Ultrafast CSpiroâO Dissociation via a Conical Intersection Drives

Article pubs.acs.org/JPCA

Ultrafast CSpiro−O Dissociation via a Conical Intersection Drives Spiropyran to Merocyanine Photoswitching Stefan Prager,*,†,‡ Irene Burghardt,‡ and Andreas Dreuw*,† †

Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany ‡ Institute of Physical and Theoretical Chemistry, Goethe-University, Max-von-Laue-Strasse 7, 60438 Frankfurt am Main, Germany S Supporting Information *

ABSTRACT: The mechanism of the photochemical conversion of spiropyran to merocyanine is investigated theoretically. Calculations were performed at TD-DFT/ ωB97XD/cc-pVDZ level of theory, which shows good agreement with the reference RI-CC2 method. A twodimensional scan of the potential energy surface has been performed along the C−O distance and the central torsion angle in the ground state and in the first excited state, where the reaction takes place. Starting at the Franck−Condon geometry, the energy of the first excited state decreases in the direction of the C−O dissociation while the ground-state energy increases. This leads to a barrierless C−O bond dissociation in the first excited state. While relaxing on the S1 PES toward longer C−O distances, the torsion angle hardly changes, but other coordinates start to vary, leading to a conical intersection of the ground state and the first excited state at a C−O distance of about 3.4 Å. Passing the conical intersection, the reaction continues on the ground-state PES. At these large C−O distances, either barrierless Cspiro−O rebinding occurs that quenches spiropyran isomerization or rotation around the central torsion angle occurs that leads to merocyanine. For the latter an energy barrier of 0.1 eV must be overcome explaining the low quantum yield of spiropyran to merocyanine photoswitching.

1. INTRODUCTION Molecular photoswitches undergo reversible chemical transformations after excitation by light, typically accompanied by characteristic changes in their absorption spectra.1 The backreaction to the initial configuration of the switch can occur thermally or photochemically as well.1−3 In general, photoswitches can be classified according to the type of photochemical reaction,2,4 for example, cis−trans isomerization of double bonds, electron transfer, hydrogen transfer, photodissociation, or pericyclic reactions and intramolecular electrocyclic reactions.2 Photoswitches are interesting not only because their absorption spectra change after irradiation by light but also, more importantly, because they induce an instantaneous, spatially localized change in the molecular environment, for instance, a mechanical force or a change in electrostatics.5 For applying a force, a fast reaction with a large geometric change is favorable, which is true for photoswitches undergoing photoisomerizations or pericyclic reactions. The most prominent photoswitch of that kind is azobenzene, whose central N−N double bond is isomerized upon excitation by light.6−11 Recently, the idea of exploiting the exerted force to fold or unfold macromolecules has received considerable attention.5,10 A well-known family of photoswitches are fulgides, which undergo photoinduced ring-closure reactions.12,13 Similarly, spiropyran (1′,3′,3′,-trimethylspiro[2H-1-benzopyrane-2,2′-in© 2014 American Chemical Society

doline] (BIPS)) and its derivatives (Figure 1), are known to isomerize to merocyanine upon excitation by UV-light (Figure 1), during which the Cspiro−O bond is broken. The structure of BIPS consists of two parts, an indoline moiety and a benzopyrane, which are covalently bound at the spiro center. In general, merocyanine can react back to spiropyran via either a thermal or photochemical pathway. Upon isomerization to merocyanine, eight different conformers are possible with respect to the configuration of the central unit. The energetically most stable one is (T)rans-(T)rans-(C)ismerocyanine, which is shown in Figure 1. The spiropyran-tomerocyanine (s2m) isomerization is also accompanied by drastic changes of the size of the delocalized π-electron system and, hence, of the absorption spectrum. The absorption spectrum of spiropyran shows prominent bands at 280 and 350 nm, but the spectrum of merocyanine is dominated by a peak at 550 nm. The electronic structure of the merocyanine molecule is typically described by two different mesomeric structures (Figure 1). The first one is uncharged and exhibits a carbonyl group, whereas the second mesomeric structure is formally zwitterionic with a positive charge at the nitrogen and Received: September 5, 2013 Revised: January 27, 2014 Published: January 27, 2014 1339

dx.doi.org/10.1021/jp4088942 | J. Phys. Chem. A 2014, 118, 1339−1349

The Journal of Physical Chemistry A

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Figure 1. Photochemical reaction from spiropyran to TTC-merocyanine. The mesomeric structures of TTC-merocyanine are shown as well.

investigated, confirming the previously determined mechanism of C−O bond breaking via a conical intersection.22 In a more recent investigation similar methods were used but spiro[chromene-2,2′-pyrrolidine] was chosen as molecular model, because it is more similar to the original spiropyran system.21 Several excited singlet states were studied in both the spiro and the mero forms, and the reaction paths leading to different S1/S0 conical intersections were analyzed. Two possible ultrafast routes to efficient conversion to the ground state were found. The first one involves the rupture of the Cspiro−O bond leading to the open mero form, whereas the second path involves lengthening of the Cspiro−N bond quenching the s2m interconversion. Despite these earlier theoretical investigations, there are still three main questions to be answered, which will be addressed in this manuscript. (1) What is the reaction mechanism of the full spiropyran molecule (Figure 1) and does it differ from the mechanisms analyzed so far for the model systems described above? (2) Which resonance structure describes the electronic structure of the TTC-merocyanine best? (3) Because all theoretical studies so far were performed simulating the gas phase species, another important question is how solvation influences this mechanism?

a negative charge at the oxygen. It is still unclear which of these forms gives the best description of the true electronic structure. The s2m interconversion has already been extensively investigated experimentally using spectroscopic methods, and several reaction mechanisms were postulated,2,14−16 but none was undoubtedly proven to date. However, ultrafast timeresolved experiments revealed the s2m conversion to occur in the time range of 10 ps, but the breaking of the C−O bond to happen in less than 100 fs. These experiments suggest that breaking the C−O bond is the driving force of the reaction followed by the unfolding of the benzopyrane structure to the merocyanine configuration. Because the initial bond breaking is so fast, it can be speculated that it takes place in an excited state (Sn) and proceeds in a barrierless fashion through a conical intersection (CI) to yield a first reaction intermediate. After that, either the unfolding of benzopyrane to merocyanine occurs most likely in the ground state or re-formation of the C−O bond occurs that leads back to spiropyran. The latter would cause a decrease of the quantum yield of photoswitching. Indeed, it has been shown that unsubstituted spiropyrans, like the one shown in Figure 1, exhibit lower quantum yields than substituted ones.2,17,18 The measured quantum yield for s2m conversion of this unsubstituted spiropyran to merocyanine is very small and amounts to only ≤0.1.18 Because the reaction mechanism could not be clarified by spectroscopic methods alone, some previous theoretical investigations were performed.19−21 A theoretical study addressing the s2m interconversion in the electronic ground state showed that there are two activation barriers of 56.4 and 77.6 kJ/mol along the Cspiro−O dissociation and the unfolding to merocyanine, respectively.20 This excludes a thermal s2m interconversion at room temperature. Because the complete BIPS molecule is rather large for a comprehensive theoretical investigation with high-level quantum-chemical methods, smaller molecular model systems were initially chosen. As first model system, benzopyrane was investigated using the complete active space self-consistent field (CASSCF) and its second-order perturbative correction (CASPT2), because only this part of BIPS was supposed to be responsible for its photoreaction.19 It was confirmed that the reaction indeed takes place in the first excited state through a conical intersection along two important multidimensional coordinates, i.e., a “benzene-ring expansion” and “ring-opening” coordinate. The photoreaction mechanism starts with geometric relaxation on the S1 surface along the benzene-ring expansion coordinate and stretching of the C−O bond. Then a small energy barrier on the S1 surface has to be overcome along the ring-opening coordinate leading to a conical intersection between S1 and S0. In the electronic ground state, a second small energy barrier leads to the merocyanine analogous. However, after passing the conical intersection, the excited molecules can also rearrange to the initial benzopyran structure quenching the s2m interconversion.19 Later, the ring-opening photoreaction of benzopyrane and the corresponding normal modes have been

2. THEORETICAL METHODOLOGY 2.1. Computational Methods. Prior to the detailed investigation of the photoinduced interconversion of spiropyran to merocyanine, a large set of methods and exchange− correlation (xc) functionals have been evaluated. The methods comprise CIS(D),23,24 CC225 and TD-DFT in combination with the following xc-functionals B3LYP,26 BHLYP,27 ωB97XD,28,29 CAM-B3LYP30 and LC-ωPBE.31−33 Although for CC2 the basis set def2-TZVP34−36 was used, in all other methods the Dunning basis set cc-pVDZ37−39 was employed. In addition, for CC2, the “resolution of the identity”40 approximation was applied with the corresponding auxiliary basis set aux-TZVP.41,42 Only restricted calculations were performed, because unrestricted spin-broken DFT calculations along the investigated dissociation pathway revealed no energetically lower-lying spin-broken solution. Hence the molecule has a close-shell configuration along the complete path. All optimizations on potential energy surfaces of excited states were performed at TD-DFT level of theory using the xc-functional ωB97XD with the basis set cc-pVDZ. The reason for the selection of this particular functional is described in detail below. Single reference methods like TD-DFT are not suited to study conical intersections in detail and multirefernce methods must be employed for their optimization.43−46 Here we fit calculated TD-DFT potential energy surfaces to approximately locate the relavant intersection. In the Supporting Information, comparison is made between TD-DFT/ωB97XD computed curves and previously published ones for benzopyran at CASSCF/CASPT2 level. The relevant C−O distance at the conical intersection differs only by 0.05 Å in this comparison. 1340



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To study also effects of solvation, a water environment was created and the resulting solvated BIPS model was employed within QM/MM calculations.47 For these calculations the ONIOM48−50 package of Gaussian09 was used, and the UFF force field51 was applied for the MM part. The QM part was described using TD-DFT/ωB97XD/cc-pVDZ for the reasons given below. For all calculations, except for the RI-CC2 calculations, for which Turbomole 6.3.152 was employed, the Gaussian 09 Rev. A.0253 program package was used. For visualization, the programs Avogadro 1.0.3,54 TmoleX 3.2,55 POV-Ray 3.7 RC6,56 and Spartan 0857 were used. 2.2. Choice of an Appropiate Excited-State Method. The molecular size of spiropyran with 40 atoms lies at the current upper limit for excited-state calculations with methods beyond simple single-electron transition theories like CIS and TD-DFT. Because excited-state optimizations are required within this study, which are particularly demanding with respect to computational effort, TD-DFT is at present the method of choice for systems of the size of spiropyran due to its computational efficiency. However, the accuracy of TD-DFT results strongly depends on the choice of the xc-functional.58 Hence thorough evaluation and comparison with experimental results or higher-level theoretical data is generally required. In this study, the optimized ground-state geometry of spiropyran obtained at the level of RI-CC2/TZVP as well as the lowest vertical excited states computed using linear-response RI-CC2/ TZVP served as benchmark values for the evaluation of CIS(D) and TD-DFT with various xc-functionals. At the RI-CC2 level of theory, the benzopyran ring of spiropyran is not orthogonal to the indoline moiety, as could have been assumed considering the simple Lewis structure (Figure 2). The most important geometrical parameter for the anticipated investigation is the Cspiro−O bond distance, which has a value of 1.468 Å in this reference structure, which we refer to as structure A (see below). For this structure, the energetically lowest excitation energies were calculated, but because only the first and the second excited state are relevant for the investigated reaction, only these two states are considered in the following analysis. At this level of theory, S1 and S2 have excitation energies of 4.05 and 4.45 eV, respectively. The first excited state exhibits a weak oscillator strength of 0.055 and is represented by mainly two orbital transitions: the HOMO → LUMO transition (44.2%) and the HOMO−1 → LUMO transition (27.5%). The second excited state has larger oscillator strength of 0.114 and is described by the same orbital transitions: HOMO−1 → LUMO (30.2%) and HOMO → LUMO (30.0%). Analysis of the transition density matrix59,60 revealed that, in both states, electron density is transferred from both parts of the spiropyran molecule to the benzopyran part. This is further supported by an inspection of the involved orbitals of the excited states (Figure 2). S1 corresponds mainly to a charge-transfer state with some contributions of a local π → π* transition on the benzopyran moiety, whereas S2 is dominated by a local π → π* transition on the benzopyran moiety with minor contributions of the charge-transfer excitation. This suggests that both lowest excited states mix strongly at the ground-state geometry possibly caused by a crossing or an avoided crossing of S1 and S2 in the region of the structure A. For the identification of a computationally less costly but equally accurate excited-state method as RI-CC2 in the description of the s2m mechanism, ground-state geometry optimizations as well as vertical excited states have been

Figure 2. Geometry of structure A (top left) and structure B (top right) and the four important frontier orbitals (HOMO−1 to LUMO +1) of structures A (left) and B (right) for the first two excited states. Despite the slightly different geometries, the orbitals of structures A and B are practically identical.

performed at various levels of theory: B3LYP, BHLYP, CAMB3LYP, ωB97XD, LC-ωPBE, and HF/CIS(D). All these methods were evaluated with respect to the optimized ground-state geometry and the character of the excited states. The coordinates of the optimized ground-state structures can be found in the Supporting Information. For the planned excited-state geometry optimization, xcfunctionals with large amounts of nonlocal HF exchange are generally required.61,62 Although the results obtained with the B3LYP xc-functional still differ from those at RI-CC2 level, BHLYP performes clearly better. The excitation energies as well as the oscillator strengths for the four energetically lowest electronically excited states are shown in Table 1. The character and the order of the excited states is in good agreement with RI-CC2. Only the energy difference between S1 and S2 is slightly to small with 0.29 eV compared to 0.4 eV at the RICC2 level. Turning to long-range-corrected hybrid functionals especially developed to mitigate the CT problem of TD-DFT, the LC-ωPBE xc-functional does not reproduce the energetic order of the excited states. Using CAM-B3LYP, the excitation energies and the character of the excited states are described correctly, but in analogy to results obtained with the standard B3LYP functional, the ground-state structure differs from the structure obtained with RI-CC2. B3LYP and CAM-B3LYP tend 1341



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Table 1. Comparison of Excitation Energies (eV) and Oscillator Strengths (in Parentheses) Calculated with Different Methods at the Equilibrium Ground-State Geometry Obtained at the RI-CC2 Level B3LYP S1 S2 S3 S4

3.63 4.21 4.66 4.79

(0.04) (0.08) (0.04) (0.00)

BHLYP 4.56 4.85 5.13 5.24

(0.07) (0.18) (0.05) (0.03)

ωB97XD 4.40 4.80 4.95 5.15

(0.06) (0.18) (0.05) (0.03)

LC-ωPBE 4.63 5.05 5.27 5.50

(0.09) (0.07) (0.12) (0.17)

CAM-B3LYP 4.40 4.74 4.94 5.15

(0.06) (0.17) (0.04) (0.03)

CIS(D) 4.50 4.93 4.97 4.98

(0.38) (0.24) (0.05) (0.08)

CC2 4.05 4.45 4.57 5.04

(0.06) (0.12) (0.04) (0.04)

length is slightly longer with 1.452 Å, the N-torsion angle is larger with −137.0°, the C-torsion angle 3.2°, the O-torsion angle 7.2° and the out-of-plane angle 50.43°. Structure B and four frontier orbitals (HOMO−1 to LUMO+1) are shown in Figure 2

to planarize the benzopyran moiety such that only one groundstate structure is obtained. Only the functional ωB97XD provides ground-state structures and the excited states, which are in good agreement with the RI-CC2 reference values. Within the ab initio CIS(D) method, only the energies are corrected for double excitations by second-order perturbation theory whereas orbital transitions and excited-state properties are calculated at CIS level of theory only. The results for excitation energies are acceptable, but the character of the states differs completely from the results of RI-CC2. Because the results obtained at TD-DFT/ωB97XD level showed the best agreement with the RI-CC2 benchmark, this approach was chosen for all further investigations. To further corroborate its aptitude for describing the s2m isomerization of spiropyran, TD-DFT/ωB97XD was used to recalculate the results for benzopyran previously obtained at CASSCF(12,11) level of theory.19 Indeed, TD-DFT/ωB97XD yields results in perfect agreement with those obtained with CASSCF. The described excited-state reaction path could be completely reproduced including the S1 equilibrium structure, the transition state on the S1 surface and even the conical intersection between S 1 and S 0 could be located by extrapolation. The main reaction coordinate in the photodissociation of benzopyran, the C−O distance, is 2.35 Å at the conical intersection at CASSCF level of theory, whereas at the TD-DFT/ωB97XD/cc-pVDZ level of theory, the conical intersection can be extrapolated to occur at a C−O distance of 2.4 Å. The detailed TD-DFT analysis of benzopyran is presented in the Supporting Information.

4. STATIC EXCITED-STATE PROPERTIES OF SPIROPYRAN Experimentally, it is known that excitation into the first absorption band of spiropyran leads to its conversion to merocyanine.14,16 Hence, the energetically two lowest excited states determine the photochemistry and are thus studied here in detail. Starting with structure A, the S1 state has an excitation energy of 4.40 eV and a small oscillator strength of 0.06 at the level of TD-DFT/ωB97XD/cc-pVDZ. The second excited state is found at 4.80 eV with a larger oscillator strength of 0.18. This is in perfect agreement with the results obtained at the RICC2/TZVP level of theory. In the following, this second excited state is called “bright state”, and the first one is named “dark state”. The “dark state” is characterized mainly as a combination of HOMO−1 → LUMO transition (58.6%) and HOMO → LUMO transition (30.8%). The “bright state” is characterized by similar orbital transitions, the local HOMO−1 → LUMO transition (28.6%) and the HOMO → LUMO transition (49.9%). In fact, the two lowest excited states mix and several low-contributing orbital transitions prohibit a direct characterization of these excited states by simple orbital transitions. However, the calculated static dipole moment of the S1 and S2 states of 11.8 and 5 D at the level of RI-CC2 characterize the first state as a charge transfer and the second as a more locally excited state. Surprisingly, in structure B, the energetic order of the first and second excited states changes, whereas their character remains untouched. At this geometry, the “bright state” is now the S1, whereas the “dark state” is S2 with excitation energies and oscillator strengths of 4.41 eV (0.09) and 4.84 eV (0.05), respectively. The “bright state” is now almost exclusively a local π → π* excitation on the benzopyran moiety, characterized by a HOMO−1 → LUMO transition (91.2%), whereas the “dark state” is still dominated by a charge-transfer character and is characterized by a HOMO → LUMO transition (56.5%) and a HOMO−1 → LUMO transition (26.4%). However, it is surprising that such subtle geometric differences lead to a state crossing between the dark and bright state. To elucidate whether the different order of these states play a role in the subsequent excited-state process, excited-state geometry optimizations have been performed in the bright and dark excited state of both structures A and B. Starting at structure A, geometry optimization in the first excited state, the “dark state”, leads to no substantial geometric changes. Most noticeable is the shortening of the Cspiro−O bond length form 1.449 Å in the ground state to 1.424 in the excited state. The N-torsion angle is increased by almost 20°, leading to a stronger bending of the benzopyran moiety toward

3. GROUND-STATE PROPERTIES OF SPIROPYRAN In the ground-state structure of spiropyran the benzopyran and indoline rings are not perpendicular to each other, but the molecular frame is twisted and bent in several ways. To analyze these distortions, five major internal coordinates are relevant. Obviously, the Cspiro−O distance is most important, which in the ground-state equilibrium structure has a value of 1.449 Å at the level of DFT/ωB97XD/cc-pVDZ. In addition, three torsion angles are important, called C-torsion (d(C1−C3−C4−C5)), Ntorsion (d(N−C1−C3−C4)), and O-torsion (d(C3−C4−C5− C6)) (Figure 1), which exhibit values of −106.0°, −1.0°, and −6.8°, respectively, and an out-of-plane angle, which is defined by the angle between the C1−C3 bond and the plane N−C1− C2 (Figure 1) which is 50.14° at this optimized geometry. In addition to this so-called structure A, a second groundstate equilibrium structure “B” was found, which is practically degenerate but slightly more stable. The energy difference between these two ground-state structures is only 0.012 eV at DFT/ωB97XD/cc-pVDZ level of theory. Assuming a Boltzmann distribution at 298 K, 62% of the molecules possess structure B and 38% structure A. Compared to structure A, B is characterized by an inversion of the heterocycle of the benzopyran moiety, which leads to a different angle between the benzopyran and indoline rings. Also, the Cspiro−O bond 1342



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the indoline, reflecting the electrostatic attraction in the CT state. The first two excited states have much stronger one orbital transition character in the equilibrium geometry of the “dark state”. The S1 (dark state) is now characterized by a HOMO → LUMO transition (91.3%) with only minor contributions of the HOMO−1 → LUMO transition (3.5%). The character of the S2 in contrast is dominated by a HOMO− 1 → LUMO transition (88.6%) and the HOMO → LUMO transition contributes only marginally (3.6%). Thus, the chargetransfer character of the “dark state” and the local excitation character of the “bright state” are enhanced. The fluorescence wavelength from this S1 state amounts to 387 nm, whereas the excitation energy of the S2 is 4.06 eV in this geometry at TDDFT/ωB97XD/cc-pVDZ level of theory. Starting again at structure A, a geometry optimization in the S2 state, the “bright state”, was then performed. This optimization did not converge onto a stable minimum structure but onto a curve crossing with the lower lying “dark” S1 state. During the optimization, the Cspiro−O bond dissociated in a barrierless way and an inversion of the heterocycle of the benzopyran ring occurred, resulting in a structure very similar to the structure B. In this structure, the bright S1 state, like in the dark-state structure before, is characterized by a dominating HOMO−1 → LUMO transition (88.5%) and the HOMO → LUMO transition contributes only slightly (6.8%). The energetically higher lying “dark state” is again characterized mainly by a HOMO → LUMO transition (83.3%) and the subtle HOMO−1 → LUMO transition (7.1%). The observed state crossing between bright and dark state corresponds most likely to a conical intersection. The reaction coordinates leading to this conical intersection are the dissociation of the Cspiro−O bond and the ring inversion. When the slightly more stable structure B is excited, the bright-state S1 is populated and the barrierless dissociation of the Cspiro−O bond starts immediately. A preceding ring inversion does not happen, because the excited-state structure exhibits a similar configuration of the benzopyran moiety as structure B. Coming back to the photochemistry of spiroypran, photoexcitation will always lead to the population of the bright state due to its much larger oscillator strength, independent of the ground-state structure. Starting from structure A, the S2 state will be populated and undergoes ring inversion to become S1. Starting from structure B, the bright state is already S1 and will dominate the excited-state process. Hence both ways lead to the same structure, from which the dissociation reaction can proceed, and it is clear that the bright state is the state of interest for further investigations of the s2m conversion (Figure 3). However, the identification of a stable CT minimum in the dark state of structure A suggests that a minor part of the excited molecules should exhibit the corresponding fluorescence, when they are directly excited into this very weakly absorbing state. This suggests performing wavelength dependent time-resolved experiments to prove this hypothesis. Laser excitation at the long wavelength edge of the energetically lowest absorption band should give rise to fluorescence.

Figure 3. Schematic representation of the initial steps of the photoreaction of spiropyran prior to the Cspiro−O dissociation. The photoreaction can start from both ground-state structures A and B.

two-dimensional scan of the PES was performed starting at structure B, because at this geometry the bright state is S1 and no ring inversion occurs prior to the Cspiro−O dissociation. In this scan, the Cspiro−O distance was varied from 1.5 to 4.5 Å in steps of 0.1 Å and the C-torsion angle was varied from 0° to 180° in steps of 10°. Unphysical structures, like for example a C-torsion angle of 180° and a Cspiro−O distance of 2.0 Å, were excluded. Within this coordinate range, a first relaxed scan of the ground-state PES with vertical excitations (Figure 4) and then a relaxed scan of the PES of the bright state (S1) (Figure 5) were performed. In Figure 4, the ground-state equilibrium structure B is in the lower right corner of the lower surface. Starting at the spiropyran minimum, the energy of the ground-state PES rises by increasing the Cspiro−O distance or the C-torsion angle. Breaking of this bond is thus not possible in S0 due to an energy barrier of about 1.3 eV. The S1 energy on the other hand rises only in the direction of increasing C-torsion angle but decreases in the direction of larger Cspiro−O distances and hence bond breaking can proceed barrierless here. The large release of energy of about 1 eV due to the dissociation of the Cspiro−O bond in the first excited state is most likely the driving force for the reaction mechanism. On the S1 surface, a minimum in the direction of the C-torsion angle occurs at around 20° and further rotation seems generally not possible due to steric repulsion. At larger values of the Cspiro−O distance, however, the energy barrier along C-torsion vanishes, indicating that this torsion is possible only after Cspiro−O dissociation. Eventually, the structure of TTC-merocyanine is reached at a Cspiro−O distance of about 4.1 Å and a C-torsion angle of 180°. In the electronic ground state, merocyanine is energetically higher than spiropyran by about 0.78 eV, but already the unrelaxed S1 surface indicates that this order is reversed in S1 at the theoretical level of TD-DFT/ωB97XD/ccpVDZ.

5. MECHANISM OF SPIROPYRAN TO MEROCYANINE INTERCONVERSION After the “bright” locally excited state has been identified as the relevant state for the s2m interconversion, the photochemical mechanism can now be investigated in detail. As a first step, a 1343



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converge and thus its structure cannot be optimized here. For that objective, multireference methods like CASSCF or MRCI are generally needed,43,44 but the methodology applied here is sufficient to identify the presence of the conical intersection via extrapolation of the curves and surfaces obtained at TD-DFT level of theory. Because the C-torsion angle has a value of 20° at the minimum of the S1 surface, a cut through the PES at this fixed C-torsion angle is drawn in Figure 5. The last point along this scan, which could be converged, was at a Cspiro−O distance of 3.3 Å. At this geometry, the energy gap between ground and first excited state amounts to only 0.067 eV, and one can thus take this last converged structure as approximate structure of the conical intersection. Starting at this point with both scanned coordinates fixed to the values of the closest point (3.3 Å and 20°), a ground-state optimization was performed, during which the total energy decreases by 1.2 eV. This optimization gives a hint on geometric changes that may occur upon passing through the conical intersection. It is clear that this is an ultrafast process, which requires nuclear quantum dynamics simulations for a quantitative description. The most noticeable change in geometry, however, is a decrease of the O-torsion angle by 42°. This will be discussed in detail below. Based on our independently calculated relaxed scans, i.e., the ground-state 2D-PES scan, the S1 2D-PES scan, and the estimated relaxation after passing through the conical intersection, a picture of the mechanism of the s2m interconversion can be drawn. Starting at the ground-state equilibrium structure, excitation of spiropyran leads to the population of the “bright state” in the Franck−Condon region. Geometry relaxation in the first excited state leads to an increase of the C-torsion angle from 0° to 20° and subsequent Cspiro−O dissociation without further geometric changes, releasing an energy of about 1.27 eV (Figure 6). This leads to a conical intersection between the ground and first excited state, where the molecules can decay nonradiatively to the ground state with a further release of about 1.2 eV. Experimentally, it is well-known that this bond breaks very fast upon excitation, i.e., within less than 100 fs. On that time scale, energy dissipation is incomplete and nuclear quantum effects will dominate the true mechanism. Nevertheless, the identified minimum energy pathway rationalizes already the observed ultrafast time scale. After reaching the electronic ground state, spiropyran unfolds further by increasing the Ctorsion angle and now the Cspiro−O distance is essentially constant. Along this path, a small activation barrier of 0.05 eV has to be overcome in the ground state, which is negligible in view of the energy released in the preceding steps. Beyond the energy barrier, the C-torsion angle and the Cspiro−O distance are increased simultaneously until the merocyanine equilibrium structure is reached. This is again accompanied by a release of 0.7 eV (Figure 6). In view of the longer experimental time scale of about 10 ps for the unfolding event, the computed minimum energy path for that part of the s2m conversion will resemble more closely the true reaction than the path preceding the conical intersection. Both parts together give a first impression of the energetics and geometric changes that occur during the photoinduced s2m interconversion. The structures along this reaction path are available in the Supporting Information. The change of the five most important geometrical parameters characterizing the s2m interconversion are summarized in Figure 7. It is noticeable that the Cspiro−O dissociation and the Ctorsion angle appear to be mostly independent. However, with

Figure 4. Relaxed two-dimensional scan of the ground-state potential energy surface along the Cspiro−O distance and the C-torsion angle. The S1 surface is calculated as single-point energies at the S0 optimized structures at DFT and TD-DFT level using the ωB97XD functional. The reaction proceeds from spiropyran (front right corner) to merocyanine (back left corner).

Figure 5. Relaxed two-dimensional scan of the PES of the first excited state. The reaction path is highlighted on the S1 and on the S0 surface.

To investigate the photoinduced s2m conversion, the relaxed potential energy surface of the bright S1 state has been analogously calculated along these coordinates. Within this two-dimensional scan, the Cspiro−O distance is varied from 2.5 to 3.3 Å and the C-torsion angle from 20° to 80°. The large decrease in energy of the first excited state and the simultaneous increase of the ground-state energy in the direction of the Cspiro−O distance is not apparent any more in this scan, because it is part of the initial geometry relaxation in S1 (Figure 5). A strong increase of the total ground-state energy can be seen at C-torsion angles below 50°, when the Cspiro−O distance is elongated. This was not observed in the previous groundstate relaxed scan (Figure 4). Most importantly, a conical intersection between the first excited state and the ground state is present at a C-torsion angle of about 20° and a Cspiro−O distance of about 3.3 Å. At the structure of the conical intersection the applied DFT single-reference theory does not 1344



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Figure 6. Energy diagram of the complete reaction pathway of the spiropyran to merocyanine interconversion. In this figure, a step corresponds to an increase of the Cspiro−O distance of 0.1 Å or a rotation of the C-torsion angle of 10° or a combination of both. In the yellow part in the middle and the orange part at the left, a step corresponds to a geometry relaxation along a multidimensional reaction coordinate of arbitrary size.

increasing Cspiro−O distance, a planarization of the out-of-plane angle is observed, leading to an almost planar Cspiro atom. While the N-torsion angle remains essentially in trans configuration, the O-torsion angle increases first until the conical intersection is reached and rotates back after passing through the CI to its original configuration. Rotation of the O-torsion angle thus seems to be essential for reaching the conical intersection (Figure 7). The role of the O-torsion is reflected by the molecular orbitals. While the HOMO has bonding character between C4 and C5, the LUMO is antibonding there, hence facilitating O-torsion in the “bright” S1 state. Because the ground-state energy concomitantly increases upon O-torsion, this leads to a conical intersection. During the second part of the reaction, the molecule unfolds; i.e., all geometric parameters approach the values of the planar equilibrium structure of TTCmerocyanine. In the final TTC-merocyanine structure, the Otorsion and the out-of-plane angle are both 0°, and the Ctorsion and the N-torsion angle amount to 180° (Figure 7). Alternatively to the presented “reactive” pathway leading from spiropyran to merocyanine, another minimum energy pathway has been identified starting at the conical intersection, which does not lead to TTC-merocyanine. Here, the molecule

Figure 7. Progression of the Cspiro−O distance, the C-torsion, Otorsion, and the N-torsion angle, and the out-of-plane angle along the full computed minimum energy pathway of the s2m conversion. The point of the conical intersection is marked with the vertical blue line.

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The out-of-plane angle is marginally reduced from 50.4° to 49.9° in the water environment. Also, the excited-state properties of spiropyran are practically not influenced by the inclusion of the water environment. The “bright state” is still the S1 with an excitation energy of 4.46 eV and an oscillator strength of 0.09, corresponding mainly to a HOMO−1 → LUMO electronic transition (88.2%). The S2 is the “dark state” with an excitation energy of 4.70 eV and an oscillator strength of 0.03, characterized, like in the gas phase, mainly by a HOMO → LUMO transition (80.2%). The equilibrium geometry of TTC-merocyanine is not completely planar at the QM/MM level, in contrast to the previously computed gas phase structure. As a consequence, the Cspiro−O equilibrium distance is decreased from 4.14 to 4.03 Å in aqueous solution. The C-torsion, N-torsion, and O-torsion angles change from 180.0°, 179.9°, and 0.0° in the gas phase to 162.5°, 179.5°, and 10.6°, respectively, resulting in a slightly bent geometry. However, despite these geometric changes, the TTC-merocyanine shows no zwitterionic character also in the QM/MM calculations modeling water solvation. Using Mulliken population analyses,63 the O as well as the N atoms are both slightly negatively charged. In addition, the TTCmerocyanine structure exhibits a clear bond length alternation, which contradicts an aromatic character, as implied in a zwitterionic form. Also the carbonyl−O distance is increased by only 0.016 Å in the solvated structure in comparison with the gas phase structure to 1.253 Å, which is still in the typical range of a C−O double bond length. To investigate the influence of the water environment onto the reaction mechanism, the same scan of the ground-state PES as described preiviously was performed at the QM/MM level of theory, starting at a fixed Cspiro−O distance of 1.5 Å and a Ctorsion angle of 0°. At each point, the “bright state” (S1) was calculated. Additionally also a relaxed scan of the PES of the “bright state” was recalculated at the QM/MM level, using a parameter range of 1.5 to 3.4 Å for the Cspiro−O distance and 0° to 60° for the C-torsion angle. In analogy to the gas phase, a conical intersection between the ground and “bright state” can be identified. At the QM/MM level, the conical intersection is shifted to a slightly larger Cspiro−O distance of about 3.6−3.8 Å in solution instead of 3.3−3.4 Å in the gas phase and to a smaller C-torsion angle of 10° in solution instead of 20° in the gas phase. At the last converged structure at an Cspiro−O distance of 3.5 Å and a C-torsion angle of 10°, the energy gap between S0 and S1 is only 0.06 eV at TD-DFT/ωB97XD/ccpVDZ, using electrostatic embedding. Interestingly, the Otorsion angle differs at the point of the conical intersection in solution with a value of 74.8° by almost 10° from the calculated gas phase value. The N-torsion as well as the out-of-plane angle are on the other side practically identical to the gas phase structure. This change of the geometry at the conical intersection, most importantly the large Cspiro−O distance, is caused by the electrostatic interaction of spiropyran with the water environment, which stabilizes the electronic ground state at large Cspiro−O distances, leading to a smaller increase of the ground-state energy along the Cspiro−O dissociation. After the conical intersection is passed, the unfolding to merocyanine occurs in the ground state in a way very similar to the analogous process in the gas phase. Again, a small reaction barrier of less than 0.1 eV has to be overcome to reach TTCmerocyanine, and again, a barrier-less reaction path back to spiropyran exists, which is most probably preferred by explaining the low quantum yield of s2m switching.

returns on the ground-state PES directly to the starting spiropyran structure by simple rebinding of Cspiro−O. This is indicated by the red path in Figure 6. This “nonreactive” reaction pathway exhibits no energy barriers and may thus be more efficient than s2m interconversion potentially explaining the experimentally determined low quantum yield of s2m interconversion. To investigate whether the Cspiro−O dissociation is homolytic or heterolytic, symmetry-broken unrestricted DFT calculations were performed along the first seven steps of the identified reaction pathway and the resulting spin densities were analyzed. All calculations converged directly to the closedshell electronic structure and no energeticly lower symmetrybroken solution could be found. Hence spiropyran dissociates along a heterolytic pathway into a closed-shell single-reference species. Along the reaction pathway, the partial charges using Mulliken population analyses63 and the electrostatic potential of the electronic ground as well as first excited state were analyzed. During the whole reaction, the O-atom as well as the N-atom are slightly negatively charged. This is in contrast to previous investigations proposing a zwitterionic form of TTCmerocyanine with a positive charge at the N-atom. In the presented mechanism, and even in the equilibrium structure, the N-atom is never positively charged. In the gas phase, it is thus unlikely that a zwitterionic form occurs. This argument is further supported by the bond length alternation pattern of the benzopyran moiety, which exhibits a clear alternation of short and long distances, showing no aromatic character as is suggested in the zwitterionic form of merocyanine. Although these analyses have been performed in the gas phase, this casts some doubts on the chemical relevance of the zwitterionic form of TTC-merocyanine. However, for a more meaningful answer, solvent effects need to be considered.

6. INFLUENCE OF SOLVATION ON PHOTOSWITCHING SPIROPYRAN To estimate the influence of polar environments onto the mechanism of the photoinduced s2m isomerization, the interaction of spiropyran with water has been modeled using a QM/MM approach47 with the ONIOM48−50 package of Gaussian09.53 Electrostatic embedding was applied.49 A QM/ MM setup is chosen to investigate the specific interaction of the environment with the spiropyran molecule during the photoreaction. For example, a water molecule could form a hydrogen bond to the oxygen of spiropyran during the dissociation. This could not be investigated using implicit solvent models like PCM. Accordingly, the equilibrium structure B of spiropyran was surrounded by 70 explicit water molecules, which correspond to approximately two solvent shells. The water molecules were created randomly around the spiropyran molecule and then equilibriated. For the water environment, the MM force field UFF51 was chosen, whereas the core system was investigated at the previously chosen DFT/ωB97XD/ccpVDZ and TD-DFT/ωB97XD/cc-pVDZ level of theory, respectively. The partial charges of the water molecules were calculated using the charge equilibration method.64 The equilibrium structure of spiropyran obtained at QM/ MM level of theory is similar to the previously calculated gas phase structure. The Cspiro−O equilibrium distance increases negligibly from 1.45 Å in the gas phase to 1.46 Å in water. The C-torsion, N-torsion, and O-torsion angles change slightly from 3.2°, 137.0°, and 7.2° to 1.9°, 131.9°, and 4.8°, respectively. 1346



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the bright state, mediated by a rotation of the O-torsion angle. The second part after passing the conical intersection is the unfolding to TTC-merocyanine due to the rotation of the Ctorsion angle in the electronic ground state. In the equilibrium structure of merocyanine, which is a planar structure, the electrostatic properties and the bond lengths indicate a nonzwitterionic electronic configuration. After the conical intersection is passed, alternatively rebinding of Cspiro−O can occur, which quenches the unfolding to merocyanine. This is the cause of the low quantum yield of spiropyran to merocyanine switching. Elaborate QM/MM calculations of spiropyran in water revealed that aqueous solution has practically no influence on the energetics and the structures along the reaction pathway. The main differences are a slightly changed geometry at the conical intersection and a distorted equilibrium geometry of TTC-merocyanine, which shows a bending in its central region. However, in the planned quantum dynamics simulation, modeling of solvation will be important, because the energy dissipation into the solvent will have a significant influence on the reaction dynamic.

Figure 8. QM/MM scan in the relaxed geometry of the first excited state. The reaction proceeds from the right border of the upper surface toward the left front corner, which represents the conical intersection.

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To conclude this section, it is noticeable that the water environment has only a minor influence onto the energetics of the reaction mechanism of s2m interconversion. The relevant conical intersection occurs in solution at a larger Cspiro−O distance, smaller C-torsion, and larger O-torsion angles. The potential energy surfaces of the ground and first excited states in aqueous solution are comparable and very similar to the ones computed without a model for solvation. However, solvation dictates energy dissipation and hence its time scale determines the true reaction mechanism. Nuclear quantum dynamic simulation of the s2m isomerization including solvation effects are thus required to obtain time scales and quantum yields of the processes. Our present static quantum chemical calculations lay the foundations for that endeavor.

ASSOCIATED CONTENT

* Supporting Information S

All coordinates of the structures along the identified photoreaction pathway. Comparison of the optimized structures using different methods and functionals. Diagram and structures of the dissociation of benzopyran at TD-DFT/ ωB97XD/cc-pVDZ level of theory. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Authors

*S. Prager: e-mail, [email protected]. *A. Dreuw: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

7. SUMMARY AND CONCLUSION The reaction mechanism of the photoinitiated isomerization of spiropyran to merocyanine has been investigated theoretically with high-level quantum chemical methods addressing, for the first time, the complete spiropyran molecule and also taking solvation effects explicitly into account. First ground-state properties have been studied and two practically degenerate ground-state equilibrium geometries were determined. They differ in the inversion of the heterocycle of the benzopyran moiety. In the energetically lower structure, the excited state with larger oscillator strength, the so-called “bright state”, is the first excited state. In the second ground-state equilibrium geometry the bright state corresponds to the second excited state. Independently of this observation, excitation into the bright state always leads to barrierless dissociation of the Cspiro− O bond. At the second ground-state geometry, first ring inversion of the benzopyran ring occurs prior to the dissociation. To determine the full reaction pathway, a two-dimensional relaxed scan of the ground-state surface as well as of the excited-state surface of the “bright state” has been performed along the Cspiro−O distance and of the C-torsion angle. According to these scans, the reaction can be separated into two parts. In the first part, the reaction takes place in the first excited bright state, in which the Cspiro−O bond dissociates, finally leading to a conical intersection between the ground and

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ACKNOWLEDGMENTS Calculation time has been generously provided by the Center of Scientific Computing of the University of Frankfurt. Support by the CRC 902 “Molecular Mechanisms of RNA-Based Regulation”, Goethe University Frankfurt, is gratefully acknowledged. S.P. acknowledges scientific discussion with Dr. Jürgen Plötner.

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REFERENCES

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