Relative Order of Acidity among Hydroxyl Groups of Oxyluciferin and Emission Light Colors in Aqueous Solution

Abstract

The magnitude of the acidity of the oxyluciferin in water in the ground and excited state is investigated, and it is found for the first time using computational approach that the enol group of the phenol-enol species is the most acidic in the ground state, but the deprotonation of the phenol of the phenol-keto form is the most favored in the excited state. The relative order of the acidity among the hydroxyl groups in the oxyluciferin is attributed to the sequence of the O-H bond lengths in the enol and phenol group of the phenol-enol form, and the phenol group of the phenol-keto species. The mechanism of determining the dominant emissive species in the excited state is proposed, and the dependence of emission light colors on the photoexcitation energy is elucidated by the high relative concentration of six chemical forms in the ground state and the absorption efficiency.

Graphical Abstract

1. Introduction

Bioluminescence is a natural phenomenon that is characterized by emission of visible light produced by a chemical reaction within a living organism. The firefly bioluminescence has been applied in various bioimaging techniques [1–4], as a reporter for adenosine triphosphate (ATP) generation and gene expression [5], and as a biosensor for environmental pollutants [6]. It is broadly accepted that firefly bioluminescence involves a two-step reaction of firefly D-luciferin (LH₂), ATP, oxygen molecule, magnesium cation and firefly luciferase to produce oxyluciferin (OxyLH₂) in the first excited singlet state. Its subsequent relaxation to the ground state releases photons of yellow-green light [1–13]. The crystal structure of the LH₂ was determined decades ago [14,15], and its spectroscopy was investigated in solutions [16,17]. The solution chemistry of the OxyLH₂ is quite complicated due to its instability in aqueous solution [18,19], especially in basic pH [20–27]. In aqueous solution, the OxyLH₂ can exist at the equilibrium with six chemical species in the ground state (S₀), see Figure 1. The neutral OxyLH₂ can adopt the enol or keto form. Either hydroxyl group in the OxyLH₂ (6’-OH or 4-OH, see Figure S1) can be deprotonated to form the phenol-enolate-OxyLH⁻, phenolate-enol-OxyLH⁻ or phenolate-keto-OxyLH⁻. At high pH, double deprotonation yields the phenolate-enolate-OxyLH²⁻. At a given pH, at least two chemical species exist concomitantly as an admixture in equilibrium in the S0 state. Due to the chemical lability of the OxyLH₂, its observation in various studies has led to controversial results [20–34]. The contradiction originates from the coexistence of several forms within a narrow pK_a range and ambiguities due to overlaps caused by additional spectral shifts from the interaction with aqueous solution [22,24,25]. The first key issue is the determination of which hydroxyl group is the most acidic in the S₀ state and the first excited state (S₁) respectively: the phenol or enol group in the phenol-enol form or the phenol in the phenol-keto species. The second one is how to theoretically identify the major emissive species in the S₁ state, which determines the emission light colors.

Figure 1.

Chemical equilibrium of six oxyluciferin forms in the ground state.

Numerous researches have focused on the deprotonation and tautomeric equilibrium of the OxyLH₂ in aqueous solution [20–34]. These efforts have given rise to the long-standing controversy on the relative order of the acidity among the hydroxyl groups in the OxyLH₂ in the S₀ and S₁ state respectively. The experimental controversy on the pK_a and ${\text{pK}}_{\text{a}}^{*}$ is illustrated in the following chronological order. By measuring pK_a, Goto et al. concluded that the enol group is more acidic than the phenol group in the S₀ state [20]. da Silva et al reported the similar experimental result [21]. Naumov et al. observed that at pH 7.8 the OxyLH₂ exists mainly as the phenolate-enol-OxyLH⁻ and phenolate-keto-OxyLH⁻ form in aqueous solution, and inferred the stronger acidity of the phenol relative to the enol group in the S₀ and S₁ state [22]. With time-resolved pico-nanosecond-scale emission data, it was found that the protolytic photodissociation of the OxyLH₂ is related to the enol rather than the phenol reactivity [23]. Erez et al. revealed that the photoacidic functional group is the hydroxyl at position six on the 6’-hydroxybenzothialzole moiety [24]. By use of steady-state UV-visible spectroscopy, it was shown that the deprotonation of 4-OH is more favored than that of 6’-OH in the ground state [25]. Based on the time-correlated single photon counting technique, it was demonstrated that the excited state photon transfer (ESPT) from the enol group is more favorable than the ESPT from the phenol group in the phenol-enol species, but the phenol-keto form is the strongest photoacid among the isomers [26]. By studying the firefly luciferin/luciferase complex in aqueous buffer solutions at various pH, Snellenburg et al. [27] observed that the complex possesses the emission spectrum almost same as that of the OxyLH₂ in water, and have similar relative order of acidity to that in Ref. [26]. On the other hand, the computational results indicated that the phenol group of phenol-keto form is the most acidic in the S₀ state [28–34], which contradicted the recent experimental results in Refs. [25–27]. In the S₁ state, da Silva et al. predicted the enol group of phenol-enol species is the most acidic [29]; but Hiyama et al. suggested that phenol group of phenol-keto form favors the deprotonation by the ESPT [29,31,33]. Under the photoexcitation of the wavelength of 370 nm, the color of the emitting light was predicted to be red based on the high computed relative concentration of six chemical forms in the S₁ state [29,31,33], which contradicted with the measured green color [22,24,26]. Under the excitation of 510 nm, the measured fluorescence light is red, but its maximum emission light intensity is much weaker than that of the green color emission observed at the excitation of 370 nm [26]. So far, no consistent interpretation of the relative order of the acidity of the OxyLH₂, the dependence of the emission spectra on the photoexcitation energy, and the colors of emitting light in aqueous solution has been presented. Different experiments and computational models, investigating the same system from different angles, arrived at different conclusions. Therefore, theory is challenged to propose a consistent theoretical model for the comparison of the acidity of the OxyLH₂ and the mechanism of determining the prevalent emissive species of the OxyLH₂ in aqueous solution.

As we know, the polarizable continuum model (PCM) [35] and its variants cannot take the hydrogen bond interaction between the OxyLH₂ and water molecules into account appropriately [36,37], and the cluster-continuum method (CCM) [36,37] with the explicit water molecule network [31] results in the difficulty on identifying the configuration with the global minimum energy. In the present work, the consistent theoretical model is proposed to clarify the controversial acidity issue, and to identify the colors of the absorption and emission light at various pH values and excitation energies. The CCM with two explicit water molecules for the O4 and O6’ position is applied to calculate the pK_as (S₀ state) and ${\text{pK}}_{\text{a}}^{*}\mathrm{s}$ (S₁ state). The orders of magnitude of the acidity among the hydroxyl groups of the OxyLH₂ in the S₀ and S₁ state are discussed and compared with the orders obtained by the PCM [35] and the CCM with the eleven explicit water molecules [31]. The prevalent absorption species are evaluated based on the computed pK_a. The relation among the abundant emissive species in the S₁ state, relative concentrations of six chemical forms in the S₀ state, oscillator strengths, fluorescent quantum yields, excitation light intensity and photoexcitation energy is investigated to determine the major emissive species in the S₁ state at different photoexcitation energies and pH values.

2. Computational Method

The density functional theory (DFT) and the time-dependent density functional theory (TDDFT) at the M06–2X [38]/6–31+G(d,p) level were applied to optimize the geometries of the six chemical species of the OxyLH₂ for the S₀ and S₁ state in gas phase and aqueous solution, respectively. Gibbs free energies were obtained from the vibrational analysis for each chemical species at the S₀ equilibrium structures. The solvation effect in aqueous solution was modeled by the cluster-continuum method [36,37]. The bulk electrostatic solvent effects were simulated by the solvation model density (SMD) approach [39], and the hydrogen bonds were taken into account by including two explicit water molecules. Each water molecule was placed in proximity to each hydroxyl group. Three thermodynamic cycles have been tested (Figure 2), and the cycle C best fits pK_a calculation for the six chemical forms of the OxyLH₂ [40,41]. The solution phase free energy is the sum of the gas phase Gibbs free energy and free energy of solvation $\mathrm{\Delta }{\text{G}}_{\text{solv}}^{*}$. The former is calculated via the DFT theory with the large basis set (M06–2X/6–311+G(2d,2p)) [42], and the free energy of solvation is consistent with the parametrization of solvation model at the DFT level in conjunction with the small basis set (M06–2X/6–31+G(d,p)) that is commonly used to optimize geometries. The relationship between the pK_a and the change of the solution phase free energy $\mathrm{\Delta }{\text{G}}_{\text{aq}}^{*}$ based on the thermodynamic cycle C (Figure 2) is [40,43]

$${\text{pK}}_{\text{a}}=\frac{\mathrm{\Delta }{\text{G}}_{\text{aq}}^{*}}{\text{RTln}10}-\text{nlog}\left[{\text{H}}_2\text{O}\right]$$ (1)

where n is the number of water molecules used in the cluster-continuum approach, and [H₂O] is the concentration of bulk water which is 55.5 mol L⁻¹ in the standard state [40,43]. The superscript * in the thermodynamic cycle and Eq. 1 denotes that the quantities are computed at the standard state of 1 mol L⁻¹ instead of 1 atm [40]. The ${\text{pK}}_{\text{a}}^{*}\mathrm{s}$ are calculated by Förster equation [44,31]: ${\text{pK}}_{\text{a}}^{*}\left({\text{S}}_1\right)={\text{pK}}_{\text{a}}\left({\text{S}}_0\right)+\mathrm{\Delta }\mathrm{\Delta }\text{E}/\text{RTln}10$, where ΔΔE is the energy difference between the emission energy of the product and that of reactant. The calculations based on the proposed model were performed by the Gaussian 16 program package [45].

Figure 2.

Thermodynamic cycles used for calculating pK_as in the ground state, where α is 0 or 1, m and n take 0 and 2, respectively in present calculation.

3. Results and Discussion

The oxidized LH₂, OxyLH₂, can adopt one of the six chemical species in aqueous solution: keto, enol or deprotonated form (Figure 1). To check which species plays an important role at a given pH in water in the absorption and emission spectra, the pK_as in the S₀ state and ${\text{pK}}_a^{*}\mathrm{s}$ in the S₁ state are calculated via the cluster-continuum approach [36,37], and are listed in Table 1. The pK_as values in Table 1 were calculated by thermodynamic cycle C. Three thermodynamic cycles A, B and C are depicted in Figure 2 [41]. The comparison of the pK_as obtained by the three cycles is listed in Table S1, which shows that the pK_a evaluated by cycle C best fits the experimental value.

Table 1.

The computed and corrected pK_a and ${\text{pK}}_{\text{a}}^{*}$ for the ground state and excited state, and the experimental pK_a [25,26] and ${\text{pK}}_{\text{a}}^{*}$ [26].

pKa type	computed pKa	corrected pKa	exp. pKa	${\text{pK}}_a^{*}$	computed ${\text{pK}}_a^{*}$	corrected ${\text{pK}}_a^{*}$	exp. ${\text{pK}}_a^{*}$
pKA: phenol-keto↔phenolate-keto	10.27	8.75	-	${\text{pK}}_{\mathrm{A}}^{*}$	3.58	2.06	−0.9
pKB: phenol-keto↔phenol-enol	1.02	−0.40	−0.39	${\text{pK}}_{\text{B}}^{*}$	2.62	1.20	-
pKC: phenolate-keto↔phenolate-enol	2.27	0.85	-	${\text{pK}}_{\mathrm{C}}^{*}$	4.78	3.36	-
pKD: phenol-enol↔phenolate-enol	11.49	9.97	-	${\text{pK}}_{\mathrm{D}}^{*}$	5.71	4.19	1.2
pKE: phenol-enol↔phenol-enolate	8.43	6.91	7.40	${\text{pK}}_{\text{E}}^{*}$	4.64	3.12	−0.5
pKF: phenolate-enol↔phenolate-enolate	8.01	6.49	-	${\text{pK}}_{\text{F}}^{*}$	7.84	6.32	-
pKG: phenol-enolate↔phenolate-enolate	10.32	8.80	9.10	${\text{pK}}_{\mathrm{G}}^{*}$	8.16	6.64	7.5

3.1. pK_as and Dominant Absorption Forms

In the ground state, the minimal pK_a among three deprotonation reactions: 1) phenol-keto↔ phenolate-keto + H⁺; 2) phenol-enol↔ phenolate-enol + H+; 3) phenol-enol↔ phenol-enolate + H⁺, is the third one (pK_E, see Table 1). However, in the previous calculations, the minimal pK_a was concluded to be the first one (pK_A) [28–34]. The discrepancy between the present and previous computational results comes from: 1) the calculations in Refs. [28–30,32–34] were done by implicit solvation models without explicit water molecules, so the hydrogen bonding interaction between the solute and solvent is missed to some extent; 2) the computed results in Ref. [31] was obtained by the cluster-continuum model with 11 explicit water molecules (too many water molecules), which made it difficult to locate the configuration with the global minimum energy and resulted in the incorrect order of the acidity among the hydroxyl groups; 3) the different thermodynamic cycles are exploited to calculate the pK_as. The overestimated $\mathrm{\Delta }{\text{G}}_{\text{aq}}^{*}$ (change of the solution phase free energy in the deprotonation process) caused by the charged molecule in the SMD model [36,37,40,41] has been corrected by the combination of the cluster-continuum model with two explicit water molecules and the thermodynamic cycle C (Figure 2). The computed pK_as indicate that in the ground state the hydroxyl group at the O4 of the phenol-enol-OxyLH₂ is the most acidic, and the relative order of the acidity is phenol-enol↔ phenol-enolate + H⁺ > phenol-keto↔ phenolate-keto + H⁺ > phenol-enol↔ phenolate-enol + H⁺, which is consistent with the order of the pK_a values measured in the recent experiments [25,26]. The present calculated pK_a values show that the enol group of the phenol-enol-OxyLH₂ should first dissociate, opposite to the previous calculation [28–34], in which the phenol of phenol-keto-OxyLH₂ deprotonated first.

To evaluate which species contribute to the absorption spectra at a given pH value, let us calculate the corrected pK_a by the equation ${\text{pK}}_{\text{a}}^{\text{corr}}(\text{AH})={\text{pK}}_{\text{a}}^{\text{calc}}(\text{AH})+\left[{\text{pK}}_{\text{a}}^{\text{exp}}(\text{BH})-{\text{pK}}_{\text{a}}^{\text{calc}}(\text{BH})\right]$. The BH is the reference compound similar to the OxyLH₂. The ${\text{pK}}_{\text{a}}^{\text{exp}}$, ${\text{pK}}_{\text{a}}^{\text{calc}}$ and ${\text{pK}}_{\text{a}}^{\text{corr}}$ are the experimental, calculated and corrected pK_as, respectively [30,32,34]. The 6’-MeOxyLH2, which possesses a methoxy group at C-6’ (Figure S1), is selected as the reference molecule for the proton dissociation in the enol group. The calculated corrected pK_a values are displayed in Table 1, which match well with the recent experimental pK_as [25,26]. Based on the ${\text{pK}}_{\text{a}}^{\text{corr}}$, the calculated relative concentrations of six chemical species with respect to the pH value are displayed in Figure 3. The relative concentrations at pH 5, 7, 9 and 11 have been listed in Table 2. Under the same excitation light intensity, the relative absorption intensity can be estimated as the product of the concentration of the species in the S₀ state and its absorption oscillator strength [28–34]. Since the oscillator strengths of six chemical forms are in the same order (Table 3), the major absorption species can be identified as the ones with the high relative concentration in the S₀ state (Table 2).

Figure 3.

Relative concentrations of six chemical species in aqueous solution in the ground state.

Table 2.

Relative concentrations of six chemical species in aqueous solution in the ground state, the maximum concentration for a given pH is underlined.

chemical species	relative concentrations
	pH 5	pH 7	pH 9	pH 11
phenol-keto-OxyLH2	2.82×10−1	1.50×10−1	1.24×10−3	2.03×10−7
phenol-enol-OxyLH2	7.09×10−1	3.77×10−1	3.12×10−3	5.10×10−7
phenolate-keto-OxyLH−	5.02×10−5	2.67×10−3	2.21×10−3	3.61×10−5
phenolate-enol-OxyLH−	7.60×10−6	4.03×10−4	3.35×10−4	5.46×10−6
phenol-enolate-OxyLH−	8.72×10−3	4.63×10−1	3.84×10−1	6.27×10−3
phenolate-enolate-OxyLH2−	1.38×10−6	7.34×10−3	6.09×10−1	9.94×10−1

Table 3.

The experimental [25,26] and computed [46] wavelengths (nm) in absorption and emission spectra^*, and computed relative oscillator strength (f_compt).

chemical species	wavelengths in absorption wavelengths in emission spectra spectra
	λexp	λcompt	fcompt	λexp	λcompt	fcompt
phenol-keto-OxyLH2	388	383	0.863	525	531	0.927
phenol-enol-OxyLH2	367	364	0.845	445	449	0.810
phenolate-keto-OxyLH−	482	485	1.000	634	605	1.000
phenolate-enol-OxyLH−	406	424	0.927	560	537	0.922
phenol-enolate-OxyLH−	414	421	0.597	555	553	0.562
phenolate-enolate-OxyLH2−	425	439	0.816	539	541	0.786

^*The absorption and emission spectra were calculated at B3LYP/6-311G(2d,p) in the framework of the QM/MM method [46].

In pH < 7, the phenol-keto-OxyLH₂ and phenol-enol-OxyLH₂ have high relative concentrations in the ground state (Figure 3), so they have major contributions to the absorption spectra with the wavelengths 388 nm (phenol-keto) and 367 nm (phenol-enol) (Table 3), respectively. The measured absorption peak at 371 nm [25,26] can be identified as the spectrum superposition of the phenol-enol-OxyLH₂ (367 nm) and phenol-keto-OxyLH₂ (388 nm). Around pH 8, the phenol-enolate-OxyLH⁻ has the maximum concentration (414 nm), which contributes to the measured shoulder at 417 nm in the absorption spectra [25,26].

In pH > 9, the concentration of the phenolate-enolate-OxyLH²⁻ (425 nm) is the largest (Table 2), and the experimental absorption peak 425 nm can be attributed to this species. The relation between the computed relative concentrations (∝ fraction of absorbed light) and the wavelengths are in line with the experimental results shown in Figure 2c (pH 7), Figure 2e (pH 9) and Figure 2g (pH 11) of Ref. 26. The previous computational results predicted that the ground state phenolate-keto-OxyLH⁻ is the major species in water in pH 7–9 [28–34]. However, Figure 3e reveals that in pH 7–9, the phenol-enolate-OxyLH⁻ (414 nm) is the dominant species in aqueous solution, and has main contribution to the absorption spectra, which is consistent with the experimental data [25,26]. The pK_a of the reaction phenolate-enol↔ phenolate-enolate + H⁺ (6.49) is smaller than that of the phenol-enol↔ phenolate-enol + H⁺ (9.97), and the equilibrium of phenol-enol↔ phenolate-enol + H⁺ has the largest pK_a value (Table 1). When the pH reaches 9.97, the phenol-enol-OxyLH₂ breaks down to the phenolate-enol-OxyLH⁻. However, after phenol-enol-OxyLH₂ becomes phenolate-enol-OxyLH₂, it is immediately deprotonated to phenolate-enolate due to its pK_F=6.49, which shows that the phenolate-enol-OxyLH⁻ is negligible in aqueous solution as revealed in Figure 3d. This computational result supports the experimental observation that in the ground state, only five species exist in water, and the phenolate-enol-OxyLH₂ should be excluded.

The successful explanation of the pH-sensitive absorption spectra comes from the fact that the present computed pK_as are more accurate than those obtained in the previous computational work [28–34]. The cluster-continuum model with two explicit water molecules ensures the correct relative order of the acidity among the hydroxyl groups of the oxyluciferin in aqueous solution. The thermodynamic cycle C reduces the overestimation of the pK_a values for the second deprotonation: phenolate-enol ↔ phenolate-enolate + H⁺ (pK_F), phenol-enolate ↔ phenolate-enolate + H+ (pK_G); and makes the computed pK_a values closer to the experimental ones [25,26] than other cycles [28–34], see Table S1. The direct consequence of the current method is that the dianion concentration (phenolate-enolate) is large even at pH 9 (see Table 2), which matches the recent experimental data [25,26]. However, it is negligible in pH < 11, if computed by other computational methods [29,31,33].

3.2. $\mathbf{p}{\mathbf{K}}_{\mathbf{a}}^{*}\mathbf{s}$ and Prevalent Emissive Species

To calculate the ${\text{pK}}_{\text{a}}^{*}$ values of the six oxyluciferin forms, we exploit the Förster equation [44,31]. The computed ${\text{pK}}_{\text{a}}^{*}$ values are listed in Table 1. The relative order of the acidity of the OxyLH₂ in the S₁ state in water is phenol-keto↔ phenolate-keto + H⁺ > phenol-enol↔ phenol-enolate + H⁺ > phenol-enol↔ phenolate-enol + H⁺, that is, the acidity magnitude between phenol-keto↔ phenolate-keto + H⁺ and phenol-enol↔ phenol-enolate + H⁺ in the S₁ state is swapped comparing to that in the S₀ state. Based on the pK_a shift $(\mathrm{p}{\mathrm{K}}_{\mathrm{a}}^{\mathrm{e}\mathrm{x}\mathrm{p}}(\text{BH})-{\text{pK}}_{\text{a}}^{\text{calc}}(\text{BH}))$, corrected by taking the 6’-MeOxyLH₂ as a reference compound in the ground state, the corrected ${\text{pK}}_{\text{a}}^{*}$ values are calculated and displayed in Table 1. The calculated data are in line with the experimental ${\text{pK}}_{\text{a}}^{*}$ [26].

Based on the computed corrected ${\text{pK}}_{\text{a}}^{*}\text{s}$, the relative concentrations of six chemical forms in the first excited state in aqueous solution have been evaluated and drawn in Figure 4. In Refs. [29,31–33], the dominant emissive species were selected by their high relative concentrations among six chemical forms in the S₁ state. In pH < 5, Figure 4a and Figure 4b indicate that the phenol-enol-OxyLH₂ and phenol-keto-OxyLH₂ have already deprotonated in the S₁ state. If one determines the major emissive form by the high relative concentration in the S₁ state as did in Refs. [29,31–33], Figure 4c suggests that in pH 5–8, the dominant emissive species should be the red-emitting phenolate-keto-OxyLH⁻ with emissive wavelength of 634 nm (Table 3). Nevertheless, at the photoexcitation of the wavelength of 370 nm, the color of the emission light observed in experiments in pH 6–7 [22–26] is green (555 nm) instead of red (634 nm) (Figure 5). This contradiction indicates that the dominant emissive species is not the phenolate-keto-OxyLH⁻, and cannot be determined by their high relative concentrations in the S₁ state, which are obtained by the ${\text{pK}}_{\text{a}}^{*}$. If the dominant emissive species were determined by their high concentrations in the S₁ state, the fluorescence spectra would not depend on the excitation energy of photons, which conflicts with the fact that the emission color has close relation to the photoexcitation energy [26].

Figure 4.

Relative concentrations of six chemical species in aqueous solution in the excited state.

Figure 5.

Emission spectra of the oxyluciferin. The maximum wavelengths at pH 6–11 are between 555 nm and 539 nm.

Why cannot the dominant emissive species be identified by their high concentrations in the S₁ state? In the excited state, molecules are not in their most stable state, and the dynamic protonation/deprotonation and keto/enol tautomerization cannot be viewed as a thermodynamic process: there is no actual equilibrium among protonated, deprotonated, keto and enol species [47]. The fluorescence time is between 0.5 ns and 10 ns [26], and the protonation/deprotonation lifetime in the excited state is about 45 ps [24,26]. The short fluorescence time (0.5 ns) is about ten times of the ESPT time constant. Since the fluorescence lifetime is not much longer than the protonation/deprotonation and keto/enol tautomerization lifetime, the excited species cannot reach the equilibrium of six chemical forms with the stable relative concentration in the S₁ state before emission [47]. Thus, the selection of the dominant emissive species by their high relative concentrations in the S1 state is inappropriate, as the absorption/emission is a fast dynamical process instead of thermodynamic equilibrium state [26,47].

To elucidate the emission light colors, we need to identify the abundant species of the OxyLH₂ in aqueous solution in the excited state. The emission light intensity (I_em) is directly proportional to the oscillator strength (f), concentration of the chemical species in the S₀ state (C), fluorescent quantum yield (Φ), excitation light intensity ( ∝ μ₀ ) and absorption efficiency (η), i.e., I_em ∝ μ₀ΦηCf [48] (its derivation is shown in Supplementary Material). The absorption efficiency, for a chemical species at a given excitation energy, is the ratio of the absorption intensity at a given wavelength of photoexcitation to the maximum absorption intensity, and proportional to the molar absorptivity (Figure 6). For the phenol-enol-OxyLH₂, the absorption efficiency (η=I_cd/I_max) at the photoexcitation of 370 nm is illustrated in Figure 6a. The emission lifetime (τ) depends on the light frequency (𝜐) and oscillator strength, i.e., τ ∝ 1/f𝜐² [48]. For the six OxyLH₂ species, the oscillator strengths, emission frequencies (Table 3) and quantum yields (0.11~0.50) [26] are in the same order, which indicates the emission lifetimes of the six species are comparable. Nevertheless, the maximal concentration of the species is about one thousand times of the minimal concentration of the species at various pH values (Table 2), and η varies greatly for the six species at a given frequency, see Figure 6. Under the same excitation light intensity and comparable values of Φf, the relative emission light intensity (I_rel) is dominated by ηC, i.e., I_rel ∝ ηC. Thus, the major emissive species in the S₁ state are the deprotonated forms of the neutral species (due to the fast ESPT) and/or the deprotonated species with 1) high relative concentrations in the ground state and/or 2) high absorption efficiency at a given excitation wavelength.

Figure 6.

Absorption spectra of oxyluciferin: absorption intensity vs wavelength. a) at pH 6; b) at pH 8. Phenol-enol-OxyLH₂ (navy), phenolateenol-OxyLH⁻ (grey), phenolate-keto-OxyLH⁻ (red), phenol-keto-OxyLH₂ (cyan), phenolenolate-OxyLH⁻ (olive), and phenolate-enolate-OxyLH²⁻ (orange). The heights of vertical black lines in a) and b) represent the absorption intensities at the photoexcitation of 370 nm and 510 nm.

At the photoexcitation of 370 nm (Figure 6a), the phenol-enol-OxyLH₂ (absorption peak 367 nm), phenol-keto-OxyLH₂ (388 nm) and phenol-enolate-OxyLH⁻ (414 nm) have comparable high absorption efficiencies, as the 370 nm is close to the 367 nm, 388 nm and 414 nm (Figure 6). In pH 6–7, under the excitation of 370 nm, the phenol-enol-OxyLH₂ and phenol-keto-OxyLH₂ with the dominant concentrations in the S₀ state (Figure 3a and Figure 3b), are excited to the S₁ state and turn into the phenol-enolate-OxyLH⁻ and phenolate-keto-OxyLH⁻ due to the fast ESPT. Another major form in the S₀ state in pH 6–7 is the phenol-enolate-OxyLH⁻ (Figure 3e), and is excited to the S₁ state. Thus, the resulting major emissive species are the phenol-enolate-OxyLH⁻ and phenolate-keto-OxyLH⁻. The third column of Table 2 shows that the phenol-enol-OxyLH₂ (37.7% of the oxyluciferin in the S0 state) is excited to the S₁ state, and becomes the phenol-enolate-OxyLH⁻ in the S₁ state. The phenol-enolate-OxyLH⁻ (46.3%) is directly excited to the S₁ state, so the total amount of the excited phenol-enolate-OxyLH⁻ is about 84.0% of the excited oxyluciferin. The phenol-keto-OxyLH₂ in the S₀ state is about 15.0% (Table 2), the corresponding excited phenolate-keto-OxyLH⁻ is only 15.0%. Thus, at the photoexcitation of 370 nm, the dominant emissive species is the phenol-enolate-OxyLH⁻ (555 nm) in pH 6–7, and the emission color is green (555 nm), which is consistent with the experimental emission spectra of the OxyLH₂ [26].

Since the dominant emissive species in pH 6–7 is the phenol-enolate-OxyLH⁻, the match of the predicted emission color with the experimental one (555 nm) indicates that after the phenol-enol-OxyLH₂ and phenol-enolate-OxyLH⁻ are excited to the S₁ state, they do not have enough time to reach the equilibrium of six chemical species in the S₁ state, or are converted to the phenol-keto-OxyLH⁻ before emission (Figure 4). As the wavelength of 510 nm is close to the absorption peak of the phenolate-keto-OxyLH⁻ (482 nm), under this excitation the only chemical species with the high absorption efficiency is the phenolate-keto-OxyLH⁻ (Figure 6b). At the photoexcitation of 510 nm, the absorption spectra show that other species with very small absorption efficiency (Figure 6b) are difficult to be excited to their S₁ state. The concentration of the phenolate-keto-OxyLH⁻ is low with respect to other species in the ground state, but it has much higher absorption efficiency than all other chemical forms at 510 nm. Thus, under the excitation of 510 nm, the dominant emissive species is the phenolate-keto-OxyLH⁻, and the fluorescence color is red (634 nm) in pH 6–7 [26]; however, this red emission peak is much lower than the green one (555 nm) caused by the excitation of 370 nm [26].

The emission spectra display the blue-shift as the pH value goes from pH 6 to pH 11 (Figure 5) [23,24,26]. The previous calculation showed that the dianion species, phenolate-enolate-OxyLH²⁻, was negligible in the ground state in pH < 11 [29,31,33]. Based on the previous recognition that the phenol-enolate-OxyLH⁻ was the only light emitter in aqueous solution in pH < 11 [49], the π-π stacking complexes was proposed to explain the pH-sensitive fluorescence spectra [49,50]. It suggested that the π-π stacking complexes adopting different conformations in different pH values could explain the lower energy of the emission in acidic/neutral pH (~550 nm), in comparison with the emission in basic pH (~540 nm), see Figure 5 [49]. Here, we propose the different mechanism of the blue-shift of emission spectra of the oxyluciferin. Under the excitation of 370 nm, in acidic/neutral pH, the dominant emissive species is the phenol-enolate-OxyLH⁻ with emissive wavelength 555 nm. However, when pH > 9, the phenolate-enolate-OxyLH²⁻ is dominant in S₀ state (Figure 3), and its excitation to the S₁ state and the subsequent emission results in the green color of the fluorescence (539 nm), which explains the blue-shift in the emission spectra as the pH value increases, and matches the recent experimental data [23,24,26].

3.3. Explanation of Relative Order of the Acidity

To explain the relative order of the acidity among the hydroxyl groups in the OxyLH₂, the O-H bond lengths and net electric charges on the O4, O6’ and the corresponding attached hydrogen atoms in the optimized structures in water are calculated and shown in Figure 7. The order of the calculated O-H bond lengths is as follows: phenol of phenol-enol in S₀ (0.989 Å) < phenol of phenol-keto in S₀ (0.991 Å) < enol of phenol-enol in S₀ (0.995 Å) < phenol of phenol-enol in S₁ (1.001 Å) < enol of phenol-enol in S₁ (1.004 Å) < phenol of phenol-keto in S₁ (1.036 Å), see Figure 7. The order of the corrected pK_a and ${\text{pK}}_{\text{a}}^{*}$ is: ${\text{pK}}_{\text{D}}(9.97)>{\text{pK}}_{\text{A}}(8.75)>{\text{pK}}_{\text{E}}(6.91)>{\text{pK}}_{\text{D}}^{*}(4.19)>{\text{pK}}_{\text{E}}^{*}(3.12)>{\text{pK}}_{\text{A}}^{*}(2.06)$, see Table 1. The exact same sequences of two characteristics of the evaluated quantities indicate that the shorter O-H bond length results in larger pK_a or ${\text{pK}}_{\text{a}}^{*}$. This is consistent with the observation that the shorter O-H bond relates to stronger O-H interaction, smaller dissociation rate or larger pK_a (${\text{pK}}_{\text{a}}^{*}$). The net electric charges on the O4 and O6’ atoms do not have the direct correlation with the order of the magnitude of the pK_a or ${\text{pK}}_{\text{a}}^{*}$. The O6’ of the phenol of phenol-keto in the S₁ state has minimal net charge (−0.680 e) among the O4 and O6’ in two neutral species and in both S₀ and S₁ state, and the phenol of phenol-keto in the S₁ indeed possesses the minimal ${\text{pK}}_{\text{a}}^{*}$.

Figure 7.

The O-H bond lengths and net electric charges on the O4, O6’ and the corresponding attached hydrogen atoms. a) phenol-enol-OxyLH₂ in the S₀ state; b) phenol-keto-OxyLH₂ in the S₀ state; c) phenol-enol-OxyLH₂ in the S₁ state; d) phenol-keto-OxyLH₂ in the S₁ state.

4. Conclusion

We have used the combination of the cluster-continuum method and the thermodynamic cycle C to calculate the pK_a values for the ground state of the six chemical species of the oxyluciferin, and found that the enol group of the phenol-enol-OxyLH₂ is the most acidic. The phenol of the phenol-keto form was concluded to be the most acidic in the previous computational results [28–34], which contradicted the recent experimental data [25,26]. The present computational results have demonstrated that the cluster-continuum model with two explicit water molecules, in which the hydrogen bonding interaction has been taken into account in more accurate way than the PCM and its variants, ensures the correct relative order of the acidity among the hydroxyl groups in the OxyLH₂; and the thermodynamic cycle C can mitigate the overestimation of the pK_a values for the second deprotonation. The major absorption species have been identified as the ones with high relative concentrations in the ground state. The absorption spectra are dominated by the phenol-enol-OxyLH₂ and phenol-keto-OxyLH₂ in pH < 7, the phenol-enolate-OxyLH⁻ around pH 8, and the phenolate-enolate-OxyLH²⁻ in pH > 9, which verifies the recent experimental results [25,26]. In the excited state, the deprotonation of the phenol of the phenol-keto-OxyLH₂ in water is the most favored. The relative order of the pK_a (${\text{pK}}_{\text{a}}^{*}$) among the hydroxyl groups in the OxyLH₂ has been correlated with the O-H bond lengths in the enol and phenol group of the phenol-enol form and phenol of phenol-keto species in the ground and excited state. As the absorption/emission is a fast-dynamical process, the dominant emissive species cannot be determined by high relative concentrations in the first excited state. The mechanism of identifying the major emissive species in the emission spectra is to pinpoint: 1) the deprotonated forms of the neutral species or the deprotonated species, possessing major relative concentrations in the ground state; or 2) the chemical forms with high absorption efficiency. At the excitation wavelength of 370 nm, the dominant emissive species is the phenol-enolate-OxyLH⁻ in pH 6–7, which emits the green light (555 nm); the phenolate-enolate-OxyLH²⁻ dominates the emission light color (539 nm) in pH > 9. As the pH value increases from 6 to 11, the wavelength of the emission light changes from 555 nm to 539 nm, which explains the blue-shift in the emission spectra of the oxyluciferin.

Highlights.

• Provide the correct relative order of acidity among the hydroxyl groups of the oxyluciferin in aqueous solution.

• Propose the mechanism of determining major emissive species.

• Predict that in basic pH, the dianion becomes the dominant species in the ground state, which explains the blue-shift of emission spectra.

• Explain the dependence of the emission colors on the excitation energy.