1,3,5-Triaza-7-Phosphaadamantane (PTA) as a 31P NMR Probe for Organometallic Transition Metal Complexes in Solution

Due to the rigid structure of 1,3,5-triaza-7-phosphaadamantane (PTA), its ³¹P chemical shift solely depends on non-covalent interactions in which the molecule is involved. The maximum range of change caused by the most common of these, hydrogen bonding, is only 6 ppm, because the active site is one of the PTA nitrogen atoms. In contrast, when the PTA phosphorus atom is coordinated to a metal, the range of change exceeds 100 ppm. This feature can be used to support or reject specific structural models of organometallic transition metal complexes in solution by comparing the experimental and Density Functional Theory (DFT) calculated values of this ³¹P chemical shift. This approach has been tested on a variety of the metals of groups 8–12 and molecular structures. General recommendations for appropriate basis sets are reported.     

A generalised model of hydrogen diffusion in metals with multiple trap types

Continuum modelling of hydrogen diffusion in metals, which accounts for both trapping and an imposed force field, is revisited. A generalised model of hydrogen diffusion and trapping is developed as a continuous interpretation of the discrete random-walk theory. A system of nonlinear equations describing the phenomenon of diffusion with multiple types of traps is derived without the assumption of a local equilibrium among hydrogen populations in dissimilar positions. Lattice-trap interchange kinetics can degenerate into local equilibrium as a limit case. Moreover, certain terms in general equations may be negligible in specific situations. By removing these terms, known particularised models of hydrogen diffusion and trapping are recovered. Determining the terms, which are disregarded in reduced models, enables a straightforward assessment of the applicability of these models. The advantages and limitations of particularised models applied to hydrogen embrittlement analyses are discussed.     

线性响应和两种态特定方法模拟AF350电子跃迁的溶剂效应

在极化连续模型框架下比较了线性响应与两种不同态特定方法计算的溶液中Alexa Fluor 350(AF350)分子激发能和光谱移动值的差异. AF350的第一激发态S0→S1电子跃迁属于π→π^*跃迁, 主要对应于最高占据分子轨道(HOMO)到最低空轨道(LUMO)的跃迁. 该分子激发态偶极矩大于基态偶极矩, 激发态时溶质溶剂相互作用比基态时更强, 随着溶剂极性增大, 会发生光谱红移的现象. 与实验值相比, 线性响应和两种态特定方法均高估了激发能, 其中以IBSF(Improta-Barone-Scalmani-Frisch)方法得到的激发能最小, 矫正的基态反应场方法(cGSRF)得到的激发能最大. 对于光谱移动值, 3种方法与实验值相比都偏小, 线性响应方法(LR)计算出的误差最大, 而IBSF方法得到的结果与实验值最吻合, 是预测溶液中AF350分子激发能和光谱移动值最准确的方法. 对比了Marcus传统理论和基于约束平衡的非平衡溶剂化理论的结果, 发现后者得到的激发能和光谱移动值更接近于实验值.     

The density wave in a new anisotropic continuum model

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg-de-Vries （KdV） equation, and the soliton solution is derived.     

Liquid–Vapor Phase Transitions for Systems with Finite-Range Interactions

We consider particles in ^d , d2, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean-field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid–gas phase transition when the interaction range is finite but long compared to the interparticle spacing for a range of temperature.     

Rules and reals

A ``-rule" is a sequence of pairwise disjoint sets , each of cardinality and subsets . A subset (a ``real') follows a rule if for infinitely many , .

Two obvious cardinal invariants arise from this definition: the least number of reals needed to follow all -rules, , and the least number of -rules with no real that follows all of them, .

Call a bounded rule if is a -rule for some . Let be the least cardinality of a set of bounded rules with no real following all rules in the set.

We prove the following: and for all . However, in the Laver model, .

An application of is in Section 3: we show that below one can find proper extensions of dense independent families which preserve a pre-assigned group of automorphisms. The original motivation for discovering rules was an attempt to construct a maximal homogeneous family over . The consistency of such a family is still open.

     

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.

     

消费者连续统集合下一种投入产出经济的均衡和一般均衡价格

本给出了一个经济模型把跨期间的一般均衡理论和neo-Ricardian的生产价格理论联系起来，并改进了Roce-Anne Oana模型[1][2]。即把消费有限改变消费连续统，并在Rose-Anne Dana模型的基础上，加了条件C.4和C.7，得出了两个重要的结果：（1）在标准条件下，此模型有一均衡使得每一个生产的每期最大利润是相等的；（2）如考虑生产价格是稳定价格；且等于最大利润；则在适当的条件下，这样的价格系统是存在且唯一的，而所定义的均衡的非折扣的价格序列收敛于生产价格。因此均衡价格依赖于技术和消费特征，但在取极限时，有关价格仅依赖于技术。     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.