Substituent Effect on the Nucleophilic Aromatic Substitution of Thiophenes With Pyrrolidine: Theoretical Mechanistic and Reactivity Study

ABSTRACT

Aromatic nucleophilic substitution (S_NAr) is a widely employed synthetic method for modifying thiophene derivatives. Herein, we computationally investigate the reaction mechanism of 2‐methoxy‐3‐X‐5‐nitrothiophenes with pyrrolidine (where X = NO₂, CN, SO₂CH₃, COCH₃, CO₂CH₃, CONH₂ or H). This S_NAr reaction follows a stepwise pathway: initially, pyrrolidine adds to the C2 position of the 2‐methoxy thiophene partner. Then, the release of methanol is triggered by a proton transfer from the newly formed ammonium intermediate to the methoxy group. With excess pyrrolidine, this proton transfer is catalyzed by an additional pyrrolidine molecule. We establish linear correlations between the experimental electrophilicity and the Gibbs free energy barrier, Parr electrophilicity (ω), and molecular softness (S). Local reactivity descriptors for the C2 position are generally non‐informative, except for the population of the C—O bond basin, the C2 population of the ELF_LUMO function, and the condensed electrophilicity index ω⁺(C2). This theoretical approach provides a robust method to further predict electrophilicity parameters in versatile thiophene derivatives chemistry.

Using DFT calculations, we investigated the SNAr mechanism of seven 2‐methoxy‐3‐X‐5‐nitrothiophenes with pyrrolidine. The reaction follows a stepwise pathway, where pyrrolidine facilitates methanol departure. Electrophilicity correlates with Gibbs energy barriers, Parr indices, and ELF descriptors, aiding predictions for thiophene derivatives' reactivity.

1. Introduction

Thiophenes are a versatile class of compounds with broad applications in the synthesis of antimicrobial and anticancer drugs [1, 2], for solar cells [3], and diverse organic electronic materials [4]. To achieve the desired level of substitution on thiophenes, simple aromatic nucleophilic substitution (S_NAr) is a method of choice. S_NAr reactions on thiophene rings are documented since the 1950's [5]. The S_NAr mechanism is generally assumed to proceed through a first step, leading to the formation of a σ complex (called Meisenheimer adduct) when the aromatic molecule contains electron withdrawing groups. This is followed by a second step consisting in the elimination of the leaving group [6]. The rate limiting step is assumed to be the first step, but influential substituent effects may affect the reaction course, and significantly modify the kinetic constants of distinctive elementary chemical events. In addition, the leaving group elimination step may require some base catalysis to effectively end up the S_NAr.

Since the introduction of the terms “electrophile” and “nucleophile” by Ingold in 1934 [7], considerable efforts have been devoted to quantify these fundamental concepts using empirical parameters. In 1953, Swain and Scott [8] developed an equation to correlate rate constants with a nucleophilicity parameter. This equation was later generalized by Ritchie with parameters independent of the two reacting species [9]. Mayr and Patz [10] provided a more general equation (Equation 1) based on the analysis of about 300 reactions.

$$\log k\left({20}^{°}C\right)=s_N\left(E+N\right)$$ (1)

In this equation E and N are the electrophilicity and the nucleophilicity indexes, respectively, and s_N is a parameter depending on the specific nucleophile (slope parameter). Concerning the kinetics of the aromatic nucleophilic substitution (S_NAr) reactions involving thiophene derivatives and amines (Scheme 1), the effect of substituents on the coupling partners has been intensively studied since the 1960's, from the pioneering work of the Spinelli group [5, 11]. A good correlation of the experimental results with Hammett's equation was in general achieved [5, 12, 13].

SCHEME 1.

Main reaction pathways studied by Smaoui et al. for the S_NAr of methylamine on substituted thiophenes.

Further investigations by Boubaker and collaborators focused on the kinetic studies of S_NAr reactions between 2‐methoxy‐3‐X‐5‐nitrothiophenes and piperidine [14], pyrrolidine, and morpholine in different solvents [12]. The second‐order rate constants k obtained experimentally were rationalized using Equation (2). A correlation between Hammett's constant, σ _P, and the electrophilicity parameter (E) was evidenced. The σ _P parameter is defined for substituents in the para position and provides an interpretation of substituent effects when dominating electronic effects are operating. The results suggested the formation of a highly dipolar transition state for the generation of a zwitterionic intermediate that was found to be the rate‐limiting step. For reactions conducted in methanol, the E values correlated with the pK _a values of the electrophiles in the σ complexation reaction with the methoxide ion (methanol addition) [15].

In order to clarify the reaction mechanism of S_NAr reactions involving substituted thiophenes with amines, and to ascertain the role of a zwitterionic intermediate to determine the rate limiting step, a computational study at the Density Functional Theory (DFT) level was recently carried out by Smaoui et al. [16] Their model system included 2‐methoxy‐5‐nitrothiophene reacting with dimethylamine used as a simplified secondary amine. The formation of a zwitterion was confirmed via a strongly dipolar transition state. The zwitterion can then decompose to the final product. They found that the most probable reaction path corresponds to the release of a methanol molecule, induced by a proton transfer catalyzed by a second amine (Scheme 1).

We used herein electronic structure calculations combined with a systematic transition state search to provide a detailed investigation of three distinct reaction pathways that lead to the substitution of the methoxy group by a secondary amine. We explored the effect of substituent X groups used experimentally and possessing different electron‐withdrawing strengths. Moreover, some groups can also act as hydrogen bond acceptors (X = NO₂, CO₂CH₃ for example) or donors (X = CONH₂). Consistent with previous experimental studies [15, 17], pyrrolidine was chosen as the nucleophilic secondary amine. The effect of the inclusion of one explicit solvent molecule on both the reaction mechanisms and activation barrier is investigated. Overall, the efficiency of different molecular and local reactivity descriptors is discussed.

2. Computational Details

All quantum calculations were performed in the framework of density functional theory (DFT) by using the Gaussian 16 software package [18]. Following a previous benchmark [17], energies and forces were computed with the M06‐2X functional [15]. A preliminary study of all mechanisms was conducted with the def2SVP basis set. The full mechanism for X = CN and X = H, as well as the main steps of all mechanisms were then re‐computed with the aug‐cc‐pVTZ basis set for all atoms [19]. The accuracy of the M06‐2X/aug‐cc‐pVTZ level was also checked against CCSD(T)/aug‐cc‐pVTZ calculations using Turbomole 7.8: [20] as detailed in the Supporting Information. We found a good agreement for the relative barriers. The bulk solvation effect of methanol was described using the polarizable continuum model (PCM) as implemented in Gaussian16 [21]. Geometry optimizations were carried out without symmetry constraints, and the corresponding frequency calculations were conducted. Gibbs free energies are estimated at T = 298 K and p = 1 bar using unscaled frequencies at the M06‐2X/aug‐cc‐pVTZ level. Gibbs free energies are computed in the usual ideal gas, rigid rotor, and harmonic oscillator (RRHO) approximation [22]. As the systems solvated by an additional methanol or pyrrolidine molecule are quite flexible, we have explored the most stable conformers using the Conformer‐Rotamer Ensemble Sampling Tool (CREST) developed by S. Grimme [23]. CREST is based on the tight‐binding DFT approach implemented in the xTB software [24]. We used a 400 ps length for the dynamics during the CREST process. CREST was also used to study the TS ₁₂ × transition states geometry using the following procedure. First, transition states connecting the reactant 1× to the zwitterion 2× were found by using the string method as implemented in the Opt'n Path software [25]. The string method interpolates the valence coordinates between 1× and 2×. The transition state was further refined using the QST3 option of Gaussian. Then, more stable conformers were searched using CREST: the C2—N bond was constrained to remain close to the value found in the first step. Last, most stable conformers were re‐optimized at the DFT level.

According to Parr and Yang [26], the electrophilicity index (ω) can be estimated using the relationship, Equation (2)

$$\omega =\frac{\mu 2}{2\eta }$$ (2)

in which μ is the chemical potential and η the chemical hardness [27] of the substituted thiophene. The chemical potential is defined as the first derivative of the energy with respect to the number of electrons. It represents the energy variation due the changes in electrons number. The chemical hardness is given by the second derivative of the energy with respect to the number of electrons, and characterizes the resistance to charge transfer between two species. Both parameters can be evaluated in the context of DFT, using the frontier molecular orbitals (FMO) energies, as expressed in Equations (3 and 4):

$$\mu =\frac{{\epsilon }_{\text{LUMO}}+{\epsilon }_{\text{HOMO}}}{2}$$ (3)

$$\eta ={\epsilon }_{\text{LUMO}}-{\epsilon }_{\text{HOMO}}$$ (4)

where ε _LUMO is the energy of the Lowest Unoccupied Molecular Orbital (LUMO) and ε _HOMO the corresponding energy for the Highest Occupied Molecular Orbital (HOMO).

Finally, the molecular softness S is defined as the inverse of the chemical hardness, given by Equation (5):

$$S=1/\eta =\frac{1}{{\epsilon }_{\text{LUMO}}-{\epsilon }_{\text{HOMO}}}$$ (5)

It is worth noting that the chemical hardness and softness introduced here are closely related to Pearson's Hard and Soft Acids and Bases (HSAB) theory [28] hard species tend to react under charge control, while soft species preferentially react under orbital control.

Additionally, one can consider local reactivity descriptors such as the electronic density itself $\rho \left(\overrightarrow{r}\right)$ or the Fukui functions defined as the derivative of the density with respect to the number of electrons, as expressed in Equations (6 and 7) [29]

$$f^{+}\left(\overrightarrow{r}\right)={\left(\frac{\partial \rho \left(\overrightarrow{r}\right)}{\partial N}\right)}_{v_{\mathit{ext}}}^{+}$$ (6)

$$f^{-}\left(\overrightarrow{r}\right)={\left(\frac{\partial \rho \left(\overrightarrow{r}\right)}{\partial N}\right)}_{v_{\mathit{ext}}}^{-}$$ (7)

where N is the number of electrons, and $v_{\mathit{ext}}$ is the external potential [27]. The $f^{+}\left(\overrightarrow{r}\right)$ function corresponds to the case in which the molecule accepts an electron, and thus describes its electrophilic sites. Conversely, the $f^{-}\left(\overrightarrow{r}\right)$ function describes the nucleophilic sites. In practice, these functions can be condensed into atomic basins using finite difference approximations. Following Yang and Mortier [30], for a given atom A, $f^{+}\left(A\right)$ is expressed as, Equation (8):

$$f^{+}\left(A\right)=q_A\left(N\right)-q_A\left(N+1\right)$$ (8)

With $q_A\left(N+1\right)$ is the charge of atom A in the radical anion, while $q_A\left(N\right)$ corresponds to its charge in the neutral molecule. These charges are computed at the fixed neutral geometry, without any structural relaxation. They can be computed using various quantum chemical approaches, such as Mulliken charges, natural charges from the NBO approach [31], or charges derived from Bader's Atoms in Molecule (AIM) theory [32].

Fukui functions can also be computed in the FMO framework assuming that the molecular orbitals do not relax upon the addition or subtraction of an electron, as expressed in Equations (9 and 10):

$$f^{+}\left(\overrightarrow{r}\right)={\rho }_{\text{LUMO}}\left(\overrightarrow{r}\right)$$ (9)

$$f^{-}\left(\overrightarrow{r}\right)={\rho }_{\text{HOMO}}\left(\overrightarrow{r}\right)$$ (10)

where ${\rho }_{\text{LUMO}}\left(\overrightarrow{r}\right)$ and ${\rho }_{\text{HOMO}}\left(\overrightarrow{r}\right)$ represent the electronic densities of the LUMO and HOMO, respectively.

Using the condensed Fukui function, one can then access the condensed descriptors by multiplying the global descriptor by the corresponding condensed Fukui function. For example, the electrophilicity condensed on atom A is given by Equation (11):

$${\omega }^{+}\left(A\right)=\omega \times f^{+}\left(A\right)$$ (11)

It is worth noting that the local hardness cannot be directly estimated in this way [27]. Therefore, we adopted the approximation introduced by Meneses et al. as given in Equation (12): [33].

$$\eta \left(A\right)\approx {\epsilon }_{\text{LUMO}}\times f^{+}\left(A\right)-{\epsilon }_{\text{HOMO}}\times f^{-}\left(A\right)$$ (12)

AIM calculations were conducted using the AIMALL software [34], while FMO ad ELF calculations were conducted using the Topchem2 software [35].

3. Results and Discussion

3.1. Global Mechanism

We have computationally explored the nucleophilic substitution mechanism for seven substituted thiophenes with X = NO₂ (1a), X = CN (1b), X = SO₂CH₃ (1c), X = COCH₃ (1d), X = CO₂CH₃ (1e), X = CONH₂ (1f) and X = H (1 g), as shown in Figure 1 with the atoms numbering.

FIGURE 1.

Atoms numbering in substituted thiophene derivatives.

The nucleophilic substitution proceeds through an addition/elimination mechanism. The different pathways are displayed in Scheme 2. The first step involves the formation of the zwitterion 2× through the nucleophilic addition of pyrrolidine to the C2 carbon of thiophene. The second step corresponds formally to the proton transfer from the nitrogen atom of the pyrrolidinium moiety to the methoxy group, followed by the elimination of a methanol molecule. The proton transfer can proceed via three distinct pathways: Pathway 1 corresponds to the non‐catalyzed proton transfer. In pathway 2, a methanol molecule catalyzes the proton transfer. This could be done either in a concerted way (Pathway 2c) or stepwise (Pathway 2s). The elimination of the methanol moiety leads to the final product. Pathway 3 follows similar routes, except that the base catalyst is now an extra pyrrolidine molecule.

SCHEME 2.

Pathways studied for the nucleophilic substitution.

The free energy profile was explored for the substituents X = CN, representing a strongly electron‐withdrawing group, and X = H, serving as a benchmark with f negligible electronic and steric effects. The most attracting nitro group X = NO₂ was not selected, as it is recognized to favor “built‐in” solvation that could bias the mechanistic investigation [36].

3.2. X = CN

Starting with 2‐methoxy‐3‐cyano‐5‐nitrothiophene 1b, the main Gibbs free energy profiles are provided in Figure 2. A complete collection of all computed pathways is reported as Supporting Information (Figure S1).

FIGURE 2.

Gibbs free energy profiles (in kcal/mol) for the nucleophilic aromatic substitution of pyrrolidine to 2‐methoxy‐3‐cyano‐5‐nitrothiophene (1b).

The formation of the zwitterion 2b by nucleophilic addition of pyrrolidine to the C2 carbon of thiophene proceeds with a low barrier of 19.0 kcal/mol.

In agreement with the experimental findings and the theoretical work by Smaoui et al. [19], the uncatalyzed pathway (Pathway 1) requires overcoming a very high barrier of ΔG ^‡ = 47.3 kcal/mol (TS ₂₅ b, Figure 2). Given that this barrier is considerably higher than those associated with the catalyzed pathways, the uncatalyzed mechanism is not further discussed. We therefore focused on the proton transfer catalyzed by a methanol molecule. Since pyrrolidine is a stronger base than methanol, the proton transfer from pyrrolidinium 2b to a methanol molecule is endergonic and thermodynamically unfavorable. This is illustrated by the high Gibbs free energy of the anionic intermediate 7b, in which methanol is protonated (ΔG = 41.6 kcal/mol). As a consequence, we could not find a stepwise pathway. On the other hand, the concerted proton transfer was easily found and proceeds with an activation free energy of ΔG ^‡ = 35.0 kcal/mol, suggesting that this is the preferred pathway.

This proton transfer deviates from the anticipated “proton shuttle mechanism,” which typically involves a 6‐membered ring transition state (TS ₂₅ bM, Figure 3a). Instead, the solvating methanol molecule facilitates the transfer by acting as a proton carrier. This process is mediated by a shallow hydrogen bond, with the cyano group serving as a pivot point, as illustrated by the TS ₂₅ bM‐f structure in Figure 3b.

FIGURE 3.

(a) 6 membered ring TS; (b) concerted transition state for the proton transfer assisted by a methanol molecule. Hydrogen atoms linked to carbon atoms are omitted. Color code: Sulfur in yellow, oxygen in red, nitrogen in blue, carbon in gray and Hydrogen in white.

While the proton transfer barrier is lower than that of the uncatalyzed pathway, it is greater than the corresponding barrier for nucleophilic addition. This contradicts experimental findings, which indicate that the rate‐determining step is the nucleophilic addition [5, 15, 17, 37, 38, 39]. Consequently, we considered the proton transfer catalyzed by a second pyrrolidine molecule. Given that pyrrolidine is present in large excess relative to the thiophene derivative, the solvation of 2b with an additional pyrrolidine molecule is a plausible scenario. This is further supported by the fact that the hydrogen bond between the pyrrolidinium ion and a second pyrrolidine molecule is stronger than that with a methanol molecule, in agreement with the higher pK _a of pyrrolidine compared to methanol.

For pyrrolidine, all attempts to isolate a concerted proton transfer failed and led to a lower free energy sequential pathway. Starting from the 2bP intermediate, the proton transfer proceeds with no free energy barrier to form 3bP that rearranged into 4bP [40]. The last step corresponds to the proton transfer from the ammonium moiety to the methoxy group. Interestingly, this proton transfer triggers the elimination of this fragment as a methanol molecule, solvated by a pyrrolidine. Structural analysis of the TS ₄₅ bP transition state confirms that both transfers occur simultaneously. As illustrated in Figure 4, the C—O(Me) bond distance expands significantly to 1.897 Å, compared to 1.416 Å in the reactant state, indicating bond cleavage. At the same time, the O—H distance shortens from 1.928 Å in the reactants to 1.369 Å, while the N—H bond distance increases from 1.028 to 1.157 Å, further supporting the concerted nature of the transition state.

FIGURE 4.

Transition state TS45bP geometry. Hydrogen atoms linked to carbon atoms are omitted. Color code: Sulfur in yellow, oxygen in red, nitrogen in blue, carbon in gray and Hydrogen in white.

This process ultimately leads to the formation of the product 6b through a process that is quite exergonic (ΔG = −13.4 kcal/mol).

Consiglio et al. [16] previously hypothesized that both nucleophilic addition and proton transfer could be catalyzed either by a methanol molecule or by a second amine. However, our computational results indicate that the hydrogen bond stabilization provided by these additional molecules is insufficient to compensate for the entropic cost associated with forming the solvated system. Specifically, the presence of a second pyrrolidine molecule increases the Gibbs free energy barrier of the addition by 6.3 kcal/mol, while using a methanol molecule increases it by 4.6 kcal/mol. Similarly, during the second pyrrolidine‐catalyzed proton transfer, the addition of a methanol molecule further raises the activation barrier by 3 kcal/mol [41].

3.3. X = H

We next studied the pyrrolidine addition on the unsubstituted 2‐methoxy‐5‐nitrothiophene (X = H, 1g). Based on the mechanisms found for X = CN and the study conducted by Smaoui et al. [19], we focused exclusively on the catalyzed pathways. The resulting Gibbs free energy profiles are reported in Figure 5.

FIGURE 5.

Free energy profile (in kcal/mol) for the nucleophilic aromatic substitution of pyrrolidine to 2‐methoxy‐5‐nitrothiophene (1g).

Contrary to substituents like NO₂ or CN, the hydrogen atom in position C3 does not provide any specific stabilization to the negative charge that appears on the thiophene ring during zwitterion formation. Consequently, the activation free energy for nucleophilic addition is significantly higher for X = H (ΔG ^‡(TS ₁₂ g) = 24.1 kcal/mol) compared to the value obtained with X = CN (ΔG ^‡(TS ₁₂ b) = 19.0 kcal/mol). As there is no substituent in position 3 of the thiophene to act as a pivot, the methanol‐catalyzed proton transfer occurs preferentially via a 6‐member ring transition state (TS ₂₃ gM, in Figure 5).

As in the case of the X = CN cyano substituent, the favored proton transfer proceeds sequentially, catalyzed by pyrrolidine, with a low activation barrier of 12.0 kcal/mol.

Given the similar energetic trends observed for X = CN and X = H, we extended this mechanistic insight to the full set of substituted thiophenes. Consequently, only Pathway 3, which involves proton transfer catalysis by an additional pyrrolidine molecule, was considered for the remaining derivatives. The Gibbs free energy profiles for these systems are reported as Supporting Information.

3.4. Correlation With the Mayr Electrophilicity Scale

The experimental electrophilicity of substituted 5‐nitro‐2‐methoxy‐3‐X‐thiophenes in reactions with secondary amines was measured by Boubaker et al. and is reported in Table 1 [15, 17]. The Mayr scale provides a predictive framework, as it allows the estimation of the kinetic rate constant for an addition reaction based on the known electrophilicity and the nucleophilicity of the two reactants In this study, we established correlations between our computational approach, conventional reactivity descriptors derived within the framework of conceptual DFT [27], and the experimentally measured electrophilicity on the Mayr scale.

TABLE 1.

Electrophilicity parameters E and Gibbs free energy barriers for thiophenes 1a–g.

	E	ΔG ‡(TS12x) (kcal/mol)
1a: X = NO2	−15.26 a	17.0
1b: X = CN	−16.60 a	19.0
1c: X = SO2CH3	−17.18 b	19.5
1d: X = COCH3	−17.65 a	20.4
1e: X = CO2CH3	−18.48 b	20.8
1f: X = CONH2	−19.09 b	22.7
1 g: X = H	−21.33 b	24.1

^a From ref. [15].

^b From ref. [17].

3.4.1. Activation Gibbs Free Energy

The correlation between the computed free energy barriers and the electrophilicity is depicted in Figure 6. The Eyring formula links the free energy barrier to the rate constant, using the Boltzmann constant $k_B$, the Planck constant $h$ and the temperature T. We assume here that there is no recrossing and no tunneling, so that the Eyring formula can be written as Equation (13):

$$k=\frac{k_{B}T}{h}\times e^{-\frac{\mathrm{\Delta }{G}^{‡}}{\mathit{RT}}}$$ (13)

FIGURE 6.

Correlation between electrophilicity E and activation Gibbs free energy.

Taking the logarithm of the Eyring formula gives Equation (14).

$$\log k=\log \frac{k_{B}T}{h}-\frac{\mathrm{\Delta }{G}^{‡}}{\mathit{RT}\ln 10}$$ (14)

This is similar to the Mayr formula written for a given nucleophile (Equation (2). Consequently, a linear relationship between the electrophilicity and the activation free energy thus emerges in Equation (15).

$$\log \frac{k_{B}T}{h}-\frac{\mathrm{\Delta }{G}^{‡}}{\mathit{RT}\ln 10}=s_N\left(N+E\right)\iff E=\frac{1}{s_N}\left(\log \frac{k_{B}T}{h}\right)-N-\frac{\mathrm{\Delta }{G}^{‡}}{\mathit{RT}\ln 10s_N}$$ (15)

As shown in Figure 6, our computational approach successfully reproduces the general trend, yielding a linear correlation coefficient of R ² = 0.967. The computational estimate of the electrophilicity for a given substituted thiophene exhibits a root mean square deviation (RMSD) of 0.35, and a maximum error of 0.6. This level of accuracy is acceptable within the criterion introduced by Mayr, which states that the predicted kinetic rate constant‐based on electrophilicity and nucleophilicity parameters of the coupling partners should fall within two log units of the experimentally measured values.

3.4.2. Global Conceptual DFT Descriptors

We correlated experimentally measured electrophilicity with selected conceptual DFT descriptors. The Parr electrophilicity (ω) was the most straightforward choice, yielding a reasonably strong correlation with the experimental electrophilicity (E), with R ² = 0.864 (Figure 7).

FIGURE 7.

Electrophilicity E as a function of Parr electrophilicity ω (in eV).

According to the HSAB theory, if the reaction was under orbital control, we should have a link between the softness S and the electrophilicity. This is verified here with R ² = 0.781. We also examined the correlation between electrophilicity (E) and hardness (R ² = 0.777), the electronic affinity, defined as the opposite of the LUMO energy in the FMO approach (R ² = 0.854), as well as the chemical potential (μ, R ² = 0.874). These four global descriptors give similar correlations with the experimentally measured electrophilicity, which suggests that the FMO approach is consistently valid for this reaction.

Finally, a satisfactorily correlation between the global electrophilicity index (ω) and the Hammett constant (σ ⁻) [16] was observed (Figure 8, R ² = 0.903 when X = H is discarded), further reinforcing the direct relationship between experimental and theoretical approaches. However, the positive deviation of thiophene 1 g (X = H) from the correlation line remains unexplained at this stage and requires further investigation.

FIGURE 8.

Correlation between the global electrophilicity index (ω, eV) calculated at M06‐2X/aug‐cc‐pVTZ level of theory in acetonitrile for thiophenes 1a–g and the Hammett substituent constants (σ ⁻). The σ ⁻ values were taken from ref. [16].

3.4.3. Local Descriptors

Thiophenes are known to be ambident reactants: [42] meaning that strong nucleophiles can react with either the C2 or C4 carbon. We thus considered local descriptors to describe the reactivity of the C2 atom, specifically the local electrophilicity ${\omega }^{+}\left(C_2\right)=\omega \times f^{+}\left(C_2\right)$. The parameter $f^{+}\left(C_2\right)$ was computed using Mulliken charges, natural charges and AIM charges. However, all three correlations between ${\omega }^{+}\left(C_2\right)$ and E were inconsistent with low values of R ² = 0.344 for Mulliken charges, R ² = 0.483 for natural charges, and R ² = 0.352 for AIM charges.

This inconsistency may arise from the fact that condensed electrophilic Fukui functions are not strongly correlated with electrophilicity. The linear correlations for other local descriptors with electrophilicity were also weak. For example, the correlation between local atomic softness $S^{+}\left(C_2\right)=f^{+}\left(C_2\right)\times \mathrm{S}$ and electrophilicity yielded, R ² = 0.599, while R ² was found at 0.781 for the global softness S.

The Fukui function can also be estimated within the FMO approximation. When only the LUMO was used to estimate $f^{+}\left(C_2\right)$, a decrease of all coefficients of determination by approximately 30% was achieved compared to the NBO method. Therefore, we adopted the weighted FMO variant described in Equation (16) [43].

$$f^{+}\left(\mathbf{r}\right)=\sum _{i=\text{LUMO}}^{\infty }{\omega }_i{\rho }_{{\phi }_i}\left(\mathbf{r}\right)$$ (16)

where ${\rho }_{{\phi }_i}\left(\mathbf{r}\right)$ is the density of the molecular orbital ${\phi }_i$, and ${\omega }_i$ a weight defined in Equation (17).

$${\omega }_i=\frac{\exp \left[-{\left(\frac{\mu -{ϵ}_i}{\mathrm{\Delta }}\right)}^2\right]}{\sum _j\exp \left[-{\left(\frac{\mu -{ϵ}_j}{\mathrm{\Delta }}\right)}^2\right]}$$ (17)

In Equation (17), $\mu$ is the chemical potential of the system, ${ϵ}_i$ the energy of the MO ${\phi }_i$ and $\Delta$ is a parameter fixing the width of the weight function, chosen at $\Delta =0.1$ Hartree. This choice improved the correlation for the some local descriptors. For example, the correlation for the condensed electrophilicity ${\omega }^{+}\left(C_2\right)$ is associated to R ² = 0.740, a value closer to that obtained for the global electrophilicity $\omega$, as well as the local affinity (see details in the Supporting Information). On the other hand, the local softness correlation decreased by a factor of 2 compared to NBO (R ² = 0.247).

Interestingly, we found that the AIM charge of the C2 atom provides an easy way of estimating the electrophilicity of this site: the coefficient of determination was found to be equal to R ² = 0.864 (see Supporting Information).

Quantum topology is a powerful tool to describe the electronic structure of molecules. In particular, the Electron Localization Function (ELF) [44] can be decomposed in basins corresponding to chemical concepts such as bonds, lone pairs, and core electrons [45]. We investigated the correlation between electrophilicity (E) and the population of the C—O bond basin (denoted as N[V(C,O)]): which yielded a consistent linear correlation with R ² = 0.781.

We considered the ELF_LUMO function, which was designed to quantify the reactivity of a given site in a molecule, based on the ELFx function introduced by Pilmé's group [46, 47]. We computed the population of the ELF_LUMO basin located on the C2 atom, denoted by N[ELF_LUMO(C2)]. Notably, we obtained a fairly good correlations between the population N[ELF_LUMO(C2)] and electrophilicity (R ² = 0.499), as shown in Figure 9.

FIGURE 9.

Correlation between the population N[ELF_LUMO(C2)] (in electron) for the C2 atom and E.

ELF appears to be a promising approach, advancing predictive approaches compared to previous local descriptors. Herein, it led to local correlations with coefficients of determination close to those obtained for the corresponding global descriptors. This newly introduced ELF_LUMO descriptor matches the global behavior of the nucleophilic reactivity for this set of thiophene derivatives.

4. Conclusion

The reaction mechanism of 2‐methoxy‐3‐X‐5‐nitrothiophenes (1a–g) with pyrrolidine was investigated using DFT calculations. The S_NAr process involves pyrrolidine addition at the C2 position, followed by proton transfer to the methoxy group, resulting in methanol elimination. Computational analysis ruled out both uncatalyzed and methanol‐catalyzed pathways due to high Gibbs free energy barriers, thereby confirming that excess pyrrolidine is the most efficient catalyst for proton transfer.

A strong linear correlation was established between the computed Gibbs free energy barriers and experimental electrophilicity parameters ( R ²   = 0.865), consistent with theoretical predictions from the Mayr reactivity scale and Eyring equations. Electrophilicity also correlated with the Parr electrophilicity index (ω, R ²   = 0.859) and global softness (S, R ²   = 0.825).

Local descriptors from conceptual DFT were analyzed to quantify electrophilicity at the C2 position, with ELF basin populations of the C—O bond and ELF_LUMO (C2) emerging as the most reliable predictors. This theoretical framework provides a robust approach for predicting electrophilicity in thiophene derivatives and related heteroaromatic systems.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Data S1. Supporting Information.

Data S2. Supporting Information.

Pouzens J.‐T., Souissi S., Ludwig B., et al., “Substituent Effect on the Nucleophilic Aromatic Substitution of Thiophenes With Pyrrolidine: Theoretical Mechanistic and Reactivity Study,” Journal of Computational Chemistry 46, no. 19 (2025): e70169, 10.1002/jcc.70169.

Data Availability Statement

The full free energy profiles at the M06‐2X/aug‐cc‐pVTZ for X=CN and X=H, at the M06‐2X/def2SVP for X=NO2, X=SO2CH3, X=CO2CH3, X=COCH3 and X=CONH2; Activation free energies at the CCSD(T)/aug‐cc‐pVTZ; all global and local descriptors for all molecules are available in the Supporting Ingormation of this article. Cartesians coordinates for all structures are available on FigShare: https://doi.org/10.6084/m9.figshare.29473952.