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.     

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.     

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.     

Spatial Structure,Electron Energy Spectrum,and Growth of HfSi<Stack><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>−</Superscript></Stack> Clusters (<Emphasis Type="Italic">n</Emphasis> = 6–20)

The optimized spatial structure and calculated electronic spectra of anionic clusters HfSi _n ^? (n = 6–20) are presented. The calculations have been performed by the density functional theory method. By comparing the calculated and available experimental data, the spatial structures of the clusters detected in the experiment have been determined. It has been established that the formation of endohedral structures begins with n = 12, when a stable structure of a prism encapsulating a hafnium atom is formed. Clusters with n = 12 and 16 have increased stability and are basic for the construction of clusters with a close number of silicon atoms.     

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.     

Theoretical study of stepwise chlorinated aluminide clusters Al<Subscript>13</Subscript>Cl<Stack><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>−</Superscript></Stack> (<Emphasis Type="Italic">n</Emphasis> = 1–9)

The electronic and geometric structures, energy stabilities, normal mode frequencies, and spin density distributions (in radicals) of different stepwise-chlorinated aluminum clusters Al₁₃Cl _n ^? (n = 1–9) are calculated within the B3LYP approximation of the density functional theory using 6-31G* and 6-311+G* basis sets. The results are compared with analogous computation data on hydrides Al₁₃H _n ^? (n = 1–12) obtained at the same level. The general qualitative pattern for related series of hydrides, chlorides, and iodides (as well as fluorides and bromides) turns out to be similar in many respects. For all Al₁₃X _n ^? clusters with different electronegative substituents X, there is a set of a considerable number of low-lying closely spaced inner isomers (with a centered icosahedral cage), marquee isomers, and outer isomers (capped). The effects found by calculations in centered icosahedral isomers—localization of spin density on the trans-Al* atom in radical anions and its associated trans addition rule for an even substituent and the zigzag (odd-even) dependence of the energies D _n (X) of successive addition of substituents X to the metal cage on n described in the framework of the molecular model of the valence states of the Al ₁₃ ^? superatom—should also be shared by many Al₁₃X _n ^? series with different X’s. The differences between hydrides Al₁₃H _n ^? and chlorides Al₁₃Cl _n ^? of the same type are quantitative. For the hydrides, inner isomers are preferable in the first half of the series (n = 1–6); and in the second half (n = 7–12), outer isomers are more favorable. For the chlorides, icosahedral isomers are preferable only at the very beginning of the series. In the other cases, nonicosahedral structures are most favorable, for which the situation becomes very complicated due to the large number of position isomers and the aforementioned simple rules found for centered icosahedral structures are fulfilled to a considerably less extent or not at all.     

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.     

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.     

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.     

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     

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.     

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.     

Electronic spectra of the linear cationic chains NC<Subscript>2<Emphasis Type="Italic">n</Emphasis></Subscript>N<Superscript>+</Superscript> (<Emphasis Type="Italic">n</Emphasis> = 1–7): an ab initio study

The ground-state equilibrium geometries of the linear carbon chain cations NC_2n N⁺ (n = 1–7) have been investigated with B3LYP, CAM-B3LYP, and RCCSD(T) calculations. The ground state (X²П_g/u) and excited state (1²П_u/g) have been optimized by using the complete active space self-consistent field method. The present study reveals that these linear cations generally have the characteristic of bond length alternation in both electronic states. The vertical excited energies for the dipole-allowed (1, 2, 3)²П_u/g ← X²П_g/u transitions as well as the dipole-forbidden 1²Φ_u/g ← X²П_g/u transitions have been computed with the complete active space second-order perturbation theory. The calculated transition energies of 1²П_u/g ← X²П_g/u for NC_2n N⁺ (n = 1–6) in the gas phase are 2.26, 2.09, 1.91, 1.72, 1.56, and 1.39 eV, respectively, which mutually agree well with the available experimental values of 2.11, 2.07, 1.88, 1.67, 1.49, and 1.34 eV. Moreover, the corresponding absorption wavelengths are predicted to have the significant nonlinear size dependence, which is different from the bands origin in NC_2n N (n = 1–7).     

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.     

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.     

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.     

Synthesis of (Ni<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>P (0 ≤ <Emphasis Type="Italic">x</Emphasis> ≤ 0.65) substitution solid solution

The phosphides (Ni_{1 ? x} Co _x )₂P (0 ≤ x ≤ 0.65) crystallizing in the hexagonal system, space group P \(\bar 6\)2m, were synthesized in two steps starting from the continuous solid solution (Ni_{1 ? x} Co _x )₃(PO₄)₂ · 8H₂O. The initial phosphates were first completely dehydrated at 800°C and then reduced with hydrogen at 900–1000°C for 1–2 h.     

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.     

Geometrical structures and dissociation channels of MP<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><Superscript>+</Superscript> (M = Fe,Co or Ni; <Emphasis Type="Italic">n</Emphasis> = 2, 4, 6 or 8) binary cluster ions

A density functional theory study on the geometrical structures and dissociation channels of MP _n ⁺ (M = Fe, Co or Ni; n = 2, 4, 6 or 8) binary cluster ions has been performed. The tetrahedral P₄ structure and linear P₂ structure are found to be two relatively stable units in these ions. The lowest energy structures of MP _n ⁺ cluster ions are constructed by bonding a twofold or fourfold M atom with a P₄ or P₂ unit. The M–P bond is clearly weaker than the P–P bond. The most likely dissociation channel of the MP _n ⁺ cluster ions is the detachment of a P₄ or P₂ fragment. This conclusion is well consistent with the published experimental data and consistent with our previously reported theoretical study on the CrP _m ⁺ (m = 2, 4, 6 or 8) cluster ions.     

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.