On a point of order

A method of using algebraic curves to obtain estimates of critical points accurate enough to identify them as simple algebraic numbers (if that is what they are) is discussed and illustrated with an application to the (q-state Potts model on the triangular lattice for cases of pure two-site interactions and pure three-site interactions. In the latter case the critical point is conjectured to be . In a similar conjecture for the critical percolation probability on thedirected square lattice,q _c ^1/2 (q _c +3)=2(q _c +p _c =1).     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Free energy of the solvable chiral Potts model

Very recently, it has been shown that there are chiralN-state Potts models in statistical mechanics that satisfy the star-triangle relation. Here it is shown that the relation implies that the free energy (and its derivatives) satisfies certain functional relations. These can be used to obtain the free energy: in particular, we expand about the critical case and find that the exponent is 1–2/N.     

应用分子图形学、分子力学、量子化学及静电势研究农药分子结构与性能关系(X)──磺酰脲分子内旋转通道的分子力学研究

磺酞豚分子是一类极其重要的低毒超高效除草剂，有着十分重要的用途．研究分子的空间结构对于了解分子的构效关系十分重要．最近，我们测定的一系列分子的晶体结构［‘－’1表明，分子1、2、3晶体结构的空间群分别为PZ；儿、Pz、Pz，说明晶体中分别有对称元素（对称面或者对称中心），分子以对映体的形式存在于晶体中．由于磺酸豚分子本身不存在手性原子，由此推断磺酷服分子在晶体中存在的对映异构体是由内旋转阻碍产生的，因而应是构象异构体．本项研究工作的目的是应用分子力学方法，计算阻碍内旋转的能垒，从而找出分子内旋转时的最低…     

Investigation of gas chromatographic interaction mechanism on permethylated cyclodextrins by molecular modelling

Summary The capillary gas chromatographic retention behavior of -pinene and tricyclene has been investigated on stationary phases of different polarities. On all but one of the columns employed, tricyclene eluted before -pinene; only permethylated -cyclodextrins dissolved in moderately polar polisiloxanes gave a reversed elution order. The intermolecular interactions which caused the unexpected retention behavior were investigated in detail, applying methods of computer simulation. To achieve this, we have developed a calculation algorithm on the basis of molecular mechanical optimizations and programmed it in a macro. This makes it possible to systematically investigate a given configuration space in which all the possible interactions can take place. It was shown that permethylated -cyclodextrin as host molecule for both guest molecules offers an optimum cavity size. As a result the number of energetically favorable contacts between host and guest molecules as well as the strength of the interactions in this stationary phase were larger. As a consequence the elution order, normally only influenced by the vapor pressure of the compounds at a given temperature, was changed. Nonspecific interactions played an especially important role for these kinds of substances.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

Own N-layered integrated molecular orbital and molecular mechanics study of the reaction of OH<Superscript>−</Superscript> with polychlorinated hydrocarbons CH<Subscript>(4−n)</Subscript>Cl<Subscript>n</Subscript> (n=2–4)

The reliability of the two-layer own N-layered integrated molecular orbital and molecular mechanics (ONIOM) method was examined for the S_N2 reaction CH_(4–n)Cl_n+OH^–. In the ONIOM calculation, only the methyl chloride and OH^–were treated at a high level and the effect of polychlorination was taken into account only at a low level. The ONIOM results were compared with the target CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ results obtained by Borisov etal. [(2001) J. Phys. Chem. A 105:7724]. The ONIOM[MP2/aug-cc-pVDZ:B3LYP/6-31+G(d)] was found to reproduce well the target geometry and energy at the MP2/aug-cc-pVDZ level. The single-point improved energetics at the ONIOM[CCSD(T)/aug-cc-pVDZ:MP2/6-31+G(d)] is found to give results nearly as accurate as the target CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ results. The substantially reduced cost, 20% for optimization and 5% for single-point improved energy of the target cost for n=4, as well as small errors suggest that ONIOM is a powerful tool for accurate potential-energy surfaces of the reaction of large polyhalohydrocarbons.     

Intramolecular charge transfer in pyrromethene laser dyes: photophysical behaviour of PM650.

Absorption and fluorescence (steady-state and time-correlated) techniques are used to study the photophysical characteristics of the pyrromethene 650 (PM650) dye. The presence of the cyano group at the 8 position considerably shifts the absorption and fluorescence bands to lower energies with respect to other related pyrromethene dyes; this is attributed to the strong electron-acceptor character of the cyano group, as is theoretically confirmed by quantum mechanical methods. The fluorescence properties of PM650 are intensively solvent-dependent. The fluorescence band is shifted to lower energies in polar/protic solutions, and the evolution of the corresponding wavelength with the solvent is analysed by a multicomponent linear regression. The fluorescence quantum yield and the lifetime strongly decrease in polar/protic solvents, which can be ascribed to an extra nonradiative deactivation, via an intramolecular charge-transfer state (ICT state), favoured in polar media.     

Computational study on the ring distortions of 1,4-dicyanobenzene in the gas phase and in the crystal

A molecular mechanics software enhanced to perform empirical energy calculations on crystals (KESSHOU) was further developed to handle intermolecular electrostatic interactions as well. The packing of the molecules of 1,4-dicyanobenzene and 1,4-diisocyanobenzene in the crystal was studied. The role of the van der Waals and the electrostatic interactions in the balance of nonbonded atom-atom interactions is analyzed. The packing forces are dominated by van der Waals forces. The electrostatic interactions have higher stabilizing contribution for the dicyano isomer than for the diisocyano form. The dependence of the results on the size of the crystal, the molecular mechanics force field (MM2 vs MM3), and the dielectric constant are also assessed. Ab initio MP2/6–311G** geometries of the isolated molecules are in accordance with the observed benzene ring distortions determined by electron diffraction.