Three two-dimensional (2D) network compounds based on Mn(III)/Mn(II) tetranuclear single-molecule magnets (SMMs) connected by dicyanamide (dcn-) linkers have been synthesized: [Mn4(hmp)4(Hpdm)2(dcn)2](ClO4)2 x 2 H2O x 2 MeCN (2), [Mn4(hmp)4Br2(OMe)2(dcn)2] x 0.5 H2O x 2 THF (3), [Mn4(hmp)6(dcn)2](ClO4)2 (4), where Hhmp and H2pdm are 2-hydroxymethylpyridine and pyridine-2,6-dimethanol, respectively. The [Mn4]/dcn- system appears very versatile, but enables its chemistry to be rationalized by a fine-tune of the synthetic conditions. The double cuboidal [Mn4] unit is preserved in the whole family of compounds, despite strong modifications of its Mn(II) coordination sphere. The chemical control of the coordination number of dcn- on the Mn(II) sites has been the key to obtain the following series of compounds: a discrete cluster, [Mn4(hmp)6(NO3)2(dcn)2] x 2 MeCN (1), 2D networks (2, 3, and 4), and the previously reported 3D compound, [Mn4(hmp)4(mu3-OH)2][Mn(II)(dcn)6] x 2 MeCN x THF. Direct current magnetic measurements show that both Mn2+-Mn3+ and Mn3+-Mn3+ intra-[Mn4] magnetic interactions are ferromagnetic leading to an S(T) = 9 ground state for the [Mn4] unit. Despite the very similar 2D lattices in 2-4, the two kinds of orientation of the [Mn4] unit (i.e., angle variations between the two easy axes) lead to different magnetic properties ranging from SMM behavior for 2 and 1 to a long-range canted antiferromagnetic order for 4. Compound 3 is more complicated as the magnetic measurements strongly suggest the presence of a canted antiferromagnetic order below 2.1 K, although the magnetization slow relaxation is simultaneously observed. Heat capacity measurements confirm the long-range magnetic order in 4, while in 3, the critical behavior is frozen by the slow relaxation of the anisotropic [Mn4] units.

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In this note we determine the full automorphism group of the twisted Grassmann graph. Further we show that twisted Grassmann graphs do not have antipodal distance-regular covers. At last, we show that the twisted Grassmann graphs are not the halved graphs of bipartite distance-regular graphs.