Multidimensional quantum trajectories: applications of the derivative propagation method

In a previous publication [J. Chem. Phys. 118, 9911 (2003)], the derivative propagation method (DPM) was introduced as a novel numerical scheme for solving the quantum hydrodynamic equations of motion (QHEM) and computing the time evolution of quantum mechanical wave packets. These equations are a set of coupled, nonlinear partial differential equations governing the time evolution of the real-valued functions C and S in the complex action, S=C(r,t) + iS(r,t)/Planck's over 2pi, where Psi(r,t)=exp(S). Past numerical solutions to the QHEM were obtained via ensemble trajectory propagation, where the required first- and second-order spatial derivatives were evaluated using fitting techniques such as moving least squares. In the DPM, however, equations of motion are developed for the derivatives themselves, and a truncated set of these are integrated along quantum trajectories concurrently with the original QHEM equations for C and S. Using the DPM quantum effects can be included at various orders of approximation; no spatial fitting is involved; there is no basis set expansion; and single, uncoupled quantum trajectories can be propagated (in parallel) rather than in correlated ensembles. In this study, the DPM is extended from previous one-dimensional (1D) results to calculate transmission probabilities for 2D and 3D wave packet evolution on coupled Eckart barrier/harmonic oscillator surfaces. In the 2D problem, the DPM results are compared to standard numerical integration of the time-dependent Schrodinger equation. Also in this study, the practicality of implementing the DPM for systems with many more degrees of freedom is discussed.     

Experimental evidence for the noninnocence of o-aminothiophenolates: coordination chemistry of o-iminothionebenzosemiquinonate(1-) pi-radicals with Ni(II), Pd(II), Pt(II)

The ligand 2-mercapto-3,5-di-tert-butylaniline, H[L(AP)], an o-aminothiophenol, reacts with metal(II) salts of Ni and Pd in CH3CN or C2H5OH in the presence of NEt3 under strictly anaerobic conditions with formation of beige to yellow cis-[M(II)(L(AP))2] (M = Ni (1), Pd (2)) where (L(AP))1- represents the o-aminothiophenolate(1-) form. The crystal structure of cis-[Pd(II)(L(AP))2][HN(C2H5)3][CH3CO2] has been determined by X-ray crystallography. In the presence of air the same reaction produces dark blue solutions from which mixtures of the neutral complexes trans/cis-[M(II)(L(ISQ))2] (M = Ni (1a/1b), Pd (2a/2b), and Pt (3a/3b)) have been isolated as dark blue-black solid materials. By using HPLC the mixture of 3a/3b has been separated into pure samples of 3a and 3b, respectively; (L(ISQ))1- represents the o-iminothionebenzosemiquinonate(1-) pi-radical. The structures of 1a.dmf and 3a.CH2Cl2 have also been determined. All compounds are square-planar and diamagnetic. 1H NMR spectroscopy established the cis <==> trans equilibrium of 1a/1b, 2a/2b, and 3a/3b in CH2Cl2 solution where the isomerization rate is very fast for the Ni, intermediate for the Pd, and very slow for the Pt species. It is shown that the electronic structures of 1a/1b, 2a/2b, 3a, and 3b are best described as diradicals with a singlet ground state. The spectro- and electrochemistries of all complexes display the usual full electron transfer series where the monocation, the neutral species, the mono- and dianions have been spectroscopically characterized. X-band EPR spectra of the monocations [1a/1b]+ and [3a]+ support the assignment of an oxidation-state distribution as predominantly [M(II)(L(ISQ))(L(IBQ))]+ where (L(IBQ))0 represents the o-iminothionequinone level. In contrast, the EPR spectra of the monoanions [1a/1b]- and [3a]- indicate an [M(II)(L(ISQ))(L(AP)-H)]- distribution but with a significant contribution of the [M(I)(L(ISQ))(2)]- resonance hybrid; (L(AP)-H)2- represents the o-imidothiophenolato(2-) oxidation level. Analysis of the geometric features of 120 published structures of complexes containing ligands of the o-aminothiophenolate type show that high precision X-ray crystallography allows to discern the differing protonation and oxidation levels of these ligands. o-Aminothiophenolates are unequivocally shown to be noninnocent ligands; the (L(ISQ))1- radical form is quite prevalent in coordination compounds and the electronic structure of a number of published complexes must be reconsidered.     

Synthesis of ether‐linked bisoxazolines and their use in step‐growth polymerization reactions with phenolics

Six new ether‐linked bisoxazolines have been synthesized via reaction of p‐hydroxyphenyl‐2‐oxazoline with dihalides. These bisoxazolines may be used as chain extenders or crosslinkers for resins, monomers or polymers containing various acidic groups, including phenolics, via step‐growth (1 : 1) reactions. As an illustration, a phenol‐formaldehyde polycondensate (Alnovol) and an enzyme oligomerized bisphenol A resin, as well as poly (p‐hydroxystyrene), was chain extended and crosslinked to produce thermosets with high glass transition temperatures. The new bisoxazolines were also polymerized with diphenol compounds, such as diphone D and bisphenol P to generate linear or branched oligomers and polymers. Differential scanning calorimetry was used to evaluate the potential for polymerization and crosslinking reactions. Preliminary results showed that the new, ether‐linked bisoxazolines have potential for formulating high performance thermosets. Copyright © 2002 John Wiley & Sons, Ltd.     

Synthesis and Structure of the new Fluoride Bromide Ba6.668(2)Ca0.332(2)F12Br2 and Solid Solutions with Composition Ba7−xCaxF12(ClyBr1−y)2 with x = ∼0.5, 0 < y < 1

Crystals of the chemical composition Ba₇F₁₂Cl₂ were modified by adding a small amount of Ca²⁺ to allow the synthesis of the corresponding bromine compound Ba^[Ca]₇F₁₂Br₂. These samples were prepared in a NaBr flux and characterized by single crystal x‐ray diffraction. The new structure crystallizes in a disordered arrangement in the hexagonal space group P6₃/m (176). The calcium ion has a coordination number of 6. Solid solutions on the heavy halide position can be synthesised in a NaCl/NaBr flux to obtain the compounds Ba_7?xCa_xF₁₂(Cl_yBr_1?y)₂ with x = ～0.5 and 0 < y < 1. Regardless the amount of calcium used in the preparation process, the Ca stoichiometry in the compound is always between 0.3 and 0.5. The lattice parameters differ depending on the Ca‐ and Br‐content between 1053.81(5) ? a = b ? 1058.93(3) pm and 421.21 ? c ? 426.78(3) pm.     

Efficient Path Delay Test Generation for Custom Designs

Due to the rapidly growing complexity of VLSI circuits, test methodologies based on delay testing become popular. However, most approaches cannot handle custom logic blocks which are described by logic functions rather than by circuit primitive elements. To overcome this problem, a new path delay test generation algorithm is developed for custom designs. The results using benchmark circuits and real designs prove the efficiency of the new algorithm. The new test generation algorithm can be applied to designs employing intellectual property (IP) circuits whose implementation details are either unknown or unavailable.     

DAC应用指南

介绍了DAC的一些典型应用:如CD唱机中的音频DAC,校准和电机控制,说明DAC就像ADC和运算放大器一样,在许多应用中正在及继续发挥关键作用,不会因数字时代而消失.