A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

Some aspects of diffusion: fluctuations in reaction diffusion,and geometric influences in nonuniform media

Summary We deal with two diffusion problems: Space-integrated conserved entities characterizing very fast - diffusion - controlled reactions, such as time lags, etc. are universal. They are given by relationships which do not reflect the failure of the mean field hydrodynamic equations. We present another application which does not reflect this failure, for determining the surface flux via a diffusion controlled reaction producing a colored product. Another anomalous diffusion process we considered is transport through cellular materials whose cell sizes are highly nonuniform. We have analyzed the effects of extreme nonuniformity by considering fractal-like models of cellular solids. The diffusion current through these models can exhibit anomalous time-dependencies which are not predicted by the diffusion equation. In particular, it is shown that the initial diffusion current can be characterized by a power-law dependence on the time. Furthermore, the exponent of the power law is given in terms of the distribution of cell sizes in the fractal-like cellular solid.     

Transition state geometry in radical abstraction reactions: comparison of interatomic distances in the intersecting parabolas and Morse curves models with quantum-chemical calculations

Interatomic distances in the transition state were estimated for the reactions of radical abstraction: H^· + H₂, H^· + HCl, H^· + CH₄, N^·H₂ + NH₃, HO^· + H₂O, HO₂ ^· + HOOH, and C^·H₃ + SiH₄. The calculation was performed by the quantum-chemical density functional method or coupled clusters method (QCH), as well as by the methods of intersecting parabolas (IPM) and Morse curves (IMM), using experimental data (activation energies and reaction enthalpies). The results of the latter two methods are close to the quantum-chemical calculation and differ only by the increment a: r(IPM or IMM) = a + r(QCH), where a = –4.5·10^–12 m for IPM and a = +1.9·10^–12 m for IMM.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors     

Resistance distance and Laplacian spectrum

The resistance distance r _ij between two vertices v _i and v _j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r _ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r _ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.     

钒氧阴离子团簇与小分子碳氢化合物反应的实验和理论研究

为了在分子层次上揭示相关催化反应的机理, 人们对过渡金属氧化物团簇与碳氢化合物分子反应进行了大量研究. 相比于过渡金属氧化物团簇阳离子, 阴离子对一些碳氢化合物的活性弱得多, 因此研究还很少. 在本工作中, 我们通过激光溅射产生钒氧团簇阴离子VxOy, 产生的团簇在接近热碰撞条件下与烷烃(C2H6和C4H10)以及烯烃(C2H4和C3H6) 在一个快速流动反应管中进行反应, 飞行时间质谱用来检测反应前后的团簇分布. 在VxOy与烷烃的反应中, 生成了产物V2O6H-和V4O11H-; 在与烯烃的反应中, 产生了相应的吸附产物V4O11X-(X=C2H4或C3H6). 密度泛函理论计算表明: V2O-6和V4O-11可以活化烷烃(C2H6和C4H10)的C—H键, 也可以与烯烃(C2H4和C3H6)发生3+2环化加成反应形成一个五元环结构(-V-O-C-C-O-), C—H键活化与环加成反应都需经历可以克服的反应能垒. 理论计算与实验观测结果相符合. V2O-6和V4O-11团簇都具有氧原子自由基(O·或O-)的成键特征, 活性O-物种也经常出现在钒氧催化剂表面, 因而本研究在分子水平上, 揭示了表面活性氧物种与碳氢化合物反应的机理.     

钒氧阴离子团簇与小分子碳氢化合物反应的实验和理论研究

为了在分子层次上揭示相关催化反应的机理, 人们对过渡金属氧化物团簇与碳氢化合物分子反应进行了大量研究. 相比于过渡金属氧化物团簇阳离子, 阴离子对一些碳氢化合物的活性弱得多, 因此研究还很少. 在本工作中, 我们通过激光溅射产生钒氧团簇阴离子VxOy, 产生的团簇在接近热碰撞条件下与烷烃(C2H6和C4H10)以及烯烃(C2H4和C3H6) 在一个快速流动反应管中进行反应, 飞行时间质谱用来检测反应前后的团簇分布. 在VxOy与烷烃的反应中, 生成了产物V2O6H-和V4O11H-; 在与烯烃的反应中, 产生了相应的吸附产物V4O11X-(X=C2H4或C3H6). 密度泛函理论计算表明: V2O-6和V4O-11可以活化烷烃(C2H6和C4H10)的C—H键, 也可以与烯烃(C2H4和C3H6)发生3+2环化加成反应形成一个五元环结构(-V-O-C-C-O-), C—H键活化与环加成反应都需经历可以克服的反应能垒. 理论计算与实验观测结果相符合. V2O-6和V4O-11团簇都具有氧原子自由基(O·或O-)的成键特征, 活性O-物种也经常出现在钒氧催化剂表面, 因而本研究在分子水平上, 揭示了表面活性氧物种与碳氢化合物反应的机理.     

卟啉酞菁模型化合物光致电子转移研究

本文采用时间相关单光子计数对卟啉酞菁ＴＴＰ－（ＣＨ２）ｎ－Ｐｃ模型化合物的光致电子转移进行了研究，发现激发Ｐｃ时，呈现单指数衰减，ｎ＝４时电子转移速率减小，活化能，重排能增加，电子转移效率下降，电子转移反应△ＧＣＳ与电荷分离活化络合物衰变速率ＫＣＴ，按以下规律：△Ｇ＾（５）ＣＳ〉△＾（３）ＣＳ〉△＾（４）ＣＳ〉△＾（２）ＣＳ，ｋ＾（２）ＣＳ〉ｋ＾（３）ＣＳ〉ｋ＾（４）ＣＳ〉ｋ＾（５）ｃｓ。其△Ｇ＾     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Extragradient and extrapolation methods with generalized Bregman distances for saddle point problems

In this paper, we introduce two Bregman-type algorithmic frameworks to generalize the extragradient and extrapolation methods. With the help of relative Lipschitzness and the Bregman distance tool, the iteration properties of the proposed frameworks are analyzed. As applied to smooth convex-concave saddle point problems, our theory rediscovers the main results in Mokhtari et al. (2020) [14] for wider frameworks under weaker assumptions via a conceptually different approach.