Guest-induced on–off switching of elastic frustration in the interpenetrated Hofmann spin-crossover framework $\{\mathrm{Fe}^{\mathrm{II}}(3,8\text{-phen})[\mathrm{Au}(\mathrm{CN})_2]_2\}\cdot x\,\mathrm{PhNO}_2$: intermediate-state structure and switching-barrier energetics of the guest-wedge mechanism

The porous Hofmann-type coordination polymer $\{\mathrm{Fe}^{\mathrm{II}}(3,8\text{-phen})[\mathrm{Au}(\mathrm{CN})_2]_2\}\cdot x\,\mathrm{PhNO}_2$ ($3,8$-phen $=$ 3,8-phenanthroline; $\mathrm{PhNO}_2$ $=$ nitrobenzene) is a singular dual system: a single-step, room-temperature hysteretic spin crossover and a four-step, elastically frustrated spin crossover can be reversibly interconverted simply by desorbing and re-adsorbing an aromatic guest that wedges itself between two interpenetrated frameworks. The microscopic mechanism of this on–off switching is unresolved. The aperiodic high-spin/low-spin ordering of the $\gamma_{\mathrm{HS}}\approx 2/3$ intermediate state was never solved (its satellite reflections were too weak for a superspace refinement), and the energetic cost of the large angular distortion that bottlenecks the half-converted state is not quantified. Two related aspects were left uncharacterized rather than open: the detailed characterization of the announced family of $1\cdot\mathrm{PhX}$ clathrates was deferred by the authors to a separate publication, and the kinetic pathway of the switching — guest rearrangement, sliding of the interpenetrated frameworks, nucleation and growth of ordered spin-state domains — was not probed. The problem asks for the microscopic structural and energetic basis of the switching. No later work on this compound is known to resolve any of these issues.

Background

Spin crossover (SCO) is the reversible switching of a transition-metal center, most commonly octahedral Fe(II) in an N6 environment, between a low-spin (LS, diamagnetic, $S=0$) and a high-spin (HS, paramagnetic, $S=2$) electronic state, driven by temperature, pressure or light. The LS state has shorter metal–ligand bonds, so a cooperative solid-state transition changes volume, color and magnetism; when elastic cooperativity is strong, the thermal transition becomes first-order with a hysteresis loop, giving molecular bistability of interest for sensing, memory and spintronic devices. The HS molar fraction is denoted $\gamma_{\mathrm{HS}}$.

Hofmann-type frameworks are cyanide-bridged Fe(II) coordination polymers in which square $\{\mathrm{Fe}_4[\mathrm{M}(\mathrm{CN})_4]_\infty\}$ grids ($\mathrm{M}$ $=$ Ni, Pd, Pt) or related cyanometallate units are pillared by bridging N-donor ligands into 2D or 3D (pcu-topology, i.e. primitive-cubic-network) porous networks. In the compound at issue, $\{\mathrm{Fe}^{\mathrm{II}}(3,8\text{-phen})[\mathrm{Au}(\mathrm{CN})_2]_2\}\cdot x\,\mathrm{PhNO}_2$ ($3,8$-phen $=$ 3,8-phenanthroline, a rod-like ditopic ligand; $\mathrm{PhNO}_2$ $=$ nitrobenzene), two identical 3D pcu-type frameworks interpenetrate, leaving 1D channels that host one nitrobenzene guest per Fe ($x=1$, denoted $1\cdot\mathrm{PhNO}_2$). The guest π-stacks against the 3,8-phenanthroline walls and makes short C···C contacts with the dicyanoaurate linkers, acting as a "molecular wedge" between the two frameworks.

Elastic frustration denotes the situation in which the lattice strains generated by LS↔HS conversion at different sites compete instead of cooperate, so that no uniform strain state satisfies all sites. Electroelastic modeling by Paez-Espejo, Sy and Boukheddaden (2016) showed that such frustration generically produces two-step and multistep transitions with antiferroelastic ordering, and the associated "spin-state ice" analogy was analyzed by Cruddas and Powell (2019). Guest molecules can act as controllable sources of elastic frustration: guest-programmable multistep SCO was demonstrated in a 2D Hofmann material by Murphy et al. (2017), and reversible on–off switching of elastic frustration by guest uptake/release in a 2D Hofmann framework by Sciortino et al. (2018). Host–guest chemistry had earlier been shown to switch one- versus two-step transitions in the 3D Hofmann clathrates $\{\mathrm{Fe}(\mathrm{bpb})[\mathrm{Pt}(\mathrm{CN})_4]\}\cdot$guest (Piñeiro-López et al. 2017).

The dual behavior of the present compound (Piñeiro-López et al. 2021) is the 3D, room-temperature, guest-reversible version of this physics. Loaded $1\cdot\mathrm{PhNO}_2$ undergoes a four-step transition HS$_1$LS$_0$ (state 1) ↔ HS$_{2/3}$LS$_{1/3}$ (state 2) ↔ HS$_{1/2}$LS$_{1/2}$ (state 3) ↔ HS$_{1/3}$LS$_{2/3}$ (state 4) ↔ HS$_0$LS$_1$ (state 5) below 280 K, while controlled thermal desorption of the guest affords compound 1 ($x=0$), which shows a complete one-step hysteretic transition centered at room temperature (hysteresis 15–20 K wide; $T_{\mathrm{down}}=290.0$ K, $T_{\mathrm{up}}=305.3$ K at 1 K min$^{-1}$); re-adsorption of PhNO$_2$ restores the four-step regime. At low temperature the loaded compound also photogenerates a metastable HS state (state 6) by the LIESST effect (light-induced excited spin-state trapping).

Structurally, states 1, 3 and 5 are solved commensurate structures, state 3 featuring ⋯HS–LS⋯ order with $\gamma_{\mathrm{HS}}=1/2$ and symmetry breaking. States 2 and 4 display weak satellite reflections in single-crystal X-ray diffraction (incommensurate modulation vector $\mathbf{q}\approx[0.43,0.50,0.36]$ in reciprocal-lattice units), the signature of aperiodic order — a phenomenon solved in superspace crystallography for another SCO material by Collet et al. (2012). For state 4 the authors succeeded in a (3+1)-dimensional superspace refinement, superspace group $P2/n(a1|2g)0s$, revealing an aperiodic modulation of the Fe–N bond lengths, of the guest and of the ligand, corresponding to long-range aperiodic order close to LS–LS–HS (HS–HS–LS). For state 2 the satellites were too weak (poor signal-to-noise): only the average structure was refined ($\langle\mathrm{Fe{-}N}\rangle=2.099(5)$ Å, consistent with $\gamma_{\mathrm{HS}}\approx 2/3$), and the authors state that the state-4 aperiodic order "could be inferred" but not demonstrated for state 2.

The angular distortion parameter $\Sigma$ (the sum of deviations from 90° of the twelve cis N–Fe–N angles of the octahedron) is diagnostic of the elastic cost of the distortion. Across the states it takes the values 3.68° (state 1), 3.40° (state 2), 6.66° for LS sites and 5.40° for HS sites (state 3), 3.76° (state 4), 4.40° (state 5 at 140 K, falling to 3.2° for state 5 at 15 K in the dark) and 4.72° (photoinduced state 6): the state-3 jump, correlated with scissor-like deformation of the $\{\mathrm{Fe}_4[\mathrm{Au}(\mathrm{CN})_2]_4\}$ windows and with the steric hindrance of the guest wedged between the frameworks, is identified qualitatively as the energy penalty that makes the half-converted state the bottleneck of the HS↔LS conversion. Calorimetry gives step enthalpies $\Delta H_i\approx 7.60, 3.36, 2.88, 5.87$ kJ mol$^{-1}$ and entropies $\Delta S_i\approx 29.45, 14.24, 13.85, 29.94$ J K$^{-1}$ mol$^{-1}$, with a total ($19.8$ kJ mol$^{-1}$, $87.48$ J K$^{-1}$ mol$^{-1}$) inconsistent with the spin-only entropy, indicating additional structural ordering. Preliminary loading with other six-membered aromatic guests (fluoro-, chloro-, bromo- and 1,3-dibromobenzene, benzaldehyde, benzonitrile) reportedly gives clathrates $1\cdot\mathrm{PhX}$ with similar four-step behavior, but their detailed characterization was deferred "elsewhere", and chemical analysis suggests ~3–4% residual PhNO$_2$ remains in the nominally desorbed compound 1.

Problem Statement

Establish the microscopic mechanism by which an included aromatic guest switches elastic frustration — and with it multistep spin-crossover behavior — on and off in the doubly interpenetrated Hofmann framework $\{\mathrm{Fe}^{\mathrm{II}}(3,8\text{-phen})[\mathrm{Au}(\mathrm{CN})_2]_2\}\cdot x\,\mathrm{PhNO}_2$: convert the qualitative "molecular wedge" picture into a verified structural and energetic account of the switching by resolving the two points the source leaves open:

(1) Intermediate-state structure. Solve the HS/LS ordering of state 2 ($\gamma_{\mathrm{HS}}\approx 2/3$, 250 K), for which the source obtained only the average 3D periodic structure because the satellite reflections were too weak for a superspace refinement. The ordering — an incommensurate superspace model or an equivalent structural model of the aperiodic order — must account for the observed satellite reflections (modulation vector $\mathbf{q}\approx[0.43,0.50,0.36]$, weak at 250 K, stronger at 206 K, still present at 140 K in state 5) together with the refined average structure ($\langle\mathrm{Fe{-}N}\rangle\approx 2.099$ Å); resolving this point requires a state-2 ordering model consistent with these reported anchors, and a fresh superspace refinement is not required. That model must establish whether state 2 is the analogue of the state-4 aperiodic LS–LS–HS modulation or a different motif with a different coupling mechanism.

(2) Switching-barrier energetics. Quantify how the guest-imposed steric hindrance, the state-3 angular distortion ($\Sigma\approx 6.7^\circ$ for LS and $5.4^\circ$ for HS sites, versus 3.2–4.72° in the other states), and sliding of the interpenetrated frameworks enter the free-energy balance and the barriers between the ordered phases, going beyond the measured step enthalpies and entropies ($\Delta H_i\approx 7.60, 3.36, 2.88, 5.87$ kJ mol$^{-1}$; $\Delta S_i\approx 29.45, 14.24, 13.85, 29.94$ J K$^{-1}$ mol$^{-1}$) and explaining why the half-converted state is the bottleneck of the HS↔LS conversion.

Two further aspects of the same wedge mechanism are documented by the source as uncharacterized rather than open, and are context for — not substitutes for — the structural and energetic account requested above: the detailed structural, magnetic and thermodynamic characterization of the announced $1\cdot\mathrm{PhX}$ clathrate family (aromatic guests of systematically varied size, electronic character and channel dielectric effect, for which the source reports preliminary four-step behavior), including the influence of the ~3–4% residual guest that remains in the nominally desorbed compound 1; and the microscopic pathway of guest rearrangement, sliding of the interpenetrated frameworks, and nucleation and growth of ordered HS/LS domains during thermally driven guest desorption from $1\cdot\mathrm{PhNO}_2$ and re-adsorption into 1.

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