Synthesis and characterization of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate: thermodynamic and kinetics investigations by computational and experimental studies

Abstract

Modern society is dependent on synthetic chromene derivatives for use as drugs, including anticancer drugs, and for their biological activities. For this reason, the kinetics and synthesis of these compounds have attracted considerable attention, facilitating further developments and approaches for their synthesis. In this study, dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate (4) was synthesized via the reaction between triphenylphosphine (1), dimethyl acetylenedicarboxylate (2) and 5-bromo-2-hydroxybenzaldehyde acid (3) in the presence of dichloromethane, and it was then characterized using IR, ¹H, ¹³C, and ³¹P NMR. The kinetics and mechanism of the reaction were theoretically and experimentally investigated using the stopped-flow and UV-vis spectrophotometry approaches. The reaction mechanism involved a number of steps, starting with the fast reaction between reactants 1 and 2 to generate I₁, and this step was investigated using stopped-flow apparatus. The consumption of the intermediate 1 (I₁) and 3 was studied using a UV-vis technique and it was found to follow a first-order kinetics. The partial order of compound 3 was determined to be zero and had no effect on the rate of the reaction. The kinetics data showed that step₄ of the proposed mechanism was the rate-determining step. Investigations of the consumption of I₁ at different temperatures allowed the activation parameters to be specified with respect to the slowest step of the proposed mechanism using two linearized forms of the Eyring equation. From the temperature, concentration, and solvent studies, the activation energy (E_a = 61.30 kJ mol⁻¹) and the related activation parameters (ΔG^‡ = 78.42 ± 4.61 kJ mol⁻¹, ΔS^‡ = −67.09 ± 7.96 J mol⁻¹ and ΔH^‡ = 58.88 ± 2.34 kJ mol⁻¹) were calculated. Theoretical investigations were performed for further understanding the proposed mechanism at the B3LYP/6-31++g(d,p) and M06/6-31++g(d,p) levels. The theoretical and experimental data indicated that the rate of the overall reaction was second-order, and depended on the concentrations of compounds 1 and 2. The proposed mechanism was confirmed with the observed kinetics data obtained from the computational and experimental studies.

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1. Introduction

Chromene (benzopyran) is an important structural component in various natural products and also has useful photochemical properties. Benzopyran derivatives can interact with a variety of cellular targets, which gives rise to a wide range of biological activities. Chromene derivatives are also used in the production of highly effective fluorescent dyes.¹ 2H-Chromene, particularly 2,2-dimethylchromene derivatives, which have antihypertensive and anti-ischemic behaviors, are classified under the family of potassium-channel-activating drugs.^2,3 Chromene derivatives have potential utility as anticancer drugs.⁴ Several natural compounds containing chromene segments have been reported to exhibit anticancer activities.^5–9

By determining the rates of the chemical reactions and the factors upon which the rates depend, one can interpret the empirical laws applying to the reaction in terms of the reaction mechanism. Several experimental techniques have been applied in kinetics studies to accomplish these measurements, such as UV-vis and stopped-flow techniques.^10–22

According to the biological characteristics, the variety of applications of chromenes and the importance of a kinetics study on this issue, we herein synthesized and investigated theoretically and experimentally the kinetics and the mechanism of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate 4 formation via the reaction between dimethyl acetylenedicarboxylate 2 and 5-bromo-2-hydroxybenzaldehyde acid 3 in the presence of triphenylphosphine 1 and dichloromethane as the solvent (see Fig. 1). The synthesis of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate 4 has previously been reported in the literature but under different conditions from the present study.²³

Fig. 1 Condensation of acetylenic esters and 5-bromo 2-hydroxybenzaldehyde in the presence of triphenylphosphine.

The main advantage of the present reaction is a different product (Fig. 1, product 4) in comparison with the previous similar reactions.^11,19,24,25 Herein, the product was a chromene derivative, whereas in previous reports the products were ylides. This provides a good opportunity to follow the kinetics and reaction mechanism created for the new product. This present report and discussion covers three parts, namely the synthesis, kinetics and computational studies.

2. Experimental

2.1. Chemicals and apparatus used

Triphenylphosphine (1), dimethyl acetylenedicarboxylate (2) and 5-bromo-2-hydroxybenzaldehyde acid (3) were acquired from Merck (Darmstadt, Germany), Acros (Geel, Belgium) and Fluka (Buchs, Switzerland), and used without further purification. All the extra-pure solvents were also obtained from Merck (Darmstadt, Germany). The product was identified by IR spectra on a Shimadzu IR-460 spectrometer. The ¹H, ¹³C, and ³¹P NMR spectra were obtained using a Bruker DRX-250 AVANCE instrument with CDCl₃ as the solvent at 250.1, 62.9, and 101.25 MHz, respectively. In addition, the mass spectra were recorded on a Shimadzu QP 1100 EX mass spectrometer operating at an ionization potential of 70 eV. A Cary UV-vis spectrophotometer model Bio-300 with a 10 mm light-path quartz spectrophotometer cell and stopped-flow apparatus (model SX-18 MV) with the associated computer system, obtained from Applied Photophysics (Surrey, UK),^26–29 were used for the kinetics and mechanistic investigations throughout the current study. For a total 100 μL sample shot into a flow cell with a 10 mm light path, the fastest time from mixing the solutions and recording the first data point was about 5 ms.

2.2. General procedure for the synthesis

To a magnetically stirred solution of 5-bromo 2-hydroxybenzaldehyde 3 (0.22 g, 1 mmol) and triphenylphosphine 1 (0.26 g, 1 mmol) in a dichloromethane solvent, dimethyl acetylenedicarboxylate 2 (0.12 mL, 1 mmol) was added dropwise at room temperature over 10 min. The reaction mixture was allowed to stir for 24 h at room temperature. The product was filtered and washed with cold diethyl ether (3 × 5 mL). The ¹H and ¹³C NMR spectra of the product clearly indicated the formation of the desired adduct 4. The ¹H NMR spectrum of compound 4 showed two sharp singlets at 3.68 and 3.85 ppm, which were related to the protons of the two methoxy groups. A singlet was observed at 5.80 ppm, which was related to O–CH. Vinyl group proton and aromatic protons appeared between 6.88 and 7.62 ppm. The ¹³C NMR spectrum of compound 4 exhibited 13 signals, which was in agreement with the proposed structure. The IR spectrum of compound 4 showed absorption bands at 1712 and 1740 cm⁻¹ for the carbonyl groups. The ³¹P NMR spectrum showed the absence of phosphorus in the product. The spectral data of the product are presented below.

2.2.1. Dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate. White powder, yield 86%, IR (KBr) (ν_max, cm⁻¹): 1636, 1712 and 1740 (C=O). ¹H NMR (250.1 MHz, CDCl₃): 3.68 and 3.85 (6H, 2S, 2OCH₃), 5.80 (1H, S, O–C–H), 6.88–7.62 (4H, m, C₆H₃, CH=C). ¹³C NMR (62.9 MHz, CDCl₃): 52.35 and 52.74 (2S, 2OCH₃), 71.61 (S, C₂), 114.35 (S, C₆), 118.38 (S, C₈), 121.47 (S, C_4a), 121.90 (S, C₃), 131.35 (S, C₄), 132.38 (S, C₅), 134.97 (S, C₇), 152.80 (S, C_8a), 164.30, and 169. O₈ (2S, C=O). MS (m/z, %): 326 (M⁺, 5), 277 (24), 269 (100), 239 (7), 101 (12), 188 (9), 75 (12).

2.3. Experimental kinetics

To learn more about the mechanism of the reaction between 1, 2 and 3, a kinetics study of the reaction was carried out using UV-vis spectrophotometry. The UV-vis spectrum was measured over the concentration range of (10⁻³ M ≤ M product ≤ 10⁻² M) to confirm a linear relationship between the absorbance and concentration values.

It was necessary to find the appropriate wavelength in order to follow the kinetics of the reaction. For this purpose, a 0.3 mL aliquots of a 3 × 10⁻² M solution of reactants 1 and 3 were pipetted into a quartz spectrophotometer cell, then a 0.3 mL aliquot of a 3 × 10⁻² M solution of reactant 2 was added to the mixture according to the stoichiometry of each reactant in the overall reaction. The reaction was monitored by recording the scans of the entire spectra with 2 min intervals during the entire reaction time at 18 °C (Fig. 2A). The downward direction of the arrow in this figure indicates the reaction progress. The recorded relevant spectrum of each compound 1, 2 and 3 had no interference with UV-vis spectra showing the reaction progress (400–460 nm).

Fig. 2 (A) The UV-vis spectra for the reaction between 1 (10⁻² M), 2 (10⁻² M), and 3 (10⁻² M); the downward direction of the arrow indicates the reaction progress. (B) The original experimental absorbance change (dotted curve) along with the first-order fitted curve (solid curve) against time at 420 nm and 18.0 °C in dichloromethane.

In order to select the appropriate wavelength with respect to the spectrum showing the progress of the overall reaction (a mixture of 1, 2 and 3, Fig. 2A), we considered only changes in absorbance to be wavelength of importance that substance must only have significant absorption at the selected wavelength compared to the other materials of reaction. According to the spectrum of the overall reaction in the range 380–440 nm (see Fig. 2A), it can be seen that adequate changes in this range and none of the materials (reactants 1, 2, 3) had a considerable absorbance. Therefore, the chosen wavelength range of 380–440 nm for the kinetics investigations was considered appropriate. On the other hand, a decrease in the spectra in the 380–440 nm wavelength range can be seen over time. Hence, in this wavelength range, we observe a decrease in the concentration of intermediate 1; albeit, this intermediate is produced during a fast step.

To determine whether the two reactants react mutually with each other or not as step₁ in the reaction mechanism, a series of two compound reactions between 1 and 2, 1 and 3, and also 2 and 3 was considered. At first, a 0.5 mL aliquot of a 2 × 10⁻² M solution of 1 and 2, to generate intermediate 1 (I₁), in dichloromethane as the solvent was pipetted into a quartz spectrophotometer cell and the mixture was monitored by recording the scan of the entire spectra. It was found that the two species react with each other, with this mixture leading to I₁. In the same way, a binary mixture of 1 and 3, and also a binary mixture of 2 and 3, were examined and it became apparent that these two binary mixtures do not react. As a result, in the reaction mechanism between 1, 2 and 3, we can say that step₁ starts with 1 and 2 reacting to generate I₁.

On investigating the spectra of the binary mixtures, it was found that only 1 and 2 reacted with each other to produce intermediate I₁, and this intermediate had the wavelength range 380–440 nm. Hence, the appropriate wavelengths were discovered to be 430, 420 and 410 nm, corresponding mainly to I₁. This allowed us the opportunity to find the practical conditions that would allow a kinetics and a mechanistic investigation of the reaction. Herein, in all the experiments, the UV-vis spectrum of the product was measured over the concentration range (10⁻³ M ≤ M product ≤ 10⁻² M) to confirm if there was a linear relationship between the absorbance and concentration values. Further experiments for detecting intermediate I₁ followed and are described in the section below.

2.3.1. Stopped-flow method. Since the production of I₁ was fast, we investigated this step₁ using the stopped-flow method. In a typical single-mixing experiment, one syringe containing 3 × 10⁻² M of 1 was mixed with 3 × 10⁻³ M of 3 (since there is no reaction between them), whereas the other syringe contained 3 × 10⁻² M of 2 in the organic solvent. For each run, equal volumes of both solutions were mixed in the mixing chamber and the changes in the absorbance were monitored at 420 nm for a chosen period of time. The rate constants are presented herein as an average of several kinetic runs (at least 6–10) and were reproducible within a ±3% margin (see Table 1).

Table 1 Kinetics data of the reaction for step₁ in dichloromethane and 1,4-dioxane as the solvents at 291.15 K

Solvent	Dichloromethane (8.93^a)	1,4-Dioxane (2.25^a)
a Dielectric constant (D).
k1 (mol^−1 s^−1)	1.1 × 10^2	1.4 × 10
Completion time (s)	20	250

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In the stopped-flow instrument, the temperature of the reaction was maintained to within ±0.1 °C at various temperatures using a circulating water bath.

Fig. 3A and B display a typical kinetic trace at 420 nm generated from a number of spectra. As can be seen, upon mixing the reagents, an increase in the absorbance peak appears at 420 nm, which then decreases slowly in intensity. Each reactant alone (1, 2 or 3) has no absorbance peak at 420 nm. Therefore, the time-resolved spectra in Fig. 3A and B provide clear evidence for the formation and decay of the intermediate (I₁), the spectra of which are characterized by an absorbance at 420 nm. At first glance, according to the graph recorded using the stopped-flow apparatus, the speed of reaction between 1 and 2 for the creation of intermediate I₁ was much faster (k₁, part P₁, Fig. 3A and B) than the speed of the reaction involving the consumption of intermediate 1 and 3 (part P₂, Fig. 3A). The intermediate was produced in much less time (20 s), but decayed over a longer time (over 500 s). It could be concluded that the rate-determining step for the overall reaction depends on the consumption of the intermediate in part P₂ (longer time, part P₂, Fig. 3A). Fig. 3B presents a second-order fitted curve for the expanded part P₁ (step₁, k₁, reaction between 1 and 2), which exactly fits the original experimental curve at 420 nm and 18 °C. Under pseudo-order conditions, the rate of the reaction was found to be first-order with respect to 1 or 2.

Fig. 3 Analyzed kinetic traces for the reaction between 1, 2, and 3: (A) the stopped-flow spectra at 420 and 18 °C in dichloromethane involving parts P₁ (1 + 2 reaction) and P₂ (I₁ + 3 reaction); (B) second-order fitted curve for the expanded part (P₁, step₁, k₁), which exactly fits the original experimental curve at 420 nm and 18 °C in dichloromethane using the stopped-flow technique; as can be seen, the reaction time for generating the intermediate (I₁, part P₁) is very short (about 20 s).

Step₁, which is associated with an increase in absorbance, was analyzed on a short timescale at 420 nm. It may be noted here that the single exponential analysis of this step (growth) resulted in almost identical rate constant values; however, it is a safer practice to analyze such kinetic traces (Fig. 3A and B) using a double exponential function in order to obtain the rate constant for the first reaction step more accurately.

The effect of solvent on the fast step (k₁), with dichloromethane (8.93 D) or 1,4-dioxane as another solvent (2.25 D), showed that the rate of step₁ (k₁) speeds up in dichloromethane solvent with a high dielectric constant (see Table 1).

2.3.2. UV-vis method. The reaction between compounds 1 and 2 leads to I₁, which the stopped-flow spectrophotometry recognizes with a completion time of about 20 s. This time is too short to be detected using the UV-vis technique, but the subsequent step (decay, longer time, P₂), which is slower than the first step and is relevant to the reaction between I₁ and 3, was investigated using the UV-vis method (Fig. 3A, P₂).

With a 10⁻² M concentration of each reactant (1, 2 and 3), experimental absorbance curves were recorded versus time at 18 °C and at wavelengths of 430, 420 and 410 nm, as shown in Fig. 2B. The original experimental absorbance curve (dotted curve) of the consumption of intermediate 1 using the UV-vis spectrophotometry method exactly fits the first-order curve (solid curve). It is evident that the order of consumption of intermediate 1 and reactant 3 is one. Therefore, the rate law can be written as follows:

Rate = k_obs[I₁]^z[3]^γ

therefore: z + γ = 1.

2.3.3. Effects of concentration. With the purpose of finding the partial order of I₁ and reactant 3 under pseudo-order conditions, experiment A was designed. In experiment A, 10⁻³ M of reactant 1, 10⁻³ M of reactant 2 and 10⁻² M of reactant 3 were used. The rate law for experiment A can be written as follows:

Rate = k_obs[I₁]^z (1)

k_obs = k_ove[3]^γ (2)

In experiment A, plots of the original experimental absorbance curves versus times provided a pseudo-first order. The experimental absorbance curve versus times, along with a first-order fit for this experiment, was recorded at 420 nm and 18.0 °C. Then, the rate constants of the reactions were automatically obtained using a software program.³⁰ Herein, according to eqn (1), the partial order with respect to intermediate 1 is 1 (z = 1).

As a result of the previous experiments:

z = 1 on the basis of experiment A. Therefore, the partial order of compound 3 can be determined as zero (γ = 0) and the experimental rate law can be expressed as follows:

Rate = k_ovr[I₁][3]⁰ (3)

Rate = k_obs[I₁][3]⁰ (4)

k_obs = k_ovr (5)

2.3.4. Effect of solvent and temperature. In order to determine the effect of temperature and the solvent environment on the overall reaction rate, previous experiments were repeated under different temperatures and solvents. For this purpose, 1,4-dioxane (2.25 D) was used as another solvent in the experiment. The results showed that the rate of the overall reaction speeds were higher in the 1,4-dioxane solvent with a low dielectric constant compared to the higher dielectric constant of dichloromethane (8.93 D) at all the investigated temperatures; nevertheless, this was reverse for the fast step (k₁, see Table 1). The obtained rate constants for the overall reaction are listed in Table 2 for different temperatures and solvents.

Table 2 k_obs (min⁻¹) for the reaction between 1 (10⁻² M), 2 (10⁻² M) and 3 (10⁻² M) in different solvent media and at different temperatures

a Dielectric constant (D).b Standard deviation (SD).
Solvent: dichloromethane (8.93)^a
T	T = 286.15 K	T = 291.15 K	T = 296.15 K	T = 301.15 K
kobs	0.0312 (0.0007)^b	0.0536 (0.0008)	0.0887 (0.0013)	0.1103 (0.0009)
Solvent: 1,4-dioxane (2.25)^a
T	T = 286.15 K	T = 291.15 K	T = 296.15 K	T = 301.15 K
kobs	0.0712	0.1016	0.1736	0.2104

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As can be seen in Table 2, the rate of reaction increases in both solvents at higher temperatures. Moreover, decreasing rate constants when using high dielectric solvents indicate that at the rate-determining step, the activated complex must have a lower charge than the reactant; therefore, the solvent stabilizes the reactants more than the activated complex does. In other words, the reactants are solvated to a greater extent in comparison to the activated complex, and this reduces the rate and increases the activation energy in high dielectric solvents (see Tables 2 and 3). In the studied temperature range, the first-order rate constant (ln k_obs) of the consumption process of I₁ was inversely proportional to the temperature, which is in agreement with the Arrhenius equation. This behavior is shown in Fig. 4. The activation energy for the reaction between 1, 2 and 3 in dichloromethane was calculated (E_a = 61.61 kJ mol⁻¹) from the slope of Fig. 4.

Table 3 Activation parameters for the reaction between compounds 1, 2 and 3 measured in different solvent media

Solvent	ΔH^‡ (kJ mol^−1)	ΔS^‡ (J mol^−1)	TΔS^‡ (kJ mol^−1)	ΔG^‡ (kJ mol^−1)	A (M^−1 min^−1)	Ea (kJ mol^−1)
a Dielectric constant (D).b According to eqn (7).c According to eqn (6).d According to this equation: Ea = ΔH^‡ + RT.e In accord with the Arrhenius equation.
Dichloromethane (8.93)^a	58.88 ± 2.34^b	−67.09 ± 7.96^b	−19.53^b	78.42 ± 4.61^b	5.85 × 10^9^d	61.30^d	61.61^e
	59.16 ± 2.38^c	−66.12 ± 8.11^c	−19.25^c	78.42 ± 4.75^c
1,4-Dioxane (2.25)^a	51.72 ± 2.03^b	−85.70 ± 6.90^b	−24.95^b	76.68 ± 4.03^b	5.86 × 10^8^d	54.14^d	54.30^e
	51.86 ± 2.037^c	−85.24 ± 7.04^c	−24.82^c	76.68 ± 4.12^c

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Fig. 4 Dependence of the observed rate constant (ln k_obs) on the reciprocal of the temperature for the reaction between compounds 1, 2, and 3 in dichloromethane at a wavelength of 420 nm.

The activation parameters, namely ΔG^‡, ΔS^‡ and ΔH^‡, can now be calculated on the basis of the Eyring equation (Fig. 5A, eqn (6)). Fig. 5B shows a different linearized form of the Eyring equation (eqn (7)). The standard errors for the activation parameters were calculated and are reported along with these parameters for both the forms of the Eyring equation used for Fig. 5A and B.³¹

Fig. 5 Eyring plots for the reaction between 1, 2 and 3 in dichloromethane at a wavelength of 420 nm: (A) according to eqn (6) and (B) according to eqn (7).

The values of the calculated activation parameters (ΔS^‡, ΔH^‡ and ΔG^‡) are listed in Table 3 for the reactions between 1, 2, and 3 in dichloromethane and 1,4-dioxane at 291.15 K, using eqn (7).

Overall, the activation enthalpy (ΔH^‡) and the activation Gibbs free energy (ΔG^‡) are positive, which suggests that the energy required for the reaction is relatively high, and therefore the reaction is chemically controlled. However, the negative value of the activation entropy (ΔS^‡) shows that energy must be partitioned into a lesser state at the transition state (TS). Therefore, the transition state in the region of the activated complex has a more ordered or more rigid structure, which indicates an associative mechanism. The reaction is enthalpy controlled because the activation enthalpy (ΔH^‡) is much greater than the TΔS^‡.

From the observations of the detailed data, the activation enthalpy is found to be higher in solvents that have a high dielectric constant (e.g., dichloromethane) compared to a lower dielectric constant (e.g., 1,4-dioxane) at the same temperature. This gives rise to higher activation energies for the reaction in solvents with a high dielectric constant (E_a = 61.30) because E_a is directly proportional to the activation enthalpy (E_a = ΔH^‡ + RT).

The data obtained from the experiments with the UV spectrophotometry method were not sufficient to obtain the rate-determining step. For this reason, theoretical investigations were employed, and are described in the section below, for obtaining more information regarding the reaction mechanism.

3. Theoretical investigations

3.1. Computational methods

All the electronic structure calculations were carried out by the GAMESS (2014-R1 version).³² Full geometry optimizations were performed for the reactants, products and saddle points at the M06 and B3LYP levels of theory using the standard 6-31++G(d,p) basis set. Harmonic vibrational frequency calculations were performed at the same levels of theory in order to determine the nature of the various stationary points, as well as zero-point-energy (ZPE) corrections applied. The activation energies (E_a), the Arrhenius factors, and the rate constants were computed using eqn (8)–(10), respectively.

E_a = ΔH^‡(T) + nRT (8)

A = (ek_BT/h)exp(ΔS^‡(T)/R) (9)

k = (k_BT/h)exp(−Δn + 1) × exp(−ΔH^‡/RT) × exp(ΔS^‡/R) (10)

The plausible mechanism is exhibited schematically in Fig. 6 in accordance with the reports in the literature^24,33–37 and from the experimental data from both the UV-vis and stopped-flow techniques. In the first step (k₁), the nucleophilic addition of triphenylphosphine 1 to acetylenic ester 2 as a Michael acceptor occurs, which generates the carbene–ylide intermediate (I₁).^38,39 Then, in step₂, I₁ is protonated by the OH-acid. In the next step (k₃), the positively charged ion (I₂) is attacked by the conjugate base of the OH-acid to create phosphorane (I₃). Finally, through an intramolecular Wittig reaction step₄ (k₄) and a subsequent elimination of triphenylphosphine oxide in step₅ (k₅), the desired product was obtained. The solvent effect indicates that the reaction rate decreases in solvents with a high dielectric constant, this becomes possible when the dipolar compound (I₃, an ionic compound) is stabilized much more than the activated complex in step₄ (k₄). Therefore, step₄ has a good potential for being the rate-determining step on the basis of the obtained results from the solvent study on the reaction environment. This needs more information to verify and this was provided by the computational methods, which are discussed in the section below.

Fig. 6 Proposed mechanism for the formation of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate from the reaction between compounds 1, 2 and 3.

3.2. Theoretical results and discussion

The vibrational frequencies calculated at the M06 and B3LYP levels of theory using the standard 6-31++G(d,p) basis set are listed in Table 4, and verify the nature of the critical points. The activation parameters (ΔH^‡, ΔG^‡, and ΔS^‡) and the reaction parameters (Δ_rH°, Δ_rG° and Δ_rS°) for each step of the proposed mechanism at 298.15 K are reported in Tables 5 and 6, respectively. Table 7 gives the rate constants (k) and activation energies (E_a) for all the steps. The calculated reaction parameters of the overall reaction obtained from the individual steps, involving (Δ_rH_total, Δ_rG_total, and Δ_rS_total) at 298.15 K, are reported in Table 8.

Table 4 The first stretching frequency for each step for the 6-31G (d,p) basis set at 298.15 K

Species	First stretching frequency (cm^−1) at B3LYP	First stretching frequency (cm^−1) at M06
Ground state of the reactants (1 and 2) of step1	8.68	9.54
TS1	−107.19	−134.97
Ground state of I1 of step1	10.11	14.87
Ground state of 3 and I1 of step2	1.32	12.63
TS2	−661.05	−558.27
Ground state of the products (I2 and B^−) of step2	6.77	13.58
Ground state of the reactants (I2 and B^−) of step3	7.09	13.58
TS3	***	***
Ground state of the product (I3) of step3	10.12	22.31
Ground state of the reactant (I3) of step4	11.70	22.31
TS4	−239.05	−177.98
Ground state of the product (I4) of step4	23.60	35.17
Ground state of the reactant (I5) for step5	23.60	35.17
TS5	−349.79	−421.27
Ground state of the final product of step5	10.75	17.51

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Table 5 The activation parameters involving ΔH^‡, ΔG^‡, and ΔS^‡ for each step for the 6-31G (d,p) basis set at 298.15 K, the energy values are in kJ mol⁻¹

	B3LYP	M06		B3LYP	M06		B3LYP	M06
ΔH^‡1	44.68	34.23	ΔG^‡1	69.01	37.66	ΔS^‡1	−0.0815	−0.0113
ΔH^‡−1	17.56	28.07	ΔG^‡−1	16.05	29.83	ΔS^‡−1	0.0050	−0.0059
ΔH^‡2	15.88	11.42	ΔG^‡2	−3.05	−6.69	ΔS^‡2	0.0635	0.0611
ΔH^‡−2	36.87	40.12	ΔG^‡−2	28.30	48.99	ΔS^‡−2	0.0288	−0.0297
ΔH^‡3	0.00	0.00	ΔG^‡3	0.04	0.00	ΔS^‡3	21.1140	0.0000
ΔH^‡−3	58.94	71.84	ΔG^‡−3	60.69	68.07	ΔS^‡−3	−0.0059	0.0126
ΔH^‡4	123.02	81.30	ΔG^‡4	144.42	92.84	ΔS^‡4	−0.0719	−0.0385
ΔH^‡−4	36.24	37.03	ΔG^‡−4	36.03	35.86	ΔS^‡−4	0.0004	0.0038
ΔH^‡5	16.34	38.37	ΔG^‡5	17.10	34.31	ΔS^‡5	−0.0025	0.0138
ΔH^‡−5	261.38	226.94	ΔG^‡−5	287.46	236.90	ΔS^‡−5	−0.0874	−0.0326

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Table 6 The reaction parameters involving Δ_rH° (298.15 K), Δ_rG° (298.15 K) and Δ_rS° (298.15 K) for each of the steps at 298.15 K; the energy values are in kJ mol⁻¹

	B3LYP	M06		B3LYP	M06		B3LYP	M06
	27.09	6.15		52.92	7.87		−0.0865	−0.0059
	−20.98	−27.45		−31.35	−55.73		0.0347	0.0908
	−58.94	−71.88		−60.78	−68.16		0.0063	−0.0126
	86.82	44.27		108.39	56.99		−0.0723	−0.0423
	−245.03	−188.53		−270.36	−202.59		0.0849	0.0469

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Table 7 Rate constants (k) and activation energies for all the steps^a

	Pre-exponential factor (frequency factor)		Ea forward (kJ mol^−1)		Ea reverse (kJ mol^−1)		Rate constant
	B3LYP	M06	B3LYP	M06	B3LYP	M06	B3LYP	M06
a F = forward step B = backward step, a = M^−1 s^−1 and b = s^−1.
Step1	3.37 × 10^8	1.56 × 10^12	47.15	36.74	20.02	30.59	4.93^a	1.56 × 10^6a
Step2	3.56 × 10^16	2.57 × 10^16	18.35	13.89	39.33	42.59	5.81 × 10^13a	2.55 × 10^14a
Step3	6.37 × 10^12F	6.21 × 10^12F	0.00	0.00	61.40	74.31	6.38 × 10^12F,a	6.21 × 10^12F,a
	2.24 × 10^13B	2.05 × 10^14B					1.03 × 10^3B,b	5.28 × 10^1B,b
Step4	2.99 × 10^9	1.61 × 10^11	125.48	83.76	38.67	39.50	7.99 × 10^−13b	9.17 × 10^−4b
Step5	3.39 × 10^13	2.39 × 10^14	18.81	40.88	263.84	229.41	4.63 × 10^10b	4.46 × 10^7b

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Table 8 The reaction parameters involving Δ_rH_total (298.15 K), Δ_rG_total (298.15 K) and Δ_rS_total (298.15 K) of the mechanism at 298.15 K; the energy values are in kJ mol⁻¹

	ΔrHtotal (298.15 K)	ΔrGtotal (298.15 K)	ΔrStotal (298.15 K)
B3LYP	−211.01	−201.14	−0.0330
M06	−238.68	−261.63	0.0770

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In order to facilitate the understanding of the changes in the energy values of the compounds during the reaction mechanism, an energy diagram for the reaction mechanism at the B3LYP/6-31++G(d,p) level for the formation of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate is shown in Fig. 7. As can be seen, the thermodynamic stability of the reaction products is remarkable.

Fig. 7 Energy diagram of the reaction mechanism at the B3LYP/6-31++G(d,p) level for the formation of dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate from the reaction between compounds 1, 2 and 3 in the gas phase at 298.15 K.

The information listed in Table 5 shows that step₄ of the reaction for achieving the activated complex suffers higher energy changes. Furthermore, Table 6 clarifies that step₄ has the most unfavorable changes in the reaction parameters for producing I₄. All of these issues prove that the slowest step of the reaction mechanism is step₄.

Both total enthalpy changes (Δ_rH_total) and the Gibbs free energy changes (Δ_rG_total) for the overall reaction mechanism are negative and have remarkably large values in both levels of theory, which implies that the reaction is exothermic and spontaneous, which makes the reaction thermodynamically favorable. The Δ_rS_total is negative, which shows that the entropy of the reaction decreases.

As step₄ is the slowest step, it is discussed in detail below. The optimized structure of the transition states for step₄ of the reaction mechanism at the B3LYP/6-31++G(d,p) level is shown in Fig. 8. The energies of the participating species in step₄ are listed in Table 9.

Fig. 8 Optimized structure of the transition states for step₄ of the reaction mechanism at the B3LYP/6-31++G(d,p) level.

Table 9 Energies of the participating species in step₄ of the proposed mechanism

	B3LYP/6-31G(d,p) (a.u.)	M06/6-31G(d,p) (a.u.)
Reactant of step4 (I3)	−4561.45212210	−4560.17017230
TS4	−4561.40338552	−4560.13882789
Product of step4 (I4)	−4561.41973967	−4560.15512122

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In this step, the Wittig reaction conditions are available and by the nucleophilic, intramolecular additions of a carbanion C₂ to the carbonyl carbon C₁, a four-membered ring structure (between C₁, C₂, O₇ and P₈ atoms) containing phosphorus and oxygen (oxaphosphacyclobutane) was generated. At the stationary point at the B3LYP level, the C₁–C₂, C₁–C₆ and O₇–P₈ bond lengths, C₆–C₁–C₂, P₈–C₂–C₁ and C₂–P₈–O₇ angles, and C₉–C₂–C₃–C₁₂ and P₈–C₂–C₉–O₁₀ dihedral angles were 4.841, 1.480 and 6.589 Å, and 75.9°, 106.2° and 62.1°, and 45.1° and 7.2°, respectively (see Table 10). The calculated vibrational frequencies at the B3LYP and M06 levels showed that the stationary point was a true minimum and showed one imaginary frequency at −239.05 cm⁻¹ and one at −177.98 cm⁻¹, respectively, which implies that TS₄ was a transition state (see Table 4). At the transition state TS₄ at the B3LYP level, the C₁–C₂, C₁–C₆ and O₇–P₈ bond lengths, C₆–C₁–C₂, P₈–C₂–C₁ and C₂–P₈–O₇ angles, and C₉–C₂–C₃–C₁₂ and P₈–C₂–C₉–O₁₀ dihedral angles were 1.850, 1.519 and 2.900 Å, and 105.2°, 102.3° and 61.1°, and 15.4° and −2.2°, respectively. The activation energies of TS₄ (step₄) at the B3LYP and M06 levels were 125.48 and 83.76 kJ mol⁻¹, respectively (see Table 7 and Fig. 9). This process is endothermic ( = 86.82 kJ mol⁻¹ at the B3LYP and = 44.27 kJ mol⁻¹ at M06, see Table 6), indicating that it is an energetically unfavorable process. At the B3LYP level, the conditions for crossing the transition state are more difficult than at the M06 level, and it appears that TS₄ with a four-membered ring structure is under a higher angular strain with longer bond lengths involved in this step.

Table 10 Some of the bond lengths, bond angles, and dihedral angles in step₄ of the proposed mechanism at the two levels (the numbering of atoms is similar to that in Fig. 7)

Step4	Geometrical parameters	Reactant (I3)		TS4		Product (I4)
		B3LYP	M06	B3LYP	M06	B3LYP	M06
Bond length (Å)	C1–C2	4.841	4.731	1.850	1.857	1.560	1.547
	C1–C6	1.480	1.473	1.519	1.508	1.512	1.503
	C1–O7	1.223	1.216	1.292	1.277	1.406	1.393
	C2–P8	1.746	1.740	1.883	1.847	1.950	1.948
	O7–P8	6.589	5.828	2.900	2.900	1.817	1.849
Angle (deg)	C6–C1–C2	75.9	75.2	105.2	103.5	113.2	111.8
	C5–O4–C3	121.6	119.4	116.4	115.0	115.9	114.8
	P8–C2–C1	106.2	87.5	102.4	102.5	87.0	87.1
	C2–P8–O7	62.1	80.7	61.1	61.1	72.8	71.9
Dihedral angle (deg)	C9–C2–C3–C12	45.1	37.7	15.4	17.2	20.5	17.5
	P8–C2–C9–O10	7.2	12.0	−2.2	−6.6	−1.8	−0.9

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Fig. 9 Potential energy profile for step₄ of the proposed mechanism at the B3LYP/6-31++g(d,p) and M06/6-31++g(d,p) levels.

The data from the two computational methods for M06 and B3LYP indicate that, at both the employed levels, the sequence of the rate constants and activation energy has not changed. For as much as the M06 method considers dispersion interactions, this method is also suitable for the kinetics studies of compounds containing main group elements and noncovalent interactions between aromatic rings (pi stacking).^40,41 A very recent report concluded that M06 calculations provide better geometries than B3LYP.⁴² Hence, the results of this method should be suitable and superior. The existence of aromatic rings and pi stacking interactions can be considered as the reason for the difference between the obtained values of activation parameters and the activation energy at the B3LYP and M06 levels.

4. Proposed mechanism

The rate law equation can be established using the final reaction step (the scheme of the proposed reaction mechanism is shown in Fig. 5):

Rate = k₅[I₄] (11)

because: k₅[I₄] = k₄[I₃], then eqn (11) is converted to eqn (12).

Rate = k₄[I₃] (12)

so, , then .

Therefore:

Clearly, the steady state approximation can be applied to obtain the concentration of all the intermediates. Only in deriving the concentration of I₂, we make the following assumption:

The concentration of I₂ with respect to the steady-state approximation is:

In the third step, we have ionic species and the kinetics of the ionic species phenomena are very fast.^43–45 Therefore, the reverse reaction of step₃ definitely has a greater energy barrier than the forward reaction. Therefore, we considered that the value of the third term is insignificant (since, k₃ = 6.38 × 10¹² is extremely higher than k₋₃ = 1.03 × 10³, see Table 7), and it is reasonable to have

Consequently, by substituting the value of the intermediate I₂, the general rate law becomes

because: k₁[1][2] = k₂[I₁][3]

Eqn (17) is the general rate law for the reaction. The rate law indicates that this is a second-order reaction, whereby in addition, it depends on the concentrations of compounds 1 and 2. As can be seen, steps 2, 3 and 5 have no chance to be the rate-determining step, since eqn (17) is independent of the k₂, k₃ and k₅ rate constants (see Table 7). Clearly, k₄, k₁ and k₋₃ in the general equation are manifestations of the participating steps 1 and 4 and the reverse of step₃ in the rate of reaction. The information obtained from Table 7 clearly states that steps 4, 1, and −3 are allocated the smallest value of rate constants, respectively. Hence, these steps play an important role in determining the speed of the reaction rather than the others. These results are consistent with the data in Tables 5 and 6.

According to the results of the theoretical investigation (see Table 7), the obtained value of the k₄ is smallest. So k₋₃ ≫ k₄ or k₋₃ = 1.03 × 10³ ≫ k₄ = 7.99 × 10⁻¹³.

herein, the transition state (step₄, Fig. 6) carries less charge in the reaction, and hence solvents with a higher dielectric constant (see the solvent study, in the Experimental section) slow the reaction rate down by stabilizing the species in the ground state (with the full charges) more than at the transition state (with the partial charges), therefore E_a would be higher (Tables 2–4).

5. Conclusion

Dimethyl 6-bromo-2H-chromene-2,3-dicarboxylate was synthesized and characterized as a possible biological compound using IR, ¹H, ¹³C, and ³¹P NMR. Kinetics investigations of the recent reaction were experimentally carried out using UV-vis spectrophotometry and stopped-flow apparatus. Moreover, the kinetics and mechanism of the reaction were theoretically investigated at the B3LYP/6-31++(d,p) and M06/6-31++(d,p) levels of theory. The following results could be rationalized from the studies:

(a) The reaction mechanism starts with a fast reaction between reactants 1 and 2. This step was recognized using the stopped-flow technique. The obtained result showed that the order of reaction with respect to each reactant (1 or 2) was one. Herein, the rate of step₁ (k₁) as a fast step speeds up in the presence of solvents with a higher dielectric constant (e.g., dichloromethane).

(b) The consumption of I₁ and 3 was studied using UV-vis and it was seen that it followed a first-order kinetics. The partial order of compound 3 was determined to be zero and its concentration had no effect on the rate of the reaction.

(c) The rate of the overall reaction decreases in solvents with a higher dielectric constant, and hence at the rate-determining step, the activated complex must have less charge than the reactant; therefore, the solvent stabilizes the reactants more than the activated complex (step₄, Fig. 6). The effect of the solvents on the overall reaction was contrary to the first step (fast step).

(d) The kinetics data experimentally and theoretically showed that step₄ of the proposed mechanism was the rate-determining step.

(e) Investigations of the consumption of I₁ at different temperatures allowed determination of the activation parameters with respect to the slow step of the proposed mechanism. From the temperature, concentration, and solvent studies, the activation energy (E_a = 61.30 kJ mol⁻¹) and the related activation parameters (ΔG^‡ = 78.42 ± 4.61 kJ mol⁻¹, ΔS^‡ = −67.09 ± 7.96 J mol⁻¹, and ΔH^‡ = 58.88 ± 2.34 kJ mol⁻¹) were calculated.

(f) The reaction was enthalpy controlled because the activation enthalpy (ΔH^‡) was much greater than TΔS^‡.

(g) The high positive values of activation Gibbs free energy (ΔG^‡) suggest that the reaction was chemically controlled.

(h) High negative values of the activation entropy suggested that the activated complex has a more ordered or more rigid structure, which indicates an associative mechanism.

(i) Theoretical investigations for further understanding the proposed mechanism at the B3LYP/6-31++g(d,p) and M06/6-31++g(d,p) levels were performed. Calculations revealed that step₄ was the rate-determining step and was an endothermic process ( = 86.82 kJ mol⁻¹ at B3LYP and = 44.27 kJ mol⁻¹ at M06), indicating that it is energetically unfavorable. The overall reaction was thermodynamically favorable, spontaneous, and had remarkably large negative thermochemistry values (Δ_rH_total and Δ_rG_total) in both levels of theory.

(j) The obtained general rate law from the proposed mechanism indicated that the overall reaction was a second-order reaction, and it depended on the concentration of compounds 1 and 2. Furthermore, the derived rate law was compatible with the observed kinetics data obtained from the experimental studies.

Acknowledgements

This study was supported financially by the Sistan and Baluchestan University.

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