Dicyanometallates as Model Extended Frameworks

We report the structures of eight new dicyanometallate frameworks containing molecular extra-framework cations. These systems include a number of hybrid inorganic–organic analogues of conventional ceramics, such as Ruddlesden–Popper phases and perovskites. The structure types adopted are rationalized in the broader context of all known dicyanometallate framework structures. We show that the structural diversity of this family can be understood in terms of (i) the charge and coordination preferences of the particular metal cation acting as framework node, and (ii) the size, shape, and extent of incorporation of extra-framework cations. In this way, we suggest that dicyanometallates form a particularly attractive model family of extended frameworks in which to explore the interplay between molecular degrees of freedom, framework topology, and supramolecular interactions.


Synthesis
The sample of [PPN] 0.5 Cd[Ag(CN) 2 ] 2.5 (EtOH) (3c) used for powder diffraction and TGA was was prepared by diffusion in a Schott bottle. Cold solutions of [PPN]Ag(CN) 2 (1.108 g in 25 mL ethanol) and Cd(NO 3 ) 2 ·4H 2 O (184 mg in 7 mL ethanol) were carefully layered with a buffer of 50 mL cold ethanol separating the layers. Crystals formed overnight. A portion of these crystals, with mother liquor, were set aside in a sealed sample tube. The remaining product was filtered and thoroughly washed with cold ethanol then left to air-dry overnight yielding 300 mg product (Yield: 69.6 %).
The sample of [PPN]Mn[Au(CN) 2 ] 3 (5a) used for powder diffraction and TGA was was prepared by diffusion in a Schott bottle. Cold solutions of [PPN]Au(CN) 2 (1.060 g in 33 mL ethanol) and Mn(NO 3 ) 2 ·4H 2 O (134 mg in 4 mL ethanol) were carefully layered with a buffer of 20 mL cold ethanol separating the layers. Crystals formed overnight. A portion of these crystals, with mother liquor, were set aside in a sealed sample tube. The remaining product was filtered and thoroughly washed with cold ethanol then left to air-dry overnight yielding 423 mg product (70.4 % yield).
The sample of [PPN]Cd[Au(CN) 2 ] 3 (5b) used for powder diffraction and TGA was was prepared by diffusion in a Schott bottle. A cold solution of [PPN]Au(CN) 2 (1.000 g in 30 mL ethanol) was carefully layered on top of a solution of Cd(NO 3 ) 2 ·4H 2 O (132 mg in 4 mL ethanol). Crystals formed overnight. A portion of these crystals, with mother liquor, were set aside in a sealed sample tube. The remaining product was filtered and thoroughly washed with cold ethanol then left to air-dry overnight yielding 436 mg product (73.6 % yield).

Powder X-ray diffraction
Room temperature powder X-ray diffraction patterns were collected using a PANalytical Empyrean diffractometer with Cu K α1 radiation. Variable divergence slits were used with a fixed sample illumination diameter of 10 mm on a rotating sample. The instrument was fitted with 0.04 rad soller slits and a PIXCel 1D detector.

Thermogravimetric Analysis
Thermogravimetric analysis was carried out using a Perkin Elmer TGA-7 Thermogravimetric Analyzer. Quantities of between 1.5 mg and 5 mg were used for TGA. Each sample was held at 40 • C for 5 min and then ramped to 1000 • C at 5 • C min −1 . determined from single crystal diffraction.
Alternatively the structure can be understood by reference to another net. Looking down the c axis, it can be thought of as pairs of corrugated, interpenetrating (6,3) nets stacked in an AB... manner. These layers are connected by perpendicular struts of linear Cd-NC-Ag-CN-Cd linkages. The shortest connection between interpenetrated (6,3) nets is via three nodes. The additional connectivity compared to the pairs of (6,3) net results in a self-catenated single network.

Tolerance factors of superperovskites
Tolerance factors, α for various 'superperovskites' were calculated using a method adapted from Ref. 9. As detailed in that paper, Goldschmidt's tolerance factor (eqn. 1): where r i are the ionic radii for the species in a perovskite ABX 3 , can be adapted for systems with molecular A and X species. Effective radii for A and X must be defined. This is done by measuring the radius from the centre of mass of the species to the outermost atom (from crystallographic data) and, to this number, adding the radius of the outermost atom. For example r A eff = r Amass + r A ion . Combining this approach with Goldschmidt's we have: where h X eff is the length of the molecular linker. Values of r Amass and r Xmass were measured from single crystal data and combined with tabulated data for ionic radii and covalent radii. S10, S11 . Where there are crystallographical distinct X both were measured and a mean taken. In the case of disordered crystal structures a mean position was used. Numerical values are listed in Table S3. While these PPN systems lack hydrogen bonding it is important to treat these tolerance factors rather cautiously. Given the flexibility of dicyanometallate linkers, the variety of conformations known for [PPN] + , and problems with defining appropriate sets of radii. However, they could be extremely useful for identifying the interactions that cause the tolerance factor concept to breakdown in these, and other, S12 systems.

Dicyanometallate tilt systems
The tilt systems of compounds 5a and 5a both correspond to the conventional Glazer notation a − a − c − . S14 However, compound 4 shows in-phase tilting of adjacent octahedra that propagates along a direction perpendicular to the rotation axis. Such a correlation is geometrically forbidden for perovskites such as oxides and halides, where neighbouring octahedra are connected by monatomic anions [ Fig S3]. S14, S15 In molecular perovskite analogues there will be many more possible tilt systems than can be described using Glazer notation (such as in 4). Consequently, we proceed to generalise the Glazer notation to allow succinct distinction of arbitrary tilt systems in these molecular systems. Our starting point is to recall the relationship between tilt axis and propagation wave-vector in conventional perovskites. In principle, octahedral tilts around the a axis can propagate with wave-vector k = [k 1 , 1 2 , 1 2 ]: the sense of rotation strictly alternates within the (100) plane but rotations between neighbouring (100) planes need not be correlated. Tilts around b and c are similarly constrained to k = [ 1 2 , k 2 , 1 2 ] and [ 1 2 , 1 2 , k 3 ] respectively; to first order these three tilt systems can operate independently. Taken together, this means that all physically realisable tilt systems of conventional perovskites can be represented by the three wave-vector components k 1 , k 2 , k 3 and the parameters 1 , 2 , 3 ∈ {0, 1} which represent whether a tilt axis is active ( = 1) or not ( = 0). Empirically, the overwhelming majority of tilt systems correspond to the special cases of "in-phase" (k i = 0) and "out-of-phase" tilts (k i = 1 2 ), although exceptions are not unknown. S16 The "+/0/−" components of Glazer notation reflect these special cases: Or, equivalently, the Glazer symbol g i is given by i exp[2πik i ].
With respect to allowed tilt systems, the key conceptual difference between conventional perovskites and molecular perovskite analogues is that tilts can be correlated with arbitrary wave-vector for the latter family. Consequently, any general notation to describe tilts in molecular perovskites must allow for three wave-vector components corresponding to each rotation axis. There are now nine Glazer terms describing the propagation of tilts about axis i along axis j; here i is as above, and k ij is the j th wave-vector component for the axis-i tilt system. The g ij can be assembled into a single tensor G, which we suggest is the most economical means of characterising these more complex tilt systems.

S8
For the specific example of compound 4, we have approximately where we use − to mean −1 and + to mean 1. For clarity, the meaning of this tensor is that tilts around a propagate with k = [ 1 2 , 1 2 , 0], tilts around b propagate with k = [0, 1 2 , 1 2 ] and tilts around c propagate with k = [ 1 2 , 0, 1 2 ]. We note that for conventionally-allowed tilt systems this notation reduces straightforwardly to conventional Glazer symbols: g i = g ii . Intensity / a.u. Intensity / a.u. Intensity / a.u. Intensity / a.u. Intensity / a.u.