Combined TDDFT and AIM Insights into Photoinduced Excited State Intramolecular Proton Transfer (ESIPT) Mechanism in Hydroxyl- and Amino-Anthraquinone Solution

Time-dependent density functional theory (TDDFT) and atoms in molecules (AIM) theory are combined to study the photoinduced excited state intramolecular proton transfer (ESIPT) dynamics for eight anthraquinones (AQs) derivatives in solution. The calculated absorption and emission spectra are consistent with the available experimental data, verifying the suitability of the theory selected. The systems with the excited-state exothermic proton transfer, such as 1-HAQ, 1,5-DHAQ and TFAQ, emit completely from transfer structure (T), while the reactions for those without ESIPT including 1,4-DHAQ and AAAQ appear to be endothermic. Three reaction properties of three systems (1,8-DHAQ, DCAQ and CAAQ) are between the exothermic and endothermic, sensitive to the solvent. Energy scanning shows that 1,4-DHAQ and AAAQ exhibit the higher ESIPT energy barriers compared to 1-HAQ, 1,5-DHAQ and TFAQ with the “barrierless” ESIPT process. The ESIPT process is facilitated by the strengthening of hydrogen bonds in excited state. With AIM theory, it is observed that the change in electrons density ρ(r) and potential energy density V(r) at BCP position between ground state and excited state are crucial factors to quantitatively elucidate the ESIPT.

nodal-plane model proposed in 1996 48 , which have also been widely explored and proved to be a reliable theory to study the ESIPT systems [49][50][51] . However, this model only qualitatively describes ESPIT process based on the molecular skeletons and functional groups, without the quantitative descriptions of the dual fluorescence distribution and energy barriers, limiting an accurate understanding of ESIPT process.
In this work, the DFT/TDDFT methods were used to investigate two series of AQs in both ground and excited states. Analysis of the hydrogen bonding interactions, electronic transition energies and infrared vibrations provides the atomic insight into their ESIPT processes. The structures in ground state (S 0 (T)) were not stable with the evidence of optimized potential energy surface (PES) except for compound 1,4-DHAQ in which both the single and double protons transfer structures are stable. The AAAQ presented the unstable structure upon ESIPT, consistent with experiments 40,43 . Other seven compounds showed the stable structures at both S 1 (N) and S 1 (T), resulting in various ESIPT properties. The PES in excited state confirmed the exothermic reaction and "barrierless" ESIPT process in 1-HAQ, 1,5-DHAQ, DCAQ and TFAQ with the dominant LWE in dichloromethane. The ESIPT processes for other four compounds are endothermic with different energy barriers. 1,4-DHAQ has the highest energy barrier in S 1 state, similar to AAAQ. The alterable ESIPT properties of 1,8-DHAQ, CAAQ and DCAQ came from their medium energy barriers. Hydrogen bond strengthening in excited state is confirmed by the redshift of vibration frequencies. AIM theory was used to investigate the relationship between ESIPT progress and property of BCP. The changes of electrons density ρ(r) and potential energy density V(r) at BCP position in ground state and excited state are significant for the ESIPT process. More importantly, the V(r) at BCP position is better than ρ(r) as a reference for hydrogen bond dynamics.
Theoretical methods. The calculations in this work were performed by the DFT/TDDFT method [52][53][54][55] with the Becke's three parameter hybrid exchange functional with Lee-Yang-Parr gradient-corrected correlation (B3LYP) functional 56-58 and 6-311 + G(d, p) basis set 59,60 by Gaussian 09 program 61 . The graph of FMO isosurfaces is drawn by Chemcraft 62 . The vertical transition energies and geometric optimization in the excited state were calculated by TDDFT method. Vibrational frequencies of both ground and excited state were computed to ensure that the geometries indeed correspond to a minimum confirmed by no imaginary frequencies.
The conductor-like polarizable continuum model (CPCM) was employed to describe the implicit solvent effect (dichloromethane) 63,64 . The PES of the S 0 and S 1 states were calculated to explore the transfer barrier and thermodynamics effect, revealing ESPIT mechanisms.
The atoms in molecules (AIM) theory proposed by Bader is used for analyzing property of wave function and other real space functions [65][66][67] . The bond critical point (BCP) generally appears between attractive atom pairs, which property is closely related to the bond or interaction strengthening [68][69][70] . Multiwfn was used to study the character of BCP 71 . More attention are paid to the electron density ρ(r) and potential energy density V(r) at BCP between the hydrogen bond 72 .

Results and Discussion
Hydrogen Bonding Dynamics. Figure 1 shows the molecular structures for AQs studied in this work. The n-heptyl group is replaced by the methyl group, as to simplify the DFT calculations. In the optimized structures in the ground and excited states, the atoms involve in ESIPT progress are in the same plane with the benzene rings. The geometric parameters of eight compounds in the ground and excited states are listed in Table 1, as to illustrate the changes in the hydrogen bonding interactions upon photoexcitation. The calculated systems are not stable in ground states (S 0 (T)), except for 1,4-DHAQ whose stable structures are successfully obtained for both single proton and double protons transfer in ground state (Fig. 2). Comparison of the hydrogen bond lengths in ground and excited states showed that the hydrogen bonds enhanced in the sequence of 1-HAQ > 1,5-DHAQ > 1,8-DHAQ > 1,4-DHAQ. The hydrogen bond distances between donor O and H atoms in S 1 (N) and S 1 (T) are 1.008 Å and 1.459 Å for 1,8-DHAQ, and 1.014 Å and 1.540 Å for 1,4-DHAQ respectively, suggesting that     Table S1. The difference is negligible, which mostly result from the strong hydrogen bond in such systems. The B3LYP-D3 assuredly improved the result. While considering the minor differences and the comparion with excited state, we used the B3LYP for the calculation.
Absorption/emission spectra and FMO analysis. The electronic excitation energies and corresponding fluorescence emission spectra of low-lying excited states for eight compounds were calculated by TDDFT method. The data are list in Table 2, which are consistent with the available experimental data. Generally, the energies of charge transfer states are underestimated in traditional functional compared with the long-range correction (LC) methods 74,75 . Then, we use the electron−hole analysis function to estimate the degree of charge transfer and calculate the vertical excitation energy with LC-BLYP. As shown in Tables S2 and S3, we think that except 1,5-DHAQ all other compounds have some portion of CT excitation. Compared with the B3LYP functional, the LC-BLYP functional significantly overestimate the excitation energy and show larger deviation with the experiment. While the B3LYP functional underestimates the energies, it give more accurate result. The molecules except for AAAQ are stable after proton transfer in excited state, with the different conformations. The relative energies of S 1 (T) were higher than S 1 (N) for 1,4-DHAQ, 1,8-DHAQ and CAAQ in ESIPT progress (Figs 2 and S1). 1,4-DHAQ and 1,5-DHAQ exist double ESIPT phenomenon with different properties in the ground and excited states (Fig. 2). 1,4-DHAQ and 1,5-DHAQ presented the S 1 energies in the order of the T1 > T2 > N and T2 > N > T1, respectively. Thus, a fast ESIPT process is expected for 1,5-DHAQ and 1,4-DHAQ with the double ESIPT process. Furthermore, the energy of 1,8-DHAQ became slightly higher after ESIPT ( Figure S1), giving rise to the solvent-sensitive ESIPT process for 1,8-DHAQ 25 .
The AYAAQs can be classified into three categories by their ESIPT proprieties ( Figure S1). AAAQ failed to get a stable structure after ESIPT in the TDDFT calculation, consistent with the experiments. After ESIPT, the energy become higher for CAAQ and slightly lower for DCAQ, verifying the double emission in dichloromethane and acetonitrile. In TFAQ, ESIPT is an intense exothermic progress, leading to a "barrierless" reaction.
Eight compounds have uneven HOMO distributions concentrating on the functional groups, and the evenly distributed LUMO (Fig. 3) Potential energy surface. Potential energy surfaces (PESs) were scanned for molecules at S 0 and S 1 states. Figure 4 shows the PESs in S 1 state for the eight compounds, while that in S 0 state are showed in Figure S2. For HAQ and DHAQs, the energy barriers for ESIPT follow an order of 1,4-DHAQ > 1,8-DHAQ > 1,5-DHAQ ≈ 1-HAQ. The energy barrier is up to 10 kJ/mol for 1,4-DHAQ with the energy of S 1 (T) much higher than S 1 (N). 1-HAQ and 1,5-DHAQ exhibit the energy barriers lower than 2 kJ/mol, suggesting a "barrierless" ESIPT process.    The bond critical point (BCP) generally appears between attractive atom pair. The value of real space functions at BCP have great significance to analyze the weak interaction [80][81][82] . For example, the value of ρ(r) at BCP is closely related to bond strengthening in analogous bond type, and the V(r) at BCP has been shown to be highly correlated with hydrogen bond energies. The relationship between hydrogen bond energy E HB and V(r) at corresponding BCP can be approximately described as 72 : The extent of the hydrogen bond strengthening after photoexcitation is calculated the change of ρ(r) and V(r) at BCP in ground states and excited states (Tables 3 and 4). Upon photoexcitation, all the hydrogen bonds are enhanced. Density of all electrons ρ(r) at BCP position show the similar tendency. For clear comparison, we define the change of ρ(r) and V(r) as Δρ% and ΔV% as Δρ% = (ρ ES − ρ GS )/ρ GS × 100% and ΔV% = (V ES − V GS )/ V GS × 100%. The three DHAQs have double hydroxyls while the calculated ρ(r) and V(r) are only characterized at single BCP. The molecules that present dominant ESIPT fluorescence emission in different solvents have a lager degree strengthening, such as 1-HAQ, 1,5-DHAQ, DCAQ and TFAQ and their ΔV% are higher than 104%. The 1,4-DHAQ and AAAQ which without ESIPT progress have lowest range of strengthening which the ΔV% are lower than 72%. Those with solvent-depended ESIPT progress have a moderate strengthening, such as CAAQ and 1,8-DHAQ. While the Δρ% of AAAQ and 1,8-DHAQ are same but with different properties. Thus, the ΔV% is a better reference than Δρ% when conjecture the property of ESIPT.

Conclusion
DFT/TDDFT methods were employed to investigate the ESIPT process of eight AQs compounds. By analyzing the geometric structures, absorption/fluorescence spectra, infrared vibration and AIM, the ultrafast ESIPT processes for eight molecules were systemically studied. Hydrogen bond strengthening in excited state verified by the decreased hydrogen bond lengths, redshift of O-H or N-H stretching vibration modes and the increase of ρ(r) and V(r) at BCP are the driving forces for proton transfer in the excited states. The electron-withdrawing groups play the role in strengthening the hydrogen bondof O A …H. The exothermic reaction and "barrierless" ESIPT process are observed for 1-HAQ, 1,5-DHAQ and TFAQ with the barrier lower than 2 kJ/mol. 1,4-DHAQ have the     Table 4. Potential energy density V(r) at BCP position.
highest transfer barrier hindering the occurrence of ESIPT. The alterable ESIPT property of 1,8-DHAQ, DCAQ and CAAQ mainly owes to their medium barrier and similar energy of S 1 (N) and S 1 (T). The change of electrons density ρ(r) and potential energy density V(r) at BCP position in ground state and excited state are the important indicators for the ESIPT process. The V(r) at BCP position is the general reference for various kinds of hydrogen bonds.