HNO(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–4) clusters: a theoretical study

The geometrical structure, binding energy, and vibrational spectra of small clusters of nitrosyl hydride (HNO) and water molecules, HNO(H₂O) _n , where (n = 1–4), have been investigated at the MP2 level of theory, using 6-311++G(2d,2p) basis set. We located three dimers, six trimers, nine tetramers, and three pentamers at the MP2/6-311++G(2d,2p) computational level. Particular attention is given to existence and magnitude of NH···O blue-shifting hydrogen bonds. Blue shifts of the NH stretching frequency upon complex formation in the ranges between 28 and 151 cm⁻¹ is predicted. Cooperative effect in terms of stabilization energy along with the many-body interaction energies analysis was performed for the studied clusters. The Atoms in Molecules (AIM) theory was also applied to explain the nature of the complexes.     

A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

The electronic structure of nanoparticle: theoretical study of small Cobalt clusters (Co<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>, <Emphasis Type="Italic">n</Emphasis> = 2–5) (part A)

Electronic and geometrical structures of small Cobalt cluster (Co _n , n = 2–5), which were used as building block in Cobalt cluster compounds, were fully investigated in this article. Since small Cobalt clusters as a nanoparticle have many applications in scientific works and technology, it is essential for understanding their relatively accurate electronic structure. The most stable symmetrically and electronically structure confirmed by frequency test for studied clusters is as follows: 5-et (quintet) Co₂ is of course linear, and its HOMOs described by degenerate d _xy orbitals in β-spin part located on both atoms; 8-et (octet) Co₃ is almost scalene triangle and its HOMO in s-orbital of α-spin part located on Co₍₁₎; 11-et Co₄ is rhombus, d _xz orbital of β-spin part located on Co₍₂₎ is its HOMO part. 12-et Co₅ is pyramidal with HOMO in p _x orbital located on Co₍₅₎ in β-spin part, which show very low (0.06) occupation number. This large depletion of electron in HOMO occupation of Co₅ explains high chemical reactivity of this species. Density functional theory, DFT, was used through software Gaussian 09. Xc-correlation functional was chosen among the many recommended xc-functionals for transition metal in the literature by calibration procedure in such a way that the results can match with experimental values. So suitable xc-functional B3P86 and 6-311++G* basis set were found. Natural bond orbital, NBO, has also been used for analysis.     

Theoretical investigation on the geometries and electronic properties of cesium–silicon CsSi<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2–12) clusters

The structures, relative stabilities, and electronic properties of pure Si _n and Cs-doped silicon clusters (n = 2–12) are systematically investigated using the density functional theory at the B3LYP level. The optimized structures indicated that the lowest-energy structures of CsSi _n are similar to those of pure Si _n clusters and prefer the 3-dimensional configuration for n = 3–12. The relative stabilities of CsSi _n clusters are analyzed based on the averaged binding energy, fragmentation energy, second-order energy difference, and HOMO–LUMO energy gap. It is found that CsSi₆ and CsSi₉ are the magic clusters, and the doping of Cs atom reduces the chemical stabilities of Si _n frame. The Mulliken population analysis pointed out that the charges in the corresponding CsSi _n clusters always transfer from Cs atom to Si _n host in the range of 0.80–0.91 electron. In addition, the partial density of states, infrared, and Raman spectra is discussed.     

Thermodynamic study of nanoclusters of lead (Pb<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>, <Emphasis Type="Italic">n</Emphasis> = 1–6): adsorption of small molecules on the Pb<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters

Nanoclusters of lead (Pb _n , n = 1–6) were studied theoretically employing MP2 and M062X methods. Structural and thermodynamic properties as well as ionization energies and electron affinities of two isomers of Pb₃, six isomers of Pb₄, seven isomers of Pb₅ and seven isomers of Pb₆ were obtained at 298 K. Rhombic, pyramidal and octagonal structures were the most stable forms of the Pb₄, Pb₅ and Pb₆ clusters, respectively. Proton affinities of the Pb _n clusters were computed, which were in the range of 200–250 kcal/mol. Adsorption of C₂H₂, C₂H₄, CO, CO₂, CH₂O, HNO, O₃, NO, N₂O, NO₂, N₂O₄ and N₂O₅ on the Pb _n clusters was studied. O₃ showed the strongest interaction with the Pb _n clusters with adsorption enthalpies of 80–130 kcal/mol. HNO, O₃, N₂O, N₂O₄ and N₂O₅ were dissociated after adsorption on the Pb _n clusters. N₂O decomposes to adsorbed O atom and a free N₂ molecule, while N₂O₄ and N₂O₅ release a NO₂ molecule.     

Combined DFT with NBO and QTAIM studies on the hydrogen bonds in (CH<Subscript>3</Subscript>OH)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2–8) clusters

The (CH₃OH) _n (n = 2–8) clusters formed via hydrogen bond (H-bonds) interactions have been studied systemically by density functional theory (DFT). The relevant geometries, energies, and IR characteristics of the intermolecular OH···O H-bonds have been investigated. The quantum theory of atoms in molecule (QTAIM) and natural bond orbital (NBO) analysis have also been applied to understand the nature of the hydrogen bonding interactions in clusters. The results show that both the strength of H-bonds and the deformation are important factors for the stability of (CH₃OH) _n clusters. The weakest H-bond was found in the dimer. The strengths of H-bonds in clusters increase from n = 2 to 8, moreover, the strengths of H-bonds in (CH₃OH) _n (n = 4–8) clusters are remarkably stronger than those in (CH₃OH) _n (n = 2, 3) clusters. The small differences of the strengths of H-bonds among (CH₃OH) _n (n = 6–8) clusters indicate that a partial covalent character is attributed to the H-bonds in these clusters. The linear relationships between the electron density of BCP (ρ_b) and the H···O bond length of H-bonds as well as the second-perturbation energies E(2) have also been investigated and used to study the nature of H-bonds, respectively.     

Planar Four-Coordinate Carbon in Star-Like Perlithioannulenes C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Li<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 3–6)

The structure and stability of perlithioannulenes C _n Li _n (n = 3–6) were examined ab initio [MP2(full)/6-311+G**] and in terms of the density functional theory (B3LYP/6-311+G**). The systems with n = 3, 5, and 6 may be stabilized as planar star-like structures with bridging lithium atoms and hypercoordinate carbon atoms. Star-like structures are the most stable isomers of odd-numbered annulenes (n = 3, 5), while the most stable isomers of even-numbered annulenes (n = 4, 6) have less symmetric nonplanar structures.     

Theoretical studies of the structures and properties of (Br<Subscript>2</Subscript>InN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–6) clusters

In an attempt to find single-source precursors, a series of small clusters of inorganic azides of indium (Br₂InN₃) _n (n = 1–6) were studied using the dispersion correction density functional theory (wB97XD). The obtained (Br₂InN₃) _n (n = 2–6) clusters have the core structures of 2n-membered ring with alternating indium and α-nitrogen atoms. The influences of cluster size (oligomerization degree n) on the structures, energies, IR spectra, and thermodynamic properties of clusters were discussed. The computed binding energies indicate the stability: 3A > 3B, 4B > 4C > 4A > 4D, 5E > 5D > 5B = 5C > 5A and 6I > 6C > 6D > 6G ≥ 6H > 6F > 6E > 6B > 6A. It is also found that (Br₂InN₃)₂ and (Br₂InN₃)₄ clusters possess higher stability than their neighbor sizes judged by the calculated second-order difference of energies (Δ₂ E). Meanwhile, thermodynamic properties for (Br₂InN₃) _n (n = 1–6) clusters increase with the increasing temperature and oligomerization degree n, and the oligomerizations are thermodynamically favorable at temperatures up to 800 K.     

Structures and electronic properties of germanium-doped Ni<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters, <Emphasis Type="Italic">n</Emphasis> = 13–23

The magnetic property and electronic properties such as binding energy, charge transfer, ionization potential and electron affinity of the Ni _n–1Ge (n = 13–23) neutral and ionic clusters have been studied using the density functional theory calculations with the PBE exchange-correlation energy functional. The calculated total magnetic moments decrease with the addition of Ge atom. Both the calculated ionization potential and electron affinity exhibit an oscillating behavior as the cluster size increases.     

Gas-phase structures of 1-adamantylphosphines,PH<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(1-Ad)<Subscript>3−<Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–3)

The gas-phase structure of 1-adamantylphosphine has been determined by electron diffraction, supplemented with data from ab initio and DFT calculations. The adamantyl fragment was modeled with local C _3v symmetry and the phosphino group was found to be in a position almost bisecting a mirror plane of the adamantyl group, giving the molecule overall approximate C _s symmetry. There is a small displacement of the C–P bond from the local threefold axis of the adamantyl group. Geometry optimizations were also performed for bis-(1-adamantyl)phosphine (C ₁ point-group symmetry) and tris-(1-adamantyl)phosphine (C ₃ symmetry), demonstrating extremely crowded environments around the phosphorus atoms leading to adamantyl groups that were much less symmetric. The adamantyl groups were also found to twist by a significant amount to minimize the strain.     

The equilibrium structures of the Li[C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>]<Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 7–12) complexes and their alternation depending on <Emphasis Type="Italic">n</Emphasis>

The equilibrium geometric configurations of the Li[C _n ]₁ (n = 7–12) complexes, where [C _n ]₁ is a cylindrical hydrocarbon containing the simplest zigzag nanotube fragment, were determined by the density functional theory method with the PBE0 exchange-correlation functional. Analytic molecular orbital (MO) estimates were obtained for isolated [C _n ]₁ hydrocarbons in the Hückel approximation. The appearance of nonbonding MOs for hydrocarbons with even n was demonstrated. Equilibrium structure types were found to alternate as n increased. This alternation correlated with the behavior of the frontier orbitals of the [C _n ]₁ hydrocarbon. At odd n, the Li atom was situated near the boundary of the π electron density of the bracelet, and the complex had C _s symmetry. Complexes with even n had the C _2v point group, and lithium was situated in the inner cylinder cavity above the center of one of benzene rings.     

Isomerization reactions of RSNO (R=H,C<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H<Subscript>2<Emphasis Type="Italic">n</Emphasis>+1</Subscript><Emphasis Type="Italic">n</Emphasis>≤ 4)

We have applied various theoretical methods to gain detailed insights into the isomers as well as the transition states (TSs) along the corresponding reaction pathways for RSNO (R=H, C _n H_2n+1 n ≤ 4). On the basis of G2 and G2MP2 results, the relative order of stability for R=H is estimated to be trans-HSNO > cis-HSNO > HNSO > cis-HONS trans-HONS, while it is cis-CH₃SNO trans-CH₃SNO > CH₃NSO > trans-CH₃ONS > cis-CH₃ONS for R=CH₃. A similar trend is also obtained from the B3P86 method with considerably less computing effort if the nearly isoenergetic isomers cis-HONS and trans-HONS are ignored. Based on the results of B3P86, cis-RSNO is more stable than trans-RSNO when R=H is replaced by alkyl groups except for R=t-Bu. Natural bond orbital analyses allow us to explore whether the high reactivity of S-nitrosothiols is due to the strong negative hyperconjugation (). The mesomeric effect of S-nitrosothiols, although non-negligible, does not cause the breakage of N–O bond due to the compensation of columbic attraction between N and O.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Structures and aromaticity of the planar Al<Subscript>2</Subscript>P<Subscript>2</Subscript><Superscript><Emphasis Type="Italic">n</Emphasis>−</Superscript> (<Emphasis Type="Italic">n</Emphasis>=1–4) clusters

Clusters Al₂P₂ ⁿ⁻ (n = 1–4) were theoretically investigated using density functional theory (DFT) methods at the B3LYP/6-311+G* and B3PW91/6-311+G* levels of theory. The calculated results showed that the planar structure (D _2h symmetry) of Al₂P₂ ⁿ⁻ (n = 1–4) species was the global minimum. And the negative nucleus-independent chemical shift (NICS) value of Al₂P₂ ⁿ⁻ (n = 1–4) species indicated the existence of a ring current in the planar structure (D _2h symmetry). A detailed molecular orbital (MO) analysis revealed that the planar structures (D _2h symmetry) had π aromaticity, which further exhibited the strongly aromatic character for Al₂P₂ ⁿ⁻ (n = 1–4) species.     

Phenyl(trimethylsiloxy)fluorosiloxanes PhSi(OSiMe<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>F<Subscript>3−<Emphasis Type="Italic">n</Emphasis></Subscript>

The siloxane bond splitting reaction in hexamethyldisiloxanes PhSiCl _n F_3?n was studied.     

Fast evaluation of molecular auxiliary functions <Emphasis Type="Italic">A</Emphasis><Subscript>α</Subscript> and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> by analytical relations

Analytical relations through the initial values are derived for the molecular auxiliary functions A _α (x) and B _n (x), where α =n+ɛ, 0⩽ ɛ < 1 and n=0,1,2,.... These relations are useful in the fast calculation of multicenter molecular integrals over integer and noninteger n Slater type orbitals. It is shown that the formulas obtained are numerically stable for all values of n,ɛ and x.PACS No: 31.15.+q, 31.20.EjAMS subject classification: 81-V55, 81-V45     

Structure of (DMF)<Subscript>m</Subscript>(HCl)<Subscript>n</Subscript> complexes (<Emphasis Type="Italic">m</Emphasis>= 2, <Emphasis Type="Italic">n</Emphasis> = 3–4)

(DMF)₂(HCl)₃ and (DMF)₂(HCl)₄ heterocomplexes were studied for the first time in terms of the B3LYP/6-31++G(d, p) density functional calculation. The resulting data about their structure, stability, strength of intermolecular bonds, and degree of proton transfer in O...H...Cl bridges are compared with the results of a similar calculation fulfilled for (DMF)_m(HCl)_n clusters (m, n = 1–2) and with the experimental data on the structure and properties of acid-base complexes in DMF solutions of HCl. An extremely stable symmetrical cycle of four molecules — (DMF)₂(HCl)₂ — is assumed to be a structure-forming element of solution in the DMF-HCl system in the range of concentrations achievable under normal conditions. When [HCl]₀ > [DMF]₀, the “excess” hydrogen chloride molecules add to the chlorine atoms of this cycle, forming heterocomplexes with a branched structure. Addition of more HCl molecules to the (DMF)₂(HCl)₂ cycle appreciably increases the degree of proton transfer from acid to base molecule.     

Phase Diagrams of the <Emphasis Type="Italic">n</Emphasis>-Decane–<Emphasis Type="Italic">n</Emphasis>-Hexadecane–Cyclododecane, <Emphasis Type="Italic">n</Emphasis>-Decane–Cyclododecane,and <Emphasis Type="Italic">n</Emphasis>-Hexadecane–Cyclododecane Systems

The n-decane–n-hexadecane–cyclododecane, n-decane–cyclododecane, and n-hexadecane–cyclododecane systems are studied by means of low-temperature differential thermal analysis using a differential scanning heat flow calorimeter. It is noted that all studied systems belong to the eutectic type. It is concluded that in the n-decane–n-hexadecane–cyclododecane system, the eutectic composition contains 85.0 wt % n-С₁₀Н₂₂, 4.0 wt % n-С₁₆Н₃₄, and 11.0 wt % С₁₂Н₂₄. It has a melting point of ?35.0°C.     

Search for the structures,stabilities, IR spectra,and thermodynamic properties of the asymmetric clusters (HClBN<Subscript>3</Subscript>)<Subscript> <Emphasis Type="Italic">n</Emphasis> </Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–6)

The density functional theory (DFT) method has been employed to systematically investigate the geometrical structures, stabilities, IR spectrum and thermodynamic properties of small asymmetric clusters (HClBN₃)_n (n = 1–6). When n ≥ 2, the optimized results suggest that the (BN_α)_2n cyclic structures with alternating boron and α-nitrogen atoms are observed in clusters. The influences of cluster size on the structures of clusters were discussed. The second-order difference in energies show that the (HClBN₃)₃ isomer is the most stable among the asymmetric clusters (HClBN₃)_n. Four main characteristic regions are obtained and assigned for the calculated IR spectra. A study of their thermodynamic properties suggests that monomer 1 forms clusters (2–6) thermodynamically favorable by the enthalpies at 298.2 K.     

DFT Study on Planar (CaO)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> Rings (<Emphasis Type="Italic">n</Emphasis> = 1–5) and Their Hydrogen Storage Behavior: Ca–O Versus Mg–O Clusters

In this work, the results of DFT-based calculations on the structures, stabilities, vibrational, electronic, and hydrogen storage behavior of (CaO) _n rings are presented and discussed systematically. The equilibrium ring structures of Ca–O clusters for n = 2–5 are found to be stable. Vibrational frequencies and IR intensities further support the enhanced stability with an increase in the size of Ca–O clusters. The HOMO–LUMO surfaces and their derived parameters are used to explain the electronic properties of the titled systems. For efficient hydrogen storage, metals especially, the transition metals with large cohesive energy (CE) suffer from the problem of cohesion as it is expected that the adsorption energies of metal decorated absorbents should be larger than the CEs of metal. In order to avoid this, hydrogen adsorbed directly on the absorbents is preferred. Due to relatively smaller CEs of the s-block metals, hydrogen adsorbs directly on the cluster which indeed solves the problem of cohesion. The hydrogen storage capacity of (CaO) _n clusters, considering hydrogen adsorption on (CaO)₄ and (CaO)₅ rings is studied. The outcomes appear to give meaningful and satisfactory results. Thus the present work is expected to lead further the applications of small clusters for easy, efficient, and eco-friendly hydrogen storage.     

Computational Studies on the Mo-Doped Gold Nanoclusters Au<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Mo(<Emphasis Type="Italic">n</Emphasis> = 1–10): Structures,Stabilities and Magnetic Properties

The geometric structures, relative stabilities, magnetic properties of Mo-doped gold clusters Au _n Mo(n = 1–10) have been investigated at the PBE1PBE/def2TZVP level of theory. The results show that molybdenum doping has a significant effect on the geometric structures and electronic properties of Au _n Mo(n = 1–10) clusters. For the lowest energy structures of Au _n Mo(n = 1–10), the two dimensional to three dimensional transition occurs at cluster size n ≥ 8, and their relative stabilities exhibit odd–even oscillation with the change of Au atom number. It is found that charge in corresponding Au _n Mo clusters transfers from Mo atom to Au _n host in the size range n = 1–7, whereas the charge in opposition direction in the size range n = 8–10. In addition, the magnetic properties of Au _n Mo clusters are enhanced after doping single Mo atom into the corresponding gold clusters. Our results are valuable for the design of magnetic material.