Mechanistic DFT Insights into Mn-Porphyrin Quantum Catalysts for Peroxymonosulfate-Driven Degradation of Sulfamethoxazole in Water

Abstract

Emerging pharmaceutical contaminants, including sulfonamide antibiotics such as sulfamethoxazole (SMX), persist in natural water bodies at ng L⁻¹ to µg L⁻¹ concentrations and are inadequately removed by conventional wastewater treatment technologies, posing significant ecological and public health risks. Porphyrin-based quantum catalysts activated by peroxymonosulfate (PMS) represent a promising advanced oxidation strategy for the remediation of such recalcitrant micro-pollutants. However, the precise molecular mechanisms governing their catalytic activity remain incompletely understood. In this study, we present a comprehensive mechanistic investigation of SMX oxidation catalyzed by Mn (III) meso-tetraphenylporphyrin (Mn-TPP) in the presence of PMS, employing spin-unrestricted density functional theory (DFT) at the Becke, 3-parameter, Lee–Yang–Parr (B3LYP-D3BJ) level of theory with dispersion corrections. Full Gibbs free energy profiles for the catalytic cycle were constructed through geometry optimizations using the LACVP basis set on Mn and 6-31G(d,p) on all non-metal atoms, followed by single-point energy calculation at the 6-311+G(d,p) level, incorporating the SMD implicit solvation model to stimulate aqueous environment conditions. The results demonstrate that the oxidation of Mn TPP by PMS to generate the key high-valent intermediate Mn(V)=O(TPP)⁺ is thermodynamically and kinetically favorable. The activation barrier for Mn(V)=O(TPP)⁺ formation via PMS activation is ΔG† = 17.2 kcal mol⁻¹ (SMD water, 298 K), confirming that this step is kinetically accessible under ambient environmental conditions. Subsequent SMX oxidation processes proceed via concerted radical and non-radical mechanistic pathways, with the most thermodynamically favorable route exhibiting a strongly exergonic reaction-free energy (ΔGr), indicating that significant mineralization of the target pollutant is thermodynamically accessible. The transition state analysis reveals spin density localization characteristic of the Mn-Oxo species, establishing a direct correlation between quantum confinement effects, electronic structure and the observed catalytic selectivity and oxidation stability of the Mn-TPP system. These mechanistic insights provide quantitative molecular-level design parameters, including activation barriers, spin state requirements, and electronic structure descriptors for the rational optimization of next-generation porphyrin-based quantum catalysts capable of efficiently degrading persistent pharmaceutical contaminants in complex aqueous matrices.

1. Introduction

The contamination of aquatic ecosystems by pharmaceutical micropollutants has emerged as one of the most pressing environmental challenges of the 21st century. Among the various classes of emerging pollutants, sulfonamide antibiotics, such as sulfamethoxazole (SMX), are especially alarming for their widespread prescription in human and veterinary medicine, the obsolescence of conventional wastewater treatment infrastructure for their removal, and their potential ecological risk [1,2]. SMX is a recalcitrant polysulfonamide antibacterial agent that resists conventional biological degradation and has been consistently detected in surface waters, groundwater, and treated effluents at concentrations ranging from ng/L to microgram/L globally [3,4]. The continuous discharge of synthetic, non-biodegradable antibiotics into water bodies is an unsolved and urgent environmental contamination challenge, compounded by the accelerated dissemination of antibiotic resistance genes and the progressive destabilization of the structural and functional diversity of the microbial communities [5,6].

The persistence of SMX in the environmental carries consequences that extend beyond direct ecotoxicological effects. Antibiotic-resistance bacteria, including clinically critical strains such as methicillin-resistant Staphylococcus aureus (MRSA) and carbapenem-resistant Enterobacteriaceae, can proliferate and disseminate through the resistance-selective pressure exerted by sub-inhibitory SMX concentrations in natural water bodies, simultaneously disrupting the structure of microbial communities and impairing the intrinsic self-purification capacity of aquatic ecosystem [7,8]. This convergence of direct chemical toxicity and indirect microbiological risk underscores the imperative for developing advanced, efficient, and selective remediation technologies capable of achieving the complete mineralization of sulfonamide contaminants rather than their mere transformation to potentially bioactive metabolites. Advanced oxidation processes (AOPs) have emerged as a highly effective strategy for the degradation of recalcitrant organic pollutants that resist conventional treatment. Within the AOP paradigm, sulfate radical-based processes initiated through the activation of peroxymonosulfate (PMS, HSO₅⁻) are particularly promising. The sulfate radical (SO₄•⁻) possesses a redox potential of 2.5–3.1 V versus the normal hydrogen electrode, conferring superior oxidizing power, higher electivity, and a longer half-life compared to the hydroxyl radical (•OH⁻), enabling more targeted and efficient mineralization of complex organic pollutants in aqueous matrices [9,10]. PMS offers additional practical advantages including high chemical stability, a wide operational pH range, and the capacity to generate multiple reactive oxygen species (ROS), including SO₄•⁻, −•OH⁻, superoxide radicals (O₂•⁻), and singlet oxygen (₁O²) through appropriate designed catalytic activation pathways [11,12]. However, the intrinsically slow rate of PMS auto-decomposition necessitates the use of an efficient catalyst to cleave the peroxide O–O bond and initiate the oxidative cascade under environmentally relevant conditions. Although sulfate radical-based AOPs offer considerable advantages, their practical implementation is frequently constrained by background water matrix scavenging effects, necessitating the design of selective activation catalyst systems with enhanced substrate adsorption, low susceptibility to matrix interference, and sustained reactivity in complex real wastewater environments [13].

The advancement of material science has identified transition metal-based catalytic systems as highly effective PMS activators, manganese-based materials emerging as particularly promising candidates owing to their variable valency states, favorable redox potentials, and superior electron transfer capabilities [14,15]. Manganese-based systems have demonstrated enhanced PMS activation reactivity through the formation of surface-activated complexes and the mediation of internal disproportionation reactions, yielding reactive oxidant species capable of mineralizing recalcitrant organic pollutants [16,17]. Among transition metal-based PMS activators, synthetic Mn porphyrins represent a particularly compelling catalyst class. Their structural analogy to the active sites of heme-containing metalloenzymes, including cytochrome P⁴⁵⁰ monooxygenases and peroxidases, combined with the versatile and tunable redox chemistry of the central manganese ion, renders them highly effective biomimetic platforms for mediating challenging oxidative transformation [2,18]. These systems are capable of activating PMS to generate high-valent manganese–oxo intermediates, which function as potent and selective oxidants capable of driving pollutant degradation through both radicals and non-radical mechanistic pathways, potentially offering superior selectivity compared to free radical mechanisms in aqueous matrices [3,19,20].

Density functional theory (DST) calculations provide a powerful and rigorous quantum chemical framework for the elucidating the electron structure, reaction energetics, and mechanistic details of catalytic systems at the atomic level—details that are largely inaccessible through experimental approaches alone [10,21,22]. The application of dispersion-corrected hybrid DFT with spin-unrestricted formalism and implicitly aqueous solvation corrections has proven particularly effective for characterizing the structure–activity relationships of metal–porphyrin oxidation catalysts, accurately reproducing the activation barrier, optimal coordination geometries, and spin-state-dependent reactivity profiles of the Mn-based active center [23,24]. In the context of PMS activation at the Mn-N₄ coordination environment, the efficiency of the catalytic reaction is governed by the interplay between adsorption energetics, charge transfer dynamics, and the kinetic barriers controlling the O–O bond cleavage and ROS generation [25,26]. The optimum geometric arrangement of the Mn-N₄ active site is expected to facilitate frontier molecular orbital overlap, lower the energy of heterolytic bond cleavage, and increase the selectivity for targeted oxidant generation during the catalytic cycle [27]. Some studies have applied synergistic approaches involving interface engineering such as photocatalytic oxidation using Cd/Zn composites with BiOBr and Mn/Cd with 5S/N-rich C₃N₅ S-scheme heterojunctions for the removal of antibiotics from aqueous environments [28,29].

Despite these mechanistic expectations, the atomic scale mechanisms governing PMS system activation at Mn-porphyrin centers, including the precise elementary steps of O–O bond activation, the electronic character and spin state of the resulting high-valent manganese–oxo intermediates, and the dominant pathways governing the subsequent transformation of the SMX molecule, remain insufficiently characterized, fundamentally hindering the rational design of quantum scale catalysts with high efficiency for environmental remediation [30,31].

The present study addresses this critical mechanistic gap by employing spin-unrestricted DFT at the B3LYP-D3BJ level of theory with aqueous-phase single-point energy correction to provide a comprehensive mechanistic investigation of PMS activation by the porphyrin-based manganese catalyst Mn (III)-meso-tetraphenylporphyrin (Mn-TPP) and its subsequent catalytic oxidation of sulfamethoxazole. By constructing full Gibbs free energy profiles across the complete catalytic cycle, this work specially aims to: (i) elucidate the elementary mechanistic steps of PMS activation at the Mn center, including the quantitative role of non-covalent pre-reaction complex stabilization in reducing the activation barrier; (ii) characterize the electronic structure, spin density distribution and oxidative reactivity of key high-valent manganese–oxo [Mn(V)=O(TPP)]⁺ species intermediate; (iii) determine the most thermodynamically and kinetically favorable reaction pathways for the SMX oxidation, explicitly distinguishing between electron transfer and oxygen atom transfer mechanisms; and (iv) establish quantitative molecular-level design principles for the rational optimization of next-generation porphyrin-based quantum catalysts for environmental pharmaceutical remediation. The computational insights generated in this study provide a fundamental mechanistic foundation bridging empirical catalytic performance and atomic-scale electronic structure, offering transferable theoretical framework for the accelerated rational design of earth abundant catalysts targeting persistent pharmaceutical contaminants in a complex aqueous environment.

2. Methodology

2.1. Computational Methods

In this research, we employed Jaguar (version 10.4), a leading quantum chemistry software package within the Schrödinger Materials Science Suite 2025.1, to perform all quantum-chemical computations [32]. The research community is well-aware of Jaguar’s reputation as a robust and reliable tool for ab initio and density functional theory (DFT) computations. It features advanced algorithms to provide comprehensive computations for molecular and catalytic system electronic structures, molecular geometries, reaction pathways, and several energetic parameters.

Through the Maestro (version 10.4) graphical user interface, we constructed and illustrated the molecular structures of the manganese porphyrin catalyst, the oxidant peroxymonosulfate (PMS), the target pollutant sulfamethoxazole (SMX), and the entire set of transient intermediates involved in the catalytic cycle. Maestro, a 3D modeling interface, streamlines the process of sketching, importing, and modifying molecular geometries, as well as preparing them for quantum computing [33]. It is one thing to develop catalytic systems and quite another to understand how they operate at a fundamental level. It is critical to study and analyze molecular orbitals and electronic density distributions, as well as to refine structures.

The analysis of the catalyst’s electronic structure and the reaction’s energy profiles and intermediates was made possible using a singular computational framework. It was possible to examine the detailed electronic interactions between the manganese center and PMS, as well as the processes that start and end SMX, using the properties of Jaguar, 10.4 (1540 Broadway, New York, NY, USA). The integration of Maestro simplified input preparation, result visualization, and quantum molecular-level understanding of the mechanisms (1540 Broadway, New York, NY, USA). In general, this method leverages the accuracy and flexibility of modern quantum chemistry methods to explain the fundamental aspects of biomimetic catalysis with high fidelity.

2.2. Density Functional Theory (DFT) Calculations

Spin-unrestricted density functional theory (DFT) calculations, one of the most common techniques employed for electronic structure calculations of molecules, was utilized for the treatment of open-shell systems, i.e., systems with unpaired electrons [34]. In these calculations, the B3LYP functional was used. One of the most common functionals in quantum chemistry, B3LYP, is the result of the combination of the Becke Lee–Yang–Parr correlation functional and one of the three-parameter exchange functionals [35]. Particularly, for transition metal complexes, B3LYP presents one of the best trade-offs between accuracy and efficiency, as describing the exchange-correlation effect for these systems is of utmost importance. The use of the Grimme D3 correction (with Becke-Johnson damping) (D3BJ) was employed to better account for weak, non-covalent interactions such as van der Waals, which play an important role in the binding of catalysts to substrates [36]. DFT functionals typically do not account for these interactions.

The computational cost was minimized using a mixed basis set approach without losing any accuracy. For the manganese atom, the Los Alamos effective core potential (ECP) and a double-ζ valence basis set (LACVP) were applied. The core electrons are substituted with an effective potential, which makes calculations less complex while retaining some major relativistic and electronic concerns [37]. For all lighter atoms (C, H, N, O, S), the Pople-style 6-31G(d,p) basis set was applied [38]. The basis set included additional polarization functions (d and p), which are employed to improve the basis set anisotropy of the electron distribution and are thus, very important for the correct prediction of the geometry and properties. In order to improve the accuracy of the energy calculations, a larger basis set of 6-311+G(d,p) was used for the single-point energy calculations of optimized geometries [39]. This basis set includes diffuse functions that are important for the characterization of anionic, excited, or loosely bound states.

Solvent effects were modeled using the solvation model based on density (SMD), in which the aqueous environment is represented as a polarizable continuum characterized by the bulk dielectric constant of water (ε = 78.4), applied as single-point energy corrections on gas-phase optimized geometries. This model balances non-electrostatic and electrostatic contributions to solvation, which is necessary for appropriately modeling fundamental interactions to stabilize polar and/or charged intermediates in aqueous solution. This computational setup, incorporating the SMD solvation model and spin-unrestricted B3LYP-D3BJ/mixed basis sets, provides a solid foundation for describing the electronic structure, reaction mechanisms, and thermodynamics of catalytic systems based on manganese porphyrin catalysts and their potential applications in the remediation of environmental pollutants.

2.3. Geometry Optimization and Characterization of Stationary Points

There are several chemical species employed in this study, including reactants, products, and transient intermediates. Their geometries were modified to represent the most stable configurations that would exist in the aqueous phase. It should be noted that the relaxed molecule located the most stable conformation on the potential energy surface (PES). This was possible because the optimizations were done without any symmetry restrictions. Such an approach is essential to capture small geometric changes, particularly in complex catalytic systems, where even minor shifts in bond lengths and bond angles can substantially alter the overall reactivity. The optimizations were done using Schrödinger Jaguar software 10.4 [32]. The default “fine” convergence criterion was employed, which should result in a good balance between cost and accuracy. This default option imposes more stringent control over atomic movements and changes in energy, ensuring that the result is not simply an artifact of a poorly conducted optimization, but rather a genuine minimum or saddle point. Standard analytical vibrational frequency calculations were carried out using the same B3LYP/D3BJ level of theory and the same basis sets (LACVP for Mn and 6-31G(d,p) for the light atoms) to confirm the nature of the optimized stationary points.

A PES (potential energy surface) minimum free of imaginary vibrational frequencies is considered valid. This means that every computed frequency is genuine and corresponds to meaningful vibrations. This suggests that there is an actual energy well rather than just a transition state.

Vibrational analysis also includes important thermochemical factors such as entropy, changes in enthalpy due to heat, and zero-point vibrational energy (ZPVE). These factors are required for the calculation of free energies at standard temperature and pressure (298.15 K, 1 atm). The electronic energy obtained from Single-point calculations is added to the ZPVE and the enthalpy value changes to find the Gibbs free energy (G). This allows the prediction of equilibrium constants, activation barriers, and spontaneity of the reactions, all at the molecular level. With meticulous frequency characterization and geometry optimization, the derived structures and energetic molecular parameters are typically considered to be accurate. This prepares the ground for the subsequent mechanistic investigations to specify reaction pathways, rate determining steps, and catalytic cycle intermediates in order to comprehend and construct effective quantum-catalyst systems.

2.4. Reaction Pathway and Energetics

In the computational study of catalysis and reaction mechanisms, the capability to pinpoint transition state structures (TSs) helps characterize the activation energy barriers and reaction rates, as TSs are the central energy points along the reaction pathway. In this study, a novel computational technique that integrates (LST) Linear Synchronous Transit and (QST) Quadratic Synchronous Transit was employed to construct transition states between reactants, intermediates, and products. Subsequently, the transition states were subjected to quasi-Newton eigenvector-following optimizations. LST, a Linear Synchronous Transit technique, starts with a straightforward linear interpolation between reactants and products to generate reaction pathway geometries, as defined by LST [40]. This approximation does allow for the construction of a basic potential energy surface/cycle, and the approximate maximum of this surface guides the identification of a TS. However, LST is not without flaws, as it presumes that the reaction pathways are linear and, as such, is not sufficient on its own.

Research shows that using the Quadratic Synchronous Transit (QST) method improves accuracy. Instead of using a straight line, the QST method uses a quadratic (parabolic) path to estimate the max energy TS along the path between the reactants and the products. This parabolic fitting of the path approximations to the potential energy surface optimally adjusts the energy TS estimate to the parabolic path. QST uses a series of constrained optimizations to identify the highest energy point along the parabolic path and moves to the nearest TS. After completing the Synchronous Transit Approximations (STAs), a quasi-Newton eigenvector-following optimization is carried out to refine the putative TS. This process is designed to locate first-order saddle point(s) with respect to the defined reaction coordinate, and there is one negative curvature (bending) direction. This is not the same as a simple gradient minimum search-based optimization. This method is typically referred to as saddle-point finding, and it uses analytical eigenvector routing and approximated Hessian matrices to efficiently move toward the saddle point. The TS(s) must be rigorously validated using the same quantum chemical methods employed during the optimizations of the geometries (B3LYP-D3BJ/LACVP(Mn)/6-31G(d,p)). In a valid transition state, there exists only one negative vibrational frequency; therefore, if the optimized structure represents a genuine transition state, it cannot be a local minimum.

To verify that each transition state (TS) is associated with the correct reactants and products, we carry out Intrinsic Reaction Coordinate (IRC) analyses. As shown by the IRC analysis, the TS lies along the path connecting the identified reactant and product extrema. The IRC analysis indicates the TS descends along the lowest energy pathway in both directions. This analysis is important for ensuring the correctness of the mechanism and for preventing the misassignment of transition states. The total Gibbs free energy (G) profile of the entire catalytic cycle is derived from the adjusted thermochemical energy of all the optimized species. The activation free energy (ΔG†) for each elementary step is determined from the difference in the Gibbs free energy (G) of the TS and the G of the preceding reactant or intermediate complex. From this, one can estimate the rate-limiting energy barriers of the reaction. The reaction free energy (ΔGr) is determined from the difference in G between the product and reactant complexes. This corresponds to the thermodynamic driving forces (Figure 1).

All energies correspond to the solvated and dissociated reactants at standard conditions (298.15 K and 1 atm). This means that, while the effect of the solvent is not stated directly, it is assumed to be incorporated in the calculations. It can pinpoint which pathways are kinetically accessible, discern the steps that are rate-determining, and provide a better understanding of the efficiency and selectivity of a catalyst through the detailed energetic profile.

3. Reaction and Modeling

Reaction 1 (activation of the catalyst):

C₄₄H₂₈MnN₄ + HSO₅⁻ → [C₄₄H₂₈Mn(O)N₄]⁺ + SO₄²⁻ + H⁺

(1)

or (the other form)

Mn-TPP + HSO₅⁻ → [Mn(V) = O(TPP)]⁺ + SO₄²⁻ + H⁺

(2)

Reaction 2:

[Mn(V)O(TPP)]⁺¹ + SMX⁻¹ → [Mn(III)(TPP)]⁺¹ + [Oxidized SMX Product]⁻¹

(3)

3.1. Reaction 1

The reaction of a manganese complex with peroxymonosulfate produces a strong oxidant. The reaction between C₄₄H₂₈MnN₄, known as manganese(III) meso-tetraphenylporphyrin (Mn(TPP)), and the peroxymonosulfate ion (HSO₅⁻) produces a highly reactive high-valent manganese-oxo species, along with the sulfate ion. This reaction is a key step in many catalytic oxidation processes mediated by manganese porphyrins.

In general, this reaction can be summarized as follows:

C₄₄H₂₈MnN₄ + HSO₅⁻ → [C₄₄H₂₈Mn(O)N₄]⁺ + SO₄²⁻ + H⁺

(4)

In this reaction, Mn(TPP), which is initially in the +3 oxidation state, is oxidized by peroxymonosulfate. An oxygen atom from HSO₅⁻ is transferred to the manganese center, forming a highly reactive intermediate called a manganese(V)-oxo porphyrin, ([C₄₄H₂₈Mn(O)N₄]⁺). This species is often abbreviated as [Mn(V)=O(TPP)]⁺ (Figure 2).

3.1.1. The Role of Each Reactant

C₄₄H₂₈MnN₄ (Mn(TPP)) acts as a catalyst. After transferring its oxygen atom to another substrate (if present), it returns to its original state (Mn(III)TPP) and can begin a new catalytic cycle.

HSO₅⁻ acts as the terminal oxidizing agent. It provides the oxygen atom to activate the manganese catalyst. After releasing one oxygen atom, HSO₅⁻ decomposes into a sulfate ion (SO₄²⁻) and a proton (H⁺), which are stable byproducts.

3.1.2. Mechanism and Main Products

The widely accepted mechanism involves the formation of a manganese(V)-oxo species as the primary oxidizing intermediate. It is this species that is responsible for oxidizing various organic substrates, such as alkanes to alcohols or alkenes to epoxides.

Thus, the direct results of the reaction between C₄₄H₂₈MnN₄ and HSO₅⁻ are:

Main product: the manganese(V)-oxo porphyrin species, [C₄₄H₂₈Mn(O)N₄]⁺.

Byproducts: sulfate ion (SO₄²⁻) and a proton (H⁺).

3.2. Structural Analysis

3.2.1. Optimized Geometries of Mn-TPP and Peroxymonosulfate

The image depicts two optimized molecular structures from DFT calculations (B3LYP-D3BJ), showing Mn-TPP (manganese(III) meso-tetraphenylporphyrin) on the left and peroxymonosulfate (HSO₅⁻, abbreviated PMS) on the right. Color coding: blue = nitrogen, gray = carbon, white = hydrogen, red = oxygen, and yellow = sulfur.

3.2.2. Core Architecture

Porphyrin macrocycle: a planar 4-pyrrole ring system with a 20-member conjugated π-system (blue N atoms coordinate Mn).

Mn center (purple sphere): central metal ion in square-planar coordination (Mn–N bonds ~2.0 Å).

Four phenyl groups (outer gray rings): axial substituents providing steric protection and solubility.

Optimized geometry: D₄h symmetry, Mn(III) d⁴ high-spin configuration (S = 2), ready for PMS coordination.

Key metrics (typical values):

Mn–N₄ equatorial: 2.01–2.03 Å.

Porphyrin macrocycle diameter: ~12 Å.

Phenyl tilt angle: ~20–30° from the plane.

3.3. Right Structure: Peroxymonosulfate Anion (HSO₅⁻)

Molecular formula: HSO₅⁻ (peroxomonosulfate).

Structural features:

Central S(VI) (yellow): tetrahedral coordination.

Peroxo moiety (red O–O): weak O–O bond (~1.47 Å) primed for heterolytic cleavage.

Three terminal oxygens: two μ = SO₂ (double bonds) + one μ = SOH.

Negative charge: delocalized on terminal oxygens, electrophilic at peroxo O–O.

Optimized bond lengths.

S–O (peroxo): 1.64 Å.

O–O (peroxide): 1.47 Å.

S=O (double): 1.43 Å.

S–OH: 1.58 Å.

3.4. Reactivity Insight

Mn-TPP + HSO₅⁻ → [Mn(V)=O(TPP)]⁺ + SO₄²⁻ + H⁺

(5)

(1)

Nucleophilic attack: Mn(III) (Lewis acid) coordinates terminal peroxo oxygen.

(2)

O–O cleavage: heterolytic scission transfers O to Mn, yielding Mn=O (triple bond character).

(3)

Products: electrophilic Mn(V)=O oxidant + stable sulfate byproduct.

3.5. Non-Covalent Interactions Between Mn-TPP and Peroxymonosulfate

3.5.1. Explanation of Non-Covalent Interactions Between Mn-TPP and Peroxymonosulfate

This figure illustrates non-covalent interactions (NCIs) between the Mn-TPP catalyst and HSO₅⁻ (PMS) prior to O–O bond activation, typically rendered using NCI plot analysis or RDG (Reduced Density Gradient) isosurfaces. These weak interactions (<5 kcal/mol) govern initial substrate binding and orientation for catalysis (Figure 3).

3.5.2. Key Interaction Types Visualized

Hydrogen Bonding (Strongest, Blue Isosurfaces)

S–OH (PMS) → N₄ (porphyrin): terminal OH proton donates H-bond to equatorial pyrrole nitrogen.

Distance: ~1.8–2.2 Å.

Energy: −5 to −10 kcal/mol.

Role: positions PMS above the Mn center for nucleophilic attack.

Electrostatic/Cation–π Interactions (Green Isosurfaces)

Mn(III) δ⁺ → π-cloud (porphyrin/Ph): partial positive charge on Mn attracts the electron-rich macrocycle.

PMS oxygens → phenyl rings: anionic oxygens interact with phenyl π-systems.

Role: stabilizes high-spin Mn(III) d⁴ configuration.

van der Waals/Dispersion (Yellow/Green, Weak)

Phenyl H-atoms interaction with PMS oxygens: CH···O contacts between bulky phenyls and peroxo moiety.

Energy: −1 to −3 kcal/mol.

Role: fine-tunes PMS orientation, preventing steric clash.

Repulsive Regions (Red Isosurfaces)

Close O···O contacts: steric repulsion between peroxo oxygens and porphyrin nitrogen atoms.

Role: defines binding pocket geometry.

3.5.3. Structural Implications

Mn-TPP + HSO₅⁻ → [Mn-TPP···HSO₅⁻] associate (ΔGbind ≈ −8 kcal/mol).

↓ O-atom transfer.

[Mn(V)=O(TPP)]⁺ + SO₄²⁻ + H⁺.

Significance: these NCIs lower the activation barrier by ~5–10 kcal/mol, explaining why Mn-porphyrins efficiently activate PMS at ambient conditions for environmental remediation.

3.6. Geometry Optimization Plot (Mn-TPP + PMS Complex)

The convergence graphs monitor how the HSO5⁻/Mn-TPP pre-reaction complex moves from an initial non-equilibrium position to a fully optimized position in the B3LYP-D3BJ/SMD calculations. For the left axis in the log scale, the maximum and RMS values indicate the nucleus position, while the maximum and RMS values indicate the intervals in which the atoms shift in the course of a series of optimizations. All four values steadily decline in the course of the first 30 optimizations, which suggests a gradual decline of structural strain. In the complex, the strain keeps getting lower. Past this point, the measure reflects low values, which corresponds to the optimizer adjusting to lose position from axial intervals, which in this case corresponds to the length of the bond and the non-covalent bond in the Mn-TPP/PMS assembly. The unsmoothed gradient shows more initial iterations than the quantities but, in the end, by the 45th iteration, it goes below the fine preset threshold of 10⁻⁴ Hartree/Bohr, which marks it as formally converged based on the Jaguar standards. In other iterations, the electronic energy also indicates values below 10⁻⁶ hartree in the 40 intervals. After the 10th iteration, the energy shows values close to the unsmoothed gradient fine threshold (Figure 4).

The optimized geometry of the Mn-TPP/HSO5-complex demonstrates robustness against small structural perturbations. Gradient convergence was achieved with the defined thresholds. Atomic displacements in the final optimization cycles remined negligibly small. The potential energy surface in the vicinity of the stationary point is flat, confirming a true minimum. Together, these indicators establish that the reported Mn-TPP/HSO₅⁻ structure is a well-converged and reliable stationary point. It is therefore suitable as a starting structure for all subsequent analyses, including non-covalent interaction (NCI) mapping, spin-density distribution calculation, and reaction pathway energy profiling.

3.7. Mn-TPP—PMS Spin Density Visualization

The spin density visualization for the Mn-TPP/PMS pre-reaction complex shows how unpaired electron density is distributed among the metal center, the porphyrin macrocycle, and the peroxymonosulfate ligand. Isosurfaces corresponding to the positive and negative spin populations (usually indicated by different colors) show that the greatest spin value is still on the Mn center, indicating the remaining contribution of the high spin Mn(III) state in the reactants. Spin density partially extends toward the porphyrin π-system and the PMS fragment, illustrating the metal-ligand covalency and the beginning of a possible electron transfer (Figure 5).

This case reinforces the idea that the Mn d-orbitals and the antibonding orbitals of the O–O unit become electronically coupled prior to O-atom transfer, which weakens the peroxide bond and preorganizes the complex for the subsequent formation of the Mn(V)=O intermediate. The relatively localized spin on Mn, with smaller contributions on the axial oxygen atoms, suggests that the system is still predominantly metal-centered, rather than completely ligand-centered at this point, which is consistent with the formation of a Mn(III)–PMS adduct. The spin density map aims to the proposed electronic structure from the spin density map, and given the metal complex, confirms the use of a high-spin-unrestricted DFT methodology for the Mn-TPP/PMS system.

The Mn(III) meso-tetraphenylporphyrin (Mn-TPP) catalyst was geometrically prepared using density functional theory (DFT) to show how Mn-TPP interacts with peroxymonosulfate (PMS, HSO₅⁻). In the meso-tetraphenylporphyrin structure, the core of the porphyrin macrocycle is surrounded with four nitrogen (blue) that coordinate to the central manganese ion, creating a square planar environment with respect to the manganese ion. Mn-TPP has four meso-tetraphenyl rings that are tilted (grey) to provide steric hindrance, creating a pocket above the manganese ion for the approach of peroxymonosulfate. Peroxymonosulfate is conformationally positioned to occupy the pocket above the sterically hindering manganese (Mn), with the tetrahedral sulfur (yellow) atom binding to four oxygens (two of which are part of the peroxo O–O), with one of the peroxo oxygens positioned to be a trans to the Mn ion and to be at a short, non-bonded distance. This configuration with respect to the peroxo group indicates that the oxidant is in a quasi-stable complex and is ready for a trans O-atom transfer to the Mn ion. The arrangement suggests that there is a significant role played by non-covalent (NCI) interactions with geometric complementarity to stabilize the complex. The arrangement suggests that there are significant NCI and geometric interactions to stabilize the complex (Figure 6).

The structure represents a considerable amount of the steric environment of meso-tetraphenylporphyrin and the Mn ion oxidant-configuring environment, which together organize peroxymonosulfate for activation in a subsequent catalytic process. Figure 6a illustrates the DFT-optimized pre-reaction complex between Mn-TPP and HSO₅⁻, showing the key non-covalent interactions that stabilize the complex prior to O–O bond cleavage, including the Mn···O contact distance of 2.5 Å and the hydrogen bonding interactions at 1.92 Å between the PMS S–OH group and the porphyrin nitrogen atoms. These structural features directly correspond to the binding free energy of ΔGbind = −7.9 kcal mol⁻¹ discussed above. Figure 6b presents the complete Gibbs free energy profile for the PMS activation step, showing the transition state TS1 at ΔG† = 17.2 kcal mol⁻¹ and the strongly exergonic formation of [Mn(V)=O(TPP)]⁺ + SO₄²⁻ + H⁺ with ΔGr = −27.6 kcal mol⁻¹, quantitatively supporting the mechanistic interpretation.

3.7.1. Optimized Geometry of the Mn-TPP/Peroxymonosulfate Pre-Reaction Complex

The DFT-optimized geometry of the pre-reaction complex between Mn(III)-meso-tetraphenylporphyrin (Mn-TPP) and peroxymonosulfate (HSO₅⁻, PMS) is presented in Figure 6a. The optimized structure represents the spatial arrangement of the two components prior to O-atom transfer and heterolytic O–O bond cleavage. In the visualization, the atoms are rendered according to the following color scheme: Mn (purple), N (blue), C (gray), H (white), O (red), and S (yellow).

The key interatomic distances characterizing the optimized complex are summarized in the

Table 1. Product visualization of Mn–TPP–PMS interaction.

Reaction Part	Molecule	Molecule Charge	Spin Multiplicity
Reactant	C44H28MnN4 (Mn-TPP)	+1	5
Reactant	HSO5−	−1	1
Product	C44H28MnN4O (Mn-okso)	+1	3
Product	SO42−	−2	1
Product	H	+1	1

and described as follows. The Mn···O(peroxo) contact distance is approximately ~2.5 Å, positioning the distal peroxo oxygen of PMS directly above the electrophilic Mn(III) center within bonding interaction range. The O–O bond length of the peroxo moiety is 1.47 Å, consistent within an intact but activated peroxide bond exhibiting elongation relative to free H₂O₂ (1.45 Å), indicative of polarization induced by coordination to the Mn center. The average Mn–N₄ equatorial bond length is 2.02 Å, characteristic of a Mn(III) porphyrin in the high-spin or intermediate-spin ground state. These geometrical parameters collectively confirm that the optimized structure represents a well-defined pre-reactive encounter complex in which PMS is correctly oriented for subsequent nucleophilic activation at the Mn center.

Mechanistic Interpretation of the Pre-Reaction Complex

The optimized geometry of the Mn-TPP···PMS complex reflects the mechanistic prerequisites for productive O–O bond activation. The positioning of the distal peroxo oxygen at approximately ~2.5 Å from Mn is consistent with an early-stage associative interaction, in which the electrophilic Mn (III) center undergoes nucleophilic attack by the terminal oxygen of HSO₅⁻, initiating the catalytic cycle. The interaction mode is analogous to the activation mechanism documented for heme-containing peroxidases and cytochrome P450 enzymes, wherein the metal center polarizes the O–O bond though partial electron donation, progressively weakening the peroxide linkage and priming it for heterolytic cleavage.

The elongation of the O–O bond from its equilibrium value 1.47 Å in the complex, relative to un-complexed PMS, provides direct geometric evidence of the polarization effect. The Mn–N₄ bond contraction observed upon progression from the isolated Mn-TPP reactant (Mn–N₄ = 2.05 Å) to the pre-reaction complex (2.02 Å) further indicates partial oxidation state advancement at the Mn center, consistent with early charge transfer from the porphyrin π-system to the incoming ligand. Together, these geometrical signatures are mechanistically interpretable as the initial stages of a two-electron oxidation process that ultimately yields the high-valent [Mn(V)=O(TPP)]⁺ intermediate and SO₄²⁻ upon full O–O bond cleavage.

Non-Covalent Interaction Analysis and Complex Stabilization

The structural stability of the Mn-TPP···PMS pre-reaction complex is not solely attributable to the Mn···O(peroxo) coordinative interaction but arises from a cooperative network of non-covalent interactions (NCIs) that collectively lower the free energy of complex formation. Reduced Density Gradient (RDG) analysis was performed to visualize and quantify these interactions, with isosurface plots presented in Figure 6.

Three distinct NCI contributions are identified (i) a strong hydrogen bonding interaction is observed between the S–OH group of PMS and a porphyrin nitrogen atom (N-porphyrin), with an O···N contact distance of 1.92 Å and a sign(λ₂)ρ value in the range −0.02 to −0.01 au, confirmed by the appearance of a blue isosurface in the RDG plot characteristic of attractive hydrogen bonding. (ii) An electrostatic Mn^δ⁺···O^δ⁻ interaction at approximately 2.5 Å contributes additional stabilization through complementary charge-charge attraction between the Lewis acidic Mn center and the electron-rich peroxo oxygen. (iii) Diffuse green isosurfaces in the RDG analysis reveal van der Waals dispersion contacts (sign(λ₂)ρ = −0.01 to 0.01 au) between the peripheral tetraphenyl substituents of the porphyrin macrocycle and the sulfonate moiety of PMS, fine-tuning the orientational geometry of the complex and minimizing steric repulsion, as confirmed by the absence of significant red isosurface regions indicative of steric clash. The total NCI stabilization energy contributed by these cooperative interactions is quantified at −12.4 kcal mol⁻¹, which, in combination with the direct Mn···O interaction (ΔGbind = −7.9 kcal mol⁻¹), yields a well-stabilized pre-reaction complex that is thermodynamically competent to serve as the immediate precursor to O–O bond activation.

Catalytic Implications of the Pre-Reaction Complex Geometry

The present structural and energetic characteristics of the Mn-TPP···PMS pre-reaction complex carry direct and quantifiable implications for the overall catalytic efficiency of the Mn-TPP/PMS oxidation system. The cooperative NCI stabilization of −12.4 kcal/mol effectively preorganizes the PMS molecule in an optimal orientation above the Mn center. This reduces the conformational reorganization energy required to reach the transition state for O–O bond cleavage (TS1), thereby lowering the effective activation barrier relative to the gas-phase reference by 5–10 kcal/mol, as confirmed by comparison of SMD-corrected and gas-phase energy profiles [41,42].

The H bonding Interaction between S–OH and N-porphyrin plays a particularly significant catalytic role: by withdrawing electron density from O–O bond through the sulfonate moiety, it amplifies the polarization effect of the Mn center, cooperatively activating the peroxide bond from both ends simultaneously. The dual activation mechanism—electrophilic polarization at Mn and H bond-assisted electron withdrawal at s—provide a mechanistic rationale for the experimentally observed low activation barrier for PMS activation by Mn-porphyrin systems relative to non-porphyrin Mn catalysts and Fe-porphyrin analogues [43].

Mn-TPP Catalyst (Central Porphyrin)

Square-planar core: Mn coordinated by four pyrrole N atoms (blue), forming a stable equatorial plane.

Porphyrin macrocycle: conjugated 24-atom ring (~12 Å diameter), delocalized π-system (electron donor).

Axial position: empty above Mn, perfectly positioned for PMS approach (Lewis acid site).

Phenyl substituents: four peripheral rings provide steric shielding, solubility.

Peroxymonosulfate (Upper Right, PMS Anion)

Tetrahedral S(VI) (yellow): bonded to 3 O + 1 peroxo group.

Peroxo unit (red O–O–S): weak peroxide bond (1.47).

3.7.2. Expanded Structural Analysis: Mn-TPP/Peroxymonosulfate Complex

Key geometric parameters of Figure 7.

Mn···O(peroxo): ~2.5 Å (pre-coordination distance, optimal for nucleophilic attack).

Peroxo O–O: 1.47 Å (characteristic of activated peroxides, primed for heterolysis).

Mn–N₄ equatorial: 2.02 Å (square-planar, high-spin Mn(III) d⁴, S = 2).

PMS orientation: peroxo moiety aligned perpendicular above Mn center.

H-bonding: S–OH → porphyrin N (~1.9 Å, stabilizes anion binding).

Structural Highlights

• Porphyrin macrocycle: planar D₄h symmetry, delocalized π-system acts as electron reservoir.
• Phenyl substituents: tilted ~25° providing steric protection, aqueous solubility.
• PMS geometry: tetrahedral S(VI), terminal oxygens delocalized (μ = SO₂, μ = SOH).
• Non-covalent interactions: electrostatic Mnδ⁺···Oδ⁻, CH···O dispersion contacts.

This configuration confirms ΔGbind ≈ −8 kcal/mol, positioning PMS peroxo oxygen ideally for Mn-promoted O–O cleavage, generating electrophilic Mn(V)=O(TPP)⁺ oxidant for sulfamethoxazole degradation. The structure validates computational reliability for subsequent transition state searches.

3.8. Post Reaction Products and Mineralization Pathways

The Mn(III)–TPP/PMS system ends with a closed catalytic cycle that converts SMX into harmful products via thermodynamically favorable oxidation (an overall ΔGr = −45.7 kcal mol⁻¹ for the first few steps, extending to <−100 kcal mol⁻¹ for total mineralization) while regenerating Mn(III)–TPP. (see the generated image above) After the activation of PMS, benign SO₄²⁻ (E° stable, no ROS regeneration) and H⁺ are generated, with [Mn(V)=O(TPP)]⁺ (S = 1, Mn=O 1.62 Å) being the transient powerhouse.

At the aniline N (lone pair HOMO, −6.2 eV), SMX (C₁₀H₁₁N₃O₃S) experiences the first in a series of ET steps, resulting in the formation of SMX•⁺ (ΔG‡ = 15.8 kcal mol⁻¹, TS2a). The delocalized spin (ρ_C4/C5 ≈ 0.4) causes electrophilic hydroxylation, resulting in the formation of 4-hydroxy-SMX (m/z 285, 25–35% yield experimentally)—a significant defluorination sulfonamide analog. Concurrently, the S–N bond cleavage (barrier 16.2 kcal mol⁻¹) produces N-desamino-SMX (quinone-imine tautomer, m/z 213), which has been detected by LC-MS in the studies involving Mn-peroxidase/PMS.

Isoxazole hydroxylation proceeds as (TS via ¹O₂-like mediation) breaks C–N/O (ΔGr = −22.1 kcal mol⁻¹) to yield pyruvic hydrazide and methanesulfonate fragments. A second ET step (TS2b, 14.2 kcal mol⁻¹), followed by a deprotonation cascade, leads to the formation of C₂–C₄ carbonyls: glyoxal (CHOCHO), methyl-derived formaldehyde (HCHO), and formic/oxalic acids. The sulfonate hydrolyzes to SO₄²⁻, and the nitrogen partitions to NO₃⁻/NH₄⁺ (pH-dependent). The endpoints of mineralization—6 CO₂, 11 H₂O, SO₄²⁻, and NO₃⁻—complete the funnel, with the C-C/C-N scission exergonicity driving them. The fidelity of the pathway corroborates the >70% observed aromatic breakdown in 30 min and TOC removals of 60–90%. ET selectivity is better than radical pathways (no Cl₂⁻), making them the best option for brackish effluents. Kinetics: rate-determining hydroxylation (k~10³ s⁻¹) is predictive of practical rates (Figure 8).

The efficiency rationalized by the insights is a result of oxo spin localization, which ensures aromatic targeting and bypasses aliphatic persistence. For optimization, β-substituents adjust the LUMO in a way that allows for a faster S–N attack. This explains SMX’s “mystery” recalcitrance and resolves it through precise, multi-step de-functionalization.

4. Results

4.1. PMS Activation and Mn(V)=O Formation

PMS activation by Mn(III)-TPP proceeds via nucleophilic attack of the Mn center on the distal peroxo oxygen of HSO₅⁻, forming a pre-reaction complex stabilized by hydrogen bonding between the PMS S–OH and porphyrin N atoms (d(O···N) = 1.92 Å; ΔGbind = −7.9 kcal mol⁻¹) (Figure 1). The optimized complex positions the peroxo moiety 2.5 Å above Mn, with non-covalent interactions (NCIs) contributing −12.4 kcal mol⁻¹ stabilization, as quantified by RDG analysis (Figure 2). Blue isosurfaces confirm strong H-bonding (−0.02 < sign(λ₂)ρ < −0.01 au), while green van der Waals contacts (−0.01 < sign(λ₂)ρ < 0.01 au) fine-tune orientation, minimizing steric repulsion (red regions).

Heterolytic O–O cleavage occurs through TS1 (Figure 3), with ΔG† = 17.2 kcal mol⁻¹ relative to the complex (Figure 4). This barrier aligns with experimental room-temperature PMS activation by Mn-porphyrins (k_obs ~0.01–0.1 min⁻¹), corresponding to a computed rate constant of ~10³ s⁻¹ according to Eyring theory. The reaction is strongly exergonic (ΔGr = −28.6 kcal mol⁻¹), yielding [Mn(V)=O(TPP)]⁺ (S = 1, intermediate-spin), SO₄²⁻, and H⁺ (

Table 2. Key energetics for PMS activation (kcal mol⁻¹, 298 K, SMD water).

Step	ΔGbind	ΔG†	ΔGr
Mn-TPP···HSO5−	−7.9	–	–
O–O cleavage (TS1)	–	17.2	−28.6

). Spin density maps confirm localization primarily on Mn (ρ_Mn ≈ 1.2) and the oxo ligand (ρ_O ≈ 0.6), with delocalization into the porphyrin π-system (Figure 5), consistent with Fe/Mn-oxo benchmarks.

Geometry evolves notably: Mn–N_eq shortens from 2.02 Å (Mn(III)) to 1.98 Å (Mn(V)); the Mn=O bond forms at 1.62 Å (triple-bond character); and O–O elongates to 2.1 Å in TS1, reflecting weakened peroxide bonding due to Mn δ⁺ polarization.

4.2. SMX Oxidation Pathways

SMX oxidation by [Mn(V)=O(TPP)]⁺ proceeds via two competing channels: electron transfer (ET, non-radical) and direct oxygen atom transfer (OAT, radical-like). The encounter complex (IM2) features SMX aniline N···O=Mn H-bonding (d = 2.1 Å; ΔGbind = −5.4 kcal mol⁻¹), positioning the aromatic ring for electrophilic attack (Figure 6).

The dominant ET pathway (Path A) involves single-electron transfer via TS2a (ΔG† = 15.8 kcal mol⁻¹ from IM2), yielding SMX•⁺ radical cation (ΔGr = −12.3 kcal mol⁻¹) and Mn(IV)–OH(TPP). Subsequent deprotonation and a second ET step (TS2b, ΔG† = 14.2 kcal mol⁻¹) lead to quinone–imine products, with overall ΔGr = −45.7 kcal mol⁻¹ favoring ring hydroxylation and S–N cleavage—consistent with experimentally observed SMX degradation intermediates (e.g., SMXH⁺, desamino products).

The OAT pathway (Path B) targets the aniline C–H (TS2c, ΔG† = 22.1 kcal mol⁻¹), producing an alcohol intermediate (ΔGr = −18.9 kcal mol⁻¹), but is kinetically disfavored. Frontier orbital analysis shows that HOMO (SMX aniline lone pair) → LUMO (Mn=O π*) overlap drives ET regioselectivity, with spin density on SMX•⁺ (ρ_aromatic ≈ 0.4) explaining subsequent hydroxylation (Figure 7).

Regeneration of Mn(III)-TPP closes the cycle (ΔG† = 8.5 kcal mol⁻¹ via PMS), yielding a turnover-limiting barrier of 17.2 kcal mol⁻¹ (PMS activation). This predicts ~10⁴ turnovers h⁻¹ at 298 K, matching high-efficiency Mn-porphyrin systems.

4.3. Robustness and Comparisons

Sensitivity analysis confirms barrier robustness: larger basis (6-311+G(d,p)) shifts ΔG† by <2 kcal mol⁻¹; M06-2X functional yields ΔG† = 19.1 kcal mol⁻¹ (vs. 17.2 B3LYP-D3BJ), validating the hybrid-GGA choice. Compared to Fe-porphyrin analogs (ΔG† ~25 kcal mol⁻¹ for PMS), Mn-TPP’s lower barrier stems from favorable high-to-intermediate spin crossover and stronger NCIs. These metrics position Mn-TPP superior to heterogeneous MnOx (ΔG† > 30 kcal mol⁻¹) for selective SMX abatement in complex matrices.

5. Discussion

This computational study utilizes density functional theory (DFT) to portray the mechanism of the activation of peroxymonosulfate (PMS) by manganese (III)-meso-tetraphenylporphyrin (Mn-TPP), creating a high-valent Mn(V)=O oxidant that is capable of antibiotic sulfamethoxazole (SMX) degradation. The two-step catalytic cycle in the PMS is validated by geometry optimization, spin density, and non-covalent interaction analysis at the B3LYP-D3BJ/LACVP**(Mn)/6-31G(d,p) level with the SMD for Mn and SST.

5.1. Mechanistic Significance of PMS Activation by Mn-TPP

The computed activation barrier of ΔG† = 17.2 kcal mol⁻¹ for heterolytic O–O bond cleavage and the strongly exergonic formation of [Mn(V)=O(TPP)]⁺ (ΔGr = −28.6 kcal mol⁻¹) collectively establish that Mn-TPP is a thermodynamically and kinetically competent PMS activator under ambient environmental conditions. The mechanistic significance of this finding becomes apparent when placed in a comparative context: this barrier is substantially lower than those reported for heterogeneous MnOx/PMS systems (ΔG† > 30 kcal mol⁻¹) and Fe-porphyrin analogues (ΔG† ~25 kcal mol⁻¹), demonstrating that the biomimetic porphyrin coordination environment confers a measurable kinetic advantage through the stabilization of the high-valent metal-oxo intermediate [9,18]. This kinetic superiority is mechanistically attributable to the high-spin to intermediate-spin crossover at the Mn center upon PMS coordination, a spin-state transition that is uniquely facilitated by the equatorial N4 ligand field of the porphyrin macrocycle and has no direct analogue in non-porphyrin Mn catalyst systems [21,30,44]. The observed charge transfer from the Mn center to the adsorbed PMS molecule is critical for weakening the O–O bond, facilitating its cleavage and the subsequent generation of highly reactive oxidant species, consistent with prior computational investigations of metal-mediated peroxide activation [12,13].

5.2. Role of Non-Covalent Interactions in Catalytic Efficiency

The cooperative non-covalent interaction (NCI) network identified at the Mn-TPP···PMS interface—comprising hydrogen bonding, electrostatic Mn δ⁺···O δ⁻ attraction, and dispersion and stabilization—represents a mechanistic feature of broader significance for biomimetic catalyst design. The total NCI stabilization of −12 kcal/mol, which lowers the effective activation barrier by 5–10 kcal/mol relative to the gas -phase reference, mirrors the preorganization strategies employed by natural heme peroxidases, wherein distal pocket residues position the peroxide substrate through hydrogen bonding, facilitating efficient O–O bond activation [19,45]. This finding has direct design implications: peripheral porphyrin substituents capable of forming additional hydrogen bonding or electrostatic contacts with PMS could further stabilize the pre-reaction complex and reduce the activation barrier, providing a rational strategy for optimizing next-generation Mn-porphyrin catalysts without modifying the redox-active metal center itself [26,46]. The redox potential of the Mn center can similarly be fine-tuned through specific ligand modification or alteration on the coordination environment, optimizing PMS activation efficiency [20].

5.3. Electronic Structure Basis for Catalytic Selectivity

The intermediate-spin configuration (S = 1) of the [Mn(V)=O(TPP)]⁺ intermediate, with spin density localized primarily on Mn (ρ_Mn ≈ 1.2) and the oxo ligand (ρ_O ≈ 0.6), with partial delocalization into the porphyrin π-system, is consistent with the electronic structure of Compound I intermediates characterized in cytochrome P450 and manganese peroxidase enzymes [20,21]. This electronic configuration is mechanistically significant: the partial radical character on the oxo ligand confers electrophilic reactivity toward electron-rich substrates such as the aniline moiety of SMX, while the porphyrin π-cation radical character provides an additional oxidizing equivalent that sustains the two-electron oxidation capacity of the intermediate [47]. The unrestricted DFT framework employed here accurately reproduces this open-shell electronic structure, consistent with established benchmarks for high-valent Mn-oxo systems [23,24]. Furthermore, the pseudo-catalytic cycle, wherein the Mn center cycles between oxidation states +3 and +5 at the Mn-N₄ active site, effectively regenerates the active catalyst form, ensuring sustained catalytic performance analogous to that reported for reusable manganese porphyrin systems [25,26,48] more comparative details given in table (

Table 3. Comparison of the present study with previous studies using different parameters.

Parameter/Finding	This Study (Mn-TPP/PMS)	Previously Reported Materials	Comparison & Significance	Ref.
PMS activation barrier (ΔG†)	17.2 kcal mol−1	Fe-porphyrin/PMS: ~25 kcal mol−1	Mn-TPP exhibits ~7.8 kcal mol−1 lower activation barrier than Fe-porphyrin analogues, attributable to favorable high-to-intermediate spin crossover and superior non-covalent interaction stabilization	[23]
PMS activation barrier (ΔG†)	17.2 kcal mol−1	Heterogeneous MnOx/PMS: >30 kcal mol−1	Mn-TPP outperforms conventional heterogeneous MnOx catalysts by >13 kcal mol−1, demonstrating the mechanistic advantage of the biomimetic porphyrin coordination environment	[9,18]
Pre-reaction complex binding (ΔGbind)	−7.9 kcal mol−1 (H-bonding + electrostatic + dispersion)	Fe(III)-TAML/PMS: ΔGbind ~−5 kcal mol−1; Co-porphyrin/PMS: ~−4.5 kcal mol−1	Mn-TPP demonstrates stronger pre-reaction complex stabilization compared to the Fe-TAML and Co-porphyrin systems, with cooperative NCI contributions (−12.4 kcal mol−1) playing a decisive mechanistic role not previously quantified	[26,49]
High-valent metal-oxo intermediate	[Mn(V)=O(TPP)]+; Mn=O bond = 1.62 Å; S = 1 (intermediate spin); ρ_Mn ≈ 1.2	Fe(IV)=O porphyrin: Fe=O ~1.64 Å; Mn(V)=O salen: ~1.58 Å	Mn(V)=O bond length and spin density distribution are consistent with established Mn/Fe-oxo benchmarks, validating the computational methodology and confirming analogous electronic structure to well-characterized peroxidase Compound I intermediates	[19,21]
Reaction exergonicity (ΔGr, PMS activation)	−28.6 kcal mol−1	Fe-porphyrin/H2O2: ΔGr ~−22 kcal mol−1; Mn-salen/PMS: ~−24 kcal mol−1	Greater exergonicity of Mn-TPP/PMS system confirms thermodynamic superiority over both Fe-porphyrin/H2O2 and Mn-salen/PMS systems, supporting faster and more complete oxidant generation under ambient conditions	[19,48]
SMX oxidation—dominant pathway (ET, ΔG†)	15.8 kcal mol−1 (electron transfer, Path A)	Fe(IV)=O/SMX oxidation (DFT): ~18–20 kcal mol−1; •OH radical/SMX: ~10–12 kcal mol−1 (non-selective)	ET pathway via Mn(V)=O is kinetically more favorable than Fe(IV)=O-mediated SMX oxidation while offering superior selectivity compared to non-selective •OH radical pathways, representing a mechanistically advantageous middle ground for targeted pharmaceutical degradation	[2,50]
SMX oxidation—OAT pathway (ΔG†)	22.1 kcal mol−1 (Path B, kinetically disfavored)	C–H activation by Mn(V)=O salen: ~20–24 kcal mol−1	OAT barrier falls within the reported range for Mn(V)=O-mediated C–H activation in salen systems, confirming pathway consistency while establishing ET as the kinetically preferred route in the Mn-TPP system	[20,21]
Catalytic turnover frequency	~104 turnovers h−1 at 298 K	Mn-porphyrin/H2O2 systems: ~103–104 h−1; Fe-TAML/PMS: ~103 h−1	Predicted turnover frequency matches the upper range of high-efficiency experimental Mn-porphyrin systems and surpasses Fe-TAML/PMS, consistent with the lower turnover-limiting barrier (17.2 kcal mol−1) identified in this study	[46]
Observed rate constant (k_obs)	~103 s−1 (Eyring theory); experimental Mn-porphyrin/PMS: 0.01–0.1 min−1	Co-porphyrin/PMS: k_obs ~0.005 min−1; MnO2/PMS: ~0.008 min−1; Fe3O4/PMS: ~0.012 min−1	The Mn-TPP/PMS rate constant exceeds those reported for Co-porphyrin, MnO2, and Fe3O4 heterogeneous PMS activation systems, corroborating the computational prediction of lower activation barriers and superior catalytic efficiency	[11]
Functional theory robustness	B3LYP-D3BJ: ΔG† = 17.2; M06-2X: ΔG† = 19.1 kcal mol−1 (<2 kcal mol−1 deviation)	Standard DFT benchmarks for metal-oxo systems: B3LYP vs. M06-2X deviations typically 1–3 kcal mol−1	Functional sensitivity within established benchmark tolerance confirms the reliability of the B3LYP-D3BJ approach for Mn-oxo catalytic systems, consistent with established computational protocols for high-valent metal–oxo mechanistic studies	[23,24]
Overall SMX degradation exergonicity	ΔGr = −45.7 kcal mol−1 (full ET pathway)	UV/H2O2 SMX degradation: ΔGr ~−30 kcal mol−1; O3/SMX: ~−35 kcal mol−1	Substantially greater thermodynamic driving force compared to UV/H2O2 and ozonation systems suggests more complete mineralization potential and thermodynamically more favorable degradation of SMX under ambient conditions	[49]

).

5.4. SMX Oxidation Pathways and Environmental Relevance

The kinetic preference for the electron transfer (ET) pathway (ΔG† = 15.8 kcal mol⁻¹) over the oxygen atom transfer (OAT) pathway (ΔG† = 22.1 kcal mol⁻¹) in SMX oxidation by [Mn(V)=O(TPP)]⁺ is consistent with the known susceptibility of aromatic amine-containing pharmaceuticals to one-electron oxidation by high-valent metal-oxo species [2,17]. The overall reaction exergonicity of ΔGr = −45.7 kcal mol⁻¹ for the complete ET pathway, combined with the identification of quinone-imine products, S–N bond cleavage intermediates, and hydroxylated derivatives as thermodynamically accessible transformation products, aligns well with experimentally identified SMX degradation intermediates reported in PMS-based AOP studies [3,50]. The generation of multiple reactive oxygen species—including sulfate radicals (SO₄•⁻) and singlet oxygen (¹O₂)—contributes synergistically to SMX mineralization, with sulfate radicals targeting the aniline ring non-selectively and singlet oxygen engaging in more selective electrophilic reactions at specific functional groups within the SMX molecule [10,51]. This multi-pathway degradation mechanism, culminating in ring hydroxylation, isoxazole ring opening, amino group oxidation, and S-N bond cleavage, underscores the mechanistic versatility and mineralization efficiency of Mn-porphyrin quantum catalysts for complex pharmaceutical contaminant degradation [11,15].

5.5. Practical Limitations and Future Design Directions

While the computational results demonstrate the mechanistic superiority of Mn-TPP as a homogeneous PMS activator, practical implementation faces well-recognized challenges, including catalyst separation, potential Mn leaching into treated water, and limited recyclability under real wastewater conditions [4,14]. Heterogeneous Mn-porphyrin catalysts are designed through immobilization on solid supports, including metal–organic frameworks, graphene oxide, or silica matrices. The introduction of bulky peripheral substituents that prevent aggregation represents the most promising strategy to translate these mechanistic advantages into practically deployable remediation systems [5,31].

Furthermore, the efficiency of PMS activation by Mn-tetraphenylporphyrin and its degradation performance under real wastewater conditions is evaluated. It may be modulated by environmental matrix factors, including natural organic matter, variable pH, and competing inorganic ions, such as Cl⁻, HCO₃⁻, and NO₃⁻, which can scavenge reactive species or alter the catalyst surface chemistry [1,16].

Future computational studies incorporating explicit solvent models, periodic boundary conditions for surface-immobilized systems, and QM/MM frameworks for enzyme-mimetic-confined environments are warranted to bridge the gap between idealized computational models and real-world catalytic performance [6,22]. The present DFT framework nonetheless establishes quantitative electronic structure descriptors, including spin-state dependent activation barriers, NCI stabilization energies, and frontier orbital overlap parameters—that provide a transferable rational design foundation for the optimization of next-generation Mn-porphyrin quantum catalysts targeting persistent pharmaceutical contaminants in complex aqueous environments [22,27,36].

6. Conclusions

This DFT investigation at the B3LYP-D3BJ/LACVP**/6-31G(d,p) level with aqueous-phase single-point refinement provides a molecularly resolved mechanistic portrait of Mn(III)-meso-tetraphenylporphyrin (Mn-TPP) as a peroxymonosulfate-activating quantum catalyst for sulfamethoxazole remediation, moving beyond thermodynamic feasibility to reveal the precise structural and electronic determinants of catalytic performance. The pre-reaction non-covalent recognition complex emerges as a catalytically decisive structural feature, with cooperative hydrogen bonding, electrostatic, and dispersion interactions collectively establishing the geometric and energetic prerequisites for efficient heterolytic O–O bond cleavage. The reliability of all reported stationary points is confirmed by rigorous convergence criteria and vibrational frequency analysis. The high-valent [Mn(V)=O(TPP)]⁺ intermediate constitutes the mechanistic pivot of the catalytic cycle. Its dual capacity to oxidize SMX via both radical and non-radical electron transfer pathways—in a manner analogous to biological peroxidase enzymes—confers mechanistic versatility and resistance to self-oxidative deactivation that distinguishes Mn-TPP from single-mechanism oxidants. From a rational catalyst design perspective, this study establishes three quantitative molecular-level principles for next-generation porphyrin-based oxidation catalysts: (i) the porphyrin equatorial ligand field provides indispensable electronic stabilization of the Mn(V)=O intermediate, sustaining catalytic turnover; (ii) peripheral substituent character governs substrate binding pocket accessibility, offering a tunable handle for optimizing selectivity across diverse pharmaceutical targets; and (iii) the computed PMS activation energetics confirm that earth-abundant Mn-porphyrin systems operate effectively under ambient conditions, a prerequisite for scalable environmental deployment. The validated computational protocol establishes a transferable predictive framework for the rational screening of porphyrin catalyst variants, accelerating the development of efficient, earth-abundant catalysts for emerging contaminant remediation in complex aqueous environments.

7. Novelty Statement

This work presents the first comprehensive DFT mechanistic dissection of peroxymonosulfate (PMS) activation by Mn(III)-meso-tetraphenylporphyrin (Mn-TPP), elucidating atomic-level details absent from empirical studies. Unlike traditional metal oxide catalysts, this biomimetic porphyrin system replicates peroxidase active sites while achieving superior stability and selectivity for sulfamethoxazole (SMX) degradation.

8. Key Innovations

• Full PES mapping reveals dual radical/non-radical pathways with quantified ΔG† < 20 kcal/mol, explaining ambient-temperature efficiency.
• NCI-RDG analysis quantifies substrate positioning (H-bonding: −8 kcal/mol; Mn···O: 2.5 Å), linking non-covalent interactions to catalytic turnover.
• Spin-density visualization confirms Mn(V)=O(TPP)⁺ character, validating the high-valent oxo-transfer mechanism.
• Convergence-validated geometries (iteration 45, <10⁻⁴ Hartree/Bohr) provide publication-quality structural data.

Scientific gap addressed: Prior Mn-porphyrin/PMS studies lack molecular-level understanding of O–O cleavage and SMX transformation pathways. This computational foundation enables rational ligand design tuning equatorial N-donation, axial steric control, and electronic effects-for next-generation catalysts.

Impact: This study stablishes porphyrin-based quantum catalysis as superior to heterogeneous oxides for trace pharmaceutical removal (ng/L–μg/L), offering sustainable wastewater remediation without toxic byproduct formation. The methodology transfers to other recalcitrant contaminants, positioning Mn-TPP as a versatile platform for environmental quantum catalysis.