Möbius环并苯的分子对称性

一般来说, 点群理论认为Möbius带环分子最高的对称性只能是C₂. 本文讨论了由18个苯环组成的环并苯的异构体分子, 包括柱面的Hückel型分子(HC-[18])和扭转180°的Möbius带环分子(MC-[18]). 结果表明除了点对称性外, Möbius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性, 为此还引用了环面正交曲线坐标系. 此外, 还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集. 根据TSR对称性的循环群特征, 可以建立此类群的不可约表示及有关特征标. 这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的, 然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

M(o)bius环并苯的分子对称性

一般来说,点群理论认为M(o)bius带环分子最高的对称性只能是C2.本文讨论了由18个苯环组成的环并苯的异构体分子,包括柱面的Hückel型分子(HC-[18])和扭转180°的M(o)bius带环分子(MC-[18]).结果表明除了点对称性外,M(o)bius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性,为此还引用了环面正交曲线坐标系.此外,还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集.根据TSR对称性的循环群特征,可以建立此类群的不可约表示及有关特征标.这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的,然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的.     

IR Emission Spectra of Carbonate-Chloride Melts 2CsCl-NaCl-Cs2CO3 Containing Lithium and Beryllium Ions

The IR emission spectra of the molten systems NaCl-CsCl-Cs₂CO₃-MCl _n (M = Li, Be) have been obtained. Spectral data shows that, at a definite limiting molar ratio n _lim = [CO₃]/[Mⁿ⁺] characteristic for each Mⁿ⁺, carbonate-chloride melts based on the NaCl-CsCl eutectic contain carbonate complexes [Li(CO₃)₃]^5? and [Be(CO₃)₃]^4? and, if n < n _lim, carbonato chloro complexes [M(CO₃) _m Cl_4?m ], where m = 1–2.     

ns2np4 (n = 4, 5) lone pair triplets whirling in M*F2E3 (M* = Kr,Xe): Stereochemistry and ab initio analyses

The stereochemistry of ns²np⁴ (n = 4, 5) lone pair LP characterizing noble gas Kr and Xe (labeled M*) in M*F₂ difluorides is examined within coherent crystal chemistry and ab initio visualizations. M*²⁺ in such oxidation state brings three lone pairs (E) and difluorides are formulated M*F₂E₃. The analyses use electron localization function (ELF) obtained within density functional theory calculations showing the development of the LP triplets whirling {E₃} quantified in the relevant chemical systems. Detailed ELF data analyses allowed showing that in α KrF₂E₃ and isostructural XeF₂E₃ difluorides the three E electronic clouds merge or hybridize into a torus and adopt a perfect gyration circle with an elliptical section, while in β KrF₂ the network architecture deforms the whole torus into an ellipsoid shape. Original precise metrics are provided for the torus in the different compounds under study. In KrF₂ the geometric changes upon β → α phase transition is schematized and mechanisms for the transformation with temperature or pressure are proposed. The results are further highlighted by electronic band structure calculations which show similar features of equal band gaps of 3 eV in both α and β KrF₂ and a reorganization of frontier orbitals due to the different orientations of the F-Kr-F linear molecule in the two tetragonal structures.     

Photoelectron spectroscopy of transition metal-sulfur cluster anions

Metal (M)-sulfur cluster anions (M = Ag, Fe and Mn) have been studied using photoelectron spectroscopy (PES) with a magnetic-bottle type time-of-flight electron spectrometer. The M_nS _m ^? cluster anions were formed in a laser vaporization cluster source. For Ag-S, the largest coordination number of Ag atoms (n _max) is generally expressed as n _max =2m ? 1 in each series of the number of S atoms (m). For Fe?S and Mn?S, it was found that the stable cluster ions are the ones with compositions of n=m and n=m±1. Their electron affinities were measured from the onset of the PES spectrum. For Ag?S, the EAs of Ag₁S_m are small and around 1 eV, whereas those of Ag_nS_m (_n ≥ 2) become large above 2 eV. The features in the mass distribution and PES suggest that Ag₂S unit is preferentially formed with increasing the number of Ag atoms. For Fe?S and Mn?S, the PES spectra of Fe_nS _m ^? /Mn_nS _m ^? show a unique similarity at n ≥ m, indicating that the Fe/Mn atom addition to Fe_nS _n ^? /Mn_nS _n ^? has little effect on the electronic property of Fe_nS_n/Mn_nS_n. The PES spectra imply that the Fe_nS_n cluster is the structural framework of these clusters, as similarly as the determined structure of the Fe_nS_n cluster in nitrogenase enzyme.     

Effect of rotational relaxation on the intensity and polarization of fluorescence emission caused by sequential two-photo excitation

General formulas are derived for the intensity and the degree of polarization of the S_m-fluorescence emission (m ? 2) of a sample excited by the sequential two-photon excitation process (S_n ← S₁ ← S₀, n ? 2) with plane-polarized pulsed light. They show how the S_m-fluorescence intensity and anisotropy depend on the relative orientation of the relevant transition dipoles within a molecule and on the degree of rotational relaxation of molecules in the intermediate state (S₁) and in the S_m state (for the case m = n), or in the S_n → S_m process (m ≠ n).     

Thermochemistry of the Reaction of Solvated Sodium Ion Clusters with Thymine in the Gas Phase: An Example of the Reaction in Microcosmic Environment

The thermochemistry of the reaction of the microsolvated Na⁺ such as [Na(H₂O) _n ; n?=?1?6]⁺, [Na(NH₃) _n ; n?=?1?6]⁺ and [Na(H₂O) _n (NH₃) _m ; n?+?m?=?2?6]⁺ with thymine (Thy), as an example of a reaction in the microcosmic environment, have been studied in this work, theoretically. It was found that the increase of the number of solvent molecules in the structure of microsolvated Na⁺ is accompanied by the decrease of the standard enthalpy (\(\Delta H_{r}^{^\circ }\)) and Gibbs free (\(\Delta G_{r}^{^\circ }\)) energies of the reaction (Thy?+?[Na(X) _n ]⁺→Thy-Na(X) _n ⁺ ; X?=?solvent molecule). Also, the calculations showed that the electronic intermolecular interaction (?E_int) between the Thy and microslovated Na⁺ decreased with the increase of solvent molecules. For the interaction of the [Na(H₂O) _n ; n?=?4, 5 and 6]⁺ ions with the Thy, there was the probability of forming of the hydrogen bond between water molecules in the structure of solvated Na⁺ and the Thy. The gas phase infrared (IR) spectra of the complexes of the microsolvated Na⁺ with the Thy for different values of n were calculated and compared with each other to follow the change in the frequency of the stretching vibration of the interaction path between the C=O group of the Thy and Na (O…Na) with n. Using the calculated values of \(\Delta G_{r}^{^\circ }\) of the reactions, the mole fractions of the complexes of microsolvated Na⁺ ions with the Thy were calculated at different humidity.     

Synthesis and study of new rod-like mesogens containing 2-aminothiophene unit

We present a synthesis and mesomorphic properties of a new series of rod-like mesogens. All the compounds possess a substituted 2-aminothiophene unit as a main element in the structure attached to a stilbene moiety with a terminal alkyloxy chain (OR¹, OR² where R¹=C_nH_2n+1, R²=C_mH_2m+1; n, m ranging from 6 to 12). The synthesis of alkyloxybiphenyl substituted 2-aminothiophenes was carried out by the Gewald reaction and the appropriate reaction conditions were investigated. The liquid–crystalline properties were studied via polarizing optical microscopy, differential scanning calorimetry and X-ray diffraction. These materials exhibit nematic and/or smectic A phases. The influence of structural changes (variation in alkyloxy chain length and symmetry of the molecule) on mesogenic behaviour is discussed. Evaluation of UV–vis, fluorescent and electrochemical properties are also included.     

Determinable partitional modelling of CayleyanSU(m \leqslant n/2) \times S_n \downarrow \mathcal{G}NMRspin symmetries of isotopomeric cage-clusters: SpecificS n≥12⊃...⊃D 3 group chains,forS n -modules in high-n weak-branching limit

The use over certain modestly branched (λ ?n) partitional models of Young'sS _n -module decomposition algorithm in the high-n limit is considered for SU(m) x $SU(m) \times S_n ( \downarrow \mathcal{G})$ nuclear spin algebras associated with both NMR and ro-vibrational (R-V) aspects of specific cluster isotopomers. This approach allows additional dual-group projective mapping over simple Hilbert spaces to be derived from the natural embedding of higher finite groups in specificS _n groups, for either the original simply-reducible (SR) SU(2)-, or various related higher non-SR SU(m) xS _n , forms. The work arises from earlier interests in the NMR spin symmetry of the [¹¹B¹H] ₁₂ ^2? borohydride anions and the nature of analogous ro-vibrational (R-V) spin statistical problems for highern ≥ 12-fold clusters. Here, the role of the scalar invariants is shown to be critical in determining the spin algebras of isotopomeric clusters within Cayley's theorem for some particular depth of SU(m) branching in the SU(m) xS _n dual-group algebra. Certain additional quasi-geometric models for the full λ (≥ λ_SA (self-associate) dominant-sector set of (λ ?n) partitions-of-n are discussed, in the context of specific determinacy of natural $S_n \supset \mathcal{G}$ group embeddings at a given branching level.     

Identification of molecules in inorganic compounds from X-ray or neutron diffraction data and correction of their structures on the basis of vibrational spectroscopy data

A method of identification of molecules in inorganic crystals with asymmetric M-X...M bridges has been suggested on the basis of analysis of interatomic distances in the structure unit M (−X...M) _n , which includes the atoms of the first and second coordination spheres. This analysis makes it possible to discern molecules (complex anions or cations) as a groups of atoms linked with each other by short M-X bonds, whereas the atoms of neighboring groups are linked by long M...X bonds. The symmetry of such a group is often lower than it follows from X-ray or neutron diffraction data. Studying vibrational spectra affords information on the true symmetry of a molecule. The use of the method is exemplified by the rhombohedral BaTiO₃ phase.     

study of liquid crystalline N -[4-(4- n -alkoxybenzoyloxy)-2-hydroxybenzylidene]methylanilines

New homologous series of N-[4-(4-n-alkoxybenzoyloxy)-2-hydroxybenzylidene]methylanilines [nAHmM(n=1-8/10; m=2: ortho, m=3: meta, m=4: para)] were synthesized. They exhibited a nematic phase except for 1AH3M. The temperature dependence of their Raman spectra was observed in the spectral range of 900–1700 cm^-1. In one group of nAHmM compounds, the Raman band at about 1360 cm^-1 abruptly decreased in intensity and wavenumber when the crystalline solid-liquid crystal phase transition was approached. In another group, the corresponding band increased through the phase transition. The bands have been assigned to the coupling mode between the in-plane CCH deformational vibration and the ring-N stretching vibration. Such a behaviour can be explained by the molecular conformation with different twist angles of the aniline ring in relation to the Schiff's base plane of the molecule. Some nAHmMs exhibited photochromism.     

Synthesis and Crystal Structure of 1,10-Diazonia-18-crown-6 Diiodide Dihydrate

Crystalline 1,10-diazonia-18-crown-6 diiodide dihydrate was synthesized and studied by single crystal X-ray diffraction. The salt exists in the crystal in the form of separate centrosymmetrical ionic molecules [(H₂DA18C6)²⁺ ? 2I^? ? 2H₂O] whose components are held together by hydrogen bonds and electrostatic attraction forces. The centrosymmetric dication DA18C6 (with two protonated nitrogen atoms) has a crown conformation with approximate D_3d symmetry. The iodide ions are arranged at the nitrogen atoms (one above and the other below) of the DA18C6 dication, and two water molecules are arranged above and below its symmetry center. Each water molecule is disordered over two positions with occupancies of 0.65 and 0.35.     

[M(NH<Subscript>3</Subscript>)<Subscript>5</Subscript>Cl][AuCl<Subscript>4</Subscript>]Cl · <Emphasis Type="Italic">n</Emphasis>H<Subscript>2</Subscript>O (M = Rh,Ru, or Cr): Synthesis,crystal structure,and thermal properties

Double complex salts [M(NH₃)₅Cl][AuCl₄]Cl · nH₂O (M = Rh, Ru, or Cr) were synthesized and structurally studied. These compounds are isostructural; space group C2/m. Their crystal structure is built of [M(NH₃)₅Cl]²⁺ complex cations, [AuCl₄]^? complex anions, Cl^? anions, and molecules of water of crystallization. The compounds were characterized by X-ray crystallography, X-ray powder diffraction, IR spectroscopy, and thermal analysis.     

Bond-alternating Hückel-Möbius and related,twisted linear,cyclic and helical systems—their molecular orbitals,energies and phase correlation upon dissociation

Cyclic group formalism and screw symmetry operation are used to clarify and generalize the definition of Hückel and Möbius systems. It is shown that the Möbius ring system has half-integral pseudo-angular momentum similar to that of spin space, and that applications of Möbius electronics to chemical reactions have been based on truncated single-circle Möbius rings which have unique beginning and end (Sect. 2). This concept is illustrated by application to the [1, 7] antarafacial hydrogen shift (Appendix A and Figs. A1–A3). Definition of a Hüickel versus Möbius ring system for in-plane and out-of-plane π, δ and φ orbitals as well as the appropriate relative angle of twists are given (Sect. 2 and Table 1). Using the concept of the compatibility of the twist (screw) angle and rotation around a ring, we also derive the proper phase coherence and energy correlation between a parent cyclic (Hückel or Möbius) molecule and its dissociated linear fragments (Sect. 4). The concept of parentage in diabatic fragmentation is discussed. Forfinite, open, helical chain molecules, an exact periodic boundary condition based on the compatibility of twist angle and number of turns in a helical ring parent molecule is applied to derive their analytic wave functions (Sect. 5 and Table 2). Forbond-alternating “linear” and cyclic Hückel and Möbius systems we also derive the explicit LCAO-MO wavefunctions, energies, their degeneracies and their exact corresponding quantum members for even and odd atom systems at highest bonding and lowest antibonding levels (Sect. 3, Figs. 1–3). The corresponding wavefunctions and energies for uniform-bond systems are given for comparison and for completeness (Sect. 3).     

Some PhCNO-containing molecules; mass spectral similarity and molecular diversity

Some diverse compounds possessing a PhC?NO unit cleave the N? O link upon electron impact to give [PhCN]⁺˙. Different and especially significant modes of N? O scission occur in metastable processes when the oxygen atom of the PhCNO group is exocyclic to a heterocyclic nitrogen atom. Upon electron impact, rupture of the N? O bond in PhCNO-containing molecules generally dominates over 1,3-dipolar cycloreversion, which generates the radical cation of benzonitrile oxide. Stable PhCNO-containing molecules survive competing fragmentations in the ion source to produce [M+H]⁺ ions of moderate relative intensity. Other ions, which are larger than [M]⁺ are implicated where M is PhCH?NOR. Several values of m/z for metastable ions are common to compounds which have a PhCNO moiety. These m/z values generally derive both from a parent ion with m/z?105 and from a PhC?NO moiety.     

Micellization in solutions of anionic surfactants with two ionogenic groups

Conductometry is employed to measure the critical micellization concentrations of homologous sodium monoalkyl sulfosuccinates with double-charged surface-active anions and alkyl radicals R containing 10–14 carbon atoms (ROOCCH₂CH(SO₃Na)COONa). The degrees of counterion binding with micelles and the Gibbs energy ΔG ^m of micellization are calculated. The incorporation of an additional ionogenic group into a surfactant molecule somewhat decreases ΔG ^m. For the examined series of surfactants, the increment of ΔG ^m due to one methylene group is ?4.44 kJ/mol.     

Mass spectrometry of homoadamantane derivatives

Homoadamantane derivatives can be divided into two groups according to their mass spectra. To the first group belong compounds with electron attracting substituents (COOH, CI, COOCH₃, Br); compounds with electron releasing substituents (OCH₃, OH, NH₃, NHCOCH₃) constitute the second group. The most characteristic feature of the first group compounds is the splitting off of the substituent. The hydrocarbon fragment [C₁₁H₁₇]⁺ thus formed then loses olefin molecules with the formation of corresponding ionic species C_11?nH_17?2n. The 3-substituted compounds of this group undergo thermal Wagner-Meerwein type rearrangements into adamantane derivatives, resulting in the [C₁₀H₁₅]⁺ (m/e 135) ion formation; this is the main difference between 1- and 3-substituted homoadamantanes. The series of [C_nH_2n?6X]⁺ ions (where X = OCH₃, OH, NH₂, NHCOCH₃, n = 6 to 10) are characteristic of the mass spectra of the second group compounds, the ion [C₆H₆X]⁺, [M ? C₅H₁₁]⁺ being the most abundant. The intensity ratio of [M ? C₅H₁₁]⁺ to [M ? C₄H₉]⁺ ions is 10:1 for 1-substituted and 3:1 for 3-substituted compounds of this group, allowing the location of the substituent. Some individual features of the spectra are also reported.     

A microsolvation approach to the prediction of the relative enthalpies and free energies of hydration for ammonium ions

Hartree–Fock (HF) and second-order Møller–Plesset (MP2) calculations were used to investigate the structures and thermochemistry of methylammonium–water clusters (Me_4-m NH _m ⁺ (H₂O) _n , m=1–4, n=1–4). Water molecules were treated ab initio and with effective fragment potentials (EFP). In addition to a thorough phase-space search, the importance of basis set, electron correlation, and thermodynamic effects was systematically examined. Cluster structures resulted from hydrogen bond formation between the ammonium group and water molecules; upon saturation of the hydrogen bonding sites of the ammonium group, water molecules entered the second hydration shell. With only four water molecules, the experimental relative enthalpies of hydration were well reproduced at the HF level, while the MP2 relative free energies were in best agreement with experiment. Absolute energies of hydration were calculated using an empirical correction. These results strongly suggest that a HF-based microsolvation approach employing a small number of water molecules can be used to compute relative enthalpies of hydration.     

[32]π Fused Core‐Modified Heptaphyrin with Möbius Aromaticity

A new fused core‐modified 32π heptaphyrin with Möbius aromatic character is reported. The ¹H NMR data indicated a weak Möbius aromaticity at 298 K; however, at 213–183 K, the molecule predominates [4n]π Möbius conformation with strong diatropic ring current, which was further confirmed by X‐ray analysis. The protonation experiment led to preservation of the Möbius aromaticity at 298 K. Nevertheless, the experimental results were further supported by theoretical studies. Overall, this study represents the first example of Möbius aromatic fused core‐modified expanded porphyrin.     

On the interaction of tetraethoxosilane with metal alkoxides: Sol-gel synthesis of alkaline-earth metal silicates

Physicochemical analyses (solubility method, conductometry, and IR spectroscopy) revealed no complex formation in M(OR)_n-Si(OR)₄-ROH systems (M = Na, Ba, Al; R = Et, Prⁱ), unlike in the systems containing alkoxides of two metals. IR and NMR spectroscopy showed that Si(OR)₄ became reactive only due to microhydrolysis, which is accompanied most likely by the formation of intermediates (asymmetric molecules [Si(OH)_n(OR)_{4 ? n} ]). The hydrolysis was studied for model systems M(OEt)₂ ? si(OEt)₄ (M = Ba, Ca), and conditions for the synthesis of silicates were optimized.