An oxo‐centred trinuclear FeIII complex: tri­aqua­hexakis(μ2‐betaine‐O:O′)‐μ3‐oxo‐triiron(III) bis­(tetra­chloro­manganate) trichloride ­hexahydrate

The title compound, [Fe₃(C₅H₁₁NO₂)₆O(H₂O)₃](MnCl₄)₂Cl₃·6H₂O, contains a triiron core linked by a μ₃‐bridging oxide ion. Each of the iron(III) ions has a distorted octahedral environment, being coordinated, in addition to the oxide ion, by four neutral betaine mol­ecules and one water mol­ecule. The N‐alkyl­ated α‐amino acid betaine is present in the dipolar zwitterionic form and chelates pairs of Fe atoms at the vertices of the triangular [Fe₃O]⁷⁺ ionic core. The Fe complex has a crystallographically imposed D3 symmetry. The water mol­ecules fully exhaust their potential as hydrogen donors, forming a two‐dimensional hydrogen‐bond network in planes parallel to (001).     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001