Orientational distribution coefficients for oriented systems,e.g., a liquid crystal matrix

For a class of measurements, UV and CD, e.g., the measurable quantities are represented by M_kl = g_ijklX_ij, where the X_ij describe a symmetric or antisymmetric tensorial property of the molecule. The g_ijkl are the orientational distribution coefficients which represent a generalized form of the Saupe order matrix. For an optically biaxial (uniaxial) system there are thirty-four(eight) independent orientational distribution coefficients which bear information about the orientational distribution function. The conditions for the determination of these g-values via independent measurable quantities M_kl are analysed. Some problems introduced by an incomplete knowledge of the molecular tensor X_ij are discussed.     

The effect of reactant vibrational state on differential charge transfer cross sections for T2+(X2 Σg+, ν0′) + T2(X1 Σg+, ν0″) collisions

Differential charge transfer cross sections for reactions of vibrationally excited incident ions and molecules have been computed for the T₂⁺(X² Σ_g⁺, ν₀′) + T₂(X¹ Σ_g⁺, ν₀″) system. Differential cross sections for the formation of neutral products become more intense and concentrated in the forward direction as the quantum number of the reactant ion and/or molecule is increased.     

Effect of the orientation of coordinated water molecules on the electronic structure of trans halo-aquo complexes: application to TiCl2(H2O) 4 + and VCl2(H2O) 4 +

The X method has been utilized to calculate the electronic structure of trans-TiCl₂(H₂O) ₄ ⁺ and trans VCl₂(H₂O) ₄ ⁺ ions. Different conformations of coordinated water molecules have been considered. It has been found that the most stable configuration in both cases is the one with the plane of the water molecules parallel to the Cl-metal-Cl axis. The nature of the tetragonally distorted ground state has been found to depend on the orientation of the water molecules in these systems.     

Rotor-synchronized two-dimensional 13C CP/MAS NMR studies of the orientational order of polymers. I. High-performance ultrahigh molecular weight polyethylene fibers

The orientational order of three morphological components, identified previously as two crystalline components, C₁ and C₂, and an amorphous component, A of four polyethylene fibers, including two gelspun ultrahigh molecular weight (PE-I and PE-II) and two meltspun moderate molecular weight (PE-D and PE) polyethylene fibers are further analyzed by rotor-synchronized two-dimensional ¹³C CP/MAS (ROSMAS) nuclear magnetic resonance (NMR) techniques. Our results indicate that the orientational order of these components differ substantially among themselves in a given fiber and among different fibers of the same component. Values of β_1/2, the polar angle at which the orientational distribution function (ODF) P 〈β〉 decays to half its maximum, are determined to be: 18° (C2 of PE-II), 21° (C2 of PE-I), 29° (C2 of PE-D), 31° (C1 of PE-I) and 50° (C2 of PE). No orientational sideband can be detected for component A, suggesting that the A component is due to the amorphous domain. The implication of this results and the technical limit of this technique are analyzed. © 1993 John Wiley & Sons, Inc.     

A new method for the measurement of vibrational-state-selected ion-molecule reactions at thermal energies

A photoelectron-secondary-ion-coincidence method is described that allows us to determine the relative vibrational-energy-dependent cross sections for reactions of molecular ions with neutral atoms or molecules at thermal energies. Results for reactions of H₂⁺(ν) in vibrational states ν = 0–8 with H₂(H₃⁺), Ne(NeH⁺) and He(He⁺) are reported.     

Influence de l'acidité, en milieu très acide,sur l'intensité de la transition secondaire de molécules de type φCX(1)X(2)X(3) sans sites formellement protonables

The 00 band of the secondary transition (towards 260 nm) of the benzenic chromophore undergoes, for many molecules whose type is φCX₍₁₎X₍₂₎X₍₃₎ (X = CO₂H, NH⁺₃, φ, OCH₃,OH, H), a surprising increase of its intensity when the acidity of the medium is lowered under pH = 0. Some, on the contrary, undergo a slight decrease. We show that these phenomena, appearing in molecules where there is no functional group to be protonated, can be explained on the grounds of an interaction involving the acid species of the medium and the π cloud of the chromophore. We also study the effect of the interaction of these acid species with the substituent.     

Electron momentum density distribution in homonuclear diatomic molecules

Individual orbital contributions to the electron momentum densities of first-row homonuclear diatomic molecules are discussed. It is shown that the nodal surfaces in the orbital EMDs arise from a diffraction factor with both geometric and electronic components. The positions of the nodal surfaces convey information on the electronic structure. The results are illustrated with a Hartree-Fock-Slater calculation of the F₂(X¹Σ_g⁺) molecule.     

Vacuum UV emission by electronically-excited N2: The radicative lifetime of the N2(a′1Σ−u state

A measurement of the electronic transition moment variation for the N₂(a'¹Σ^?_uX¹Σ^+g) band system has allowed a reassessment of the radiative lifetime of N₂(a′). Relaxation to N₂(a′,υ=0) is established as the major channel for quenching of N₂(a¹Π_g, υ = 0) molecules by Ar.     

Application of the Seth-Paul-Van Duyse equation—I : A simple relation defining new X+(R) substituent constants on the basis of electrophilic σ+ constants

The Seth-Paul-Van Duyse equation (SPVDE) correlating the CO stretching frequencies of a great number of R₁COR₂ molecules with X (R) substituent constants has been reinvestigated. A simple empirical relation defining new X⁺(R) constants on the basis of electrophilic σ constants has been derived: X⁺ (R) = 0·238 σ⁺ + 1·077. The three earlier reported relationships between the X(R) constants and Hammett σ values have been replaced by this single relationships and a set of new X⁺(R) constants has been calculated. The new X⁺(R) constants applied to 287 R₁COR₂ compounds containing the para- or meta-substituted benzene rings fit very well the SPVDE. It has been possible to extend the SPVDE to various aromatic systems.     

Dependence of molecular polarizability on the orientational order in nematic liquid crystals

The dispersion dependences of refractive indices in the visible range were used to obtain experimental values of the Lorentz tensor components L _j and the mean molecular polarizability $ \bar \gamma $ \bar \gamma for five nematic liquid crystals belonging to two homological series. The dependence of L _j components on the homologue number, mesophase temperature, birefringence value, and the orientational order of molecules in the nematic phase and upon a nematic-smectic A phase transition was revealed. The effect of the isotropization of the Lorentz tensors and the local field tensor with decreasing birefringence and molecular polarizability anisotropy Δγ was confirmed. The quadratic dependence $ \bar \gamma $ \bar \gamma (S) on the molecular orientational order parameter S in the nematic phase was found. It was invariant with respect to the nematic-smectic A transition. The dependences $ \bar \gamma $ \bar \gamma (S) and Δγ(S) are explained within molecular statistical theory as consequences of the correlation between orientational and conformational degrees of freedom of molecules. These conformational degrees of freedom are related to the internal rotation of molecular fragments, which affects the electronic conjugation of the fragments and the oscillator strengths of molecular transitions.     

General methods of analysing molecular vibrations

An acute need may arise to develop for the complete analysis of molecular vibrations practically convenient general methods based on coordinates other than “chemical coordinates”. One reason is the proven proposition: Among independent internal coordinates corresponding to a molecule, there cannot be one which describes a small displacement of a chemical group as a whole relative to a certain molecular plane, provided this group contains more than two linearly or three non-linearly arranged atoms. Two methods are presented in some detail. The first is based on the use of X⁰_δ coordinates which are components of “bond vectors” in the “sown” (for each “bond”) Cartesian coordinate system. The second method utilizes X⁰ coordinates, i.e. the components of atomic displacements in the “down” (for each atom) Cartesian coordinate system. Computation of the torsional vibration of transdichloroethane is given as an example illustrating the first method. The Mayants treatment of the symmetry of a molecule, proceeding from elementary considerations which do not use the group theory explicitly and are valid for any coordinates, is expounded in a somewhat improved version. The peculiarities arising when considering the mean-square amplitude matrix, Σ, in X⁰_δ and X⁰ coordinates are also discussed.     

N2O+经由B2Пi←X2П跃迁的光解离机理研究

在超声分子束条件下,利用360.50 nm的电离激光使N₂O分子经由[3+1]共振增强多光子电离（REMPI）产生纯净的N₂O⁺（X²Π（000））分子离子,用另一束解离激光在230-275 nm范围扫描获得N₂O⁺经由B²П_i←X²Π跃迁产生的光解碎片（NO⁺和N₂⁺）激发（PHOFEX）谱. 获得的光解碎片激发谱可以归属为B²П_i（00n）←X²Π（000）序列跃迁. 我们分别将线性三原子分子离子N₂O⁺中N―N伸缩振动简化成NO和N之间的简谐振动,N―O伸缩振动简化成N₂和O之间的简谐振动,用谐振子的简谐势能曲线和波函数对N₂O⁺分子离子X²Π和B²П_i电子态振动能级间跃迁的Franck-Condon因子进行计算,和实验得到的碎片离子增强谱实验强度进行比较,对前人给出的分子数据（分子平衡核间距）进行验证,讨论了N₂O⁺经由B²П_i（00n）←X²Π（000）电子态跃迁的光解离机理和碎片离子的分支比.     

b1Σ+ Emissions from group V–VII diatomic molecules. b 0+ → X1 0+, X2 1 emissions of AsI and SbI

Chemiluminescence from the b 0⁺ → X₁ 0⁺ band system of AsI and of the b 0⁺ → X₁ 0⁺, X₂ 1 systems of SbI in the near-infrared spectral region has been observed in a discharge flow system. Analysis of the spectra led to the spectroscopic constants (in cm^?1) of AsI: ω_e(X₁, X₂) = 257 ± 2, ω_ex_e(X₁, X₂) = 0.82 ± 0.2, T_e(b 0⁺) = 11738 ± 5, ω_e(b 0⁺) = 271 ± 2, ω_ex_e(b 0⁺) = 0.66 ± 0.2, and of SbI: T_e(X₂ 1) = 965 ± 10, ω_e(X₁, X₂) = 206 ± 6, T_e(b 0⁺) = 12328 ± 10, ω_e(b 0⁺) = 211 ± 6. The intensity ratio of the two sub-systems b 0⁺ → X₂ 1 and b 0⁺→ X₁ 0⁺ was found to be ≈0.013 in the case of SbI and ? 0.01 for AsI.     

A modified wigner function set for the smoluchowski operator representation in anisotropic liquids

The set of non-orthogonal functions D^j_pq(Ω)^P1/2(Ω), in which the Wigner rotation functions are multiplied by the equilibrium orientational distribution, is shown to provide a convenient basis for the solution of the rotational diffusion problem in anisotropic liquids,in the entire range of orientational ordering.     

Synthesis,Structure, and Magnetic Properties of Three Novel Sandwich‐type Tungstobismuthates with Triethanolamine

Three novel sandwich‐type polyoxotungstates ( 1 – 3 ) were synthesized in good yield using an in‐situ conventional solution synthesis method by reaction in aqueous media below 80 °C. Compounds 1 – 3 represent the first structurally characterized β‐B‐BiW₉ sandwich‐type polyoxometalates with triethanolamine cations. All three compounds have the same building unit [(X(H₂O)₃)₂(X_0.5W_0.5O)₂(β‐B‐BiW₉O₃₃)₂)]^10– [X = Mn^II ( 1 ), Co^II ( 2 ), Ni^II ( 3 )]. The adjacent units of 1 or 2 are joined by Na⁺ cations in different ways to construct 1D chains or 2D sheets. A 3D supramolecular structure is further formed by hydrogen bond interactions among water molecules and protonated triethanolamine cations. Meanwhile only compound 3 shows a 0D structure. The compounds were characterized by elemental analysis, IR spectroscopy, TG analysis, and single‐crystal X‐ray diffraction. Magnetic measurements on a sample of 1 show the presence of paramagnetic interactions.     

New 1,3-disubstituted side-chain functionalized indenyl ligands and zirconium complexes derived from them

New functionalized indenyl ligands Ind^X = 1,3-C₉H₅(Prⁱ)(CH₂CH₂X) (X = OMe or NMe₂) and 1,3-C₉H₅(Prⁱ)[CMe₂CH₂(2′-py)] and the zirconium sandwich complexes (Ind^X)Cp*ZrCl₂ (Cp* is pentamethylcyclopentadienyl) were synthesized. The photochemical behavior and the reduction reactions of zirconocene dichlorides were investigated. The properties of these compounds are determined mainly by the high lability of Zr-Ind bonds. The reduction of (Ind^X)Cp*ZrCl₂ (X = NMe₂) selectively affords the complex Cp*[η⁵:η²-(C,N)-C₉H₅(Prⁱ)CH₂CH₂N(Me)CH₂]ZrH as the intramolecular NCH₂-H bond activation product. The molecular structures of the complex (Ind^X)Cp*ZrCl₂ (X = OMe) and its photochemical decomposition product [Cp*ZrCl₂(OMe)]₂ were established by X-ray diffraction.     

Heat capacity and transition phenomena of structure I and II trimethylene oxide clathrate hydrates

Heat capacities of structure I and II trimethylene oxide (TMO) clathrate hydrates doped with small amount of potassium hydroxide (x=1.8×10^–4 to water) were measured by an adiabatic calorimeter in the temperature range 11–300 K. In the str. I hydrate (TMO·7.67H₂O), a glass transition and a higher order phase transition were observed at 60 K and 107.9 K, respectively. The glass transition was considered to be due to the freezing of the reorientation of the host water molecules, which occurred around 85 K in the pure sample and was lowered owing to the acceleration effect of KOH. The relaxation time of the water reorientation and its distribution were estimated and compared with those of other clathrate hydrates. The phase transition was due to the orientational ordering of the guest TMO molecules accommodated in the cages formed by water molecules. The transition was of the higher order and the transition entropy was 1.88 J·K^–1(TMO-mol)^–1, which indicated that at least 75% of orientational disorder was remaining in the low temperature phase. In the str. II hydrates (TMO·17H₂O), only one first-order phase transition appeared at 34.5 K. This transition was considered to be related to the orientational ordering of the water molecules as in the case of the KOH-doped acetone and tetrahydrofuran (THF) hydrates. The transition entropy was 2.36 JK^–1(H₂O-mol)^–1, which is similar to those observed in the acetone and THF hydrates. The relations of the transition temperature and entropy to the guest properties (size and dipole moment) were discussed.Contribution No 57 from the Microcalorimetry Research CenterThe authors would like to express their sincere thanks to the Nissan Science Foundation for their financial support.     

Free energy perturbation calculations on parallel computers: Demonstrations of scalable linear speedup

A coarse-grain parallel implementation of the free energy perturbation (FEP) module of the AMBER molecular dynamics program is described and then demonstrated using five different molecular systems. The difference in the free energy of (aqueous) solvation is calculated for two monovalent cations ΔΔG_aq(Li⁺ Δ Cs⁺), and for the zero-sum ethane-to-ethane′ perturbation ΔΔG_aq(CH₃? methyl? X → X? methyl? CH₃), where X is a ghost methyl. The difference in binding free energy for a docked HIV-1 protease inhibitor into its ethylene mimetic is examined by mutating its fifth peptide bond, ΔG(CO? NH → CH?CH). A potassium ion (K⁺) is driven outward from the center of mass of ionophore salinomycin (SAL^?) in a potential of mean force calculation ΔG_MeOH(SAL^? · K⁺) carried out in methanol solvent. Parallel speedup obtained is linearly proportional to the number of parallel processors applied. Finally, the difference in free energy of solvation of phenol versus benzene, ΔΔG_oct(phenol → benzene), is determined in water-saturated octanol and then expressed in terms of relative partition coefficients, Δ log(P_o/w). Because no interprocessor communication is required, this approach is scalable and applicable in general for any parallel architecture or network of machines. FEP calculations run on the nCUBE/2 using 50 or 100 parallel processors were completed in clock times equivalent to or twice as fast as a Cray Y-MP. The difficulty of ensuring adequate system equilibrium when agradual configurational reorientation follows the mutation of the Hamiltonian is discussed and analyzed. The results of a successful protocol for overcoming this equilibration problem are presented. The types of molecular perturbations for which this method is expected to perform most efficiently are described. © 1994 by John Wiley & Sons, Inc.     

Theoretical study of the relative stabilities of H+(X)2 and H+(X)3 conformers and their clustering energies: X  CO and N2

Third-order Møller–Plesset perturbation theory (MP 3) with a 6-31G** basis set was applied to study the relative stabilities of H⁺(X)₂ conformations (X ? CO and N₂) and their clustering energies. The effect of both basis set extensions and electron correlation is not negligible on the relative stabilities of the H⁺(CO)₂ clusters. The most stable conformation of H⁺(CO)₂ is found to be a C_∞v structure in which a carbon atom of CO bonds to the proton of H⁺(CO), whereas that of H⁺(N₂)₂ is a symmetry D_∞h structure. The second lowest energy conformations of H⁺(CO)₂ and H⁺(N₂)₂ lie within 2 kcal/mol above the energies of the most stable structures. Clustering energies computed using MP 3 method with the 6-31G** basis set are in good agreement with the experimental findings of Hiraoka, Saluja, and Kebarle. The low-lying singlet conformations of H⁺(X)₃ (X ? CO and N₂) have been studied by the use of the Hartree–Fock MO method with the 6-31G** basis set and second-order Møller–Plesset perturbation theory with a 4-31G basis set. The most stable structure is a T-shaped structure in which a carbon atom of CO (or a nitrogen atom of N₂) attacks the proton of the most stable conformation of H⁺(X)₂ clusters.