# Systematic Theoretical Study on the pH-Dependent Absorption and Fluorescence Spectra of Flavins

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}) and the first singlet excited (S

_{1}) states have different protonated species, which are cationic oxidized form ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$ and ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$, respectively [9]. The structures and acid-base equilibrium of flavins are shown in Figure 1.

_{0}-state and ${\mathrm{p}K\mathrm{a}}^{\mathrm{*}}$ of the S

_{1}-state flavin were calculated, which was helpful to confirm whether the flavin was a photoacid. For photoacids, the ${\mathrm{p}K\mathrm{a}}^{\mathrm{*}}$ was considerably less than the pKa. Moreover, based on the $\mathrm{p}K\mathrm{a}$ and ${\mathrm{p}K\mathrm{a}}^{\mathrm{*}}$ of each flavin, the chemical equilibrium of the three-redox state of the flavin was studied, and pH-dependent absorption spectra and fluorescence spectra were simulated.

## 2. Computational Details

**Quantum mechanics (QM) calculations.**The density functional theory (DFT) [24,25] and the time-dependent (TD) DFT [26,27] were employed. Functionals, basis sets, and solvent models were tested based on the reaction (${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ → ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ + ${\mathrm{H}}^{+}$) with an experimental $\mathrm{p}K\mathrm{a}$ of 6.5 [28,29]. As the test results in Table S1 show, the M06-2X [30] /6-31 + G** level with solvation model density (SMD) approach [31] provided sufficient precision for calculating $\mathrm{p}K\mathrm{a}$. Therefore, all calculations in the S

_{0}state were carried out at the M06-2X/6-31 + G** computational level in this paper. In addition, the SMD approach considering the polarity and nonpolarity was adapted to simulate the solution conditions. The geometries of the ten forms of flavin in Figure 1 were optimized at the M06-2X/6-31 + G** level for the S

_{0}state in gas and water. Gibbs free energies were obtained from the vibrational analysis. For the photophysical properties of flavin, the B3LYP is usually employed for calculating the spectra and behaves well [17,18]. For radicals and anions, a relatively big basis set should be used. Therefore, the vertical absorption spectra of nine forms of flavin in water in the S

_{0}state were predicted at the TD B3LYP/6-311 ++G** level, and 20 excited states were involved. Solvent relaxation was not included during excitation. The geometries of nine forms of flavin in the S

_{1}state in water were optimized, and their fluorescence spectra were predicted at the TD B3LYP/6-311 ++G** level. All the above calculations were performed by the Gaussian09 program package [32].

**Calculation of the**$\mathit{p}\mathit{K}\mathit{a}$

**and**${\mathit{p}\mathit{K}\mathit{a}}^{\mathit{*}}$. The ability of AH to deprotonate to A

^{−}can be expressed by the negative logarithm of the acid constant of AH, which is $\mathrm{p}K\mathrm{a}$ for the S

_{0}state and ${\mathrm{p}K\mathrm{a}}^{\mathrm{*}}$ for the S

_{1}state. $\mathrm{p}K\mathrm{a}$ is related to the dissolution free energy $\u2206{G}_{\mathrm{a}\mathrm{q}}$, which can be computed by the Born–Haber thermodynamic cycle [33] (see Figure 2). The specific steps are as follows [34]:

^{−}, respectively, which can be obtained by vibration analysis of the optimized optimal geometric configuration of AH and A

^{−}. ${G}_{\mathrm{g}\mathrm{a}\mathrm{s}}^{{\mathrm{H}}^{+}}$ refers to the free energy of the proton in gas phase (−6.28 kcal/mol) [35].

^{−}, calculated from the variation of the single-point energy between the gas and water. $\u2206{G}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}}\left({\mathrm{H}}^{+}\right)$ is the solvation free energy of the hydrogen ion (−265.9 kcal/mol) [36], and $\u2206{G}_{\mathrm{a}\mathrm{d}\mathrm{d}}$ represents the transfer of a solute molecule from the 1 atm gas phase to the 1 M solvent standard state (1.89 kcal/mol).

**Calculation of the relative concentration and the pH-dependent spectra.**The relative concentration of each form of flavins in the S

_{0}state at a specific pH can be calculated with the $\mathrm{p}K\mathrm{a}$. The calculation process is as follows:

_{1}state at a specific pH can be calculated with the ${\mathrm{p}K\mathrm{a}}^{\mathrm{*}}$. In addition, the pH-dependent fluorescence spectra can be simulated by the same method with the pH-dependent absorption spectra.

## 3. Results and Discussion

#### 3.1. Absorption and Fluorescence Spectra of Flavins in Solution

_{0}state to the S

_{1}state and the ${\pi}_{1}\to {\pi}_{3}$ transition from the S

_{0}state to the S

_{2}state. The ${\pi}_{1}\to {\pi}_{3}$ transition corresponds to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ at 366.0 nm, corresponding to the experimental maximum (${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$) around 394.0 nm [15]. The absorption spectrum of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ has two absorption peaks: the lowest-energy peak is represented by the ${\pi}_{2}\to {\pi}_{3}$ transition from S

_{0}to S

_{1}, and the highest-energy peak is represented by the ${\pi}_{1}\to {\pi}_{3}$ transition from S

_{0}to S

_{2}. The ${\pi}_{2}\to {\pi}_{3}$ and the ${\pi}_{1}\to {\pi}_{3}$ transitions correspond to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ values at 427.5 and 358.7 nm, corresponding to the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ values around 445.0 and 370.0 nm [15,39], respectively. The absorption spectrum of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ also has two peaks: the lowest-energy peak is mainly represented by the ${\pi}_{2}\to {\pi}_{3}$ transition from S

_{0}to S

_{2}, and the highest-energy peak involves the ${\pi}_{1}\to {\pi}_{3}$ transition from S

_{0}to S

_{4}and the ${\pi}_{0}\to {\pi}_{3}$ transition from S

_{0}to S

_{5}. The ${\pi}_{1}\to {\pi}_{3}$ transition and ${\pi}_{0}\to {\pi}_{3}$ transition correspond to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ values at 424.0 and 354.2 nm, corresponding to the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ values of 450.0 and 350.0 nm [15], respectively. The absorption spectra of ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$, ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ all reproduce the spectral characteristics (single-peaked spectrum for ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$, double-peaked spectra for ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$). In Figure 3B, the transitions from S

_{1}to S

_{0}for ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$, ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$, and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ are ${\pi}_{3}\to {\pi}_{2}$ transitions, and the ${\pi}_{3}\to {\pi}_{2}$ transition for ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ corresponds to the fluorescence wavelength (${\lambda}_{\mathrm{F}})$ at 526.0 nm, closely reproducing the experimental value around 530.0 nm [15]. The large f of flavin quinone is consistent with the experimental high bright fluorescence of oxidized flavin [39].

_{0}state to the first three excited singlet states. The highest-energy peak mainly comes from the contributions of the ${\pi}_{3}^{\alpha}\to {\pi}_{5}^{\alpha}$ and ${\pi}_{3}^{\alpha}\to {\pi}_{6}^{\alpha}$ transitions from the S

_{0}state to the S

_{5}state and the S

_{6}state. The triple-peaked absorption spectra of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ involves many electronic transitions, where the bright ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$, ${\pi}_{1}^{\beta}\to {\pi}_{3}^{\beta}$, and ${\pi}_{3}^{\alpha}\to {\pi}_{6}^{\alpha}$ transitions are found at 568.6, 460.3, and 340.2 nm, respectively, corresponding to the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ around 571.0, 481.0, and 340.0 nm, respectively [40]. For ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$, the ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$ transition and the ${\pi}_{3}^{\alpha}\to {\pi}_{6}^{\alpha}$ transition correspond to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ values at 450.8 and 363.1 nm, corresponding to the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ around 480.0 and 370.0 nm, respectively [40]. There is no experimental report on the absorption spectra of ${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$. The absorption spectra of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ and of ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ well reproduce the experimental spectral characteristics (triple-peaked spectrum for ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ and double-peaked spectrum for ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$). In Figure 3D, the transitions from S

_{1}to S

_{0}are the ${\pi}_{3}^{\beta}\to {\pi}_{2}^{\beta}$ transitions for ${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ and the ${\pi}_{4}^{\alpha}\to {\pi}_{3}^{\alpha}$ transition for ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$. The f of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ is large, and it is much larger than that of ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$. This is consistent with the results that flavin semiquinone yielded in the nitronate monooxygenase [23]. Due to flavin semiquinone not being stable in solution and being a transient species in the excited state, there is no experimental study on the fluorescence spectra of flavin semiquinone in aqueous.

_{0}to S

_{1}is 295.6 nm. Therefore, there is no absorption peak for ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ in Figure 3E. In Figure 3E, the absorption spectra of both ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ have a peak [39]. For ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$, the absorption peak comes from the contribution of the ${\pi}_{3}\to {\pi}_{4}$ transition, which corresponds to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ at 392.4 nm, matching the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ around 395.0 nm. For ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$, the ${\pi}_{3}\to {\pi}_{5}$ transition corresponds to the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ at 330.4 nm, corresponding to the ${\lambda}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ around 342.0 nm [39]. In Figure 3F, the transitions from S

_{1}to S

_{0}for ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$, ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$, and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ are ${\pi}_{4}\to {\pi}_{3}$ transitions, which correspond to the ${\lambda}_{\mathrm{F}}$ values at 496.9, 626.8, and 563.7 nm, respectively. ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ does not exist in the pH range of 1~14. In addition, the f of ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ is low. All these are consistent with the experimental result of flavin hydroquinone that ${\lambda}_{\mathrm{F}}$ is not below 500 nm and essentially nonfluorescent in aqueous solutions [39].

#### 3.2. Chemical Equilibrium of Flavins in Solution

_{1}state is greater than the $\mathrm{p}K\mathrm{a}$ value of ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$ in the S

_{0}state. This shows that the acidity of the oxidized cationic form in the S

_{1}state is weaker than that in the S

_{0}state, which is consistent with the previous research results [9]. This can indicate that the cationic quinone is not a photoacid but a photobase. From Table 2, we can see that the $\mathrm{p}K{\mathrm{a}}^{\mathrm{*}}$ values of ${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$ and ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ are less than their $\mathrm{p}K\mathrm{a}$ values, which indicates that they are photoacids. By contrast, the $\mathrm{p}K{\mathrm{a}}^{\mathrm{*}}$ values of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$, ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$, and cationic quinone are greater than their $\mathrm{p}K\mathrm{a}$ values, which indicates that they are photobases. There is little difference between the $\mathrm{p}K{\mathrm{a}}^{\mathrm{*}}$ value and $\mathrm{p}K\mathrm{a}$ value of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}.$ Based on the $\mathrm{p}K\mathrm{a}$ and $\mathrm{p}K{\mathrm{a}}^{\mathrm{*}}$, the relative concentrations of each form of flavins in the S

_{0}state and S

_{1}state at different values are listed in Tables S4 and S5, respectively. In addition, the diagrams of the relative concentrations of different forms of flavins in the S

_{0}state and S

_{1}state with various pH values are shown in Figure 4. For the flavin quinone (Figure 4A,B), in the S

_{0}state, ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$ almost does not exist in the entire pH range. When the pH value is less than 8, ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ is the dominant form. When the pH is larger than 8, the relative concentration of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ decreases gradually with the increase of pH, and the relative concentration of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ increases gradually, and they are equal at the pH value of 10.8. Later, with the pH increasing, ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ gradually becomes the dominant form. Different from the S

_{0}state, ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$ in the S

_{1}state exists in the pH range of 1.0~2.1. For the flavin semiquinone (Figure 4C,D), ${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$ exists when the pH is less than 2 for the S

_{0}state but does not exist in the whole range of pH for the S

_{1}state. For the S

_{0}and S

_{1}states, ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ are the dominant forms when the pH is less than 6 and 7, and when the pH is larger than 6 and 7, the relative concentration of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ gradually decreases, and the relative concentration of ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ gradually increases. They reach equilibrium when the pH is 8.6 and 9.2 for the S

_{0}state and the S

_{1}state, respectively. Then, with the increase of the pH, ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ gradually becomes the dominant form for both the S

_{0}and S

_{1}states. For the flavin hydroquinone (Figure 4E,F), the cationic form ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ does not exist in the whole pH range for both the S

_{0}and S

_{1}states. The neutral form ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ and the anionic form ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ are the dominant forms before and after they reach equilibrium, respectively.

#### 3.3. The pH-Dependent Absorption and Fluorescence Spectra of Flavins in Solution

_{0}and S

_{1}states of the ten forms of flavins. The pH-dependent absorption and fluorescence spectra of flavins in solution are shown in Figure 5. In Figure 5A, the absorption spectra of flavin quinone in the pH range of 1~8 and 13~14 are consistent with the absorption spectra of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ in Figure 2A, respectively. In addition, the peak positions or intensities of the spectra in the pH range of 9~12 are different from those of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$, which is attributed to the coexistence of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ in this pH range (see Figure 4A). In Figure 5B, the fluorescence spectra of flavin quinone in the pH range of 2~14 only have a shark peak when the pH equals to 1; the fluorescence spectrum of flavin quinone has a hump, which can be attributed to the fact that ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ coexist when the pH equals to 1 (see Figure 4B); and the fluorescence intensity of ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ is stronger than that of ${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$ (see Figure 3B). In the range of 8~13, the intensity of spectra gradually increases, which can be attributed to the fact that ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}^{-}$ gradually becomes the dominant form (see Figure 4B). In Figure 5C, the absorption spectra of flavin semiquinone in the pH range of 2~6 and 11~14 are consistent with the absorption spectra of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ in Figure 3C, respectively. In the pH range of 1~6, the spectra present a short and wide triple-peak feature. In the pH range of 7~10, the triple-peak feature of the spectra gradually disappears with the increase of pH, because the relative concentration of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ decreases, and the relative concentration of ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ gradually increases in this pH range (see Figure 4C).The spectrum at pH equal to 1 is different from others, which can be attributed to the coexistence of ${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ at pH equal to 1. In Figure 5D, the fluorescence intensity of flavin semiquinone gradually decreases as the pH increases to 7, which is attributed to ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ gradually becoming the dominant existing form (see Figure 4D). In Figure 5E, the spectra in the pH range of 1~4 and 9~14 are consistent with the absorption spectra of ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ in Figure 2E, respectively. In the pH range of 5~8, the shape of the spectrum gradually changes from that of ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ to that of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$, because the relative concentration of ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ decreases in this pH range, while the relative concentration of ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ increases in this pH range (see Figure 4E). The fluorescence spectra of flavin hydroquinone are short and wide in Figure 5F, which indicates that there is no ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ in the pH range of 1~14 (see Figure 3F and Figure 4F). The ${\lambda}_{\mathrm{F}}$ values and the fluorescence intensity of the fluorescence spectra at the pH range of 1~9 are larger and stronger than those at the pH range of 11~14, and the fluorescence spectrum have two peaks when pH is 10.

## 4. Conclusions

_{0}state and the cationic flavin semiquinone and hydroquinone in the S

_{1}state do not exist throughout the pH range. The cationic flavin quinone in the S

_{0}state and the cationic flavin semiquinone in the S

_{1}state exist when the pH is lower than 2. For all the redox states of flavins in both the S

_{0}and S

_{1}states, their dominant forms are their neutral forms before reaching chemical equilibrium, and their anionic forms become the dominant forms after reaching chemical equilibrium when the pH is in the range of 2~14. Moreover, the pH-dependent absorption and fluorescence spectra of flavin were simulated, which provided a spectral basis for determining the presence form of each flavin. For flavin quinone, the pH-dependent absorption spectra retained the double-peaked characteristics in the pH range of 1~14, and the fluorescence intensity of the pH-dependent fluorescence spectra increased as the pH increased. For flavin semiquinone, the triple-peaked absorption spectrum significantly changed to a double-peaked spectrum in the pH range of 7~9, and the fluorescence intensity of the pH-dependent fluorescence spectra decreased as the pH increased. For flavin hydroquinone, the ${\lambda}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ values of the absorption spectra underwent a blue shift in the pH range of 4~9. In addition, the fluorescence spectra were short and wide in the pH range of 1~14, and the spectrum had two peaks when the pH was 10.

## Supplementary Materials

_{0}state at different pH values; Table S5: The relative concentrations of each form of flavins in S

_{1}state at different pH values; Table S6: The Cartesian coordinates was optimized equilibrium structures reported in this paper.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 1.**Structures and acid-base equilibrium of flavins and labels. The molecules in the black dotted box are the forms that exist under physiological conditions.

**Figure 3.**The computational absorption spectra (

**A**,

**C**,

**E**) and fluorescence spectra (

**B**,

**D**,

**F**) of flavin quinone, flavin semiquinone, and flavin hydroquinone in aqueous solution. Thin vertical lines represent the electronic excited states, with the corresponding transition analysis next to them. Values in parentheses represent the f of fluorescence spectra.

**Figure 4.**The diagrams of relative concentrations for the S

_{0}state (

**A**,

**C**,

**E**) and S

_{1}state (

**B**,

**D**,

**F**) of different forms of flavins in aqueous solution at different pH values.

**Table 1.**Comparison of absorption spectra of flavin between this paper and previous theoretical studies. Experimental results for ${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ were taken from Refs. [15,39]; for ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ and ${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ from Ref. [40]; and for ${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ and ${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ from Ref. [39].

TD State Order | Transition | ${\mathit{\lambda}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | f | ${\mathit{\lambda}}_{\mathbf{e}\mathbf{x}\mathbf{p}}$ | ||
---|---|---|---|---|---|---|

${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ | This paper | 1 | ${\pi}_{2}\to {\pi}_{3}$ | 427.5 | 0.22 | 445.0 |

Ref. [38] | ${\pi}_{2}\to {\pi}_{3}$ | 391.0 | 0.25 | |||

Ref. [17] | 1 | 422.7 | 0.24 | |||

This paper | 2 | ${\pi}_{1}\to {\pi}_{3}$ | 358.7 | 0.31 | 370.0 | |

Ref. [38] | ${\pi}_{1}\to {\pi}_{3}$ | 326.0 | 0.26 | |||

Ref. [17] | 4 | 345.3 | 0.25 | |||

${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ | This paper | 1 | ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$ | 568.6 | 0.11 | 571.0 |

Ref. [38] | ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$ | 535.0 | 0.13 | |||

Ref. [17] | 1 | 581.0 | 0.13 | |||

This paper | 2 | ${\pi}_{1}^{\beta}\to {\pi}_{3}^{\beta}$ | 460.3 | 0.06 | 485.0 | |

Ref. [38] | ${\pi}_{1}^{\beta}\to {\pi}_{3}^{\beta}$ | 406.0 | 0.06 | |||

Ref. [17] | 3 | 431.3 | 0.06 | |||

This paper | 6 | ${\pi}_{3}^{\alpha}\to {\pi}_{6}^{\alpha}$ | 340.2 | 0.08 | 340.0 | |

Ref. [38] | ${\pi}_{0}^{\beta}\to {\pi}_{3}^{\beta}$ | 296.0 | 0.11 | |||

Ref. [17] | 5 | 360.3 | 0.09 | |||

${\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet -}$ | This paper | 2 | ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$ | 450.8 | 0.04 | 480.0 |

Ref. [38] | ${\pi}_{2}^{\beta}\to {\pi}_{3}^{\beta}$ | 423.0 | 0.13 | |||

Ref. [17] | 3 | 437.5 | 0.14 | |||

This paper | 7 | ${\pi}_{3}^{\alpha}\to {\pi}_{6}^{\alpha}$ | 363.1 | 0.37 | 370.0 | |

Ref. [38] | ${\pi}_{1}^{\beta}\to {\pi}_{3}^{\beta}$ | 359.0 | 0.101 | |||

Ref. [17] | 6 | 357.6 | 0.297 | |||

${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ | This paper | 1 | ${\pi}_{3}\to {\pi}_{4}$ | 392.4 | 0.06 | 395.0 |

Ref. [38] | ${\pi}_{3}\to {\pi}_{4}$ | 400.0 | 0.03 | |||

Ref. [17] | 1 | 411.4 | 0.03 | |||

${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{-}$ | This paper | 2 | ${\pi}_{3}\to {\pi}_{5}$ | 330.4 | 0.08 | 342.0 |

Ref. [38] | ${\pi}_{3}\to {\pi}_{5}$ | 347.0 | 0.12 | |||

Ref. [17] | 2 | 345.4 | 0.13 |

Form | $\mathbf{p}\mathit{K}\mathbf{a}$ | $\mathbf{p}\mathit{K}{\mathbf{a}}^{\mathbf{*}}$ | ||
---|---|---|---|---|

calc. | exp. | calc. | exp. | |

${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}1$ | −2.8 | 0.0 [9] | −4.9 | - |

${\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{o}\mathrm{x}}^{+}\_\mathrm{N}5$ | −10.1 | - | 0.2 | 1.7 [9] |

${\mathrm{F}\mathrm{L}}_{\mathrm{o}\mathrm{x}}$ | 10.8 | 10.8 [15] | 10.5 | 10.8 [15] |

${{\mathrm{H}}_{2}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet +}$ | 0.1 | 2.3 [45] | −3.1 | - |

${\mathrm{H}\mathrm{F}\mathrm{L}}_{\mathrm{s}\mathrm{q}}^{\bullet}$ | 8.6 | 8.5 [28,29] | 9.2 | - |

${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}\mathrm{H}}_{\mathrm{r}\mathrm{e}\mathrm{d}}^{+}$ | −3.6 | - | −21.1 | - |

${\mathrm{H}}_{2}{\mathrm{F}\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{d}}$ | 6.6 | 6.5 [28,29] | 9.7 | - |

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**MDPI and ACS Style**

Wang, J.; Liu, Y.
Systematic Theoretical Study on the pH-Dependent Absorption and Fluorescence Spectra of Flavins. *Molecules* **2023**, *28*, 3315.
https://doi.org/10.3390/molecules28083315

**AMA Style**

Wang J, Liu Y.
Systematic Theoretical Study on the pH-Dependent Absorption and Fluorescence Spectra of Flavins. *Molecules*. 2023; 28(8):3315.
https://doi.org/10.3390/molecules28083315

**Chicago/Turabian Style**

Wang, Jinyu, and Yajun Liu.
2023. "Systematic Theoretical Study on the pH-Dependent Absorption and Fluorescence Spectra of Flavins" *Molecules* 28, no. 8: 3315.
https://doi.org/10.3390/molecules28083315