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.     

Directed Aminomethylation of Pyrrole,Indole, and Carbazole with <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N′</Emphasis>,<Emphasis Type="Italic">N′</Emphasis>-Tetramethylmethanediamine

Catalytic aminomethylation of pyrrole and indole with N,N,N′,N′-tetramethylmethanediamine in the presence of 5 mol % of ZrOCl₂·8H₂O proceeds selectively at the positions 2, 5 of pyrrole and 1, 3 of indole. Carbazole under the same conditions affords 3-formyl-9-aminomethyl derivative. The reaction in the presence of 5 mol % of K₂CO₃ occurs as monoaminomethylation: for pyrrole at the position 2, for indole at the position 3, and for carbazole at the nitrogen atom of the substrate. Water-soluble 1,1′-(1H-pyrrole-2,5-diyl)bis(N,N-dimethylmethanamine) exhibits a fungistatic activity with respect to phytopathogenic fungi Rhizoctonia solani.     

Thermophysical properties of <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dimеthylacetamide mixtures with <Emphasis Type="Italic">n</Emphasis>-butanol

The refraction, dielectric, viscosity, density, data of the binary mixtures of N,N-dimethylacetamide (DMA) with n-butanol at 308.15 and 313.15 K. The measured parameters used to obtain derived properties like Bruggeman factor, molar refraction and excess static dielectric constant, excess inverse relaxation time, excess molar volume and excess viscosity, excess molar refraction. The variation in magnitude with composition and temperature of these quantities has been used to discuss the type, strength and nature of binary interactions. Results confirm that there are strong hydrogen-bond interactions between unlike molecules of DMA+ n-butanol mixtures and that 1: 1 complexes are formed and strength of intermolecular interaction increases with temperature.     

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.     

Complex formation of magnesium and calcium ions with trimethylenediamine-<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>’,<Emphasis Type="Italic">N</Emphasis>’-tetraacetic acid

Stability constants and heat effects of the formation reactions of magnesium and calcium trimethylenediaminetetraacetates at 298.15 K and ionic strength of 0.1, 0.5, and 1.0 (mol/L KNO₃) have been determined by means of potentiometry and calorimetry. Standard thermodynamic parameters (log K⁰, Δ_rG⁰, Δ_rH⁰, and Δ_rS⁰) of the studied equilibriums have been determined.     

1,3-Diamino-2-Hydroxypropane-<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′,<Emphasis Type="Italic">N</Emphasis>′-Tetraacetic Acid: Crystal and Molecular Structures

The synthesis, IR spectroscopic study, and X-ray diffraction analysis (CIF file CCDC no. 1574078) are carried out for 1,3-diamino-2-hydroxypropane-N,N,N′,N′-tetraacetic acid (I). The structural units of a crystal of compound I are (H_4.5HPdta)^0.5– anions, (H_5.5HPdta)^0.5+ cations, and molecules of water of crystallization joined by a branched network of hydrogen bonds: strong intermolecular O–H…O and intramolecular N–H…O bonds.     

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.     

<Emphasis Type="Italic">β</Emphasis>-Chloro-<Emphasis Type="Italic">α</Emphasis>,<Emphasis Type="Italic">β</Emphasis>-unsaturated carbonyls as convenient precursors of highly substituted benzenes

The Diels–Alder reactions of three β-chloro-α,β-unsaturated carbonyl compounds 1–3 with different dienes were carried out to afford highly functionalized cyclohexenes 4–9, bearing quaternary centers, in good yields. These cycloadducts (CAs) undergo dehydrochlorination with subsequent aromatization in the presence of 1,8-diazabicyclo[5.4.0]undec-7-ene DBU to produce new substituted benzenes 11–14. Compound 10 is the product of lactonization and removal of an HCl molecule from compound 7. All products were characterized by NMR, IR, elementary analysis and some of them by MS. Structure assignments of isomers were carried out on the basis of NMR chemical shifts and coupling constants using 1D, 2D and heteronOe NMR techniques.     

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.     

Converting dipyrrinones to lactim ethers to fluorescent <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>′-difluoroboryl derivatives

A high-yield straightforward conversion of lactams to lactim ethers is shown by the conversion of (10H)-dipyrrin-1-ones to (11H)-dipyrrin-1-ol methyl and ethyl ethers in 90% yield from heating in neat trimethyl or triethyl phosphite at 160°C. Unlike the parent dipyrrinones, which form intermolecularly hydrogen-bonded dimers in CHCl₃, their lactim ethers are shown to be monomeric by vapor pressure osmometry. The latter react with boron trifluoride etherate to N,N′-bridged BF₂ derivatives that exhibit strong fluorescence (φ_F 0.6–0.8) near 535 nm. X-Ray crystal structures were obtained of the lactim ethyl ether of kryptopyrromethenone and the BF₂ derivative of the lactim ethyl ether 2,3-diethyl-7,8-dimethyl-(10H)-dipyrrin-1-one. Correspondence: David A. Lightner, Department of Chemistry, University of Nevada, Reno, Nevada 89557-0020 USA.     

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.     

Spectroscopic and electrical characterization of <Emphasis Type="Italic">α</Emphasis>,<Emphasis Type="Italic">γ</Emphasis>-bisdiphenylene-<Emphasis Type="Italic">β</Emphasis>-phenylallyl radical as an organic semiconductor

The semiconductor properties of the earliest known stable radical, α,γ-bisdiphenylene-β-phenylallyl radical (Koelsch radical, 1^?) were assessed using spectroscopic and electrical techniques. This radical undergoes reversible redox processes, and it has low redox potentials. In addition, 1^? possesses long wavelength absorption bands, owing to the existence of a singly-occupied molecular orbital whose energy level lies between those of the HOMO and LUMO. A spin-coated thin-film of 1^? displays photocurrent and an electron mobility of 6.3 × 10^?7 cm² V^?1 s^?1 on a trially-fabricated organic field effect transistor.     

Excess molar enthalpies of dichloropropane + <Emphasis Type="Italic">n</Emphasis>-alkane mixtures

We have determined the excess molar enthalpies H_\textm^\textE H_{\text{m}}^{\text{E}} at 298.15 K and normal atmospheric pressure for the binary mixtures containing dichloropropane and n-alkane [{xCH₂ClCHClCH₃ + (1−x) C _n H_2n+2 (n = 6, 8, 10, 12)} and {xCH₂ClCH₂CH₂Cl + (1−x) C _n H_2n+2 (n = 8, 10)}] using a Calvet microcalorimeter. The H_\textm^\textE H_{\text{m}}^{\text{E}} values for all the mixtures show endothermic behaviour for the whole composition range. The Redlich–Kister equation was used to correlated the experimental values. The experimental excess molar enthalpies were examined on basis of the DISQUAC group-contribution model and the UNIFAC group-contribution method using the version considered by Larsen et al. The experimental and calculated results are discussed in terms of molecular interactions and the proximity effect.     

<Emphasis Type="Italic">N</Emphasis>′-tetrazolylmethoxyl derivatives of <Emphasis Type="Italic">N</Emphasis>-methyldiazene <Emphasis Type="Italic">N</Emphasis>-oxides

A preparation method was developed for previously unknown tetrazole derivatives containing in the 1, 2, and/or 5 positions of the tetrazole ring N-methyldiazene-N-oxide-N′-oxymethyl groups.     

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.     

Phase Equilibrium States in the <Emphasis Type="Italic">n</Emphasis>-Dodecane–<Emphasis Type="Italic">n</Emphasis>-Hexadecane–Cyclododecane System

A three-component system comprising cyclododecane and n-alkanes is studied by means of differential thermal analysis on a differential scanning microcalorimeter. It is concluded that the investigated system is of the eutectic type and the n-dodecane–n-hexadecane–cyclododecane eutectic mixture system is 73.0 wt % n-С₁₂Н₂₆, 9.0 wt % n-С₁₆Н₃₄, and 18.0 wt % С₁₂Н₂₄. Its melting point is found to be ?17.7°C.     

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.     

Computer models of eutectic-type <Emphasis Type="Italic">T</Emphasis>–<Emphasis Type="Italic">x</Emphasis>–<Emphasis Type="Italic">y</Emphasis> diagrams with allotropy

Using the eutectic-type T–x–y diagram as an example, it can be represented the analysis of its geometrical construction dependence on the temperature of a component two polymorphous modifications which participate in mono- and invariant metatectic and invariant eutectic (eutectoid) transformations above or below (and within) binary eutectics temperature intervals and below a ternary eutectic temperature. Computer models for considered phase diagrams have been designed. Such models help to solve applied tasks like visualization, isopleths and isothermal sections decoding, mass balances calculation and evaluation of phase and conglomerate concentration in microstructure.     

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.