A density functional study of chemical,magnetic and thermodynamic properties of small palladium clusters

Structural, chemical, magnetic and thermodynamic properties of palladium clusters Pd_n with n = 2–11 are studied using density functional methods. The average bond length, entropy, enthalpy and polarisability are observed to increase as the cluster grows in size. The binding energy per atom also increases with cluster size. Stability function and atom addition energy change predict that Pd₄, Pd₆ and Pd₉ are relatively more stable than their neighbouring clusters. Electron affinity, electronegativity and electrophilicity values suggest that larger clusters have stronger tendency to accept electrons, thereby supporting the relative stability of Pd₄ and Pd₆. Chemical hardness is also seen to decrease with cluster size, which suggests that large clusters are more prone to changes in their electronic structure. The magnetic properties of these clusters are reported.     

The influence of Sc doping on structural,electronic and optical properties of Be<Subscript>12</Subscript>O<Subscript>12</Subscript>, Mg<Subscript>12</Subscript>O<Subscript>12</Subscript> and Ca<Subscript>12</Subscript>O<Subscript>12</Subscript> nanocages: a DFT study

Density functional theory (DFT) calculations were used to study the effect of scandium doping on the structural, energetic, electronic, linear and nonlinear optical (NLO) properties of Be₁₂O₁₂, Mg₁₂O₁₂ and Ca₁₂O₁₂ nanoclusters. Scandium (Sc) doping on nanoclusters leads to narrowing of their E _g, which enhances their conductance greatly. Also, the polarizability (α) and first hyperpolarizability (β₀) of nanoclusters were dramatically increased as Be, Mg or Ca atoms are substituted with a Sc atom. Among all clusters, α and β₀ values for Sc-doped Ca₁₂O₁₂ were the largest. Consequently, the effect of the doping atom, as well as of cluster size, on electronic and optical properties was explored. Time dependent (TD)-DFT calculations were also carried out to confirm the β₀ values; the results show that the higher value of first hyperpolarizability belongs to Sc-doped Ca₁₂O₁₂, which has the smallest transition energy (ΔEgn). The results obtained show that these clusters can be candidates for using in electronic devices and NLO materials in industry.     

Structures and stabilities of ScBn (n = 1–12) clusters: an ab initio investigation

The geometries, stabilities, and electronic properties of ScB_n (n?=?1–12) clusters have been systematically investigated by using density functional theory B3LYP method and coupled–cluster theory CCSD(T) method. It is found that the ground state isomers of ScB_n have planar or quasi–planar structure when n?≤?6, which can be viewed as a B atom of the corresponding B_n+1 cluster is substituted by a Sc atom. From n?≥?7, the ground state isomers favor nest–like structure, in which the Sc atom sits on a nest–like B_n cluster. The calculated second–order differences of energies manifest that the magic numbers of stability are n?=?3, 7, 8, 9 and 11 for the ScB _n clusters. Further analysis indicates that the ScB₇ cluster with C _6v symmetry represents the outstanding stable ScB_n cluster, as confirmed by its electronic structure and molecular orbitals.     

Electronic, magnetic and optical properties of Cu, Ag, Au-doped Si clusters

The structural, optical and magnetic properties of Cu, Ag, Au-doped Si₇ Clusters have been systematically investigated using density functional theory calculations. The global optimized structures of Cu, Ag, Au-doped Si clusters are predicted to have a lower HOMO–LUMO gap and higher magnetic moment. M-doping (M?=?Cu, Ag, Au) in Si cluster widens a range of adsorption wavelength, especially Au-doping. The characteristics in electronic density of states (DOSs) show that C_5v-Si₆Cu has a big asymmetrical spin-up and spin-down. The average atomic moment is 0.428 mμ_B per atom for the Si₆Cu cluster with C_5v symmetry, while the average paramagnetic moment is 0.143 mμ_B per atom for other M-doped (M?=?Cu, Ag, Au) Si₇ clusters.     

Hydrogen sequential dissociative chemisorption on Nin(n = 2~9,13) clusters: comparison with Pt and Pd

Hydrogen dissociative chemisorption and desorption on small lowest energy Ni_n clusters up to n = 13 as a function of H coverage was studied using density functional theory. H adsorption on the clusters was found to be preferentially at edge sites followed by 3-fold hollow sites and on-top sites. The minimum energy path calculations suggest that H₂ dissociative chemisorption is both thermodynamically and kinetically favorable and the H atoms on the clusters are mobile. Calculations on the sequential H₂ dissociative chemisorption on the clusters indicate that the edge sites are populated first and subsequently several on-top sites and hollow sites are also occupied upon full cluster saturation. In all cases, the average hydrogen capacity on Ni_n clusters is similar to that of Pd_n clusters but considerably smaller than that of Pt_n clusters. Comparison of hydrogen dissociative chemisorption energies and H desorption energies at full H-coverage among the Ni family clusters was made.     

Ab initio calculation of the geometries, stabilities, and electronic properties for the bimetallic Be2Au(n) (n = 1-9) clusters: comparison with pure gold clusters

Ab initio methods based on density functional theory at BP86 level were applied to the study of the geometrical structures, relative stabilities, and electronic properties of small bimetallic Be₂Au _n (n = 1–9) clusters. The optimized geometries reveal that the most stable isomers have 3D structures at n = 3, 5, 7, 8, and 9. Here, the relative stabilities were investigated in terms of the averaged atomic binding energies, fragmentation energies and second-order difference of energies. The results show that the planar Be₂Au₄ structure is the most stable structure for Be₂Au _n clusters. The HOMO−LUMO gap, vertical ionization potential, vertical electron affinity and chemical hardness exhibit a pronounced even–odd alternating phenomenon. In addition, charge transfer and natural electron configuration were analyzed and compared.     

One-step synthesis and reduction of triphenylphosphine carbonyl palladium clusters of variable nuclearities

Heteroleptic triphenylphosphine carbonyl palladium clusters of different nuclearities were prepared under mild conditions by only varying the amount of ligand (PPh₃) used in the synthesis: three different clusters were successfully isolated after CO bubbling in a solution of [Pd₂(dba)₃] (dba = dibenzylideneacetone) with 3, 1 or 0.5 equiv of PPh₃, which led, respectively, to [Pd₄(CO)₅(PPh₃)₄] (1), [Pd₁₀(CO)₁₂(PPh₃)₆] (2) and [Pd_n(CO)_x(PPh₃)_y] (3) (n ≈ 24). The molecular structures of compounds 1 and 2 were determined by X-ray crystallography. The metal cores in these compounds were shown to consist in a butterfly for 1 and a bridged octahedron for 2. Compound 3 was shown to be at the boundary between molecular clusters and colloidal particles with tentative formulation arising from characterization data. These three clusters and the known [Pd₁₀(CO)₁₂(PBu₃)₆] and [Pd₁₂(CO)₁₅(PBu₃)₇] were submitted to NaBH₄ reduction. The Pd₄ cluster 1 did not react. The colloidal Pd_n species led to no isolable product. By contrast, the two Pd₁₀ and the Pd₁₂ clusters led to reduction products, isolated as salts. In the case of the reduced Pd₁₂ cluster, its structure was resolved by X-ray crystallography: the metal core consists of a face-capped octahedron. The reduced species reacted readily with Au(PPh₃)⁺, confirming their anionic nature.     

Aromaticity of azines through dyotropic double hydrogen transfer reaction

The thermodynamic stabilities and IR spectra of the three water clusters (H₂O)_20, (H₂O)_54,, and (H₂O)₁₀₀ are studied by quantum-chemical computations. After full optimization of the (H₂O)_20,54,100 structures using the hybrid density functional B3LYP together with the 6-31+G(d,p) basis set, the electronic energies, zero-point energies, internal energies, enthalpies, entropies, and Gibbs free energies of the water clusters at 298 K are investigated. The OH stretching vibrational IR spectra of (H₂O)_20,54,100 are simulated and split into sub-spectra for different H-bond groups depending on the conformations of the hydrogen bonds. From the computed spectra the different spectroscopic fingerprint features of water molecules in different H-bond conformations in the water clusters are inferred.     

Highly Air‐Stable Single‐Crystalline β‐CsPbI3 Nanorods: A Platform for Inverted Perovskite Solar Cells

The synthesis of single‐crystalline β‐CsPbI₃ perovskite nanorods (NRs) using a colloidal process is reported, exhibiting their improved photostability under 45–55% humidity. The crystal structure of CsPbI₃ NRs films is investigated using Rietveld refined X‐ray diffraction (XRD) patterns to determine crystallographic parameters and the phase transformation from orthorhombic (γ‐CsPbI₃) to tetragonal (β‐CsPbI₃) on annealing at 150 °C. Atomic resolution transmission electron microscopy images are utilized to determine the probable atomic distribution of Cs, Pb, and I atoms in a single β‐phase CsPbI₃ NR, in agreement with the XRD structure and selected area electron diffraction pattern, indicating the growth of single crystalline β‐CsPbI₃ NR. The calculation of the electronic band structure of tetragonal β‐CsPbI₃ using density functional theory (DFT) reveals a direct transition with a lower band gap and a higher absorption coefficient in the solar spectrum, as compared to its γ‐phase. An air‐stable (45–55% humidity) inverted perovskite solar cell, employing β‐CsPbI₃ NRs without any encapsulation, yields an efficiency of 7.3% with 78% enhancement over the γ‐phase, showing its potential for future low cost photovoltaic devices.     

Probing the structural, electronic and magnetic properties of multicenter Fe2S2 0/−, Fe3S4 0/− and Fe4S4 0/− clusters

The structural, electronic and magnetic properties of neutral and anion Fe₂S₂, Fe₃S₄ and Fe₄S₄ have been investigated with the aid of previous photoelectron spectroscopy and density functional theory calculations. Theoretical electron detachment energies (both vertical and adiabatic) of anion clusters for the lowest energy structure were computed and compared with the experimental results to verify the ground states. The optimized structures show that the ground state structures of Fe₂S₂ ^0/?, Fe₃S₄ ^0/? and Fe₄S₄ ^0/? favor high spin state and are similar to their structures in proteins. The electron delocalization pattern for all the clusters and the nature of bonding between Fe and S atoms were studied by analyzing molecular orbitals. Natural population analysis demonstrates that Fe atoms act as an electron donor in all clusters, and the electron density difference map clearly shows the direction of the electron flow over the whole complex. Furthermore, the investigated magnetism shows that the Fe atoms carried most of the magnetic moments, which is due mainly to the 3d state, while only very small magnetic moments are found on S atoms.     

Structures and excitation energies of ozone-water clusters O3(H2O)n (n = 1-4)

Hybrid density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations have been carried out for ozone-water clusters O₃(H₂O)_n (n = 1-4) in order to obtain hydration effects on the absorption spectrum of ozone. The first water molecule in n = 1 is bound to the ozone molecule by an oxygen orientation form in which the oxygen atom of H₂O orients the central oxygen atom of O₃. In n = 2, the water dimer is bound to O₃ and then the cyclic structure is formed as the most stable structure. For n = 3 (or n = 4), the cyclic water trimer (or tetramer) is bound by a hydrogen bond to the ozone molecule. The TD-DFT calculations of O₃(H₂O)_n (n = 0-4) show that the first and second excitation energies of O₃ are blue-shifted by the interaction with the water clusters. The magnitude of the spectral shift is largest in n = 2, and the shifts of the excitation energies are +0.07 eV for S₁ and +0.13 eV for S₂ states. In addition to the spectral shifts (S₁ and S₂ states), it is suggested that a charge-transfer band is appeared as a low-lying excited state above the S₁ and S₂ states. The origin of the spectrum shifts was discussed on the basis of theoretical results.     

Stabilization of gold nanowires inside nanoaggregates of cyclo[8]thiophene, cyclo[8]selenophene, and cyclo[8]tellurophene: a theoretical study

The stabilities and electronic properties of gold clusters containing up to six atoms trapped inside cyclo[8]thiophene (CS8), cyclo[8]selenophene (CSe8), and cyclo[8]tellurophene (CTe8) nanoaggregates have been studied using the M06 functional. The 6-31G(d) basis set was used for all atoms except Au and Te, for which the LANL2DZ(d,p) pseudopotential basis set was applied. Single-point energy calculations were performed with the 6-311G(d,p) basis set for all atoms except for Au and Te, for which the cc-TZVP-pp pseudopotential basis set was used. Among the three studied macrocycles, only CS8 and CSe8 were found to be capable of nanoaggregate formation. In the lowest-energy conformer of CTe8, the tellurophene fragments adopt an anti orientation, thus impeding a tubular arrangement of the macrocycles. The formation of gold clusters inside the CS8 and CSe8 nanoaggregates is a thermodynamically favorable process, and could represent a potentially useful method of stabilizing metal nanowires. The binding energy between the nanoaggregate and the gold cluster is always higher for selenium-containing complexes than for sulfur-containing ones because Se has a higher affinity than S for Au in such complexes. Interactions of the gold cluster with the nanoaggregate walls can change the geometry of the most stable isomer for the cluster. The relative energies of different isomers are rather similar, suggesting that they coexist. For nanoaggregates containing Au₆ clusters, the cluster geometry when it is inside a nanoaggregate is different from the geometry of the cluster when it is not inside the nanoaggregate, due to the geometric restrictions imposed by the nanoaggregate cavity. The reorganization energy needed to change the geometry leads to lower binding energies for these complexes compared to those of some smaller systems, although the formation of a complex between Au₆ and a nanoaggregate with six CS8 or CSe8 macrocycles is still thermodynamically viable.     

DFT model cluster studies of O2 adsorption on hydrogenated titania sub-nanoparticles

In the present paper, we examine the general applicability of different TiO₂ model clusters to study of local chemical events on TiO₂ sub-nanoparticles. Our previous DFT study of TiO₂ activation through H adsorption and following deactivation by O₂ adsorption using small amorphous Ti₈O₁₆ cluster were complemented by examination of rutile-type and spherical Ti₁₅O₃₀ nanoclusters. The obtained results were thoroughly compared with experimental data and results of related computational studies using other TiO₂ models including periodic structures. It turned out that all considered model TiO₂ model systems provide qualitatively similar results. It was shown that atomic hydrogen is adsorbed with negligible activation energy on surface O atoms, which is accompanied by the appearance of reduced Ti³⁺ species and corresponding localized band gap 3d-Ti states. Oxygen molecule is adsorbed on Ti³⁺ sites spontaneously forming molecular O₂ ^– species by capturing an extra electron of Ti³⁺ ion, which results in disappearance of Ti³⁺ species and corresponding band gap states. Calculated g-tensor values of Ti³⁺ and O₂ ^– species agree well with the results of EPR studies and do not depend on the used TiO₂ model cluster. Additionally, it was shown that the various cluster calculations provide results comparable with the calculations of periodic structures with respect to the modeling of chemical processes under study. As a whole, the present study approves the validity of molecular cluster approach to study of local chemical events on TiO₂ sub-nanoparticles.

The composition effect for the thermal properties of PdnAg(42-n)Pt13 ternary nanoalloys: a molecular dynamics study

In this study, the classical molecular dynamics simulations in canonical ensemble conditions (NVT) were used to investigate the dynamical properties of trimetallic Pd–Pt–Ag nanoalloy clusters with the interatomic interactions modelled by the Gupta many-body potential. The optimisations for best homotops were performed using the basin-hopping algorithm for 55 atom icosahedral Pd_nAg_(42-n)Pt₁₃ trimetallic clusters. We performed optimisations to search the best chemical ordering of icosahedron structure not allowing any geometric changes. The icosahedron structures which are the best homotops have a core-shell segregation. The obtained icosahedral structures with best homotops were taken as the initial configurations for MD simulations. The temperature ranges were explored which the surface sites of the clusters stay thermally stable. We estimated the melting temperatures of Pd_nAg_(42-n)Pt₁₃ trimetallic clusters using caloric curves and Lindemann parameters. No simple correlation between alloy composition and melting temperatures was determined. The Pd₃₅Ag₇Pt₁₃ composition has the highest melting temperature, however, the Pd₂₁Ag₂₁Pt₁₃ is the most stable composition according to the relative stability investigation. The simulation results showed that the melting of all Pd_nAg_(42-n)Pt₁₃ clusters takes place as a whole without any surface premelting.     

Thermal stability of water polyhedra with square faces

The remarkable properties of pristine B₃O₃ nanosheet as a nanocarrier for adsorption and desorption of TEPA anticancer drug for designing potential drug delivery platform were investigated using periodic DFT calculations. We studied the adsorption energy of all stable complexes formed between the drug molecule and B₃O₃ in gas and aqueous phases along with electronic structure analysis of complexes. Different adsorption configurations were studied for drug/B₃O₃ complexes, including the interaction of the C atom of the triangular ring, O atom in the TEPA drug with the B atom in B₃O₃, and indirect drug interaction the middle of the R1 ring cavity of the B₃O₃ nanosheet. The take-up of TEPA prompts a substantial change of 68.13% in the band gap (E_g) of the B₃O₃ nanosheet in the most stable complex. The present study results affirmed the application of B₃O₃ nanosheet as a potential vehicle for TEPA drugs in the treatment of cancerous tissues.

     

Energy gaps of graphene clusters: the first-principles calculations based on high-throughput screening

Abstract

With the enumeration of the triangular lattice fragments, we have systematically investigated the graphene clusters (C_nH_m, n = 14 – 24) with various sizes and shapes, whose structural stabilities and electronic properties are studied by the Hückel molecular orbital (HMO) method and the first-principles calculation. According to the formation energies, we show the structural stabilities of the clusters are closely related to the shape and size, as well as the chemical potential of hydrogen. The energy gaps obtained from the HMO method are in the same trend with the ones calculated by the first-principles calculations, indicating the effective screening of the gap minimum and maximum in a fast speed. There is a general decreasing of the energy gaps with the size increment due to the quantum confinement, meanwhile, the gaps are also highly dependent on the shape of the clusters for those with the same number of carbon atom.     

Magnetic behaviour of Mn12 single-molecule magnet nanospheres

Sub-50 nm spherical particles that exhibit single-molecule magnet (SMM) behaviour have been fabricated by direct precipitation of [Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄] clusters in a mixture of acetonitrile and toluene. The magnetic properties clearly indicate that particle formation does not affect the molecular composition of Mn₁₂O₁₂ clusters, although some interesting differences appear when the magnetic behaviour exhibited by such nanoparticles is compared with a polycrystalline sample of [Mn₁₂O₁₂(CH₃COO)₁₆(H₂O)₄].     

Efficient Bifunctional Polyalcohol Oxidation and Oxygen Reduction Electrocatalysts Enabled by Ultrathin PtPdM (M = Ni,Fe, Co) Nanosheets

Despite intense research in past decades, the development of high‐performance bifunctional catalysts for direct ethylene glycol or glycerol oxidation reaction (EGOR or GOR) and oxygen reduction reaction (ORR) remains a grand challenge in realizing fuel‐cell technologies for portable electronic devices and fuel‐cell vehicle applications. Here, a general method is reported for controllable synthesis of a class of ultrathin multimetallic PtPdM (M = Ni, Fe, Co) nanosheets (NSs) with a thickness of only 1.4 nm by coreduction of metal precursors in the presence of CO and oleylamine. With the optimized composition and components, ultrathin Pt₃₂Pd₄₈Ni₂₀ NSs exhibit the highest electrocatalytic activity for EGOR, GOR, and ORR among all different ultrathin PtPdM NSs, ultrathin PtPd NSs, and the commercial catalysts. The mass activities of ultrathin Pt₃₂Pd₄₈Ni₂₀ NSs for EGOR, GOR, and ORR are 7.7, 5.4, and 7.7 times higher respectively than a commercial catalyst, and they are the most efficient nanocatalysts ever reported for EGOR/GOR. The ultrathin PtPdNi NSs are also very stable for EGOR/GOR/ORR. It is further demonstrated that these ultrathin multimetallic NSs can be readily generalized to other sensor‐related electrocatalysis system such as high‐sensitivity electrochemical detection of H₂O₂.     

A comparative theoretical study on the electrical and nonlinear optical properties of Li atom adsorbed on AlN and BN single-walled nanotubes

The geometrical structures, electrical properties, and nonlinear optical (NLO) properties of AlNNT–Li and BNNT–Li nanotube systems were investigated by means of the density functional theory (DFT) method. Frontier molecular orbitals and density of states analyses show that adsorption of the Li atom can significantly narrow the wide HOMO–LUMO gaps of pure AlNNT and BNNT. The results reveal that AlNNT–Li and BNNT–Li systems containing diffuse excess electrons can be regarded as inorganic electrides. The formation of diffuse excess electrons leads to a decrease in transition energies, thereby increasing the first hyperpolarizabilities (β ₀) of AlNNT–Li and BNNT–Li. This work may contribute to the development of potential high-performance NLO materials.

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Graphical abstract The structural characteristics and nonlinear optical properties of the AlNNT–Li and BNNT–Li systems were studied by means of density functional theory. Introduction of Li atoms greatly enhances the static first hyperpolarizabilities of AlNNT–Li and BNNT–Li

     

Ab initio investigations on planar (MgO)n clusters (n = 1–5) and their hydrogen adsorption behaviour

Ab initio calculations (B3LYP and PBE-D3) of the structures, stabilities, vibrational, electronic and hydrogen adsorption behaviour of (MgO)_n clusters are performed using 6-311+ + G(d,p) basis set. The planar (MgO)_n clusters are found to be global minima for n ≤ 3 and local minima for n = 4 and 5. In addition, we have also analysed global minimum structures of (MgO)₄ and (MgO)₅. The binding energies suggest that their stabilities increase successively. Vibrational frequencies and IR intensities further support the enhanced stability with an increase in the size of (MgO)_n clusters. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) surfaces are used to explain and discuss the electronic properties. Finally, we have demonstrated hydrogen storage capacity of (MgO)_n clusters, considering hydrogen adsorption on planar as well as global minimum (MgO)₄ and (MgO)₅ clusters. We have noticed that four and five H₂ molecules can be easily adsorbed by (MgO)₄ and (MgO)₅ clusters having adsorption energy of 0.13–0.14 eV with mass ratio of 4.76%. Thus, the present study is expected to motivate further the applications of small clusters for efficient hydrogen energy storage.