Columnar Aggregates of Azobenzene Stars: Exploring Intermolecular Interactions,Structure, and Stability in Atomistic Simulations

We present a simulation study of supramolecular aggregates formed by three-arm azobenzene (Azo) stars with a benzene-1,3,5-tricarboxamide (BTA) core in water. Previous experimental works by other research groups demonstrate that such Azo stars assemble into needle-like structures with light-responsive properties. Disregarding the response to light, we intend to characterize the equilibrium state of this system on the molecular scale. In particular, we aim to develop a thorough understanding of the binding mechanism between the molecules and analyze the structural properties of columnar stacks of Azo stars. Our study employs fully atomistic molecular dynamics (MD) simulations to model pre-assembled aggregates with various sizes and arrangements in water. In our detailed approach, we decompose the binding energies of the aggregates into the contributions due to the different types of non-covalent interactions and the contributions of the functional groups in the Azo stars. Initially, we investigate the origin and strength of the non-covalent interactions within a stacked dimer. Based on these findings, three arrangements of longer columnar stacks are prepared and equilibrated. We confirm that the binding energies of the stacks are mainly composed of π–π interactions between the conjugated parts of the molecules and hydrogen bonds formed between the stacked BTA cores. Our study quantifies the strength of these interactions and shows that the π–π interactions, especially between the Azo moieties, dominate the binding energies. We clarify that hydrogen bonds, which are predominant in BTA stacks, have only secondary energetic contributions in stacks of Azo stars but remain necessary stabilizers. Both types of interactions, π–π stacking and H-bonds, are required to maintain the columnar arrangement of the aggregates.     

Data-Driven and Multiscale Modeling of DNA-Templated Dye Aggregates

Dye aggregates are of interest for excitonic applications, including biomedical imaging, organic photovoltaics, and quantum information systems. Dyes with large transition dipole moments (μ) are necessary to optimize coupling within dye aggregates. Extinction coefficients (ε) can be used to determine the μ of dyes, and so dyes with a large ε (>150,000 M⁻¹cm⁻¹) should be engineered or identified. However, dye properties leading to a large ε are not fully understood, and low-throughput methods of dye screening, such as experimental measurements or density functional theory (DFT) calculations, can be time-consuming. In order to screen large datasets of molecules for desirable properties (i.e., large ε and μ), a computational workflow was established using machine learning (ML), DFT, time-dependent (TD-) DFT, and molecular dynamics (MD). ML models were developed through training and validation on a dataset of 8802 dyes using structural features. A Classifier was developed with an accuracy of 97% and a Regressor was constructed with an R2 of above 0.9, comparing between experiment and ML prediction. Using the Regressor, the ε values of over 18,000 dyes were predicted. The top 100 dyes were further screened using DFT and TD-DFT to identify 15 dyes with a μ relative to a reference dye, pentamethine indocyanine dye Cy5. Two benchmark MD simulations were performed on Cy5 and Cy5.5 dimers, and it was found that MD could accurately capture experimental results. The results of this study exhibit that our computational workflow for identifying dyes with a large μ for excitonic applications is effective and can be used as a tool to develop new dyes for excitonic applications.     

Metastable Kitaev Magnets

Nearly two decades ago, Alexei Kitaev proposed a model for spin-1/2 particles with bond-directional interactions on a two-dimensional honeycomb lattice which had the potential to host a quantum spin-liquid ground state. This work initiated numerous investigations to design and synthesize materials that would physically realize the Kitaev Hamiltonian. The first generation of such materials, such as Na2IrO3, α-Li2IrO3, and α-RuCl3, revealed the presence of non-Kitaev interactions such as the Heisenberg and off-diagonal exchange. Both physical pressure and chemical doping were used to tune the relative strength of the Kitaev and competing interactions; however, little progress was made towards achieving a purely Kitaev system. Here, we review the recent breakthrough in modifying Kitaev magnets via topochemical methods that has led to the second generation of Kitaev materials. We show how structural modifications due to the topotactic exchange reactions can alter the magnetic interactions in favor of a quantum spin-liquid phase.     

Anharmonic Vibrational Frequencies of Water Borane and Associated Molecules

Water borane (BH3OH2) and borinic acid (BH2OH) have been proposed as intermediates along the pathway of hydrogen generation from simple reactants: water and borane. However, the vibrational spectra for neither water borane nor borinic acid has been investigaged experimentally due to the difficulty of isolating them in the gas phase, making accurate quantum chemical predictions for such properties the most viable means of their determination. This work presents theoretical predictions of the full rotational and fundamental vibrational spectra of these two potentially application-rich molecules using quartic force fields at the CCSD(T)-F12b/cc-pCVTZ-F12 level with additional corrections included for the effects of scalar relativity. This computational scheme is further benchmarked against the available gas-phase experimental data for the related borane and HBO molecules. The differences are found to be within 3 cm−1 for the fundamental vibrational frequencies and as close as 15 MHz in the B0 and C0 principal rotational constants. Both BH2OH and BH3OH2 have multiple vibrational modes with intensities greater than 100 km mol−1, namely ν2 and ν4 in BH2OH, and ν1, ν3, ν4, ν9, and ν13 in BH3OH2. Finally, BH3OH2 has a large dipole moment of 4.24 D, which should enable it to be observable by rotational spectroscopy, as well.     

GPCR Pharmacological Profiling of Aaptamine from the Philippine Sponge Stylissa sp. Extends Its Therapeutic Potential for Noncommunicable Diseases

We report the first isolation of the alkaloid aaptamine from the Philippine marine sponge Stylissa sp. Aaptamine possessed weak antiproliferative activity against HCT116 colon cancer cells and inhibited the proteasome in vitro at 50 µM. These activities may be functionally linked. Due to its known, more potent activity on certain G-protein coupled receptors (GPCRs), including α-adrenergic and δ-opioid receptors, the compound was profiled more broadly at sub-growth inhibitory concentrations against a panel of 168 GPCRs to potentially reveal additional targets and therapeutic opportunities. GPCRs represent the largest class of drug targets. The primary screen at 20 µM using the β-arrestin functional assay identified the antagonist, agonist, and potentiators of agonist activity of aaptamine. Dose-response analysis validated the α-adrenoreceptor antagonist activity of aaptamine (ADRA2C, IC₅₀ 11.9 µM) and revealed the even more potent antagonism of the β-adrenoreceptor (ADRB2, IC₅₀ 0.20 µM) and dopamine receptor D4 (DRD4, IC₅₀ 6.9 µM). Additionally, aaptamine showed agonist activity on selected chemokine receptors, by itself (CXCR7, EC₅₀ 6.2 µM; CCR1, EC₅₀ 11.8 µM) or as a potentiator of agonist activity (CXCR3, EC₅₀ 31.8 µM; CCR3, EC₅₀ 16.2 µM). These GPCRs play a critical role in the treatment of cardiovascular disease, diabetes, cancer, and neurological disorders. The results of this study may thus provide novel preventive and therapeutic strategies for noncommunicable diseases (NCDs).     

Influence of Liquid Crystallinity and Mechanical Deformation on the Molecular Relaxations of an Auxetic Liquid Crystal Elastomer

Liquid Crystal Elastomers (LCEs) combine the anisotropic ordering of liquid crystals with the elastic properties of elastomers, providing unique physical properties, such as stimuli responsiveness and a recently discovered molecular auxetic response. Here, we determine how the molecular relaxation dynamics in an acrylate LCE are affected by its phase using broadband dielectric relaxation spectroscopy, calorimetry and rheology. Our LCE is an excellent model system since it exhibits a molecular auxetic response in its nematic state, and chemically identical nematic or isotropic samples can be prepared by cross-linking. We find that the glass transition temperatures (Tg) and dynamic fragilities are similar in both phases, and the T-dependence of the α relaxation shows a crossover at the same T* for both phases. However, for T>T*, the behavior becomes Arrhenius for the nematic LCE, but only more Arrhenius-like for the isotropic sample. We provide evidence that the latter behavior is related to the existence of pre-transitional nematic fluctuations in the isotropic LCE, which are locked in by polymerization. The role of applied strain on the relaxation dynamics and mechanical response of the LCE is investigated; this is particularly important since the molecular auxetic response is linked to a mechanical Fréedericksz transition that is not fully understood. We demonstrate that the complex Young’s modulus and the α relaxation time remain relatively unchanged for small deformations, whereas for strains for which the auxetic response is achieved, significant increases are observed. We suggest that the observed molecular auxetic response is coupled to the strain-induced out-of-plane rotation of the mesogen units, in turn driven by the increasing constraints on polymer configurations, as reflected in increasing elastic moduli and α relaxation times; this is consistent with our recent results showing that the auxetic response coincides with the emergence of biaxial order.     

Spectral Signatures of Hydrogen Thioperoxide (HOSH) and Hydrogen Persulfide (HSSH): Possible Molecular Sulfur Sinks in the Dense ISM

For decades, sulfur has remained underdetected in molecular form within the dense interstellar medium (ISM), and somewhere a molecular sulfur sink exists where it may be hiding. With the discovery of hydrogen peroxide (HOOH) in the ISM in 2011, a natural starting point may be found in sulfur-bearing analogs that are chemically similar to HOOH: hydrogen thioperoxide (HOSH) and hydrogen persulfide (HSSH). The present theoretical study couples the accuracy in the anharmonic fundamental vibrational frequencies from the explicitly correlated coupled cluster theory with the accurate rotational constants provided by canonical high-level coupled cluster theory to produce rovibrational spectra for use in the potential observation of HOSH and HSSH. The ν6 mode for HSSH at 886.1 cm−1 is within 0.2 cm−1 of the gas-phase experiment, and the B0 rotational constant for HSSH of 6979.5 MHz is within 9.0 MHz of the experimental benchmarks, implying that the unknown spectral features (such as the first overtones and combination bands) provided herein are similarly accurate. Notably, a previous experimentally-attributed 2ν1 mode, at 7041.8 cm−1, has been reassigned to the ν1+ν5 combination band based on the present work’s ν1+ν5 value at 7034.3 cm−1. The most intense vibrational transitions for each molecule are the torsions, with HOSH having a more intense transition of 72 km/mol compared to HSSH’s intensity of 14 km/mol. Furthermore, HOSH has a larger net dipole moment of 1.60 D compared to HSSH’s 1.15 D. While HOSH may be the more likely candidate of the two for possible astronomical observation via vibrational spectroscopy due to the notable difference in their intensities, both HSSH and HOSH have large enough net dipole moments to be detectable by rotational spectroscopy to discover the role these molecules may have as possible molecular sulfur sinks in the dense ISM.     

Give or Take: Effects of Electron-Accepting/-Withdrawing Groups in Red-Fluorescent BODIPY Molecular Rotors

Mapping microviscosity, temperature, and polarity in biosystems is an important capability that can aid in disease detection. This can be achieved using fluorescent sensors based on a green-emitting BODIPY group. However, red fluorescent sensors are desired for convenient imaging of biological samples. It is known that phenyl substituents in the β position of the BODIPY core can shift the fluorescence spectra to longer wavelengths. In this research, we report how electron-withdrawing (EWG) and -donating (EDG) groups can change the spectral and sensory properties of β-phenyl-substituted BODIPYs. We present a trifluoromethyl-substituted (EWG) conjugate with moderate temperature sensing properties and a methoxy-substituted (EDG) molecule that could be used as a lifetime-based polarity probe. In this study, we utilise experimental results of steady-state and time-resolved fluorescence, as well as quantum chemical calculations using density functional theory (DFT). We also explain how the energy barrier height (Ea) for non-radiative relaxation affects the probe’s sensitivity to temperature and viscosity and provide appropriate Ea ranges for the best possible sensitivity to viscosity and temperature.     

Naphthazarin Derivatives in the Light of Intra- and Intermolecular Forces

Our long-term investigations have been devoted the characterization of intramolecular hydrogen bonds in cyclic compounds. Our previous work covers naphthazarin, the parent compound of two systems discussed in the current work: 2,3-dimethylnaphthazarin (1) and 2,3-dimethoxy-6-methylnaphthazarin (2). Intramolecular hydrogen bonds and substituent effects in these compounds were analyzed on the basis of Density Functional Theory (DFT), Møller–Plesset second-order perturbation theory (MP2), Coupled Clusters with Singles and Doubles (CCSD) and Car-Parrinello Molecular Dynamics (CPMD). The simulations were carried out in the gas and crystalline phases. The nuclear quantum effects were incorporated a posteriori using the snapshots taken from ab initio trajectories. Further, they were used to solve a vibrational Schrödinger equation. The proton reaction path was studied using B3LYP, ωB97XD and PBE functionals with a 6-311++G(2d,2p) basis set. Two energy minima (deep and shallow) were found, indicating that the proton transfer phenomena could occur in the electronic ground state. Next, the electronic structure and topology were examined in the molecular and proton transferred (PT) forms. The Atoms In Molecules (AIM) theory was employed for this purpose. It was found that the hydrogen bond is stronger in the proton transferred (PT) forms. In order to estimate the dimers’ stabilization and forces responsible for it, the Symmetry-Adapted Perturbation Theory (SAPT) was applied. The energy decomposition revealed that dispersion is the primary factor stabilizing the dimeric forms and crystal structure of both compounds. The CPMD results showed that the proton transfer phenomena occurred in both studied compounds, as well as in both phases. In the case of compound 2, the proton transfer events are more frequent in the solid state, indicating an influence of the environmental effects on the bridged proton dynamics. Finally, the vibrational signatures were computed for both compounds using the CPMD trajectories. The Fourier transformation of the autocorrelation function of atomic velocity was applied to obtain the power spectra. The IR spectra show very broad absorption regions between 700 cm−1–1700 cm−1 and 2300 cm−1–3400 cm−1 in the gas phase and 600 cm−1–1800 cm−1 and 2200 cm−1–3400 cm−1 in the solid state for compound 1. The absorption regions for compound 2 were found as follows: 700 cm−1–1700 cm−1 and 2300 cm−1–3300 cm−1 for the gas phase and one broad absorption region in the solid state between 700 cm−1 and 3100 cm−1. The obtained spectroscopic features confirmed a strong mobility of the bridged protons. The inclusion of nuclear quantum effects showed a stronger delocalization of the bridged protons.     

Fluorescent Liquid Tetrazines

Tetrazines with branched alkoxy substituents are liquids at ambient temperature that despite the high chromophore density retain the bright orange fluorescence that is characteristic of this exceptional fluorophore. Here, we study the photophysical properties of a series of alkoxy-tetrazines in solution and as neat liquids. We also correlate the size of the alkoxy substituents with the viscosity of the liquids. We show using time-resolved spectroscopy that intersystem crossing is an important decay pathway competing with fluorescence, and that its rate is higher for 3,6-dialkoxy derivatives than for 3-chloro-6-alkoxytetrazines, explaining the higher fluorescence quantum yields for the latter. Quantum chemical calculations suggest that the difference in rate is due to the activation energy required to distort the tetrazine core such that the nπ*S1 and the higher-lying ππ*T2 states cross, at which point the spin-orbit coupling exceeding 10 cm−1 allows for efficient intersystem crossing to occur. Femtosecond time-resolved anisotropy studies in solution allow us to measure a positive relationship between the alkoxy chain lengths and their rotational correlation times, and studies in the neat liquids show a fast decay of the anisotropy consistent with fast exciton migration in the neat liquid films.     

Explorations on Thermodynamic and Kinetic Performances of Various Cationic Exchange Durations for Synthetic Clinoptilolite

Various cation–exchanged clinoptilolites (M–CPs, M = Li⁺, Cs⁺, Ca²⁺, Sr²⁺) were prepared, and their exchanged thermodynamic (and kinetic) properties and adsorption performances for CH₄, N₂, and CO₂ were investigated. The results demonstrated that the relative crystallinity of M–CP_S decreased with the increase of exchange times. Their chemisorbed water weight loss gradually increased with the increasing exchange times, except that of Cs–x–CP. The Δ_rGmθ values of exchange process of Li⁺, Cs⁺, Ca²⁺, or Sr² presented the increased trend with the enhanced exchange times, but they decreased as the temperature increased. The negative Δ_rGmθ values and the positive Δ_rHmθ and Δ_rSmθ values suggested that the exchanged procedure belonged to spontaneous, endothermic, and entropy-increasing behaviors; their kinetic performances followed a pseudo–second–order model. However, the calculated E_a values of exchange process showed the increased tendencies with the enhanced exchange times, indicating that the exchange process became more difficult. Finally, the preliminary adsorption results indicated that the maximum adsorption amount at 273 K and 1 bar was 0.51 mmol/g of CH₄ and 0.38 mmol/g of N₂ by (Na, K)–CP, and 2.32 mmol/g of CO₂ by Li–6–CP.     

Operando Raman Shift Replaces Current in Electrochemical Analysis of Li-ion Batteries: A Comparative Study

Li-rich and catalytically active γ-LixV2O5 (x = 1.48) was investigated as a cathode for its heterogeneous charge transfer kinetics. Using a specially designed two-electrode system lithium half cell, Butler–Volmer analysis was performed, and Raman spectra were acquired in 18 mV intervals. A direct correlation was observed between the Raman shift of the active modes Ag,Bg, Au, and Bu, and the development of the Faraday current at the working electrode. The Raman intensity and the Raman shift were implemented to replace the current in a Tafel plot used for the analysis of Butler–Volmer kinetics. Striking similarities in the charge transfer proportionality constants α were found for current and Raman-based analysis. The potential of this new method of Raman-aided electrochemical detection at the diffraction limit is discussed.     

Interaction Energy Analysis of Monovalent Inorganic Anions in Bulk Water Versus Air/Water Interface

Soft anions exhibit surface activity at the air/water interface that can be probed using surface-sensitive vibrational spectroscopy, but the structural implications of this surface activity remain a matter of debate. Here, we examine the nature of anion–water interactions at the air/water interface using a combination of molecular dynamics simulations and quantum-mechanical energy decomposition analysis based on symmetry-adapted perturbation theory. Results are presented for a set of monovalent anions, including Cl⁻, Br⁻, I⁻, CN⁻, OCN⁻, SCN⁻, NO2−, NO3−, and ClOn− (n=1,2,3,4), several of which are archetypal examples of surface-active species. In all cases, we find that average anion–water interaction energies are systematically larger in bulk water although the difference (with respect to the same quantity computed in the interfacial environment) is well within the magnitude of the instantaneous fluctuations. Specifically for the surface-active species Br⁻(aq), I⁻(aq), ClO4−(aq), and SCN⁻(aq), and also for ClO⁻(aq), the charge-transfer (CT) energy is found to be larger at the interface than it is in bulk water, by an amount that is greater than the standard deviation of the fluctuations. The Cl⁻(aq) ion has a slightly larger CT energy at the interface, but NO3−(aq) does not; these two species are borderline cases where consensus is lacking regarding their surface activity. However, CT stabilization amounts to <20% of the total induction energy for each of the ions considered here, and CT-free polarization energies are systematically larger in bulk water in all cases. As such, the role of these effects in the surface activity of soft anions remains unclear. This analysis complements our recent work suggesting that the short-range solvation structure around these ions is scarcely different at the air/water interface from what it is in bulk water. Together, these observations suggest that changes in first-shell hydration structure around soft anions cannot explain observed surface activities.     

Galvano-Fenton Engineering Solution with Spontaneous Catalyst’s Generation from Waste: Experimental Efficiency,Parametric Analysis and Modeling Interpretation Applied to a Clean Technology for Dyes Degradation in Water

In this paper, the degradation of the diazo dye naphthol blue black (NBB) using the Galvano-Fenton process is studied experimentally and numerically. The simulations are carried out based on the anodic, cathodic, and 34 elementary reactions evolving in the electrolyte, in addition to the oxidative attack of NBB by HO• at a constant rate of 3.35×107 mol−1·m3·s−1 during the initiation stage of the chain reactions. The selection of the operating conditions including the pH of the electrolyte, the stirring speed, and the electrodes disposition is performed by assessing the kinetics of NBB degradation; these parameters are set to 3, 350 rpm and a parallel disposition with a 3 cm inter-electrode distance, respectively. The kinetics of Fe(III) in the electrolyte were monitored using the principles of Fricke dosimetry and simulated numerically. The model showed more than a 96% correlation with the experimental results in both the blank test and the presence of the dye. The effects of H2O2 and NBB concentrations on the degradation of the dye were examined jointly with the evolution of the simulated H2O2, Fe2+, and HO• concentrations in the electrolyte. The model demonstrated a good correlation with the experimental results in terms of the initial degradation rates, with correlation coefficients exceeding 98%.     

Cross-Correlated Motions in Azidolysozyme

The changes in the local and global dynamics of azide-labelled lysozyme compared with that of the wild type protein are quantitatively assessed for all alanine residues along the polypeptide chain. Although attaching -N3 to alanine residues has been considered to be a minimally invasive change in the protein it is found that depending on the location of the alanine residue, the local and global changes in the dynamics differ. For Ala92, the change in the cross-correlated motions are minimal, whereas attaching -N3 to Ala90 leads to pronounced differences in the local and global correlations as quantified by the cross-correlation coefficients of the Cα atoms. We also demonstrate that the spectral region of the asymmetric azide stretch distinguishes between alanine attachment sites, whereas changes in the low frequency, far-infrared region are less characteristic.     

Electronic Currents Induced by Optical Fields and Rotatory Power Density in Chiral Molecules

The electric dipole–magnetic dipole polarizability tensor κ′, introduced to interpret the optical activity of chiral molecules, has been expressed in terms of a series of density functions kαβ′, which can be integrated all over the three-dimensional space to evaluate components καβ′ and trace καα′. A computational approach to kαβ′, based on frequency-dependent electronic current densities induced by monochromatic light shining on a probe molecule, has been developed. The dependence of kαβ′ on the origin of the coordinate system has been investigated in connection with the corresponding change of καβ′. It is shown that only the trace kαα′ of the density function defined via dynamic current density evaluated using the continuous translation of the origin of the coordinate system is invariant of the origin. Accordingly, this function is recommended as a tool that is quite useful for determining the molecular domains that determine optical activity to a major extent. A series of computations on the hydrogen peroxide molecule, for a number of different HO–OH dihedral angles, is shown to provide a pictorial documentation of the proposed method.     

Carbon Nanotubes Hybrid Hydrogels for Environmental Remediation: Evaluation of Adsorption Efficiency under Electric Field

The performance of Carbon Nanotubes hybrid hydrogels for environmental remediation was investigated using Methylene Blue (MB), Rhodamine B (RD), and Bengal Rose (BR) as model contaminating dyes. An acrylate hydrogel network with incorporated CNT was synthesized by photo-polymerization without any preliminary derivatization of CNT surface. Thermodynamics, isothermal and kinetic studies showed favorable sorption processes with the application of an external 12 V electric field found to be able to influence the amount of adsorbed dyes: stronger interactions with cationic MB molecules (qexp and qexp12 of 19.72 and 33.45 mg g⁻¹, respectively) and reduced affinity for anionic RD (qexp and qexp12 of 28.93 and 13.06 mg g⁻¹, respectively) and neutral BR (qexp and qexp12 of 36.75 and 15.85 mg g⁻¹, respectively) molecules were recorded. The influence of pH variation on dyes adsorption was finally highlighted by reusability studies, with the negligible variation of adsorption capacity after five repeated sorption cycles claiming for the suitability of the proposed systems as effective sorbent for wastewater treatment.     

Optical Dynamic Nuclear Polarization of 13C Spins in Diamond at a Low Field with Multi-Tone Microwave Irradiation

Majority of dynamic nuclear polarization (DNP) experiments have been requiring helium cryogenics and strong magnetic fields for a high degree of nuclear polarization. In this work, we instead demonstrate an optical hyperpolarization of naturally abundant 13C nuclei in a diamond crystal at a low magnetic field and the room temperature. It exploits continuous laser irradiation for polarizing electronic spins of nitrogen vacancy centers and microwave irradiation for transferring the electronic polarization to 13C nuclear spins. We have studied the dependence of 13C polarization on laser and microwave powers. For the first time, a triplet structure corresponding to the 14N hyperfine splitting has been observed in the 13C polarization spectrum. By simultaneously exciting three microwave frequencies at the peaks of the triplet, we have achieved 13C bulk polarization of 0.113 %, leading to an enhancement of 90,000 over the thermal polarization at 17.6 mT. We believe that the multi-tone irradiation can be extended to further enhance the 13C polarization at a low magnetic field.     

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO2, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters (α1,α2,β1,β2,k) are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency.