A method for selection and use of numerical integration points for molecules with cylindrical symmetry

Boys and Handy [1] have discussed the solution of the bivariational equations with restricted numerical integration. One of the weaknesses of the method was that in the numerical summations over points, some points arose with r _ij= 0 and non-zero weights. This makes the method quite impractical for the Schrodinger Hamiltonian (because of the singularity at r _ij= 0), and it cannot be advantageous for the transcorrelated Hamiltonian C^–1HC because there will be some discontinuous higher derivatives at r _ij=0. Here it is shown how the symmetry of cylindrically symmetric molecules can be used to eliminate such points, without losing any of the advantages of the overall method, such as the convergence of the eigensolutions. It is also shown how the primary numerical integration points (z _i, r_i) may be chosen in any calculation such that each is associated with an equal amount of one-electron density. The choice of the angular coordinates are governed by the removal of the r _ij=0 points and maintaining the natural orthogonality between orbitals of different symmetry types. The method has been programmed and found to be practical, although no new molecular calculations have yet been performed. It is to be hoped that these points will give a basis for new transcorrelated calculations on diatomic molecules.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed.     

The crystal structure of NH4MnFeF6: Re-refinement in a higher symmetry space group

The crystal structure of NH₄MnFeF₆, which was originally described in space groupPb2n, can be better described inPbcn. Refinement inPbcn has led to an improvedR of 0.018, smaller standard deviations, and a more regular structure. One of the two structurally independent ammonium groups appears to be ordered, the other disordered.     

Asymmetric synthesis of 1,2-disubstituted cycloalkanecarboxaldehydes. procedures for the highly stereoselective preparation of cis- and trans-isomer

Procedures for the asymmetric synthesis of 1,2-disubstituted cycloalkanecarboxaldehydes ($\text{7}$) having assymetric tertiary and quaternary carbon atoms in vicinal positions from the corresponding cycloalkenecarboxaldehydes ($\text{2}$) in high diastereomeric and enantiomeric purities are described.     

PCILON. perturbative configuration interaction using localized orbitals and numerical integration. I. Numerical integration techniques for the calculation of Hamiltonian matrix elements between localized orbitals

Modern techniques for multidimensional numerical integration, Korobov's and Sobol's formulas namely, are used for the direct computation of matrix elements between the localized molecular orbitals needed for a configuration interaction calculation by a perturbation method. A minimal orbital basis of Slater functions is used for formaldehyde and ethylene taken as example. The resulting precision is satisfactory.     

The use of sequential extraction procedures for the characterization and management of contaminated soils

Metal mobility and availability in solid samples, such as soils, sediments and sludges, is frequently studied with sequential extraction procedures, which allow to partition the total metal content into classes of different reactivity. From the experimental point of view, each extraction step requires many practical operations, which can represent sources of error if they are not properly executed. The first part of the paper gives indication on how to perform sequential extractions, from sample pretreatment to extract analysis, in order to reduce experimental errors. The second part describes the main applications of sequential extraction schemes for the characterization and management of contaminated soils: the assessment of the risks associated to metal pollution, the evaluation of the feasibility and efficiency of remediation techniques, the study of soil properties and of metal behaviour and plant availability.     

The influence of molecular symmetry and topological factors on the internal heavy atom effect in aromatic and heteroaromatic compounds.

The absorption and fluorescence properties of 26 specially selected aromatic and heteroaromatic compounds, from different classes, are studied quantum chemically and experimentally at room temperature (293 K). Seven of these compounds have not been studied before. The compounds are arranged in seven groups, which illustrate different cases of the internal heavy atom effect. The quantum yield of fluorescence, gamma and fluorescence decay time, tau(f) of deaerated and non-deaerated cyclohexane or ethanol solutions are measured. The oscillator strength, f(e), fluorescence rate constant, k(f), natural lifetime, tau(0)t, and intersystem crossing rate constant, kST, were calculated for each compound. The orbital nature of the lowest excited singlet state and direction of polarization of the S0 --> S1 transitions are determined using the PPP-Cl method for each molecule. The investigation shows that substitution of a heavy atom(s) (Cl, S, Br, I etc.) into an aromatic or heteroaromatic molecule may produce different changes in all the fluorescence parameters (sometimes dramatically) and not necessarily lead to the quenching of fluorescence. Substitution of a heavy atom(s) may increase the value of the spin-orbit operator, Hso, if the S0 --> S1 excitation is localized to some extent on a carbon atom bonded to a heavy atom(s) or on the heavy atom itself (O or S). Such substitution may change the symmetry of a molecule and hence the values of the [psiS1/Hso/psi'T1] matrix elements would change (in molecules of higher symmetry groups not all Ti states are able to mix with the perturbing S1 state). Such substitution may change the arrangement of Ti states below the S1, state and hence, the Franck-Condon factors would change. Such substitution may also change the value of the [psiS0/Mj/psiS1] matrix element and, consequently, the oscillator strength of the S0 --> S1 transition would change. A combination of all these possible changes determines the value of k(f) and kST and, consequently, determines the value of gamma and tau(f). It is observed that in many cases, the value of the spin-orbit operator is related to the dipole moment operator, e.g. if the introduction of a heavy atom increases kST then, as a rule, it decreases f(e)(1A --> 1La).     

铅基复合钙钛矿型弛豫铁电单晶的生长基元与生长机理1: PMNT单晶的表面形貌 、负晶结构及生长基元的组装与拆分

铅基复合钙钛矿型弛豫铁电单晶体PMNT的生长基元为多种[BO~6]配位八面体,晶体生长过程可视为多种八面体基元与Pb^2^+的组装过程。这些生长基元向{111}面叠合时易采取法向生长机制,向{001}面叠合时易采取层状生长机制,由此决定了晶体生长速度的各向异性与晶体的形貌。Bridgman法生长的PMNT晶体在生长过程中由内向生长机制形成规则的负晶结构;在晶体生长过程中,在其自然表面上可形成正形与负形两种形貌;在高温退火过程中,由于PbO的分解,晶体表面上可形成类似"蚀象"的构型,这些可从[BO~6]八面体生长基元的组装或拆分方面获得解释。     

铅基复合钙钛矿型弛豫铁电单晶的生长基元与生长机理1: PMNT单晶的表面形貌 、负晶结构及生长基元的组装与拆分

铅基复合钙钛矿型弛豫铁电单晶体PMNT的生长基元为多种[BO~6]配位八面体,晶体生长过程可视为多种八面体基元与Pb^2^+的组装过程。这些生长基元向{111}面叠合时易采取法向生长机制,向{001}面叠合时易采取层状生长机制,由此决定了晶体生长速度的各向异性与晶体的形貌。Bridgman法生长的PMNT晶体在生长过程中由内向生长机制形成规则的负晶结构;在晶体生长过程中,在其自然表面上可形成正形与负形两种形貌;在高温退火过程中,由于PbO的分解,晶体表面上可形成类似"蚀象"的构型,这些可从[BO~6]八面体生长基元的组装或拆分方面获得解释。     

Evaluation of piezoelectric PVDF polymers for use in space environments. II. Effects of atomic oxygen and vacuum UV exposure

The effects of atomic oxygen (AO) and vacuum UV radiation simulating low Earth orbit conditions on two commercially available piezoelectric polymer films, poly(vinylidene fluoride) (PVDF) and poly(vinylidene fluoride‐trifluoroethylene) P(VDF‐TrFE), have been studied. Surface erosion and pattern development are significant for both polymers. Erosion yields were determined as 2.8 × 10^?24 cm³/atom for PVDF and 2.5 × 10^?24 cm³/atom for P(VDF‐TrFE). The piezoelectric properties of the residual material of both polymers were largely unchanged after exposure, although a slight shift in the Curie transition of the P(VDF‐TrFE) was observed. A lightly cross‐linked network was formed in the copolymer presumably because of penetrating vacuum ultraviolet (VUV) radiation, while the homopolymer remained uncross‐linked. These differences were attributed to varying degrees of crystallinity and potentially greater absorption, and hence damage, of VUV radiation in P(VDF‐TrFE) compared with PVDF. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2503–2513, 2005     

Evaluation of piezoelectric poly(vinylidene fluoride) polymers for use in space environments. I. Temperature limitations

Smart materials, such as thin‐film piezoelectric polymers, are interesting for potential applications on Gossamer spacecraft. This investigation aims to predict the performance and long‐term stability of the piezoelectric properties of poly(vinylidene fluoride) (PVDF) and its copolymers under conditions simulating the low‐Earth‐orbit environment. To examine the effects of temperature on the piezoelectric properties of PVDF, poly(vinylidenefluoride‐co‐trifluoroethylene), and poly(vinylidenefluoride‐co‐hexafluoropropylene), the d₃₃ piezoelectric coefficients were measured up to 160 °C, and the electric displacement/electric field (D–E) hysteresis loops were measured from ?80 to +110 °C. The room‐temperature d₃₃ coefficient of PVDF homopolymer films, annealed at 50, 80, and 125 °C, dropped rapidly within a few days of thermal exposure and then remained unchanged. In contrast, the TrFE copolymer exhibited greater thermal stability than the homopolymer, with d₃₃ remaining almost unchanged up to 125 °C. The HFP copolymer exhibited poor retention of d₃₃ at temperatures above 80 °C. In situ D–E loop measurements from ?80 to +110 °C showed that the remanent polarization of the TrFE copolymer was more stable than that of the PVDF homopolymer. D–E hysteresis loop and d₃₃ results were also compared with the deflection of the PVDF homopolymer and TrFE copolymer bimorphs tested over a wide temperature range. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1310‐1320, 2005     

Pyrrolidine-5,5-trans-lactams. 2. The use of X-ray crystal structure data in the optimization of P3 and P4 substituents

[reaction: see text] In this, the second of two letters, we describe the elaboration of the pyrrolidine-5,5-trans-lactam template to delineate the requirements for optimal substitution of the pyrrolidine and lactam nitrogen atoms. Central to the strategy is the use of rapid iterative synthesis in conjunction with X-ray crystal structure determination of ligand-protein complexes.     

Evaluation of piezoelectric PVDF polymers for use in space environments. III. Comparison of the effects of vacuum UV and gamma radiation

Films of piezoelectric PVDF and P(VDF‐TrFE) were exposed to vacuum UV (115–300 nm VUV) and γ‐radiation to investigate how these two forms of radiation affect the chemical, morphological, and piezoelectric properties of the polymers. The extent of crosslinking was almost identical in both polymers after γ‐irradiation, but surprisingly, was significantly higher for the TrFE copolymer after VUV‐irradiation. Changes in the melting behavior were also more significant in the TrFE copolymer after VUV‐irradiation due to both surface and bulk crosslinking, compared with only surface crosslinking for the PVDF films. The piezoelectric properties (measured using d₃₃ piezoelectric coefficients and D‐E hysteresis loops) were unchanged in the PVDF homopolymer, while the TrFE copolymer exhibited more narrow D‐E loops after exposure to either γ‐ or VUV‐radiation. The more severe damage to the TrFE copolymer in comparison with the PVDF homopolymer after VUV‐irradiation is explained by different energy deposition characteristics. The short wavelength, highly energetic photons are undoubtedly absorbed in the surface layers of both polymers, and we propose that while the longer wavelength components of the VUV‐radiation are absorbed by the bulk of the TrFE copolymer causing crosslinking, they are transmitted harmlessly in the PVDF homopolymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3253–3264, 2006     

Kinetics of partly diffusion controlled reactions, XVIII. The use of liquid state physics concepts for bimolecular quenching models in bidimensional space

Theory of diffusion controlled reaction kinetics is reinvestigated, by taking into account results of pseudobidimensional liquid physics (as in the case in membranes), and leads to important changes on the apparent rate constant of reaction.

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The first example of a liquid crystalline side-chain polymer with bent-core mesogenic units: ferroelectric switching and spontaneous achiral symmetry breaking in an achiral polymer

A dimethylsiloxane diluted polysiloxane side chain co-polymer with non-chiral banana-shaped mesogenic units shows an optically isotropic ferroelectric switching polar smectic C phase (SmCPF) consisting of a conglomerate of homogeneously chiral domains with opposite handedness.     

Combined use of data from liquid crystal N.M.R. and electron diffraction in structural studies of fluorophosphine derivatives

Liquid Crystal Nuclear Magnetic Resonance was used to obtain structural information on certain difluorophosphine pseudohalides. This was combined with data from Electron Diffraction in a joint analysis. Some results are given and problems encountered discussed.     

Group theoretical methods for determining permitted terms of the electronic states of complexes in crystals. III. The use of plethysm for classification of the permitted terms of impurity complexes in crystal

A procedure for the use of the plethysm operation for classification of the permitted electronic terms of impurity complexes in a crystal is presented. The cases of polyatomic symmetrical complexes are discussed as examples.     

The use of wavelength-selective plastic cladding materials in horticulture: understanding of crop and fungal responses through the assessment of biological spectral weighting functions

Plant responses to light spectral quality can be exploited to deliver a range of agronomically desirable end points in protected crops. This can be achieved using plastics with specific spectral properties as crop covers. We have studied the responses of a range of crops to plastics that have either (a) increased transmission of UV compared with standard horticultural covers, (b) decreased transmission of UV or (c) increased the ratio of red (R) : far-red (FR) radiation. Both the UV-transparent and R : FR increasing films reduced leaf area and biomass, offering potential alternatives to chemical growth regulators. The UV-opaque film increased growth, but while this may be useful in some crops, there were trade-offs with elements of quality, such as pigmentation and taste. UV manipulation may also influence disease control. Increasing UV inhibited not only the pathogenic fungus Botrytis cinerea but also the disease biocontrol agent Trichoderma harzianum. Unlike B. cinerea, T. harzianum was highly sensitive to UV-A radiation. These fungal responses and those for plant growth in the growth room and the field under different plastics are analyzed in terms of alternative biological spectral weighting functions (BSWF). The role of BSWF in assessing general patterns of response to UV modification in horticulture is also discussed.     

The use of calix[6]arene molecules for actinides analysis in urine and drinking water: an alternative to current procedures

In this work the applicability of calix[6]arene columns for actinides analysis in urine samples and drinking water was investigated. A radiochemical procedure has been developed for U, Pu, Am analysis in urine. A simple and effective method has also been proposed on a specific column named AQUALIX, for the separation and preconcentration of U from drinking water. These procedures are suitable for routine analysis and require a considerably reduced number of steps of sample treatment as compared to current procedures.     

Clebsch–Gordan coefficients for chains of groups of interest in quantum chemistry. III. The point symmetry groups

This work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch–Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch–Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU(2) ? U(1). The Clebsch–Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch–Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU(2) ? G through the resolving of a system of nonlinear equations.