Migration of Holstein Polarons in Anatase TiO₂

A simple yet reliable valence bond theory was applied to ascertain the effective size and shape for the electron and hole polarons in bulk anatase TiO₂ by examining the extent of polaron charge delocalization. It was found that the electron polaron is approximately 2 times as large as its hole counterpart, leading to a faster electron diffusion than hole hopping with regard to the electron–phonon coupling strength. Moreover, the oblate hole polaron exhibits a pronounced directional heterogeneity in migration, whereas the nearly spherical electron polaron tends to diffuse along all possible lattice directions. In light of the notable delocalization characteristics of both polarons, their migration should proceed in an adiabatic manner, and their rates can be calculated by the Arrhenius equation. It turns out that our calculated polaron mobilities at 300 and 1300K are both in excellent agreement with experimental values, justifying our novel approach for Holstein polaron modeling in crystalline semiconductors

N–H Bond Activation Catalyzed by an Anderson-Type Polyoxometalate-Based Compound: Key Role of Transition-Metal Heteroatom

Polyoxometalates (POMs) have a broad array of applied platforms with well-characterized catalysis to achieve N–H bond activation. Herein, the mechanism of the Anderson-type POM-based catalyst [FeIIIMoVI6O18{(OCH2)3CNH2}2]3– ([TrisFeIIIMoVI6O18]3–, Tris = {(OCH2)3CNH2}2) for the N–H bond activation of hydrazine (PhHNNHPh) was investigated by density functional theory calculations. The results reveal that [TrisFeIIIMoVI6O18]3– as the active species is responsible for the continuous abstraction of two electrons and two protons of PhHNNHPh via a proton-coupled electron transfer pathway, resulting in the activation of two N–H bonds in PhHNNHPh and thus the product PhNNPh. H2O2 acts as an oxidant to regulate catalyst regeneration. Based on the proposed catalytic mechanism, the key role of the heteroatom FeIII in [TrisFeIIIMoVI6O18]3– was disclosed. The d-orbital of FeIII in [TrisFeIIIMoVI6O18]3– acts as an electron receptor to promote the electron transfer (ET) in the rate-determining step (RDS) of the catalytic cycle. The substitution of the heteroatom FeIII of [TrisFeIIIMoVI6O18]3– with CoIII, RuIII, or MnIII is expected to improve the catalytic activity for several reasons: (i) the unoccupied molecular orbitals of POM-based compounds containing CoIII or RuIII are low, which is beneficial for the ET of RDS; (ii) For N–H bond activation catalyzed by the MnIII-containing POM-based compound, the transition state of RDS is stable because the d-orbital of its active site is half-filled, which results in a low free-energy barrier

The Effect of Dyes with Different π‑Linkers on the Overall Performance of P‑DSSCs: Lessons from Theory

A series of Keggin-type polyoxometalate (POM)-based organic–inorganic complexes (systems 2–8) were designed with different π-linkers on the basis of the molybdate–pyrene hybrid (system 1). UV–vis spectra and charge transfer (CT) parameters of designed systems were systematically analyzed by density functional theory (DFT) and time-dependent DFT (TD-DFT). The results indicate that the absorption spectra are red-shifted and the absorption intensities are enhanced with increasing number of phenylacetylene π-oligomers and introducing benzodifuranone between benzene and ethyne. However, the π-linkers near POMs are “dissolved” in the total system and the excitation occurs in a local region with increasing π-linkers. Systems 3 and 6 possess the maximum CT distance and CT charge among systems 1–5 and systems 6–8, respectively, resulting from the balance point between effectiveness of structures and delocalization. The absorption spectra of systems 6–8 obviously red-shift in comparison to systems 1–5. The present study is a further step toward the optimal absorption and CT properties

Mo₃C₂: Active Electrocatalysts for Spontaneous Nitrogen Reduction Reaction

Electrocatalytic nitrogen reduction reaction (NRR) is an ideal alternative to the traditional Haber-Bosch method. However, the current lack of suitable electrocatalysts to achieve both high activity and selectivity hinders the practical application of NRR. Herein, we find that Mo3C2 is a promising N2 electroreduction catalysts. All hydrogenation processes are spontaneous and exothermic. In addition, Mo3C2 has a good suppressed effect on the competitive hydrogen evolution reaction (HER). The present work provides valuable information for experimental and theoretical studies to explore the catalytic potential of Mo-based MXenes catalysts for NRR

Electronic Properties of Unprecedented Bridging Organoimido-Substituted Hexamolybdate: New Insights from Density Functional Theory Study

The organoimido functionalization of polyoxometalates (POMs) has drawn tremendous attention due to particular merits in fabricating POM-based hybrid materials with finely tunable properties. The electronic properties, orbital and bonding characters of unprecedented bridging organoimido-substituted hexamolybdate are investigated using density functional theory methods. Among the organoimido-bridged hexamolybdates, [Mo6O16(2,6-Me2-NC6H3)2(μ2-2,6-Me2-NC6H3)]2− (3-Ar-1), which features two terminal and one bridging organoimido ligand, is more favorable. The calculations confirm that the three-center (3c) π bond originates from the coplanarity of bridging nitrogen atom with two Mo atoms and the hybridization of bridging nitrogen. The 3c bond stabilizes the organoimido-bridged anion 3-Ar-1. Compared with cis-bifunctionalized organoimido derivative [Mo6O17(2,6-Me2-NC6H3)2]2− (2-Ar), the bonding interaction between terminal organoimido ligand and hexamolybdate cluster in 3-Ar-1 is strengthened by the bridging organoimido. The results are in good agreement with the analysis of the Wiberg bond index of the Mo−N bond. The organoimido segment modifies the occupied molecular orbitals of organoimido hexamolybdates. The unoccupied molecular orbitals in 3-Ar-1 are largely nonbonding Op and Mod orbitals in character, which resemble those of 2-Ar

Metal-Free Z‑Scheme aza-CMP/C₂N Heterostructure to Facilitate Photocatalytic CO₂ Reduction: A Computational Study

Inspired by photosynthesis in nature, Z-scheme heterostructures have attracted increasing attention due to their narrow forbidden bandwidth and strong redox capability. Herein, by means of density functional theory (DFT) computations, a metal-free Z-scheme aza-CMP/C2N heterostructure was proved to be an effective CO2 reduction reaction (CO2RR) photocatalyst. Compared with aza-CMP and C2N, aza-CMP/C2N has excellent photocatalytic activity due to its narrow band gap and strong light absorption capacity. By calculating the free energy change during the CO2 reduction process, we found that aza-CMP/C2N can catalyze CO2 reduction to CH4 and CH3OH, among which CO2 → COOH* is the rate-determining step with a ΔG of 0.58 eV. Therefore, the Z-scheme aza-CMP/C2N heterostructure is expected to be an excellent metal-free catalyst for photocatalytic CO2 reduction

Theoretical Insight into Oxidation of Anilines to Azobenzenes Catalyzed by Hexamolybdate: Outer-Sphere Electron and Proton Transfer

Recently, the catalytic activity of Lindqvist-type hexamolybdate [Mo6O19]2– in the oxidation of an aniline derivative (LPhNH2, L = substituent) was demonstrated by Wei and co-workers (Angew. Chem. Int. Ed. 2021, 60, 6382–6385). Herein, taking phenylamine (PhNH2) oxidation to azobenzene (PhNNPh) as a model reaction, we report the density functional theory investigation of the catalytic mechanism of [Mo6O19]2– and illustrate the critical experimental phenomena. During the catalytic reaction, once the preassociation of [Mo6O19]2– and PhNH2 takes place, electron transfer and proton transfer immediately proceed to form an N radical intermediate. The higher the highest occupied molecular orbital energy of the substrate, the easier the formation of the N radical intermediate. The N–N bond formation proceeds via the second PhNH2 nucleophilic attack on the N radical intermediate. The substituent position and the N reaction site of the substrate have a significant effect on the second PhNH2 nucleophilic attack process. In the reaction process, the six MoVI of [Mo6O19]2– are still hexacoordinated, which is defined as the outer-sphere pathway. One of the factors determining the product selectivity is the electrostatic repulsion between LPhNH2 and the N radical intermediate. The experiment reveals that the product yield is increased by the addition of Na2S2O3, while the catalytic reaction is completely deactivated with Na2CO3 or K3PO4. Based on the proposed mechanism, the experimental observation was rationalized. The S2O32– part of Na2S2O3 has a similar function as the electron-withdrawing substituent due to its low lowest unoccupied molecular orbital (LUMO) energy, which reduces the LUMO energy of the N radical intermediate and thus facilitates PhNH2 nucleophilic attack, while the CO32– part of Na2CO3 or PO43– part of K3PO4 has an undesirable effect on the electrophilicity of the N radical intermediate, resulting in the interruption of the catalytic reaction. This work would provide a detailed understanding of the catalytic reaction

A Rational Design for Dye Sensitizer: Density Functional Theory Study on the Electronic Absorption Spectra of Organoimido-Substituted Hexamolybdates

The novel dyes of organoimido-substituted hexamolybdates for positive type dye-sensitized solar cells (p-type DSSCs) have been studied on the basis of time-dependent density functional theory (TDDFT) calculations. The electronic absorption spectra, light harvesting efficiency (LHE), charge separation efficiency (CSE), and holes injecting efficiency (HJE) of designed systems have been systematically investigated. The results reveal that the long π-conjugated bridge and auxochrome play crucial roles in red-shifting the absorption bands and reinforcing the intensity of the bands. Based on [(<i>n</i>-C₄H₉)₄N]₂[Mo₆O₁₈(N-1-C₁₀H₆-2-CH₃)], the designed systems <b>6</b> and <b>4</b> are good candidates for p-type DSSC dyes due to the strong absorption in the visible region as well as high LHE, CSE, and HJE. The maximum absorption of the one-electron-reduced system obviously red-shifts to the visible region. Therefore, the highly efficient dyes of p-type DSSC can be prepared by reducing POM-based organic–inorganic hybrids which have both long π-conjugated bridge and auxochrome

Theoretical Study on the Electronic Spectrum and the Origin of Remarkably Large Third-Order Nonlinear Optical Properties of Organoimide Derivatives of Hexamolybdates

Electronic spectrum of organoimide derivatives of hexamolybdates have first been calculated within the time-dependent density-functional theory in conjunction with Van Leeuwen−Baerends (LB94) exchange correlation potential, statistical average of orbital potentials (SAOP), and gradient-regulated connection potential (GRAC), respectively. The GRAC yields much better agreement with experiments for the excitation energies comparing with both LB94 and SAOP. The analysis of transition nature indicates that there is a significant difference between the diagonal and the orthogonal substituted derivatives. The static and dynamic third-order polarizabilities are calculated using time-dependent density-functional theory combined with the sum-over-states method. The results show that these derivatives possess remarkable large molecular third-order polarizabilities, especially for system 8 with −17882.6 × 10-36 esu. This value is about 250 times that for the C60 molecule. Adding the organoimide segment to the [Mo6O19]2- can substantially increase the γ value. This variation can be traced to the different electronic transition characteristics between the derivatives of [Mo6O19]2- and [Mo6O19]2-. For our studied systems, increasing the conjugation length and diagonal substituted are efficient ways to enhance the third-order polarizability. Thus, the organoimide derivatives of hexamolybdates may comprise a new promising class of nonlinear optical materials from the standpoint of large γ values, small dispersion behavior, and high transparency

On the Origin of Alternating Bond Distortions and the Emergence of Chirality in Polyoxometalate Anions

Alternating short and long bond length (ABL) distortions observed within the ring structures of molecular metal oxide anions or polyoxometalates (POMs) are reminiscent of the cooperative linear ABL distortions in perovskite d0 metal oxides. We show herein that these distortions have a common origin: a pseudo Jahn−Teller (PJT) vibronic instability. Four POM structural types with different MnOn ring sizes are investigated herein using density functional theoretical methods: Lindqvist [M6O19]q− (n = 4), Keggin α-[XM12O40]q− (n = 6), Wells−Dawson α-[X2M18O62]q− (n = 8), and Preyssler [(Na)P5W30O110]14− (n = 10), where M = MoVI and WVI and X = SiIV, GeIV, PV, AsV, SVI, and SeVI. Chirality is induced within the latter three structural types by the ABL ring distortions. The calculations confirm the PJT vibronic origin of the ABL distortions with good agreement between calculated geometries and published single-crystal X-ray diffraction data. Both theory and experiment show that the vibronic interaction and distortion magnitude increase for (1) molybdates relative to that of tungstates, (2) larger MnOn ring sizes, (3) increases in negative charge of the internalized fragments (O2− or XO4q−), and (4) d0 versus dn metal oxidation states. The PJT vibronic coupling model explains these observations in terms of the energy gap between Kohn−Sham frontier molecular orbitals (MOs) concomitant with the propensity for metal−oxygen π-bonding within the MnOn rings. The frontier MOs for the undistorted nuclear configurations are largely nonbonding π-Op (occupied) and π-Md (unoccupied) in character, where smaller HOMO−LUMO (H−L) gap energies lead to greater metal−oxygen π-orbital mixing under the influence of the nuclear distortion. A reduction in π-bond order decreases the distortion in mixed-valence POMs. Of the tungstates examined, only the Preyssler anion shows pronounced ABL ring distortions, which derive from its large ring size and concomitant small H−L gap