Geometric critical exponent inequalities for general random cluster models

A set of new critical exponent inequalities,d(1 –1 /)2 –, dv(1 – 1/), andd> 1, is proved for a general class of random cluster models, which includes (independent or dependent) percolations, lattice animals (with any interactions), and various stochastic cluster growth models. The inequalities imply that the critical phenomena in the models are inevitably not mean-field-like in the dimensions one, two, and three.The present work was reported at the 56th Statistical Mechanics Meeting (Rutgers, December 1986).     

On the existence of thermodynamics for the generalized random energy model

Derrida's generalized random energy model is considered. Almost sure andL ^p convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn is discussed.     

Lifschitz singularities for periodic operators plus random potentials

UsingX-bounding (lower bounds by Laplacians with mixed boundary conditions and discrete analogs), we obtain the Lifschitz exponent at the bottom of the spectrum for random operators of typeH =T+V , withT a (periodic) generator of a positivity-preserving semigroup, extending results by Kirsch and Simon.     

Accurate Gaussian basis sets for the H2O molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H₂O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H₂O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.     

二维高分子链形态的计算机模拟

介绍在“高分子物理实验”教学中新开设的又一个计算机模拟实验，即应用自编的改进型四位置模型，模拟二维空间中的自回避行走链和无规行走链，并验算均方末端距和均方回转半径与聚合度的标度关系，所得结果与de Gennes的理论符合良好。     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

虚拟原子探针随机采样法用于氨基酸结构描述及其构效关系研究

考虑药物与蛋白质受体的3类非键作用模式, 利用8类虚拟原子探针和Monte Carlo随机采样技术, 得到了一套新的氨基酸侧链表面静电、立体及疏水势能场(ASSPF)参数. 在此基础上对苦味二肽和血管舒缓激五肽进行了结构表征和QSAR研究, 所建模型复相关系数R2和留一法交互检验复相关系数QLOOCV2分别为0.8457, 0.851和0.7688, 0.7952, 同时分析了肽链不同位置上氨基酸侧链对活性的影响, 取得较好的结果.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.