1 The origin of bistability in the butyl-substituted spiro-biphenalenyl-based neutral radical material

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Introduction
Bistability is an intriguing phenomenon exhibited by a few materials that present two stable phases that can both exist within a given range of temperatures. Moleculebased bistable materials have been the subject of intense research during the last years because they hold great promise for application in sensors, displays and switching devices. 1 , 2 , 3 , 4 , 5 The numerous examples of molecular bistable materials include: materials based on transition metal complexes undergoing spin transitions 6,7,8,9,10,11,12,13,14 , organic spin-transition materials 15,16,17,18,19,20,21,22 , compounds whose phase transition is induced by a charge transfer between an electron-donor and an electron-acceptor 23 , 24 , 25 , 26 , 27 , compounds featuring charge-transfer-induced spin transitions 28 , 29 , 30 , inorganic-organic hybrid frameworks undergoing phase transitions 31,32 , molecular crystals whose phase transitions are triggered by changes in the orientation of molecules 33 16,34,35,36,37,38,39,40 The numerous spiro-biphenalenyl (SBP) boron radicals reported by Haddon and coworkers constitute a very important class of PLY derivatives. 41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57 SBPs present two nearly perpendicular phenalenyl units connected through a boron spiro-linkage. The N-and O-functionalized SBPs (ie, SBPs in which each phenalenyl unit is bonded to the central boron atom via an oxygen and a nitrogen atom) exhibit diverse packing motifs in the solid state, and hence different physical properties, depending on the substituents attached to the nitrogen atom. Ethyl (1) and butyl-substituted (2) SBPs (see Figure 1) present a crystal structure containing π-dimers as the basic building block (see Figure 2 and Figure S1).
These two compounds undergo a phase transition that is accompanied by a change in their optical, conductive and magnetic properties. 16,42 The phase transition of ethyl-SBP is reversible and occurs at about 140 K, while that of butyl-SBP occurs with an hysteretic loop 25-K wide and is centered at a much higher temperature (~ 335 K). At this point, it is worth mentioning that butyl-SBP is one of the few multifunctional bistable materials that switch the response in multiple physical channels upon phase transition. 25,30,32,26 Besides, the volume of the crystals of butyl-SBP significantly change upon phase transition; specifically, a notable expansion of the crystal is observed when the system switches from its low-temperature (LT) phase to its high-temperature (HT) phase. 58 This volume change in response to external stimuli is currently a sought-after phenomenon in the context of new functional materials due to its potential applicability to microscale or nanoscale actuators. 33 The experimental 58,59 and theoretical studies 60,61,62,63,64 conducted over the last years on ethyl-and butyl-SBP have culminated in a clear understanding of their electronic structure and the different magnetic and conducting properties of their phases. Upon phase transition in the heating mode, the constituent π-dimers of these materials undergo a spin transition from a closed-shell diamagnetic singlet state to an open-shell paramagnetic state. Below the spin transition temperature, the structures of the πdimers are governed by the potential energy surface (PES) of the ground singlet state ( 1 A g state), whose minimum structure features a partial localization of the unpaired electrons of each SBP radical in the superimposed phenalenyl (sup-PLY) rings, that is, on the phenalenyl (PLY) units directly involved in the π-dimer (see Figure 2a). The strong coupling between the SBP unpaired electrons in this configuration leads to a magnetically silent state, and, thus, to a diamagnetic LT phase. Above the spin transition temperature, the π-dimers adopt a configuration characterized by a localization of the SBP unpaired electrons in the nonsuperimposed phenalenyl (non-PLY) units, that is, on the PLYs not directly involved in the π-dimer (see Figure 2b), which leads to a paramagnetic phase. This configuration is exclusively governed by the PES of the ground triplet state ( 3 A u state) because the corresponding open-shell singlet does not feature any minimum in that region of the PES even if it lies slightly below in energy than the triplet state. In a recent article 64 , we have shown that the high-spin (HS) state is energetically competitive with the low-spin (LS) state because the electrostatic component of the interaction energy between SBP radicals in the πdimers is more attractive in the high-temperature 3 A u state than in the low-temperature 1 A g state. This electrostatic stabilization of the high-temperature 3 A u state was ascribed to the zwitterionic nature of the SBP moieties, in particular, to the interaction between the positively-charged superimposed PLYs in the triplet state ( Figure 2b) and the negatively-charged spiro-linkages with the central boron atom. These electrostatic interactions also explain why the unpaired electrons prefer to localize on the nonsuperimposed PLYs in the high-temperature triplet state. 64 Despite the current good understanding of the electronic structure of the π-dimers of ethyl-and butyl-SBP and several theoretical studies on other phenalenyl-based systems 65,66,67,68,69,70,71,72,73,74,75,76,77,78 , there are two crucial questions concerning the phase transitions of ethyl-and butyl-SBP that remain unsettled, namely: i) why is the transition temperature of butyl-SBP so much higher than that of ethyl-SBP?, and ii) why does butyl-SBP display an hysteretic phase transition, in contrast with ethyl-SBP, which features a smooth phase transition? A meticulous study carried out by Haddon and coworkers in Ref. 58 on numerous crystal structures of butyl-SBP at different temperatures led to the suggestion that the HT phase is the thermodynamically stable phase within the bistability region, while the existence of the LT phase within the hysteretic loop was rationalized on the basis of the large energy barrier that the system needs to overcome when switching from LT to HT. Even if this barrier was estimated to be larger than 24 kcal/mol, the specific molecular rearrangements responsible for that barrier were not identified. In the computational study herein presented, not only do we provide a rationale for the higher spin-transition temperature of butyl-SBP but also disclose the hitherto elusive origin of its hysteresis loop. In particular, our study reveals that the bistability arises from a very simple molecular rearrangement, namely, a conformational rearrangement of the butyl groups attached to the SBP radicals.

Results and discussion
The presentation of the results is organized as follows. We will first demonstrate that the higher phase-transition temperature of compound 2 (compared to that of 1) arises from a coupling of its spin transition with a conformational rearrangement of the butyl groups (subsection 1). Then, we will disclose that the significant expansion of crystals of 2 upon LT→HT phase transition is governed by this very conformational rearrangement of butyl groups (subsection 2). After that, we will show that the dynamic disorder exhibited by the butyl chains in the high-temperature phase of 2 implies that the conformational change of these chains brings about an order-disorder transition (subsection 3). Finally, we will decipher the mechanism of the coupling between the spin transition and the conformational rearrangement, we will demonstrate that the LT→HT phase transition is assisted by structural cooperative effects, and we will reveal that the hysteresis loop featured by 2 originates in the high-energy penalty associated with the conformational change of the butyl groups in the crystal lattice of the lowtemperature phase (subsection 4).

1) Phase transition of butyl-SBP: a spin transition coupled with a conformational rearrangement of the butyl groups.
As mentioned in the Introduction, the phase transition undergone by 1 and 2 is a spin transition in which the corresponding SBP π-dimers switch between two states: a singlet state ( 1 A g ) and a triplet state ( 3 A u ). The low-spin (LS) state is the thermodynamically stable state at low temperatures (LT), while the high-spin (HS) state is the thermodynamically stable state at high temperatures (HT). In the LS state the unpaired electrons of the SBP are strongly coupled and mainly localized in the superimposed PLY units (see HOMO in Figure S2a), while in the HS state they move to the non-superimposed PLYs (see one of the two SOMO in Figure S2b).
In this subsection, we shall first investigate why the spin-transition of 2 is shifted 200 K towards higher temperatures with respect to the spin-transition temperature of 1. The key quantity to rationalize this behavior is the adiabatic energy gap between the LS and HS minima (ΔE adia = E LS − E HS ). The values of ΔE adia in the gas phase and in the solid state for 1 and 2 were evaluated upon geometry optimization of the corresponding isolated π-dimers and the π-dimers in the crystalline phases. The initial configurations for these geometry optimizations were taken from the LT and HT X-Ray nuclear coordinates (Table S1 and Table 1, respectively). As previously reported 64 , the ΔE adia obtained for compound 1 in the solid state is -2.6 kcal/mol. This value is virtually identical to that found in the gas phase, which means that ΔE adia is not affected by the crystal packing. On the other hand, the ΔE adia values for an isolated π-dimer and for a π-dimer in the solid-state of compound 2 are -3.6 and -9.5 kcal/mol, respectively. The larger adiabatic gap in the solid state for 2 (compared to that of 1) is in line with its higher spin-transition temperature. The large difference between the solid-state and gas-phase ΔE adia values of 2, in turn, reflects the notable influence exerted by crystalpacking effects on the spin-transition properties of this material. It is worth mentioning that such effects have already been observed in Fe(II)-based spin crossover compounds. 79,80,81 In the following, we shall examine the origin of the different ΔE adia values of ethyl and butyl-SBP. We shall now turn our attention to this issue. Note that the butyl chains linked to the N atoms of the non-PLY rings do not change their conformation in going from LT to HT.
Hence, in what follows we will not deal with the conformations of these particular butyl chains.
So far, we have shown that the LS state of the π-dimers of 2 in combination with the gauche conformation of the butyl chains give rise to a minimum energy configuration that will hereafter be referred to as LS(gau) configuration. We have also shown that the combination of the HS state of the π-dimers and the anti conformation of the butyl chains gives rise to another minimum energy configuration, which will be referred to as HS(anti) configuration. We only considered these two configurations since they correspond to the experimental observation. However, at this point, one could hypothesize that the LS(anti) and the HS(gau) configurations might also exist as minima even if they have not been experimentally detected. Variable-cell optimizations demonstrated that the LS(anti) and HS(gau) configurations correspond indeed to minima. A scheme of the relative energies of the different polymorphs of 2 considered in this work is presented in Figure 3. The most stable polymorph of 2 is the LS(gau) polymorph, in agreement with the fact that this is the phase detected at low temperatures for compound 2. Concerning the polymorphs containing π-dimers in their HS state, our calculations bring to light that HS(gau) is lower in energy than HS(anti), even if the polymorph experimentally detected at high temperatures is the latter one.
The energetic preference for the gauche conformations in the condensed phase (irrespective of the spin state of the π-dimers) is also observed for isolated π-dimers (see Figure 3 It is thus concluded that the higher phase-transition temperature of 2 (compared to that of 1) stems from the coupling between an electronic transition and a conformational change.

2) Origin of the main structural differences between the two polymorphs of 2.
The detailed structural analysis reported by Haddon and coworkers in Ref. 58 showed that the main structural differences between the LT and HT polymorphs of 2 are the interplanar distance between the sup-PLY units of the π-dimers (D) and the distance associated with a CH···π interaction formed by an aromatic C-H of one π-dimer and one of the sup-PLY rings of a neighboring π-dimer (see Figure S3 for definition). Both types of distances increase by 0.1 Å upon LT→HT phase transition. Furthermore, this phase transition is accompanied by a large change in the unit cell volume, which increases by 3.5% in going from LT to HT. As shown in Table 2, all these structural changes detected in the X-ray crystals are properly captured by the optimized structures of the LS(gau) and HS(anti) polymorphs. We shall now trace the origin of these structural changes.
The results collected in Table 2 show that for a given conformation of the butyl groups (be it either gauche or anti) the D value (see Figure S3 for its definition) of the π-dimers in the optimized HS polymorphs is ca. 0.08 Å larger than in the optimized LS polymorphs. On the other hand, for a given spin state of the π-dimers (be it either LS or HS), the D value in the optimized anti polymorphs is ca. 0.05 Å larger than in the optimized gauche polymorphs. It then follows that the increase of D upon LT→HT phase transition is due to both the change in the spin state of the π-dimers and the conformational rearrangement of the butyl chains, the former effect being the dominant one. On the contrary, the increase of the CH···π distance upon LT→HT phase transition should be mainly ascribed to the conformational rearrangement of the butyl groups (see Table 2).
Finally, the results of Table 2 show that a LS→HS spin transition by itself (ie, a spin transition that is not accompanied by any conformational change of the butyl chains) entails only a very small volume cell increase (ca. 0.4%), similarly to that reported for compound 1. In stark contrast, Table 2 discloses that for a given spin state (be it either LS or HS) the gauche→anti conformational rearrangement of the butyl chains brings about an increase of ca. 4% in the volume unit cell. It is thus concluded that the remarkable volume increase of compound 2 upon LT→HT phase transition originates in the conformational change of its butyl chains. As shown in Table S2, the experimentally observed increase in the volume unit cell mainly originates in the increase of the cell parameter b, which lengthens by about 0.3 Å upon LT→HT phase transition. The notable elongation of b can be understood on the basis of the fact that the butyl chains lie parallel to this axis when they adopt the anti conformation.

3) Driving forces of the phase transition of butyl-SBP. Order-disorder transition involving the butyl chains.
We shall now focus on the driving force of the complex phase transition undergone by 2. In our previous study of compound 1 64 , we demonstrated that the HS state of the πdimers have a larger vibrational and electronic entropy than the LS state, as a result of which the HS state become the thermodynamically stable state above a certain temperature. As observed in Figure 4 (red curve), the HS(gau) state of an isolated πdimer of 2 is also entropically stabilized with respect to the LS(gau) state. The key question at this point is whether the gauche à anti conformational change is accompanied by any extra change in the vibrational entropy of the system. The green curve of Figure 4 proves that this is indeed the case for isolated π-dimers. Such trend is not only maintained but also enhanced in the solid state (dashed green line of Figure   4). As a result of the extra gain in vibrational entropy in going from a gauche to an anti conformation, the entropic stabilization of the HS(anti) configuration of the π-dimers of 2 with respect to the LS(gau) configuration as the temperature increases is much larger than the entropic stabilization of the HS state with respect to the LS state in compound 1 (see dark blue curve in Figure 4). The large vibrational entropy gained by the πdimers of 2 when their butyl chains adopt an anti conformation is thus crucial in enabling this compound to clear a HS(anti)-LS(gau) adiabatic gap that is much larger than the HS-LS adiabatic gap of compound 1.
The fact that the hysteretic phase transition of butyl-SBP is centered at a high temperature (~335 K), together with the large thermal ellipsoids of the carbon atoms of the butyl chains observed in the X-ray crystal structure of the HT phase of 2 58 , strongly suggest that going beyond the static perspective so-far adopted in this article by explicitly considering the thermal fluctuations of the system might offer an improved description of the phase transition of butyl-SBP. The thermal fluctuations of the system were considered by performing ab initio molecular dynamics simulations (AIMD) for the LT and HT phases of compound 2. These AIMD simulations, which span a time interval of more than 60 picoseconds, were done at 340 K because this temperature is within the hysteresis loop. The simulation box of the unit cell employed in the simulations includes four spiro-biphenalenyls monomers, which gives rise to two π-dimers, such that the dynamics of four non-equivalent butyl-ligands bonded to the sup-PLY was followed along the trajectories (see Figure S3). The conformational dynamics of the butyl chains can be analyzed by monitoring the time-resolved evolution of the dihedral angle (θ) between the carbon atom bonded to the N atom and the carbon atom of the terminal methyl group along the central C-C bond of the butyl chain (see Figure 5 for the definition of θ). For practical purposes, the anti conformer will hereafter be considered as the reference conformation, which means that the anti conformation will be associated with a dihedral angle of θ=0 and the rest of θ values will be given with respect to the position of the terminal methyl group in the anti conformation ( Figure 5).
The AIMD simulations of LT-340 ( Figure 6a) show that the butyl groups present most of the time a conformation for which θ ≈ -107º. As shown in Figure 5, this value of θ corresponds to a gauche conformation in which the terminal methyl group is pointing to a non-PLY unit (gauche-IN conformation). Sporadic transitions to another conformation for which θ ≈ 107º took place individually on three of the four butyl-groups. In this conformation, the butyl chain is in another gauche conformation in which the terminal methyl group is not pointing to a non-PLY (gauche-OUT conformation, see Figure 5).
The simulations also show that the probability of a given butyl chain to be in the anti conformation is of ca. 4%, thus suggesting that this spatial arrangement is energetically disfavored in the unit cell of the LT phase at 340 K.
Two simulations were performed for the HT-340 structure. One simulation was computed starting from the anti polymorph, whereas the second one was performed by The dynamic disorder found for the butyl chains in the HT phase of 2 strongly suggests that the vibrational entropy of HT is largely underestimated when using the harmonic approximation, as done to obtain the results displayed in Figure 4. It thus follows that the TΔS T values of the blue and both the green curves of Figure 4 would be larger (in absolute value) if the anharmonic effects associated with the dynamic disorder had been taken into account in the calculations. The extra entropic stabilization of the HS(anti) polymorph by virtue of the dynamic disorder of its chains supports the mechanism proposed by Haddon and coworkers 58 , which ascribes the presence of the LT polymorph within the hysteresis loop due to the existence of an energy barrier to reach the HT phase, which is the thermodynamic free energy minimum in the range of temperatures of the bistability mainly due to its large vibrational entropy term. The key question that needs to be addressed at this point (see next subsection) is which is the origin of the barrier that LT needs to overcome to transform into the HT phase.  The X-ray resolved structures of the LT phase at 100 and 340 K (see Table S3) show that the shrinkage of the vector cell c is one of the main structural changes undergone by the LT phase upon cooling. This is in line with our computational results, which show that the computed vector cell c at 0 K is significantly smaller than that of the crystal structures refined at finite temperatures (Table S3). Concomitantly with this variation, some key intermolecular distances also decrease upon cooling. As shown in Therefore, the butyl chains cannot undergo the gauche-IN à anti conformational change until the LT phase of 2 reaches a sufficiently high temperature such that the accompanying thermal expansion of the crystal leads to a sufficiently small energy barrier that can be surmounted. It is thus concluded that the barrier associated with this very conformational rearrangement is responsible for the hysteretic phase transition of

2.
Having reached this point, it should be stressed that the energy barrier discussed in the two previous paragraphs corresponds to the conformational switch of a single butyl chain. The phase transition of 2 entails many of these conformational switches and each of them is an activated process. Therefore, this phase transition cannot be rationalized by means of a single energy barrier. The key question at this point is whether the phase transition is assisted by cooperativity, that is to say, whether the conformational switch of a given butyl chain favors the conformational switch of the butyl chain of a neighboring SBP radical. In order to explore the role of cooperativity, the LS(gau) à LS(anti) phase transition was driven by successively rotating the butyl chains of our simulation cell from a gauche-IN to an anti conformation (overall, we manually induced four conformational rearrangements). After every rotation to an anti conformation, the system was allowed to relax by means of a variable-cell optimization and the change in energy of the system due to the conformational switch was then evaluated. As shown in Figure 9, the first conformational switch of a butyl chain entails a large energy penalty of 10.6 kcal/mol (the energy barrier associated with this process is 12 kcal/mol; see Table S4). Among the three different existing possibilities for the rotation of a second butyl group, the one requiring a smaller energy cost is the conformational switch of the butyl group belonging to the same π-dimer of the butyl group that underwent the first switch. Should the conformational rearrangements of the butyl chains occur independently from each other, the rotation of the second butyl chain would entail an energy penalty of 10.6 kcal/mol. In stark contrast with this scenario, our calculations reveal that the rotation of the second butyl chain entails an extra energy penalty as small as 1.8 kcal/mol (Figure 9). The conformational switch of a third butyl chain, in turn, has an associated extra cost of 4.1 kcal/mol ( Figure 9).  64 , whose phase transition takes place at ~140 K. 16 Let us now consider the mechanism of the HTàLT phase transition of 2. Starting from the HS(anti) polymorph, there are two conceivable mechanisms for the phase transition in the cooling mode: i) HS(anti) à LS(anti) à LS (gau), or ii) HS(anti) à HS(gau) à LS(gau). Note that the first mechanism entails a spin switch as a first step, followed by a conformational switch. The second mechanism, in turn, entails a conformational switch as a first step, followed by a spin switch. Should the phase transition of 2 occur via the first mechanism, such phase transition would have been observed at temperatures around 140 K because the energy gap between HS(anti) and LS(anti) coincides with the HS-LS gap for compound 1. Yet the phase transition in the cooling mode of 2 occurs at much higher temperatures (~320 K), i.e, in a temperature range in which HS(anti) should still be more stable (in terms of free energy) than LS(anti). This means that we can safely rule out the first mechanism. It is thus concluded that the first step in the phase transition of 2 in the cooling mode is the HS(anti) à HS(gau) transformation. Having established which is the first step in the phase transition of 2 upon cooling, we shall now explain why the conformational switch induces the spin switch of the π-dimers of 2. As mentioned above, the conformation adopted by the butyl chains exerts a notable influence on the HS-LS energy gap of these π-dimers.
When switching from the anti to the gauche conformation of the butyl chains, the HS-LS energy gap increases by 1.1 kcal/mol. As a consequence of the larger HS-LS gap, the LS state is the thermodynamically stable state over a wider range of temperatures that extends much beyond 140 K. In particular, as inferred from the red curve of Figure   4, which accounts for the entropy that is needed to clear the energy gap upon phase transition, an increase of 1.1 kcal/mol in the energy gap leads to a large broadening of about 200 K of the temperature range in which the LS state is the thermodynamically stable state. As a result of this, at the phase transition temperature in the cooling mode (~320 K), the LS state is more stable than the HS state and, consequently, once the π- in the LS(gau) polymorph being more stable than the HS(gau) polymorph over a broad range of temperatures that extends much beyond room temperature. This strongly suggests that the phase transition cannot be initiated by the spin transition, which means that the phase transition takes place via the second mechanism, that is to say, the conformational switch precedes the spin transition 88  Finally, it is worth commenting on the solid-state properties of the propyl-SBP radical, which also forms π-dimers in the solid state. 43 Given that the π-dimers of both ethyl-SBP and butyl-SBP feature spin-transitions, one might expect that the π-dimers of propyl-SBP should also present such behavior. However, magnetic susceptibility measurements showed that the dimers of propyl-SBP are in their HS state over the whole temperature range (T > 30 K), thus giving rise to a paramagnetic material without switching properties. 43 The adiabatic energy gap between the LS and HS minima, ΔE adia , of the π-dimers of propyl-SBP in the solid state is -1.9 kcal/mol, which is considerably smaller than the ΔE adia values for 1 and 2 (-2.6 and -9.5 kcal/mol, respectively). This small ΔE adia value explains why the π-dimers of propyl-SBP remain in their HS state in the whole range of temperatures without undergoing any spin transition 89 . The ΔE adia value for an isolated π-dimer of propyl-SBP is significantly larger in absolute value (-2.7 kcal/mol) and very close to the ΔE adia value found for ethyl-SBP, which means that the absence of any spin-transition in the material originates in solidstate effects. In order to get more insight into such effects, we carried out single point energy calculations of an isolated π-dimer excised from the optimized LS polymorph and an isolated π-dimer excised from the optimized HS polymorph. The difference in energy between these two π-dimers (-2.9 kcal/mol) is almost identical to the ΔE adia value obtained in gas phase (-2.7 kcal/mol). This is not suprising in view of the fact that the structure of the π-dimers in the optimized polymorphs is very similar to the structure of the optimized isolated π-dimers (see Figure S4). It is thus concluded that the absence of any spin-transition in the butyl-SBP material is due to intermolecular interactions between π-dimers and not to the fact that crystal-packing effects impose a particular structure of the π-dimers that favors the HS state.

Conclusions
Our computational study on the phase transition of butyl-SBP puts the spotlight on the conformational changes of the butyl chains bonded to the N atoms of the superimposed PLY rings. Neither the thermodynamics of its phase transition nor its hysteretic behavior can be understood without considering the conformational degrees of freedom of the butyl groups. Indeed, the phase transition of butyl-SBP occurs at temperatures higher than room temperature because of the coupling of the spintransition of its π-dimers with an order-disorder transition involving the butyl chains.
This order-disorder transition in the heating mode is triggered by a rotation of the terminal methyl group of the butyl chains, which drives the methyl group from a gauche conformation (with respect to the methylene unit of the butyl bonded to the N atom of the superimposed PLY) to an anti conformation. The significant expansion of the crystal upon phase transition in the heating mode is due to this particular gauche à anti conformational rearrangement. The phase transition of butyl-SBP is initiated via the conformational rearrangement of the butyl chains both upon heating and cooling.
Such conformational switch is readily followed by the spin switch of the π-dimers due to the coupling between the two types of switch, which arises from the strong influence exerted by the conformation adopted by the butyl chains in the crystal on the energy difference between the high-and low-spin states of the π-dimers. In particular, this energy gap considerably decreases upon the gauche à anti transition, which means that the crystal packing associated with the anti conformation tends to favor the highspin states of the π-dimers, whereas the crystal packing associated with the gauche conformation tends to favor the low-spin states.
Our investigations reveal that the hysteresis observed in the phase transition of butyl-SBP originates in the fact that the conformational energy landscape of the butyl chains in the crystal lattice of the LT phase is completely different from that found in the crystal lattice of the HT phase. Specifically, the gauche à anti conformational switch in the crystal lattice of LT entails a larger energy penalty, which is mainly due to the steric repulsion associated with a short H···H contact between the terminal methyl group of a butyl chain in its anti conformation and the PLY ring of the adjacent SBP radical. The large energy penalty associated with this conformational switch and the strong structural cooperativity that assists the order-disorder transition of the butyl chains control the temperature at which the LT à HT phase is initiated and, as a result, the width of the hysteresis loop.
The herein unveiled key role of the conformational changes of the butyl changes in controlling the phase transition of butyl-SBP not only provides a rationale for its intriguing and enigmatic bistable behavior but also provides valuable information that might serve for the rational design of new spirobiphenalenyl-based bistable materials.
Transcending the specific material herein studied, our results highlight the great potential of coupling a conformational rearrangement of a flexible moiety with an electronic transition for the design and preparation of new bistable materials.

Computational details
All the electronic structure calculations performed in this work were carried out using the PBE exchange-correlation functional 90 within the spin-unrestricted formalism. The semiempirical dispersion potential introduced by Grimme 91 was added to the conventional Kohn-Sham DFT energy in order to properly describe the van der Waals interactions. The parametrization employed in this work is the so-called DFT-D2. The use of PBE together with the Grimme correction is known to lead to good predictions for the structure and cohesive energies of molecular crystals. 92 In the following, we provide further details of the methodology employed to obtain the results presented in each subsection of the Results and Discussion. The optimizations of the isolated π-dimers of 2 (carried out with the goal of evaluating the gas-phase ΔE adia values) were also done with plane wave pseudopotential calculations using Vanderbilt ultrasoft pseudopotentials. In these calculations, in which the plane wave basis set was expanded at a kinetic energy cutoff of 60 Ry, the π-dimers were placed in a cell of 60-30-30 Bohr length sides trying to minimize the interactions between the equivalent images.

1) Phase transition of butyl-SBP
All the results presented in this subsection were obtained with the QUANTUM ESPRESSO package. 95 2) Origin of the main structural differences between the two polymorphs of 2.
The analysis presented in this subsection was done using the results obtained in the previous subsection

3) Driving forces of the phase transition of butyl-SBP. Order-disorder transition involving the butyl chains.
The vibrational entropy of the different polymorphs and the isolated π-dimers was evaluated after computing the vibrational frequencies of these systems in the harmonic approximation. The analytical frequencies of the isolated LS and HS π-dimers of 2 were computed using the re-optimized geometries obtained with the 6-31g(d) atomic basis 96 set within the Gaussian09 package. 97  The AIMD simulations were carried out using the efficient Car-Parinello propagation scheme 98 as implemented in the CPMD package. 99 In these simulations the plane wave basis set was expanded at a kinetic energy cutoff of 25 Ry. The molecular dynamics time step was set to 4 a.u. and the fictitious mass for the orbitals was chosen to be 400 a.u. All dynamic simulations were performed in the canonical ensemble using the Nosé-Hoover chain thermostats 100 in order to control the kinetic energy of the nuclei and the fictitious kinetic energy of the orbitals. The lattice parameters employed in the AIMD simulations of the LT and HT phases at 340 K were taken directly from the X-ray crystals refined at 340 K of the LT and HT polymorphs, respectively. In the simulations of the LT phase, the electronic structure of the π-dimers was that corresponding to their singlet ground state. Conversely, in the simulations of the HT phase, the electronic structure of the π-dimers was that corresponding to their triplet ground state.  Figure S1. X-ray crystal structures of the LT and HT phases of the ethyl and butyl radicals showing their characteristic crystal-packing motif: the π-dimers. Figure   S2. Highest occupied molecular orbitals of the lowest singlet state ( 1 A g ) and the triplet state ( 3 A u ) of the π-dimer of butyl-SBP. Figure S3. Definition of the parameter that corresponds to the interplanar distance between sup-PLY units, and the parameter that corresponds to the CH···π distance depicted in the unit cell of the butyl-SBP system. Figure S4. Optimized structures of the π-dimers (both in the solid state and in the gas phase) of propyl-SBP. Table S1. Selected structural parameters for the SBP π-dimers present in two different X-ray crystal structures of ethyl-SBP and the corresponding structural parameters obtained upon geometry optimization of these SBP π-dimers in their 1 A g and 3 A u states. Table S2. Cell parameters of the reported LT-340 and HT-340 X-ray crystal structures of 2. Table S3. Cell parameters of the LT-0 minimum energy structure of butyl-SBP and of the LT crystallographic structures resolved at 100 and 340 K. Table S4      In the LT-340 case, one of the butyl chains was rotated to an anti conformation and all the atomic coordinates were allowed to relax while keeping the X-ray cell parameters of the LT-340 crystal structure. In the LS(gau) case, one of the butyl chains was rotated to an anti conformation and all the atomic coordinates were allowed to relax while keeping the cell parameters obtained from a previous variable-cell optimization in which no butyl chain was manually rotated to an anti conformation.  Table 1. Selected structural parameters for the SBP π-dimers present in (a) the X-ray crystal structures of butyl-SBP at two different temperatures and the corresponding structural parameters obtained upon geometry optimization of these SBP π-dimers in their 1 A g and 3 A u states in (b) solid-state and in (c) gas-phase conditions. All distances are given in Angstrom.  a D refers to the interplanar distance between the superimposed PLYs. D has been measured as the distance between the central carbon (i.e., the carbon atom shared by the three fused benzene rings) of the two superimposed PLYs.