On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

Identification of radicals spin-trapped in autoxidized linoleic acids: A high performance liquid chromatography and electron spin resonance study

Radicals generated in linoleic acid and deuterated linoleic acid have been trapped by the spin trap 2-methyl-2-nitroso-propane (MNP) and identified by electron spin resonance (ESR) and ENDOR spectroscopy. The formation of two distinct secondary alkyl radical adducts (one conjugated, the other non-conjugated, as shown by their UV absorption spectra) was demonstrated by 11, 11-dideuterio-9-cis-12-cis-linoleic acid using HPLC and ESR spectroscopy.     

Preliminary study on dual fluorescence behavior of porphyrin

It is well known that porphyrin derivatives play a key role in the primary process of photo-synthesis[1], in which porphyrins directly absorb the sunlight or indirectly acquire excitation en-ergy from light-harvesting antenna system to reach their excited state, and then donate electrons to quinone acceptors to yield a series of charge-separated species. In general, only first singlet ex-cited state of porphyrins is involved in energy transfer process[2]. However, highly excited state (S2 stat…     

Measurement of the sign and the magnitude of heteronuclear coupling constants from spin-state-edited J-cross-polarization NMR experiments

New spin-state-selective (S3) NMR pulse sequences exclusively applying cross-polarization schemes to achieve optimum homonuclear and heteronuclear 1H-X coherence transfer are reported for the simple and accurate measurement of the magnitude and sign of heteronuclear coupling constants for samples at natural abundance. The proposed spin-edited HCP-TOCSY experiments are based on clean heteronuclear S3 excitation, generated by simultaneous co-addition of two independent in-phase and anti-phase components created during the mixing heteronuclear J-cross-polarization (HCP) step, which is finally transferred to other protons by a conventional homonuclear TOCSY mechanism. Selective 1D and non-selective 2D approaches for the easy determination of long-range proton-carbon and proton-nitrogen coupling constants on any protonated and non-protonated heteronuclei are presented and discussed for several organic molecules.     

Spin crossover in polyaniline

Solutions of the basic form of polyaniline in m-cresol were studied by ESR and optical spectroscopy in the visible region. m-Cresol can slowly (during one month) protonate polyaniline. For the first time characteristic features of spin crossover were found: sharp changes in the magnetic susceptibility and the ESR line width of polyaniline at ∼200 and 250 K, a smooth decrease in the susceptibility and absorption with the temperature increase from 293 to 423 K, and the temperature hysteresis. The temperature-induced structural rearrangements of polyaniline are caused, most likely, by singlet-triplet transitions in relatively short sections of the polymer chain. The model of short sections permits to explain the origin of the temperature-independent part of susceptibility. Quantum-chemical calculations for the aniline dimers and tetramers describe correctly the singlet-triplet splitting value, thermochromism, and HFS constants in the spectrum of polyaniline. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1959–1966, October, 2007.     

Quantum chemical calculations of the isomer shift in iron(II) complexes of 1,2,4-triazoles with a 1 A 1 ⇔ 5 T 2 spin transition

DFT calculations have been performed to determine the isomer shift for a series of iron(II) clusters with nitrogen-containing ligands which serve as models of coordination units in Fe(II) complexes with 1,2,4-triazoles possessing a ¹ A ₁ ? ⁵ T ₂ spin transition. Good agreement has been found between the theoretical and experimental values of the isomer shift for both low-and high-spin phases. Our calculations confirmed the hypothesis about relationship between the experimentally observed differences in the isomer shift for the low-spin phases of the complexes and variations of the Fe-N mean bond length.     

银络合物在催化核上的还原反应

研究了尿嘧啶银络合物在胶态金属及其硫化物核上被对苯二酚还原的反应，并以Ａｇ和Ｐｔ电极代替催化核与对苯二酚显影剂和银络合物组成原电池作为电化学模型，分别测定该络合物阴极反应和对苯二酚阳极反应的电流。结果表明，原电池的电流大小与反应速度成正比关系，从而为物理显影电极理论提供实验依据。     

Polynuclear manganese grids and clusters—A magnetic perspective

High nuclearity paramagnetic, spin-coupled transition metal clusters and grids are fascinating chemists and physicists partly because of their structural beauty, and the challenge of creating them, but also because of their novel physical properties. Magnetic interactions between the spin centers are a primary focus. This review will examine a selection of Mn(II) polynuclear grids and clusters, with nuclearities in the range Mn₄ to Mn₉. Theoretical treatments of the magnetic properties are discussed, and approaches to solving the exchange problem for ‘large’ spin systems related to computational difficulties. A freely available software package (MAGMUN4.1) is presented as a means of dealing simply with spin-coupled clusters in general, and symmetry reduction methods are discussed briefly as a means of dealing with ‘large’ spin systems.     

Non empirical quantum mechanical calculations of the1H,13C,15N and17O magnetic shielding constants and of the spin-spin coupling constants in formamide,hydrated formamide and N-methylformamide

The magnetic shielding constants of the different atoms of formamide, hydrated formamide and N-methylformamide are calculated by anab initio method. For the protons of formamide the measured differences between their chemical shifts are correctly reproduced by theory, provided that the molecular geometry used as input is carefully chosen. The differences between the values of the magnetic shielding constants calculated for formamide and hydrated formamide show that intermolecular hydrogen bonding produces variations of chemical shifts for all the atoms of the molecule except the formyl proton. The calculated chemical shift variations between formamide and N-methylformamide are compared to the experimental values and discussed in relation with different hydrogen bonding possibilities of the two molecules. The calculation of the contact term of the spin-spin coupling constants of formamide and hydrated formamide shows that in most cases the measured trends are satisfactorily reproduced and that the variations of these terms upon hydration are less than 3%.