Natural Population Analysis Charges Research Articles

Atomically Precise Nanometer‐Sized Pt Catalysts with an Additional Photothermy Functionality

AbstractAtomically precise ~1‐nm Pt nanoparticles (nanoclusters, NCs) with ambient stability are important in fundamental research and exhibit diverse practical applications (catalysis, biomedicine, etc.). However, synthesizing such materials is challenging. Herein, by employing the mixture ligand protecting strategy, we successfully synthesized the largest organic‐ligand‐protected (~1‐nm) Pt23 NCs precisely characterized with mass spectrometry and single‐crystal X‐ray diffraction analyses. Interestingly, natural population analysis and Bader charge calculation indicate an alternate, varying charge ‐layer distribution in the sandwich‐like Pt23 NC kernel. Pt23 NCs can catalyze the oxygen reduction reaction under acidic conditions without requiring calcination and other treatments, and the resulting specific and mass activities without further treatment are sevenfold and eightfold higher than those observed for commercial Pt/C catalysts, respectively. Density functional theory and d‐band center calculations interpret the high activity. Furthermore, Pt23 NCs exhibit a photothermal conversion efficiency of 68.4 % under 532‐nm laser irradiation and can be used at least for six cycles, thus demonstrating great potential for practical applications.

Atomically Precise Nanometer-Sized Pt Catalysts with an Additional Photothermy Functionality.

Atomically precise ~1-nm Pt nanoparticles (nanoclusters, NCs) with ambient stability are important in fundamental research and exhibit diverse practical applications (catalysis, biomedicine, etc.). However, synthesizing such materials is challenging. Herein, by employing the mixture ligand protecting strategy, we successfully synthesized the largest organic-ligand-protected (~1-nm) Pt23 NCs precisely characterized with mass spectrometry and single-crystal X-ray diffraction analyses. Interestingly, natural population analysis and Bader charge calculation indicate an alternate, varying charge -layer distribution in the sandwich-like Pt23 NC kernel. Pt23 NCs can catalyze the oxygen reduction reaction under acidic conditions without requiring calcination and other treatments, and the resulting specific and mass activities without further treatment are sevenfold and eightfold higher than those observed for commercial Pt/C catalysts, respectively. Density functional theory and d-band center calculations interpret the high activity. Furthermore, Pt23 NCs exhibit a photothermal conversion efficiency of 68.4 % under 532-nm laser irradiation and can be used at least for six cycles, thus demonstrating great potential for practical applications.

Oxygen locations and electronic structures of oxygenated coinage-metal clusters

The structure features and stability of MnO (M = Cu, Ag and Au; n = 2–9) clusters are investigated using the genetic algorithm combined with the density functional theory (DFT). It is found that CunO and AgnO are more inclined to 3-dimension compact structures, while the transition of AunO from 2 to 3-dimensions occurs at n = 7, in which O atoms prefer to be located on the vertexes regardless of different sizes and configurations of metal Mn cores. Due to the relativistic effect, the stability of AunO is maximum, while the AgnO are less stable, and that of CunO is in between them. The molecular dynamics simulations show that the structures of M4O can maintain integrity with only slight disturbances of individual atoms at a temperature of 300 K. But only the Au4O is stable at 500K, and the Ag4O and Cu4O have severely structural deformation. In most cases, the density of states of larger-sized MnO can be regarded as the superposition of small clusters, and distributions of the curves are in good agreement on the whole. The molecular orbitals reveal that the HOMO/LUMO orbitals are mainly distributed around the M atoms. The natural population analysis charges show that the charge-transferring direction is from M to O atoms, where the charge of O atoms exhibits odd–even oscillation behaviors, with different intensity peaks at the same n.

Theoretical Quantification of the Lewis Acidity of N‐Heterocyclic Iodonium Salts

AbstractThe quantitative Lewis acidity of N‐heterocyclic iod(az)olium salts is helpful for their further application in organic chemistry. The acidity scales of different N‐Heterocyclic iodonium salts (NHISs) in acetonitrile are investigated using Density functional theory (DFT) studies. There are a total of 121N‐Heterocyclic iodonium salts that have been designed by combining N‐heterocyclic and iodonium salt structures in this research. Theoretical calculations systematically established the 31P NMR chemical shifts of NHISs, and the relative Lewis acidity scale was derived. The Lewis acidity trend is analyzed and explained by the natural population analysis (NPA) charges, molecular electrostatic potential, and the interaction between the iodonium center and the N‐heterocyclic substituents. This study is expected to provide a practical quantitative theoretical scale for the understanding and design of hypervalent iodine(III) reagents with versatile Lewis acidity.

Vibrational spectroscopic analysis of 2, 3:4,5-Bis-O-(1-methylethylidene)beta-D-fructopyranose Sulfamate(Topiramate) by density functional method

2,3:4,5-Bis-O-(1-methylethylidene)-beta-D- fructopyranose sulfamate otherwise called as Topiramate is a drug used for the treatment of alcohol dependence. Topiramate is a safe and consistently efficacious medication for treating alcohol dependence. The spectroscopic properties of Topiramate are investigated by Fourier Transform Infrared (FT-IR), Fourier Transform Raman (FT-Raman), Fourier Transform Nuclear magnetic Resonsnce(FT-NMR) andUltra Violet Visible (UV–visible) spectroscopic techniques. The FTIR, FT-Raman, FT-NMR and UV–visible spectra of Topiramate have been recorded and analyzed. Theoretical vibrational frequencies, geometric parameters, thermodynamic properties, Natural population analysis and Mulliken atomic charges of Topiramateare obtained by the Restricted Hartree–Fock (RHF) and density functional theory (DFT) using 6–31 + G(d,p) basis set. The calculated harmonic vibrational frequencies for Topiramate are compared with the experimental values of FTIR and FT-Raman spectra. The observed and the calculated frequencies are found to be in good agreement. Stability of the molecule arising from hyperconjugative interactions and charge delocalization has been analysed using natural bond orbital (NBO) analysis. The first-order hyperpolarizability (βtot) and other related properties such as dipole moment(µ), polarizability(αo)values of the investigated molecule are computed using HF and DFT/B3LYP with 6–31 + G(d,p) basis set. The calculated results also show that the Topiramate molecule may have microscopic nonlinear optical (NLO) behaviour.

Pharmacophore Oriented MP2 Characterization of Charge Distribution for Anti-SARS-CoV-2 Inhibitor Nirmatrelvir

Quantum mechanical second order Møller–Plesset (MP2) perturbation theory and density functional theory (DFT) Becke, 3-parameter, Lee-Yang-Parr (B3LYP) and Minnesota 2006 local functional (M06L) calculations were performed to optimize structure of nirmatrelvir and compute the Merz-Kollman electrostatic potential (MK ESP), natural population analysis (NPA), Hirshfeld, charge model 5 (CM5), and mulliken partial charges. The mulliken partial charge distribution of nirmatrelvir exhibits a poor correlation with the MK ESP charges in MP2, B3LYP, and M06L calculations respectively. The NPA, Hirshfeld, and CM5 partial charge scheme of nirmatrelvir indicate a reasonable correlation with MK ESP charge assignments in B3LYP and M06L calculations. The above correlations were not improved by the inclusion of implicit solvation model. The MK ESP and CM5 partial charges show a strong correlation between the results of MP2 and two DFT methods. The three optimized structures present a certain degree of differences from the crystal bioactive conformation of nirmatrelvir, suggesting the nirmatrelvir-enzyme complex is formed in the induced-fit model. The Reactivity of warhead electrophilic nitrile is justified by the relatively weaker strength of π bonds in the MP2 calculations. The nirmatrelvir hydrogen bond acceptors consistently show strong delocalization of lone pair electrons in three calculations, whereas hydrogen bond donors are found to have high polarization on the heavy nitrogen atoms in MP2 computations. This work helps to parametrize the force field of nirmatrelvir and improve accuracy of molecular docking and rational inhibitor design.

Iridium/Zinc-Co-Catalyzed Ring-Opening Reactions of Oxabicyclic Alkenes with Indole Nucleophiles: A Combined Experimental and Theoretical Study

An experimental and theoretical investigation on the iridium/zinc-co-catalyzed ring-opening reactions of oxabicyclic alkenes with indole nucleophiles is reported. The reaction affords trans-3-indolyl-1,2-dihydronaphthalen-1-ol products in good yield with no N-alkylated products observed. The C–C bond-forming reaction does not require prior functionalization and is entirely atom-economic. The mechanism and origins of selectivity in the iridium-catalyzed ring-opening reaction have been examined at the M06-D3/Def2TZVPP level of theory. Orbital analysis and natural population analysis charges demonstrate that the Cα site of the π-allyliridium intermediate is the most electrophilic site of attack. Distortion/interaction analysis reveals that the chemoselectivity likely originates from an earlier-stage transition state between Cα and C3, which requires less distortion energy compared to Cα–N1 during the rate-determining intermolecular nucleophilic attack. Moreover, conceptual density functional theory was used to conceptualize the preferential reactive sites of the nucleophiles probed. The C–C bond-forming step is speculated to proceed through a Friedel–Crafts-type reaction.

Trinuclear and Cyclometallated Organometallic Dinuclear Pt-Pyrazolato Complexes: A Combined Experimental and Theoretical Study

Two differently substituted pyrazole ligands have been investigated with regard to the topology of their Pt complexes: upon deprotonation, two mononuclear 1:2 PtII-pyrazole complexes—one of the sterically unhindered 4-Me-pzH and one of the bulky 3,5-tBu-pzH (pzH = pyrazole)—yield the corresponding 1:2 PtII-pyrazolato species; the former a triangular, trinuclear metallacycle (1), and the latter a dinuclear, half-lantern species (2) formed via the unprecedented cyclometallation of a butyl group. Stoichiometric oxidation of the colorless PtII2 complex produces the deep-blue, metal–metal bonded PtIII2 analog (3) with a rarely encountered unsymmetrical coordination across the Pt-Pt bond. All three complexes have been characterized by single crystal X-ray structure determination, 1H-NMR, IR, and UV-vis-NIR spectroscopic methods. The XPS spectra of the PtII2 and PtIII2 species are also reported. Density functional theory calculations were carried out to investigate the electronic structure, spectroscopic properties, and chemical bonding of the new complexes. The calculated natural population analysis charges and Wiberg bonding indices indicate a weak σ-interaction in the case of 2 and a formal Pt-Pt single bond in 3.

The change of hydrogen position on π-conjugated bridge to affect NLO property of D(–NH2)-π(DHTPs)-A(–NO2) system

The donor-π-conjugated bridge-acceptor (D-π-A) is a classical framework to design high-performance organic electro-optical materials. In this work, based on the π-conjugated dihydrotetraazapentacenes (DHTPs), four isomers (1–4) with D(–NH2)-π(DHTPs)-A(–NO2) framework are designed and characterized. The 2 and 3 originate from single-hydrogen migration of 1, and 4 derives from double-hydrogen migration of 1. Significantly, the change of hydrogen position on DHTPs bridge can affect their nonlinear optics (NLO) property. Compared with the first hyperpolarizability (βtot) (4.08 × 103a.u.) of 1, the 6.90 × 103-2.56 × 104 a.u. of 2–4 are enhanced. More interestingly, the 4 has largest βtot value of 2.56 × 104, which is approximately equal to the sum of 6.90 × 103 a.u. of 2 and 1.82 × 104 a.u. of 3. Furthermore, the change of hydrogen position on DHTPs brings some distinctive changes in their geometric structure, nucleus-independent chemical shifts (NICS) value, natural population analysis (NPA) charge, UV–vis absorption spectrum along with its other electronic property that might be beneficial to explore their structure–property relationships.

Atomic chemical environment of tungsten in coal: Implication for the evolution of the germanium coal deposits

The Wulantuga, Lincang, and similar germanium deposits are abnormally enriched in organically associated Ge and W. In this study, the Density Functional Theory (DFT) calculation is employed to investigate the structure and bonding nature of W in coal, which helps for a better knowledge of the mode of occurrence of organically bound metals and the evolution of the coal-hosted Ge deposits.Five model compounds (ethanol, phenol, catechol, acetic acid, and benzoic acid) that represent all hydroxyls in coal structure are used to simulate the formation of W-O complexes. According to the binding energies and Natural Population Analysis (NPA) charges, W is preferred to be bonded with O-exposed model compounds to form stable W-O complexes. The phenolic hydroxyls are easier to break OH bond, suggesting that the fragments of catechol and phenol are more reactive. The carbon rings in coal are capable of bonding W, but there is less chance for graphene to be the binding site.The W-O complex can be coordinately saturated if W connects with three (catechol, acetic acid, and benzoic acid) or four (phenol and ethanol) O-exposed molecules. Generally, due to stronger binding energies, W is likely to form more stable complexes with hydroxyls relative to Ge. It is noted that W is preferred to be bonded with both O in each molecule of acetic acid or benzoic acid, and the W-O complex can reach saturation with three molecules in a distorted octahedral structure at the center. In contrast, Ge is tended to be bonded with one O in each molecule, and the Ge-O complex can be saturated with four molecules in a tetrahedral structure.The deposit evolution includes two stages: (1) Formation. The peat/lignite possesses abundant hydroxyls capable of capturing Ge and W from hydrothermal solutions and meteoric waters. Germanium and W can be fixed in the coal structure by O-bridged complexes until coal rank reaching lignite/subbituminous coal. (2) Redistribution. Along with coal rank advance to bituminous coal/anthracite, oxygen as heteroatom is expelled out from coal structure, and the bonding sites for Ge and W disappear as O-containing groups (especially hydroxyls) vanish. Thus, Ge and W can be liberated from coal.

Intra-ring proton transfer effect on the Structure-NLO property relationships of phthalocyanine derivatives

Based on the phthalocyanine, four models (1–4) are designed to explore the intra-ring proton transfer effect on structure–property relationships. The results show that small differences in structure bring fascinating changes in nucleus-independent chemical shifts (NICS) values, anisotropy of the induced current density (AICD), natural population analysis (NPA) charge, electrostatic potential (ESP), UV–vis absorption spectrum as well as unit sphere representation (USR). Significantly, the largest static first hyperpolarizability βtot value (1.47 × 104) of 4 is approximately 15 times larger than that (8.98 × 102 au) of 1 due to the intra-ring proton transfer regulating conjugation degree of the conjugation section. Furthermore, the dynamic first hyperpolarizability βHRS at the wavelengths λ = 1907, 1460 nm is elaborated in detail. We hope that the present work may evoke the possibility to probe into a promising field for nonlinear optics (NLO) application.

Evodiamine and Rutaecarpine as Potential Anticancer Compounds: A Combined Computational Study.

Evodiamine (EVO) and rutaecarpine (RUT) are the main active compounds of the traditional Chinese medicinal herb Evodia rutaecarpa. Here, we fully optimized the molecular geometries of EVO and RUT at the B3LYP/6-311++G (d, p) level of density functional theory. The natural population analysis (NPA) charges, frontier molecular orbitals, molecular electrostatic potentials, and the chemical reactivity descriptors for EVO and RUT were also investigated. Furthermore, molecular docking, molecular dynamics simulations, and the analysis of the binding free energies of EVO and RUT were carried out against the anticancer target topoisomerase 1 (TOP1) to clarify their anticancer mechanisms. The docking results indicated that they could inhibit TOP1 by intercalating into the cleaved DNA-binding site to form a TOP1–DNA–ligand ternary complex, suggesting that they may be potential TOP1 inhibitors. Molecular dynamics (MD) simulations evaluated the binding stability of the TOP1–DNA–ligand ternary complex. The calculation of binding free energy showed that the binding ability of EVO with TOP1 was stronger than that of RUT. These results elucidated the structure–activity relationship and the antitumor mechanism of EVO and RUT at the molecular level. It is suggested that EVO and RUT may be potential compounds for the development of new anticancer drugs.

Redox induced electron transfer in lithium polysulfide – A DFT study

This study reports the existence of redox-induced electron transfer in lithium polysulfides (RIET). The presence of redox-induced electron transfer in lithium polysulfides is confirmed using a DFT study. The sulfur gets oxidized, and lithium gets reduced during the removal of an electron from lithium polysulfides. The condensed Fukui function from Natural Population Analysis (NPA) charge and electron density augment RIET. The higher number of sulfur contributes to the total nucleophilic character of lithium polysulfide and holds lithium tightly. The presence of an electric field enhances the nucleophilicity of sulfur atoms and, hence, the reactivity of lithium polysulfides.

Chromium Nitride Umpolung Tuned by the Locus of Oxidation.

Oxidation of a series of CrV nitride salen complexes (CrVNSalR) with different para-phenolate substituents (R = CF3, tBu, NMe2) was investigated to determine how the locus of oxidation (either metal or ligand) dictates reactivity at the nitride. Para-phenolate substituents were chosen to provide maximum variation in the electron-donating ability of the tetradentate ligand at a site remote from the metal coordination sphere. We show that one-electron oxidation affords CrVI nitrides ([CrVINSalR]+; R = CF3, tBu) and a localized CrV nitride phenoxyl radical for the more electron-donating NMe2 substituent ([CrVNSalNMe2]•+). The facile nitride homocoupling observed for the MnVI analogues was significantly attenuated for the CrVI complexes due to a smaller increase in nitride character in the M≡N π* orbitals for Cr relative to Mn. Upon oxidation, both the calculated nitride natural population analysis (NPA) charge and energy of molecular orbitals associated with the {Cr≡N} unit change to a lesser extent for the CrV ligand radical derivative ([CrVNSalNMe2]•+) in comparison to the CrVI derivatives ([CrVINSalR]+; R = CF3, tBu). As a result, [CrVNSalNMe2]•+ reacts with B(C6F5)3, thus exhibiting similar nucleophilic reactivity to the neutral CrV nitride derivatives. In contrast, the CrVI derivatives ([CrVINSalR]+; R = CF3, tBu) act as electrophiles, displaying facile reactivity with PPh3 and no reaction with B(C6F5)3. Thus, while oxidation to the ligand radical does not change the reactivity profile, metal-based oxidation to CrVI results in umpolung, a switch from nucleophilic to electrophilic reactivity at the terminal nitride.

Interaction of Cysteine with Li+ and LiF in the Presence of (H2O) n (n = 0-6) Clusters.

The interaction between cysteine with Li+ and LiF in the microcosmic water environment was investigated to elucidate how ions interact with amino acids and the cation–anion correlation effect involved. The structures of Cys·Li+(H2O)n and Cys·LiF(H2O)n (n = 0–6) were characterized using ab initio calculations. Our studies show that the water preferentially interacts with Li+/LiF. In Cys·Li+(H2O)0–6, Li+ interacts with amino nitrogen, carbonyl oxygen, and hydrophobic sulfur of Cys to form a tridentate mode, whereas in Cys·LiF(H2O)n, Li+ and F– work in cooperation and interact with carbonyl oxygen and hydroxyl hydrogen of Cys to form a bidentate type. The neutral and zwitterionic forms are essentially isoenergetic when the water number reaches three in the presence of Li+, whereas this occurs at four water molecules in the presence of LiF. Further research revealed that the interaction between Li+/LiF and Cys was mainly electrostatic, followed by dispersion, and the weakest interaction occurs at the transition from the neutral form to zwitterionic form. Natural population analysis charge analyses show that for Cys·Li+(H2O)n, the positive charge is mostly concentrated on Li+ except for the system containing three water molecules. For Cys·LiF(H2O)n, the positive charge is centered on the LiF unit in the range n = 0–6, and at n = 5, electron transfer from Cys to water occurs. Our study shows that the contribution of anions in zwitterionic state stabilization should be addressed more generally along with cations.

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Plasma-Assisted Dinitrogen Activation via Dual Platinum Cluster Catalysis: A Strategy for Ammonia Synthesis under Mild Conditions

Structural diversity of copper(II) complexes with three dimensional network: Crystal structure, Hirshfeld surface analysis, DFT calculations and catalytic activity

Three new copper(II) complexes containing benzoic acid (2-hydroxy-3-methoxy-benzylidene)-hydrazide (HL) viz., [Cu(L)(H2O)]NO3∙H2O 1, [Cu(L)(NO3)(H2O)] H2O 2 and [Cu4(L)4](ClO4)43 have been synthesized and characterized using physicochemical and spectroscopic methods. Complexes 1 and 2 are mononuclear while 3 is tetranuclear. In these complexes the center Cu(II) ions are four, five and six-coordinated in 1–3, respectively. All complexes involve hydrogen bonds and π⋯π interactions which develop supramolecular assemblies of different dimensionalities and architectures. The Hirshfeld surface analysis with 2D fingerprint plots revealed the short-range possible intermolecular interactions in these complexes. The molecular geometries in the ground state have been calculated using density functional theory (DFT) method with 631G(d) and 6–311++G(d,p) basis sets. The natural population analysis (NPA) and Mulliken charge distribution analysis showed the different electron donors which coordinate with copper. Some global reactivity descriptors like chemical potential (μ), electronegativity (χ), hardness (η) and electrophilicity index (ω) were also evaluated using DFT method. Additionally, antioxidant superoxide catalytic activity was also measured. The results of catalytic measurements exhibited that 2 provide an effective and selective catalytic system for dismutation of superoxide anion (O2∙-).

Theoretical investigation of mechanism and ligand effects on half-sandwich iridium complexes for direct reductive amination

The reaction mechanisms of direct reductive amination catalyzed by half-sandwich Cp*Ir complexes and the possible side reactions — transfer hydrogenation of ketones and N-formylation of amines have been explored by density functional theory (DFT). The reaction involves two steps: (1) the hydridoiridium formation as a rate-determining step, and (2) the hydride transfer to obtain amines. The relationships between the structure and activity of Cp*Ir complexes were analyzed by natural population analysis (NPA), Bader's atoms in molecules theory (AIM) and frontier molecular orbital (FMO). In general, the picolinamidato ligands are more favorable than the sulfonamidato ones due to the electronic effect. The catalyst with the phenyl ring bearing functional groups on the N-amide exerts the positive effect on the catalytic activity. Furthermore, the electron-donating group on the pyridine ring provides better performance owing to the higher NPA charge on the Ir atom, the lower electron density at the Ir-Cl bond critical point, and the destabilization of the highest occupied molecular orbital (HOMO).

Understanding the molecular mechanism of the chlorine atom transfer between ammonia and hypochlorous acid with electron localisation function (ELF)

The nature of the chlorine atom transferred between ammonia and hypochlorous acid was investigated using the bonding evolution theory (BET). The application of topological analysis of electron localisation function (ELF) and Thom's catastrophe theory enabled a detailed description of the evolution of chemical bonds and non-bonding electron density. The BET analysis was performed at the DFT(MN15)/def2-TZVPPD computational level. The Hausdorff distance was used as a qualitative view on the evolution of the ELF field. The molecular mechanism of the chlorination reaction consisted of 11 structural stability domains (SSDs) and 10 ELF catastrophes. Four SSDs were observed before the transition state (TS). The TS was found in SSD V, and six SSDs were distinguished after the TS. The energy barriers were analysed with six different DFT functionals (B3LYP, CAM-B3LYP, LC-ωPBE, M11, MN15, ωB97XD) and def2-TZVPPD basis set. The energy barrier between transition state and reagents was smaller than transition state and products, thus the chlorination of ammonia is thermodynamically favourable. Alongside BET analysis, NPA (natural population analysis), AIM (atoms in molecules) and APT (atomic polar tensor) charge analysis was also applied to the transferred chlorine atom.

Tuning catalytic activity of dimolybdenum paddlewheel complexes by ligands: mechanism study on the radical addition reaction of CCl4 to 1-hexene

The detailed catalytic mechanism of a series of paddlewheel complexes [Mo2L4] featuring Mo-Mo quadruply-bond on radical addition of CCl4 to 1-hexene was studied using density functional theory. Different ligands of Mo-Mo bond are investigated to illustrate the ligand effect on the catalytic activity. The results show that the Mo-Mo quadruply-bond paddlewheel complexes have high catalytic activities on the title reaction. The whole reaction involves 4 steps. Firstly, the C-Cl bond of first CCl4 is activated by [Mo2L4] catalyst, and [Mo2L3Cl] and CH3COOCCl3 are obtained. Then the second CCl4 adds to [Mo2L3Cl] to produce [Mo2L3Cl2] and·CCl3 radical;·CCl3 radical interacts with 1-hexene to get an addition, the addition product which reacts with one Cl atom of [Mo2L3Cl2] to get the last product nBuCHClCH2CCl3 and regenerate [Mo2L3Cl]. The addition of the first CCl4 to [Mo2L4] catalyst is the rate-determining step of the whole reaction. Because this step is not in the catalytic cycle, the reaction would speed up after a certain period of time. The catalytic activity of dimolybdenum paddlewheel complex is depended on the natural population analysis (NPA) charge of Mo and the redox potential E(Mo24+/Mo25+). The higher NPA of Mo atom and higher E(Mo24+/Mo25+) of the catalyst, the higher catalytic activity it has. Our results provide an explanation for experimental observations and useful insights for further development of bimetallic catalysts in radical addition reactions.