A Surface Hopping Molecular Dynamics Study - ACS Publications

Article pubs.acs.org/JPCA

The Photoinduced E → Z Isomerization of Bisazobenzenes: A Surface Hopping Molecular Dynamics Study Gereon Floß and Peter Saalfrank* Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam, Germany S Supporting Information *

ABSTRACT: The photoinduced E → Z isomerization of azobenzene is a prototypical example of molecular switching. On the way toward rigid molecular rods such as those for opto-mechanical applications, multiazobenzene structures have been suggested in which several switching units are linked together within the same molecule (Bléger et al., J. Phys. Chem. B 2011, 115, 9930−9940). Large differences in the switching efficiency of multiazobenzenes have been observed, depending on whether the switching units are electronically decoupled or not. In this paper we study, on a time-resolved molecular level, the E→ Z isomerization of the simplest multiazobenzene, bisazobenzene (BAB). Two isomers (ortho- and paraBAB), differing only in the connectivity of two azo groups on a shared phenyl ring will be considered.To do so, nonadiabatic semiclassical dynamics after photoexcitation of the isomers are studied by employing an “on-the-fly”, fewest switches surface hopping approach. States and couplings are calculated by Configuration Interaction (CI) based on a semiempirical (AM1) Hamiltonian (Persico and coworkers, Chem. Eur. J. 2004, 10, 2327−2341). In the case of para-BAB, computed quantum yields for photoswitching are drastically reduced compared to pristine azobenzene, due to electronic coupling of both switching units. A reason for this (apart from altered absorption spectra and reduced photochromicity) is the drastically reduced lifetimes of electronically excited states which are transiently populated. In contrast for meta-connected species, electronic subsystems are largely decoupled, and computed quantum yields are slightly higher than that for pristine azobenzene because of new isomerization channels. In this case we can also distinguish between single- and double-switch events and we find a cooperative effect: The isomerization of a single azo group is facilitated if the other azo group is already in the Z-configuration.

I. INTRODUCTION Azobenzenes are versatile molecular switches, showing bistable behavior. The switching between trans (E) and cis (Z) forms can be induced optically,1−5 or by an electric current.6,7 The metastable Z-state has a lifetime at room temperature of several days, before thermally reacting back to the stable E form.8 Both states have distinct optical spectra, different electrical dipole moments, nonlinear properties, and molecular shape and size. Because of this latter property azobenzene or its derivatives can be used to induce motion in macroscopic samples upon irradiation.9,10 En route to optimizing organic materials for optomechanical applications, multiple individual azo units can and have been combined in more complex molecular structures. Examples are photoresponsive polymers and surfaces, or multiazobenzenes with more than one switching unit in one and the same molecule.10 In this context it is to be noted that the ability of a functional unit to switch depends on the presence or absence of neighboring switching units. An example is the possible suppression of switching in self-assembled monolayers (SAMs) of molecules that contain azo groups on surfaces, due to either steric hindrance or excitonic coupling.3−5,11,12 For molecular multiazobenzenes also intramolecular effects, for example, the influence of a second switching unit on a first one, © 2015 American Chemical Society

must be accounted. In what follows, we will study such effects for a simple bisazobenzene molecule. Different types of multiazobenzenes of varying complexity have been synthesized.10,13−23 The mentioned bisazobenzenes are the simplest variant, with just two switching units, that is, azo groups. These can be either attached to the same phenyl ring or to different ones.20 Depending on whether the two switching units “communicate” electronically or not, this has a strong influence on the optical spectra, photochromicity, and in the end, also on the switchability of the molecules. If both units are decoupled, this is beneficial for quantitative photoswitching.20 For instance, in linear bisazobenzenes with two azo units connected by a biphenyl bridge, decoupling of the individual π-systems for each switch can be realized by sterically forcing one of the two benzene rings of the biphenyl bridge to rotate relative to the other, thus interrupting π-conjugation. In the case of bisazobenzenes with azo groups attached to the same, central benzene ring, decoupling is possible by attaching the NN-units in the meta-position. In contrast, for para- (or ortho-) positioning, the π-systems are conjugated. As a Received: March 27, 2015 Revised: April 30, 2015 Published: April 30, 2015 5026

DOI: 10.1021/acs.jpca.5b02933 J. Phys. Chem. A 2015, 119, 5026−5037

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The Journal of Physical Chemistry A

Figure 1. (AM1/FOCI-Optimized) structures of (E,E)-para-bisazobenzene (left) and (E,E)-meta-bisazobenzene (right). On the left also the CNNbond angles αij (i,j = 1,2) and CNNC dihedrals ωi (=1,2) are shown, with an obvious rotation.

consequence, in ref 20 it has been demonstrated that a parabisazobenzene similar to the one shown in Figure 1 (left) is a much less quantitative switch than its meta counterpart, cf. Figure 1 (right). For instance, para-bisazobenzene (with four tert-butyl groups on the outer rings in addition), gave only 3% (Z,Z)-composition for the photostationary state (PSS) upon irradiation with UV light in cyclohexane, while for a decoupled (albeit biphenyl-connected) bisazobenzene up to 95% (Z,Z)form was obtained. In another experiment using BABs with yet another substitution at the outer rings, the fraction of Z-azo units in the PSS was determined as 32% for para- and 79% for meta-BAB.13 Here and in what follows, the most stable configuration is denoted as (E,E), where both CNNC dihedral angles are about 180°. After excitation, (Z,E), (E,Z), and (Z,Z) species can be formed. Reference 20 also demonstrated by experiment and stationary quantum chemistry that the performance loss in conjugated bisazobenzenes is accompanied by strongly overlapping absorption spectra for E- and Z-subunits, that is, a loss of photochromicity. It is not clear, however, if this is the only reason for less efficient switching, and there is also no real microscopic explanation for it. A deeper insight can be provided by (nonadiabatic) molecular dynamics. The latter will not only unravel mechanistic details of switching, but also deliver excited state lifetimes and isomerization yields. It is the purpose of the present manuscript to shed light on the switching dynamics of bisazobenzenes after their photoexcitation, for the model compounds para-bisazobenzene and meta-bisazobenzene as shown in Figure 1. To this end we use a methodology already proven successful for azobenzenes, namely trajectory surface hopping (TSH) with CI based on the AM1 Hamiltonian as suggested elsewhere.24 This method has been used for isolated azobenzene24−26 and azobenzene in solvents,27,28 for substituted29 and bridged azobenzenes,30,31 as well as for a substituted azobenzene on geometry-constraining substrates.32 Related work is by Thiel and co-workers who use another semiempirical Hamiltonian, OM2 instead of AM1, in combination with CI for TSH simulations of azobenzene.33−37 Further, Marx and co-workers

adopted a Car−Parrinello approach for TSH studies of the switching dynamics of azobenzene in solution,38 in bulk material,39,40 and bridged azobenzene.41,42 TSH studies of azobenzenes based on the CAS-SCF (complete active space self consistent field) method are also known.43,44 The paper is organized as follows. In the next section II, we will recall the TSH approach in combination with the AM1-CI method. Section III describes our results, namely (i) UV−vis spectra of bisazobenzenes, (ii) quantum yields and excited state lifetimes obtained from TSH, as well as some technical details of the dynamical calculations. We end with a summary and outlook in section IV

II. METHOD A. General Procedure. To simulate the E → Z switching dynamics of para- and meta-bisazobenzenes as well as general properties of educts and products, we perform the following steps: (1) Optimize the geometries of the (E,E)-, (E,Z)-, and (Z,Z)-configurations of both isomers and compute their UV− vis absorption spectra. (2) Sample the phase space around the (E,E)- and (E,Z)-minima to define initial conditions for dynamics. (3) Start trajectories on excited states that eventually lead to E → Z switching. For all three steps we employ the AM1/CI method to compute the electronic structure and excitation energies. Step (3) necessitates a surface hopping algorithm and a method to compute nonadiabatic couplings. B. Floating Occupation Numbers Configuration Interaction (FOCI). In this work we employ the Floating Occupation Numbers Configuration Interaction method (FOCI) as described in ref 45. The method is based on the AM1 Hamiltonian46 with semiempirical parameters given in ref 24. The general procedure is well described elsewhere, so here we restrict some system-specific details. In the method, an “open orbital space” with floating occupation numbers is used. For the bisazobenzenes, we define an active space consisting of π- and n-type orbitals (22 electrons in 21 orbitals) as open orbitals. Optimal molecular orbitals and ground state energies are computed by a Self Consistent Field (SCF) procedure with occupation numbers of the open orbitals 5027


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Table 1. Equilibrium Geometries of Azobenzene, meta-Bisazobenzene, and para-Bisazobenzene, Determined with the AM1/ FOCI Methoda system

meta-BAB

AB

para-BAB

configuration

E

Z

(E,E)

(E,Z)

(Z,Z)

(E,E)

(E,Z)

(Z,Z)

ω1/deg α11/deg α12/deg ω2/deg α21/deg α22/deg ΔE/eV

180.0 122.1 122.1

0.4 133.8 132.2

180.0 122.5 122.5 180.0 122.5 122.6 0.00

180.0 122.6 122.4 5.0 133.8 133.3 0.50

3.5 132.5 133.7 0.7 134.1 132.7 1.16

180.0 122.7 122.4 180.0 122.5 122.7 0.00

179.8 122.5 122.6 0.1 134.7 132.4 0.64

1.1 132.2 135.3 10.0 123.9 141.8 1.68

0.00

0.65

a

Shown are values of the angles defined in Figure 1 for different configurations of the azo groups. Energies relative to the respective most stable BAB or AB molecule are also given.

floating between 0 and 2 with a probability resembling an error function. This way virtual orbitals are optimized to some extent. To get excited states, CI calculations are performed. In the CI matrix we include all (including multiple) excitations in a smaller, complete active space (CAS), that is, CAS-CI, plus the remaining single excitations within the space of the open orbitals. Here we use eight electrons in six orbitals for the CAS, corresponding to (a subset of) orbitals localized at the azo groups. The choice of the active space is further motivated by comparing excitation energies calculated with different spaces (see below): increasing the CAS beyond (8,6) did not significantly affect the spectra. In contrast, a larger (and computationally more costly) space for the “open orbitals” for which all single excitations are included did affect the excitation energies somewhat. The space chosen here, sometimes called (22,21)/(8,6), is a compromise between accurate excitation energies and the need to compute many trajectories for good statistics. In total, the CI matrix is of size 429 × 429. Singlet and higher multiplet states (triplets, quintets, etc.) are calculated; however, only the singlet states are used below for dynamics and spectra. In passing we note that the semiempirical parameters for the AM1 method are optimized for single azobenzenes.24 They may perform better for meta-BAB than for para-BAB with its strongly coupled extended π system. C. Trajectory Surface Hopping (TSH). In the TSH method the nuclei move on only one of N adiabatic potential energy surfaces (PES) at a time, according to Newton or Langevin-type equations of motion. The PES, forces, and nonadiabatic coupling vectors are calculated along the trajectory “on the fly”. Here we consider the lowest 15 (N = 15) singlet states Sn (n = 0,2,...,14), that is, no triplets or other multiplets are included. Nonadiabatic transitions between singlet states Sn and Sk are simulated by stochastic hops between the PESs, in this case, generated according to Tully’s fewest switches algorithm.47 At each time step a hopping probability is computed as Wn → k =

Bnk A n*A n

transforming back to the adiabatic representation, the change and flux in population in eq 1 can be calculated. One then draws a random number r ∈ [0,1] and a hop from n to k is k made if ∑ik−1 = 0 Wn→i < r < ∑i = 0 Wn→i. Although hops generally occur near state crossings (where couplings are large), there may still be a non-negligible energy gap between Vn(R̲ 0) and Vk(R̲ 0) for hops occurring at geometry R̲ 0. In this case this energy is added/subtracted to/from the nuclear kinetic energy by adjusting the momentum vector parallel to the coupling vector, d̲nk = ⟨ψn|∇̲ R|ψk⟩. Observables were obtained by averaging over a set of trajectories (see below).

III. RESULTS A. Stable Structures. Using the AM1/FOCI method, we computed optimal geometries (in the ground state S0) for azobenzene (AB) and meta- and para-bisazobenzene (BAB), either switched or not. The angles describing the azo groups are listed in Table 1. (The pictorial representation of the (E,E) forms of para- and meta-BAB is shown in Figure 1.) From the table we note that all E-configured azo groups are completely flat, showing dihedrals of 180°. Also the bond angles αij, (i,j = 1,2) of all E-forms are in a narrow range of 122.1° to 122.7°, with E-azobenzene at the lower and para-bisazobenzene at the higher end. For Z-azobenzene we have a dihedral ω angle of 0.4°, while the Z-configured azo group of meta-BAB is ω2 = 5° and 0.1° for para-BAB. If both azo groups are in Zconfiguration, ω1 and ω2 are quite different, one at about 1° and one at 3.5° to 10°. The α angles of Z-configured azo groups are again in a narrow range, from 132.2° to 134.7°, with the exception of para-BAB with α22 = 141.8°. All values for the E-configurations are in good agreement with results obtained with f irst-principles (mostly B3LYP/6311G*) methods in our earlier work, ref 20. There is also no pronounced difference between azobenzene and bisazobenzene, even if the other azo group is in the Z-configuration. In “pure” Z-compounds, however, there are some differences between AM1/FOCI and first principle values: Generally with B3LYP/ 6-311G* the bond angles αij are about 8° smaller and ωi are the same amount greater, compared to AM1/FOCI. The overall small differences to first-principles results in geometries that are expected to have no big effect on dynamics, because we start from the E-forms and also average over different initial conditions reflecting the vibrating molecules. In Table 1, we also list energy differences between the various species, all with respect to the most stable form (which is all E). Switching an E-unit to Z costs an energy of around 0.65 eV in AB. This compares well to B3LYP/6-31+G* (0.69 eV) or MP2/6-311G** (0.80 eV, both values from ref 48).

(1)

where Bnk is the population growth in Sk due to flux from state Sn within the time step Δt, and An is the CI-coefficient in the CI expansion of the electronic wave function, Ψ = ∑i Ai ψi (ψi are the eigenstates of the CI matrix). To calculate the flux, a “local diabatization” is used (see ref 45) for details. In this representation the electronic wave function can safely be linearly interpolated in time, even near state crossings. After 5028


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respect to N−N. The splitting between the two orbitals is 8.58 eV on the AM1/FOCI level of theory, cf. Figure 2. (The LUMO − 1 (not shown) is the bonding π-orbital.) The HOMO and LUMO levels split upon the addition of a second azo group in the BABs. For both meta- and para-BAB the HOMO splits into HOMO and HOMO − 1, formally forming bonding and antibonding linear combinations of two n-orbitals, and therefore located at the azo groups. The energetic splitting is 0.06 eV in meta- and 0.19 eV in para-bisazobenzene. This splitting is comparatively small, somewhat larger for para-BAB than for meta-BAB, indicating a larger electronic coupling between the two subunits for the former. The LUMO of azobenzene (π*, antibonding) splits also in the bisazobenzenes, into LUMO and LUMO + 1 orbitals. They retain the π* character within an azo unit and are bonding (LUMO) or antibonding (LUMO + 1) linear combinations of isolated π* orbitals of individual azo units. The energetic gap between the two is 0.10 eV in meta- and 1.63 eV in para-configuration, respectively. This indicates that the interaction between isolated π* fragment orbitals is small in meta-BAB, and large in paraBAB. Quite simply, this behavior is a consequence of the fact that the LUMO (and also the HOMO) of E-AB has nodes at meta-positions, in contrast to para (and also ortho). This general pattern of pairwise split orbitals (with larger splittings for para than for meta) is repeated upward and downward in energy for most of the π orbitals. Going beyond the qualitative orbital picture, we calculate excited states by the AM1/FOCI (22,21)/(8,6) method as described above, and determine UV−vis absorption spectra from there. For this purpose, we calculate vertical excitation energies ωn (and excitation wavelengths λn) out of minimum energy structures of azobenzene (E and Z), meta-BAB ((E,E), (E,Z), and (Z,Z) forms) and para-BAB ((E,E), (E,Z), and (Z,Z) forms), as well as transition dipole moments μ̲0n (and oscillator strengths f 0n = ((2meωn)/(3ℏe2))|μ0n|2) for transitions S0 → Sn. (Triplet states and states with higher multiplicity were calculated but do not show up in spectra due to vanishing transition dipole moments.) In Figure 3 we show the decadal extinction coefficient ϵ(ω) ∝ ∑n f 0n g(ω−ωn), obtained by broadening the vertical excitation energies with Gaussians g(ω − ωn) with a width of σ = 1300 cm−1 each. The spectrum of E-azobenzene shows a π−π* (HOMO − 1 → LUMO) excitation at 270 nm, followed by another π−π* (HOMO − 2 → LUMO) excitation at 250 nm. More excitations are found above 200 nm, predominantly of the two-electron type. Note that the n−π* (HOMO → LUMO) excitation is forbidden at the E-minimum; it is located at 450 nm at the present level of theory. (Note also that this corresponds to 2.76 eV, which is much smaller than the orbital energy gap of 8.58 eV, cf. Figure 2.) The n−π* peak compares well with experimental spectra (see, for example, ref 13 and ref 52) while the π−π* peak appears at somewhat smaller wavelengths than in experiments. Z-Azobenzene shows the characteristic double-peak structure with an n−π* (HOMO → LUMO) excitation at 460 nm, (weak on the scale of Figure 3) and π−π* (HOMO − 1 → LUMO) and (HOMO − 2 → LUMO) excitations slightly blue-shifted with respect to Eazobenzene. Here all peaks compare well to experimental spectra. All of these features are also in reasonable agreement with f irst-principles data (see, e.g., ref 20 and references therein). A possible exception is the small oscillator strength of the n−π* transition.

More values for energies and geometries may be found in the Supporting Information along with earlier results of semiempirical calculations,26 ab initio results48,49 and experimental values.50,51 For the BABs, the energy cost for a first E → Z switching is about the same for para-BAB, but the second switching (to (Z,Z)) is associated with a further energy increase of more than one eV. For meta-BAB, the energetic costs for the first and second switches are 0.50 and 0.66 eV, that is, both close to the value for AB. This is a first indication that for paraBAB, the two azo groups are coupled more strongly than for meta-BAB: The second group “feels” in which state the first one is, at least in the ground state. B. Orbitals, Excitations, and Absorption Spectra. We now turn to excited states of BABs playing a role during photoisomerization. The excited states can be classified, in a one-electron picture, according to the orbitals involved in the excitations. As an illustration how these orbitals change through the addition of a second azo group, relative to the azobenzene parent molecule, we show the (AM1/FOCI) frontier orbitals of E-azobenzene, (E,E)-meta-BAB and (E,E)-para-BAB in Figure 2. In azobenzene the highest occupied molecular orbital (HOMO) is the well-known nonbonding n-orbital of σsymmetry, located at the azo group, and the lowest unoccupied molecular orbital (LUMO) is the π*-orbital, antibonding with

Figure 2. Frontier orbitals of E-azobenzene (left), (E,E)-metabisazobenzene (middle), and (E,E)-meta-bisazobenzene (right), on the AM1/FOCI level of theory. The orbital energies, relative to the HOMO in each case, are as follows. E-AB: HOMO = 0.00 eV, LUMO=8.58 eV. (E,E)-meta-BAB: HOMO − 1 = −0.06 eV, HOMO = 0.00 eV, LUMO = 8.48 eV, LUMO + 1 = 8.58 eV. (E,E)-para-BAB: HOMO − 1 = −0.19 eV, HOMO = 0.00 eV, LUMO = 7.60 eV, LUMO + 1 = 9.23 eV. 5029


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Figure 3. UV−vis spectra of AB (left column), meta-BAB (middle column), and para-BAB (right column) computed with AM1/FOCI (22,21)/ (8,6). Spectra of all-E species are shown in the top row, all-Z in the bottom row, and spectra of mixed species in the middle row. The broadened spectra (Gaussian broadening, σ = 1300 cm−1) show the decadal extinction coefficient ϵ. The stick spectra refer to the oscillator strengths scaled by a factor of 50000. The lowest 100 CI states were calculated in each case, but only the singlet states (with nonvanishing transition dipole moments) are shown.

The situation for para-bisazobenzene bears similarities to the meta-form but also clear differences, because the azo groups are now more strongly coupled. (E,E)-para-BAB, like its meta counterpart, has three forbidden n−π* transitions, now at 510, 500, and 460 nm (S1−S3). At 320 nm the first π−π* transition occurs (S4), accompanied by two nonvisible transitions of mixed character. Two further π−π* transitions (only one optically allowed) follow at 270 nm, and three (again only one optically active) at 250 nm. Here we observe a strong redshift from E-azobenzene together with a change in the energetic gaps, indicating the expected large coupling of azo groups. For (Z,Z)-para-BAB, we observe a strong redshift of (three) n−π*like transitions compared to Z-azobenzene, and higher (mostly π−π*) transitions behave similar to (Z,Z)-meta-BAB. The spectrum of (E,Z)-para-BAB again shows three optically active n-π* transitions from 490 to 480 nm. The first three π−π* transitions are at 290, 270, and 250 nm, followed by a band of multiple electron transitions. This means the n-π* transitions behave as for (E,Z)-meta-BAB while the higher transitions show a completely new pattern. Also this latter fact indicates the mentioned, stronger coupling between the two azo groups in para-BAB.20 The comparison with TD-DFT and experimental data shows a good qualitative agreement, while the π−π* peaks again appear at smaller wavelengths. Also AM1/FOCI does not reproduce the strong oscillator strength of the n−π* transition of (Z,Z)-para-BAB, which is of no consequence to the dynamics, as we did not study n−π* excitations. C. Nonadiabatic Dynamics. C.1. Initial Condition Sampling. Initial conditions for the “on the fly” nonadiabatic TSH simulations are chosen such that a swarm of trajectories serves to (i) resemble the phase space distribution around a particular minimum of the ground state S0, which (ii) are then excited vertically to optically allowed excited states, Sn. Here we only consider π−π* transitions, out of E-configurations.

According to the AM1/FOCI calculations, (E,E)-metabisazobenzene exhibits three n−π* transitions, two of them at 490 nm, one at 450 nm, all of them optically forbidden. They correspond to singlet states S1−S3. Two of them (S1 and S2 at lower energies) can be characterized as one-electron transitions from the HOMO to the slightly split, LUMO and LUMO + 1 orbitals of above, respectively. The third one, S3, is of mixed orbital, two-electron character. These three low-energy n−π* states are found in most BABs to be considered in what follows. The first visible excitation (from S0 to S4) in (E,E)-meta-BAB is of the π−π* type at 280 nm, slightly red-shifted with respect to E-AB. Other π−π* transitions are found (to Sn, n > 4), some of them with vanishing oscillator strengths. The general picture is that the shape of the absorption spectrum of (E,E)-meta-BAB is very similar to the one of E-AB, with (E,E)-meta-BAB being only slightly red-shifted compared to E-AB. Inspection of absolute intensities reveals that these are about twice as large for (E,E)-meta-BAB compared to E-AB. Similarly, the absorption spectrum of (Z,Z)-meta-BAB resembles basically twice the spectrum of Z-AB. The three n−π* transitions are now visible and slightly red-shifted compared to Z-AB (two at 500 nm, one at 490 nm), followed by a series of allowed or forbidden π−π* transitions starting around 260 nm. Further, (E,Z)-meta-BAB corresponds to a spectrum being roughly the sum of the spectra of an E- and a Zazobenzene. Here we find only one visible n−π* transition (to S1, 500 nm), followed by a series of π−π* transitions starting around 270 nm. Most of the findings above (apart from low-energy states with double-excitation character), in particular the clear electronic decoupling of azo groups in meta-connected BAB is in good agreement with earlier theoretical work based on TD-DFT.20,53 An exception is again the too small wavelength of the π−π* transitions, compared to both TD-DFT and experimental findings.13 5030


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The Journal of Physical Chemistry A In the first step (thermalization), we model a thermal ensemble at T = 300 K by starting four Brownian trajectories at the respective geometric minimum, using Langevin dynamics. Here we choose a (rather arbitrary) friction coefficient of Γ = 1/0.2326 ps−1, and random forces calculated from the second fluctuation−dissipation theorem to maintain the selected temperature. The Langevin trajectories run for 13000 fs and, after discarding the first 600 fs, snapshots along these trajectories are randomly taken as possible initial states for optical excitation. In this second step (excitation), for the geometries corresponding to chosen snapshots excitation energies ωn and transition dipole moments μ̲0n to excited states are calculated by AM1/FOCI (22,12)/(8,6). We define an energy window [E1,E2] to select a wavelength (range) of the exciting light source (but also to get reasonable statistics, see below). If a snapshot exhibits an excitation energy E1 ≤ En ≤ E2, the absolute value of the corresponding ground to excited state transition dipole moment, μ0n, is compared to a reference dipole moment, μr. If μ0n ≥ μr, the corresponding snapshot will be accepted as initial condition for a trajectory starting in the electronic state Sn. (If several excited states in the selected interval fulfill this criterion, all of them are accepted as possible initial states.) The concrete values E1, E2, |μr|, and the number of resulting initial conditions are shown in Table 2. The energy

consecutive period of time of at least 10 fs, (2) both dihedral angles ω1 and ω2 are below 15° or above 165° during the 10 fs, and (3) all bond angles αij < 150° (i,j = 1,2) during the 10 fs. The individual azo groups are then considered reactive or unreactive according to the values of ωi (i = 1,2), see also section C.3. The results are compared to the E → Z switching dynamics of azobenzene, computed with the same method. 1. Azobenzene. The light-induced E → Z isomerization of azobenzene after π−π* excitation has been studied extensively.24−26,32,33 The emerging picture (neglecting the role of triplets) is that the isomerization is via a S1/S0 conical intersection, located approximately at ω = 90° with one of the αn being almost 180°. Such a structure with a linear αn is called an “invertomer”, due to the inversion of an α angle; it is a possible intermediate of the E → Z isomerization. (A linear NNC unit occurs also as a transition state in thermal isomerizations54). More specifically, the E → Z isomerization of AB, as also found in the present study (and described in some detail in ref 32), is a three-step scenario: (1) Initially, a π−π* excitation to higher-lying states Sn (n = 2−4) occurs. The ω dihedral vibrates around 180°, the two CNN angles α around 120°. From there, the trajectories start to move, undergoing frequent nonadiabatic transitions to other π−π* excited states Sn (n ≥ 1). From those states the trajectories relax to the n−π* state (S1) after a certain lifetime, τ1 (see below). (2) When on S1, the α angles assume typically larger values (around 130° or so), and the ω dihedrals becomes more movable. When on the n−π* state also a movement toward the S1/S0 conical intersection may occur, with one of the α angles now approaching 180°. The transition from S1 → S0 occurs on a time scale τ2. During this transition the E → Z switching can take place, whereby the ω angle changes to from about 180° to about 0° in a few femtoseconds. (3) Subsequent motion occurs on S0, accompanied by vibrational relaxation and settling down in the Z-well (in simulations only visible if cooling is accounted for). The ω angle vibrates around 0° and both α angles vibrate around a value slightly larger than 120°. Of course, not all excited trajectories are reactive, and often the relaxation from Sn to S1 and further to S0 is not accompanied by an E → Z isomerization. A statistical evaluation will be given below. 2. meta-Bisazobenzene. A similar analysis may now be done for BABs. The switching dynamics of meta-bisazobenzene is examplified by two single trajectories shown in Figure 4, one reactive (showing the example of a double-switch event) in the top panel, and one unreactive in the bottom panel. The figure shows all angles over time as defined in Figure 1 as colored lines (right scale). The actual electronic state of the molecule (S0 to S7) is indicated as a black line (left scale). In the reactive case (upper panel), the following phases emerge. (1) The example trajectory starts in the π−π*-excited state S6. After excitation rapid and frequent nonadiabatic transitions are observed to and from other π−π* excited states, Sn (n ≥ 4). This is due to the very small energetic gaps between those states, and similar to the situation described above for E-AB. After 310 fs the molecule changes to one of the three n−π* states (S1 to S3) for the first time, hopping back and forth between n−π* states for a short while. (2) Then, the molecule isomerizes one of the azo groups along ω 2 (which changes from 180° to 0°), while

Table 2. Parameters and Results of Initial Condition Samplinga AB trajectories E1, E2 (eV) μr (D) ω1/deg α11/deg α12/deg ω2/deg α21/deg α22/deg

meta-BAB

para-BAB

E

(E,E)

(E,Z)

(E,E)

(E,Z)

104 4.1, 5.1 5.5 174 ± 4 122 ± 3 122 ± 4

105 4.2, 5.2 12.0 181 ± 5 123 ± 3 123 ± 3 177 ± 7 123 ± 3 122 ± 3

106 4.0, 5.0 6.5 175 ± 5 123 ± 3 122 ± 3 9±6 134 ± 4 134 ± 3

107 3.4, 4.4 15.0 179 ± 6 123 ± 3 123 ± 3 180 ± 6 123 ± 3 123 ± 3

108 3.7, 4.7 9.2 176 ± 3 123 ± 3 123 ± 3 6±5 133 ± 3 134 ± 4

a

In particular, the number of started trajectories, excitation energy window [E1,E2], and reference dipole μr. The lower part shows mean plus RMSD spread of angles as defined in Figure 1.

range is chosen such that the excited states with the highest ground to excited state transition dipole moments are included. The reference dipole |μr| is somewhat arbitrary, chosen such that a statistically relevant number of trajetories (around 100) was selected for each case. As a consequence the yields to be computed below, are per excitation event. Altogether, five cases were considered as possible starting configurations, namely Eazobenzene, (E,E)- and (E,Z)-forms of meta-BAB, and (E,E)and (E,Z)-forms of para-BAB. Table 2 also shows the mean and spread (computed as Root Mean Square Deviation, RMSD) of selected angles and dihedrals (see Figure 1), resulting from thermal sampling. They generally show values near the ground state minima as indicated in Table 1. C.2. Dynamics after Excitation. As mentioned, we describe the E → Z switching of meta- and para-bisazobenzene after π−π* excitation, starting from both (E,E) and (E,Z). Trajectories run for a maximum of 5 ps. After a simulation time t > 3 ps they are aborted subject to the following conditions: (1) The molecule is on the ground state S0 for a 5031


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NNC linearization. As will be seen later, for meta-AB a good portion of all trajectories leads to isomerizations, sometimes double-isomerizations. A statistical analysis of yields (and lifetimes) will follow later. 3. para-Bisazobenzene. The situation is different for paraBAB, where the switching probabilities will be found to be lower. Nevertheless, switchings do occur. In Figure 5, we show

Figure 4. Two trajectories of meta-BAB after π−π* excitation. Shown are the angles defined in Figure 1 (colored, right scale) and the electronic state over time (black, left scale). The upper panel shows a (double-) reactive trajectory, and the bottom panel shows an unreactive trajectory.

simultaneously hopping from S1 to S0. So far, everything is analogous to E-AB. (3) A difference to E-AB is that now the meta-BAB molecule (now being (E,Z) rather than (E,E)) frequently hops back from S0 to the n−π* states and back from there again. In this second phase the vibrations along αij and ωi become “slower” (lower frequency) and “higher” (larger amplitude) and the mean αij changes from 120° to 130°. E-AB shows only infrequent backhopping from S0 to S1 and reasons for the difference between BAB and AB are not entirely clear. Apart from BAB having a different potential energy surface, a possible reason is the larger number of accessible n-π* states. (4) Since the system is frequently in one of the n−π* excited states even after the first switch, the chance for switching also the second azo unit from E to Z is given, which indeed happens after about 1200 fs in the present example. (5) Thereafter, the molecule resides in S0. The unreactive example trajectory in the bottom part of Figure 4 starts in S7, and remains on the π−π* excited-state manifold S4−S7 for about 450 fs. Then it makes a transition to the n−π* manifold S1−S3, residing there for a short while (40 fs) only before reaching the ground state, S0. As previously, also here the αij change from 120° to 130° and all vibrations increase in amplitude. There is, however, no isomerization associated with the S1 to S0 transition in this case but instead both ωi run to the transition state (i.e., values much smaller than 180°) and back to E again (with ωi ∼180°) within about 1000 fs. It should be noted that this and all other switching events observed in this work are over the invertomer, in contrast to earlier findings for the E → Z switching of AB.24 Not only can this be seen from the ω1 and ω2 angles changing from 180° to 0°, but also the respective peripheric angles α11 or α22 change abruptly to large values of 150° and larger, indicating a transient

Figure 5. Two trajectories of para-bisazobenzene after π−π* excitation. Shown are the angles defined in Figure 1 and the electronic state over time, as before. The upper panel shows a reactive trajectory, and the bottom panel shows an unreactive trajectory.

for (E,E)-para-BAB, a reactive trajectory in the upper and an unreactive trajectory in the lower panel. The reactive trajectory in the top panel starts in S7, rapidly hopping back and fourth between other π−π* excited states thereafter. Already after 70 fs, however, a transition to the n−π* manifold (S1−S3) occurs, and from there to the ground state S0 after 210 fs. During the relaxation a large-amplitude motion along both ωi dihedrals is observed, finally leading to an isomerization of one of the azo groups along ω2 about 300 fs after relaxation to S0. At the same time α22 reaches values above 150°, so this is via the invertomer again. We note that for para-bisazobenzene about one-third of all reactive trajectories isomerize via this postrelaxation mechanism, while the other two-thirds react simultaneously with a S1 to S0 transition as before. We are tempted to interpret the postexcitation reactive trajetories as “thermal” reactions (albeit with a kinetic energy fed from photoexcitation and subsequent photorelaxation), in contrast to the “photochemical” reactions accompanied by S1 → S0 transitions. The bottom part of Figure 5 shows a similar trajectory, also relaxing to the ground state in 210 fs and performing large scale motions along ω1 afterward. After 500 fs this angle is temporarily trapped in a minimum. There are two differences to the above trajectory: (1) The lower trajectory cannot overcome the potential barrier between E and Z and remains unreactive. (2) The relaxation to lower states is twice as fast as above. The lower trajectory returns to S1 from S0 four times after it has reached S0 for the first time, the last time at about 5032


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Table 3. Lifetimes τ and Quantum Yields ϕ for E → Z Isomerizations of Azobenzene, meta- and para-Bisazobenzene, Starting from Different Minimaa meta-BAB

AB τ1/fs τ2/fs ϕ1 ϕ2 ϕ12 ϕtot

E

(E,E)

438 ± 1 106 ± 2 0.12 ± 0.03

255.0 ± 0.5 416 ± 6 0.13 ± 0.03 0.15 ± 0.04 0.02 ± 0.01 0.27 ± 0.04

para-BAB (E,Z)

0.21 ± 0.04 0.27 ± 0.04 0.08 ± 0.03

(E,E)

(E,Z)

31.8 ± 0.1 147 ± 1 0.04 ± 0.03 0.04 ± 0.02 0.009 ± 0.009 0.07 ± 0.02

0.13 ± 0.03 0.28 ± 0.04 0.06 ± 0.02

ϕ1: yield of the first azo group, ϕ2: yield of the second azo group, ϕ12: yield of trajectories switched on both azo groups, ϕtot: yield of trajectories switched on at least one azo group. For isomerizations starting in (E,Z) minima, the fraction of Z-configured molecules is used although the second azo group starts out in Z-configuration. a

for the population of the π−π*-states and their lifetime τ1, and

600 fs. This is a common behavior of trajectories in this system. It is also noteworthy that this molecule often keeps rotating around ωi after isomerizing, sometimes by more than 360°. This occurs in 9 of the computed 107 trajectories. We do not consider such a trajectory reactive if it remains in the Zminimum for only a few femtoseconds, not being trapped there. C.3. Lifetimes and Quantum Yields. 1. Observables and Their Computation. We are now ready to perform and analyze statistics over many trajectories (cf. Table 2). The observables we are interested in are excited state lifetimes, and quantum yields ϕ for E → Z isomerization. Quantum yields are computed as the ratio of the number of trajectories ending in the Z minimum, by the total number of trajectories started, N,

ϕ=

NE → Z N

Pnπ *(t ) =

1/τ1 (e−t / τ1 − e−t / τ2) 1/τ2 − 1/τ1

(5)

for the population of the n−π* states and their lifetime τ2. The functions 4 and 5 are fitted to the TSH data via τ1 and τ2, yielding the numbers presented in Table 3 below. The Marquardt−Levenberg algorithm56 was used for the fit, which also gives an asymptotic standard error which is listed in the table as well. 2. Lifetimes. As an example, Figure 6 shows the population according to TSH simulations for each of the groups over time.

(2) 55

A standard error can be estimated by the bootstrap method as δϕ = (ϕ(1−ϕ)/N)1/2. For the bisazobenzenes we calculate different sorts of quantum yields. ϕ1 is the yield of trajectories which predict a switching of the first azo group, ϕ2 is the same for the second azo group. ϕ12 is the yield of double-switches, that is, both azo groups are switched at the end. ϕtot is the yield of all trajectories switched on any one or two of the azo groups. The nonradiative, excited-state lifetimes are due to nonadiabatic transitions and computed as follows. According to energetic gaps between them and electronic character, we can categorize the relevant states in three groups. The first group is made up of the ground state S0 only. The second group comprises the n−π* excited states (S1 for azobenzene, S1 to S3 for bisazobenzenes). The third group comprises all states above, in most cases π−π* excited states. After optical excitation, we start in the π−π* manifold, that is, the initial population of this manifold is unity, Pππ*(0) = 1. After that, dynamics and interstate transitions set in, and we can calculate, by averaging over different trajectories, populations Pππ*(t), Pnπ*(t), and PS0(t), all as a function of time. Two lifetimes τ1 (for the π−π* manifold) and τ2 (for the n−π* manifold), can be obtained from fitting the averaged TSH populations to a simplified kinetic model. The latter is obtained by assuming a consecutive reaction, τ1

τ2

(π − π*) → (n − π*) → S0

Figure 6. Populations Pππ*(t), Pnπ*(t), and population of the ground state PS0(t) over time after excitation from the E- or (E,E)-minima, obtained from averaged TSH. The top panel shows data for azobenzene, the middle panel shows data for meta-bisazobenzene, and the bottom panel shows data for para-bisazobenzene.

(3)

The top panel shows the populations of E-azobenzene after π−π* excitation, averaged over all (104) trajectories, reactive or not. The population of π−π* states clearly falls off exponentially. The n−π* state population increases and decays again. It follows eq 5 generally well, however, showing a (weak)

without backreactions. In this approximate framework there are analytical formulas for the populations,32 namely Pππ *(t ) = e−t/ τ1

(4) 5033


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The Journal of Physical Chemistry A second maximum at around 1000 fs. Still the fit of τ2 (and also of τ1) is good. In Table 3 below, we find a π−π* lifetime τ1 of 438 fs, and 106 fs for the n−π* lifetime τ2. This compares to τ1 = 178 fs and τ2 = 467 fs using the original method from Persico et al.57 The deviation in τ1 is probably due to the second maximum in the n−π* state population. The middle panel of Figure 6 shows the populations for (E,E)-meta-bisazobenzene, averaged over all 105 trajectories. The π−π* states again clearly exhibit exponential behavior, while the n−π* states do not quite show ideal behavior; in particular they have a long tail extending to the end of the propagation time. A fit gives a π−π* lifetime τ1 of 255 fs in this case, and 416 fs for the n−π* lifetime τ2. Finally the lower panel of Figure 6 shows the populations for (E,E)-meta-bisazobenzene, averaged over all 107 trajectories. Again Pππ* falls exponentially, in this case so fast that Pnπ* only approximately obeys eq 5: τ1 = 32 fs. The n−π* lifetime τ2 is 147 fs. Comparing the lifetimes in Table 3, we note that τ1 of E-AB of 438 fs decreases modestly when going to (E,E)-meta-BAB, but dramatically (to the 32 fs mentioned above) for (E,E)-paraBAB. There is no clear trend for τ2. While for azobenzene τ2 is around 100 fs (in agreement with earlier results24), both bisazobenzene species show longer n−π* state lifetimes, about 400 fs in meta- and 150 fs in para-configuration. The trend in π−π* state lifetimes τ1 is easily explained. Figure 7 shows unrelaxed scans along the symmetric

states to the n−π* state. In fact in azobenzene most hops from S2 (π−π*) to S1 (n-π*) occur around αij = 120°, while in both bisazobenzenes the hops from S4 (π−π*) to S3 (n-π*) are distributed over a line with αi1 = αi2. Therefore, we conclude that in bisazobenzenes there is an additional route for the relaxation from π−π* states to the n−π* state. In parabisazobenzene this route is extremely efficient, more efficient than in meta-BAB, because the potential gradient is pointing from the Franck−Condon point right to the crossing, where the π−π* → n−π* transition may readily occur. The differences in τ2 are harder to explain. Here the longer lifetimes of bisazobenzenes are due to the long tail of Pnπ*(t) observed in Figure 6, particularly so in the middle panel for meta-BAB. This tail consists mainly of trajectories that come back from the ground state to n−π* states. In fact if these reexcitations in meta-bisazobenzene are neglected (i.e., the trajectories are aborted when reaching S0 for the first time), then τ2 for meta-BAB is shorter than for all other considered systems. It can well be that upon inclusion of vibrational energy relaxation (which was not done here), τ2 values become similar for all species investigated here. It is currently an open question if vibrational relaxation can be efficient on the relevant time scales. 3. Quantum Yields. Differences in lifetimes will, together with other mechanisms, also cause differences in isomerization yields. Table 3 also shows reaction yields, per excitation event, i.e., quantum yields. This is done for the three species considered so far, E-AB, (E,E)-meta-BAB and (E,E)-paraBAB. In addition we also treat species (E,Z)-meta-BAB and (E,Z)-para-BAB which are to be reexcited by a second photon when already one azo unit had been switched before by a first photon (and the molecule has then fully relaxed). This way we can study cooperative effects, that is, the effect of a first switched or unswitched azo group, on the switching behavior of the second one. For azobenzene we find an E → Z yield after π−π* excitation, of 0.12 ± 0.03 in good agreement (within the error bars) with previous work.24 For the BABs, we have two switching yields ϕ1 and ϕ2, one for each group. These are a little higher for (E,E)-meta-BAB (0.13 and 0.15 without error bars) and considerably lower for (E,E)-para-BAB (0.04 and 0.04) compared to azobenzene. A few double-switches also occur, indicated by ϕ12, however, the numbers shown arise from rare events (one or two events per about 100 trajectories), so a comparison of the two isomers is not useful. We also give the total isomerization yields ϕtot, showing the same trend as ϕ1 and ϕ2. Note that ϕtot counts trajectories with one or two switched azo groups the same way; that is, if all azo groups were to switch, ϕtot would reach 1. In effect, the two azo groups of (E,E)-meta-BAB can each be switched more or less independently from the other, leading to about twice the yield per molecule (however, slightly larger, see below), since the molecule contains two switches rather than only one. In contrast, (E,E)-para-BAB is a bad switch, the total yield being almost halved compared to AB, despite the doubled number of switching units. The observed trends can be rationalized as follows. (1) For the reasons given above we find a very fast π−π*-deexcitation in particular for para-BAB. The rapid energy loss and short residence time in general leads to little momentum along the reaction coordinate and thus to a small quantum yield for paraBAB. (2) (E,E)-meta-BAB tends to stay near the E → Z transition state after reaching the ground state. This leads to

Figure 7. Unrelaxed scans along α11 forced to be equal to α12 for (E,E)-meta-BAB (top) and (E,E)-para-BAB (bottom). The relaxation from the Franck−Condon point of S4 (π−π*, red circle) to states S3 and S2 (both n−π*, via the conical intersection, blue circle) is indicated by red arrows.

combination of α11 and α12 (i.e., both angles are forced to the same value), for the (E,E)-forms of both BABs. The minimum energy corresponds to α11 ≈ α12 ≈ 120°. In both isomers the π−π* states S4 and above are clearly separated from the n−π* states S1 to S3 at the optimal ground state geometry. At increasing angles, S3 detaches from S1 and S2, reaching a crossing with S4 where nonadiabatic transitions can be efficient. In meta-BAB this crossing occurs at about 150° around 0.4 eV above the energy of the Franck−Condon point of S4. In paraBAB the crossing already occurs at around 140° and, more importantly, at a lower energy than the Franck−Condon point. In azobenzene there is no such state leading from the π−π* 5034


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The Journal of Physical Chemistry A additional isomerizations, increasing the quantum yield and in fact slightly overcompensating a reduced-lifetime effect (which is also there for meta-BAB). As a consequence, the ϕtot value of (E,E)-meta-BAB is a little larger than twice the quantum yield of two isolated E-AB molecules. In other words, the two azo groups in (E,E)-meta-BAB are largely decoupled, but small, cooperative effects remain leading to some chance for S0 → n−π* reexcitations which slightly increase the yields. (Still, the possibility of diminishing this channel upon inclusion of vibrational energy relaxation as mentioned above exists.) For (E,E)-para-BAB, on the other hand, the larger coupling leads to larger orbital and state splittings accompanied by larger nonadiabatic transition rates, which in the end diminishes yields. To study cooperative effects within a molecule in more detail, the situation of an already partly switched molecule (in (E,Z)-configuration) was also considered. Using the (E,Z)configurations as initial states, further isomerizations can occur. Also, backreactions Z → E will happen, possibly followed by an E → Z reswitching. We use the notation that the initially switched unit is unit 2, formally describable by a yield ϕ2. This yield can be lower than 1 after the molecule is reexcited. When the initial conditions detailed in Table 2 for (E,Z)meta and (E,Z)-para compounds are used, yields shown in Table 3, columns 4 and 6 were found. Several changes from the situation characteristic for (E,E)-species are visible. The E → Z isomerization yield of the first azo group (ϕ1) in both meta- and para-BAB are higher than the corresponding values for initial (E,E)-states. The value for meta-BAB increases by close to a factor of 2 (from 0.13 to 0.21), that of para-BAB by a factor of about three (from 0.04 to 0.13). Note that the other azo group was switched back to a large extent to E, however, a relativley large fraction of the Z-form is maintained, about 0.27 and 0.28 for the two molecules. Note also that events where both azo units are switched to Z after the second photon, are relatively frequent, close to 10%. We conclude that a second azo group when already switched from E to Z by a first photon, will positively affect the E → Z switching probability for the first azo unit, by a second photon. This positive cooperative effect may root in the larger energy content of the (E,Z) compared to the (E,E) forms: This energy, when released, can positively affect the switching of the other unit. The energy difference is about 0.50 eV for meta-BAB and slightly higher, 0.64 eV for para-BAB according to the present theory (cf. Table 1), which may explain why this type of positive cooperativity appears to be somewhat larger for paraBAB than for meta-BAB.

para-Bisazobenzene shows a more pronounced redshift and overall a different spectrum; only the energetic separation of n−π* and π−π* transitions is maintained. Thus, the two switching units in meta-BABs behave largely as isolated from each other, while the coupling is strong for para-BABs, in full agreement with earlier experimental and first-principles theory.20 Also the E → Z switching mechanism after π−π* excitation shows some changes when going from azobenzene to bisazobenzene. (E,E)-meta-BAB behaves basically as two isolated azo units as in azobenzene. Two additional small and counteracting effects, namely (i) slightly lowered excited state lifetimes and (ii) possible S0 → n−π* reexcitations lead, in effect, to a slight increase of the overall switching yield per switching unit. In the case of (E,E)-para-BAB, strongly reduced residence times in n−π* and in particular in π−π* states lead to clearly reduced quantum yields, making para-BAB an ineffective switch. For all BABs, if switching occurs, the dominant mechanism is, however, similar to the one on AB, that is, (1) π−π* photoexcitation, (2) nonadiabatic transitions to n−π* states, (3) return to S0 accompanied by switching. For both BAB isomers the simulation gives a mixture of (E,E)-, (E,Z)-, and (Z,Z)-configurations. We found that switching an individual azo group is more probable if the other azo group of the same molecule is already in the Zconfiguration, both in meta- and para-azobenzene. A possible explanation is the energy content of the Z-prepared azo group, which, when released, may contribute to the switching of the other unit. This positive cooperativity will only have a limited influence of apparent isomerization yields, because the Z → E back-isomerization is very effective. This may also explain the slowdown in isomerization rate visible after irradiating a sample of (E,E)-bisazobenzene for a longer time.13,21 The determination of a photostationary state and the wavelength dependence of the switching process in general are worthwhile investigations for the future. Also, intermolecular interaction and solution effects, as well as vibrational relaxation should be included.

IV. CONCLUSION AND OUTLOOK We have computed optical absorption spectra, quantum yields for photoinduced E → Z isomerization after π−π* excitation, and associated excited state lifetimes (π−π* as well as n−π* lifetimes) for meta- and para-bisazobenzene. We used a TSH approach based on the semiempirical AM1 Hamiltonian with Tully’s fewest switches algorithm. For a reference we also reconsidered the E → Z isomerization of azobenzene using the same method and parameters. The results for azobenzene are very similar to earlier studies employing the same method (with a smaller active space),24 which makes us confident that comparisons between AB and the BABs are meaningful. Differences between azobenzene and bisazobenzenes which we find first of all refer to altered UV−vis spectra. metaBisazobenzene shows a small redshift compared to azobenzene.

Notes

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ASSOCIATED CONTENT

S Supporting Information *

Geometrical data and excitation wavelengths of azobenzene and bisazobenzene. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpca.5b02933.

■

AUTHOR INFORMATION

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Fruitful discussions with M. Persico and G. Granucci (both from Pisa, Italy), S. Hecht (Berlin, Germany), and T. Klamroth (Potsdam) are gratefully acknowledged. We thank the Deutsche Forschungsgemeinschaft (DFG) for funding through SFB 658 “Elementary Processes of Molecular Switches on Surfaces”, project C2.

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REFERENCES

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