TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

A θ-stable approximations of abstract Cauchy problems

Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL _t ² (H _x ¹ ) L _t (L _x ² ).     

Cyclic actions on some Klein bottle bundles over S1

Leth be a cyclic action of periodn onM, whereM is eitherS ¹×K, K is the Klein bottle or on , the twisted Klein bottle bundle overS ¹, such that there is a fiberingq:MS ¹ with fiber a Klein bottleK or a torusT with respect to which the action is fiber preserving. We classify all such actions and show that they might be distinguished by their fixed points or by their orbit spaces.     

Quantitative weight of evidence method for combining predictions of quantitative structure-activity relationship models

ABSTRACT

A method for combining statistical-based QSAR predictions of two or more binary classification models is presented. It was assumed that all models were independent. This facilitated the combination of positive and negative predictions using a quantitative weight of evidence (qWoE) procedure based on Bayesian statistics and the additivity of the logarithms of the likelihood ratios. Previous studies combined more than one prediction but used arbitrary strengths for positive and negative predictions. In our approach, the combined models were validated by determining the sensitivity and specificity values, which are performance metrics that are a point of departure for obtaining values that measure the weight of evidence of positive and negative predictions. The developed method was experimentally applied in the prediction of Ames mutagenicity. The method achieved a similar accuracy to that of the experimental Ames test for this endpoint when the overall prediction was determined using a combination of the individual predictions of more than one model. Calculating the qWoE value would reduce the requirement for expert knowledge and decrease the subjectivity of the prediction. This method could be applied to other endpoints such as developmental toxicity and skin sensitisation with binary classification models.     

Michael addition reactions of acetoacetates and malonates with acrylates in water under strongly alkaline conditions

Michael addition reactions of acetoacetates and malonates with acrylates in a 5 M KOH aqueous solution without using any other catalysts are described. When they are either tert-butyl or benzyl esters, the reaction proceeded very rapidly to afford moderate to high yields of the corresponding bis-Michael adducts that are unexpectedly stable under these conditions.     

簇离子Mo_3S_4M~（n＋）中M与Mo成键作用及电子光谱（M＝Fe、Ni，n＝4；M＝Cu，n＝5）

应用ＩＮＤＯ／Ｓ半经验量子化学方法，对簇合物离子Ｍｏ３Ｓ和Ｍｏ３Ｓ４Ｍｎ＋（Ｍ＝Ｆｅ、Ｎｉ，ｎ＝４；Ｍ＝Ｃｕ，ｎ＝５）分别进行分子轨道计算。根据计算得到的簇离子中的原子表观电荷和成键指标，说明Ｆｅ、Ｎｉ、Ｃｕ＋与Ｍｏ３Ｓ成键作用的相对强度依次是Ｆｅ－Ｍｏ＞Ｎｉ－Ｍｏ＞Ｃｕ＋－Ｍｏ。比较了用含组态作用的ＩＮＤＯ／Ｓ方法计算得到的电子跃迁能与实验得到的电子吸收光谱值，并讨论了吸收峰归属情况。对于Ｍ为Ｆｅ、Ｎｉ的簇离子Ｍｏ３Ｓ４Ｍ４＋，最低能量的电子跃迁吸收峰起源于异金属间电荷转移跃迁（ＭＭ’ＣＴ）；而Ｍｏ３Ｓ４Ｃｕ（５＋）簇离子观察到的吸收峰主要是Ｍｏ３Ｓ芯的局域内电荷转移跃迁。根据理论计算结果，由Ｃｕ＋离子到Ｍｏ３Ｓ的电荷转移跃迁谱线，大约在４６０００ｃｍ－１以上才能观察到吸收峰。从Ｍｏ３Ｓ４Ｆｅ４＋次低能量吸收峰的实验值１６６００ｃｍ－１和理论值１６５００ｃｍ－１与Ｍｏ３Ｓ的最低能量吸收峰的实验值１６６００ｃｍ－１和理论值１６９００ｃｍ－１比较，表明无论从理论上或实验上都能证实簇离子Ｍｏ３Ｓ４Ｆｅ４＋在能量为１６６００ｃｍ－１处的吸收峰是起因于Ｍｏ３Ｓ芯的局域内电荷转移跃迁。     

Intramolecular proton transfer induced by divalent alkali earth metal cation in the gas state

Interactions between divalent alkali earth metal (DAEM) ions M (M?Be, Mg, Ca, Sr, Ba) and the second stable glycine conformer in the gas phase, which can transfer into the ground‐state glycine‐M²⁺ (except the glycine–Be²⁺) among each corresponding isomers when these divalent metal ions are bound, are studied at the hybrid three‐parameter B3LYP level with three different basis sets. Proton transfers from the hydroxyl to the amino nitrogen of the glycine without energy barriers have been first observed in the gas phase in these glycine–M²⁺ systems. The interaction between the glycine and these DAEM ions except beryllium and magnesium ion only create an amino hydrogen pointing to the original hydroxyl due to their weaker interaction relative to those divalent transition metal (DTM) ion‐bound glycine derivatives, being obviously different from that between the glycine and DTM ions, in which two amino hydrogens point to the original hydroxyl oxygen when these metal‐chelated glycine derivatives are produced. The interaction energy between the glycine and divalent magnesium would be the boundary of one or two amino hydrogens pointing to the hydrogyl oxygen, i.e., the ?170.3 kcal/mol of binding energy is a critical point. Similar intramolecular proton transfer has also been predicted for those DTM ion‐chelated glycine systems; however, that in the gas state has not been observed in the monovalent metal ion‐coordinated glycine systems. The binding energy between some monovalent TM ion and the glycine is similar to that of the glycine–Ba²⁺, which has the lowest binding strength among these DAEM–ion chelated glycine complexes. The difference among them only lies in the larger electrostatic and polarized effects in the latter, which favor the stability of the zwitterionic glycine form in the gas phase. According to these observations, we predict that the zwitterionic glycine would exist in the field of two positive charges in the gas phase. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 205–214, 2003     

Dependence of the relative retention of organic compounds on the nature and pressure of the carrier gas and on the thickness of the PEG-20M film in the capillary column

The effects of the carrier gas nature and pressure on the relative retention values of organic compounds were studied using a series of capillary columns differing in the film thickness of the polar stationary phase (PEG-20M). Relative retention depends linearly on the carrier gas pressure. This dependence becomes more pronounced in the following order of carrier gases: helium < nitrogen < carbon dioxide. The limiting relative retention at a carrier gas pressure approaching zero rather than relative retention values measured experimentally (relative retention time, Kovats retention index,etc.) is an invariant characteristic of a compound subjected to chromatography. For the carrier gases studied, the limiting retention values almost does not depend on the nature of the carrier gas used. The limiting indicating the complex absorption-adsorption nature of these parameters. Dissolution of a carrier gas in the stationary liquid phase has an effect on the relative retention. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2177–2186, December, 1997.     

Discrete mechanics and its application to the solution of the n-body problem

A theory of discrete mechanics is developed based on the results of D. Greenspan. Discrete dynamical equations in an inertial frame, in a coordinate system related to some material point, and in a rotating frame are given and the consistency, stability, and convergence of the methods are studied and some numerical examples presented.