Analysis of the updated Hessian matrices for locating transition structures

We present an analysis of the behavior of different updating Hessian formulas when they are used for the location and optimization of transition structures. The analysis is based on the number of iterations, the minimum of the weighted Euclidean matrix norm, and first-order perturbation theory applied to each type of Hessian correction. Finally, we give a derivation of a family of updated Hessians from the variational method proposed by Greenstadt. We conclude that the proposed family of updated Hessians is useful for the optimization of transition structures. © 1995 John Wiley & Sons, Inc.     

Using operators to expand the block matrices forming the Hessian of a molecular potential

We derive compact expressions of the second‐order derivatives of bond length, bond angle, and proper and improper torsion angle potentials, in terms of operators represented in two orthonormal bases. Hereby, simple rules to generate the Hessian of an internal coordinate or a molecular potential can be formulated. The algorithms we provide can be implemented efficiently in high‐level programming languages using vectorization. Finally, the method leads to compact expressions for a second‐order expansion of an internal coordinate or a molecular potential. © 2014 Wiley Periodicals, Inc.     

A variational principle for transition and density matrices and approximations to the equations-of-motion

A general variational principle for transition and density matrices is proposed. The principle is closely related to Rowe's variational treatment of the equations-of-motion method. It permits the simultaneous construction of coupled approximations for two eigenstates, and it is a straightforward extension of the usual variational method.     

Higher approximations for transition matrices and their application to the calculation of atomic spectra

Theoretical and Experimental Chemistry -     

Another way to view the chain conformation broadening of the line-width distribution measured in dynamic light scattering

In dynamic laser light scattering (LLS), for a given polydisperse sample, a line-width distribution G(Γ) or the translational diffusion coefficient distribution G(D) can be obtained from the measured time correlation function. For rigid colloid particles, G(Γ) can be directly related to the hydrodynamic size distribution. However, for flexible polymer chains, G(Γ) depends not only on the chain length distribution, but also on the relaxation of the chain conformation; that is, even for a monodisperse polymer sample there still exists a chain conformation distribution. If the time scale of the chain conformation relaxation is comparable to that of the translational diffusion, such as in the case of a very long polymer chain, the conformation relaxation might lead to an additional broadening in G (Γ). This "conformation broadening" has been directly observed for the first time by comparing two G(Γ) s obtained from a poly(N-isopropyl-acrylamide) solution at～25℃ and～32℃ at which the solution is ther     

Dynamics of dissipative structures and the transition to turbulence in a nematic liquid crystal

It has been observed for the first time that the domain oscillations of a nematic liquid crystal subject to a transverse DC electric field are self-organized in space as concentric and spiral phase waves. The formation of the phase wave sources has been described. The transition of the hexagonal convective structure to turbulence has been investigated by the temporal Fourier analysis method. It has been found that a route to turbulence passes through a continuous widening of peaks in the power spectrum of light intensity transmitted through the cell.     

QRC: a rapid method for connecting transition structures to reactants in the computational analysis of organic reactivity

A new procedure, QRC calculation, is presented which provides useful information for analysing organic reactions and links transition structures to starting materials and products. QRC calculations are an alternative to computationally demanding IRC calculations, which find more information than is needed for this analysis.     

Cloud point curve of nonionic surfactant related to the structures of mesoporous materials

We have investigated the phase behavior of a fluorinated surfactant R(7)(F)(EO)(7) in water. The cloud point is situated at 19 degrees C for 2 wt% of surfactant. Using this surfactant, mesoporous materials have been synthesized with micellar solution prepared either at 10 degrees C (below the cloud point) or at 40 degrees C (above the cloud point). Results show that whatever the syntheses conditions, only wormhole-like structure is recovered. The effect of perfluorodecalin addition on the fluorinated surfactant/water system was also investigated. Swollen micelles, microemulsion, and lamellar (L(alpha)) liquid crystals were identified. When perfluorodecalin is added, the cloud point is shifted toward higher temperature. As regards the mesoporous syntheses, perfluorodecalin plays a dual role. First, incorporation of perfluorodecalin leads to the formation of well ordered materials. Secondly, the pore size enlargement occurs when perfluorodecalin is added. Our results evidence that the ratio between the volume of the hydrophilic headgroup (V(H)) and the hydrophobic part (V(L)) of the surfactant is not an efficiency parameter to explain the ordering improvement of mesoporous materials and that we should rather consider the existence of the cloud point curve, which disturbs the cooperative templating mechanism (CTM).     

Critical brush density for the transition between carpet-only and carpet/brush double-layered structures

The critical brush density, where transition from carpet-only structure to carpet/brush double-layered structure occurs, was estimated for a weakly ionic amphiphilic diblock copolymer, (diethylsilacyclobutane)34-b-(methacrylic acid)50, monolayer on water by an in situ X-ray reflectivity technique. The brush density in the monolayer was controlled from 0.11 to 0.60 brush chain/nm2 by changing surface pressure and mixing a poly(diethylsilacyclobutane) homopolymer separately synthesized. Only a carpet layer was formed at a low brush density condition, but a carpet and brush double layer was found for a higher brush density of more than 0.48/nm2. This brush density, which is fairly high, would be valuable for discussing the polyelectrolyte brush nanostructure.     

Exploring transition state structures for intramolecular pathways by the artificial force induced reaction method

Finding all required transition state (TS) structures is an important but hard task in theoretical study of complex reaction mechanisms. In the present article, an efficient automated TS search method, artificial force induced reaction (AFIR), was extended to intramolecular reactions. The AFIR method has been developed for intermolecular associative pathways between two or more reactants. Although it has also been applied to intramolecular reactions by dividing molecules manually into fragments, the fragmentation scheme was not automated. In this work, we propose an automated fragmentation scheme. Using this fragmentation scheme and the AFIR method, a fully automated search algorithm for intramolecular pathways is introduced. This version for intramolecular reactions is called single‐component AFIR (SC‐AFIR), to distinguish it from multicomponent AFIR for intermolecular reactions. SC‐AFIR was tested with two reactions, the Claisen rearrangement and the first step of cobalt‐catalyzed hydroformylation, and successfully located all important pathways reported in the literature. © 2013 Wiley Periodicals, Inc.     

Automated sample preparation-fractionation for the measurement of dioxins and related compounds in biological matrices: a review

This article reviews some of the recent developments in the extraction and clean-up areas of biological samples dedicated to dioxin and related compound analysis. A brief introduction on the major dioxin contamination events, which have occurred in the food chain, is given to illustrate the need of fast high throughput methods in case of crises. The emphasis of this paper is the method development based upon reliable instrumental extraction techniques for rapid sample processing and automation such as; supercritical fluid extraction (SFE), microwave-assisted extraction (MAE), pressurized liquid extraction (PLE) and, solid-phase extraction (SPE). The PLE and SPE are also discussed in conjunction with the use of a multi-column automated clean-up system that can accommodate up to 5 g of extracted lipids. The fractionation in sub-groups of analytes during the clean-up process allows the isolation of various types of toxicants from a single sample and illustrates the versatility of the system. An integrated extraction and clean-up instrument is finally presented in terms of feasibility and attainable sample turnover for the parallel processing of liquid and solid biological samples.     

A method for the gas chromatographic determination of vitamin D and related structures.

A procedure is described for the separation of Vitamin D and related compounds by gas-liquid chromatography using flame ionization detection. The method involves a two-step conversion: isomerization to the corresponding (all trans) isotachysterol(s) followed by methyl ether derivatization of the alcohol group(s). The procedure provides a means for identification as well as a possible basis for quantitation of Vitamin D and analogs.     

Fickle hexadienes. Manipulating the relative energies of chairlike and boatlike transition structures for the cope rearrangement

We report calculations on various hexadienes that can assume both chairlike and boatlike conformations, yet turn out (theoretically) to have transition structures for boatlike Cope rearrangement that are equal to or lower in energy than those of alternative chairlike structures. Pathways connecting boatlike and chairlike transition states in these systems also allow for unusual and facile isomerization pathways of certain strained alkenes.     

Core-shell structures in single flexible-semiflexible block copolymers: finding the free energy minimum for the folding transition

We investigate the folding transition of a single diblock copolymer consisting of a semiflexible and a flexible block. We obtain a Saturn-shaped core-shell conformation in the folded state, in which the flexible block forms a core and the semiflexible block wraps around it. We demonstrate two distinctive features of the core-shell structures: (i) The kinetics of the folding transition in the copolymer are significantly more efficient than those of a semiflexible homopolymer. (ii) The core-shell structure does not depend on the transition pathway.     

Triple-decker-sandwich versus rice-ball structures for tris(benzene)dimetal derivatives of the first-row transition metals

Compounds of the type M(2)Bz(3) (Bz = benzene, C(6)H(6)) have been of interest since the related triple-decker mesitylenechromium sandwich (1,3,5-Me(3)C(6)H(3))(3)Cr(2) has been synthesized and characterized structurally by X-ray crystallography. Theoretical studies predict the lowest-energy M(2)Bz(3) structures of the early transition metals Ti, V, and Cr to be the triple-decker sandwiches trans-Bz(2)M(2)(η(6),η(6)-μ-C(6)H(6)) having quintet, triplet, and singlet spin states, respectively. In these structures, the central benzene ring functions as a hexahapto ligand to each metal atom. The singlet rice-ball cis-Bz(2)M(2)(μ-C(6)H(6)) structures with a 2.64-? Mn═Mn double bond or a 2.81-? Fe-Fe single bond are preferred for the central transition metals Mn and Fe. Singlet triple-decker-sandwich structures trans-Bz(2)M(2)(μ-C(6)H(6)) return as the lowest-energy structures for the late transition metals Co and Ni but with the central benzene ring only partially bonded to each metal atom. Thus, the lowest-energy cobalt derivative has a trans-Bz(2)Co(2)(η(3),η(3)-μ-C(6)H(6)) structure in which the central benzene ring acts as a trihapto ligand to each metal atom. Similarly, the lowest-energy nickel derivative has a trans-Bz(2)Ni(2)(η(2),η(2)-μ-C(6)H(6)) structure in which the central benzene ring acts as a dihapto ligand to each metal atom, leaving an uncomplexed C═C double bond. The metal-metal bond orders in the singlet "rice-ball" structures cis-Bz(2)M(2)(μ-C(6)H(6)) (M = Mn, Fe) and the hapticities of the central benzene rings in the singlet late-transition-metal triple-decker-sandwich structures trans-Bz(2)M(2)(μ-C(6)H(6)) (M = Co, Ni) are governed by the desirability for the metal atoms to attain the favored 18-electron configuration.