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CONTEXT: Describing chemical processes at solid-liquid interfaces as a function of a fixed electron chemical potential presents a challenge for electronic structure calculations and is essential for understanding electrochemical phenomena. Grand Canonical Density Functional Theory (GCDFT) allows treating solid-liquid interfaces in such a way that studying the influence of a fixed electron potential arises naturally. In this work, GCDFT is used to compute the adsorption grand potential (AGP), a key parameter for understanding and predicting the behavior of adsorbates on surfaces. We focused on the adsorption of an OH molecule on three metallic surfaces commonly used in electrochemical processes, such as the oxygen evolution reaction (OER). Our study aims to offer insights into how AGP can be used to compare adsorption strengths under different fixed electron chemical potentials, which is crucial for designing efficient electrode materials. By determining the average number of electrons self-consistently under varying chemical potentials, we showed how one can distinguish between electron acquisition and depletion during the adsorption process, offering a deeper understanding of the adsorbate-surface interactions. METHODS: The approach used in this work employs the Kohn-Sham-Mermin formulation of the Grand Canonical Density Functional Theory. The computations were performed using the periodic open-source density functional theory software, JDFTx, with the Garrity-Bennett-Rabe-Vanderbilt library of ultrasoft pseudopotentials. Calculations were made using truncated Coulomb potentials and the auxiliary Hamiltonian method with the PBE exchange-correlation functional, along with DFT-D2 long-range dispersion corrections. The implicit solvation model CANDLE was used to describe the electrolyte with a 1 M concentration.
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CONTEXT: Exploring potential energy surfaces (PES) is fundamental in computational chemistry, as it provides insights into the relationship between molecular energy, geometry, and chemical reactivity. We introduce Kick-MEP, a hybrid method for exploring the PES of atomic and molecular clusters, particularly those dominated by non-covalent interactions. Kick-MEP computes the Coulomb integral between the maximum and minimum electrostatic potential values on a 0.001 a.u. electron density isosurface for two interacting fragments. This approach efficiently estimates interaction energies and selects low-energy configurations at reduced computational cost. Kick-MEP was evaluated on silicon-lithium clusters, water clusters, and thymol encapsulated within Cucurbit[7]uril, consistently identifying the lowest energy structures, including global minima and relevant local minima. METHODS: Kick-MEP generates an initial population of molecular structures using the stochastic Kick algorithm, which combines two molecular fragments (A and B). The molecular electrostatic potential (MEP) values on a 0.001 a.u. electron density isosurface for each fragment are used to compute the Coulomb integral between them. Structures with the lowest Coulomb integral are selected and refined through gradient-based optimization and DFT calculations at the PBE0-D3/Def2-TZVP level. Molecular docking simulations for the thymol-Cucurbit[7]uril complex using AutoDock Vina were performed for benchmarking. Kick-MEP was validated across different molecular systems, demonstrating its effectiveness in identifying the lowest energy structures, including global minima and relevant local minima, while maintaining a low computational cost.
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CONTEXT: We perform density functional theory calculations to study the dependence of the structural and electronic properties of the amino acid sarcosine crystal structure on hydrostatic pressure application. The results are analyzed and compared with the available experimental data. Our findings indicate that the crystal structure and properties of sarcosine calculated using the Grimme dispersion-corrected PBE functional (PBE-D3) best agree with the available experimental results under hydrostatic pressure of up to 3.7 GPa. Critical structural rearrangements, such as unit cell compression, head-to-tail compression, and molecular rotations, are investigated and elucidated in the context of experimental findings. Band gap energy tuning and density of state shifts indicative of band dispersion are presented concerning the structural changes arising from the elevated pressure. The calculated properties indicate that sarcosine holds great promise for application in electronic devices that involve pressure-induced structural changes. METHODS: Three widely used generalized gradient approximation functionals-PBE, PBEsol, and revPBE-are employed with Grimme's D3 dispersion correction. The non-local van der Waals density functional vdW-DF is also evaluated. The calculations are performed using the projector-augmented wave method in the Quantum Espresso software suite. The geometry optimization results are visualized using VMD. The Multiwfn and NCIPlot programs are used for wavefunction and intermolecular interaction analyses.
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Checkpoint kinases 1 and 2 (CHK1 and CHK2) are enzymes that are involved in the control of DNA damage. At the present time, these enzymes are some of the most important targets in the fight against cancer since their inhibition produces cytotoxic effects in carcinogenic cells. This paper proposes the use of spirostans (Sp), natural compounds, as possible inhibitors of the enzymes CHK1 and CHK2 from an in silico analysis of a database of 155 molecules (S5). Bioinformatics studies of molecular docking were able to discriminate between 13 possible CHK1 inhibitors, 13 CHK2 inhibitors and 1 dual inhibitor for both enzymes. The administration, distribution, metabolism, excretion and toxicity (ADMETx) studies allowed a prediction of the distribution and metabolism of the potential inhibitors in the body, as well as determining the excretion routes and the appropriate administration route. The best inhibition candidates were discriminated by comparing the enzyme-substrate interactions from 2D diagrams and molecular docking. Specific inhibition candidates were obtained, in addition to studying the dual inhibitor candidate and observing their stability in dynamic molecular studies. In addition, Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital (HOMO-LUMO) interactions were analyzed to study the stability of interactions between the selected enzymes and spirostans resulting in the predominant gaps from HOMOCHKs to LUMOSp (Highest Occupied Molecular Orbital of CHKs-Lowest Unoccupied Molecular Orbital of spirostan). In brief, this study presents the selection inhibitors of CHK1 and CHK2 as a potential treatment for cancer using a combination of molecular docking and dynamics, ADMETx predictons, and HOMO-LUMO calculation for selection.
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Quinase 1 do Ponto de Checagem , Quinase do Ponto de Checagem 2 , Simulação de Acoplamento Molecular , Inibidores de Proteínas Quinases , Quinase 1 do Ponto de Checagem/metabolismo , Quinase 1 do Ponto de Checagem/química , Quinase 1 do Ponto de Checagem/antagonistas & inibidores , Quinase do Ponto de Checagem 2/metabolismo , Quinase do Ponto de Checagem 2/química , Humanos , Inibidores de Proteínas Quinases/química , Inibidores de Proteínas Quinases/farmacologia , Neoplasias/tratamento farmacológico , Neoplasias/metabolismo , Simulação por Computador , Antineoplásicos/química , Antineoplásicos/farmacologia , Simulação de Dinâmica MolecularRESUMO
The first step in comprehending the properties of Au10 clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au10 nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme's dispersion with Becke-Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50-800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.
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Machine learning interatomic potentials (MLIPs) are one of the main techniques in the materials science toolbox, able to bridge ab initio accuracy with the computational efficiency of classical force fields. This allows simulations ranging from atoms, molecules, and biosystems, to solid and bulk materials, surfaces, nanomaterials, and their interfaces and complex interactions. A recent class of advanced MLIPs, which use equivariant representations and deep graph neural networks, is known as universal models. These models are proposed as foundation models suitable for any system, covering most elements from the periodic table. Current universal MLIPs (UIPs) have been trained with the largest consistent data set available nowadays. However, these are composed mostly of bulk materials' DFT calculations. In this article, we assess the universality of all openly available UIPs, namely MACE, CHGNet, and M3GNet, in a representative task of generalization: calculation of surface energies. We find that the out-of-the-box foundation models have significant shortcomings in this task, with errors correlated to the total energy of surface simulations, having an out-of-domain distance from the training data set. Our results show that while UIPs are an efficient starting point for fine-tuning specialized models, we envision the potential of increasing the coverage of the materials space toward universal training data sets for MLIPs.
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The cubic α-CsPbI3 phase stands out as one of the most promising perovskite compounds for solar cell applications due to its suitable electronic band gap of 1.7 eV. However, it exhibits structural instability under operational conditions, often transforming into the hexagonal non-perovskite δ-CsPbI3 phase, which is unsuitable for solar cell applications because of the large band gap (e.g., â¼2.9 eV). Thus, there is growing interest in identifying possible mechanisms for increasing the stability of the cubic α-CsPbI3 phase. Here, we report a theoretical investigation, based on density functional theory calculations, of the surface passivation of the α-, γ-, and δ-CsPbI3(100) surfaces using the C6H4(NH3)2 [p-phenylenediamine (PPD)] and Cs species as passivation agents. Our calculations and analyses corroborate recent experimental findings, showing that PPD passivation effectively stabilizes the cubic α-CsPbI3 perovskite against the cubic-to-hexagonal phase transition. The PPD molecule exhibits covalent-dominating bonds with the substrate, which makes it more resistant to distortion than the ionic bonds dominant in perovskite bulks. By contrasting these results with the natural Cs passivation, we highlight the superior stability of the PPD passivation, as evidenced by the negative surface formation energies, unlike the positive values observed for the Cs passivation. This disparity is due to the covalent characteristics of the molecule/surface interaction of PPD, as opposed to the purely ionic interaction seen with the Cs passivation. Notably, the PPD passivation maintains the optoelectronic properties of the perovskites because the electronic states derived from the PPD molecules are localized far from the band gap region, which is crucial for optoelectronic applications.
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CONTEXT: In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density functional theory (DFT) and density matrix renormalization group (DMRG) have emerged as two powerful computational methods for addressing electronic correlation effects in diverse molecular systems. We compare ground-state energies ( e 0 ), density profiles ( n ), and average entanglement entropies ( S ¯ ) in metals, insulators and at the transition from metal to insulator, in homogeneous, superlattices, and harmonically confined chains described by the fermionic one-dimensional Hubbard model. While for the homogeneous systems, there is a clear hierarchy between the deviations, D % ( S ¯ ) < D % ( e 0 ) < D ¯ % ( n ) , and all the deviations decrease with the chain size; for superlattices and harmonic confinement, the relation among the deviations is less trivial and strongly dependent on the superlattice structure and the confinement strength considered. For the superlattices, in general, increasing the number of impurities in the unit cell represents lower precision in the DFT calculations. For the confined chains, DFT performs better for metallic phases, while the highest deviations appear for the Mott and band-insulator phases. This work provides a comprehensive comparative analysis of these methodologies, shedding light on their respective strengths, limitations, and applications. METHODS: The DFT calculations were performed using the standard Kohn-Sham scheme within the BALDA approach. It integrated the numerical Bethe-Ansatz (BA) solution of the Hubbard model as the homogeneous density functional within a local-density approximation (LDA) for the exchange-correlation energy. The DMRG algorithms were implemented using the ITensor library, which is based on the matrix product states (MPS) ansatz. The calculations were performed until the energy reaches convergence of at least 10 - 8 .
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CONTEXT: Hydrazones have been studied for a myriad of chemical and physiochemical properties, such as sensors, chelators and numerous biological activities. Experimental data indicates that hydrazones are unstable under cathodic potentials irrespective of the solvent. The single electron reduction of hydrazones to produce radical anions result in unstable species that cleaves at the N-N bond in a heterolytic manner. The literature has proposed a mechanism favouring the radical on the imine moiety, however in this study DFT calculations suggest the radical on the amine product is more likely upon bond cleavage. This has implications on electrochemical mechanisms, and the active molecule in biological studies viz the method of delivery to target areas. METHODS: Density functional theory calculations were carried out using the GAMESS software package. The structures were optimized in the gas phase (B3LYP/6-31G(d,p)) as indicated by the absence of imaginary frequencies in the Hessian, and in CH3CN (B3LYP/6-31G(d,p)/SMD) with the Pople polarization functions. As a comparison, selected pathways were fully optimized using PBE0/6-31G(d,p) and PBE0/6-31G(d,p)/SMD for gas phase and CH3CN, respectively with the Pople polarization functions. The values were not significantly different (< 5% difference). As such only the B3LYP is evaluation is discussed.
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The increasing global demand for food and agrarian development brings to light a dual issue concerning the use of substances that are crucial for increasing productivity yet can be harmful to human health and the environment when misused. Herein, we combine insights from high-level quantum simulations and experimental findings to elucidate the fundamental physicochemical mechanisms behind developing graphene-based nanomaterials for the adsorption of emerging contaminants, with a specific focus on pesticide glyphosate (GLY). We conducted a comprehensive theoretical and experimental investigation of graphene-based supports as promising candidates for detecting, sensing, capturing, and removing GLY applications. By combining ab initio molecular dynamics and density functional theory calculations, we explored several chemical environments encountered by GLY during its interaction with graphene-based substrates, including pristine and punctual defect regions. Our results unveiled distinct interaction behaviors: physisorption in pristine and doped graphene regions, chemisorption leading to molecular dissociation in vacancy-type defect regions, and complex transformations involving the capture of N and O atoms from impurity-adsorbed graphene, resulting in the formation of new GLY-derived compounds. The theoretical findings were substantiated by FTIR and Raman spectroscopy, which proposed a mechanism explaining GLY adsorption in graphene-based nanomaterials. The comprehensive evaluation of adsorption energies and associated properties provides valuable insights into the intricate nature of these interactions, shedding light on potential applications and guiding future experimental investigations of graphene-based nanofilters for water decontamination.
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In this paper, we investigate the optical, electronic, vibrational, and excitonic properties of four two-dimensional ß -pnictogen materials-nitrogenene, phosphorene, arsenene, and antimonene-via density functional theory calculations and the Bethe-Salpeter equation. These materials possess indirect gaps with significant exciton binding energies, demonstrating isotropic behavior under circular light polarization and anisotropic behavior under linear polarization by absorbing light within the visible solar spectrum (except for nitrogenene). Furthermore, we observed that Raman frequencies red-shift in heavier pnictogen atoms aligning with experimental observations; simultaneously, quasi-particle effects notably influence the linear optical response intensively. These monolayers' excitonic effects lead to optical band gaps optimized for solar energy harvesting, positioning them as promising candidates for advanced optoelectronic device applications.
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Boronate esters are a class of compounds containing a boron atom bonded to two oxygen atoms in an ester group, often being used as precursors in the synthesis of other materials. The characterization of the structure and properties of esters is usually carried out by UV-visible, infrared, and nuclear magnetic resonance (NMR) spectroscopic techniques. With the aim to better understand our experimental data, in this article, the density functional theory (DFT) is used to analyze the UV-visible and infrared spectra, as well as the isotropic shielding and chemical shifts of the hydrogen atoms 1H, carbon 13C and boron 11B in the compound 4-(4,4,5,5-tetramethyl-1,3,2-dioxoborolan-2-yl)benzaldehyde. Furthermore, this study considers the change in its electronic and spectroscopic properties of this particular ester, when its boron atom is coordinated with a fluoride anion. The calculations were carried out using the LSDA and B3LYP functionals in Gaussian-16, and PBE in CASTEP. The results show that the B3LYP functional gives the best approximation to the experimental data. The formation of a coordinated covalent B-F bond highlights the remarkable sensitivity of the NMR chemical shifts of carbon, oxygen, and boron atoms and their surroundings. Furthermore, this bond also highlights the changes in the electron transitions bands n â π* and π â π* during the absorption and emission of a photon in the UV-vis, and in the stretching bands of the C=C bonds, and bending of BO2 in the infrared spectrum. This study not only contributes to the understanding of the properties of boronate esters but also provides important information on the interactions and responses optoelectronic of the compound when is bonded to a fluorine atom.
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Benzaldeídos , Benzaldeídos/química , Espectroscopia de Ressonância Magnética , Teoria da Densidade Funcional , Flúor/química , Boro/química , Modelos Moleculares , Ésteres/química , Espectrofotometria Infravermelho , Estrutura Molecular , Íons/químicaRESUMO
Phosphorene is a recently developed two-dimensional (2D) material that has attracted tremendous attention because of its unique anisotropic optical properties and quasi-one-dimensional (1D) excitons. We use first-principles calculations combined with the maximally localized Wannier function tight binding Hamiltonian and Bethe-Salpeter equation (BSE) formalism to investigate quasiparticle effects of 2D and quasi-1D blue and black phosphorene nanoribbons. Our electronic structure calculations shows that both blue and black monolayered phases are semiconductors. On the other hand black phosphorene zigzag nanoribbons are metallic. Similar behavior is found for very thin blue phosphorene zig-zag and armchair nanoribbon. As a general behavior, the exciton binding energy decreases as the ribbon width increases, which highlights the importance of quantum confinement effects. The solution of the BSE shows that the blue phosphorene monolayer has an exciton binding energy four times higher than that of the black phosphorene counterpart. Furthermore, both monolayers show a different linear optical response with respect to light polarization, as black phosphorene is highly anisotropic. We find a similar, but less pronounced, optical anisotropy for blue phosphorene monolayer, caused exclusively by the quasi-particle effects. Finally, we show that some of the investigated nanoribbons show a spin-triplet excitonic insulator behavior, thus revealing exciting features of these nanoribbons and therefore provides important advances in the understanding of quasi-one dimensional phosphorus-based materials.
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In recent decades, two-dimensional (2D) perovskites have emerged as promising semiconductors for next-generation photovoltaics, showing notable advancements in solar energy conversion. Herein, we explore the impact of alternative inorganic lattice BX-based compositions (B=Ge or Sn, X=Br or I) on the energy gap and stability. Our investigation encompasses BA2Man-1BnX3n+1 2D Ruddlesden-Popper perovskites (for n=1-5 layers) and 3D bulk (MA)BX3 systems, employing first-principles calculations with spin-orbit coupling (SOC), DFT-1/2 quasiparticle, and D3 dispersion corrections. The study unveils how atoms with smaller ionic radii induce anisotropic internal and external distortions within the inorganic and organic lattices. Introducing the spacers in the low-layer regime reduces local distortions but widens band gaps. Our calculation protocol provides deeper insights into the physics and chemistry underlying 2D perovskite materials, paving the way for optimizing environmentally friendly alternatives that can efficiently replace with sustainable materials.
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Lithium-oxygen batteries show promising energy storage potential with high theoretical energy density; however, further investigation of chemical reactions is required. In this study, experimental Raman and theoretical analyzes are performed for a Li-O2 battery with LiClO4/dimethyl sulfoxide (DMSO) electrolyte and carbon cathode to understand the role of intermediate species in the reactional mechanism of the cell using a high donor number solvent. Operando Raman results reveal reversible changes in the DMSO bands, in addition to the formation and decomposition of Li2O2. On discharge, a decrease in DMSO polarizability is observed and bands of DMSO-Li+-anion interactions are evidenced and supported by ab initio density functional theory (DFT) calculations. Molecular dynamics (MD) force field simulations and operando Raman show that DMSO interacts with LiO2(sol), highlighting the stability of the electrolyte compared to the interaction with reactive O 2 - ${\rm O}_2^{-}$ . On charging, the presence of Li+ indicates the formation of a lithium-deficient phase, followed by the release of Li+ and oxygen. Therefore, this study contributes to understanding the discharge/charge chemistry of a Li-O2 cell, employing a common carbon cathode and DMSO electrolyte. The combination of a simple characterization technique in operando mode and theoretical studies provides essential information on the mechanism of Li-O2 system.
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In this study, we analyzed the impact of hydroxyl and epoxy groups on the properties of graphene oxide (GO) for the adsorption of methylene blue (MB) dye from water, addressing the urgent need for effective water purification methods due to industrial pollution. Employing a dual approach, we integrated experimental techniques with theoretical modeling via density functional theory (DFT) to examine the atomic structure of GO and its adsorption capabilities. The methodology encompasses a series of experiments to evaluate the performance of GO in MB dye adsorption under different conditions, including differences in pH, dye concentration, reaction temperature, and contact time, providing a comprehensive view of its effectiveness. Theoretical DFT calculations provide insights into how hydroxyl and epoxy modifications alter the electronic properties of GO, improving adsorption efficiency. The results demonstrate a significant improvement in the dye adsorption capacity of GO, attributed to the interaction between the functional groups and MB molecules. This study not only confirms the potential of GO as a superior adsorbent for water treatment, but also contributes to the optimization of GO-based materials for environmental remediation, highlighting the synergy between experimental observations and theoretical predictions in advances in materials science to improve sustainability.
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The continued interest in 2D carbon allotropes stems from their unique structural and electronic characteristics, which are crucial for diverse applications. This work theoretically introduces PHOTH-Graphene (PHOTH-G), a novel 2D planar carbon allotrope formed by 4-5-6-7-8 carbon rings. PHOTH-G emerges as a narrow band gap semiconducting material with low formation energy, demonstrating good stability under thermal and mechanical conditions. This material has slight mechanical anisotropy with Young modulus and Poisson ratios varying between 7.08-167.8 GPa and 0.21-0.96. PHOTH-G presents optical activity restricted to the visible range. Li atoms adsorbed on its surface have a migration barrier averaging 0.38 eV.
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The stability and reactivity of Pd4Ni4 and Pd4Cu4 clusters embedded on graphene modified by monovacancy and nitrogen doping were investigated using auxiliary density functional theory (ADFT) calculations. The most stable structure of the Pd4Ni4 cluster is found in high spin multiplicity, whereas the lowest stable energy structure of the Pd4Cu4 cluster is a close shell system. The interaction energies between the bimetallic clusters and the defective graphene systems are significantly higher than those reported in the literature for the Pd-based clusters deposited on pristine graphene. It is observed that the composites studied present a HOMO-LUMO gap less than 1 eV, which suggests that they may present a good chemical reactivity. Therefore, from the results obtained in this work it can be inferred that the single vacancy graphene and pyridinic N-doped graphene are potentially good support materials for Pd-based clusters.
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This study outlines the investigation into how the compounds CO2, CO, and O2 interact with the active center of titanium (Ti) on the surface of MgCl2 and how these interactions impact the productivity of the Ziegler-Natta catalyst, ultimately influencing the thermal stability of the produced polypropylene. The calculations revealed that the adsorption energies of Ti-CO2-CO and O2 were -9.6, -12.5, and -2.32 Kcal/mol, respectively. Using the density functional theory in quantum calculations, the impacts of electronic properties and molecular structure on the adsorption of CO, O2, and CO2 on the Ziegler-Natta catalyst were thoroughly explored. Additionally, the Gibbs free energy and enthalpy of adsorption were examined. It was discovered that strong adsorption and a significant energy release (-16.2 kcal/mol) during CO adsorption could explain why this gas caused the most substantial reductions in the ZN catalyst productivity. These findings are supported by experimental tests showing that carbon monoxide has the most significant impact on the ZN catalyst productivity, followed by carbon dioxide, while oxygen exerts a less pronounced inhibitory effect.
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The reactivity of 22 unsaturated molecules undergoing attack by a methyl radical (â CH3) have been elucidated using the condensed radical general-purpose reactivity indicator (condensed radical GPRI) appropriate for relatively nucleophilic or electrophilic molecules. Using the appropriate radical GPRI equation for electrophilic attack or nucleophilic radical attack, seven different population schemes were used to assign the most reactive atoms in each of the 22 molecules. The results show that the condensed radical GPRI is sensitive to the population scheme chosen, but less sensitive than the radical Fukui function. Therefore, the reliability of these methods depends on the population scheme. Our investigation indicates that the condensed radical GPRI is most accurate in predicting the dominant products of the methyl radical addition reactions on a variety of unsaturated molecules when the Hirshfeld, Merz-Singh-Kollman, or Voronoi deformation density population schemes are used. Furthermore, for all populations schemes in the majority of instances where the radical Fukui function failed the radical GPRI was able to identify the most reactive atom under certain reactivity conditions.