“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Thermodynamics for Coulomb systems: A problem at vanishing particle densities

In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.     

Fermionic perturbation theory for the statistical mechanics of the nonlinear Schrödinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures.     

单核锌双卟啉配合物构象平衡的理论研究及光谱分析

合成了一系列以不同长度柔韧链相连的p/p型单核锌双卟啉配合物。选用Tripos力场,利用分子动力学模拟退火和分子力学构象搜索相结合的方法对该系列双卟啉进行了能量优化和构象分析。理论计算结果表明:该类双卟啉稳定存在的最低能量构象为叠合式,最高能量构象为伸展式,并存在一系列的中间能量构象;双卟啉分子内π-π作用和能量转移与双卟啉存在的两种主要构象密切相关;分析了分子内π-π作用的本质。运用不同光谱测试手段验证了理论计算结果: 利用可见和相应二阶导数吸收光谱研究了双卟啉主要存在的叠合式和伸展式构象,通过红外光谱观察了对双卟啉构象和卟啉环间π-π作用较为敏感的吸收谱带;利用荧光光谱计算了双卟啉的分子内能量转移效率。     

A new approach to the determination of the statistical segment length of wormlike polymers

The Stockmayer-Fixman-Burchard (SFB) and the Dondos-Benoit (DB) equations have been applied to determine the unperturbed dimensions parameterK of wormlike polymers. An empirical relation between the Flory's constant and the Mark-Houwink-Sakurada (MHS) exponenta has been proposed. The values found by this equation are lower than the value 2.5×10²³ used in the case of flexible polymers and this deviation is attributed to the influence of the draining effect. From theK value and the so calculated value of , we calculate the Kuhn statistical segment length of wormlike polymers. The obtained — for a great number of wormlike polymers — statistical segment lengths are almost the same as these calculated by the Yamakawa-Fujii and the Bohdanecky methods. The molecular mass regions in which the SFB, the DB, and the MHS equations are valid are explored. A criterion for the distinction between flexible and wormlike polymers is proposed based on the way of approach to the power law.     

高岭石吸附乙烯和苯的Delft分子力学研究

运用Ｄｅｌｆｔ分子力学（ＤＭＭ）程序及其粘土和共轭烯烃力场，计算研究了高岭石对乙烯和苯的吸附作用，探讨了吸附对粘土晶体和有机分子的结构、电荷分布和能量的影响，求得了高岭石吸附乙烯和苯的吸附热等重要物理量．     

Molecular basis for antifreeze activity difference of two insect antifreeze protein isoforms

The insect spruce budworm(Choristoneura fumiferana) produces antifreeze protein(AFP) to assist in the protection of the over-wintering larval stage and contains multiple isoforms. Structures for two isoforms,known as CfAFP-501 and CfAFP-337,show that both possess similar left-handed β-helical structure,although thermal hysteresis activity of the longer isoform CfAFP-501 is three times that of CfAFP-337. The markedly enhanced activity of CfAFP-501 is not proportional to,and cannot be simply accounted for,by the increased ice-binding site resulting from the two extra coils in CfAFP-501. In or-der to investigate the molecular basis for the activity difference and gain better understanding of AFPs in general,we have employed several different computational methods to systematically study the structural properties and ice interactions of the AFPs and their deletion models. In the context of intact AFPs,a majority of the coils in CfAFP-501 has better ice interaction and causes stronger ice lattice disruption than CfAFP-337,strongly suggesting a cooperative or synergistic effect among β-helical coils. The synergistic effect would play a critical role and make significant contributions to the anti-freeze activity β-helical antifreeze proteins. This is the first time that synergistic effect and its implica-tion for antifreeze activity are reported for β-helical antifreeze proteins.     

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.     

Role of the tautomerism of 2-azaadenine and 2-azahypoxanthine in substrate recognition by xanthine oxidase

The tautomerism of 2-azaadenine and 2-hypoxanthine has been examined in the gas phase and in aqueous solution. The tautomerism in the gas phase has been studied by means of semiempirical and ab initio quantum-mechanical computations, as well as density-functional calculations. The influence of the aqueous solvent on the relative stability between tautomers has been estimated from self-consistent reaction field calculations performed with different high-level continuum models. The results provide a detailed picture of the tautomeric preference for these purine bases. The importance of tautomerism in the substrate recognition by xanthine oxidase is discussed. Finally, the rate of oxidation of 2-azaadenine and 2- hypoxanthine by xanthine oxidase is discussed in terms of the recognition model at the enzyme active site.     

Intraframework potential energy function of zeolites

Potential energy functions suitable for the (Cs_1–xNa_xT₂O₄)-A type zeolite family were obtained from the known crystal structure of Cs₇Na₅-A zeolite. Using these potential functions, several other crystal structures in these family were obtained by molecular mechanical calculations. The activation energy - to -cage transmission of the H₂ molecule and the void volume of Cs₃Na₉-A zeolite were calculated.