TDDFT Studies of Electronic Structure and First Hyperpolarizability of Tetra-nuclear Cubane-like Transition Metal Clusters

A series of tri-nuclear transition metal clusters with incomplete cubane-like configurations have been studied by TDDFT method. The calculations show that they have enormously large second-order polarizabilities () and are potential nonlinear optical materials for infrared double frequency conversion1. In this paper some tetra-nuclear transition metal clusters with cubane-like configurations, MCu3X4 (PPh3)3 (M=W, Mo; X= S, O, Cl, Se, Br), were studied by TDDFT method for a reference…     

双圈图的零度与其匹配数之间的关系

Let G be a graph with n(G) vertices and m(G) be its matching number.The nullity of G,denoted by η(G),is the multiplicity of the eigenvalue zero of adjacency matrix of G.It is well known that if G is a tree,then η(G) = n(G)-2m(G).Guo et al.[Jiming GUO,Weigen YAN,Yeongnan YEH.On the nullity and the matching number of unicyclic graphs.Linear Alg.Appl.,2009,431:1293 1301]proved that if G is a unicyclic graph,then η(G)equals n(G)-2m(G)-1,n(G)-2m(G),or n(G)-2m(G) +2.In this paper,we prove that if G is a bicyclic graph,then η(G) equals n(G)-2m(G),n(G)-2m(G)±1,n(G)-2m(G)±2or n(G)-2m(G) + 4.We also give a characterization of these six types of bicyclic graphs corresponding to each nullity.     

A phenomenological theory for polarization flop in spiral multiferroic TbMnO<Subscript>3</Subscript>

A phenomenological Landau theory has been used to explain magnetic field-driven polarization flop in TbMnO ₃. The Néel wall-like magnetic structure in spiral multiferroics induces a space-dependent internal magnetic field which exerts a torque on spins to rotate bc-spiral to ab-spiral. The external magnetic field is argued to be competing with easy axis anisotropy and the system stabilizes when anisotropy is minimum. With the help of Landau free energy with DM magnetoelectric coupling and a general ansatz for magnetization, the phenomenon of polarization flop has been explained. Relation between T_flop and critical magnetic field has been established and found to be in good agreement with the experiment. This could be an indication that anisotropy of the system is temperature- and magnetic field-dependent.     

BiPh3--a convenient synthon for heavy alkaline-earth metal amides

Environmentally friendly, commercially available BiPh(3) reacts with heavy alkaline-earth metals (Ae) and bulky trimethylsilylamines to give the corresponding amides [Ae{N(SiMe(3))(R)}(2)(thf)(n)] (R = SiMe(3), 2,4,6-Me(3)C(6)H(2), 2,6-(i)Pr(2)C(6)H(3)) in good yields, providing proof of concept for a general synthetic method.     

Protic ionic liquids based on the dimeric and oligomeric anions: [(AcO)xH(x-1)]-

We describe a fluidity and conductivity study as a function of composition in N-methylpyrrolidine-acetic acid mixtures. The simple 1 : 1 acid-base mixture appears to form an ionic liquid, but its degree of ionicity is quite low and such liquids are better thought of as poorly dissociated mixtures of acid and base. The composition consisting of 3 moles acetic acid and 1 mole N-methylpyrrolidine is shown to form the highest ionicity mixture in this binary due to the presence of oligomeric anionic species [(AcO)(x)H(x-1)](-) stabilised by hydrogen bonds. These oligomeric species, being weaker bases than the acetate anion, shift the proton transfer equilibrium towards formation of ionic species, thus generating a higher degree of ionicity than is present at the 1 : 1 composition. A Walden plot analysis, thermogravimetric behaviour and proton NMR data, as well as ab initio calculations of the oligomeric species, all support this conclusion.     

A numerical scheme for the impulse control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB)

In this paper, we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum withdrawal benefit (GMWB) assuming the policyholder is allowed to withdraw funds continuously. We develop a numerical scheme for solving the Hamilton–Jacobi–Bellman (HJB) variational inequality corresponding to the impulse control problem. We prove the convergence of our scheme to the viscosity solution of the continuous withdrawal problem, provided a strong comparison result holds. The scheme can be easily generalized to price discrete withdrawal contracts. Numerical experiments are conducted, which show a region where the optimal control appears to be non-unique.     

Synthesis and Structural Properties of Anhydrous Rare Earth Cinnamates, [RE(cinn)3]

Anhydrous rare earth tris(cinnamates) [RE(cinn)₃] (RE = La–Lu, Y and Sc and cinnH = trans‐cinnamic acid) were prepared by metathesis in water and by direct reaction of the metal with cinnamic acid in a 1,2,4,5‐tetramethylbenzene flux at ca. 200 °C. X‐ray crystal structure determinations and X‐ray powder data show that, in the solid state, the larger lanthanoids (La–Dy) form an isomorphous polymeric series consisting of homoleptic nine‐coordinate metal centres bonded to three chelating and bridging tridentate cinnamates. The late RE^III cinnamate (RE = Dy, Ho–Lu, Y) complexes also form linear one‐dimensional polymeric chains with all RE metal atoms being seven‐coordinate. The cinnamates are either bound tridentate bridging in a μ‐η²:η¹ fashion, or μ‐η¹:η¹ syn‐syn bidentate bridging. A structural break occurs at dysprosium which has been characterised in both crystallographic forms, and gives solely the late RE form when precipitated at 80 °C. Sc^III cinnamate was also isolated as an analytically pure precipitate which was, again, found to be anhydrous in nature. A structural change was identified by powder XRD between the late RE^III cinnamates and Sc^III cinnamate.     

High order perturbation solution of the electrochemical smoothing problem

A high order perturbation solution of the electrochemical smoothing problem is investigated. This method is found to diverge for large time periods unless a reinitialization is attempted. With this modification, the results are in good agreement with other methods of solution.     

Synthesis and properties of ambient temperature molten salts based on the quaternary ammonium ion

The synthesis of 16 tetraalkyl ammonium bis(trifluoromethane sulfonyl) imide salts, are reported in this paper. Trends in properties of these salts are discussed. The symmetrical tetraalkyl ammonium salts with the bis(trifluoromethyl sulfonyl) imide anion exhibited a lower melting point than that of corresponding ammonium halides. The salts with low symmetry ammonium cations were found to be of generally lower melting point, and many were stable liquids at room temperature. Several of these did not crystallize during cooling below room temperature and exhibited glass transition temperatures in the region of −60 °C∼−80 °C. A comparison of properties between the ammonium imide salts and corresponding trifluoromethane sulfonates is also presented.