Electron‐ and nuclear‐spin relaxation in an integer spin system, tris‐(acetylacetonato)Mn(iii) in solution

Expressions are derived for the intermolecular contribution to the nuclear‐spin relaxation rate in solutions containing dissolved paramagnetic ions with spin S≥1. The calculation assumes that the electron‐spin Hamiltonian is dominated by a large axial zero‐field splitting, and it accounts for effects of Zeeman interactions to first order. The expressions are used to analyze proton‐spin relaxation of the acetone solvent in solutions of tris‐(acetylacetonato)Mn(iii)/ acetone. The main objective was to measure electron‐spin relaxation times of Mn(iii), which in this complex is a high‐spin, d4 ion with integer spin S=2. Spin‐lattice relaxation measurements were conducted over a range of magnetic field strengths (0.28–1.1 T) where the zero‐field splitting is large compared to the Zeeman energy. Electron‐spin relaxation times of Mn(iii) were found to be 8±2 ps, with little dependence on temperature over the range 215–303 K and on magnetic field strength up to 1.1 T. Use of the assumption that Zeeman splittings dominate zero‐field splittings (Solomon–Bloembergen–Morgan theory) resulted in computed electron‐spin relaxation times that are too short by a factor of 3–4.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71073/2/JCPSA6-92-10-5892-1.pd

Some problems in combinatorial topology of flag complexes

In this work we study simplicial complexes associated to graphs and their homotopical and combinatorial properties. The main focus is on the family of flag complexes, which can be viewed as independence complexes and clique complexes of graphs. In the first part we study independence complexes of graphs using two cofibre sequences corresponding to vertex and edge removals. We give applications to the connectivity of independence complexes of chordal graphs and to extremal problems in topology and we answer open questions about the homotopy types of those spaces for particular families of graphs. We also study the independence complex as a space of configurations of particles in the so-called hard-core models on various lattices. We define, and investigate from an algorithmic perspective, a special family of combinatorially defined homology classes in independence complexes. This enables us to give algorithms as well as NP-hardness results for topological properties of some spaces. As a corollary we prove hardness of computing homology of simplicial complexes in general. We also view flag complexes as clique complexes of graphs. That leads to the study of various properties of Vietoris-Rips complexes of graphs. The last result is inspired by a problem in face enumeration. Using methods of extremal graph theory we classify flag triangulations of 3-manifolds with many edges. As a corollary we complete the classification of face vectors of flag simplicial homology 3-spheres