Spirooxazine-Fulgide Biphotochromic Molecular Switches with

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Spirooxazine-Fulgide Biphotochromic Molecular Switches with Nonlinear Optical Responses across Four States Jianyong Yuan, Yizhong Yuan, Xiaohui Tian, Jinyu Sun, and Ya Ge J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04849 • Publication Date (Web): 10 Jun 2016 Downloaded from http://pubs.acs.org on June 13, 2016

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The Journal of Physical Chemistry

Spirooxazine-Fulgide Biphotochromic Molecular Switches with Nonlinear Optical Responses across Four States

Jian-Yong Yuan,† Yi-Zhong Yuan,*,† Xiao-Hui Tian,*,† Jin-Yu Sun,† Ya Ge†

†

Key Laboratory for Ultrafine Materials of Ministry of Education and Shanghai Key

Laboratory of Advanced polymeric Materials, School of Materials Science and Engineering, East China University of Science and Technology, Shanghai 200237, China

E-mail: [email protected], [email protected]

1

ACS Paragon Plus Environment


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Abstract: A new type of prototypical biphotochromic switches combining spirooxazine and fulgide has been synthesized and their nonlinear optical (NLO) responses have been theoretically studied based on density functional theory (DFT). Our DFT calculations show that the introduction of fulgide fragment (E and C) into spirooxazine host can largely enhance the static second and third-order NLO responses. Moreover, the photoisomerization of spirooxazine derivatives (SO-E and SO-C) brings forth a pronounced change in the geometry accompanied with the formation of larger π-conjugated system, and thus the corresponding merocyanine derivatives (PMC-E and PMC-C) obtain ~3.5 times’ enhancement of static second and third-order NLO responses. Nevertheless, the difference in NLO responses between E-form series (SO-E and PMC-E) and C-form series (SO-C and PMC-C) respectively is not substantial, which means the fulgide fragment in the prototypical biphotochromic system does not considerably differentiate the corresponding optical nonlinearities. To well separate the NLO responses of four states in our prototype, we further propose a structural modification strategy by introducing the furan moiety (2-vinylfuran) into the π-bridge, and the corresponding NLO performances from DFT results finally meet our demands, indicating that such revised biphotochromic system based on our prototype is a fascinating choice for the architecture of multistate NLO switches.

2


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1. INTRODUCTION Photochromic materials1-2 have attracted considerable attention due to their widespread applications such as anti-counterfeiting systems,3 optical storage and memory devices,4-5 and optical molecular switches.6-8 Therein, some of the photochromic dyes exhibit excellent nonlinear optical (NLO) responses and hence can be devised as NLO switches. Typically, NLO switches contain π-conjugated systems end-capped with donor (D) and acceptor (A) moieties by tuning which large molecular hyperpolarizabilities can be achieved,9 and therefore such potentially useful NLO switches may play an important role in the development of electro-optic devices.10 The prerequisite for effective NLO switches is the stability of two reversible states matching the binary zero and one, respectively. Bistable molecules thus have been regarded as a good candidate for traditional binary logic switches. However, the conventional binary digital architectures are somewhat redundant and tedious when integrated into the complicated combinational logic devices. In consequence, to obtain smaller and more powerful logic components, frameworks of ternary or higher-order digit representations should have many superiorities over that of general binary expression.11 Such non-binary system requires that the molecular information carriers should exist in more than two stable states which are independently addressable for the relevant high-order digit logic functions.11-12

3



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Chart 1. Photoisomerization between spirooxazine and its merocyanine form.

To date, the spirooxazine derivatives have attracted great attention because of their high photostability and fatigue resistance upon hundreds of photochromic cycles, compared with other photochromic compounds with similar chemical structures such as spiropyran series.7,13 When exposed to UV light, the spirooxazine exhibits a significant change of geometric structure (Chart 1), especially the conjugation of π-electrons, thus leading to a remarkable switching effect in various properties such as absorption

spectra,8,13 luminescent efficiency5

and NLO

responses.6,8 The

second-order NLO molecular switches utilizing reversible photochromism between spirooxazine and its merocyanine form were preliminarily probed by Sun, H. et al, and their reports show the potential values of spirooxazine derivatives on NLO responses.14 Chart 2. Photocyclization of fulgide between E and C form.

Fulgide series are another photochromic dyes of great interest to the physical chemists. On the contrary to the spirooxazine derivatives mentioned before, fulgide 4


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undergoes ring-closed reaction when stimulated by UV irradiation (Chart 2). Such photochromism features allow for the practical applications of fulgides.15-18 In addition, the NLO properties of fulgides are also attractive in electro-optic and data storage applications.19-21 Recently, switchable NLO responses of fulgides have been reinvestigated by Garza et al. According to their theoretical calculations of three types of fulgide isomers, the calculated static first hyperpolarizability of C-form (panel B in Figure 1) is considerably large, promising to be the underlying candidates of NLO switches.22 As is mentioned above, both spirooxazine and fulgide compounds can be potentially used as NLO switches. To seek the carriers of higher-order digit representations, molecules with more than three stable states in terms of NLO responses are often considered in molecular designs. In view of the distinguished performance of spirooxazine and fulgide families, we therefore design and synthesize a new prototypical biphotochromic system in this work, by combining spirooxazine and fulgide fragments through a shared naphthaline ring (panel C in Figure 1). Switching behaviors of the first hyperpolarizabilities for spirooxazine and fulgide derivatives have been computationally confirmed, respectively.6,14,22 Nevertheless, the theoretical study on second- and third-order NLO switching behaviors of spirooxazine-fulgide biphotochromic dyes are still in shortage at present. Based on the rapid development of density functional theory (DFT)23-28 and time-dependent DFT29-31 which opens up a new perspective to the theoretical study of optical/spectroscopic properties and electronic structures of large-size molecular 5



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systems, we hereof perform DFT calculations to demonstrate the systematic NLO responses and the potential capabilities of our biphotochromic systems working as multistate NLO switches. We also verify the structural modifiability of the prototypical biphotochromic system, which can markedly improve the NLO performance of four-state-switches with enhanced switching ratios. Unlike other multistate NLO switches involving redox and protonation reactions,32-34 which are inconveniently manipulated by using extra reagents to trigger the corresponding reactions so as to realize the switching behaviors, the biphotochromic multistate NLO switches can be simply controlled by two different incident lasers and no other additional reagents will help to modulate the switching process. In other words, it means that such biphotochromic system upon two outstanding fragments (spirooxazine and fulgide) can be treated as all-optical controlled quaternary NLO switches, and can be preserved in a sealed vessel tuned by the completely isolated external stimulations (UV lights). Therefore, multistate NLO switches with such advantage are more welcomed and practical to work in the logic integrated circuits. 2. EXPERIMENTAL AND COMPUTATIONAL DETAILS Experimental

Details.

The

1,3,3-trimethylspiro[indoline-2,3'-naphtho[2,1-b][1,4]oxazine]-8'-carbaldehyde (M1) was

prepared

by

the

oxidization

of

(1,3,3-trimethylspiro[indoline-2,3'-naphtho[2,1-b][1,4]oxazin]-8'-yl)methanol 6


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(reactant of M1) with Dess-Martin Periodinane (DMP).35-37 The diethyl 2-(propan-2-ylidene)succinate

(M2)

and

the

biphotochromic

compound

(E)-3-(propan-2-ylidene)-4-((1,3,3-trimethylspiro[indoline-2,3'-naphtho[2,1-b][1,4]ox azin]-8'-yl)methylene)dihydrofuran-2,5-dione (SO-E) were prepared via Stobbe condensation reaction.38 Note that, the oxidant DMP and two intermediates M1, M2 were synthesized according to the procedures described in previous works,35-38 while the synthetic route of the target compound SO-E was presented in Scheme 1.

Scheme 1. Synthesis of the prototypical biphotochromic SO-E.

Synthesis of SO-E. The intermediate M2 (1.18 g, 5.5 mmol) which had been dissolved in THF (15 mL) was cautiously added dropwise into a flask containing solution of NaH (1.8 g, 75 mmol) and THF (25 mL) in ice-water bath under nitrogen atmosphere. Three droplets of absolute ethanol triggered the reaction. After 30 mins’ 7



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agitation, the intermediate M1 (0.3 g, 0.85 mmol) which had been dissolved in THF (20 mL) was slowly added into the flask in ice-water bath. The reaction was further conducted at ambient temperature (25°C) for one hour. After removal of THF using rotary distillation, the residue which had been dissolved in ethyl acetate was repeatedly washed by 10% Na2CO3. Then the lower inorganic layer was collected and adjusted to the pH of 1-2 by diluted HCl solution (5 mol/L). The crude sticky product (half-ester) was obtained after a series of manipulation in sequence: Extraction by ethyl acetate, dehydration of upper organic layer with anhydrous MgSO4, filtration (removal of MgSO4) and rotary distillation. The semi-finished product (half-ester) was redissolved in a mixture of 10% KOH and ethanol (50 mL, wt. 5:45) and refluxed for 8 h. The precipitate in the bottom of flask was orderly rotary distilled, dissolved in dichloromethane and washed by 10% Na2CO3. Then the pH of the inorganic layer was adjusted to 1-2 using diluted HCl solution (5 mol/L). The crude product (diacid) was obtained via another suite of operations (addressed by ethyl acetate, anhydrous MgSO4 and rotary distillation). Next, the diacid product dissolved in dichloromethane (40 mL) was cautiously injected with acetyl chloride (10 mL) in the ice-water bath. The final purified yellow solid was collected after rotary distillation, purification by column chromatography using a mixture of petroleum ether and ethyl acetate (vol. 6:1) as the eluent, and recrystallization in dichloromethane. Yield: 32%. Mass spectrum (MS) of SO-E is shown in Figure S1 of Supporting Information. MS (m/z): 478.2 (M+), 479.2 (M++1), 480.2 (M++2). 1H-NMR spectrum (6.5 ppm ~ 9.0 ppm) of SO-E is presented in Figure S2. Chemical shift δ (ppm): 8.58 (d, 1H), 8.24 (s, 1H, the 8


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hydrogen atom on olefinic bond connecting spirooxazine fragment and anhydride fragment), 7.89 (d, 1H), 7.55 (d, 2H), 7.00 (s, 1H, the hydrogen atom on another olefinic bond of oxazine ring). Instrumentation. UV-visible absorption spectra were recorded from 200-800 nm on a 756MC spectrometer. Photochromic properties were studied by alternate irradiation with a UV-LED electric light source: UV light at 365 nm (ZF5-B, 16W, 150×50 mm wide band-pass filter) and UV light at 400 nm (400 nm blue-ray flashlight). MS spectrum was recorded on a G2577A spectrometer (EI, 70 eV). 1

H-NMR spectrum was recorded on an Avance-500 instrument with tetramethylsilane

(TMS) served as the internal reference and CDCl3 as the solvent. Computational Details. The geometries of all compounds were optimized and characterized as the energy minima at B3LYP/6-31G(d) level in ethanol.26-27,39-40 Time-dependent DFT (TD-DFT)41-42 is a useful tool to compute the linear and nonlinear molecular properties due to the desired compromise between computational efficiency and accuracy.43 However, conventional global hybrid functionals such as B3LYP often suffer from the charge-transfer (CT) problem44-46 and consequently give poor description of electronic absorption characteristic and great overestimation on static first hyperpolarizabilities (β). To address this CT issue and predict reasonable β values, hybrid functionals with range-separated exchange (RSE) have been developed47 and considered to be more suitable to calculate the electronic absorption spectra of organic dyes48 and the hyperpolarizabilities of conjugated systems.49-50 Accordingly, the CAM-B3LYP51-52 and ωB97XD53 RSE functionals were utilized in 9



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this study, along with the conventional hybrid functionals (B3LYP26-27, PBE054, BMK55-56 and M06L57-58). Especially, the optimally tuned RSE functional41,57,59-60 ω*B97XD was also employed to further refine the ωB97XD results, and their optimal ω values were precalculated and listed in Figure S3. Moreover, all computations with 6-31+G(d) basis set were performed in the ethanol solvent mimicked by the polarizable continuum model (PCM),61-62 and then the corresponding results were compared to the available experimental absorption spectra. On the basis of optimized geometries, the static first hyperpolarizabilities (β) were evaluated by the analytical coupled-perturbed

Hartree-Fock

(CPHF)

method63

and

its

DFT

analog

(coupled-perturbed Kohn-Sham, CPKS) according to the following equations: β = ( + + ) / (1) where β is defined as follows:

1 = + ( + + ) (2) 3

In addition, the β values were also given by sum-over-states (SOS) method for comparison64 and the static second hyperpolarizabilities (γ) were calculated in the same way. More details about SOS method were supplied in the note boxes of Figure S4 and Figure S5. The quantitative charge-transfer analysis was based on the natural population analysis (NPA) charges derived from the natural bond orbital (NBO) procedure.65 Contour surfaces of both electron density difference and revised static first hyperpolarizability density presented in this work were generated by Multiwfn 3.3.9 (dev) program66 and visualized with VMD 1.9.2 tool.67 All the calculations were 10


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carried out by Gaussian 09 program package.68 3. RESULTS AND DISCUSSION Geometrical and electronic structures. The prototypical biphotochromic system (panel C in Figure 1) in this paper originates from the combination of spirooxazine and fulgide which can be converted to the corresponding open form (photomerocyanine, PMC) and closed form (C-form of fulgide, C), after the irradiation of ultraviolet light. Typically, the closed spirooxazine consists of an indoline fragment and a napthoxazine moiety that are held almost orthogonally by a chiral “spiro” carbon atom. When exposed under ultraviolet light, two isolated π-conjugated parts in spirooxazine are extensively conjugated as a large coplanar structure, i.e. PMC (panel A in Figure 1), while inversely, fulgide undergoes the ring-closure process from the E-form to the C-form (panel B in Figure 1) of which the geometric variation is relatively small, compared with spirooxazine. Moreover, given the chirality of spiro carbon in spirooxazine and the trans/cis configuration about each of the three partial double bonds in the central conjugated bridge of photomerocyanine, two possible ring-closure enantiomers and eight stable ring-opening isomers can be found, respectively. In this work, the (R)-enantiomer of spirooxazine was chosen for computation and the geometry optimization for the corresponding open form was performed on the trans-trans-cis isomer (TTC) due to its most thermodynamic stability.69 As to fulgide, the choice is rather scarce since only three stable forms are included, namely, Z-form (not presented here), E-form and 11



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C-form (panel B of Figure 1). We select the latter two because the primary photoreversible ring-closure/ring-opening reactions of fulgide take place within the interconversion between E-form and C-form.70

Figure 1. Interconversion of the prototypical biphotochromic system (SO-E, SO-C, PMC-E and PMC-C) wherein spirooxazine (SO and PMC) and fulgide (E and C) working as the reference molecules.

Table 1. The bonda length alternation (BLA) values (Å) of spirooxazines (SO and PMC), fulgides (E and C) and their combinations (SO-E, SO-C, PMC-E and PMC-C) in ground state at B3LYP/6-31G(d) level in ethanol. Compound Spirooxazine moietyb Fulgide moietyc

SO

SO-E

SO-C

PMC

PMC-E

PMC-C

E

C

0.0648

0.0632

0.0647

0.0089

0.0021

0.0034

-

-

-

0.0482

0.0983

-

0.0526

0.0947

0.0762

0.0986

a

All relevant bonds have been defined in Figure 1.

b

BLA values for spirooxazine moiety: |(R1+R3+R8)/3－(R2+R4+R9)/3|. 12


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c

BLA values for fulgide moiety: |(R10+R12+R14)/3－(R11+R13+R15)/3|.

All eight photochromic dyes presented in Figure 1 were optimized at B3LYP/6-31G(d) level in ethanol, which is proved to be reliable for similar system in ground state.14 Their BLA values were collected in Table 1. The BLA value, defined here as the absolute values of the difference between the average length of the single and double bonds, is a quantitative tool to evaluate the degree of π-conjugation for the specific molecule with conjugated bonds. Smaller BLA values imply more sizeable π-conjugation of the system. Compared with SO series (SO, SO-E and SO-C), PMC series (PMC, PMC-E and PMC-C) obtain sharply decreased BLA values of spirooxazine moiety (~0.005 Å vs ~0.065 Å, seen in Table 1), which indicate higher π-conjugation of the photochromic system and further prove that two isolated π-conjugated parts in spirooxazine can be extensively conjugated upon UV light exposure. Furthermore, PMC series with more extensively conjugated moieties may promisingly have large hyperpolarizabilities to be devised as NLO systems.14,33-34 As to fulgide, E-form series (E, SO-E and PMC-E) are more favored in delocalized structures with larger π-conjugation in comparison to C-form series (C, SO-C and PMC-C), according to the smaller BLA values of fulgide moiety (~0.059 Å vs ~0.097 Å).

Photochromic and absorption properties. Photochromism of our prototypical biphotochromic system occurs under UV irradiation. In this study, the biphotochromic properties of SO-E, SO-C, PMC-E and PMC-C were studied using different excitation wavelengths and their experimental adsorption spectra were integrated into 13



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Figure 2. Under the irradiation of UV light (365 nm), the colorless solution (SO-E) turned to light blue (PMC-E) accompanied with a new absorption peak at 621 nm and a slight decline of absorption peak strength at 356 nm, evidencing the ring-open reaction of spirooxazine fragment. Similarly, another new absorption peak at 518 nm was found when one irradiated the colorless solution (SO-E) with long wavelength UV light of 400 nm, and meanwhile the solution turned to red (SO-C). This phenomenon can be ascribed to the ring-closed reaction of fulgide fragment. It is worth noting that both red (SO-C) and blue (PMC-E) solutions can further turn to magenta with the formation of absorption peak at 577 nm, under the UV light of both 356 nm and 400 nm. Obviously, the final magenta solution is the product of both photoisomerization reactions (of spirooxazine and fulgide) which bring forth PMC-C. Overall, the biphotochromic system can be interconverted across four independent states by two different UV lights (365nm and 400 nm) and color variations can be intuitively observed by naked eye. Therefore, such biphotochromic system can be treated as the quaternary photochromic switches with four independently addressable states on the basis of the well-separated maximum absorption peaks.

14


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Figure 2. Experimental UV-Vis absorption spectra of the prototypical biphotochromic system (SO-E, SO-C, PMC-E and PMC-C) in ethanol (1×10-5 mol/L).

TD-DFT calculations at various functionals (B3LYP, CAM-B3LYP, ωB97XD, ω*B97XD and M06L) with 6-31+G(d) basis set were performed in ethanol to study crucial excited states and compared to the available experimental results. The resultant benchmarks of electronic absorption energies were gathered in Table 2. Apparently, the traditional global hybrid B3LYP substantially underestimates the absorption energies of SO series, whereas the “better” agreement for PMC series (except for PMC) with experimental values may be just attributed to the error cancellation.14 Actually, though traditional global hybrid functionals (like B3LYP) can give desirable results when describing the local excitation (LE) process, they always suffer from the charge-transfer (CT) problem.44-46 Therefore, hybrid functionals with range-separated exchange (RSE) should be introduced to properly depict the electronic absorption characteristic of organic dyes. The common RSE functionals 15



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(CAM-B3LYP and ωB97XD) in this paper satisfactorily reproduce the electronic absorption energies in SO series with the deviation less than 0.1 eV. However, it seems that the common RSE functionals in our case always give larger electronic absorption energies with respect to the experimental data of PMC series. The slightly large errors (~0.4 eV) are probably related to the static correlation nature of merocyanines,71 which can be addressed by the multi-reference state methods such as CASSCF and CASPT2. Unfortunately, multi-reference state methods with large active space require high-demanding computational conditions which are far beyond our ability. Instead, M06L functional with lower percentage of HF exchange was applied here for reference, which can partially deal with static electron correlation.72 The errors in PMC series (~0.25 eV) are acceptable with M06L, but it greatly underestimates electronic absorption energy of SO by up to 0.6 eV and hence is not suitable for describing the whole system. To choose reliable functional to reasonably improve calculation results, we also adopt optimally tuned RSE functional ω*B97XD combined with more rigorous TD convergence threshold (10-6, compared with the default of 10-3). The predicted results are quite satisfactory with deviation of ~0.15 eV in PMC series and ~0.2 eV in SO series, compared with experimental data.73 This phenomenon can be ascribed to the reduction of delocalization errors by virtue of the optimally tuned RSE functional (such as ω*B97XD), so as to improve the CT excitation energies.74 Note that the practical PMC series in ethanol are mixtures of various isomers, whereas calculations performed here were simply based on the most stable ones (Figure 1). Therefore, the difference of realistic and ideal system results in 16


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a certain discrepancy on electronic absorption energies. In brief, ω*B97XD/6-31+G(d) level in ethanol is eventually chosen to get more insights into the electronic absorption characteristic of the system. Table 2. Calculated electronic absorption energies (∆Ecal) of the prototypical biphotochromic system in ethanol at various functionals (B3LYP, CAM-B3LYP, ωB97XD, ω*B97XD and M06L) with 6-31+G(d) basis set, compared with experimental data (λexp, ∆Eexp). Compound SO

∆Ecal (eV)

λexp, ∆Eexp (eV)

CAM-B3LYP

ωB97XD

ω*B97XDb

M06L

c

3.81 [-0.08]

3.82 [-0.07]

3.65 [-0.24]

3.29 [-0.60]

B3LYP

319 (3.89)

a

3.47 [-0.42]

SO-E

356 (3.48)

2.87 [-0.61]

3.46 [-0.02]

3.53 [0.05]

3.27 [-0.21]

3.38 [-0.10]

SO-C

518 (2.39)

2.05 [-0.34]

2.46 [0.07]

2.50 [0.11]

2.26 [-0.13]

2.20 [-0.19]

PMC

610 (2.03)a

2.40 [0.37]

2.53 [0.50]

2.54 [0.51]

2.27 [0.24]

2.36 [0.33]

PMC-E

621 (2.00)

2.24 [0.24]

2.43 [0.43]

2.45 [0.45]

2.18 [0.18]

2.11 [0.11]

PMC-C

577 (2.15)

2.17 [0.02]

2.42 [0.27]

2.44 [0.29]

2.17 [0.02]

2.44 [0.29]

E

-

3.18

3.64

3.69

3.44

3.37

C

-

2.16

2.51

2.54

2.35

2.06

a

Gathered from Ref. 73.

b

The best ω values of optimally tuned RSE functional ω*B97XD for each dye were precalculated and summarized

in Figure S3. c

The differences between calculated values and experimental values are given in the square brackets, and hereof

the minus sign represents that the calculated electronic absorption energy underestimates the experimental one.

Table 3. Calculated electronic absorption energies (∆Ecal), oscillator strengths (f) and excitation assignments of the prototypical biphotochromic system at TD-ω*B97XD/6-31+G(d) level in ethanol. Compound

SO

∆Ecal (eV)

3.65

f

0.25

Crucial a

Excitation

State

Assignmentb

S1

H-1→L (64%)

Occupied Orbital

Unoccupied Orbital

H→L (30%)

SO-E

3.27

0.70

S1

H-1→L (51%)

H→L (40%)

17



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a

SO-C

2.26

0.37

S1

H→L (67%)

PMC

2.27

1.14

S1

H→L (99%)

PMC-E

2.18

1.46

S1

H→L (97%)

PMC-C

2.17

1.36

S2

H→L+1 (67%)

E

3.44

0.92

S1

H→L (94%)

C

2.35

0.35

S1

H→L (95%)

Page 18 of 55

The crucial state is defined as the lowest optically allowed excited state with substantial oscillator strength in this

work. b

H-1, H, L and L+1 represents HOMO-1, HOMO, LUMO and LUMO+1, respectively; the percentage

contributions of orbital pairs to the wave functions of excited states are given in parentheses.

18


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Figure 3. The electron density difference (isovalue=0.002) of the prototypical biphotochromic system from the ground state to the crucial excited state calculated at TD-ω*B97XD/6-31+G(d) level in ethanol. Quantitative charge-transfer analysis is based on NPA charges collected in Table S1.

The calculated excited energies (∆Ecal), oscillator strengths and corresponding orbital transitions are listed in Table 3. It can be found in biphotochromic dyes (SO-E, SO-C, PMC-E and PMC-C) that almost all the unoccupied molecular orbitals (UMOs) are concentrated in anhydride moiety, indicating its typical character working as the electron acceptor when π-electrons are excited from the ground state. In SO series, indoline moiety served as the electron donor owns the majority of occupied molecular orbitals (OMOs). Because of the orthogonality between indoline moiety and napthoxazine moiety which leads to little overlap between orbital pairs, the oscillator strength of SO is rather small (0.25) and meanwhile a weak CT transition (only 0.018e transferred) can be observed via electron density difference 19



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Page 20 of 55

plots (Figure 3). Although the orthogonal indoline moiety in SO series contributes little to the CT process, SO-C and SO-E still exhibit significant CT transitions with 0.185e and 0.275e transferred, respectively. This behavior can be illustrated by comparison of charge-transfer properties to the fulgides (C and E): As is shown in Table 3, UMOs of SO-C, SO-E, C and E are predominantly localized in the anhydride moiety, whereas part (for SO-C and SO-E) and most (for C and E) of OMOs

are accumulated in the

napthoxazine and naphthaline fragments,

correspondingly. Furthermore, the electronic excitation energies and oscillator strengths of SO-C and C (2.26 eV vs 2.35 eV; 0.37 vs 0.35), SO-E and E (3.27 eV vs 3.44 eV; 0.70 vs 0.92) are quite close to each other, respectively. Consequently, such similarities in charge-transfer properties give rise to similar CT behaviors: C and E display strong CT transitions with 0.183e and 0.227e transferred, respectively; and hence homologous SO-C and SO-E in which fulgide fragment occupies a dominant role, also reveal strong CT transitions. With regard to PMC series, the OMOs are distributed uniformly in indoline and napthoxazine moieties. A sufficient overlap between OMO and UMO brings about large oscillator strength with 1.14, 1.46 and 1.36 for PMC, PMC-E and PMC-C, respectively. The coplanar indoline moiety (in PMC series) attached to merocyanines decreases the electronic excitation energies (3.65 eV for SO vs 2.27 eV for PMC; 3.27 eV for SO-E vs 2.18 eV for PMC-E; 2.26 eV for SO-C vs 2.17 eV for PMC-C) and meanwhile increases the π-conjugation (The declines of BLA values of spirooxazine moiety in Table 1: 0.0648 Å for SO vs 0.0089 Å for PMC; 0.0632 Å for 20


Page 21 of 55

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SO-E vs 0.0021 Å for PMC-E; 0.0647 Å for SO-C vs 0.0034 Å for PMC-C), compared with corresponding orthogonal indoline moiety in SO series. Nevertheless, slightly weak CT transitions of PMC series with lower electron transfers (from 0.019e to 0.049e) were detected in Figure 3. This phenomenon may possibly be ascribed to the fact that large π-conjugation system without stronger electron donor/acceptor to drive π-electrons, can result in enormous delocalization and dispersion of π-electrons all over the biphotochromic merocyanine, a situation which damps the oriented charge-transfer and cuts down the net transferred electrons. It is also worth to note that the coplanar PMC series with larger π-conjugation, lower excited energy and stronger oscillator strength may promisingly generate a large increase in static first hyperpolarizability.34

Switchable second-order and third-order NLO behaviors. In order to theoretically investigate the switchable NLO behaviors of the biphotochromic systems and to confirm the aforementioned speculation that PMC series may display large static first hyperpolarizabilities, DFT method with a series of different functionals including range-separated exchange (RSE) functionals (CAM-B3LYP and ωB97XD), global hybrid functionals (BMK, B3LYP and PBE0), Hartree-Fock (HF) method and the second-order Møller-Plesset (MP2) method were employed in this section. Given the limited computational resources, the MP2 results of the biphotochromic dyes (SO-E, SO-C, PMC-E and PMC-C) in our case are computationally inaccessible. Instead, four smaller reference molecules (SO, PMC, E and C) were calculated at MP2 level for comparison. Moreover, we also adopted SOS method based on 21



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Page 22 of 55

electronic absorption characteristic to work as a reference (100 states were tested to sufficiently acquire the converged β values, Figure S4). The calculated total static first hyperpolarizabilities (β) are summarized in Table 4. As expected, all the methods adopted consistently produce large β values of PMC series, which are in keeping with the previous conjecture from electronic absorption characteristic analysis. Table 4. Calculated static first hyperpolarizabilities β (10-30 esu) of the prototypical biphotochromic system in ethanol (by DFT, HF, MP2 and SOS method with 6-31+G(d) basis set). Range-separated

Hartree-

exchange

Fock

Post-H

Global hybrid

F

Compound

SOS CAM-B3L YP

a

ωB97XD

HF

B3LYP

PBE0

BMK

(100%)a

(20%)

(25%)

(42%)

MP2

SO

4.0

4.1

4.0

4.4

4.1

3.8

3.6

4.1

SO-E

82.4

72.4

32.1

161.6

140.7

99.8

-

70.0

SO-C

94.5

86.5

43.1

149.8

131.8

106.0

-

79.3

PMC

158.6

157.7

137.2

165.1

161.1

151.3

414.3

110.2

PMC-E

325.5

295.2

199.4

502.4

457.0

369.7

-

250.0

PMC-C

290.3

275.1

177.5

442.9

397.7

314.8

-

253.2

E

40.1

36.3

18.4

55.5

49.7

41.8

50.0

32.5

C

86.5

79.8

41.3

125.3

112.6

94.0

98.9

66.9

The percentages of HF exchange in various functionals are given in parentheses.

The conventional B3LYP greatly overestimates the β values, which can be attributed to its incorrect asymptotic and poor CT description.14,34 Whereas, HF method with correct asymptotic behavior14 seems to give relatively small β values (except for SO), compared with MP2 results. This phenomenon can be ascribed to the failure of HF method to address dynamic electron correlation. RSE functionals such as CAM-B3LYP and ωB97XD are better choices to evaluate the first hyperpolarizabilities in similar systems,14,33-34 and hence produce reasonable medium β values (Table 4) in our case. Actually, these RSE functionals hold a well-balanced percentage between exact exchange from HF and electron correlation from DFT, and 22


Page 23 of 55

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thus exhibit correct asymptotic and CT behavior with small delocalization errors. Currently, RSE functionals with such superiority are more preferred than the traditional functionals to predict NLO properties of large π-conjugated systems with significant CT effect. Global hybrid functionals with different compositions of HF exchange (B3LYP, PBE0 and BMK) were also applied in this study to reveal the relationship between the percentages of HF and corresponding β values. Generally, the calculated β values decrease with more HF mixed in functionals. In particular, BMK containing a higher percentage of HF than B3LYP and PBE0 can produce better β values which seem to be comparable to the results of RSE functionals. However, rather than the conventional global hybrid functionals above-mentioned, the RSE functionals (CAM-B3LYP and ωB97XD) can properly describe the electronic absorption characteristic which is ultimately in relation to the hyperpolarizability. On the other hand, the results of CAM-B3LYP or ωB97XD are quite acceptable, compared to those of SOS method. Note that SOS method can give approving β values provided that the sufficient number of states with accurate excitation characteristics (electronic absorption energies, oscillator strengths, etc) are considered in summation. In our case, the converged SOS results were based on the electron absorption calculations at TD-ω*B97XD/6-31+G(d) level which had proved in the preceding section to be suitable to describe exact excitation characteristics, and consequently corresponding SOS results can be regarded as the tentative benchmark. Such similarity of CAM-B3LYP or ωB97XD results to the SOS benchmark indicates the reliability of 23



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Page 24 of 55

CPKS calculations with RSE functionals to predict second-order NLO response in our case. Therefore, we use the result of ωB97XD as an example to discuss the multistate second-order NLO behaviors of biphotochromic systems. Moreover, the following relevant computations and illustrations are completely based on the reliable ωB97XD functional. For SO series, the calculated β value of unsubstituted SO is only 4.1×10-30 esu. When fulgide fragment is attached to SO, prominent reinforcement of second-order NLO response can be obtained with enhanced β values (72.4×10-30 esu for SO-E and 86.5×10-30 esu for SO-C) that are about 18-22 times larger than that of SO. Noteworthily, β values of fulgides (36.3×10-30 esu for E and 79.8×10-30 esu for C) are also 9-20 times as large as that of SO. In consequence, the evidently improved β values of SO-C and SO-E are mainly due to the formation of a larger π-conjugated system with the aid of fulgides which, as is mentioned before, play a vital and predominant role on the electronic absorption characteristic of SO series. As to PMC series, the predicted β value of PMC is around 157.7×10-30 esu which is almost 40 times larger than that of SO. It is noteworthy to note that the β value of PMC-C and PMC-E is 275.1×10-30 esu and 295.2×10-30 esu, respectively, which is ~2 times larger than PMC (157.7×10-30 esu). As a consequence, the incorporation of fulgide still reinforces the second-order NLO response in PMC series. Our CPKS calculations also show that the photochromic reaction of spirooxazine and its derivatives significantly alters the static first hyperpolarizabilities of the biphotochromic dyes (PMC series vs SO series). The β values of PMC-C and 24


Page 25 of 55

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PMC-E get ~3-fold improvement in comparison to SO-C and SO-E, respectively. By contrast, the photoisomerization of fulgide cannot largely affect the second-order NLO response with merely ~1.07 and ~1.19 times’ promotion from PMC-C to PMC-E and from SO-E to SO-C, correspondingly. Molecular NLO properties are intimately related to the electronic absorption characteristic, and thus the static first hyperpolarizability can be elucidated from the perspective of electronic absorption characteristic through the two-level model established by Oudar and Chemla,75-76

β ∝ μ − μ

" (3) Δ!

where μ and μ are the ground and excited state dipole moments, denotes the oscillator strength, and Δ! represents the electron transition energy. To shed light on the nature of static first hyperpolarizability in our case, the two-level model simplified from the complicated sum-over-states expression (in the note box of Figure S4)64 was qualitatively applied here, with relevant parameters tabulated in Table 5 and visualized in Figure 4. Therein, we use two descriptors (P term and U term) derived from the two-level model formula in Eq. (3) to probe into the second-order optical nonlinearities: P term is defined as the quotient of the oscillator strength (f) and the cubic electronic absorption energy (∆Ecal), namely P=103×f/(∆Ecal)3, whereas U term represents the difference of the dipole moments between excited state and ground state, i.e. U=µee ― µgg. It is self-explanatory that the product of P term and U term (P×U) should be theoretically proportional to the β 25



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Page 26 of 55

value. For this system, the P×U products qualitatively reproduce the general trend of the static first hyperpolarizabilities (Figure 4) with little deviations resulting from the limitation of two-level model. This consistency implies that the crucial states we have noted before (Table 3) make major contributions to the β values. Table 5. Calculated electronic absorption energies (∆Ecal), oscillator strengths (f) and dipole moments (µgg and µee) of the prototypical biphotochromic system at ω*B97XD/6-31+G(d) level in ethanol. Compound

a

∆Ecal (eV)

f

P=103×f/(∆Ecal)3

µgg

µee

U=µee ― µgg

(Debye)

(Debye)

(Debye)

P×U

β -30

(10

esu)a

SO

3.65

0.25

5.14

0.86

1.76

0.90

4.7

4.1

SO-E

3.27

0.70

20.02

11.34

19.13

7.79

155.9

72.4

SO-C

2.26

0.37

32.05

9.90

17.55

7.65

245.2

86.5

PMC

2.27

1.14

97.46

5.91

9.21

3.30

321.4

157.7

PMC-E

2.18

1.46

140.92

15.08

17.61

2.53

356.8

295.2

PMC-C

2.17

1.36

133.09

16.50

19.99

3.49

464.7

275.1

E

3.44

0.92

22.60

10.07

14.89

4.82

108.9

36.3

C

2.35

0.35

26.97

9.19

16.43

7.23

195.1

79.8

β values were obtained at ωB97XD/6-31+G(d) level in ethanol from Table 4.

Figure 4. The comparison between the static first hyperpolarizabilities (β) from CPKS calculation and the P×U products from two-level model.

26


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Generally, larger P term can predominantly give larger β values despite the constraint of U term which reflects their charge transfer character (µee ― µgg). Therefore, the large β values of PMC series can be primarily ascribed to the lower electronic absorption energy paired with stronger oscillator strength (large P terms), while their moderate CT characteristic (medium U terms: 3.30 Debye for PMC, 3.49 Debye for PMC-C and 2.53 Debye for PMC-E) does not significantly restrain the final results. The same situation is found in SO series, where P term also plays a decisive role in determining static first hyperpolarizability. As is shown in Table 5, SO-C and SO-E with the largest two U terms (7.65 Debye for SO-C and 7.79 Debye for SO-E) imply the pronounced CT behaviors of them, which are consistent with previous findings from electron density difference analysis (Figure 3) that the remarkable transferred charge of SO-C and SO-E can be seen (0.185e and 0.275e, respectively). However, SO-C and SO-E still present β values smaller than that of PMC series, because the relatively smaller P terms of SO-C and SO-E ultimately attenuate the β values in spite of their stronger CT transitions (large U terms). As for SO, its negligible β value can be rationalized by the collective effects of its highest electronic absorption energy (3.65 eV), weakest oscillator strength (0.25) and smallest U term (0.90 Debye). Note that when the P terms of two dyes are close and comparable, their U terms then predominantly determine the β values. A typical case of fulgides (C and E) is presented here where the great improvement of β value of C, compared with E, is mostly attributed to the larger U term (7.23 Debye for C vs 4.82 Debye for E). Furthermore, we recall that the β values of PMC-C and PMC-E (SO-C 27



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Page 28 of 55

and SO-E) are somewhat approximate to each other. This phenomenon can be accounted for by their similarities of corresponding P terms and U terms, which then bring about similar P×U products proportional to the β values (Figure 4). We also examine the spatial contributions of different molecular regions to the static first hyperpolarizability via using the hyperpolarizability density77-79 in the

$%) can be Taylor expanded finite-field (FF). As is known to all that dipole moment μ(F in powers of the external field $F% as

$% = − μF

&! 1 1 " $% + βF $% + γF $% + ⋯ (4) = μ' + αF $% 2 6 &F

Similarly, Taylor expansion of the electron density function -(r/, $F/) can also be conducted as

1 1 -r%, $F% = -(') (r%) + - ( ) (r%)$F% + -() (r%)$F% + -(") (r%)$F% " + ⋯ (5) 2 6 From Eq. (4) and Eq. (5), the static β can thus be expressed by

β = 2 − -() (r%) ⋅ r%4r% (6) where

-() (r%) =

& -(r%) 5 (7) $% $6%7' &F

This second-order derivative of the electron density with respect to the applied electric field is referred to as the β density. In this study, we confine our attention to ()

the β density (- (r%)) corresponding to β , which is the most crucial component of ()

β (Table S2). The - (r%) can be calculated at each spatial point in the discretized space by using the following second-order numerical differentiation formula: () - (r%)

-(r%, 9 ) − 2-(r%, 0) + -(r%, −9 ) = (8) (9 ) 28


Page 29 of 55

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where -(r/, 9 ) represents the electron density at a spatial point r% in the presence of electric field 9 . The electron densities over a three-dimensional grid of points are evaluated via the density matrix obtained from Gaussian 09 program package.68

(>)

Figure 5. The contour surface (isovalue=7) of −

Spirooxazine-Fulgide Biphotochromic Molecular Switches with

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