A coumarin derivative-Cu2+ complex-based fluorescent chemosensor for detection of biothiols

Herein, a novel fluorescent sensor has been developed for the detection of biothiols based on theoretical calculations of the stability constant of the complex between a Cu2+ ion and (E)-3-((2-(benzo[d]thiazol-2-yl)hydrazono)methyl)-7-(diethylamino) coumarin (BDC) as a fluorescent ligand. In this study, on the basis of density functional theory method, the Gibbs free energy of ligand-exchange reaction and the solvation model were carried out using thermodynamic cycles. The obtained results are in good agreement with the experimental data. The BDC–Cu2+ complex can be used as a fluorescent sensor for the detection of biothiols in the presence of non-thiol containing amino acids, with a detection limit for cysteine at 0.3 μM. Moreover, theoretical calculations of excited states were used to elucidate variations in the fluorescence properties. The computed results show that the excited doublet states D2 and D1 are dark doublet states, which quench the fluorescence of the complex.


Introduction
Cysteine (Cys), homocysteine (Hcy), and glutathione (GSH) are thiol biomolecules that play an important role in human biological processes. Some diseases are believed to be related to abnormalities in the concentrations of these compounds in biological systems. A low level of Cys may cause a decline in the immune system, resulting in diseases such as infections, cancer, Parkinson's, Alzheimer's, retarded growth, liver damage, and skin lesions. [1][2][3][4] A high level of Hcy is believed to be associated with heart disease, thromboembolic disease, stroke, atherosclerosis, renal and thyroid dysfunction, psoriasis, diabetes, and cancer. 5,6 Disturbances in GSH homeostasis are associated with some diseases including immune diseases, inammatory, cancer, metabolic diseases, diseases of aging, cystic brosis, cardiovascular, and neurodegenerative diseases. 1,7 As a result, the development of selective and sensitive detection methods for biothiols has been attracting the attention of scientists. In particular, analytical methods based on uorescence technique have been widely developed due to their outstanding advantages. 8,9 This technique, in particular, can be used to detect biothiols in living cells. 10,11 A number of uorescent sensors have been reported based on various interactions with biothiols, such as Michael addition, 12,13 addition-cyclization with acrylates or aldehydes, 14,15 cleavage reactions of sulfonamide, sulfonate ester, disuldes, [16][17][18] substitution reactions, 19 and disulde exchange reactions. 20 Recently, sensors for biothiols have been widely synthesized and reported; their working mechanism is based on the reactions between biothiols and complexes of uorescent ligands with metal ions. 21,22 This approach has opened a new research direction taking advantage of complexes between uorescent sensors and metal ions towards the detection of biothiols. These works become more convenient if the stability constants of complexes can be determined. Recently, some theoretical computational models for determining the stability constants of complexes have been proposed with the aim of replacing traditional experimental methods. [23][24][25] However, the accuracy of these models needs to be veried before their application. This problem can be effectively solved by combining theoretical calculations and empirical investigations to determine the stability constant of complexes.
In the present study, a complex between a Cu 2+ ion and a uorescent ligand is reported as a novel chemosensor for the detection of biothiols based on complex exchange reactions. The stability constant of the complex, also known as the complexation equilibrium constant in aqueous solutions, was calculated using the Gibbs free energy of the ligand-exchange reaction determined by a solvation model based on density (SMD), a density functional theory (DFT) method, and thermodynamic cycles. 26,27 The calculated results are in good agreement with the experimental data obtained by a nonlinear curve-tting method. 28,29 From the value of the stability constant, the applicability of the complex as a uorescent sensor for the detection of biothiols based on the complex exchange reaction was predicted. This was further conrmed by the experimental data obtained by applying this complex as a uorescent sensor. In addition, herein, theoretical calculations of the excited states were used to explain the uorescence properties of the substances.
All solvents were purchased from Merck. Ethanol was HPLCgrade without uorescent impurities and used without further purication. DMF was also HPLC-grade; however, it was redistilled before use. H 2 O was two times distilled water.

Computational methodology
2.3.1 Optimization of the geometries, energies, and absorption and uorescence properties. Quantum chemical calculations were performed using the Gaussian 09 program package. 30 The optimization of the geometries of related moieties was carried out using density functional theory (DFT) at the PBE0/6-31+G(d) level of theory. [31][32][33][34] Single-point energies of the optimized geometries in the gas phase were calculated at the higher 6-311++G(d,p) basis set. [35][36][37][38][39] The variation in the Gibbs free energy (DG) of reactions was determined by the difference between the sums of the electronic and thermal free energies of products and reactants. The absorption and uorescence properties were investigated based on the electron excited states of the optimized geometries using the time-dependent density functional theory (TD-DFT) at the PBE0/6-311++G(d,p) level. [40][41][42][43] 2.3.2 Theoretical method for determining the stability constants of the complex. The stability constant of the complex, also known as the complexation equilibrium constant in aqueous solutions (log b), is calculated by the Gibbs free energies of ligand-exchange reactions determined using thermodynamic cycles, the DFT theory method, and the SMD solvent model (Scheme 1). [23][24][25][26][27] Accordingly, the complexation equilibrium constant in aqueous solutions (log b) is calculated by the following equation:  2 ] 2+ , which was used as a reference complex for calculation. DG aq is the Gibbs free energy of the ligandexchange reaction in the aqueous solution, which was determined by Scheme 1 and calculated using eqn (2): DG g and DDG solv were calculated by eqn (3) and (4), respectively: where DG g (the variation in the Gibbs free energy of the reaction) is the difference between the sums of the electronic (3 0 ) and Scheme 1 Thermodynamic cycle for the calculation of the Gibbs free energy of a ligand-exchange reaction in an aqueous solution, DG aq .
thermal free energies (G corr ) of products and reactants in the gas phase at the PBE0/6-311++G(d,p) level of theory and DG solv is the free energy of solvation of each compound, which was calculated using the solvent model density (SMD) model at the M052x/6-31+G(d) level of theory. 46-49 2.3.3 Experimental method for determining the stability constants of the complex. The experimental complexation equilibrium constant can also be determined by a nonlinear curve-tting method. 28,29 In this case, the experimental complexation equilibrium constant (b ex ) of reaction (5) is calculated by a nonlinear curve-tting method based on the uorescence titration spectra of a uorescent ligand solution (L) with the gradual addition of Cu 2+ ions.
According to this method, the experimental complexation equilibrium constant (b ex ) is detected by the nonlinear curve-tting method based on the relationship between the two quantities y ¼ C M and x ¼ F/F 0 , as shown below (see details in the ESI †): where C M is the total concentration of the Cu 2+ ions added to the solution, F 0 is the uorescence intensity of the free L solution (concentration of L is C L ) at the time when the concentration of Cu 2+ ions was zero, and F is the uorescence intensity of the L solution at the time when the concentration of Cu 2+ ions was C M .

Characterization of the uorescent ligand and its complex with a metal ion
was synthesized in about 30% overall yield using 4-(diethylamino)salicylaldehyde via the four steps shown in Fig. 1. The structural characteristics of BDC were conrmed by the 1 H NMR, 13 C NMR, and mass spectra (ESI †).
The experimental results show that the free ligand BDC is a uorescent compound. It exhibits a characteristic emission band peaked at 536 nm, with a uorescence quantum yield (F) of 0.11 calculated using uorescein in 0.1 N NaOH (F ¼ 0.85) as a ref. 50. When 1 equivalent of Cu 2+ was added to the BDC solution, the uorescence intensity of the solution was almost   (Fig. 2a). The uorescence titration spectra of BDC with the gradual addition of Cu 2+ ions, as shown in Fig. 2b, indicated that the reaction between BDC and Cu 2+ occurred in a 1 : 1 stoichiometry. In another experiment, when 1 equivalent of EDTA was added to the solution obtained aer adding 1 equivalent of Cu 2+ to the BDC solution, the uorescence intensity was almost restored to the original uorescence intensity of the free ligand BDC. These results indicated that the reaction between Cu 2+ ions and BDC was a reversible reaction and led to the formation of a complex with a 1 : 1 stoichiometry. The optimization of the geometries of BDC and its 1 : 1 complex with Cu 2+ was performed using the PBE0 functional with the 6-31+G(d) basis set. The calculated results are presented in Fig. 3 and 4 and Tables S1-S7. † Herein, three optimized geometries of BDC were dened and denoted as L, L-1, and L-2. In each of these geometries, most atoms are in the same plane except for the atoms of the ethylamino groups. In the L geometry, the conguration of the two chain bonds C16-C15-C17-N36 and N36-N35-C41-N34 is similar to trans-trans conguration. Moreover, in the L-1  geometry, the conguration of these two chain bonds is similar to cis-trans conguration. In the L-2 geometry, the conguration of these two chain bonds is similar to cis-cis conguration. The calculated results show that L is the most energetically favorable geometry. Consequently, the L geometry was used to dene the conguration of the complex as well as calculate the Gibbs free energy of the ligand-exchange reaction in the aqueous solution.
Moreover, four optimized geometries of the 1 : 1 complexes between L and Cu 2+ ion were dened and denoted as S-1, S-2, S-  Fig. S5, S6 and Tables S10 and S11 in the ESI †). The calculation results presented in Table 1 indicate that S-1 is the most stable conguration with a calculated complexation equilibrium constant of 10 7.16 . Consequently, the S-1 conguration was used for all subsequent studies of the BDC-Cu 2+ complex.
In order to verify the calculated complexation equilibrium constant before studying the applications of the complex, the experimental complexation equilibrium constant was also determined by a nonlinear curve-tting method. The uorescent titration and nonlinear curve-tting results are shown in Fig. 5. Accordingly, the experimental complexation equilibrium constant was determined to be 10 7.15 (M À1 ).
This result is in good agreement with the above calculated complexation equilibrium constant. These results provide further important evidence conrming the correctness of the proposed method for the determination of the complexation equilibrium constants in aqueous solutions using DFT theory and the SMD solvent model.
In terms of application, this value of the complexation equilibrium constant of Cu 2+ ions with BDC is signicantly smaller than that of the Cu 2+ ions with biothiols. For example, the Cu 2+ ions react with Cys to form a [CuX 2 ] 2+ complex with an equilibrium constant of 10 16.57,58 Moreover, the Cu 2+ ions react with Hcy to form a [CuHY] 2+ complex with an equilibrium

Application of the BDC-Cu 2+ complex in the detection of biothiols
The application of the BDC-Cu 2+ complex as a uorescent sensor for the detection of cysteine was investigated. As shown in Fig. 6, when Cys was gradually added to the solution of the BDC-Cu 2+ complex, the uorescence intensity at 536 nm accordingly changed and increased. It almost restored to the original uorescence intensity of free BDC when Cys was added to the solution at a concentration greater than or equal to twice that of the BDC-Cu 2+ complex. These results show that the stoichiometry of the reaction between Cys and the BDC-Cu 2+ complex is 2 : 1, and this reaction leads to the formation of the [CuX 2 ] 2+ complex (X: Cys) and the release of free BDC, resulting in the restoration of uorescence intensity (Fig. 7). This result is also consistent with those reported in previous studies on the composition of the complex of Cys and Cu 2+ ion. 57,58 To use the BDC-Cu 2+ complex as a uorescent sensor for the determination of Cys, the interactions of the BDC-Cu 2+ complex with H 2 S and other amino acids were also investigated. The experimental results in Fig. 8 show that thiol-containing amino acids, such as GSH and Hcy, also cause uorescence recovery. Moreover, H 2 S and non-thiol containing amino acids, such as   alanine (Ala), arginine (Arg), aspartic acid (Asp), glutamic acid (Glu), glycine (Gly), histidine (His), isoleucine (Ile), leucine (Leu), lysine (Lys), methionine (Met), serine (Ser), threonine (Thr), tyrosine (Tyr), tryptophan (Trp) and valine (Val), did not cause any changes in the uorescence spectrum of the BDC-Cu 2+ solution. These results indicate that the BDC-Cu 2+ complex can be used as a uorescent sensor for the detection of thiol-containing amino acids in the presence of H 2 S and nonthiol containing amino acids in the concentration range from 0 to 10 mM (from 0 to 2 equivalent). In addition, the experimental results show that the presence of H 2 S at concentrations greater than 10 mM affects the performance of BDC-Cu 2+ in the detection of biothiols (Fig. S7 †).
Similar to the cases of previous studies reported on uorescent sensors based on complex exchange reactions, 63,64 the BDC-Cu 2+ complex also reacted with thiols, including Cys, Hcy, and GSH, and provided similar results. However, in many actual samples, these thiols do not occur simultaneously. For example, in human whole blood, the concentration of reduced glutathione is signicantly higher (up to 1 mM) than that of the other thiols. Furthermore, in human plasma, the total concentration of Cys species is up to 250 mM, whereas the concentrations of GSH and Hcy are almost negligible. [65][66][67] Therefore, the BDC-Cu 2+ complex can be used as a uorescent sensor for the detection of Cys, HCy, or GSH depending on the actual cases.
The applicability of the BDC-Cu 2+ complex as a uorescent sensor for the quantication of Cys was also investigated. As shown in Fig. 6b, there is a good linear relationship between the uorescence intensity of the BDC-Cu 2+ solution and the concentration of Cys when Cys is added to the BDC-Cu 2+ solution (5 mM). In the Cys concentration range from 0 to 10 mM, the calibration curve equation was determined as follows: F I536 ¼ (3.8 AE 10.4) + (87.1 AE 1.8) Â [Cys], R ¼ 0.996. The limit of detection (LOD) and the limit of quantitation (LOQ) of the method were also evaluated by the linear regression method using a calibration curve with a range of low concentrations of Cys (0-5 mM). 68 The values of these parameters were 0.3 and 1.1 mM, (Fig. S8 †). Moreover, the intracellular concentration of Cys was 30-200 mM. 63 These results indicate that the BDC-Cu 2+ complex can be used as a uorescent sensor for the quantication of intracellular Cys and has greater sensitivity than that of the similar previously reported sensors. 69,70 3.3 Theoretical investigation of the changes in the uorescence properties of the complexes and ligands The uorescence properties of the ligand and complex were investigated based on the electronic excited states using timedependent density-functional theory (TD-DFT) at the PBE0/6-31+G(d) level. The obtained results are presented in Table 2 and Fig. 9.
The results provided in Table 2 indicate that in BDC, the S 0 / S 1 transition plays a key role in all the singlet electronic transitions from ground state (S 0 ) to excited states (S n ). This is due to the fact that the oscillator strength (f) of this transition is 1.2659, substantially larger than those of the other transitions. The S 0 / S 1 transition energy is 2.74 eV (452.9 nm). The calculated result is completely consistent with the empirical investigations, indicating that BDC exhibits a maximum absorption peak at 460 nm. The HOMO / LUMO transition plays a key role in all the orbital transitions from S 0 to S 1 , with a percentage contribution of 98.58%. This transition occurs between two adjacent MOs. Therefore, it can be rmly affirmed that photoinduced electron transfer (PET) does not occur in BDC, and the abovementioned transition leads to a green emission at 536 nm, as observed via empirical investigations. 71,72 The formation of the BDC-Cu 2+ complex leads to a signicant decrease in the energy gap between the ground state and the excited states of BDC. As a result, the energy gap between the excited state and the D 0 state reaches 2.88 eV (430.7 nm) Fig. 9 The characteristics of the main transition between the electron excited states and ground states of BDC and BDC-Cu 2+ at the PBE0/6-31+G(d) level.
This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 36265-36274 | 36271 only when the D 10 excited state is attained. The D 0 / D 10 transition has an oscillator strength of 1.2645, signicantly bigger than that of the other transitions; therefore, this transition plays a key role in all the electronic transitions. The D 0 / D 10 transition is mainly contributed by the SOMO / LUMO and HOMO / LUMO transitions, with the percentage contributions of 39.49% and 41.68%, respectively. These transitions are believed to lead to a strong absorption spectrum, as observed in the experiments. Regarding the uorescence properties of the BDC-Cu 2+ complex, on the basis of Kasha's rule, the uorescence occurs from the lowest-lying electron excited state D 1 , 73,74 in which the D 1 / D 0 transition is mainly contributed by the LUMO / SOMO. However, the lack of overlapping between the LUMO and SOMO makes the radiation transition D 1 / D 0 strongly forbidden. Instead, the internal conversion process occurs from D 1 to D 0 as a radiationless transition. Considering the exceptions of the Kasha rule, from the D 2 state to the D 10 state, the energy gap between adjacent excited states is quite small, less than 0.42. Thus, according to the energy gap law for radiationless transitions, the internal conversion processes from the excited states at higher energy level to the excited state at adjacent low energy levels quickly occur, competing with the uorescent radiation process, which quenches the D n / D 0 uorescence (n > 2). 75,76 Only the energy gap between the D 2 and D 1 states is quite large, 0.52 eV, which should be considered. The D 2 / D 0 transition is mainly contributed by the SOMO / HOMOÀ2 and SOMO / HOMOÀ1 transitions. However, the lack of overlapping between the SOMO and HOMOÀ2 or HOMOÀ1 makes the radiation transition D 2 / D 0 strongly forbidden. As a result, the IC process is also preferred over the uorescent radiation process, which quenches the D 2 / D 0 uorescence. In summary, in the BDC-Cu 2+ complex, since the energy gap between adjacent excited states is small, the transitions from the excited states D n (n > 2) to the excited state D 2 are dominated by the internal conversion processes. Moreover, due to the lack of overlapping between MOs during each transition, the D 1 / D 0 and D 2 / D 0 transitions are dominated by the internal conversion processes. The D 2 and D 1 states are dark doublet states that quench the uorescence. 77

Conclusions
In summary, herein, a complex exchange reaction-based uorescent chemosensor was investigated for the detection of Table 2 The calculated excitation energy (E), wavelength (l), and oscillator strength (f) for BDC and BDC-Cu 2+ at the PBE0/6-31+G(d) level of theory biothiols. This sensor was designed based on the theoretical calculations of the stability constants of the complex between the Cu 2+ ions and uorescent ligands. The obtained results are completely consistent with the experimental results. The BDC-Cu 2+ complex can be used for the detection of biothiols in the presence of non-thiol containing amino acids. The limit of detection and the limit of quantitation of the proposed chemosensor for Cys are 0.3 and 1.1 mM, respectively. This result opens a new research direction toward the utilization of the complexes between metal ions and uorescent ligands for the detection of biothiols based on the theoretical calculations of the stability constants. In this study, the theoretical calculations of the excited states were also used to elucidate the changes in the uorescence properties of compounds. The quenching of the uorescence of the BDC-Cu 2+ complex occurred because the internal conversion processes dominated the uorescence process due to the small energy gap between adjacent excited states, from the excited states D n (n > 2) to the excited state D 2 . Moreover, the D 2 and D 1 states are dark doublet states because of the lack of overlapping between MOs during each transition.

Conflicts of interest
There are no conicts to declare.