Tracking of Azobenzene Isomerization by X-ray Emission

Article pubs.acs.org/JPCA

Tracking of Azobenzene Isomerization by X‑ray Emission Spectroscopy H. Ebadi* Max-Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany S Supporting Information *

ABSTRACT: Cis−trans isomerizations are among the fundamental processes in photochemistry. In azobenzene or its derivatives this dynamics is, due to its reversibility, one of the reactions widely used in photostimulation of molecular motors or in molecular electronics. Though intensively investigated in the optical regime, no detailed study exists in the X-ray regime so far. Because the X-ray emission spectroscopy echoes the electronic structure sensitive to the geometry, this theoretical report based on the density functional theory and its timedependent version presents different nitrogen K-edge X-ray emission spectra for cis and trans isomers with close interrelation to their electron configuration. Considering the spectrum along the isomerization path, these structural signatures can be utilized to probe the isomerization dynamics in the excited molecule. The scheme can further be generalized to the element specific photoreactions.

I. INTRODUCTION The advanced spectroscopic technologies allow the investigation of not only the static structure but also the dynamical properties of matter at the atomic and molecular level.1−3 These characteristics rely on features like energy tunable, high repetition frequency, and high flux radiations at free-electron and synchrotron facilities. At the molecular scale, electron transfer and electron redistribution processes are considered as important dynamical signatures for molecular electronics. With conjugate electronic systems, several molecules have been shown as suitable candidates for this type of applications.4−6 Recently, great attention has been given to the role of molecular orbitals in the static structure of molecules4,5 and in the dynamical process during interaction with light.7−10 Among these molecules stilbene and azobenzene (AZB), provide benchmark11 for the fundamental studies of electron transfer in complex systems, where they are switchable via push−pull isomerization. This isomerization, intensively studied in the UV−vis regime,12−17 can usually be achieved, when light falls on the molecule in the electronic ground state. Although different relaxation paths for the same or different adiabatic electronic excited states have been proposed,16−20 this dynamics can always be tracked along the dihedral angle (one of the internal coordinates).18 Figure 1 shows this dynamics through the lowest singlet adiabatic electronic excited state. The molecule is pumped from the electronic ground state in S0 to the excited state S0 + ω(R̲ ) via absorption of light with frequency ω(R̲ ). Within the Born−Oppenheimer (BO) approximation, Si stands for the ith singlet adiabatic electronic state or potential energy surface (PES) as a function of nuclear coordinates indicated by vector R̲ . Therefore, the excitation energy depends also parametrically on R̲ . For convenience, the energy (radius) in the units of electronvolt (eV) is given with respect to the trans isomer in S0 as a reference point. Then, the © 2014 American Chemical Society

Figure 1. PESs for the cis−trans isomerization of AZB along the dihedral angle θ: red dashed-double dot S0; blue-dashed, S1; gray dashed-dot, S0 + ω(R̲ ). For the convenience, the nitrogen atoms and phenyl rings are shown with small and large circles, respectively.

molecule relaxes from the static S0 + ω(R̲ ) through the relaxed S1 excited state either into cis or trans mainly via a nonradiative process. So, the isomerization takes place between two phenyl rings around the two central atoms almost close to θ = 90°, where ES1 − ES0 is the minimum.21 With this introduction, knowledge of the excited state is required for studying this dynamics, which is related to the symmetry of the ground and excited states. Due to the collective dynamics and many-body effects, the allowed transition can be described by methods of Received: July 1, 2014 Revised: August 18, 2014 Published: August 18, 2014 7832

dx.doi.org/10.1021/jp506543d | J. Phys. Chem. A 2014, 118, 7832−7837

The Journal of Physical Chemistry A

Article

48 in this work) electrons is given by Kohn−Sham (KS) determinant of N lowest orbitals {ϕi(r), i = 1, ..., N} with N auxiliary energies {Ei, i = 1, ..., N} in density-functional theory (DFT). Then, these orbitals will be used for post processing and for calculation of observables.27 In the case of XES, the dipole matrix element ⟨d⟩j = ⟨ΦI(r)̲ |r|̲ ΦF(r)̲ ⟩ has to be calculated, where

configuration interactions or time-dependent density functional theory (TDDFT), which is employed in this study. The validity of density functional theory and TDDFT for AZB has been examined in earlier studies,17,22 which can also be understood from the good agreement between the PESs here and in the previous reports13,17 (see also Supporting Information). For the dynamics part of this work, the excited state is considered to be the first singlet adiabatic electronic excited state, because of negligible overlap with the double excitations and the reliable description by the linear response TDDFT with minimal basis sets. Moreover, the nonadiabatic coupling of this state with the other singlet excited states is small according to their energy gap from this state. An evidence for this issue is a larger quantum yield for the isomerization through S1 which should occur mainly around θ = 90°. Because the structure of the AZB isomers is completely different, the X-ray spectroscopy provides an alternative approach to consider their characteristics, where spectral features are strongly geometry dominated. Furthermore, as Xray spectroscopy is an element sensitive method,23 it allows us to study isomerization around the center of reaction via nitrogen K-edge emission indicating the advantage of AZB over stilbene. This theoretical report aims at studying the emission spectrum of this molecule under isomerization in the X-ray regime. First, the simulated spectra present a clear difference in the nitrogen K-edge X-ray emission spectrum (XES) for the two isomers. Further, on the basis of structural dependence of the XES along the PESs, a time-resolved scheme is proposed to probe the isomerization by pump−probe setup at free-electron laser facilities. The theory and methods are presented in the next section. In section III, the results are discussed, and finally conclusions are given in section IV.

|Φ I( r ̲)⟩ = ba†bc Φg[{ϕ(r)}]

(1)

and

|Φ F( r ̲)⟩ = bc†bj|Φ I ( r ̲)⟩

(2)

are initial and final states, respectively, with b†a and bi the particle creation and annihilation operators (atomic units are used throughout unless otherwise stated). In this expression, one electron from the core orbital ϕc(r) is excited to the unoccupied orbital ϕa(r) and afterward another electron from a valence orbital ϕj(r) will fill the core hole. By neglecting the relaxation and core-hole effects, whose consideration will be sophisticated for such a big molecule, the matrix element attains the simple form ⟨d⟩j ≃ ⟨ϕc(r)|r|ϕj(r)⟩

(3)

as zero-order approximation but describes the main part of XES. The oscillator strength and intensity I(Ω) for this transition is proportional to Ω|⟨d⟩j|2 with Ω = Ej − Ec being the emission energy. Although the KS eigenvalues rarely represent accurate binding energies in the absence of exact exchange− correlation potential,27 the difference of the KS eigenvalues and in particular for the valence orbitals are well-defined quantities for the prediction of Ω.27,28 This statement can be examined by applying different exchange−correlation functionals and also self-interaction corrected as the most proper one.5 This failure of DFT, however, is more pronounced for the core orbitals, and therefore, an additional treatment is required to simulate the experimental spectrum. To this end, the total spectrum is shifted to the higher energies.29

II. THEORY AND METHOD In molecular spectroscopy, the vibrational motions of the nuclei affect the electronic transitions in the UV−vis regime via fine structure and broadening.24 A clear fine structure has been observed also in the X-ray emission spectrum of small molecules such as the nitrogen molecule.25 Nevertheless, as applied in this work, the isomerization or other element specific photoreactions can be tracked by X-ray emission spectroscopy without considering vibrational effects. However, it might not be possible to resolve the vibrational effect in the current experimental setups as there are several vibrational modes for this molecule.26 It is noticed that the use of BO approximation is meaningless for isomerization dynamics through the excited states, where the process is in fact characterized by the nuclear dynamics. The prediction of XES for the dynamics will be presented in the last section. Let |Ψ(r,̲ R̲ ,t)⟩ be the many-body wave function approximated by |Ψ(r,̲ R̲ ,t)⟩ ≈ |Φ(r,̲ t)⟩|χ(R̲ ,t)⟩, where |Φ(r,̲ t)⟩ and |χ(R̲ ,t)⟩ are the solutions of the time-dependent Schrödinger equation for the electronic and nuclear parts, respectively. Here r ̲ presents the coordinates of the electrons. Further, within the BO approximation and in the absence of an external field assumed in this study, the nuclear motion is frozen and the electronic wave function |Φ(r;̲ R̲ ,t)⟩ ≡ |Φ(r)̲ ⟩ fulfills the timeindependent Schrödinger equation. In fact, the wave function is parametrically time-dependent via change in R̲ for those dynamics characterized by the nuclei such as chemical reactions. As further approximation, the ground state |Φg(r)̲ ⟩ ≡ Φg[{ϕ(r)}] of a closed shell molecule containing 2N (N =

III. RESULTS AND DISCUSSION The importance of the present molecule in fundamental studies relies on the push−pull isomerization with mechanical or electrical applications in the nanodevices. For the basic studies, the isomerization can routinely be done in the liquid phase, when light in the UV−vis regime is shone on a solution of AZB. After a while, the sample will have a significant amount of cis in equilibrium with trans. Two samples with and without shining on by a UV−vis light are considered trans and cis isomers, respectively. As a static part, the X-ray emission spectra of these two structures are discussed in the next subsection, on which an experimental report will be given elsewhere. Then the section is closed with the prediction of XES for the isomerization through S1 for the dynamics part. The simulation of nitrogen XES has been done taking into account the solvent effect (here ethanol) on the conductor-like screening model (COSMO). For clarity, the spectra are also compared with those obtained in the gas phase. All calculations have been carried out using ORCA30 and Gaussian packages with Avogadro for visualizing the molecular orbitals. On the theory level, the B3LYP exchange−correlation functional has been employed with the 6-31G basis set for the geometry optimization and the TZVP basis set for the simulation of spectra with ORCA leading the converged results. The validity 7833



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of this functional for the small organic molecules has been reported in ref 31. For taking into account the core-hole and instrumental lifetime, the spectra are convoluted by a Gaussian envelope with 0.9 eV full width at half-maximum. Moreover, due to the lack of the correct energies of the core orbitals, the spectra are shifted approximately by 10 eV. A. Static Structure. From the theoretical point of view, the reliable structure of single molecules in cis or trans isomers and the related spectroscopic properties can be simulated by quantum chemistry methods. As can be seen in Figure 2, there

Figure 2. XES for trans (black) and cis (blue-gray) AZB simulated with B3LYP exchange−correlation functional and TZVP basis set for the geometries optimized by 6-31G basis set. For the spectrum in the inset, the geometry optimization has been carried out by TZVP basis set.

Figure 3. Simulated molecular orbitals of AZB in ethanol from j = N(HOMO) to j = N − 4 and N − 46 (core orbital) for cis (left) and trans (right) with N = 48. Red and blue colors indicate positive and negative isosurfaces. For convenience, the hydrogen atoms have been removed and the carbon atoms (phenyl rings) can be distinguished from the two central nitrogen atoms.

is a distinct difference between the simulated spectra of cis and trans above 392 eV. Regarding the minor effect of a larger basis set (TZVP) for the geometry optimization (inset of this figure), the analysis continues with the results obtained with smaller basis sets (6-31G) for the geometry optimization. This basis set is currently employed in the surface hopping and multiple spawning methods32 as tools for further time-resolved investigations. It is seen that the spectrum of trans contains one intense peak, whereas an additional peak appears for the cis at 1.2 eV lower energy compared to the first peak. Hereafter, the peak with highest energy is called the first peak, and the discussion is focused on the energy above 392 eV. In fact, the other peaks at lower energies may not be well assigned to the certain isomer with the current experimental setups because of their lower intensity. For both isomers, the first peak arises by the decay of the electron from the highest occupied molecular orbital (HOMO) to the core orbital. Due to the nonbonding character of HOMO containing a significant atomic p orbital, the first peak is the most intense for both isomers. The valence orbitals, responsible for the second peak in cis, should also contain the character of an atomic p orbital. Equivalently, these orbitals should have the same structure as HOMO, which may also be understood from eq 3. As can be seen in Figure 3, HOMO to HOMO−3 have similar structures of spatial distribution on the molecule center (the emphasis is on the nitrogen atoms) for cis in contrast to trans. Now the question arises why the intensity of the second peak for cis is high? First, this peak is due to the convolution of X-ray emission via three valence orbitals. Second, with the assumption of a localized rc 3 core orbital on one atom, the integral ∫ ∞ 0 r ϕc*(r) ϕj(r) dr ≃ ∫ 0 3 r ϕc*(r) ϕj(r) dr required for the calculation of ⟨d⟩j, is limited

by the radius of the core orbital rc. This upper limit of integration implies that the extension (diffuse character) of valence orbitals on the nitrogen atoms is also involved in the transition probability. Thus, although the electron density in HOMO is much higher on the nitrogen atoms, the two peaks have the same intensity. For this molecule, special attention should be devoted to the symmetry of the core orbitals. Considering the nitrogen atoms only, the molecule is a binuclear compound. With this assumption, the core orbitals are approximately given by 1 ϕc;g (r) ≃ [φ (r) + φ2(r)] (4) 2 1 and ϕc;u(r) ≃

1 [φ (r) − φ2(r)] 2 1

(5)

which are gerade and ungerade, respectively, with φi(r) being the 1s orbital of ith nitrogen atom. Now, in addition to the p character of the valence molecular orbitals, the symmetry of both core and valence orbitals are important in the XES.25 It has been found that the emission spectra fit to the decaying of valence orbitals to the ungerade core orbital. This interrelation may be confirmed via a simulated X-ray absorption spectrum from these core orbitals, where transition probability for the creation of core-hole in near-edge X-ray absorption spectrum is much higher for ϕc;u(r) than for ϕc;g(r). Consequently, the decaying (emission) probability should also be higher for ϕc;u(r). With this allowed electron transition from the ungerade 7834



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The above discussion was for the XES in ethanol as one of the polar solvents of AZB. Because of the sensitivity of the spectroscopic properties to the environment, consideration of the XES of this molecule in the gas phase as a reference is useful to address the solvent effect. In Figure 4, the XES spectra

core orbital to the lowest unoccupied gerade molecular orbital (LUMO) in the absorption process, the spectrum of Figure 2 specifies the symmetry of the occupied valence molecular orbitals. As the symmetry of HOMO is gerade in both cis and trans isomers, the electron transition probability from this orbital to the core is high and leads to the first intense peak. Due to the high symmetry of trans (C2h), HOMO−1 has ungerade symmetry, even with a significant amplitude on the nitrogen atoms, and thus the electron transition from this orbital to the core orbital is zero. For the cis isomer, the trace of gerade and ungerade symmetry can also be seen in these orbitals, when only the nitrogen atoms are considered. Furthermore, the spatial distribution of HOMO−1 to HOMO−3 flows to the nitrogen atoms due to the lower symmetry of this isomer (C2). Thus, regarding the spatial distribution and the symmetry around the molecule center (on the nitrogen atoms), electron transition from these orbitals to the ungerade core orbital is expected. Because of the twisted structure of the cis isomer, the different components of a nonzero dipole matrix element in eq 3 are always nonzero for an arbitrary molecule alignment. This statement is, however, not valid for the trans isomer. For instance, if the trans AZB lies in the xz-plane, the y-component of ⟨d⟩48 becomes zero. An alternative test for the interrelation of XES and KS orbitals is to map the role of valence orbitals to the lowest singlet electronic excited state, represented very well within TDDFT. According to Casida anzats, the lth electronic excited state |Φl(r)̲ ⟩ is written |Φl( r ̲)⟩ =

Figure 4. Simulated XES of AZB in ethanol (black) and in the gas phase (blue-gray) (a) for trans and (b) for cis.

of both trans and cis AZB in ethanol have been compared with those simulated in the gas phase. It can be seen that the intensity of the second peak is suppressed for the cis isomer in the gas phase. This change is due to the fact that the molecule has a nonzero dipole moment and performs the dipole−dipole interaction with polar solvents. As a consequence, this interaction leads to the modification of the spatial distribution of the individual molecular orbitals. It is expected that the amplitude of this distribution should increase in the direction of the dipole moment corresponding to the position of the nitrogen atoms. Because the HOMO has a nonbonding character localized mainly on the nitrogen atoms, this variation is pronounced for the lower molecular orbitals. Thus, with spatial distribution toward the nitrogen atoms in HOMO−1 to HOMO−3, the intensity of the second peak is enhanced for cis in a polar solvent. In the case of the trans isomer, there is no permanent dipole moment to interact with a polar solvent, due to the high symmetry of molecule, and therefore, the spectra in the gas phase and in a polar solvent are similar (inset of Figure 4). B. Dynamics. Continuing with the isomerization dynamics after initial excitation of molecule to S1, the electronic wave function

∑ Cliaba†bi Φg[{ϕ(r)}] (6)

i ,a

where occupied KS orbitals ϕi(r) are prompted, at a turn, to the unoccupied orbitals ϕa(r) of the ground state calculation.33 In the practical application, few terms in this summation are dominant. Here, for the first excited state, known as the n → π* Table 1. Weight |C1ja|2 and Oscillator Strength Ω|⟨d⟩j|2 of KS Orbitals in |Φ1(r)̲ ⟩ and in XES, Respectivelya cis (a = N + 1)

trans (a = N + 1)

N−j

|C1ja|2

Ω|⟨d⟩j|2

N−j

|C1ja|2

Ω|⟨d⟩j|2

0 1 2 3

0.897 0.030 0.000 0.073

1.000 0.207 0.192 0.634

0 1 2 3

1.000 0.000 0.000 0.000

1.000 0.037 0.000 0.000

a

For convenience, the oscillator strengths have been scaled by a factor of 1/max(Ω|⟨d⟩j|2) with j ∈ {1, ..., 48}.

|Φ( r ̲;R̲ ,t )⟩ ≃ cS0(t )|ΦS0( r ̲;R̲ ,t )⟩ + cS1(t )|ΦS1( r ̲;R̲ ,t )⟩

transition, this sum, tabulated together with Ω|⟨d⟩j|2 in Table 1, is reduced to |Φ1( r ̲)⟩ ≃

∑

C1iN + 1bibN† + 1Φg[{ϕ(r)}]

i=N−3

(7)

for cis and |Φ1( r ̲)⟩ ≃ C1NN + 1bN bN† + 1Φg[{ϕ(r)}]

(9)

with |cS0(t)| + |cS1(t)| = 1 and |cS1(t = 0)| = 1 as the initial conditions, evolves along the relaxation path until trapping in one of the end points (trans or cis) in the ground state, i.e., | cS1(t)| = 0 and |cS0(t)| = 1. During this dynamics with few hundred femtoseconds relaxation time, which has intensively been studied by the quantum-classical surface hopping method,18,34−36 the structure of the molecule and associated KS orbitals should vary smoothly or suddenly. The former occurs far from θ = 90°, whereas the latter takes place close to this point accompanied by a nonadiabatic coupling with the ground state. On the other hand, the creation of the nitrogen core hole with a lifetime of a few femtoseconds1 allows the probing of change in the spectrum and consequently the 2

(8)

for trans. In Table 1, the weight of HOMO and HOMO−3 in |Φl(r)̲ ⟩ as well as their oscillator strength in the XES are larger compared to HOMO−1 and HOMO−2 for cis, which are in good agreement with Figures 3 and 2. 7835

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IV. CONCLUSIONS In summary, the theoretical investigations of structural signatures on XES of azobenzene have shown excellent interrelations with the spatial distribution and symmetry of simulated molecular orbitals on the molecule center (on the nitrogen atoms). These properties have been examined also by contribution of valence molecular orbitals in the first singlet electronic excited state. On the basis of the structural dependence of the present XES, an ultrafast X-ray spectroscopy has been proposed to investigate the isomerization at freeelectron laser facilities. Thus, it will bear the possibility for exploring the electronic redistributions at configurational points in reaction space, which are in turn characterized by nuclear dynamics.

isomerization path via structure of XES. To realize this concept, first the isomerization path is required, which has been defined by simulation of the two-dimensional potential energy surface (S1) along the CNNC angle (for the rotation) and CNN angle (for the inversion). It is well-known that the isomerization path is characterized via these variables.18,34,35 Then, the spectra for the geometries on S1 has been simulated. When this dynamics is tracked, for each dihedral angle (θ) the sum of spectra along the CNN angle presents the evolution of XES along the isomerization path. As shown in Figure 5, apart from θ around

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinate representation of the potential energy surfaces corresponding to Figure 1 of the manuscript. This material is available free of charge via the Internet at http:// pubs.acs.org

■

Figure 5. Simulated XES of AZB in S1 of Figure 1. For each dihedral angle, the distribution of geometries along the CNN angle has been taken into account.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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180°, there are two peaks with increasing energy difference when moving toward θ = 90°. Hence, the isomerization dynamics after an initial excitation can be monitored via these characteristics. With an appropriate coordinate to time mapping, θ → t,37,38 this figure is analogous to the time profile of XES in a time-resolved perspective. This scheme presents a uniform change in the evolution of geometry as a function of t, but it is independent of this assumption. It is noticed that this map does not fully apply to the real experimental conditions, where the quantum yield for both trans → cis or cis → trans isomerization is smaller than one.18 Also, the excited electron should influence the X-ray emission spectrum. With regard to this issue there are currently frequent discussions on further investigations combining with the surface-hopping approach and taking into account the spreading of geometries in the phase space of the nuclei. However, for pumping to the first optical excitation as assumed here, the excitation and deexcitation should mainly involve HOMO and LUMO of the ground state calculation. It seems that apart from a decrease in the intensity of the first peak, the spectrum structure should not significantly be changed. In particular, the second peak and its position, as the main characteristics for the tracking of this isomerization, should not be altered. If the measurements of a time-resolved experiment will deviate from the predicted one, then the exchange and correlation of valence electrons and also the validity of the adiabatic approximation will be examined. The present scheme provides a route to investigate this dynamics via time-resolved X-ray emission spectroscopy. In an appropriate experimental setup, the molecules in the sample should coherently be pumped to the first electronic excited state by an intense laser with wavelengths around 450 nm. Then, the XES will be measured as a function of time to probe the development of the spectrum during relaxation.

ACKNOWLEDGMENTS I thank I. Rajkovic for useful discussions and Gesellschaft für wissenschaftliche Datenverarbeitung mbH Göttingen for using their scientific computer cluster. Further, I am grateful to S. Techert for giving me this subject. This work was supported by SFB755 and SFB1073 of (DFG), DESY, and MPI-BPC.

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REFERENCES

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Tracking of Azobenzene Isomerization by X-ray Emission

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