Computational Insights on the Isomerization of Photochromic

Article pubs.acs.org/JPCA

Computational Insights on the Isomerization of Photochromic Oxazines Françisco M. Raymo* Laboratory for Molecular Photonics, Department of Chemistry, University of Miami, 1301 Memorial Drive, Coral Gables, Florida, 33146-0431, United States S Supporting Information *

ABSTRACT: We investigated the isomerization of the simplest member of a family of photochromic oxazines with the aid of density functional theory, using three different functionals. Specifically, we simulated the thermal interconversion of the two enantiomers, associated with this compound, and established that the opening of the oxazine ring dictates the rate of the overall degenerate process. The M062X functional provides the best match to experimental data, whereas B3LYP calculations fail to model accurately the ground-state potential-energy surface of this system. In addition, we also modeled the absorption spectra of this compound and its photogenerated isomer with time-dependent calculations. The resulting data support the original assignment of the experimental spectra and confirm that the oxazine ring opens upon excitation. The MPW1PW91 functional provides the best match to experimental data, whereas M062X calculations fail to model accurately the spectroscopic parameters of this particular system. Furthermore, the MPW1PW91 calculations demonstrate that the photoinduced opening of the oxazine ring occurs along the potential-energy surface of the first triplet excited state. Indeed, the photoinduced isomerization appears to involve: (1) the initial excitation of one isomer to the second singlet excited state, (2) its thermal relaxation to the first triplet excited state, (3) its ring opening to produce the other isomer, and (4) the thermal relaxation of the product to the ground state. Thus, our calculations provide valuable information on the elementary steps governing the isomerization of this particular photochromic compound in the ground state and upon excitation. These useful mechanistic insights can guide the design of novel members of this family of photoresponsive compounds with specific properties.

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photoresponsive components.9−16 The time scale for a photoinduced change in property at the nanoscale and beyond, for example, is predominantly controlled by the kinetics that regulate the chemical reactions responsible for interconversion at the molecular level. Similarly, the fatigue resistance of the overall nanoscaled construct or macroscopic material is mainly related to the photobleaching quantum yields and thermal stabilities of the interconverting molecular states. Therefore, the understanding of the subtle stereoelectronic factors that regulate the photochemistry and photophysics of these molecules is essential for the design of constructs and materials with tailored properties. In most instances, however, experimental investigations alone cannot provide sufficient information for a thorough understanding of a photochromic process. The short lifetimes of the excited states mediating these transformations, and often also those of the photogenerated products, essentially preclude structural elucidations with conventional spectroscopic techniques and leave mechanistic interpretations to assumptions and indirect evidence. In this

INTRODUCTION Photochromic compounds1−8 interconvert reversibly between states with distinct absorption spectra in the visible region under the influence of optical stimulations. Their photoinduced transformations are generally a result of ring-opening/closing steps, cis/trans isomerizations and proton- or electron-transfer processes. These photochemical reactions impose significant stereoelectronic changes on the interconverting system that alter its absorption coefficients across the ultraviolet and visible regions. In addition, they can also modify its dipole moment, luminescence quantum yields and redox potentials together with its physical dimensions and shape. In turn, such photoinduced changes at the molecular level can be exploited to control the dynamics and morphology of nanoscaled constructs and can translate into pronounced modifications of macroscopic properties. Indeed, photochromic compounds can be employed to regulate the functions and structures of biomolecules and supramolecular assemblies as well as to switch the color, conductivity and refractive index of a diversity of macroscopic materials.9−16 The overall performance of a nanoscaled photochromic construct or a macroscopic photochromic material is mostly dictated by the basic molecular design of the constituent © 2012 American Chemical Society

Received: September 26, 2012 Revised: November 7, 2012 Published: November 8, 2012 11888

dx.doi.org/10.1021/jp3095787 | J. Phys. Chem. A 2012, 116, 11888−11895

The Journal of Physical Chemistry A

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isomer (structure b in Figure 1). We also believe that the photoinduced opening of the oxazine ring of our compounds occurs along the potential-energy surface of a triplet state. However, our interpretation of their excitation dynamics is based, once again, on indirect experimental evidence, coming from the spectroscopic analysis of multichromophoric assemblies.33 In addition, variable temperature 1H NMR spectroscopic studies demonstrate that the configuration of the chiral center on the oxazine ring inverts on the NMR time scale. Presumably, this degenerate process involves the thermal opening of the oxazine ring with the transient formation of the very same zwitterionic isomer that is generated photochemically. In search of support to corroborate our interpretation of these experimental observations, we envisaged the possibility of resorting to computational methods to investigate further the isomerization of our compounds in the ground state and upon excitation. Indeed, the rationalization of the elementary steps controlling these processes can facilitate the design of novel members of this family of photoresponsive molecules. In fact, these compounds are particularly valuable for the assembly of multichromophoric constructs with photoswitchable emission34 that can even permit the acquisition of fluorescence images with subdiffraction resolution.34d,g Thus, the elucidation of the basic factors controlling the isomerization of these molecules can, ultimately, evolve into the realization of unique fluorescent probes for imaging applications.

context, computational methods can be a precious complement to experimental analyses.17 Indeed, they can provide invaluable information on the elementary steps involved in a photochromic transformation that cannot otherwise be accessed with experiments.18−31 Recently, we developed a family of photochromic compounds with fast switching speeds and excellent fatigue resistances.32 These molecules share a common heterocyclic skeleton, fusing a 2H,3H-indole to a benzo-2H,4H-[1,3]oxazine (structure a in Figure 1), and differ in the nature of their

Figure 1. Reversible interconversion of the ring-closed (a) and -open (b) isomers of photochromic oxazines.

substituents. Upon illumination with a nanosecond laser, an absorption band develops in the visible region within the duration of the excitation pulse. This transient absorption decays monoexponentially with lifetimes varying from tens of nanoseconds to a few microseconds with the substituents (R1− R4 in Figure 1) on the heterocyclic skeleton. These relatively short time scales prevent the structural characterization of the transient species by nuclear magnetic resonance (NMR) spectroscopy. As a result, we had to rely exclusively on the comparison of the transient band with the steady-state absorptions of appropriate model compounds to postulate the structure of the photogenerated species.32a,b On the basis of such indirect experimental evidence, we assigned the transient band to a ground-state absorption of a phenolate chromophore and concluded that the formation of this anionic fragment is indicative of the cleavage of the [C−O] bond at the junction of the two heterocycles with the generation of a zwitterionic

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COMPUTATIONAL METHODS Ground-State Calculations. Density-functional theory35 (DFT) calculations were performed with the 6-311+G(d,p) basis set and the restricted B3LYP,36,37 MPW1PW91,38,39 and M062X40 functionals implemented in Gaussian 09.41 Geometry optimizations and frequency calculations were carried out without and with the polarizable continuum model (PCM) for acetonitrile, using the integral equation formalism (IEF) variant.42 Molecular orbitals were computed at the same level of theory, including the solvation model.

Figure 2. Interconversion of the two enantiomers of 1a and the associated free-energy profile modeled with the M062X functional.48 11889



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nitrophenolate anion of the final geometry of scan 1 was rotated in ten consecutive steps of 21.09° each. At each step, this dihedral angle was constrained and the remaining coordinates were optimized. The optimized energy at each step was plotted, relative to that of the initial step of scan 1, against the [N−C] bond dihedral angle to reconstruct a profile (scan 2 in Figure S1, Supporting Information) of the conformational change for each functional.46 The distance between the carbon and oxygen atoms of the cleaved bond in the final geometry of scan 2 was decreased in ten consecutive steps of 0.349 Å each. At each step, the [C−O] distance was constrained and the remaining coordinates were optimized. The optimized energy at each step was plotted, relative to that of the initial step of scan 1, against the [C−O] distance to build a profile (scan 3 in Figure S1, Supporting Information) of the ring-closing process for each functional. The initial and final geometries of each scan were optimized again at the same level of theory, allowing all coordinates to relax and including the IEFPCM for acetonitrile. The frequencies of the optimized geometries were calculated and no imaginary frequencies were found, confirming that these structures are minima on the respective potential-energy surfaces of 1a.47,48 With the same solvation model, the geometry with the highest energy of each scan was optimized to a transition state and subjected to frequency calculations. In all instances, one imaginary frequency was found, confirming that the optimized geometries are transition states on the respective potential-energy surfaces of 1a.49 Animations (videos S1−S3, Supporting Information) of the corresponding vibrations reveal that these geometries are, indeed, the transition states responsible for (1) the cleavage of the [C− O] bond, (2) rotation of the two fragments, and (3) reformation of the [C−O] bond. The relative free energies of the minima and transition states were then estimated from the frequency calculations and compiled into a single plot (Figure 2) to reconstruct a profile of the overall interconversion of the two enantiomers of 1a. The free-energy barriers for ring-opening (ΔG‡Op), calculated with the MPW1PW91 and M062X functionals, are 11.73 and 14.09 kcal mol−1, respectively (Table 1). These values are remarkably close to that (cf., 14.31 kcal mol−1) determined

Excited-State Calculations. Time-dependent43 (TD) DFT calculations were performed with the same basis set of the ground-state calculations. The energies of the first ten singlet excited states were computed with the restricted B3LYP, MPW1PW91, and M062X functionals without and with the IEFPCM for acetonitrile. Those of the first ten triplet excited states were calculated with the unrestricted MPW1PW91 functional without solvation. Geometry optimizations were carried out with the unrestricted MPW1PW91 functional and the IEFPCM for acetonitrile by computing the energies of the first ten excited states and solving for half singlet and half triplet states. For comparison, these unrestricted functional and solvation model were also used to optimize geometries in the ground state.

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RESULTS AND DISCUSSION Isomerization in the Ground State. The chiral center at the junction of the two heterocyclic fragments of our photochromic oxazines (a in Figure 1) imposes two distinct environments on the adjacent pair of methyl groups. As a result, their 1H NMR spectra show two singlets for the two sets of diastereotopic methyl protons at low temperature. However, the two distinct resonances broaden and, eventually, coalesce into a single one with an increase in temperature. This behavior indicates that the two degenerate configurations of the chiral center interconvert rapidly on the NMR time scale at high temperature. The free-energy barrier for interconversion can be estimated from the analysis of the temperature dependence of the line width associated with the coalesced resonances of the methyl protons.44 For example, this parameter is 14.31 kcal mol−1 for the simplest member of this family of photochromic compounds (1a in Figure 2) in deuterated acetonitrile at 298 K.32a,45 Presumably, this degenerate process involves (1) the opening of the oxazine ring in one configuration, after the cleavage of the [C−O] bond at the junction of the two heterocycles, with the formation of the corresponding zwitterionic isomer (1b in Figure 2), (2) the rotation of the cationic fragment, relative to the anionic one, about the [N−C] bond connecting them, and (3) the closing of the oxazine ring in the other configuration. To support our mechanistic interpretation, we envisaged the possibility of modeling the interconversion of the two enantiomers of 1a with DFT calculations. Specifically, the structure adopted by 1a in the solid state32a was optimized with the restricted B3LYP, MPW1PW91, and M062X functionals, using the 6-311+G(d,p) basis set. The frequencies of the optimized geometries were calculated at the same level of theory. No imaginary frequencies were found, confirming that the optimized geometries are minima on the respective potential-energy surfaces of 1a. Comparison of the three optimized geometries to the crystal structure revealed negligible differences with average bond-angle and -length displacements smaller than 0.3° and 0.06 Å respectively. The length of the [C−O] bond at the junction of the two heterocycles within the three optimized geometries was increased in ten consecutive steps of 0.150 Å each. At each step, the [C−O] bond was constrained and the remaining coordinates were optimized at the same level of theory. The optimized energy at each step was plotted, relative to that of the initial step, against the [C−O] bond length to build a profile (scan 1 in Figure S1, Supporting Information) of the ringopening process for each functional. The dihedral angle about the [N−C] bond linking the 3H-indolium cation to the 4-

Table 1. Calculateda and Experimentalb Free-Energy Barriers for the Three Consecutive Steps Responsible for the Interconversion of the Two Enantiomers of 1ac ‡

−1

ΔG Op (kcal mol ) ΔG‡Ro (kcal mol−1) ΔG‡Cl (kcal mol−1)

B3LYP

MPW1PW91

M062X

experiment

7.67 5.51 7.82

11.73 5.39 6.44

14.09 6.70 5.85

14.31 7.07

a

The free-energy barriers were calculated in MeCN at 298 K.48 bThe experimental ΔG‡Op was determined by variable-temperature 1H NMR spectroscopy in CD3CN at 298 K.32a,50 The experimental ΔG‡Cl was determined by time-resolved absorption spectroscopy in MeCN at 298 K.32a cThe experimental and calculated ΔG‡Op for 2a are 17.99 and 17.05 kcal mol−1, respectively.

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experimentally by variable-temperature 1H NMR spectroscopy for the overall degenerate site-exchange process.50 Thus, the ring-opening step is essentially dictating the kinetics for the interconversion of the two enantiomers. In fact, the free-energy barriers for rotation (ΔG‡Ro) and ring closing (ΔG‡Cl) are significantly lower than ΔG‡Op and range from 5.39 to 6.70 kcal mol−1 (Table 1). To support even further the role of the ring-opening step, we also modeled the interconversion of the two enantiomers of 2a (Table 1) with the M062X functional. Indeed, this particular functional provided the best match to the experimental data for ΔG‡Op in the case of 1a. Variable-temperature 1H NMR spectroscopy indicates the free energy of interconversion for 2a to be 17.99 kcal mol−1.32a In turn, the calculated ΔG‡Op for this system is 17.05 kcal mol−1. Once again, the excellent agreement between calculated and experimental data suggests that the opening of the oxazine ring is the dominant step in the interconversion of the two enantiomers. Furthermore, these data reveal that the replacement of the methyl group of 1a with the phenyl ring of 2a raises ΔG‡Op by ca. 3 kcal mol−1 and, as a result, slows the rate for the overall degenerate site-exchange process.51 In contrast to the excellent agreement between the experimental data and the MPW1PW91 and M062X values for ΔG‡Op, the B3LYP functional underestimates this parameter by ca. 7 kcal mol−1 (Table 1). Inspection of the transition-state geometries predicted by the three models for the interconversion of 1a reveals noticeable differences in bond angles and lengths around the carbon atom associated with the cleaving [C−O] bond in the case of the B3LYP functional. Similar differences are also observed in the optimized geometries of the ring-open isomer 1b. Once again, the bond angles and lengths around the carbon atom adjacent to the positively charged nitrogen atom of 1b are somewhat different in the B3LYP geometry, relative to the other two. In fact, this functional greatly underestimates the energy difference between 1a and 1b and suggests that the two isomers are essentially degenerate. This conclusion is inconsistent with the 1H NMR spectroscopic evidence, which instead indicates that 1a is significantly more stable than 1b.32a In agreement with this experimental observation, the MPW1PW91 and M062X functionals indicate free-energy differences of 5.29 and 8.23 kcal mol−1 respectively between the two isomers. Thus, the B3LYP functional fails to model accurately this particular system. Isomerization in the Excited State. The absorption spectrum (Figure 3) of 1a in acetonitrile shows a band centered at 318 nm that resembles the one observed for 4-nitroanisole under the same conditions.32a As a result, we assigned this absorption to the 4-nitrophenoxy chromophore of 1a. To confirm this interpretation of the spectroscopic data, we envisaged the possibility of modeling the absorption properties of 1a with TDDFT calculations. In particular, the geometries of 1a optimized in the ground state (S0) with the restricted B3LYP, MPW1PW91, and M062X functionals at the 6311+G(d,p) level, including the IEFPCM for acetonitrile, were subjected to single-point TDDFT calculations at the same level of theory to determine the energies of the first ten S0 → Sn transitions (Table S1, Supporting Information). In agreement with the experimental spectrum, the B3LYP and MPW1PW91 functionals estimate an electronic absorption at 344 and 323 nm, respectively (Figure 3) with an oscillator strength of ca. 0.4. In both instances, this absorption involves an electronic transition from [HOMO−1] to [LUMO]. Visualization of

Figure 3. Experimental absorption spectrum of 1a (0.1 mM, MeCN) and electronic transitions calculated with the B3LYP, MPW1PW91, and M062X functionals.

the corresponding isosurfaces (Figure 4) reveals that these molecular orbitals are mostly localized on the 4-nitrophenoxy chromophore, confirming the original assignment of the experimental spectrum. Interestingly, the M062X functional predicts the occurrence of the very same electronic transition but underestimates its wavelength by 36 nm (Figure 3), relative to the experimental value. The [HOMO−1] → [LUMO] transition responsible for the observed absorption band results in the population of the second singlet excited state (S2) of 1a. The electronic configuration associated with the first singlet excited state (S1), instead, involves the formal transfer of one electron from [HOMO] to [LUMO]. These two molecular orbitals are localized on the 2H,3H-indole and 4-nitrophenoxy fragments respectively (Figure 4) and, therefore, S1 is essentially an intramolecular charge-transfer state. This particular electronic transition, however, is not observed experimentally and, consistently, all three functionals predict a negligible oscillator strength for this forbidden process. Nonetheless, thermal relaxation of 1a from S2 can populate S1 and allow the participation of this state in the isomerization process. The excitation of 1a at 355 nm with a pulsed laser results in the appearance of a band centered at 440 nm (Figure 5) within the pulse duration (6 ns).32a This transient band resembles the ground-state absorption of a 4-nitrophenolate chromophore and, therefore, we assigned it to the ring-open isomer 1b. To confirm this assignment, we performed single-point TDDFT calculations also on the geometries of 1b optimized with the B3LYP, MPW1PW91, and M062X functionals at the 6311+G(d,p) level, including the IEFPCM for acetonitrile, to determine the energies of the first ten S0 → Sn transitions (Table S2, Supporting Information). In agreement with the experimental spectrum, the B3LYP and MPW1PW91 models estimate an electronic absorption at 452 and 422 nm, respectively (Figure 5), with an oscillator strength of ca. 0.1. In both instances, this absorption involves an electronic transition from [HOMO] to [LUMO]. Visualization of the isosurfaces (Figure 6) indicates that the occupied molecular orbital is mostly localized on the 4-nitrophenolate chromophore of 1b and the unoccupied molecular orbital extends over the entire molecule. In contrast to the B3LYP and MPW1PW91 functionals, the M062X method underestimates the wavelength for this electronic transition by 87 nm (Figure 5), relative to the experimental value. Thus, this particular 11891



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Figure 4. Isosurfaces of [HOMO−1], [HOMO], and [LUMO] of 1a calculated with the MPW1PW91 functional.

assignment of the transient absorption to 1b and its decay to the ring-closing step. The time-resolved spectroscopic analysis of 1a did not provide any information on the excitation dynamics of this system and the mechanism responsible for its photoinduced transformation into 1b. Indirect experimental evidence suggests that the photoisomerization occurs along the potential-energy surface of a triplet state.33 This tentative mechanistic interpretation is based on the spectroscopic investigation of a molecular dyad, pairing 1a covalently to a borondipyrromethene (BODIPY) chromophore. These studies demonstrate that the local excitation of the 4-nitrophenoxy fragment sensitizes the population of the BODIPY triplet, instead of encouraging the opening of the oxazine ring. Furthermore, they also reveal that the transfer of energy from one component to the other occurs in the triplet state. These experimental observations indicate that intersystem crossing follows the excitation of the 4-nitrophenoxy chromophore and suggest that the resulting triplet state, in the absence of a BODIPY quencher, is responsible for ring opening. To confirm this interpretation, we envisaged the possibility of modeling the ring opening of 1a along the potential-energy surfaces of the electronic states that can be populated after excitation at 355 nm. Specifically, the eleven geometries of scan 1 (Figure S1, Supporting Information) were subjected to single-point TDDFT calculations to determine the energies of the first ten S0 → Sn transitions. These calculations were performed with the restricted MPW1PW91 functional and the very same basis set for the optimizations in S0. Indeed, this particular functional provided the best match between experimental and calculated spectroscopic parameters for 1a and 1b (Figures 3 and 5) and, therefore, appears to be the most appropriate one for modeling the excited states of this system. Furthermore, the very same geometries were also subjected to single-point TDDFT calculations with the unrestricted MPW1PW91 functional at the 6-311+G(d,p) level to determine also the energies of the first ten triplet excited states. The energies calculated for S1, S2, and the first triplet excited state (T1) in each geometry were plotted, relative to that of the first geometry in S0, against the [C−O] bond length to build three profiles of the ring-opening process (Figure 7). Inspection of the resulting plots reveals that the potentialenergy surface of T1 is relatively flat, whereas significant energy barriers are associated with ring opening in S1 and S2. These indications are in agreement with the postulated participation of a triplet state in the ring-opening process.33 It is important to stress, however, that the energy profiles for the three excited states were constructed on the basis of single-point calculations on ground-state geometries. This general protocol is computationally convenient and is known to provide a good qualitative estimate of the course of a photochemical reaction.53,54

Figure 5. Experimental absorption spectrum of 1a (0.1 mM, MeCN), recorded 30 ns after pulsed laser excitation (355 nm, 6 ns), and electronic transitions calculated with the B3LYP, MPW1PW91, and M062X functionals.

Figure 6. Isosurfaces of [HOMO] and [LUMO] of 1b calculated with the MPW1PW91 functional.

functional fails to model accurately the excited states of both 1a and 1b.52 The transient absorption (Figure 5), observed upon excitation of 1a, decays monoexponentially on a nanosecond time scale.32a Curve fitting of the absorbance decay indicates the lifetime of the transient species to be 25 ns in acetonitrile at 298 K. This value corresponds to a free-energy barrier of 7.07 kcal mol−1. We ascribed this behavior to the spontaneous reisomerization of the photogenerated isomer 1b back to the original species 1a. This transformation involves the very same ring-closing step associated with the thermal interconversion of the two enantiomers of 1a (Figure 2). Indeed, the experimental free-energy barrier (cf. 7.07 kcal mol−1) is remarkably close to the calculated ΔG‡Cl, which ranges from 5.85 to 7.82 kcal mol−1 (Table 1). Thus, the excellent agreement between experimental and calculated values support, once again, our original 11892



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also reproduces successfully the influence of the substituent, attached to the chiral center at the junction of the two heterocycles, on the kinetics of the ring-opening step. In contrast, the B3LYP functional fails to model accurately the interconversion of the two enantiomers. In particular, this method underestimates significantly the free-energy barrier for ring-opening and the free-energy difference between 1a and 1b. The B3LYP and MPW1PW91 functionals ascribe the absorption band observed experimentally for 1a to a [HOMO−1] → [LUMO] transition centered predominantly on the 4-nitrophenoxy chromophore, confirming the original assignment of the experimental spectrum. Similarly, both functionals indicate that the transient band, observed upon excitation of 1a, corresponds to a [HOMO] → [LUMO] transition for 1b and, therefore, support the photoinduced formation of this isomer. The two functionals also provide estimates of the wavelengths for both bands that are in excellent agreement with the corresponding experimental values. Instead, the M062X model underestimates significantly the wavelengths for both transitions and appears to be inadequate for modeling the excited states of this system. The three functionals provide estimates for the free-energy barrier of ring closing that are in excellent agreement with the experimental value determined for the temporal decay of the transient band by time-resolved absorption spectroscopy. These observations support the assignment of the transient absorption to the ring-open isomer 1b and confirm, once again, the photoinduced formation of this species. The MPW1PW91 functional indicates that the photoinduced isomerization of 1a into 1b occurs preferentially along the potential-energy surface of T1. Specifically, 1a is first excited to S2 and then relaxes to T1 through the formation of S1. Ring opening in T1 converts 1a into 1b, which then relaxes to S0. This mechanistic interpretation agrees with the established involvement of a triplet state in the excitation dynamics of these compounds, emerged from the spectroscopic investigations of related multichromophoric assemblies. In summary, our calculations (1) elucidate the elementary steps involved in the thermal equilibration of our oxazines, (2) confirm the original assignments of their experimental absorption spectra, (3) support the structural identity of the photogenerated species, and (4) provide a mechanistic model for their excitation dynamics. Thus, these valuable computational insights on the isomerization of these photochromic compounds in the ground state and upon excitation can facilitate the future design of novel members of this family of photoresponsive molecules with engineered properties.

Figure 7. Energy profiles for the ring-opening of 1a in the ground and excited states calculated with the MPW1PW91 functional.

Nonetheless, it does not take into account the relaxation of each geometry in the corresponding excited state. To corroborate further our mechanistic interpretation, the initial and final geometries of scan 1 were optimized in S0, S1, and T1 with the unrestricted MPW1PW91 functional at the 6311+G(d,p) level, including the IEFPCM for acetonitrile.55,56 The relative energies (Figure 8) of the resulting geometries indicate that 1a is more stable than 1b in S1 by 0.61 eV, but that the former isomer is less stable than the latter in T1 by 0.04 eV. These values suggest, once again, that the oxazine ring opens along the potential-energy surface of T1. Thus, the path highlighted in Figure 8 can be postulated for the photoinduced transformation of 1a into 1b on the basis of these data. Specifically, the illumination of 1a at 355 nm excites this compound from S0 to S2. The subsequent internal conversion from S2 to S1 and intersystem crossing from S1 to T1 populates the electronic state responsible for ring opening.57 Indeed, the opening of the oxazine ring of 1a generates 1b in T1 and intersystem crossing from T1 to S0 brings the ring-open isomer to the ground state.

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CONCLUSIONS The MPW1PW91 and M062X functionals provide estimates of the free-energy barrier for the ring-opening of 1a that are in excellent agreement with the experimental value determined for the interconversion of its two enantiomers by variable temperature 1H NMR spectroscopy. These observations suggest that the ring-opening step determines the rate of the overall degenerate process. In addition, the M062X functional

Figure 8. Energies of the optimized geometries of 1a and 1b in S0, S1, and T1 and of the Franck−Condon geometry of 1a in S2, calculated with the MPW1PW91 functional, together with the postulated path for the photoinduced transformation of 1a into 1b. 11893



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ASSOCIATED CONTENT

S Supporting Information *

Energy profiles of the three elementary steps associated with the interconversion of the two enantiomers of 1a in the ground state. Animations of the vibrations associated with the imaginary frequencies of the transition states for the three consecutive steps of the interconversion of the two enantiomers of 1a in the ground state. Coordinates of the optimized geometries of 1a, 1b, 2a, 2b and the corresponding transition states in the ground state. Coordinates of the optimized geometries of 1a and 1b in the excites states. Calculated spectroscopic data for the first ten S0 → Sn transitions of 1a and 1b. Coordinates of the optimized geometries of 1a and 1b in the ground and excited states. Complete ref 41. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the National Science Foundation (CAREER Award CHE-0237578, CHE-0749840 and CHE-1049860) for supporting our research program, Arghya Barman for technical assistance and Rajeev Prabhakar for insightful discussions.

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REFERENCES

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(37) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (38) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671− 6687. (39) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664−675. (40) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215−241. (41) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision A.02; Gaussian, Inc.: Wallingford, CT, 2009. (42) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. Rev. 2005, 105, 2999−3093. (43) Furche, F.; Ahlrichs, R. J. Chem. Phys. 2002, 117, 7433−7447. (44) Nelson, J. H. Nuclear Magnetic Resonance Spectroscopy; PrenticeHall: Upper Saddle River, NJ, 2003. (45) The synthesis of 1a was originally reported in: (a) Shachkus, A. A.; Degutis, J.; Jezerskaite, A. In Chemistry of Heterocyclice Compounds; Kovac, J., Zalupsky, P., Eds.; Elsevier: Amsterdam, 1987; Vol. 35, pp 518−520. (b) Shachkus, A. A.; Degutis, J.; Urbonavichyus, A. G. Khim. Geterotskil. Soed. 1989, 5, 672−676; Chem. Heterocycl. Compd. 1989, 562−565. (c) Barkauskas, M.; Martynaitis, V.; Shachkus, A. A.; Rotomskis, R.; Sirutkaitis, V.; Vengris, M. Lithuanian J. Phys 2008, 48, 231−242. (46) In principle, rotation about this dihedral angle in the opposite direction can also exchange the two configurations. However, the corresponding energy barrier is significantly higher than that associated with scan 2 in Figure S1, Supporting Information. (47) The geometries optimized without and with the solvation model are essentially identical for all three functionals. The average bondangle and -length displacements are smaller than 0.08° and 0.003 Å. However, the energies calculated with the solvation model are ca. 8.1 kcal mol−1 lower than those estimated without. (48) In principle, the structures optimized from the initial geometry of scan 1 and the final geometry of scan 3 should be degenerate mirror images. Consistently, the three functionals predict negligible energy differences between these two structures. Similarly, the structures optimized from the initial and final geometries of scan 2 should also be degenerate mirror images. However, the B3LYP, MPW1PW91, and M062X functionals predict free-energy differences of 0.43, 0.12, and 1.85 kcal mol−1 respectively in favor of the first geometry. As a result, the values of ΔG‡Cl reported in Table 1 were estimated from the data determined from scan 1, rather than from those obtained from scan 3. (49) In principle, the transition states optimized from the geometries found with scan 1 and scan 3 should be degenerate mirror images. Consistently, the three functionals predict negligible free-energy differences between these two structures. (50) Variable-temperature 1H NMR spectroscopy monitors the overall rate of exchange of the two diastereotopic environments, rather than probing the individual elementary steps responsible for interconversion. As a result, the free-energy barrier determined with this technique reflects the whole process. Nonetheless, the excellent agreement between this value and those calculated for just ring opening suggests that this particular step is essentially determining the rate of the overall degenerate process. (51) Inspection of the geometries optimized for 1a and the corresponding transition state for ring opening shows that one of the [C−H] bonds of the methyl group on the chiral center is antiperiplanar to the breaking [C−O] bond in both structures. Furthermore, this particular [C−H] bond elongates by ca. 0.01 Å in the transition state, whereas the other two [C−H] bonds of the methyl group remain unaffected. These observations suggest that hyperconjugation of the electrons in the anti-periplanar [C−H] bond with the cleaving [C−O] bond facilitates the opening of the oxazine ring, relative to the phenyl analog 2a. (52) The fractions of Hartree−Fock (HF) exchange in the B3LYP, M062X, and MPW1PW91 functionals are 20, 54, and 25%, respectively.39,40 Presumably, the large HF exchange fraction of the M062X functional is mostly responsible for the discrepancy in the calculated excited-state energies. Indeed, the HF exchange fraction is

known to have a significant role in the prediction of spectroscopic properties with DFT calculations: Mikhailov, I. A.; Bondar, M. V.; Belfield, K. D.; Masunov, A. E. J. Phys. Chem. C 2009, 113, 20719− 20724. (53) Salassa, L.; Garino, C.; Salassa, G.; Gobetto, R.; Nervi, C. J. Am. Chem. Soc. 2008, 130, 9590−9597. (54) Iwamura, M.; Watanabe, H.; Ishii, K.; Takeuchi, S.; Tahara, T. J. Am. Chem. Soc. 2011, 133, 7728−7736. (55) Comparison of the geometries of 1a optimized in S0, S1, and T1 shows differences predominantly around the chiral center at the junction of the two heterocyclic fragments and on the nitro group. Specifically, the [C−O] and [C−N] bonds of the former shorten by ca. 0.06 Å in the excited states, whereas the [N−O] bonds of the latter elongate by approximately the same amount. Similar changes are also observed for 1b around the charged nitrogen and oxygen atoms and the nitro group. (56) The choice of an unrestricted functional is based on a literature precedent.53 The very same geometries were also subjected to restricted calculations and no significant differences in energies were observed. (57) In principle, intersystem crossing from S2 into T2 and internal conversion from T2 to T1 can also result in the population of the electronic state responsible for ring opening. Nonetheless, internal conversion is generally significantly faster than intersystem crossing. Therefore, thermal relaxation from S2 to T1 through the intermediate formation of S1, rather than T2, appears to be the most probable pathway for the excitation dynamics of 1a.

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Computational Insights on the Isomerization of Photochromic

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