关于凸过程的有界性和可测性*

设Ｘ是实序列完备的局部凸拓扑向量空间,Ｙ是拓扑向量空间．设Ｔ：Ｘ→２Ｙ是凸过程（ＣｏｎｖｅｘＰｒｏｃｅｓｓ）,且它的定义域Ｄｏｍ（Ｔ）是Ｘ的闭子空间．本文证明了若对Ｘ上的每一可分子空间Ｍ,Ｔ在Ｍ上的限制是绝对可测的,则Ｔ是有界的．     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

Dynamic stability of carbonyl ylides

The non- and fluorine-substituted singlet carbonyl ylides are studied by using ab initio MCSCF calculations. The thermodynamic stability of the carbonyl ylides and the intramolecular stability to isomerization or fragmentation reaction coordinates is demonstrated in terms of the topological structure of the ab initio potential energy surfaces. The allylic resonance is found to be dynamically unstable, considering out-of-plane vibrational mode. The instability is studied by the symmetries of the low-lying excitations out of the MCSCF wave function.     

双核金属酞菁类化合物催化脱硫机理研究Ⅳ──中心金属离子对MPc－PcM催化活性的影响

实验研究结果表明双核金属酞菁类化合物ＭＰｃ－ＰｃＭ（Ｍ＝Ｖ、Ｃｒ、Ｍｎ、Ｆｅ、Ｃｏ、Ｎｉ、Ｃｕ）是催化Ｈ＿２Ｓ液相氧化反应的良好催化剂，且其催化活性顺序为Ｃｏ＞Ｎｉ＞Ｖ＞Ｆｅ＞Ｃｕ＞Ｃｒ＞Ｍｎ．采用量子化学理论计算方法（ＩＮＤＯ／Ｓ）分析了其前线分子轨道的构成特征，结果表明这几种ＭＰｃ－ＰｃＭ的ＬＵＭＯ轨道皆为有金属离子参与形成的π轨道，但ＨＯＭＯ轨道间的差异却很大．Ｍ＝Ｃｏ、Ｎｉ、Ｃｕ、Ｃｒ时，其ＨＯＭＯ为π轨道；而Ｍ＝Ｆｅ、Ｍｎ时，其ＨＯＭＯ却为σ轨道．正是在前线分子轨道的轨道类型、共轭程度及金属轨道贡献三方面因素的协同作用下，才导致ＭＰｃ－ＰｃＭ的催化活性顺序并非按中心金属离子价电子层ｄ电子数的递变而呈现出规律性的变化．     

Polarized basis sets of Slater-type orbitals: H to Ne atoms

We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions.     

卡宾单重态与乙烯环加成反应中的轨道作用图象

卡宾单重态与乙烯环加成反应已有很多计算工作和轨道作用的解释。由于该反应的C_(2v),对称性反应道的反应为禁阻反应,故反应取先由分子平面互相平行而后转向互相垂直的C_s对称性反应道。本文拟就这个反应过程中前线轨道的相互作用及变化情况提出一个简化模型,以期得到对全过程的清晰面象。1.正则轨道图象:     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

A simple method for the calculation of π-bond orders in alternant hydrocarbons

A new method for the calculation of bond orders in alternant hydrocarbons is presented. The method requires a summation over the contributions of various superposition diagrams. Quantitatively, the method is almost as reliable as PPP, and due to its simplicity it can be used for fast and relatively accurate calculation of bond orders. In addition some simple rules are derived, which in many cases can be used to predict the signs of bond orders between nonbonded atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayResearch supported by the Robert A. Welch Foundation of Houston, Texas     

Structural study of pyrimidine nucleoside analogues. I: Molecular mechanics and semiempirical calculations of 2′-deoxy-2′-fluoroarabinofuranosyluracils

Molecular mechanics (MM) calculations have been performed on the title compounds. For the MM minimum energy conformation obtained by conformational analysis, molecular orbital (MO) calculations (MNDO and AM1) have also been performed. The geometries obtained have been compared with the experimental ones extracted from the Cambridge Structural Database (CSD). A qualitative structure-activity relationship has been pointed out based on the electrostatic potentials calculated at different positions on the electronic surface.     

Two-dimensional commensurate soliton structures

A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.