The molecular and electronic structure of the Mo12S24 macromolecule as a model of the active component of a hydrodesulfurization catalyst

The density functional theory (DFT) with the B3P86 hybrid exchange-correlation functional was used to calculate the molecular and electronic structure of the Mo₁₂S₂₄ macromolecule as a single MoS₂ layered structure slab. Calculations with geometry optimization are indicative of insignificant relaxation of the coordinatively unsaturated Mo and S atoms, which corresponds with the literature DFT data on the MoS₂ single slab obtained with periodic boundary conditions. The calculated forbidden band width (0.85–0.98 eV) is comparable with its experimental value (1.30 eV) and the results of DFT calculations of MoS₂ with periodic boundary conditions (0.89 eV). An analysis of the electronic state of the surface Mo centers in the Mo₁₂S₂₄ macromolecule showed that these centers were reduced to a greater degree than the Mo(IV) atoms in the bulk. The adsorption complex between the Mo₁₂S₂₄ macromolecule and six H₂S molecules was calculated to characterize the adsorption ability of the coordinatively unsaturated Mo centers. The structure and energy characteristics of the adsorption complex corresponded to weak donor-acceptor interaction between the π lone pair of H₂S and the surface (reduced) Mo centers. The suggestion was made that the active center of the catalytic cycle of thiophene hydrodesulfurization should induce the oxidative addition of H₂ followed by the occlusion of hydrogen into the MoS₂ matrix.     

Interpretation of the difference of optimal Mo density in MoS<Subscript>2</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and MoS<Subscript>2</Subscript>-TiO<Subscript>2</Subscript> HDS catalysts

The first part of this paper deals with the morphology of the MoS₂ phase and its oxide precursor, the MoO₃ phase, mainly from a geometrical point of view. After giving a brief review of the literature describing the structure of these compounds, Mo densities in both phases were calculated along various crystallographic planes. Further, using structural models recently proposed by others, Mo densities in MoS₂ were also calculated in the case of an epitactic growth on γ-Al₂O₃ and TiO₂ model surfaces. Then, the calculated Mo densities were compared with experimental results (Mo density when HDS activity is maximal) previously obtained for catalysts constituted of MoS₂ supported on a low SSA TiO₂, a high SSA TiO₂ and a conventional γ-alumina. It was suggested that either on alumina or titania the MoS₂ phase is growing as (100) MoS₂ planes. However, while on the alumina the optimal MoS₂ phase might be constituted of dispersed MoS₂ slabs covering only a part of the alumina surface (2.9–3.9 Mo atoms/nm²), on titania the optimal MoS₂ phase might be constituted of a uniform MoS₂ monolayer (5.2 atoms/nm² for the high SSA titania, which is equal to the Mo density of a perfect MoS₂ (100) plane). This difference may originate in the creation of a 'TiMoS' phase enhancing the S atoms mobility over Mo/TiO₂-sulfided catalysts. Indeed, while in the case of a γ-alumina carrier the active sites (labile S atoms) are located on the edge of MoS₂ slabs making the ratio Mo_edge/Mo_total a crucial parameter for the catalytic performances, in the case of a titania carrier the labile sulfur atoms might be statistically distributed all over the TiMoS active phase. Further, the higher Mo density observed over the high SSA titania (5.2 atoms/nm²) when compared to that over the low SSA titania (4.2 atoms/nm²) was supposedly due to the pH-swing method advantageously used to prepare the former carrier. Indeed, this method allows giving a solid with enhanced mechanical properties providing a good stability to the derived catalysts under experimental conditions. In addition, this TiO₂ carrier exhibits a great homogeneity, with a surface structure substantially uniform, which might be adequate for a long-range growth of (100) MoS₂ slabs.     

Elucidation by computer simulations of the CUS regeneration mechanism during HDS over MoS<Subscript>2</Subscript> in combination with <Superscript>35</Superscript>S experiments

The first part of this paper is a short review of the ³⁵S radioactive tracer methods developed in recent years. Then, the experimental results obtained so far on Mo/Al₂O₃ catalysts are compared with computer simulation results recently claimed in order to elucidate the coordinatively unsaturated site (CUS) creation/replenishment/ regeneration mechanism over MoS₂ crystallites. The computer simulations allowed us to pre-select thermodynamically acceptable mechanisms among a set of suggested ones. Then, by comparison of the calculated activation energies with the ³⁵S experiments results we could further validate the most probable mechanism. This mechanism involved the dissociative adsorption of an H₂ molecule on the metallic edge of a MoS₂ crystallite surface with further creation of a CUS by release of one H₂S molecule in the gas phase. Both laboratory and computer simulated experiments permitted to calculate the activation energy for the H2S liberation reaction. In both cases, this energy was about 10- 12 kcal/mol, confirming the accuracy of the proposed mechanism. Moreover, the calculated activation energy of the rate-limiting step for the creation of one CUS by the proposed mechanism was about 23 kcal/mol, which was also in good agreement with the experimental activation energy of the dibenzothiophene (DBT) hydrodesulphurisation (HDS) reaction (typically about 20- 22 kcal/mol). This correlation indicated that the DBT HDS reaction rate might be intrinsically governed by the CUS formation/replenishment process, i.e. that the vacancy formation process is a crucial parameter in the global HDS reaction mechanism. Nevertheless, in the case of the 4,6-dimethyl DBT (4,6-DMDBT) HDS reaction, the experimental activation energy is higher (approx. 30 kcal/mol), confirming that external parameters induced by the 4,6-DMDBT-specific properties themselves are likely to play an important role in the reaction process, in addition to the ones intrinsic to the catalytic phase.     

Thermal stability and surface structure of Mo/CeO<Subscript>2</Subscript> and Ce-doped Mo/Al<Subscript>2</Subscript>O<Subscript>3</Subscript> catalysts

In order to explore the influence of CeO₂ on the structure and surface characteristics of molybdena, an investigation was undertaken by using N₂ adsorption (BET method), thermal analysis and in-situ diffuse reflectance infrared (DRIFT) techniques. In this work, the Mo/CeO₂ and Ce-Mo/Al₂O₃ samples were prepared by impregnation and co-precipitation methods with high Mo loadings. Combining the results one may notice that the presence of ceria led to the increase of polymerized surface Mo species so as to forming Mo-O-Ce linkages besides the formation of coupled O=Mo=O bonds indicative of polymeric MoO₃. From thermal analysis, it can be inferred that Mo/Al₂O₃ is the thermally most stable material in the temperature range used in the experiment (up to 900°C), whereas Ce-Mo/Al₂O₃ and Mo/CeO₂ samples undergo morphological modifications above 700°C resulting in lattice defects, which motivate the mobility of Mo and Ce ions and thus enhance the possibility of interaction between them. Additionally, their activity towards CO adsorption needs reduced ceria and molybdena containing coordinatively unsaturated sites (CUS), oxygen vacancies and hydroxyl groups to form various carbonate species.     

Structure and surface properties of ZrO<Subscript>2</Subscript>, CeO<Subscript>2</Subscript>, and Zr<Subscript>0.5</Subscript>Ce<Subscript>0.5</Subscript>O<Subscript>2</Subscript> prepared by a microemulsion method according to X-ray diffraction,TPR, and EPR data

It was established by X-ray diffraction, TPR, and EPR that microemulsion (m.e.) synthesis yields the binary oxides ZrO₂(m.e.) and CeO₂(m.e.) and the mixed oxide Zr_0.5Ce_0.5O₂(m.e.) in the form of a tetragonal, cubic, and pseudocubic phase, respectively, having crystallite sizes of 5–6 nm. The bond energy of surface oxygen in the (m.e.) samples is lower than in their analogues prepared by pyrolysis. Hydrogen oxidation on the oxides under study occurs at higher temperatures than CO oxidation. ZrO₂(m.e.) and CeO₂(m.e.) are active in O₂⁻ formation during NO + O₂ adsorption, while CeO₂ is active during CO + O₂ adsorption, too. However, its amount here is one-half to one-third its amount in the pyrolysis-prepared samples, signifying a reduced number of active sites, which are Zr⁴⁺ and Ce⁴⁺ coordinatively unsaturated cations and Me⁴⁺-O²⁻ pairs. O₂⁻ radical anions are stabilized in the coordination sphere of Zr⁴⁺ coordinatively unsaturated cations via ionic bonding, and in the sphere of Ce⁴⁺ cations, via covalent bonding. Ionic bonds are stronger than ionic-covalent bonds and do not depend on the ZrO₂ phase composition. Zr_0.5Ce_0.5O₂ is inactive in these reactions because of the strong interaction of Zr and Ce cations. It is suggested that Ce^{(4 + β)+} coordinatively unsaturated cations exist on its surface, and their acid strength is lower than that of Zr⁴⁺ and Ce⁴⁺ cations in ZrO₂ and CeO₂, according to the order ZrO₂ > CeO₂ ≥ Zr_0.5Ce_0.5O₂. Neither TPR nor adsorption of probe molecules revealed Zr cations on the surface of the mixed oxide.     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

A New Molybdophosphate Constructed From {Mo<Stack><Subscript>2</Subscript><Superscript>V</Superscript></Stack>O<Subscript>4</Subscript>(H<Subscript>2</Subscript>O)<Subscript>6</Subscript>}<Superscript>2+</Superscript> and 1-Hydroxyethylidenediphosphonate

A new molybdophosphate (NH₄)₈{Mo₂^VO₄[(Mo₂^VIO₆)CH₃C(O)(PO₃)₂]₂}·14H₂O (1), has been synthesized by the reaction of {Mo₂^VO₄(H₂O)₆}²⁺ fragments with 1-hydroxyethylidenediphosphonate (hedp HOC(CH₃)(PO₃H₂)₂), and it is characterized by ³¹P NMR, IR, UV, element analysis, TG and single-crystal X-ray analysis. The structure analysis reveals that the polyoxoanion can be described as two {(Mo₂^VIO₆)(CH₃C(O)(PO₃)₂} units connected by a {Mo₂^VO₄}²⁺ moiety. In the structure, the six Mo atoms are arranged into a new “W-shaped” structure, which represents a new kind of molybdophosphate.     

First heteroleptic Mo<Subscript>3</Subscript>S<Subscript>7</Subscript> clusters containing non-innocent phenanthroline ligands

Reaction of the thiobromide [Mo₃S₇Br₆]²⁻ cluster anion with 5,6-dimethyl-1,10-phenanthroline (Me₂Phen) in solution leads to the substitution of two bromide ligands and the subsequent formation of a new mixed-ligand neutral complex [Mo₃S₇Br₄(Me₂Phen)] (I). Reaction of [Mo₃S₇Br₆]²⁻ with 5,6-dimethyl-1,10-phenanthroline in CH₂Cl₂ followed by treatment of I with Na(Dtc) · 3H₂O (Dtc = diethyldithiocarbamate) results in the new mixed-ligand cluster complex [Mo₃S₇(Dtc)₂(Me₂Phen)]²⁺ (IIa). Slow evaporation of the CHCl₃ solution of the complex in the presence of PF₆⁻ gives crystals of {[Mo₃S₇(Dtc)₂(Me₂Phen)]Br}PF₆ · 3CHCl₃ (II) characterized by X-ray structural analysis. Close contacts S...S result in the formation of cationic dimers {[Mo₃S₇(Dtc)₂(Me₂Phen)]₂}⁴⁺ which form infinite chains through additional S_ax...Br contacts. All compounds were characterized by IR, elemental analysis and ESI-MS. Synthesized complexes represent the first examples of heteroleptic Mo₃S₇ clusters containing phenanthroline ligands.     

Reaction of Sulfur and Oxygen-Bridged 8-Quinolinolato Trinuclear Molybdenum Cluster [Mo<Subscript>3</Subscript>OS<Subscript>3</Subscript>(qn)<Subscript>3</Subscript>(H<Subscript>2</Subscript>O)<Subscript>3</Subscript>]<Superscript>+</Superscript> with Acetylene Carboxylic Acids

The reaction of a sulfur and oxygen-bridged 8-quinolinolato trinuclear molybdenum cluster [Mo₃OS₃(qn)₃(H₂O)₃]⁺ (3; Hqn = 8-quinolinol) with equimolar amounts of acetylene carboxylic acid, 4-pentynoic acid, 5-hexynoic acid, acetic acid, and pimelic acid gave clusters having μ-carboxylato groups, [Mo₃OS₃(qn)₃(H₂O)(μ-HC≡CCOO)] (6), [Mo₃OS₃(qn)₃(H₂O)(μ-HC≡C(CH₂)₂COO)] (7), [Mo₃OS₃(qn)₃(H₂O)(μ-HC≡C(CH₂)₃COO)] (8), [Mo₃OS₃(qn)₃(H₂O)(μ-CH₃COO)] (4), and [{Mo₃OS₃(qn)₃(C₂H₅OH)}₂(μ-C₇H₁₀O₄)] (5), respectively. X-ray structural analyses, ¹H NMR, and electronic spectra of these clusters made clear that each of the COO⁻ groups of the reagents bridges two Mo atoms in each cluster and that no adduct formation occurred at the sulfurs in the clusters. The reaction of 3 with a large excess-molar amount (50 times) of acetylene carboxylic acid gave [Mo₃OS(μ₃-SCH=C(COOH)S)(qn)₃(H₂O)(μ-HC≡CCOO)] (9) with two molecules of acetylene carboxylic acid, one acting as a carboxylato bridge and the other in adduct formation, as supported by the electronic and ¹H NMR spectra. The corresponding aqua cluster [Mo₃OS₃(H₂O)₉]⁴⁺ (1), on the contrary, reacts with acetylene carboxylic acid to give adduct [Mo₃OS(μ₃-SCH=C(COOH)S)(H₂O)₉]⁴⁺ (2). Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Composite electrocatalyst Mo<Subscript>x</Subscript>W<Subscript>1-x</Subscript>S<Subscript>2</Subscript> nanosheets on carbon fiber paper for highly efficient hydrogen evolution reaction

Molybdenum disulfide (MoS₂) or tungsten disulfide (WS₂), as a promising catalyst, is widely investigated for hydrogen evolution reaction (HER). In this work, a composite electrocatalysts Mo_xW_1-xS₂ is successfully decorated on carbon fiber paper (CFP) through a facile hydrothermal method. The three-dimensional porous CFP can enable the diffusion and penetration of electrolyte. Comparing with MoS₂ and WS₂ catalyst, the composite electrocatalyst Mo_xW_1-xS₂ nanosheets can expose the large number of electrochemically active sites. Hence, the as-prepared Mo_xW_1-xS₂/CFP (3:1) exhibit the outstanding HER catalytic activity with the small Tafel slope of 68 mV dec^?1 and the low overpotential of ??178.4?±?0.5 mV at a current density of 10 mA cm^?2. Chronoamperometric current test for 18 h confirm the long-term stability of the composite electrocatalyst.     

Reactivity of triangular oxalate cluster complexes [M<Subscript>3</Subscript>Q<Subscript>7</Subscript>(C<Subscript>2</Subscript>O<Subscript>4</Subscript>)<Subscript>3</Subscript>]<Superscript>2−</Superscript> (M = Mo or W; Q = S or Se)

The reactions of the oxalate complexes [M₃Q₇(C₂O₄)₃]²⁻ (M = Mo or W; Q = S or Se) with Mn^II, Co^II, Ni^II, and Cu^II aqua and ethylenediamine complexes in aqueous and aqueous ethanolic solutions were studied. The previously unknown heterometallic complexes [Mo₃Se₇(C₂O₄)₃Ni(H₂O)₅]·3.5H₂O (1) and K₃{[Cu(en)₂H₂O]([Mo₃S₇(ox)₃]₂Br)}·5.5H₂O (2) were synthesized. In these complexes, the oxalate clusters serve as monodentate ligands. The K(H₂en)₂[W₃S₇(C₂O₄)₃]₂Br·4H₂O salt (3) was isolated from solutions containing Co^II, Ni^II, or Cu^II aqua complexes and ethylenediamine. The reaction of [Mo₃Se₇(C₂O₄)₃]²⁻ with HBr produced the bromide complex [Mo₃Se₇Br₆]²⁻, which was isolated as (Bu₄N)₂[Mo₃Se₇Br₆] (4). Complexes 1–3 were characterized by X-ray diffraction, IR spectra, and elemental analysis. The formation of 4 was detected by electrospray mass spectrometry. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1645–1649, September, 2007.     

Solvothermal Syntheses,Crystal Structures,and Properties of New [Mn(<Emphasis Type="BoldItalic">dien</Emphasis>)<Subscript>2</Subscript>]<Superscript>2+</Superscript> Complexes

Summary.  The two new compounds Mn(dien)₂[MoS₄] (1) and Mn(dien)₂[Mo₂O₂S₆] (2) (dien = diethylenetriamine) were prepared under solvothermal conditions. Both compounds were obtained as phase-pure products. The structures consist of new [Mn(dien)₂]²⁺ cations and isolated tetrahedral [MoS₄]²⁻ (1) or [Mo₂O₂S₆]²⁻ (2) anions. Between the anions and the cations, hydrogen bonding is observed. Compound 1 crystallizes in the tetragonal space group I (a = 10.219(2), c = 9.259(2) ?, Z = 2), whereas 2 crystallizes in the monoclinic space group P2₁/c (a = 8.703(2), b = 18.390(4), c = 14.603(3) ?, β = 103.18(3)°, Z = 4). The thermal behaviour of the thiomolybdates was investigated using difference thermoanalysis (DTA) and thermogravimetry (TG). Both compounds decompose under argon with a single endothermic signal in the DTA curve (peak maximum: 252 (1) and 242°C (2)). Received November 5, 2001. Accepted December 27, 2001     

Density functional theory (DFT) study of O<Subscript>3</Subscript> molecules adsorbed on nitrogen-doped TiO<Subscript>2</Subscript>/MoS<Subscript>2</Subscript> nanocomposites: applications to gas sensor devices

Density functional theory calculations were carried out to investigate the adsorption behaviors of O₃ molecules on the undoped and N-doped TiO₂/MoS₂ nanocomposites. With the inclusion of vdW interactions, which correctly account the long-range dispersion energy, the adsorption energies and final geometries of O₃ molecules on the nanocomposite surfaces were improved. For O₃ molecules on the considered nanocomposites, the binding sites were located on the fivefold coordinated titanium atoms of the TiO₂ anatase. The structural properties of the adsorption systems were examined in view of the bond lengths and bond angles. The variation of electronic structures was also discussed in view of the density of states, molecular orbitals and distribution of spin densities. The results suggest that the adsorption of the O₃ molecule on the N-doped TiO₂/MoS₂ nanocomposite is more favorable in energy than that on the pristine one, indicating that the N-doped nanocomposite has higher sensing capability than the pristine one. This implies that the N-doped TiO₂/MoS₂ nanocomposite would be an ideal O₃ gas sensor. However, our calculations thus provide a theoretical basis for the potential applications of TiO₂/MoS₂ nanocomposites as efficient O₃ sensors, leading to very interesting results in the context of air quality measurement.     

Dimeric [Mo2S12]2− Cluster: A Molecular Analogue of MoS2 Edges for Superior Hydrogen‐Evolution Electrocatalysis

Proton reduction is one of the most fundamental and important reactions in nature. MoS₂ edges have been identified as the active sites for hydrogen evolution reaction (HER) electrocatalysis. Designing molecular mimics of MoS₂ edge sites is an attractive strategy to understand the underlying catalytic mechanism of different edge sites and improve their activities. Herein we report a dimeric molecular analogue [Mo₂S₁₂]^2?, as the smallest unit possessing both the terminal and bridging disulfide ligands. Our electrochemical tests show that [Mo₂S₁₂]^2? is a superior heterogeneous HER catalyst under acidic conditions. Computations suggest that the bridging disulfide ligand of [Mo₂S₁₂]^2? exhibits a hydrogen adsorption free energy near zero (?0.05 eV). This work helps shed light on the rational design of HER catalysts and biomimetics of hydrogen‐evolving enzymes.     

Synthesis,crystal structure and magnetic properties of the complex Co[Me<Subscript>2</Subscript>NC(S)NP(S)(OPr-<Emphasis Type="Italic">i</Emphasis>)<Subscript>2</Subscript>]<Subscript>2</Subscript>

The reaction of N-(diisopropoxyphosphorothioyl)-N′,N′-dimethylthiourea [Me₂NC(S)NHP(S)(OPr-i)₂, HL) potassium salt with Co(II) cation in aqueous ethanol gave the chelate complex Co(L-S,S′)₂(CoL₂). The structure of the resulting compound was studied by means of IR spectroscopy, microanalysis, and X-ray analysis. The metal center was found to occur in a tetrahedral S₄ environment formed by the C=S and P=S sulfur atoms of two deprotonated ligands L. Magnetic properties of the complex CoL₂ were also studied.     

A local spin evaluation into the active site models of [2Fe2S] ferrodoxin [Fe<Subscript>2</Subscript>S<Subscript>2</Subscript>(SR)<Subscript>4</Subscript>]<Superscript>2−</Superscript> (R=—H, —CH<Subscript>3</Subscript>)

To test the feasibility of local spin theory of Davidson and Clark for ferrodoxin clusters, the models [Fe₂S₂(SR)₄]²⁻ (R=—H, —CH₃) are chosen for evaluation. This purpose is realized by calculating the local spin expectation values 〈S _A·S _B〉, 〈S _A ² 〉, and m _A and discussing the connection between these expected values and the Heisenberg spin model (HSM) and the Noodleman broken-symmetry approach. In practical calculation, the spin-unrestricted Hartree-Fock (UHF) and spin-polarized density functional theory (DFT) are used and the calculational qualities of these two methods are also discussed. In addition, the theoretical magnetic coupling constants J _AB of these models are calculated by various computational schemes for comparison with both theoretical and experimental results previously reported. Supported by the Doctorial Initial Foundations of Hainan Normal University (Grant No. 13140252)     

Models of Molecular Structures of Al<Subscript>2</Subscript>Cr<Subscript>3</Subscript> and Al<Subscript>2</Subscript>Mo<Subscript>3</Subscript> Metal Clusters according to Density Functional Theory Calculations

The geometrical parameters of the molecular structures of aluminum–chromium and aluminum–molybdenum clusters Al₂Cr₃ and Al₂Mo₃ have been calculated by the OPBE/TZVP density functional theory (DFT) method with the Gaussian09 programL package. It has been found that each of these metal clusters can exist in twenty structural modifications, which significantly differ in stability and geometric parameters. Bond lengths and bond and torsion (dihedral) angles are reported for each of these modifications.     

Complexes of CuCl<Subscript>2</Subscript> with G1-8S-Dec dendrimer. DFT calculations of the structure and physicochemical properties

The calculations of the structure of dendrimer G1-8S-Dec (Si₅C₁₁₆H₂₄₄S₈) and its com-plexes with one, two, three, or four CuCl₂ molecules were carried out for the first time using the density functional theory (DFT). The geometric structures of the complexes and the spin density distribution were determined. The states with the maximum multiplicity are most favorable for the complexes studied. The interaction energies of dendrimer G1-8S-Dec with CuCl₂ molecules were calculated. Under standard conditions, the formation of complexes with a higher multiplicity of up to four CuCl₂ molecules is most favorable. All the four considered complexes contain paramagnetic centers in which an unpaired electron is “local-ized” on the tetrahedra with the central Cu atom and two S atoms and two Cl atoms at the vertices of the tetrahedron.     

Benzene Adsorption on C<Subscript>24</Subscript>, Si@C<Subscript>24</Subscript>, Si-Doped C<Subscript>24</Subscript>, and C<Subscript>20</Subscript> Fullerenes

The absorption feasibility of benzene molecule in the C₂₄, Si@C₂₄, Si-doped C₂₄, and C₂₀ fullerenes has been studied based on calculated electronic properties of these fullerenes using Density functional Theory (DFT). It is found that energy of benzene adsorption on C₂₄, Si@C₂₄, and Si-doped C₂₄ fullerenes were in range of –2.93 and –51.19 kJ/mol with little changes in their electronic structure. The results demonstrated that the C₂₄, Si@C₂₄, and Si-doped C₂₄ fullerenes cannot be employed as a chemical adsorbent or sensor for benzene. Silicon doping cannot significantly modify both the electronic properties and benzene adsorption energy of C₂₄ fullerene. On the other hand, C₂₀ fullerene exhibits a high sensitivity, so that the energy gap of the fullerene is changed almost 89.19% after the adsorption process. We concluded that the C₂₀ fullerene can be employed as a reliable material for benzene detection.     

Quantum-chemical modeling of defects in PbTe crystals doped with VTe<Subscript>2</Subscript> and V<Subscript>3</Subscript>Te<Subscript>4</Subscript>

Quantum-chemical modeling of defects in PbTe crystals doped with VTe₂ and V₃Te₄ (PbTe(V)) has been performed. It has been shown that, at the B3LYP/LanL2DZP level, the effect of single defects (like vanadium atoms or lead vacancies) in the charges and electrostatic potentials is small and does not exceed 0.1e and 0.3 eV, respectively. Calculations predict that the location of a lead vacancy in the vicinity of a vanadium atom is energetically favorable. Fragments of chains of tellurium atoms formed upon association of vacancies can serve as active annihilation centers (AACs). In PbTe clusters, Te-Te chains are most abundant, Te-Te-Te-Te chains are less abundant, and Te-Te-Te chains are even less frequently encountered. AACs form beginning with association of three vacancies in PbTe clusters and beginning with association of two vacancies in PbTe(V) clusters. This fact that a smaller number of vacancies are required for formation of AACs in the PbTe(V) cluster can be responsible for that the number of annihilation centers experimentally found by the positron annihilation method in PbTe(V) is ∼1.2–1.4 times as large as the number of AACs in undoped PbTe.