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.     

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.     

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.     

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.     

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.     

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.     

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.     

Magnetic properties of CuCr<Subscript>2–<Emphasis Type="Italic">х</Emphasis></Subscript>Sb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>4</Subscript> (<Emphasis Type="Italic">х</Emphasis> = 0–0.5) solid solutions

Magnetic properties of spinel solid solutions CuCr_2–х Sb _x Se₄ (х = 0–0.5) were measured in the temperature range 5–300 K in a constant (50 Oe and 10 kOe) magnetic field. The results are interpreted in terms of the ionic model suggested earlier for CuCr₂Х₄ compounds.     

Crystal structures of [<Emphasis Type="Italic">M</Emphasis>(Еn)<Subscript>3</Subscript>](ReO<Subscript>4</Subscript>)<Subscript>2</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Ni,Zn)

The structures of two isostructural phases of [M(Еn)₃](ReO₄)₂ (M = Ni, Zn; Еn is ethylenediamine) are studied. The crystal structures belong to the triclinic system, but demonstrate a pseudohexagonal packing motif. It is shown that the product of thermal decomposition of [Zn(Еn)₃](ReO₄)₂ (hydrogen atmosphere, 400 °C) is a homogeneous mixture of nanocrystalline zinc and rhenium powders with coherent scattering regions of ~30 nm.     

The Merrifield–Simmons index in (<Emphasis Type="Italic">n</Emphasis>, <Emphasis Type="Italic">n</Emphasis> + 1)-graphs

A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. In this paper, we determine the upper bound for the Merrifield–Simmons index in (n, n + 1)–graphs in terms of the order n, and characterize the (n, n + 1)–graph with the largest Merrifield–Simmons index.     

DFT study on oxidation of HS(CH<Subscript>2</Subscript>)<Subscript> <Emphasis Type="Italic">m</Emphasis> </Subscript>SH (<Emphasis Type="Italic">m</Emphasis> = 1–8) in oxidative desulfurization

Density functional theory was employed for calculation of HS(CH₂)_mSH (m = 1–8) and its derivatives at B3LYP method at 6-31++g (d,p) level. Using eigenvalues of LUMO and HOMO for HS(CH₂)_mSH, the standard electrode potentials were estimated by a stepwise multiple regression techniques (MLR), and obtained as E° = 1.500 + 7.167 × 10^–3 HOMO–0.229 LUMO with high correlation coefficients of 0.973 and F values of 43.973.     

Theoretical study on structures and infrared spectroscopy of Cu<Superscript>2+</Superscript>(H<Subscript>2</Subscript>O)Ar<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–4)

The binding energy of Cu²⁺(H₂O) is computed to be 98.4 kcal/mol and thus one-photon photodissociation is not possible in the 3400–3800 cm^–1 (9.7–10.9 kcal/mol) region. To study whether the infrared photodissociation processes of Cu²⁺(H₂O) can occur by multiple argon atoms tagging technique, density functional and CCSD(T) methods are used to investigate the geometries, OH stretching frequencies and the argon atom binding energies of Cu²⁺(H₂O)Ar _n (n = 1–4) complexes. Various isomers are found resulting from the different coordination sites of argon atoms. The OH stretches in these complexes are shifted to lower frequencies than those of the free water molecule, and the corresponding vibrational red shifts are progressively smaller as more argon atom is added to Cu²⁺ while binding an argon atom to an OH site should lead to additional sizable red shift to the OH stretching vibrations.     

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     

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.     

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.     

Interaction between threonine and cadmium cation in [Cd(Thr)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>]<Superscript>2+</Superscript> (<Emphasis Type="Italic">n</Emphasis> = 1–3) complexes: density functional calculations

Structures corresponding to energy minima and the binding of cadmium cation to threo- nine (Thr) in model systems [Cd(Thr) _n ]²⁺ (n = 1–3) were studied theoretically. Quantum chemical computations were performed within the framework of the density functional theory using the B3LYP, BLYP, and P functionals. In the optimized structures of the complexes [CdThr]²⁺ and [Cd(Thr)₂]²⁺, threonine acts as a bidentate ligand and cadmium binds to oxygen atoms of carbonyl and hydroxyl groups with the formation of one and two six-mem- bered rings, respectively. In the complex [Cd(Thr)₃]²⁺, cadmium binds to three nitrogen atoms and three oxygen atoms of carbonyl groups in three Thr molecules to form three five-mem- bered rings.     

Quantum chemical modeling of nanostructured silicon Si<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2—308). The snowball-type structures

To search for advanced anode materials for Li-ion rechargeable batteries, the structures, stabilities, and electronic properties of crystalline silicon and those of the snowball-type (SB) and core-shell (CS) silicon clusters Si_{zyubin@icp.ac.ru} (n = 2—308) were quantum chemically modeled within the framework of the density functional theory with inclusion of gradient correction and periodic boundary conditions. The formation of SB agglomerates from smaller Si_{zyubin@icp.ac.ru} clusters (n ≤ 7) is energetically preferable. At n ≥ 105 and circumscribed sphere diameters (D) ≥ 17—20 Å, CS isomers comprised of quasi-crystalline cores surrounded by small clusters are energetically more favorable than the SB isomers.     

Phase equilibria in the condensed system <Emphasis Type="Italic">n</Emphasis>-docosane–cyclododecane–<Emphasis Type="Italic">n</Emphasis>-decane

Phase equilibria in the system n-docosane–cyclododecane–n-decane are studied by means of differential thermal analysis. It is found that the system is of the eutectic type. The temperature of eutectic melting is found to be–34.9°C, the n-docosane content is 3.5 wt %, the n-decane content is 86.5 wt %, and the cyclododecane content is 10.0 wt %. It is concluded that the results can be used to create new optimal heatstorage materials.