The Molecular Mechanism of Photochromism in Photo-Enolizable

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The Molecular Mechanism of Photochromism in Photo-Enolizable Quinoline and Napthyridine Derivatives S. Knippenberg,*,† M. Schneider,‡ P. Mangal,‡ and A. Dreuw‡ †

Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc 20, B-7000 Mons, Belgium, and Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany

‡

S Supporting Information *

ABSTRACT: Photochromism, the change of color upon irradiation, is a general property of quinoline derivatives, yet subtle differences in the geometric structure influence its occurrence. To investigate this relation, the mechanism of photoenolization of the photochromic compounds 3-benzoyl-2-benzyl-1-methyl-1H-quinoline-4-one (1) and 3-benzoyl-1,2-dibenzyl-1H-1,8 naphtyridin-4-one (2) as well as of the structurally closely related but nonphotochromic 3-benzoyl-1-benzyl-2-methyl-1H-1,8naphtyridin-4-one (3) has been investigated theoretically using state-of-the-art quantum chemical methods. Focusing on the difference between 2 and 3 and stressing the absence of a phenyl group in the latter, the excited state potential energy surfaces along the photoenolization coordinate have been calculated for both. While the initial proton transfer initializing photoenolization is feasible when the phenyl group is present in 1 and 2, it is suppressed in 3.

1. INTRODUCTION Photochromism generally describes a reversible color change of a molecule or material upon light exposure. This change of the absorption spectrum in the visible region is the consequence of some reversible photochemical process.1,2 o-Alkylphenylketones, for example, are prototypical examples showing photochromism induced by a light-triggered1,5 sigmatropic H-shift, a so-called photoenolization, leading to the formation of colored but unstable o-xylylenol photoproducts.3,4 Attempts have been made to stabilize the photogenerated enol form of oalkylphenylketones, to make the photochromism longerlived.5,6 Along this line of thought, it has been suggested to replace the phenyl ring by heterocycles with additional carbonyl groups leading to 1,3-diketone-like structural motifs, for which the enol form is known to be stabilized by an intramolecular hydrogen bond.7,8 Accordingly, a plethora of compounds has been synthesized and tested with respect to the occurrence of photochromism.9−13 A promising class of compounds in this © XXXX American Chemical Society

context are substituted quinoline and naphthyridine compounds, which exhibit a favorable 1,3-diketone structure (Figure 1) and which can be suitably substituted at various positions of the rings and alkyl chains.7,8,14 Recently, the photochromism and the underlying photoenolization mechanism of 3-benzoyl-2-benzyl-1-methyl-1Hquinoline-4-one 1, 3-benzoyl-1,2-dibenzyl-1H-1,8-naphthyridine-4-one 2 and 3-benzoyl-1-benzyl-2-methyl-1H-1,8-naphthyridine-4-one 3 (Figure 1) have been thoroughly investigated using time-resolved spectroscopy.15 On the basis of previous experimental and theoretical works on photoenolization processes,5,16−21 the identified intermediates have been assigned to triplet states and a preliminary reaction scheme has been suggested.15 However, despite the similarity in the Received: October 2, 2012 Revised: November 26, 2012

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TDDFT26−29 and a set of exchange-correlation (xc) functionals, with Hartree−Fock (HF) exchange varying from 0% (BLYP), over 20% (B3LYP) up to 50% (BHLYP). Also, the long-range corrected xc-functional ωB97x has been employed.30,31 In addition, configuration interaction singles with perturbative doubles (CIS(D))32,33 has been applied as simplest wave function-based ab initio method. For benchmarking, the singlet excited states of the smallest model systems have also been computed with more accurate methods like the strict and extended second order diagrammatic construction scheme [ADC(2)-s and ADC(2)-x, respectively]34−37 and the approximate coupled-cluster approach in second order (CC2).38−40 In all these calculations, the resolution-of-theidentity approximation is exploited and the 6-31G* basis set is used in combination with the corresponding fitting basis. For the TDDFT, CIS(D) and ADC(2) calculations a development version of the Q-Chem package of programs has been used,41 while for the CC2 calculations Turbomole 5.10 has been employed. The chosen moderate basis set size suffices to describe the relevant ππ* and nπ* excitations of the quinoline and naphtyridine derivatives accurately enough, and larger basis sets have frequently been shown to provide not a significant improvement of the energetics.42−45 The identified triplet intermediates along the photoenolization reaction paths of the investigated molecules have been optimized at the standard unrestricted Kohn−Sham DFT as well as linear-response TDDFT level using B3LYP/6-31G*. It turned out that the differences in the geometrical parameters were only minor. For the investigation of the photoenolization reaction pathways, relaxed scans of the potential energy surfaces along the coordinate representing the hydrogen transfer from the o-methylene group to the ketone oxygen have been computed at the TDDFT/B3LYP/6-31G* level for the reduced molecular models. The accuracy of these calculations has been checked by comparison to calculations at CC2 level for selected representative structures. In general the CC2 and TDDFT/ B3LYP results agree nicely (Supporting Information). To arrive from the computed optimized structures of the intermediates at a chemically more intuitive picture, analyses of Wiberg bond indices of the initial ground state structure and various triplet structures have been performed.46,47

Figure 1. Molecular structures of 3-benzoyl-2-benzyl-1-methyl-1Hquinoline-4-one 1, 3-benzoyl-1,2-dibenzyl-1H-1,8 naphtyridin-4-one 2 and 3-benzoyl-1-benzyl-2- methyl-1H-1,8-naphtyridin-4-one 3, compared to the structures of the molecular model compounds 0, 0A, and 0B. Note that 1 and 2 are photochromic, while 3 is not. A notation like C8(H)3 denotes a molecular fragment which consists out of three hydrogen atoms bound to the carbon atom C8.

structure and the presence of the 1,3-diketone structural motif in all three compounds, only 1 and 2 are photochromic, but 3 is not. Obviously, the 2-benzyl substitutent has a crucial influence on the occurrence of photoenolization in 1 and 2. To shed some light onto this puzzle and to clarify the relation between substitution pattern and photochromism, we have studied the relevant excited states of the photoenolization process theoretically using quantum chemical methods and investigated the reaction mechanism acting in compounds 1−3. The paper is organized as follows. After outlining the applied theoretical methods (section 2), the accuracy and applicability of time-dependent density functional theory (TDDFT) for the description of the photoenolization of the molecules 1 to 3 as well as of the reduced molecular models will be thoroughly evaluated (subsection 3.1). Afterward, the vertical excited singlet and triplet states of the compounds 1 to 3 will be investigated in detail (subsection 3.2), before the photoenolization pathways are studied in the subsequent subsection 3.3. The paper concludes with a brief summary of the main conclusions (section 4).

3. MOLECULAR MECHANISM OF PHOTOENOLIZATION The photoenolization leading to the observed photochromism occurs after initial excitation of an optically allowed ππ* singlet state after intersystem crossing within the triplet state manifold. The triplet state is assumed to possess nπ* character and is related to a biradicaloid state of the ketone,3,16,19,48 which promotes hydrogen transfer and the formation of a first enoltype structure via a [1,5] hydrogen shift. From this first intermediate the molecules relax back to the electronic singlet ground state again via intersystem crossing to eventually form the colored ground state enol form. This mechanism explains the photochromism of many compounds and was recently corroborated using stationary and time-resolved spectroscopy techniques.15,49 However, the electronic structure of the states involved is the key factor determining the occurrence of photochromism in different molecules and generally requires individual attention.50−52 Hence, to gain more detailed insight into this mechanism and to explain the differences in the photochromism of the structurally closely related naphthyridine derivatives 2 and 3,

2. COMPUTATIONAL DETAILS The geometries of the model compounds as well as of the parent molecules 1, 2, and 3 have been optimized using DFT along with the B3LYP functional22,23 and Pople’s 6-31G*24 basis set as implemented in Turbomole 5.10.25 The lowest excited singlet and triplet states of 0 have been calculated using B

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Table 1. Computed Vertical Excitation Energies of the Four Energetically Lowest Singlet and Triplet Excited States of the Molecular Model Compound 0a BLYP S1 S2 S3 S4 T1 T2 T3 T4

2.32 nπ* 3.27 nπ* 3.34 nπ* 3.50 ππ* 2.14 nπ* 2.76 ππ* 2.99 nπ* 3.08 nπ*

(0.00) (0.00) (0.00) (0.07)

B3LYP 3.09 nπ* 3.95 nπ* 3.97 ππ* 4.09 nπ* 2.73 nπ* 2.95 ππ* 3.48 ππ* 3.56 nπ*

(0.00) (0.00) (0.09) (0.00)

BHLYP 3.82 nπ* 4.58 ππ* 4.61 nπ* 5.42 nπ* 2.98 ππ* 3.26 ππ* 3.26 nπ* 4.07 ππ*

(0.00) (0.12) (0.00) (0.00)

ωB97x 3.65 nπ* 4.45 nπ* 4.51 ππ* 5.15 nπ* 3.11 ππ* 3.16 nπ* 3.52 ππ* 4.01 nπ*

CIS(D)

(0.00) (0.00) (0.12) (0.00)

3.65 nπ* 4.28 nπ* 4.36 nπ* 4.42 ππ* 3.36 nπ* 3.94 ππ* 4.07 nπ* 4.14 ππ*

CC2 3.40 nπ* 4.28 nπ* 4.30 ππ* 4.40 nπ* 3.16 nπ* 3.57 ππ* 4.04 nπ* 4.08 ππ*

(0.00) (0.00) (0.14) (0.00)

ADC(2)-s

ADC(2)-x

3.20 nπ* 4.02 nπ* 4.16 ππ* 4.19 nπ* − − − − − − − −

2.46 nπ* 3.25 nπ* 3.39 ππ* 3.42 nπ* − − − − − − − −

(0.00) (0.00) (0.17) (0.00)

(0.00) (0.00) (0.13) (0.00)

a Energies [eV], oscillator strengths (in parentheses) and the character of the transition are given. The 6-31G* basis set has been used in all calculations.

ADC(2)-x levels of theory, the S1, S2, S3, and S4 states are consistently found as nπ*, nπ*, ππ*, and nπ* states, respectively (Table 1). In general, comparison of ADC(2)-s and ADC(2)-x results can be employed as a simple diagnostic for relevant doubly excited states in the low-energy region:60−62 the ADC(2)-s secular matrix contains only the orbital energy differences on the diagonal of the two particle−two hole (2p− 2h) block, and, as a result, the double excitations appear at too high energies and hardly mix with low-lying single excitations. In the ADC(2)-x secular matrix, by contrast, the diagonal matrix elements of this block represent the first-order expressions for the 2p−2h excitation energies. In the current study, all excited states are consistently shifted to lower energies by 0.8 eV going from ADC(2)-s to ADC(2)-x and the order of states is conserved (Table 1). Also, the excited states S1 to S4 do not exhibit significant contributions of doubly excited configurations in their ADC vectors at ADC(2)-x level. Hence, single electron excitation theories like TDDFT, ADC(2)-s or CC2 can safely be applied. The lowest excited singlet state with significant oscillator strengths is S3 given at 4.30 and 4.16 eV at CC2 and ADC(2)-s level with oscillator strengths of 0.14 and 0.17, respectively, possessing typical ππ* character (Table 1). For the evaluation of the applicability of TDDFT, the standard xc-functionals BLYP, B3LYP, and BHLYP as well as the long-range separated ωB97x xc-functional have been applied for the calculation of the lowest excited states of 0, because they possess different amounts of Hartree−Fock exchange, which is essential to diagnose a possible CT failure.63,64 All xc-functionals yield the first excited singlet state S1 as an electron transition from the highest occupied molecular orbital (H) to the lowest unoccupied molecular orbital (L) with nπ* character referring to molecular orbitals (not shown) and detachment/attachment density plots at B3LYP/6-31G* level (Figure 2). However, the excitation energy of S1 increases strongly from BLYP to B3LYP and BHLYP from 2.32 eV to 3.09 and 3.82 eV, i.e., by as much as 1.5 eV. This shift is larger than the typical blue shift of excitation energies seen with increasing amount of HF exchange at TDDFT level,65 and thus hints at a problem of

their excited singlet and triplet states need to be computed reliably. Hence, as first step, a suitable theoretical method needs to be identified, which is capable of describing the essential steps and relevant excited states efficiently. Then, in a second step, the vertical excited states of 1 to 3 are to be calculated and their electronic structure analyzed, before finally, the photoenolization mechanism can be studied conclusively for the compounds 2 and 3 to identify differences and similarities explaining the occurrence of photochromism in the first but not in the latter. 3.1. Vertical Excited States of the Simplest Model Compound. The large molecular size of the compounds 1, 2 and 3 (Figure 1) requires a theoretical method with moderate requirements with respect to computation time and resources. In such cases, TDDFT is often chosen along with a specific exchange-correlation (xc) functional. However, one has to cope with its general draw-backs, like the well-known problems for Rydberg excited states, states with double excitation character and charge-transfer (CT) excited states.27,53 However, for certain classes of molecules and, in particular, for locally excited states energetically well below the ionization potential (e.g., ππ* or nπ* transitions), TDDFT provides high-quality results at low computational cost. Thus, to test for the known deficiencies and to take advantage of the merits of (TD)DFT, one has to carefully study the applicability of TDDFT to the problem of interest by comparison to more reliable ab initio approaches like for example symmetry adapted cluster configuration interaction (SAC−CI),54−56 complete active space self consistent field (CASSCF),57,58 CC2,39,59 or ADC(2).34−37 For that objective, however, the molecular size of the three molecules under investigation 1, 2, and 3 has to be reduced by neglecting the annealed aromatic ring and by replacing the phenyl substituents by hydrogen atoms. This results in the minimal molecular model 0 (Figure 1), which allows for calculations of its excited states at the abovementioned theoretical levels still capturing the states relevant for the photoenolization process, as will be demonstrated below. Let us first turn to the discussion of the results obtained for the singlet excited states of 0. At the RI-CC2, ADC(2)-s, and C

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in the xc-functional than in the case of the singlets. While BLYP underestimates the excitation energies of nπ* states due to their partial CT character, BHLYP overestimates them. Hence, both give a wrong triplet state ordering as compared to CC2. Again, B3LYP yields the best agreement, only the order of the practically degenerate states T3 and T4 is interchanged, which however is only of minor relevance for the planned investigation. In summary, since TDDFT in combination with the B3LYP xc-functionals yields the same order for the relevant singlet and triplet states, and their excitation energies are consistently underestimated by reasonable 0.3−0.4 eV (singlet) and 0.4−0.6 eV (triplet states), the B3LYP xcfunctional is suitable for the description of the excited-state processes occurring in the larger molecules 1, 2, and 3. 3.2. Vertical Excited States of the Quinoline and Napthyridine Derivatives. After we have shown in the previous section that TDDFT in combination with the standard B3LYP xc-functional yields reliable vertical excitation energies for the lowest excited states of the quinoline model system 0, we are now in a position to thoroughly investigate the vertical excited states of the complete quinoline and naphthyridine derivatives 1 to 3 (Figure 1) including all ligands into the calculation. The structural differences between the reduced model 0 and the complete molecules may have a significant influence on the excited states, which shall also be addressed in the following. Let us first inspect the relevant valence orbitals of 1−3, since they are important for the characterization of the excited states. It can be seen in Figure 3 that the HOMO (H) of all three

Figure 2. Detachment/attachment density plots for the energetically lowest four excited singlet states of 0 obtained at the TDDFT/ B3LYP/6-31G* level. S1, S2, and S4 exhibit nπ* character, while S3 is a typical ππ* excitation.

TDDFT with the CT character of that state. Using the ωB97x functional, the excitation energy is 3.65 eV. However, xcfunctionals with large fractions of HF exchange often overestimate the excitation energies of nπ* states, which seems to be here the case, since the vertical excitation energy of this state is much lower at CC2 and ADC(2) level than using TDDFT/BHLYP or TDDFT/ωB97x. Comparing all TDDFT computed values with those obtained at CC2 and ADC(2) levels of theory, and given the fact that B3LYP yields the same state ordering as CC2 and ADC(2), B3LYP offers here an ideal compromise between accuracy and efficiency for the calculation of the lowest excited singlet states. Also ωB97x is a reasonable alternative, however the deviation from the ADC(2) and CC2 results is larger. Obviously, the necessity to properly describe the balance between nπ* and ππ* states overweights the charge-transfer problem for this class of molecules. Detachment-attachment density plots of the energetically lowest four excited states obtained at TDDFT/B3LYP/6-31G* level are displayed in Figure 2. The detachment density represents that part of the one-electron ground state density that is removed upon excitation and rearranged as attachment density. From these plots it is clear that all lower excitations involve the formyl group C10HO11 (for the numbering scheme see Figure 1), and none of these excitations are located at the methyl groups attached to N5 and C6. The S1, S2 and S4 states correspond clearly to nπ* states, while S3 is a typical ππ* excitation, the only one with considerable oscillator strength (Table 1). Turning to the excited triplet states of 0, the results for the four lowest triplet excited states are compiled in Table 1. At CC2 level of theory, the T1, T2, T3, and T4 have nπ*, ππ*, nπ*, and ππ* character, respectively. T3 and T4 are nearly degenerate, with excitation energies of about 4.05 eV. The comparison of the TDDFT data with the ones obtained at CC2 level reveals a stronger influence of the amount of HF exchange

Figure 3. B3LYP/6-31G* orbitals of 1, 2, and 3, optimized at the B3LYP/6-31G* level of theory. H and L denote the highest occupied and the lowest unoccupied molecular orbitals, respectively.

compounds 1 to 3 corresponds to a π-orbital localized at the quinoline and naphtyridine rings. An oxygen lone pair character is seen in the H-1 of the three compounds, which represents mainly an n-orbitals of the carbonyl oxygen O11. The H-2 of 1 and 3, as well as the H-3 of 2 correspond to π-orbitals at the phenyl ring attached to C10, and, in the case of 2, also at the one at C9. For 2 and 3, the LUMO (L) and L + 1 orbitals are dominated by a profound π* character. While the latter is mainly at the phenyl ring at C10, the LUMO has mostly contributions at the naphtyridine rings. For 1, it is the L which has a large contribution from the phenyl ring at C10, while the L + 1 has a large electron density at the quinoline rings. The computed vertical excitation energies of the four lowest excited singlet and triplet states of 1 to 3 are compiled in Table D

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The vertical excited state structure of all three compounds is overall very similar, in particular the one of 2 and 3. Hence, the static vertical excited singlet states can not explain the difference in photochromism between these two molecules, since 2 is photochromic, while 3 is not. However, the photoenolization reaction responsible for photochromism is thought to occur after intersystem crossing in a triplet states. Analysis of the four lowest excited triplet states of 1 to 3 reveals that the lowest T1 state is a ππ* state, which is in the molecular orbital picture best represented as H → L + 1 for 1 and H → L transition for 2 and 3. Physically, these are the same states, since the L of 1 is essentially the same orbital as the L + 1 of 2 and 3. The T1 state is in all compounds found 0.5 to 0.6 eV below the first singlet excited states. Also T2 is identical in all three molecules and corresponds to a ππ* transition, which is given as H → L transition in 1 and as H → L+1 transition in 2 and 3. The corresponding ππ* excited state, which is found as T3 in 1 as H-2 → L transition, is the T4 state in 2 and 3. The only nπ* excited triplet state among the four lowest ones is the T4 state in 1 and its identical partners, the T3 states of 2 and 3. Overall, also the four lowest excited triplet states of the three compounds are very similar and can thus not account for the observed differences in photochromism of 2 and 3. To further corroborate the applicability of TDDFT/B3LYP to the excited states of the three compounds investigated here, we calculated the four lowest singlet and triplet states of 3 also with the long-range corrected ωB97x functional. The same state ordering has been obtained, and only the quasi degenerate S1 (ππ*) and S2 (nπ*) states with excitation energies of 3.91 and 4.13 eV interchange their positions with respect to the B3LYP results. The S3 (H → L) and S4 (H → L + 1) states with ππ* character are found at 4.56 and 4.78 eV. The T2 and T3 states have nπ* and ππ* character at 3.14 and 3.36 eV, respectively. They switch their places with respect to the B3LYP results, too. The T1 and T4 states, both referring to ππ* excitations, are found at 3.06 and 3.55 eV, respectively. The observed changes are small and not relevant for the identified mechanism. Hence B3LYP is clearly sufficient for the study of the photoenolization mechanism. Let us finally compare the excited states of the compounds 1 to 3 with those of the model compound 0. It can be noted that

2. At the level of TDDFT/B3LYP, the lowest excited singlet state of 1 corresponds to a ππ* transition with little oscillator Table 2. Calculated Vertical Excitation Energies of the Four Energetically Lowest Singlet and Triplet Excited States of 1, 2, and 3 at the Theoretical Level of TDDFT/B3LYP Using the 6-31G* Basis Seta 1 S1 S2 S3 S4 T1 T2 T3 T4

3.46 3.61 3.76 4.02 2.91 3.04 3.19 3.26

(0.03) (0.00) (0.04) (0.08)

2 ππ* nπ* nπ* ππ* ππ* ππ* ππ* nπ*

3.48 3.49 3.84 3.87 2.87 3.02 3.15 3.21

(0.01) (0.02) (0.03) (0.11)

3 nπ* ππ* ππ* ππ* ππ* ππ* nπ* ππ*

3.48 3.52 3.87 3.91 2.89 3.03 3.16 3.24

(0.00) (0.02) (0.05) (0.09)

nπ* ππ* ππ* ππ* ππ* ππ* nπ* ππ*

a

Excitation energies [eV], oscillator strengths (in parentheses), and the character of the excited state is given.

strength, which in the molecular orbital picture can be mainly represented as an H → L transition. S2 and S3 of 1 correspond to nπ* states and are energetically only slightly higher than S1. Both states can be described as excitations of an electron out of the H-1orbital into the virtual L + 1 and L orbitals, respectively. Note that S1, S2 and S3 are separated by only 0.15 eV. The fourth excited singlet state S4 of 1 has again ππ* character and is mostly a H-2 → L electronic transition. This state has substantial oscillator strength of 0.08 at this level of theory. In 2 and 3, the lowest excited singlet state is an nπ* state best described as an electronic H-1 → L transition. While in 2 the S2 corresponds to a state with mixed nπ* and ππ* character mainly characterized as linear combination of the determinants H-1 → L and H → L + 1, the S2 of 3 is a clear ππ* transition, i.e. H → L + 1. The S3 of 2 is again a mixed nπ* and ππ* state, while in 3 is given as a ππ* excited one. The fourth excited singlet state of 2 and 3 exhibits ππ* character with a large oscillator strength. In both molecules, however, the S1 and S2 states as well as the S3 and S4 states are practically degenerate.

Figure 4. The potential energy surfaces of the electronic ground state (blue), the lowest excited singlet S1 state (red) and the lowest triplet state (green) of the model 0A resembling 1 and 2 along the photoenolization reaction path, which corresponds first to a proton transfer and then to a dihedral angle rotation (see text). SA0 and SE0 are optimized in the singlet ground state using DFT/B3LYP. From SA1 to SB1 and from TC1 to TE1 , the optimizations have been performed in the S1 and T1 states, respectively, at LR-TDDFT/B3LYP level of theory. E

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pure ππ* character, efficient intersystem crossing can be expected to occur at this point according to El-Sayed’s rule.66 Equivalently or even more likely, the excited S1 state population can at this structure SB1 go through a conical intersection with S0 and return to the electronic ground state and undergo thermal back-proton transfer. However, in the case intersystem crossing occurs the excited state population resides in T1 at the structure TC1 , which corresponds to a local minimum on the triplet surface. From there on, the reaction coordinate on the first triplet state leading to the final photoenolization product is now expressed by the dihedral angle C6−C1−C10−O11. As can be seen in Figure 4, for the rotation around this dihedral angle an energy barrier of only 11 kcal/mol needs to be crossed when the dihedral angle reaches 90° at the structure T1D. The corresponding energy barrier in the first excited singlet state would be higher with 15 kcal/mol. Along this rotation coordinate, the singlet ground state crosses even the T1 at an angle of 75° and 110°, in other words, T1 becomes the electronic ground state for values of C6−C1−C10−O11 between 75° and 110°. At a dihedral angle of 180°, the structure TE1 is reached, which is about 10 kcal/mol lower in energy than the initial structure TC1 but practically energetically degenerate with the singlet ground state. Hence, intersystem crossing can again occur and the excited triplet state population relaxes back to the electronic ground state equilibrium structure S0E, which corresponds to the photoenolization product and the colored species responsible for the observed photochromism. The identified reaction pathway nicely explains the observed photochromism of 1 and 2. It also explains the change of the experimental absorption spectrum at a time scale of minutes, i.e., the slow increase of the concentration of the photochromic species. Indeed, only a small part of the initially excited molecules can be expected to reach SE0 , as at least two (singlet− triplet) inter system crossing are needed. Most importantly, the first intersystem crossing occurs at a three-state degeneracy, where it competes with ultrafast relaxation via a S1/S0 conical intersection. Hence, most of the initially excited molecules will undergo ultrafast excited state proton transfer and immediate back-proton transfer in the ground state to return to the initial structure SA0 . Wiberg bond indices quantifying the bond order have been calculated for the relevant structures along the reaction mechanism on the singlet (SA0 and SE0 ) and triplet (TC1 , TD1 , and TE1 ) surfaces (Figure 5). The bonds that are most affected by the proton transfer from C9 to O11 are C9−C6, C6−C1, C1− C10 and C10−O11 ones. Going from the structure SA0 to the photoenolization product SE0 , the C9−C6 single bond turns into a double bond, the bond index of C6−C1 decreases from 1.54 to 1.08, the C1−C10 again increases the bond index from 1.02 to 1.46, and most importantly, the carbonyl C10−O11 bond becomes a single bond with bond order 1.20. Neighboring bonds like C4−C3 and C2−O7 are not affected and keep their double bond character along the process with Wiberg bond indices of 1.54−1.68, and 1.49−1.62, respectively. The calculated bond indices for the triplet structures are for all of them very similar. Not surprisingly, the sum of the bond indices is decreased by one compared to the singlet structures, and this decrease is found in the four bonds discussed above. This is in agreement with the Mulliken spin densities, which indicate that the unpaired electrons are found at C9 and C10. Having identified the photoenolization mechanism and the origin of the photochromism of 1 and 2, the next step is to

the S1 states of all molecules, which play the most important roles in determining the photochemistry, are strictly analogous to each other, because orbitals with identical character are involved and the same nπ* character is of the S1 states is hence found. For the triplet states, however, the H-1 → L ππ* transition of the model system 0 is found as T2 at about the same energy of 2.951 eV (Table 1) as in the full systems. In the model system 0, the nπ* H → L excited state has a lower energy of only 2.73 eV, while for the real molecules 1, 2, and 3, the energetically lowest nπ* triplet excited states are found as T4, T3 and T3 at 3.26, 3.15, and 3.16 eV, respectively. For the lowest lying triplet states, it is seen that for all three compounds, 1 to 3, the first two clearly have ππ* character, which contradicts previous assumptions.15 3.3. Mechanism of Photoenolization Invoking Photochromism. As we have seen above, the vertical excited states of the compounds 1 to 3 alone can not explain the observed differences in photochromism, since all compounds exhibit very similar excited singlet and triplet states. To find the reason for the observed photochromism of 1 and 2 and its absence in 3, the excited state potential energy surfaces of the relevant singlet and triplet states need to be computed along the reaction coordinate representing the photoenolization responsible for the photochromism. However, this is not possible for the complete compounds due to their large molecular size and the concomitant immense computational effort. Therefore, we resort again to molecular model systems in analogy to 0, which we used before to benchmark the excited state methodology. Since we are aiming at explaining the photochromism of 1 and 2 and its absence in 3, we need to capture the structural differences between them within the model. We have chosen the molecular model 0A resembling 1 and 2, since this possesses a phenyl group at C9, while model system 0B in analogy to 3 does not. The phenyl group at C9 is the only structural difference between photochromic 2 and nonphotochromic 3 (see Figure 1). For the model structure 0A resembling the photochromic compounds 1 and 2 (Figure 1), a relaxed scan of the excited state potential energy surfaces has been performed at the theoretical level of TDDFT/B3LYP/6-31G* along the proton transfer coordinate initializing the photoenolization (Figure 4). Vertical photoexcitation of the molecule at the ground state equilibrium structure SA0 and ultrafast relaxation within the singlet excited state takes the excited state population to a structure SA1 on the energetically lowest singlet excited state surface, in which the proton is still attached to the methylene carbon at C9. This relaxed structure lies already 12 kcal/mol below the Franck−Condon point. From this point, however, a continuous decrease of the potential energy is observed when the proton is continuously transferred from C9 to O11. Eventually, the structure SB1 is obtained, which is a further 12 kcal/mol lower in energy, where the proton resides now at O11. This structure does also not represent a local minimum structure, but moreover, a three state crossing point between the lowest singlet S1 state, the lowest triplet T1 state and the electronic ground state S0 (Figure 4). Because of the applied single-reference method, we can not optimize the structure of the degeneracy, however, from the shape of the potential energy surfaces (Figure 4) it is apparent a region of the potential energy is reached where these states become practically degenerate. This region is already reached, when the C9H bond is slightly stretched beyond 1.35 Å. Since the S1 state corresponds to an nπ* excited state and the T1 state has F

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which the initializing excited state proton transfer proceeds barrierless from C9 to O11, an energy barrier of 7 kcal/mol needs to be overcome in 0B. In addition, the structures SA1 and SB1 are practically degenerate in 0B, while the latter is more stable in 0A by 12 kcal/mol providing the driving force for the efficient excited state proton transfer in 0A representing the photochromic compounds 1 and 2. Of course, these numbers might change when higher-level methods are employed or when a (polar) solvent is taken into account, but they clearly give a sound trend. The Wiberg bond indices have also been calculated for the relevant ground state singlet and triplet structures for the model compound 0B. Not surprisingly, the bond indices are very similar for 0A and 0B pointing toward similar electronic structures along reaction mechanism (see Figure S7 of the Supporting Information). The most striking difference is an increase of Mulliken spin density on C9 in the triplet structures of 0B. For example, in TC1 of 0A it amounts to 0.70, while it is 0.96 in 0B. The lower spin density on 0A originates from the additional phenyl ring which is bound to C9 in 0A and stabilizes the unpaired electrons. This stabilizing effect of the radical center by the phenyl group, which is of course also active in the singlet structure SB1 of 0A, leads to a lowering of the energy of that intermediate in 0A in comparison to 0B. As a consequence, the proton transfer from C9 to O11 proceeds barrierless in 0A leading to a more stable structure, in which the proton is bound at O11, while the same proton transfer is connected with an energy barrier in 0B and no energy is gained by the transfer. The reliability of the obtained potential energy curves is substantiated by the so-called Λ overlap parameter proposed by Peach et al.,67 which measures the degree of CT character and hence the probability of a charge-transfer failure of TDDFT. For all relevant states of the mechanism, Λ is comfortably larger than the critical value of 0.30 and supports therefore the relevance of the investigated mechanism: for the S1 and T1 states of 0A, values of 0.49 and 0.51 have been obtained, while for the same states of 0B Λ amounts to 0.50 and 0.51, respectively. Finally, the relative energies of the discussed important structures along the reaction pathway of 0A and 0B obtained at TDDFT/B3LYP level have been compared to CC2 computed values, which can be found in Tables S3 and S4 of the Supporting Information. The TDDFT and CC2 values agree overall very nicely and the mechanism described above is further substantiated.

Figure 5. The Wiberg bond indices along the PES for 0A (See Figure 4) obtained at the B3LYP/6-31G* level of theory. For TC1 , TD1 , and TE1 the highest Mulliken spin densities are found at C6(0.40), C9 (0.70), and C10 (0.48); C9 (0.69) and C10 (0.83); and C6 (0.38), C9 (0.75), and C10 (0.43), respectively.

perform the same calculations for 0B resembling the structure of 3 (Figure 1) and to analyze the corresponding potential energy surfaces to identify possible differences and hence the reason for the absence of photochromism in this compound. Thus, relaxed scans of the potential energy surfaces of the singlet ground state S0 and the energetically lowest singlet S1 and triplet T1 excited states have been computed along the initial proton transfer coordinate and the subsequent rotation around the C6−C1−C10−O11 dihedral for 0B in strict analogy to the calculations performed for 0A. The obtained potential energy surfaces are displayed in Figure 6. Along this reaction path identical structures are identified for 0B as have been found for 0A previously. Upon excitation of the initial ground state structure SA0 , a local minimum is found on the S1 surface, in which the transferred proton is bound to C9. Although the calculated potential energy surfaces do not reveal the existence of a three state degeneracy between S0, S1, and T1 that clearly as in the case of the model 0A, from the shape of the potential energy surfaces it is clear that such a region is also reached here, when the proton is transferred. In analogy to 0A, the molecules can there either return to the ground state or decay into the triplet state via intersystem crossing. Once in the T1 states, the molecules can rotate around the dihedral angle practically barrierless and eventually form the colored photoenolization product (Figure 6). Comparing the potential energy curves obtained for 0A and 0B (Figures 4 and 6), an important difference in the energetics of the mechanism becomes apparent. In contrast to the model compound 0A, for

4. BRIEF SUMMARY AND CONCLUSIONS The photochemical properties of the quinoline and naphthyridine derivatives 3-benzoyl-2-benzyl-1-methyl-1H-quinoline-4one (1) and 3-benzoyl-1,2-dibenzyl-1H-1,8 naphtyridin-4-one (2) as well as of the structurally closely related but nonphotochromic 3-benzoyl-1-benzyl-2-methyl-1H-1,8-naphtyridin-4-one (3) have been investigated using quantum chemical methods. The focus of this work has been put on the explanation why 1 and 2 are photochromic via a photoenolization, while 3 is not. As a first step, the reliability and accuracy of time dependent density functional theory for the investigation has been extensively tested by comparison against ab initio methods. Therefore, the energetically lowest excited singlet and triplet states of a reduced molecular model capturing the essential properties of the compounds 1 to 3 have been calculated at TDDFT using the BLYP, B3LYP, and BHLYP and ωB97x xcfunctionals as well as with CIS(D), ADC(2), and CC2. From a G

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Figure 6. The potential energy surfaces of the electronic ground state (blue), the lowest excited singlet S1 state (red) and the lowest triplet state (green) of the model 0B resembling 3 along the photoenolization reaction path, which corresponds first to a proton transfer and then to a dihedral angle rotation (see text). SA0 and SE0 are optimized in the singlet ground state using DFT/B3LYP. From SA1 to SB1 and from TC1 to TE1 , the optimizations have been performed in the S1 and T1 states, respectively, at LR-TDDFT/B3LYP level of theory.

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thorough analysis of the obtained results, it has been deduced that TDDFT/B3LYP represents a sufficiently accurate yet computationally efficient approach to study the photochemical properties of the quinoline and naphthyridine derivatives. Since the vertical excited states of 1 to 3 are overall very similar, they do not provide a basis for an explanation of the different photochromic properties. Instead, relaxed scans of the potential energy surfaces of a molecular model 0A representing the photochromic species 1 and 2 and of a molecular model 0B representing the nonphotochromic species 3 have been calculated along the photoenolization pathway at the theoretical level of TDDFT/B3LYP. The accuracy of this theoretical approach has once more been confirmed by single-point CC2 calculations of relevant structural intermediates along the path. The photoenolization mechanism proceeds in all compounds via an initial intramolecular excited state proton transfer subsequent intersystem crossing and final rotation around a dihedral angle to eventually arrive a the colored photochromic form. While the initial proton transfer proceeds barrierless in 0A representing the photochromic species, an energy barrier is present in 0B hence suppressing the photoenolization of 3. The key factor is indeed the phenyl group present in 1 and 2, which stabilizes the formation of an unpaired electron at C9, which hence facilitates the proton transfer. The identified mechanism agrees with experimental findings, and moreover, also explains the inefficiency of the photochromism, which occurs experimentally only after minutes of continuous irradiation. In addition to intersystem crossing, excited molecules of 1 and 2 can efficiently decay radiationless back to the original ground state via a conical intersection, which is generally more efficient than ISC.

ASSOCIATED CONTENT

S Supporting Information *

Wiberg bond indices S0A, T1C, T1D, T1E and S0E along the PES for 0B, as they calculated at the B3LYP/6-31G* level of theory, and relative CC2 energies for some structures taken from the potential energy surfaces of 0A and 0B , which provide a benchmark to the TDDFT results here presented. 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 S.K. is grateful to the Alexander von Humboldt foundation for his research grant in Germany and to the European Marie Curie (COFUND) programme along with the Belgian science policy office (“Belspo”) for the current funding. Computation time has been generously provided by the Center of Scientific Computation of the University of Frankfurt. For useful discussions, the authors are grateful to C. M. Marian, J. Borowka, P. H. P. Harbach, and J. Plötner.

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