Elaboration and controlling excited state double proton transfer mechanism of 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol

In the present work, we theoretically illuminate the excited state double proton transfer (ESDPT) process about a novel synthesized system 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol (BBTD). Minor changes of both structure and charge redistribution deriving from photoexcitation result in obviously different excited state dynamical process. Exploration about our constructed S1-state potential energy surface (PES) indicates a stepwise ESDPT mechanism for BBTD. In addition, we present a new mechanism about regulating and controlling stepwise ESDPT process via external electric field.

the confined media also largely have effect on ESIPT process 24 . And the most common in experiment is that PH controls excited state dynamical process. In effect, electric field effects are of considerable interest in exploring biological environments [25][26][27] . In 4′ -N,N-(diethylamino)-3-hydroxyflavone (DEHF) molecule, Klymchenko et al. studied electric field effect on ESIPT reaction and found apparent variation about intensity of its fluorescence 28 .
Recently, a new system 2,5-bis(benzoxazol-2-yl)thiophene-3,4-diol (BBTD) including two intramolecular hydrogen bonds is designed and synthesized 29 . As a model compound, Chen et al. use BBTD to explore single or double proton transfer process in the S 1 state. Measuring absorption and emission spectra of BBTD, they find two large Stokes shifted fluorescence bands, which are attributed to BBTD-SPT and BBTD-DPT configurations (shown in Fig. 1), respectively. Moreover, considering the fluorescence decay of BBTD, they ensure excited-state single or double proton transfer process existing in the S 1 state.
In effect, the explicit mechanism (stepwise or synchronous) about the ESDPT process is missing for BBTD system in previous work 29 . It is understandable that spectroscopic techniques such as absorption and emission spectra, time-resolved fluorescence spectroscopy, and so on, could only provide some indirect information about photophysical or photochemical properties [30][31][32][33] . In this work, to provide a clear and detailed ESDPT overall perspective, we theoretically study the excited state dynamical process of BBTD using density functional theory (DFT) and time-dependent DFT (TDDFT) methods [34][35][36][37] . We confirm a stepwise ESDPT process for BBTD. To the best of our knowledge, in addition, no study has reported on electric field effects on ESDPT reaction. We present a new mechanism about regulating and controlling ESDPT reaction via external electric field effect for the first time.
Our paper is organized as follows. Initially, we describe details of the calculations. Then the following section describes and discusses the results, which is organized by subsections consider electronic spectra, geometric structures, frontier molecular orbitals (MOs) and lastly potential energy surfaces. A final section summarizes and gives the conclusions of this study.

Computational Details
In this work, all the quantum chemical calculations are mainly accomplished based on the density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods with Beckes three-parameter hybrid exchange function with the Lee-Yang-Parr gradient-corrected correlation functional (B3LYP) 38 in combination with the triple-ζ valence quality with one set of polarisation functions (TZVP) 39 basis set by Gaussian 09 programs 40 . To be consistent with the previous experiment 29 , chloroform solvent is selected based on the Polarizable Continuum Model (PCM) using the integral equation formalism variant (IEFPCM) 41,42 , which considers the solute in a cavity of overlapping solvent (with an average area of 0.4 Å 2 ) that has apparent changes to reproduce the electrostatic potential due to the polarized dielectric within the cavity. All the geometries of S 0 and The thermal correction to Gibbs free energies of all the stable structures are shown in Table S1, ESI †. Vertical excitation energy calculations are performed from the S 0 -state optimized structure using TDDFT method with six low-lying absorption transitions. In addition, we construct S 0 and S 1 PESs to further illustrate the ESDPT mechanism of BBTD system. All the stationary points along the reaction coordinate are scanned by constraining optimizations and frequency analyses (no imaginary frequency) to obtain the thermodynamic corrections in the corresponding electronic state.

Results and Discussion
Structures and MOs. The six low-lying absorbing transitions and fluorescence of BBTD, BBTD-SPT and BBTD-DPT structures are calculated (see Fig. 2). Our calculated absorption and fluorescence peaks of BBTD are 397 nm and 440 nm, respectively, which are consistent with experimental results (394 nm and 430 nm) 29 . In addition, our fluorescence peaks for BBTD-SPT and BBTD-DPT are 499 nm and 560 nm, they are also in line with the experimental results (475 nm and 550 nm) 29 , respectively. Herein, we confirm adequately the accuracy of the theoretical methods we adopted in this work.
The structures of BBTD (normal BBTD), BBTD-SPT (single-proton transfer BBTD) and BBTD-DPT (dual-proton transfer BBTD) (shown in Fig. 1) are obtained within the framework of DFT and TDDFT methods as mentioned above, with a subsequent vibrational frequency analysis to insure the validity of the stationary points. We list some significant parameters involved in these two intramolecular hydrogen bonds (O 1 -H 2  N 3 and O 4 -H 5  N 6 ) in Table 1. Obviously, for BBTD structure, both O 1 -H 2 and O 4 -H 5 are elongated in the S 1 state, whereas hydrogen bonds H 2  N 3 and H 5  N 6 are shortened with the concomitant enlargement of bond angle δ (O 1 -H 2  N 3 ) and δ (O 4 -H 5  N 6 ). Thus these two intramolecular hydrogen bonds are strengthened upon the photoexcitation 3 . Further, monitoring the infrared (IR) vibrational spectral shifts 3 , as another effective way to verify the changes about excited state hydrogen bond, is also adopted in this work. We show the vibrational spectra of BBTD form in the conjunct vibrational region of both O 1 -H 2 and O 4 -H 5 stretching modes in Fig. S1, ESI †. It is worth mentioning that red shift from S 0 to S 1 is around 12 cm −1 , which is ascribed to the enhanced effect of excited-state hydrogen bonds (O 1 -H 2  N 3 and O 4 -H 5  N 6 ). Even though extent of variation of both bond lengths and bond angles is not big, it can result in important excited state dynamical process.

Table 1. The primary bond lengths (Å) and bond angles δ (°) of BBTD, BBTD-SPT and BBTD-DPT structures in chloroform solvent.
In addition, it is well known that charge redistribution stemming from photo-excitation could depict qualitatively the corresponding properties of electronically excited state. In this work, we show the frontier molecular orbitals (MOs) of BBTD molecule in Fig. 3. Since the S 1 state of BBTD mainly refer to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) with a large oscillator strength (1.466), thus we only provide these two orbitals in this figure. Obviously, BBTD is a ππ*-type transition. Since the changes of charge distribution are not obvious, quantificational contributions above primary atoms involved in hydrogen bonds (O 1 -H 2  N 3 and O 4 -H 5  N 6 ) are also calculated. The contribution of both O 1 and O 4 atoms drops from 4.8% (HOMO) to 4.0% (LUMO), where that of N 3 and N 6 increases from 13.8% to 14.9%. In addition, to be more visual, the electron-density difference (EDD) map are also calculated shown between HOMO and LUMO orbital in Fig. 3. The EDD map displays that upon excitation from S 0 to S 1 state net electron densities shift from hydroxyl groups to N 3 and N 6 moieties. It suggests that after the excitation a driving force can be induced to facilitate the proton transfer reaction in the S 1 state. This is consistent with the physical picture obtained from the HOMO-LUMO transition. In effect, these minor variations of charge distributions reveal the tendency of ESDPT and provide the possibility for ESDPT process.

Analysis of mechanism.
To explore specific ESDPT mechanism of BBTD system, we construct the S 0 -state and S 1 -state PESs as functions of both O 1 -H 2 and O 4 -H 5 bond distances from 0.85 to 2.25 Å (shown in Fig. 4). In this range, all the relative structures (BBTD, BBTD-SPT and BBTD-DPT) could be included. For convenience narration, we separate the S 1 -state projective plane in Fig. 5. It can be clearly found that four stable structures exist in this PES (i.e. N* point stands for BBTD form; ⁎ T 1 and ⁎ T 2 point stand for BBTD-SPT form; ⁎ T 3 point stands for BBTD-DPT form). Due to the symmetry of BBTD, the PES is symmetrical along with diagonal line. That is to say, ⁎ T 1 point and ⁎ T 2 point correspond to the same structure (BBTD-SPT). Since some previous papers have demonstrated that TDDFT method can relatively accurate excited state pathways [43][44][45] , the potential energy barriers Figure 3. View of frontier molecular orbitals (HOMO and LUMO) for BBTD system. Herein, pink moiety means positive charge distribution and green moiety means negative charge distribution. Electron-density difference (EDD) map are shown between S 1 and S 0 . In the EDD map, the regions with increasing electron density from S 0 to S 1 state are shown in cyan, and those with decreasing electron density are shown in yellow. among these four stable configurations are calculated at TDDFT/B3LYP/TZVP level. In fact, to check the level of B3LYP is appropriate to describe this system, the results of potential energy curves are compared between B3LYP functional and a long-range corrected functional (i.e. Cam-B3LYP 46 ) (see Fig. S2, ESI †). It can be clearly found that the trend of potential energy curves are consistent under these two functionals and the barriers are almost the same, which confirms the feasibility of B3LYP functional adopted in this work. Our results show that a 7.21 kcal/mol potential barrier separates N* point from ⁎ T 1 or ⁎ T 2 point, and a low barrier (4.58 kcal/mol) is needed to cross from point ⁎ T 1 or ⁎ T 2 to point ⁎ T 3 . However, a high potential barrier (14.3 kcal/mol) separates point N* and point ⁎ T 3 , which is difficult for transferring a proton in the S 1 state. Comparing these two kinds of excited state paths, we confirm a stepwise ESDPT mechanism for BBTD system. Under the stepwise ESDPT mechanism, the reaction pattern of BBTD system are shown (see Fig. S3, ESI † for detail). Under the pre-equilibrium among N*, ⁎ T 1 and ⁎ T 3 , that is, K 1 , K 2 , K 3 and K 4  ⁎ K N , External electric field effects. Taking electric field effects into consideration, we apply external electric field along axis direction (see Fig. 6). The strengths of external electric field selected in this work are 5 × 10 −4 and 10 −3 au. For convenience, for example, by E X = + 5 × 10 −4 we mean a 5 × 10 −4 au external electric field is applied along the x axis. So the E X = − 5 × 10 −4 indicates a 5 × 10 −4 au external electric field is applied against the X axis.  To reveal differences induced by external electric field, within the framework of DFT and TDDFT B3LYP/ TZVP/IEFPCM(chloroform) level, we optimize the BBTD molecule under E X = + 5 × 10 −4 and E X = + 10 −3 . The most obvious change is the dipole moment (list in Table 2). It can be found clearly that external electric field does not have distinguishable influences on the S 0 state, whereas it results in large changes of dipole moment in the S 1 state. That is to say, excited state dynamical process could be largely affected by external electric field. In addition, we construct the S 0 -state and S 1 -state PESs under E X = + 5 × 10 −4 and E X = + 10 −3 . Results show that the S 0 -state PES among no electric field (E X = 0), E X = + 5 × 10 −4 and E X = + 10 −3 are almost the same, which confirms again that electric field has few influences on the S 0 state. However, it is worth mentioning that external electric field changes the potential energy barriers to a great extent in the S 1 state. Since projective plane of E X = + 5 × 10 −4 or E X = + 10 −3 is similar with that of normal BBTD (i.e. Fig. 5), we list primary excited-state potential barriers among these four stable points (N*, ⁎ T 1 , ⁎ T 2 and ⁎ T 3 ) in Table 3. Also, to confirm the accuracy of B3LYP functional under external electric field, we provide the comparition between B3LYP and Cam-B3LYP functionals in Fig. S2, ESI †. It confirms the feasibility of B3LYP functional once again. In addition, the potential energy curves of characterising stepwise ESDPT under external electric field are shown in Fig. 7. Combining potential energy barriers and potential energy curves, it is obvious that the excited state path (N*-⁎ T 1 -⁎ T 3 ) changes to be more easily along with increase of X-axle external electric field, while the second S 1 -state path (N*-⁎ T 2 -⁎ T 3 ) becomes more difficult to occur. Even though barrier from point N* to point ⁎ T 3 is depressed, it is still a infeasible excited state path compared to others. In addition, to aviod the situation that the changes of the potential barriers are caused by the error of the theoretical method, we also increase the external electric field to E X = + 3 × 10 −3 and E X = + 5 × 10 −3 (shown in Figs S5 and S6, ESI †). It can be clearly found that the enlarged external electric field do result in reduction of potential barrier for N*-⁎ T 1 -⁎ T 3 path and enlargement of potential barrier for N*-⁎ T 2 -⁎ T 3 path. And even though potential barriers along with N*-⁎ T 3 path also decrease, the extent of reduction is too small to have sufficient impact. Accordingly, we theoretically confirm that external electric field along the X axis indeed plays a part in regulating and controlling stepwise ESDPT process for BBTD system.
Similarly, we also study the external electric field along with Y axle and Z axle (i.e. E Y = + 5 × 10 −4 and E Z = + 5 × 10 −4 ). Results demonstrate that the dipole moments for BBTD in both S 0 and S 1 states are almost no changes, which implies that Y-axle and Z-axle external electric fields do not have obvious influences on BBTD in the S 1 state. Indeed, we confirm this viewpoint based on constructing S 1 -state potential energy curves among four stable points. Our theoretical results show that all the S 1 -state potential energy curves are almost superposed for no external electric field, E Y = + 5 × 10 −4 and E Z = + 5 × 10 −4 . In fact, it is worth noticing that Y-axle or Z axle external electric field is perpendicular to ESIPT orientation (see Fig. 6), while X-axle external electric field is almost   Table 3. Potential barriers (kcal/mol) among four stable points (N*, ⁎ T 1 , ⁎ T 2 and ⁎ T 3 ) of BBTD molecule under E X = 0, E X = +5 × 10 −4 and E X = +10 −3 on S 1 -state PESs.
parallel to the direction of ESIPT reaction. It further explains why X-axle external electric field does have obvious effects on ESDPT reaction but Y-axle or Z axle external electric field does not.

Conclusions
In this work, within the framework of DFT and TDDFT methods, we theoretically investigate excited state dynamical process of BBTD system. Based on photoexcitation, changes about intramolecular hydrogen bonds (O 1 -H 2  N 3 and O 4 -H 5  N 6 ) and charge redistribution indicate tendency of ESDPT reaction. Analysis about potential energy barriers in the S 1 -state PES of BBTD reveals a stepwise ESDPT process. Considering electric field effect, we present a new mechanism about controlling S 1 -state stepwise double proton transfer path via external electric field for the first time. Herein, we sincerely wish our work can facilitate researchers to have a deeper understanding about excited state dynamical process and to pave the way for revealing new features of excited state dynamics brought by field effects.