-mesh of 10 × 10 × 1 points was generated using the Monkhorst-Pack technique,55 and an energy cutoff of 415.0 eV was used after testing (see Supporting Information for further details). These calculations were carried out using VASP.56 Electron Transfer Hamiltonian. The simulation of the ET dynamics employs a first-principles based model Hamiltonian, which is represented in a (quasi)diabatic basis of charge localized electronic states including states localized in the donor fragment (the organic adsorbate), |ψd⟩, and the quasicontinuous set of acceptor states, |ψa⟩, localized in the Au substrate. In this basis, the model ET Hamiltonian reads H=

a,d

(2)

where S is the atomic orbital overlap matrix with elements Sij = ⟨ϕi|ϕj⟩. In this way we ensure that the transformed orthogonal orbitals |ϕ̃ i⟩ are the closest in a least-squares sense to the original nonorthogonal orbitals, thus preserving the localization of the basis and therefore keeping the donor−acceptor separation. In the next step, the matrix S−1/2 is used to transform the Kohn−Sham matrix F obtained from the DFT calculations to the new orthogonal basis. The transformed Kohn−Sham matrix F̃, given by

a

∑ (|ψd⟩Vda⟨ψa| + |ψa⟩Vad⟨ψd|)

∑ (S−1/2)ji |ϕj⟩ j

∑ |ψd⟩ϵd⟨ψd| + ∑ |ψa⟩ϵa⟨ψa| d

+

|ϕi⟩̃ =

(1)

where ϵd and ϵa are the energies of the donor and acceptor states involved in the ET process, respectively, and the offdiagonal elements, Vad, are the donor−acceptor coupling matrix elements. Below we detail how these parameters are obtained. Determination of the Electronic Energies and Donor− Acceptor Couplings. The parameters used in the ET Hamiltonian in eq 1 have been determined using a partitioning method. The details of this method have been discussed elsewhere.45,46,56 Here we mention only the most important characteristics. The donor and acceptor electronic states used in (eq 1) are constructed following a procedure consisting of three steps: (i) a partitioning of the Hilbert space associated to the problem into donor and acceptor subspaces using a localized basis, (ii) a partitioning of the Hamiltonian according to the donor−acceptor separation, and (iii) a separate diagonalization of the donor and acceptor blocks of the Hamiltonian. In this

F ̃ = S −1/2FS −1/2

(3)

has a structure that reflects the partitioning of the system into donor and acceptor moieties ⎛ F̃ F̃ ⎞ dd da ⎟ F ̃ = ⎜⎜ ⎟ ̃ ̃ F F ⎝ ad aa ⎠

(4)

The last step of the partitioning method is the separate diagonalization of the donor F̃dd and acceptor F̃aa blocks and the transformation of the off-diagonal F̃ad elements to the new basis defined in terms of the eigenstates of the F̃ dd and F̃ aa blocks. After this transformation, the Kohn−Sham matrix has the structure 25336



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RESULTS AND DISCUSSION The methodology discussed in the previous section has been applied to the simulation of the electron injection dynamics in a series of nitrile-substituted alkanethiolate SAM models (C2, C3, C4, and C8, see Figure 2) characterized by having aliphatic spacers of different chain lengths (−(CH2)2−, −(CH2)3−, −(CH2)4−, and −(CH2)8−, respectively) adsorbed at the Au(111) surface. In particular, we have considered the injection dynamics from the donor π*1 and π*2 states (see Figure 3) in The diagonal elements of this matrix are the energies of the donor (d) and acceptor (a) states while the off-diagonal block elements are the electronic couplings between the different donor and acceptor states. The eigenvectors of the diagonal blocks represent molecular orbitals localized in the donor (|ϕ̃ d⟩) and acceptor (|ϕ̃ a⟩) moieties, respectively. Within this mean-field approach, the donor (|ψd⟩) and acceptor (|ψa⟩) states of the ET Hamiltonian in eq 1 are identified with these localized orbitals (|ϕ̃ d⟩) and (|ϕ̃ a⟩), respectively, and the corresponding energies ϵd, ϵa and coupling matrix elements are given by the diagonal and nondiagonal block elements of the Kohn−Sham matrix F̅.45 Following previous work,45 we have also investigated the effect that the extended nature of the Au surface has in the donor−acceptor interaction using a simple model inspired by the surface Green’s function approach.62 In this model, the selfenergy (which accounts for the effects of the part of the infinite surface not included in the cluster models) is approximated by a complex absorbing potential (CAP,63 see below). In this formulation, the interaction between a donor state |ψd⟩ and the set of acceptor states is fully characterized by the continuous function Γ(ϵ) = 2π ∑ |Vda|2 δ(ϵ − ϵa)

(6)

a

known as the energy-dependent decay width that depends on the density of acceptor states and the strength of the donor− acceptor couplings (see ref 45 for further details). Dynamics. The dynamics of the electron transfer process is described by the time-dependent population of a selected donor state |ψd⟩, given by Pd(t ) = |⟨ψd|e−iHt |ψd⟩|2

(7)

Thereby all donor and acceptor states with energies above the Fermi energy are considered. To account for the extended nature of the Au substrate in the dynamical simulations, and prevent artificial reflections due to boundary (finite-size) effects, we have employed a CAP in the simulations. Specifically the following CAP was added to the Hamiltonian in eq 1 ⎧−iα(R − 5)δ if VCAP(R ) = ⎨ ⎩0 if ⎪

⎪

Figure 3. Orbitals representing the π*-donor states obtained with the partitioning procedure for the different systems investigated in this work (from top to bottom, C2, C3, C4, and C8, left π*1 and right π*2 donor state, respectively).

R > 5 bohr R ≤ 5 bohr

(8)

these systems. These states provide a model of the two π* resonances of the CN group that have been selectively monitored using core-hole clock spectroscopy techniques recently.30,50,51 Characterization of the Systems and Donor−Acceptor Separation. We first discuss the geometrical and electronic structure of the systems. The geometry of the different organic molecules adsorbed at the Au(111) surface was optimized in

where R is the distance between a general point and the sulfur atom and α and δ are constants with values −1.0 × 10−7 hartree/bohr4 and 4, respectively, that were obtained after detailed test calculations. With these parameters, the CAP increases gradually in the Au cluster creating a region where the outgoing wave packet is absorbed efficiently without causing a significant change of the results at short time. 25337



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Figure 4. Energy level schemes of the systems investigated. Shown are from left to right the energy levels of the isolated molecule, the donor states (localized on the molecule), the acceptor states (Au(111) surface), and the overall molecule−Au complexes for the different SAMs models investigated in this work. The blue line and the red line depict the π1* and π2* donor states, respectively.

Figure 5. |Vda| (vertical bars) values and Γ(ϵ) function (continuous blue line) for the π*1 donor state in all the systems analyzed (from left to right, top C2 and C3, bottom C4 and C8). The red line shows the energy of the π1* state.

the low coverage limit. The most stable adsorption geometry was found to be a fcc bridge-like configuration with the molecules tilted against the surface normal, in agreement with previous results found for similar systems.64 The relative orientation of the CN group against the surface normal depends on the number of methylene units in the spacer chain. Specifically, for the SAMs with spacers containing an even

number of methylene units, the values ranged from 68.8° in C4, over 70.7° in C2, to 73.6° in C8 whereas in the case of C3, the only system having an odd number of methylene units, the CN group was found to be nearly parallel to the surface normal with a tilting angle of 10.3° (see Figure 2). Figure 4 shows the energy levels of the molecular orbitals of the overall molecule−Au complex as well as the energies of the 25338



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Figure 6. |Vda| (vertical bars) values and Γ(ϵ) function (continuous blue line) for the π2* donor state in all the systems analyzed (from left to right, top C2 and C3, bottom C4 and C8). The red line shows the energy of the π*2 state.

states in an energy window close to the donor state energy are key aspects for an efficient ET. For the systems investigated in this work, which all involve metal substrates with a smooth density of states, the coupling of the donor state to the acceptor states is the decisive factor. The results in Figures 5 and 6 show that the modulus of the donor−acceptor couplings |Vda| decreases with the length of the aliphatic chain (note the different scales of the |Vda| and Γ(ϵ) axes), consistent with the change of the localization of the donor states. An exception from this trend is the system C3, where the π2* donor state has values of |Vda| very close in magnitude to those of C2. It is also noticed that, for all systems investigated, the values of the donor−acceptor couplings of the π1* donor state are systematically larger than those obtained for the π2* state in the range of energies of interest. This can again be understood in terms of the degree of localization of the respective states. While the π*2 states always show a strong localization in the CN moiety, the π1* states have a more delocalized character (in particular for C2 and C3) with density contributions at the aliphatic linker and at the headgroup (sulfur atom), therefore resulting in larger couplings to the substrate. Electron Transfer Dynamics. We finally consider the ET dynamics in the different systems. Figure 7 shows the time evolution of the population of the initially prepared π*1 donor state for the C2, C3, and C4 systems. The decay of the population reflects the injection of the electron from the donor state localized on the molecule into the metal substrate. The results exhibit an ultrafast femtosecond ET in all systems with injection times that increase with the length of the aliphatic chain (τ1/2 = 1.0 fs (C2), τ1/2 = 2.1 fs (C3) and τ1/2 = 2.2 fs (C4)). In the specific case of C8, the electron injection time scale is too long to be appropriately described by the CAPmethod employed for the simulations. However, an educated guess based on our model indicates that the electron injection in C8 takes place on a picosecond time scale or even longer. The trend of the ET times is a consequence of the values of the

donor and acceptor orbitals as obtained using the partitioning method for the different systems investigated in this work. For comparison, also the energies of the molecular orbitals of the isolated molecules are depicted. For all the systems, the energy levels of the overall complex and the acceptor states exhibit a dense level structure, thus confirming a sufficient size of the cluster models used. The energies of the two π* donor states are highlighted in red and blue in Figure 4. The corresponding orbitals are depicted in Figure 3. These donor states can be associated with the two lowest unoccupied orbitals of the isolated molecule, and have both π* character. They exhibit, however, a different characteristic. While the π*2 state is, for all systems investigated, completely localized at the CN group, the π1* state also has contributions at the alkyl bridge. These contributions decrease for longer alkyl chains, pointing to a decrease of the hyperconjugative mixing of the π*1 molecular orbitals with the σ orbitals of the bridge. This is a consequence of the different symmetry of the CN π* orbitals that determines the extent of their mixing with the σ skeleton of the alkyl spacer. The different localization of the states causes also a different characteristics of the energy levels. The energy level of the π2* donor state is for all systems very similar to that of its molecular orbital counterpart in the isolated molecule. The trend obtained for the π*1 donor state, on the other hand, is more complex and depends on the length of the alkyl bridge. For the systems with shorter bridge lengths (C2 and C3), the π1* state energy shows a moderate blue shift compared to that of the corresponding molecular orbital in the isolated molecule. This energy shift gets smaller for C4 and is virtually negligible for the longest chain length system, C8. This behavior reflects the degree of localization of the π1* donor state at the CN group. Donor−Acceptor Couplings. Figures 5 and 6 depict the donor−acceptor coupling matrix element (see eq 5) obtained for the π1* and π2* donor states, respectively. The magnitude of the couplings together with the density of available acceptor 25339



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negligible contributions at the aliphatic bridge or the sulfur atom (see Figure 3). This leads to smaller values of the |Vda| couplings (see Figures 5 and 6) which ultimately results in slower electron injection dynamics. The length dependence of ET rates in aliphatic chains is often analyzed in terms of an exponential model, ∼ e−βn, where n is some parameter related to the donor−acceptor distance, typically the linker chain length or the number of methylene units or C−C σ bonds in the aliphatic chain.66 From the results for the injection times, we estimate a damping factor β of 0.94 per methylene group (0.85 Å−1) in good agreement with the results obtained by Kao et al.51 C3 departs from this trend, which may indicate that the binding pattern of the experimental sample could be, as already pointed out by the authors,51 different from the “standard” thiolate-type bond used in this work. Furthermore, the π1* donor state does not follow the exponential model either, a consequence of the delocalized character of this state that has significant contributions at the aliphatic linker and sulfur atom. While the trend of ET times obtained here agrees well with the available experimental data, the theoretical results predict, in general, somewhat faster injection times.51 This discrepancy is presumably related to the limitations of the model used, which does not account for the possible effects that temperature, the existence of defects in the Au(111) surface or electronic-vibrational coupling may have on the ET process. In particular, it is expected that the inclusion of the latter in the ET Hamiltonian will result in a somewhat slower ET rate for those situations where electron injection times are comparable to the characteristic vibrational times of the system.45 The study of this effect will be the subject of future work.

Figure 7. Population dynamics of the π1* donor state for C2 (red), C3 (green), and C4 (blue).

donor−acceptor couplings obtained for the π1* state that, as discussed above, decrease with increasing length of the aliphatic chain (see Figure 5). The stronger localization of the π*1 state in the CN group for the systems with longer alkyl chains implies a less pronounced hyperconjugative mixing of the π1* molecular orbitals with the σ orbitals of the bridge. This, together with the increase in the spatial separation between the donor and acceptor moieties, lead to a decrease in the magnitude of the donor−acceptor couplings and therefore to slower electron injection dynamics, as both the through-space and the throughbond mechanisms are simultaneously affected.37 The ET dynamics for the π2* donor state depicted in Figure 8 follow the same trend but are significantly slower (τ1/2 = 12.3 fs

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CONCLUSIONS We have investigated ET dynamics in a series of SAMs consisting of nitrile-substituted alkanethiolate molecules of different length adsorbed at the Au(111) surface. The ET dynamics has been simulated employing an ET model Hamiltonian, which was determined by first-principles DFT electronic structure calculations. Motivated by recent experiments, we have specifically focused on the process of electron injection from π* donor states localized at the terminal CN group of the molecule into the Au substrate. The results show that the electron injection dynamics depends sensitively on the orbital symmetry of the specific π* donor state. This finding confirms and extends previous experimental and theoretical results for short chain alkanethiolate systems30,51 and suggests that a rational control of the dynamics of the ET process is possible even if the donor states are very close in energy. Furthermore, we have also investigated the dependence of the ET dynamics on the length of the aliphatic spacer chain. The results show that the ET times increase from a few femtoseconds for the shortest alkyl chain (C2) to picoseconds for the system with the longest alkyl chain investigated (C8). This characteristic dependence of the ET times can be explained in terms of the extension of the donor states onto the aliphatic backbone and the headgroup. The degree of delocalization of the donor state affects the magnitude of the donor−acceptor couplings and therefore the ET rate. The greater the spatial localization of the donor state in the CN moiety and the larger the distance separation between donor and acceptor sites, the smaller the magnitude of the donor−acceptor couplings and the slower the electron injection.

Figure 8. Population dynamics of the π*2 donor state for C2 (red), C3 (green), and C4 (blue).

(C2),65 τ1/2 = 15.1 fs (C3), τ1/2 = 80.5 fs (C4), and C8 expected to have again an electron injection time at least in the picosecond time-scale). The pronounced difference of the electron injection times of the two π*-orbitals, which was also found recently in experimental studies on C2 using polarization sensitive core−hole clock spectroscopy, is a consequence of intrinsic, symmetry-related differences between both types of donor states.30 Contrary to the π1* state, which due to the symmetry-allowed mixing of the CN π* orbital with the σ skeleton shows a spatial extension with contributions at the sulfur atom and at the aliphatic chain of the adsorbed molecule, the π2* donor state is well localized in the CN group with 25340



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The results reported in this work are in qualitative agreement with the experimental data available, recovering the basic physical mechanisms underlying the charge transfer process. Further improvements may be achieved by an extended model, which includes thermal effects and the influence of vibronic coupling. Work along these lines is in progress.

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ASSOCIATED CONTENT

S Supporting Information *

Further details on the electronic structure calculations and injection dynamics without CAPs for the different systems investigated. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank P. Feulner and M. Nest for numerous interesting discussions. M.T. thanks the Chemistry Department at the University of California, Berkeley for a visiting Pitzer Professorship and W. H. Miller (UC Berkeley) and J. Neaton (Molecular Foundry, LBNL) for their hospitality. P.B.C. thanks L. M. Frutos for his hospitality during his stay at the Department of Physical Chemistry of the University of Alcalá. Generous allocation of computing time at the computing centres in Erlangen (RRZE), Munich (LRZ), and Jülich (JSC) is greatly acknowledged. This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through the Clusters of Excellence “Engineering of Advanced Materials” (EAM) and “Munich Center of Advanced Photonics” (MAP) as well as projects CTQ2009-07120, CTQ2012-36966 (MICINN), and UAH2011/EXP-041 (UAH).

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Dynamical Simulation of Electron Transfer Processes in Alkanethiolate

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