Low Temperature Structures and Magnetic Interactions in the Organic-based Ferromagnetic and Metamagnetic Polymorphs of Decamethylferrocenium 7,7,8,8-Tetracyano- p -quinodimethanide, [FeCp* 2 ] ·+ [TCNQ] ·-Saul

To identify the genesis of the differing magnetic behaviors for the ferro- ( FO ) and metamagnetic ( MM ) polymorphs of [FeCp* 2 ][TCNQ] (Cp* = pentamethylcyclopentadienide; TCNQ = 7,7,8,8-tetracyano- p -quinodimethane) the low temperature (18 ± 1 K) structures of each polymorph were determined from high-resolution synchrotron powder diffraction data. Each polymorph possesses chains of alternating S = 1/2 [FeCp* 2 ] •+ cations and S = 1/2 [TCNQ] •+ , but with differing relative orientations. These as well as an additional paramagnetic polymorph do not thermally interconvert. In addition, the room and low (<70 ± 10 K) temperature structures of the MM polymorph, MM RT and MM LT , respectively, differ from that previously reported at 167 K (-106 o C) MM structure, and no evidence of either phase transition was previously noted even from the magnetic data. This transition temperature and enthalpy of this phase transition for MM RT ⇌ MM was determined to be 226.5 ± 0.4 K (-46.7 ± 0.4 o C) and 0.68 ± 0.04 kJ/mol upon warming, respectively, from differential calorimetry studies (DSC). All three MM phases are triclinic ( P 1- ) with the room temperature phase having a doubled unit cell relative to the other two. The lower temperature phase transition involves a small rearrangement of the molecular ions and shift in lattice parameters. These three MM and FO polymorphs have been characterized and form extended 1-D chains with alternating S = 1/2 [FeCp* 2 ] •+ cations, and S = 1/2 [TCNQ] •- anions, whereas the fifth, paramagnetic ( P ) polymorph possesses S = 0 p -[TCNQ] 22- dimers. At 18 ± 1 K the intrachain Fe•••Fe separations are 10.738(2) and 10.439(3) Å for the FO A computational nearest-neighbor magnetic coupling analysis based upon the low temperature (18 ± 1 K) structures suggest dominating intrachain [FeCp* 2 ] •+ •••[TCNQ] •-ferromagnetic spin couplings (4.95 and 6.5 cm -1 for FO and MM LT , respectively) as a consequence of their spins ( S = 1/2) residing in orthogonal orbitals. All of the nearest neighbor magnetic interactions are ferromagnetic ( J ij > 0) for the FO polymorph in accord with the observed ferromagnetically ordered ground state. Similar results were reported for ferromagnetic


Introduction
Organic-based materials possessing bulk, cooperative physical properties are a contemporary research area that spans chemistry, materials science, and physics. 1 Examples of organic-based magnets, 2 superconductors, 3 and ferroelectrics 4 have been established. These materials have the common feature of having delocalized p-electrons that are essential for the physical property.
[Fe III Cp*2] •+ [TCNQ] •- (TCNQ = 7,7,8,8-tetracyano-p-quinodimethane; Cp* = pentamethylcyclopentadienide, C5Me5 -) was reported to order as a metamagnet below 2.55 K, 5,6,7 and by substitution of TCNQ with TCNE (tetracyanoethylene) led to the discovery of the first organic-based ferromagnet, [Fe III Cp*2] •+ [TCNE] •-, 8,9 which has a similar structural motif, 10,11 but magnetically orders as a bulk ferromagnet with a magnetic ordering temperature (Tc) of 4.8 K. 12,13 [FeCp*2] [TCNQ] has been reported to form three different magnetic polymorphs, namely, a dimeric paramagnet (P), 6,14 a ferromagnet (FO) (Tc = 3.1 K), 7,15 and the aforementioned metamagnet (MM). 6,7 The FO and MM polymorphs possess parallel … D + A -D + A -… 1-D chains (D = FeCp*2; A = TCNQ), which is similar to that reported for the ferromagnet [FeCp*2][TCNE]. 10,11,16 Based upon their respective reported room temperature and 167 K (-106 o C) structures, only a few key structural differences exist, but these are sufficient to render the significantly different properties observed for differing polymorphs. 17,18 Note that the structure of the P polymorph 6,14 along with the metamagnetic properties of MM 5 were reported first. The structure of MM was subsequently reported, 6 however, in a preliminary communication, 16 the structure of the then-unknown FO polymorph was described. 15 The previous structural determinations of [FeCp*2] [TCNQ] were performed significantly above Tc, where the cation C5Me5 (Cp*) rings are in an eclipsed conformation (D5h) for FO, but staggered (D5) for MM. Additionally, the interchain arrangements have some small, but notable differences: the [TCNQ] •anions in adjacent layers of MM in are arranged in the same direction, but zigzag for FO. 15 Thus, the closest N•••N [TCNQ] •-··· [TCNQ] •distance in MM is 4.080 Å vs. 4.337 Å for FO, albeit at different temperatures. Due to the closer distance in MM than in FO, the expectation that this interaction should lead to stronger antiferromagnetic coupling, and the antiferromagnetic ground state is expected for this configuration. 7,12,19 Above the 1300 Oe critical field the MM polymorph switches to a ferromagnetic-like state. 7 To understand the magnetic couplings, however, requires the knowledge of the structures at temperatures as close as feasible to where the magnetic ordering is observed.
To understand the subtle structural differences between the FO and MM polymorphs and how they affect the magnetic properties of this unique system, where different polymorphs have ferro-and antiferromagnetic ground states, very low temperature structures are herein reported (although still above than the magnetic ordering temperatures) for both phases. These form the basis for theoretical evaluations of the magnetic interactions with a very high degree of accuracy, aiming at providing benchmark results that will provide a solid foundation for the analysis and rationalization of the subtle spin coupling interactions that lead to the different magnetic ground states. 20 In addition, although there is no evidence from the magnetic data, two reversible structural phase transitions MM phase were discovered; both at higher (MM ⇌ MMRT) and at low temperature (MM ⇌ MMLT) that have not been previously published.

Experimental Section
The purple-reflecting crystals of the MM and FO polymorphs were prepared as previously reported. 7 Differential scanning calorimetry (DCS) studies utilized a TA Instruments Model 2910 DSC equipped with a LNCA liquid nitrogen cooling accessory enabling operation between of -150 to 550 o C using a 1 o C/min scan rate and ~5 mg samples. Consecutive heating and cooling cycles were performed to ensure reversibility and reproducibility of the phase transitions.
Computational results were obtained as previously reported. 10 High resolution powder diffraction measurements for the Rietveld structure analysis for the MM and FO polymorphs at various temperatures were performed at Beam Line X16C of the National Synchrotron Light Source at Brookhaven National Laboratory. The powdered samples were held in 1.0 mm diameter thin-wall quartz capillaries. X-Rays of a single wavelength were selected by a Si(111) channel cut crystal. Diffracted X-rays were selected by a Ge(111) analyzer and detected by a NaI scintillation counter. Samples were cooled either by an Oxford Cryostream (T ³ 100 K) or an APD closed cycle refrigerator (T < 100 K). To improve particle statistics, the sample was spun in the former case, and rocked in the latter, during data collection. The incident intensity was monitored by an ion chamber and used to normalize the measured signal. The TOPAS-Academic program was used to index, solve, and refine the crystal structures. 21,22,23 Rietveld plots are given in Figures S1 -S3.
The single crystal structures of MM were determined on a Nonius KappaCCD diffractometer equipped with Mo Ka radiation All the reflections were merged and only those for which Io> 2s(I) were included in the refinement, where s(Fo) 2 is the standard deviation based on counting statistics. The data were integrated using the Bruker SAINT software program. 24 The structures were solved by a combination of direct methods and heavy atom methods. Direct methods and the refinement by full-matrix least-squares methods using SHELXL-97 were used for the structures of MM at several temperatures. All the non-hydrogen atoms were refined with anisotropic displacement coefficients. Hydrogen atoms were assigned isotropic displacements U(H) = 1.2U(C), and their coordinates were allowed to ride on their respective carbons using SHELXL97. 25

Results and Discussion
A fundamental understanding as the genesis of the magnetic couplings for the FO and for the MM polymorphs of [FeCp*2][TCNQ] that lead to their observed ferro-and antiferromagnetic ordering and their subtle differences has yet to be identified. Insight into this system will provide a salient understanding of the couplings and competition among couplings that led to net antiferromagnetic as well as ferromagnetic couplings and subsequently long range, bulk magnetic ordering. A computational study of the magnetic couplings requires the structure determination preferably at or below the ordering temperature. The structures of the MM and FO polymorphs [FeCp*2] [TCNQ] have been reported at 167 K and at room temperature, respectively, but herein they are redetermined via high-resolution powder X-ray diffraction (PXRD) data at 18 ± 1 K. As part of these studies the room temperature structures were also obtained. The unit cell of the FO phase at room temperature is in accord with that previously reported, 15  to a disordered phase, whereas that in MnCp*2 is a rotation of the Cp* rings, which is therefore more similar to that observed for MM.
In addition, a rearrangement of the structure was observed between 60 and 80 K, emphasizing the importance of using data collected at or near the magnetic ordering temperature to interpret magnetic interactions in molecular solids. The evolution of the temperature dependence of the lattice parameters of the MM phase is shown in Figure 1. Selected powder diffraction patterns, including two-phase coexistence at both transitions are shown in Figure S4.
The phase transitions are clearly noted from the abrupt change in several unit cell parameters, e.g. b, c, a, b, and g, over the entire temperature range, but the molar volume evolves continuously,  [TCNQ] •radical ions in roughly a triangular arrangement, e.g. Figure S7, but there are significant differences in their local arrangements. Figure       coupling leading to magnetic ordering arises from the intra-and interchain couplings.

Structure of FO
The structure of the FO polymorph at 19 K is similar to that previously reported at room temperature, 15 but with a 3.5% volume contraction, and the intrachain Fe•••Fe separation decreases by 0.9% to 10.738 Å, Table 2. Each chain is surrounded by six parallel chains, Figure Figure 3a. Thus, the FeC10 core has approximate D5h symmetry.

Structure of MMLT
The structure of MM at 17 K (MMLT) belongs to the same P1 space group, it was not isomorphous with the previously reported 167-K structure for MM, 6 Table 1, and has a 1.9% volume contraction and the intrachain Fe … Fe separation decreases by 1.0% to 10.439 Å, Table 2. Each chain is surrounded by 6 parallel chains, Figure S7, forming two identical pairs out-of-registry nearest neighbor chains, I-II (and I-II') and I-III (and I-III') separated by 9.245 and 8.389 Å, respectively, and one pair of in-registry nearest neighbor chains I-IV (and I-IV') separated by 8.631 Å, Figure   S7,  Figure 3b. Thus, the FeC10 core has D5d symmetry.
As part of the structural investigation of MM at low temperature, the room temperature unit cell was determined, and although MMRT had the same P1 space group, it was not isomorphous with the previously reported 167-K structure for MM, 6 Table 1

Thermal behavior of MM
A DSC study confirmed the phase transition upon warming above -55 o C, Figure 5. The transition temperature (Twarm) was determined from extrapolation of the most linear portion of the onset of absorption in the heat flow to an approximated baseline established from the internal standard heat flow. A slight variation was observed in this value with that observed upon cooling (Tcool), and these differences were found to depend on the temperature scan rate and was determined to be an artifact of finite temperature scan rates. The Twarm and enthalpy of transition were determined to be 226.5 ± 0.4 K (-46.7 ± 0.4 o C) and 0.68 ± 0.04 kJ/mol (0.16 ± 0.01 kcal/mol), respectively, transition (3.32 kJ/mol) is significantly larger than reported for MM, but includes the neighboring anomaly at 281.8 K, which adds substantially to the enthalpy. 27 The transition at 248.7 K for [FeCp*2][TCNE] was classified as an order-disorder type on the basis of entropy, 27 which was consistent with later temperature dependent diffraction studies. 11 The absence of disorder in diffraction data of MM indicate that the behavior observed at 226.5 K is more likely to resemble that of MnCp*2. 6 However, unlike for MnCp*2 where an anomaly occurs in the temperature dependent magnetic susceptibility data, 6 there is no evidence of such a transition for either MM or [FeCp*2][TCNE]. The investigation of the 70 ± 10 K MM to MMLT phase transition was beyond the limits of our DSC and thus unfortunately could not be studied.

SOMOs
The ground state of [FeCp*2] + is a doublet that has a strong multi-referent character involving two   identical to that previously reported using the CASSCF(8,7) wave function 10 (a different isosurface is presented for a clearer view of the nodal structure).

Results of the spin coupling analysis
The Jij values were evaluated for each symmetry-unique radical pair found in the crystal structures  Table 3. The differences in the relative orientations present for the FO and MMLT polymorphs is presented in Figure 8. All the Jij couplings between the nearest neighbor [FeCp*2] •+ •••[FeCp*2] •+ pairs were computed to be negligible and will therefore not be further considered. Table 3. •interaction is computed to be 6.5 cm -1 for MMLT , which on average is 24% lower for FO, Table 3. Note that the intrachain interaction for MMLT has higher symmetry than for FO; thus, the two different 5.2 and 4.7 cm -1 interactions (J1 and J2) for FO become equivalent (6.5 cm -1 ) for MMLT , Table 3. This, in part, is due to the 2.8% shorter separation for Fe•••Fe separation for MMLT with respect to FO, and differing orientations (Figure 8).
The MOs shown in Figures 7 and 9 provide a rationale for the ferromagnetic nature of the intrachain couplings. It should be noted that the degenerate SOMOs of ferrocenium, which are essentially localized on the dxy and dx2-y2 orbitals of the Fe ion, are nearly orthogonal by symmetry to the SOMO of [TCNQ] •-. In fact, when the SOMOs of the intrachain [FeCp*2] + ••• [TCNQ] •pairs are plotted using a very small threshold for the electron density (see Figure 9) it is observed that the dxy and dx2-y2-centered orbitals do not combine with the π* orbital of [TCNQ] •-. The vanishingly small overlap between the degenerate SOMOs of ferrocenium and the SOMO of [TCNQ] •- (Table 4) Table 3.
[FeCp*2][TCNE], in contrast, only forms one polymorph at room temperature, however, upon cooling two additional phases reversibly form at 280 and 245 K, Scheme 1. 10,27 Furthermore, solvated pseudo polymorphs of [FeCp*2][TCNE] have been reported, 11 which have yet to be reported for [FeCp*2] [TCNQ]. Based upon Kitaigorodskii's principle 34 that the more stable polymorph has the higher density, 35 based on the room temperature structure, Table 1, P is the more stable than the MMRT and FO polymorphs. This is in accord with P also having extra stabilization arising from the intradimer p-[TCNQ]2 2multicenter bonding, 36,37 in addition to the van der Waals interactions that are also present for MMRT and FO.