Stability of hollow spheroidal silicon clusters Sin and SinHn

The structures of Si_n and Si_nH_n fullerenes with 20 ≶n ≶60 are calculated in the MINDO/3 approximation using the Monte Carlo technique for geometry optimization. The calculations show that spheroidal silicon clusters consisting of more than 36 atoms are stable and the bond energy increases with their size. This increase is not noticed for compact clusters calculated as an alternative. For n ≥40-50, the latter have lower bond energies compared to fullerenes. The geometry optimization of the tetrahedral cluster Si₄₅ results in a structure close to spheroidal, which gains in bond energy. The addition of hydrogen atoms to small deformed fullerenes and their geometry optimization make it possible to obtain stable spheroidal structures Si_nH_n whose bond energy is greater than that of alternative compact silicon hydride clusters. When the size of spheroidal clusters Si_nH_n increases, i. e., when n > 36, the hydrogen elimination barriers decrease abruptly; the Si_nH_n diamond structure of the cluster is more advantageous when n ≥50.     

Photoionization,Structures, and Energetics of Na-Doped Formic Acid–Water Clusters

The influence of formic acid on water cluster aggregation has been investigated experimentally by mass spectrometry and tunable UV laser ionization applied to Na-doped clusters formed in the supersonic expansion of water vapors seeded with formic acid (FA) as well as theoretically using high level quantum chemistry methods. The mass spectra of Na−FA(H₂O)_n clusters show an enlarging of mass distribution toward heavier clusters with respect to the Na−(H₂O)_n clusters, suggesting similar mass distribution in neutral clusters and an influence of formic acid in water aggregation. Density functional theory and coupled-cluster type (DLPNO-CCSD(T)) calculations have been used to calculate structures and energetics of neutral and ionized Na−FA(H₂O)_n as well as neutral FA(H₂O)_n. Na-doped clusters are characterized by very stable geometries. The theoretical adiabatic ionization potential values match pretty well the measured appearance energies and the calculated first six electronic excited states show Rydberg-type characters, indicating possible autoionization contributions in the mass spectra. Finally, theoretical calculations on neutral FA(H₂O)_n clusters show the possibility of similarly stable structures in small clusters containing up to n=4–5 water molecules, where FA interacts significantly with waters. This suggests that FA can compete with water molecules in the starting stage of the aggregation process, by forming stable nucleation seed.     

Structures,stabilities, and electronic properties of Al n Au (n = 1–15) clusters: A density functional study

We present density functional calculations of Al _n Au clusters for n = 1–15. The growth pattern for Al _n Au (n = 1–7, 12, 14, 15) clusters is the Au atom occupying a peripheral position of Al _n clusters, and the growth pattern for Al _n Au (n = 8, 10 and 13) clusters is Au-substituted Al _n+1 clusters. It is found that the Au atom replaces the surface atom of an Al _n+1 cluster and occupies a peripheral position. In addition, the ground state structures of Al _n Au clusters are more stable than pure Aln clusters. It is found that the Al₁₃Au cluster exhibits high stability.     

Theoretical Study of the Structure and Stability of Stepwise Hydrogenated Aluminum Clusters Al<Subscript>44</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1−24)

The energies and structural and spectroscopic characteristics of a series of model stepwise hydrogenated aluminum clusters Al₄₄H _n (n = 1?24) obtained by successive introduction of hydrogen atoms into various surface positions of the Al₄₄ cluster have been calculated by the density functional theory method (B3LYP). According to these calculations, the [Al₃₉] surface layer of the cage retains a closed “nested doll” shape with a pentaatomic inner core [Al₅]. With increasing n, both the surface layer and the core tend to experience increasing asymmetric distortions. The surface is corrugated and undergoes significant axial and equatorial extensions and contractions, some of the Al?H two-center terminal bonds are transformed into threecenter hydrogen bridges, and some Al atoms are displaced from the surface layer to the outer sphere and are bound to the surface through hydrogen bridges. The inner core [Al₅] at n = 24 loses its bipyramidal shape and shifts to the surface layer so that one or two of its atoms are “built-in” into the concave regions of the surface layer. The calculated average energies of Al?H bonds are within the range ~55.5 ± 2.5 kcal/mol. The averaged energies of the Al₄₄H _n → Al₄₄H_n–2 + Н₂ dissociation reactions with elimination of a hydrogen molecule are on the order of a few kilocalories per mole and are evidence of small exothermicity (or isothermicity) of these reactions. For the Al₄₄H, Al₄₄H₂, and Al₄₄H₆ clusters as an example, the relative stabilities of isomers with terminal Al?H bonds in various nonequivalent positions of the [Al₃₉] surface layer are compared.     

ChemInform Abstract: Structure,Ionization, and Fragmentation of Hydrogenated Aluminoboron Clusters: Al2B2H2n (n = 0—6).

Energetic and structural stability of Al₂B₂H_2n (n = 0—6) clusters is investigated by DFT calculations and a stochastic search algorithm.     

Theoretical investigation of the structures and spectroscopic properties of (H2O4)n (n = 1–4) clusters

Density functional theory and ab initio calculations were performed to elucidate the hydrogen interactions in (H₂O₄)_n (n = 1–4) clusters. The optimized geometries, binding energies, and harmonic vibrational frequencies were predicted at various levels of theory. The trans conformer of the H₂O₄ monomer was predicted to be the most stable structure at the CCSD(T)/aug‐cc‐pVTZ level of theory. The binding energies per H₂O₄ monomer increased in absolute value by 9.0, 10.1, and 11.8 kcal/mol from n = 2 to n = 4 at the MP2/cc‐pVTZ level of theory (after the zero‐point vibrational energy and basis set superposition error corrections). This result implies that the intermolecular hydrogen bonds were stronger in the long‐chain clusters, that is, the formation of the longer chain in the (H₂O₄)_n clusters was more energetically favorable.     

Theoretical Study of Electronic Structure and Stability of Mixed AlmBn−mH n 2− and CmBn−mH n 2−m (n = 6, 10, 12 and m = 1, 2) Clusters

Density functional theory (DFT) method with B3LYP functional and 6-311++G(d,p) basis set has been used to predict the geometries, relative stabilities, electronic structures and bonding analysis of Mixed Al_mB_n?mH _n ^2? and C_mB_n?mH _n ^2?m (n = 6, 10, 12 and m = 1, 2) clusters; being compared to the B_nH _n ^2? ones. Therefore, the DFT results suggest that the replacing of boron by aluminium or carbon is governed by Natural net charges following Gimar’s and Williams’s rules. The Al_mB_n?mH _n ^2? structures are relatively distorted compared to those of B_nH _n ^2? and C_mB_n?mH _n ^2?m . In Al_mB_n?mH _n ^2? structures Al atoms prefer the adjacent sites, however for the C₂B_n?2H_n cluster cages, the carbon atoms are positioned at diametrically opposed sites. The large HOMO–LUMO gaps show that the predicted clusters have chemical stabilities, principally, those of Al_mB_n?mH _n ^2? ones, which are not experimentally isolated. The optimized geometries obtained through boron substitution by Al and C lead to compactness and to contracted structures, respectively, where B–B bonds are the shortest in mono- and di-carbaboranes.     

Ab initio studies of small AlmFen clusters

The equilibrium geometrical structures of small Al_mFe_n clusters have been determined through ab initio calculation of the cluster total energy at the UB3LYP/Lanl2dz level. For dimers of iron and aluminum, the dissociation energies, the equilibrium atomic distances, and the vibrational frequencies were calculated. The agreement between calculations and experiments is reasonable. The ground stable geometrical structures of Fe₄, FeAl₃, Fe₃Al and Fe₂Al₂ clusters favor three-dimension configurations, but Al₄ tetramers are planar structures. The Al-rich tetramers are more stable than the other two composition tetramers. This is different from that of bulk alloys.     

Stability of molecular form of HCl in water vapor: A computer simulation

The free energy and entropy of the dissociation of HCl molecule into ions in water vapor, HCl(H₂O) _n + mH₂O → H₃O + (H₂O) _n+m -1Cl^?, were calculated. The dependences of various parameters on the interionic distance at 273 K and various vapor pressures were obtained. A detailed model taking into account unpaired covalent-type interactions, polarization interactions, charge transfer effect, and hydrogen bonds was applied. The numerical values of the parameters were reconstructed from the experimental data on the free energy and enthalpy of the first reactions of addition of vapor molecules to ions, and also from the results of quantum-chemical calculations of the energy and geometry of locally stable configurations of clusters HCl(H₂O) _n . Despite lower internal energy of the dissociated state, the molecular form is absolutely stable in clusters of water molecules. The dissociated state is relatively stable. Accumulation of unrecombined ion pairs in clusters is possible with a decrease in the temperature to 200 K.     

A theoretical study on the hydrogen storage properties of planar (AlN)<Subscript>n</Subscript> clusters (<Emphasis Type="Italic">n</Emphasis> = 3-5)

The structures and hydrogen storage capacities of (AlN)_n (n = 3-5) clusters have been systematically investigated by using density functional theoretical calculations. At ωB97xD/6-311 + G(d, p) level, the planar structures of (AlN)_n (n = 3-5) can adsorb 6-10 H₂ molecules with average adsorption energies in the range 0.16 to 0.11 eV/H₂, which meet the adsorption energy criteria of reversible hydrogen storage. The gravimetric density of H₂ adsorbed on (AlN)_n clusters can reach 8.96 wt%, which exceed the target set by Department of Energy. The hydrogen adsorption energies with Gibbs free energy correction indicate that the adsorption of 6 H₂ in (AlN)₃, 8 H₂ in (AlN)₄ and 10 H₂ in (AlN)₅ is energetically favorable below 96.48, 61.43, and 34.21 K, respectively. These results are expected to motivate further the applications of clusters to be efficient hydrogen storage materials.     

DFT study of small aluminum and boron hydrides: isomeric composition and physical properties

The structure, energetics, and physical properties, including rotational constants, characteristic vibrational temperatures, dipole moment, static polarizability, HOMO-LUMO gap, formation enthalpy and collision diameter of different isomeric forms of atomic Al _n H _m and B _n H _m clusters with n = 1..4 and all feasible m numbers are studied within the density functional theory framework. The search of isomer structures has been accomplished using multistep hierarchical algorithm. Temperature dependences of thermodynamic functions (enthalpy, entropy and specific heat capacity) have been calculated both for the individual isomers and for the ensemble of isomers with equilibrium composition for each class of clusters, taking into account the anharmonicity of cluster vibrations and the contribution of excited electronic states. The prospects of the application of small atomic Al _n H _m and B _n H _m clusters as the components of energetic and hydrogen storage materials are also discussed.     

Are closed clusters expected from the (n + 1) skeletal electron pairs rule in alanes and gallanes? A DFT structural study of AnHn + 2 (A = Al, Ga, and n = 4-6)

It has been suggested recently that the alanes Al_nH_n + 2 can be treated by the polyhedral skeletal electron pair theory (PSEPT) of Wade and Mingos (W-M) as it was successful for their borane congeners such as B_nH_n + 2, well known as the deprotonated B_nH_n²⁻. To do so, the neutral Al_nH_n + 2 have been considered as Al_nH_n²⁻ + 2H⁺. The additional hydrogens donate their electrons to the Al_nH_n polyhedral framework and according to the n + 1 electron pairs rule; these clusters should have closo-polyhedral structures. In this work the homologous gallanes, the structures and stabilities of Ga_nH_n + 2 are studied at high levels of calculational theory and we investigated the applicability of the W-M rule to the alanes and gallanes A_nH_n + 2 (n = 4-6; A = Al, Ga). It will be shown that the presence of bridging hydrogen atoms reduces the compactness of the corresponding polyhedron and so these species do not have the closed structures. The computations were performed at B3LYP/6-311+G(d,p), BPW91/6-311G(d,p) and B3LYP/6-311+G(3df,2p) levels of theory. Our interest in these compounds includes their potential use as hydrogen storage species and future clean sources of energy.     

A density functional study on the aggregation of alumina clusters

A calculation has been performed to explore the mechanism of aggregation reaction between two small molecular clusters [(Al₂O₃) _n1 and (Al₂O₃) _n2] by the density functional theory method. Five pathways of aggregation reactions between two different (Al₂O₃)₁ clusters isomers were identified. The detailed process of (Al₂O₃)₁ interaction with (Al₂O₃)₂ were also obtained. All the products of the aggregation reactions between two cage structures are cage-dimer structures. We calculated the thermodynamic properties of all the aggregate clusters. The Gibbs free energy changes of aggregation reactions in 0–1000 K were negative and increased with the temperature increase. The energy changes of enthalpy and entropy were also obtained.     

Acetylene aggregates via cluster-building algorithm and molecular tailoring approach

Acetylene clusters are prototypical of simple non-aromatic systems bonded through C–H…π interactions. The present work explores structures and properties of acetylene clusters (C₂H₂) _n , n = 8 and 10, employing cluster-building algorithm and molecular tailoring approach (MTA). The former uses electrostatics guidelines for building (C₂H₂)₈ and (C₂H₂)₁₀ structures. These clusters are treated at MP2 level of theory with correlation-consistent basis sets using MTA. The Hessian matrix and vibrational spectra for the best five structures of (C₂H₂)₈ and (C₂H₂)₁₀ are computed employing MTA. Actual calculations on these clusters using conventional methods employing large basis sets are prohibitively difficult to perform. All the frequencies for these structures extracted using MTA-based Hessian matrix are found to be real, confirming their local minimum nature. This study points to the possibility of using the present approach for exploring structures, energetics and vibrational spectra of even larger clusters at higher levels of theory.     

A theoretical investigation on the structures of (NH3)·(H2SO4)·(H2O)0-14 clusters

Ternary clusters (NH₃)·(H₂SO₄)·(H₂O)_n have been widely studied. However, the structures and binding energies of relatively larger cluster (n > 6) remain unclear, which hinders the study of other interesting properties. Ternary clusters of (NH₃)·(H₂SO₄)·(H₂O)_n, n = 0-14, were investigated using MD simulations and quantum chemical calculations. For n = 1, a proton was transferred from H₂SO₄ to NH₃. For n = 10, both protons of H₂SO₄ were transferred to NH₃ and H₂O, respectively. The NH₄⁺ and HSO₄⁻ formed a contact ion-pair [NH₄⁺-HSO₄⁻] for n = 1-6 and a solvent separated ion-pair [NH₄⁺-H₂O-HSO₄⁻] for n = 7-9. Therefore, we observed two obvious transitions from neutral to single protonation (from H₂SO₄ to NH₃) to double protonation (from H₂SO₄ to NH₃ and H₂O) with increasing n. In general, the structures with single protonation and solvated ion-pair were higher in entropy than those with double protonation and contact ion-pair of single protonation and were thus preferred at higher temperature. As a result, the inversion between single and double protonated clusters was postponed until n = 12 according to the average binding Gibbs free energy at the normal condition. These results can serve as a good start point for studies of the other properties of these clusters and as a model for the solvation of the [H₂SO₄-NH₃] complex in bulk water.     

Homocatenation of Aluminum: Alkane‐like Structures of Li2Al2H6 and Li3Al3H8

A new class of aluminum homocatenated compounds (Li_nAl_nH_2n+2) is proposed based on quantum chemical calculations. In these compounds, Al abstracts an electron from Li, becoming valence isoelectronic with C, Si, and Ge, thus mimicking respective structural features of Group 14 hydrides. Using the Coalescence Kick search program coupled with density functional theory calculations, we investigated the potential energy surfaces of Li₂Al₂H₆ and Li₃Al₃H₆. Then single‐point‐energy coupled‐cluster calculations were performed for the lowest energy structures found. Indeed, the global minima established for Li₂Al₂H₆ and Li₃Al₃H₆ contain the Al₂H₆^2? and Al₃H₆^3? kernels, which are isostructural with ethane (C₂H₆), disilane (Si₂H₆), digermane (Ge₂H₆) and propane (C₃H₈), trisilane (Si₃H₈), trigermane (Ge₃H₈) molecules, respectively. Structural, energetic, and electronic characteristics of the Li₂Al₂H₆ and Li₃Al₃H₈ compounds are presented and the viability of their synthesis is discussed.     

Calculation of the properties of small boron and aluminum clusters

CNDO calculations were carried out for B _n and Al _n clusters, n=2–7, 12, and 13. The energetically most stable cluster structures were determined for each n. The results show that the stability of the more compact structures increases in going from boron to aluminum. We conclude that the CNDO model used is suitable for discerning the difference in the structure formation of boron and aluminum, which is manifest, in particular, in the formation of crystalline modifications by boron based on an icosahedral structural element, while crystalline aluminum has an FCC lattice.Institute of Theoretical and Applied Mechanics, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 5, pp. 48–54, September–October, 1989.     

A Quantum-Chemical Study of Dissociation of H2 Molecule on Palladium Clusters

The mechanism of the reaction of Pd _n clusters with an H₂ molecule was suggested on the basis of DFT B3LYP/HW calculations. The catalytic center in an elementary event of the process is one of the vertices of the Pd _n cluster; spillover of hydrogen atoms along the cluster edges results in the formation of a stable Pd _n H₂ complex with a significant energy gain in the case of the singlet reaction channel. In such a mechanism, the cluster size should not significantly affect the reaction up to a certain moment; therefore, when simulating processes involving large clusters, we can restrict ourselves to relatively small sites of their surface.     

B12Sc4和B12Ti4团簇的储氢性质

提出了两个稳定的团簇B₁₂Sc₄和B₁₂Ti₄, 基于理论计算, 研究了它们的结构与储氢性质. 结果发现, 在这两个稳定的团簇中, 过渡金属原子不会聚合在一起而影响它们对氢气的吸附. B₁₂Sc₄最多可以吸附12个氢分子, 达到7.25% (质量分数)的储氢量. 它的平均每氢分子吸附能量为10.5 kJ·mol^-1. B₁₂Ti₄最多只能吸附8个氢分子, 储氢量为4.78%. 但平均每氢分子吸附能量可达50.2 kJ·mol^-1. 进一步计算表明, 即使在77 K,也需要很高的氢气压力才能使12个氢分子都吸附到B₁₂Sc₄上. 电子结构分析表明, B₁₂Ti₄-nH₂吸附结构中的Kubas作用要大于相应B₁₂Sc₄-nH₂结构中的Kubas作用.     

Striking Size and Doping Effects of Ti−Si−O Clusters on Methane Conversion Reactions

The size and doping effects in methane activation by Ti−Si−O clusters have been explored by using a combination of gas-phase experiments and quantum chemical calculations. All [Ti_mSi_nO_2(m+n)]^.+ (m+n=2, 3, 8, 10, 12, 14) clusters can extract a hydrogen from methane. The associated energies and structures have been revealed in detail. Moreover, the doping and size effects have been discussed involving generalized Kohn-Sham energy decomposition analysis, natural population analysis, Wiberg bond indexes (WBI), molecular polarity index (MPI) and ionization potential (IP). It suggested that Ti−Si−O clusters with a low Ti : Si ratio is beneficial to adsorbing methane and inclination to the hydrogen atom transfer (HAT) process, while the clusters with a high Ti : Si ratio favors the generation of a terminal oxygen radical and results in high reactivity and turnover frequency. On the other hand, a cluster size of m+n=12 is recommended considering both the ionization potential and the turnover frequency of the reaction. Hopefully, these finding will be instructive for the design of high-performance Ti−Si−O catalyst toward methane conversion.