Bistability in Organic Magnetic Materials: A Comparative Study of the Key Differences between Hysteretic and Non-hysteretic Spin Transitions in Dithiazolyl Radicals

A Journal of

Accepted Article

Title: Bistability in organic magnetic materials. A comparative study of

the key differences between hysteretic and non-hysteretic spin

transitions in dithiazolyl radicals

Authors: Sergi Vela, Michael B. Reardon, Charles E. Jakobsche, Mark

M. Turnbull, Jordi Ribas, and Juan J. Novoa

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To be cited as: Chem. Eur. J. 10.1002/chem.201700021

Link to VoR: http://dx.doi.org/10.1002/chem.201700021

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Bistability in organic magnetic materials. A comparative study

of the key differences between hysteretic and non-hysteretic

spin transitions in dithiazolyl radicals

Sergi Vela^[a,c], Michael B. Reardon^[b], Charles E. Jakobsche^[b], Mark M.

Turnbull^[b], Jordi Ribas-Arino*^[a]and Juan J. Novoa*^[a]

^[a]Departament de Ciència de Materials i Química Física, Universitat de

Barcelona and IQTCUB, Av. Diagonal 645, 08028 Barcelona (Spain)

^[b]Carlson School of Chemistry & Biochemistry, Clark University, 950 Main

Street, Worcester, MA 01610, USA

[c]

Laboratoire de Chimie Quantique, Institut de Chimie, UMR 7177, CNRS-

Université de Strasbourg, 1 Rue Blaise Pascal, 67000 Strasbourg, France

* j.ribas@ub.edu, juan.novoa@ub.edu

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Abstract

Dithiazolyl (DTA)-based radicals have furnished many examples of organic spin-

transition materials, some of them occurring with hysteresis and some others without.

Here, we present a combined computational and experimental study aimed at

deciphering the factors controlling the existence or absence of hysteresis by comparing

the phase transitions of 4-cyanobenzo-1,3,2-dithiazolyl and 1,3,5-trithia-2,4,6-

triazapentalenyl radicals, which are prototypical examples of non-bistable and bistable

spin transitions, respectively. Both materials present low-temperature diamagnetic and

high-temperature paramagnetic structures, characterized by dimerized (···A-A···A-

A···)_nand regular (···A···A···A···A···)_nπ-stacks of radicals respectively. We show that

the regular π-stacks are not potential energy minima but average structures arising

from a dynamic interconversion between two degenerate dimerized configurations:

(···A-A···A-A···)_n (-A···A-A···A-)_n. The emergence of this intrastack dynamics upon

heating gives rise to a second-order phase transition that is responsible for the change

in the dominant magnetic interactions of the system. This suggests that the promotion

of a (···A-A···A-A···)_n (-A···A-A···A-)_ndynamics is a general mechanism for

triggering spin transitions in DTA-based materials. Yet, this intrastack dynamics does

not suffice to generate bistability, which also requires a rearrangement of the

intermolecular bonds between the π-stacks via a first-order phase transition.

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Introduction

Research in bistable molecule-based magnets (that is, crystals of radicals presenting

two polymorphic forms that feature different magnetic properties within a range of

temperatures, called the bistability range) has generated a great deal of attention in

recent years in view of their potential as nano-devices that could be used as sensors

and memory storage units in molecular electronics and spintronics.^1,2The achievement

of a deep understanding of the features governing the existence of bistability is a

necessary step towards the rational design of new bistable materials. Let us mention

that bistability is merely a shorter form for naming hysteretic spin-switch systems. In

non-hysteretic spin-switch systems, crystals can be obtained in their low-temperature

(LT) polymorph or high-temperature (HT) polymorph depending on the temperature, T:

(a) above the spin-transition temperature (T_c) (i.e, at T > T_c) all crystals transform into

the HT polymorph, and (b) below the spin-transition temperature (i.e, at T < T_c) all

crystals transform into the LT polymorph. However, in hysteretic spin-switch systems,

the LT  HT transition takes place at a different temperature than that of the HT  LT

transition. If we denote these two different transition temperatures by T_cand T_c,

respectively, there is a range of temperatures comprised between T_cand T_c(known

as the bistability region) in which both the HT and LT phases can exist depending on

the history of the system. At T < T_c, only the LT polymorph exists, while at T > T_conly

the HT polymorph exists. Bistable materials based on transition-metal complexes have

been associated with spin transitions for many years ^{3 , 4 , 5}, but recent work has

demonstrated that purely-organic radicals can also be versatile building blocks to

achieve bistability^{6,7,8,9,10,11,12,13,14,15,16,17}

.

Among the purely organic radicals exhibiting spin-switch behavior, the family of

dithiazolyl (DTA) neutral radicals^{18 , 19}is particularly interesting, as it has furnished

numerous switchable materials, some of them presenting hysteretic phase

20

transitions^{6,7,10,11,12,16,}

, and some of them presenting non-hysteretic phase

transitions^21,22. It is worth mentioning that the closely related family of dithiadiazolyl

radicals has most recently furnished two examples of non-hysteretic spin transition

compounds.^23,24Among the group of bistable DTA radicals, the case of 1,3,5-trithia-

2,4,6-triazapentalenyl (TTTA) is especially remarkable, since its bistability region spans

70 degrees and encompasses room temperature (T_c= 310K, T_c= 230

K)^{7,25,26,27,28,29,30,31,32,33,34,35}(Figure 1a). The crystal structure of the 4-cyanobenzo-1,3,2-

dithiazolyl radical (4-NCBDTA, hereafter referred to as 1, see Figure 1b), in turn, is a

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prototypical example of a DTA-based crystal featuring a non-hysteretic spin transition²¹.

Its phase transition occurs at T_c= 250 K, a temperature in between the T_cand T_c

values of TTTA. Last, it should be mentioned that in the DTA family there are also

radicals, such as the [1,2,5]thiadiazolo[3,4-f][1,3,2]benzodithiazol (TBDTA) radical¹²

(see Figure 1c), whose crystaline samples do not show any magnetic phase transition.

In previous works^32,34,35, we have revealed key aspects of the physical and structural

properties of TTTA as well as of the nature of its magnetic phase transition:

a) The different magnetic response of the LT and HT phases of TTTA originates in the

different ways in which the TTTA radicals pile in each polymorph. The columns of

radicals of LT(TTTA) are distorted π-stacks that comprise π-dimers, i.e., pairs of nearly

eclipsed radicals. Conversely, the columns of HT(TTTA) are regular π-stacks of

radicals where each molecule exhibits a slipped overlap with its two adjacent

molecules along the stacking direction. The dominant magnetic interactions in both

polymorphs are found within the π-stacks. The very strong antiferromagnetic coupling

between the spins of the two radicals forming the π-dimers of the LT(TTTA) phase

explains the diamagnetism of this phase. The moderate antiferromagnetic coupling

between adjacent radicals in the regular stacks of HT(TTTA), in turn, accounts for the

reduced paramagnetism of this phase.

b) The dimerized stacks of LT(TTTA) correspond to a minimum energy structure in the

potential energy surface (PES) of the system. In contrast, a full geometry optimization

of the experimental crystal structure of HT(TTTA) led to an intrastack dimerization

process. Yet, the resulting dimerized minimum structure is different from the structure

of the LT polymorph because it features different interstack contacts.

c) The PES of a stack of TTTA radicals obeys a periodic double-well model (Figure

1d), where each of the wells represents one of the two equivalent dimerized

configurations (···A-A···A-A···)_nand (-A···A-A···A-)_n(in which A-A represents an

eclipsed pair and A···A represents the interaction between adjacent eclipsed pairs) and

the transition state separating these two wells represents the regular structure

(···A···A···A···A···)_n. At low temperatures, the motion of the molecules within the

columns is restricted to one of the two wells, while at higher temperatures, the

molecules populate higher vibrational levels and eventually achieve enough energy to

overcome the energy barrier. When this happens, the stacks explore both sides of the

double well and continually hop from one well to the other one. This means that each

TTTA radical continually exchanges (in the picosecond timescale) the adjacent

neighbor (upper or lower) with which it forms a dimer. As a result of this particular

dynamics, which was called Pair Exchange Dynamics (PED)³⁴, the regular structure

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(···A···A···A···A···)_nbecomes the most probable configuration (Figure 1d) and, thus, is

the one observed by X-ray crystallography.

d) While the stacks of HT(TTTA) exhibit PED at T > 200 K (i.e, within the bistability

region of TTTA), the stacks of LT(TTTA) remain dimerized over the whole range of

temperatures up to at least 310 K. The PED of the HT phase results in a large

vibrational entropy, which stabilizes this polymorph (with respect to the LT polymorph)

at finite temperatures. Therefore, the PED is a driving force of the LT  HT phase

transition.

Despite the relevance of the above mentioned findings, there is one key aspect of the

phase transition of TTTA that still remains poorly understood, namely, the origin of the

hysteresis. In broader terms, the key factors controlling the existence or absence of

hysteresis in the spin transitions of the different DTA-based switchable compounds are

still largely unknown, thereby precluding a rational design of new DTA-based bistable

materials. The work herein presented aims to shed light on this important issue by

means of a combined computational and experimental work in which the properties

and phase transition of a prototypical example of a DTA crystal undergoing a non-

hysteretic spin transition are compared with those of a prototypical example of a

bistable DTA crystal. Specifically, we will thoroughly analyze the magnetic response,

the structural properties and the nature of the phase transition of 4-NCBDTA (1) and

compare them with those of TTTA. This comparison, which is based on a

computational study and new experiments designed to validate the theoretical

predictions, will explain why TTTA is bistable while 1 is not and will bring to light the

idea that the promotion of PED is a general mechanism to induce spin transitions in

DTA-based crystals (and very likely in crystals of other organic radicals presenting π-

stacks), although this mechanism by itself does not suffice to generate bistability.

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Results and Discussion

The presentation of the results is organized as follows. We will first analyze the crystal

packing of the two phases of 1 (Subsection 1). Second, we will investigate the

microscopic origin of the different magnetic properties of the two phases of 1

(Subsection 2). Then, we will explore the potential energy surface of 1 and will

establish whether or not its phases correspond to minimum energy structures

(Subsection 3). After that, we shall examine the dynamics exhibited by the radicals in

the two phases of 1 and establish the nature of its phase transition (Subsection 4).

Following this, we will present experimental evidence based on magnetic and

differential scanning calorimetry measurements that supports the computational results

of the preceding subsections (Subsection 5). Finally, we will compare the properties

and phase transitions of 4-NCBDTA and TTTA in order to understand why only the

latter exhibits bistability (Subsection 6).

1. Crystal packing analysis of the LT and HT polymorphs of 4-NCBDTA

The analysis of the crystal packing of the LT and HT polymorphs of 1 was carried out

using the previously-reported crystal structures refined at 180 K (1-180K structure) and

at 300 K (1-300K structure), respectively²¹. In both polymorphs, the radicals (A) pile on

top of each other giving rise to π-stacks. As in the TTTA case, the π-stacks of the LT

polymorph are distorted or dimerized stacks that present an alternation between

eclipsed and slipped pairs of radicals (Figure 2). If we denote the eclipsed pairs or π-

dimers by A-A, the dimerized stacks can be schematized as (···A-A···A-A···)_n. Note

that the dimerized stack can also be represented by the following isoenergetic

configuration: (-A···A-A···A-)_n. The stacks of the HT polymorph of 1, in turn, are regular

π-stacks, where each molecule exhibits a slipped overlap with its two adjacent

molecules along the stacking direction (Figure 2). This regular stacking motif, which

can be schematized as (···A···A···A···A···)_n, is analogous to that found in the HT phase

of TTTA.

2. Magnetic properties of the LT and HT polymorphs of 4-NCBDTA

Given that the phase transition of 1 entails changes in the magnetic properties of the

compound, it is important to identify the origin of these changes. In order to understand

the different magnetic properties of 1 upon phase transition, we computed the value of

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the magnetic exchange coupling (J) between pairs of radicals after excising them from

the 1-180K and 1-300K crystal structures. According to our calculations (see Table 1

and Figure 3), the eclipsed pairs of LT(1) and the slipped pairs of HT(1) display strong

antiferromagnetic couplings of ca. −1700 cm⁻¹and ca. −340 cm⁻¹, respectively (similar

to those computed for the two phases of TTTA^32,35). These values are in agreement

with the diamagnetic and weak paramagnetic response (reduced paramagnetism)

observed, respectively, for the LT and HT phases of 1. On the other hand, it was found

that the exchange couplings between radicals belonging to different stacks are much

smaller than the couplings within the stacks (Table 1), thus showing that the dominant

magnetic interactions in 1 occur along the π-stacks. Therefore, the change in the

magnetic response of 1 upon phase transition can be traced to the structural changes

in the π-stacks, a scenario that is completely analogous to that found in the TTTA

case.

3. Optimum structure of the LT and HT polymorphs of 4-NCBDTA

Variable-cell geometry optimizations of 1 starting from the atomic coordinates and

lattice parameters of the previously reported 1-180K and 1-300K crystal structures

were carried out in order to establish whether the LT and HT polymorphs are minimum

energy structures in the potential energy surface of the crystal. The model system

employed in our calculations, which was designed to represent the LT and HT crystals

on an equal footing, was a supercell containing sixteen 4-NCBDTA radicals, arranged

in 4 columns of 4 molecules each (see Supporting Section S1).

The geometry optimizations of both the LT and HT polymorphs ended in the same

optimized structure, which we label as 1-0K, since the minimum-energy structures can

be understood as the 0-K crystal structure. As shown in Figure 4 (see also Table S1),

1-0K preserves the eclipsed π-dimers and is in excellent agreement with the 1-180K

crystal structure. The fact that the optimization starting from 1-300K resulted in an

intrastack dimerization process that produced the same 1-0K structure demonstrates

that the regular stacking motif observed for the HT phase does not correspond to a

minimum in the PES of the system. Although the HT phase of TTTA was also found not

to be a minimum in the PES³⁴there is a crucial difference between TTTA and 1. In the

former, each phase (LT and HT) has a different optimized minimum-energy structure

(the two phases differ in the relative orientation of the TTTA radicals and in the

interstack contacts), whereas the two phases of 1 have the same optimized minimum-

energy structure.

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4. Dynamics of the LT and HT polymorphs of 4-NCBDTA

To assess the importance of vibrational entropy in the structures of 4-NCBDTA (1), we

conducted ab initio molecular dynamics (AIMD) simulations at 180, 240, 260 and 300

K, in the canonical ensemble using the Car-Parrinello propagation scheme.³⁶It is worth

mentioning that this computational strategy has been successfully used in the past to

characterize the magnetic and structural properties of other organic radicals^35,37

.

The average structure obtained from the AIMD simulations at 300 K is very close to the

regular structure observed by X-ray crystallography at this temperature (Figure 2a and

Figure 4d) including the uniform separation of the molecules of 1. The good agreement

between the computed and experimental structures, together with the good agreement

between the computed and experimental thermal ellipsoids (see Supporting Section

S.2.1), validates the choice of the model system and the AIMD simulations performed

to investigate the dynamical properties of 1. The regular stacks obtained when

considering the thermal fluctuations suggest that PED is operative at this temperature.

The time-resolved evolution of the centroid-centroid distance (d_CM) between

neighboring molecules (shown in Figure 5) confirms that this is indeed the case. Such

time-resolved evolution shows that each pair of molecules presents roughly the same

kind of intermolecular vibrations, in terms of their amplitude (ca. 1 Å) and of their mean

value (ca. 3.68 Å), which indicates that the three pairs of the stack are equivalent. Our

results thus show that the regular stacks observed in the 1-300K crystal structure are

the average structures resulting from an intrastack (···A-A···A-A···)_n (-A···A-A···A-)_n

dynamics whereby eclipsed π-dimers between radicals are continually formed and

broken on the picosecond timescale. Compound 1 is the second example of a DTA

radical (the first one was TTTA) whose HT phase has been shown to exhibit PED. This

strongly suggests that such PED is a general phenomenon within the family of

switchable DTAs. It should also be mentioned that the timescale in which the PED

occurs in the HT phase of 1 at 300 K coincides with the timescale associated with the

PED in the HT polymorph of TTTA at the same temperature.

At 180 K, the average structure obtained from the AIMD simulations, which is in

excellent agreement with the 1-180K crystal structure, displays the common alternation

of eclipsed and slipped pairs, the former type having shorter inter-radical N-N distances

than the latter (Figure 2b and Figure 4c). As shown in Figure 5, the intermolecular

vibrations of the eclipsed pairs can easily be distinguished from those of the offset pair

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since the corresponding d_CMvalues oscillate around a different average value.

Therefore, the eclipsed π-dimers are preserved over the whole AIMD trajectory, that is

to say, the PED is inactive at this temperature. The good agreement between the

computed and experimental thermal ellipsoids (see Supporting Section S2.1) fully

supports our results. The average structure of the stacks obtained from the AIMD

simulations run at 240 and 260 K (i.e., at temperatures slightly below and slightly

above the previously reported spin-transition temperature²¹) is different depending on

the stack of molecules that we analyze. Two columns display a totally dimerized

configuration similar to that of 1-0K, whereas the other two display a nearly-regular

arrangement (see Supporting Section S2.2), which indicates that some PED events

have occurred along the simulations. This also suggests that the change in the

dynamics of one stack upon heating/cooling occurs independently of the adjacent

stacks.

The presence of PED processes in 1 can be further analyzed on the basis of the 2-

dimensional pair-distribution functions (2D-PDF) associated with the interplanar

distance (d_ip) and the relative slippage (d_sl) (see Figure 6 and also Supporting Section

S2.3) These variables decompose the centroid-centroid distance (d_CM) between

neighboring molecules, and allow for a precise analysis of the thermal fluctuations

undergone by 1 (see Section S3.2 for an extended analysis). The 2D-PDF of our AIMD

simulation at 180 K presents two peaks. The left-hand side peak corresponds to the

eclipsed pair, and the right-hand side one corresponds to the slipped pair. The

presence of these two well-defined peaks is fully consistent with the absence of PED at

this temperature (Figure 5a) and the dimerized average structure obtained from the

AIMD simulations at 180 K. As the temperature is increased to 240 and 260 K, the two

peaks broaden and slightly overlap, which is the result of larger-amplitude oscillations

and some pair-exchange events. Finally, at 300 K the PED is fully operative (Figure 5b)

and, as a result, the two peaks completely merge into a single broad peak, which

indicates that the most-probable structure is the regular stack of radicals (Figure 4d).

The evolution of the 2D-PDFs displayed in Figure 6, which is similar to that observed

for the monoclinic polymorph of TTTA³⁴, reveals that the activation of the PED is a

gradual process that entails an order-disorder transition within the π-stacks.

Both the order-disorder transition of 4-NCBDTA crystal and the results obtained upon

optimization of its two polymorphs can be rationalized on the basis of the energy profile

displayed in Figure 7, which shows the variation of the potential energy of an isolated

π-stack of 4-NCBDTA radicals (considering periodic boundary conditions along the

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stacking direction) as an intrastack dimerization process takes place. The shape of this

profile is that of a double-well model potential, where the two minima correspond to two

degenerate dimerized configurations and the maximum to the regular structure

observed at 1-300K crystal structure. This profile demonstrates that the regular

stacking motif is not a minimum energy structure in the PES of the system. It also

shows that the PED arises from a dynamic interconversion between two degenerate

dimerized stacks that takes place when the system has enough thermal energy to

overcome the barrier separating these two dimerized stacks.

The gradual activation of the PED process observed for 1 strongly suggests that the

phase transition undergone by this material is a second-order phase transition (i.e, a

gradual transition without an abrupt release of thermal energy and without significant

thermal hysteresis). However, this conclusion is in contradiction with the abrupt

variation observed in the magnetic susceptibility curve of 1 at 250 K in Ref. 21, which

suggests that the phase transition of this crystal should be first-order. In order to

address this contradiction, the temperature-dependence of the magnetic susceptibility

of 1 was re-measured under thermal equilibration conditions and differential scanning

calorimetry (DSC) experiments were conducted. The results of these new experiments

will be presented in the next subsection.

5. Experimental confirmation of the theoretical predictions of the phase

transition of 4-NCBDTA

As mentioned above, the final step of our study was aimed at checking the validity of

the most relevant theoretical conclusions drawn for compound 1. For such a task, a

sample of 4-NCBDTA was synthesized and crystallized, using procedures slightly

modified from those reported in the literature²¹(see Supporting Section S3). X-ray

powder diffraction experiments at 180 and 300 K showed that the high and low

temperature phases are in good agreement with the previously reported unit cells and

structures (see Supporting Section S4). In fact, single-crystal diffraction analysis (see

Supporting Section S5) confirms that the high- and low-temperature phases of 4-

NCBDTA obtained in this work correspond to the previously reported structures²¹. In

addition, EPR and HRMS data are also consistent with the expected molecular formula

and nitrogen-centered radical (see Supporting Section S3 and Supporting Section S6).

The magnetic susceptibility of a polycrystalline sample of 1 was collected every 5 K in

the 225-305 K range by cooling from room temperature and then warming the sample

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back to room temperature (Figure 8a and Supporting Section S7). Special care was

payed to make sure that thermal equilibration was achieved at each temperature

before collecting the value of the magnetic susceptibility. In addition, the sample was

recentered before each data point was collected through the region of the transition.

The data thus obtained (Figure 8a) clearly shows a gradual, non-abrupt phase

transition in the 260–272 K temperature range with minimal, if any, hysteresis. As

expected, the magnetic susceptibility value becomes negative as the LT material

becomes fully diamagnetic. Both the gradual nature of the transition and the

temperature range in which it occurs are in good agreement with the predictions of the

2D-PDF analyses discussed above, thus supporting our conclusion that the phase

transition of 1 is second order.

In order to obtain an independent evaluation of the first or second order nature of the

phase transition of 1, DSC experiments were also performed over the 240 to 305 K

range. The DSC curves were obtained at three cooling/heating rates. As shown in

Figure 8b (see also Supporting Section S8), in all three DSC curves the phase

transition was observed in the 260-272 K range, which is fully consistent with the

temperature range observed in the new magnetic susceptibility measurements. Unlike

a first-order phase transition (which would be expected to produce an abrupt

release/absorbance of thermal energy at the transition temperature), a smooth release

of thermal energy is observed, thus providing an independent experimental

confirmation that the magnetic phase transition of 1 is second order.

To conclude this subsection, let us mention that the phase transition of 4-NCBDTA can

be classified as a spin-Peierls transition because it involves the transformation of

regular S=1/2 antiferromagnetic chains into dimerized stacks presenting an alternating

exchange coupling between adjacent spins. However, the phase transition of this

material features some unique characteristics (the absence of a minimum energy

structure in the PES associated with the regular stacking motif, the presence of a PED

process in the high-temperature phase and the fact that it is an order-disorder

transition) that are nor shared by all spin-Peierls-type transitions. For this reason, the

use of the PED and order-disorder concepts allows for a better description of the

nature of the phase transition of 4-NCBDTA.

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6. Rationalizing the different nature of the phase transitions of TTTA and 4-

NCBDTA

The results so far presented provide solid evidence that the non-hysteretic spin

transition of 4-NCBDTA is a second order phase transition. Such a second-order phase

transition is in contrast with TTTA, whose hysteretic spin transition is first-order. In

order to understand why the nature of the phase transition of these two compounds is

different, let us first recapitulate their main common characteristics:

a) The LT polymorphs of both materials present dimerized π-stacks, while the

corresponding HT polymorphs exhibit regular π-stacks.

b) The LT polymorphs of both materials present very strong antiferromagnetic

interactions within the π-stacks, which are responsible for the diamagnetic character of

these crystals. Conversely, in the corresponding HT polymorphs, the intrastack

exchange interactions become much weaker and are responsible for the dominant, but

weak, paramagnetic character of these two crystals.

c) The HT polymorphs of the two compounds are not minimum energy structures in the

PES of the crystal. The regular stacking motifs of these polymorphs are the average

structures resulting from PED processes, which are operative above the spin-transition

temperatures. The PED mechanism is the source of a large vibrational entropy that

stabilizes the HT polymorphs above the spin-transition temperature.

The common characteristics between 4-NCBDTA and TTTA provide evidence that in

DTA-based materials the thermal promotion of an intrastack PED process constitutes a

general mechanism to trigger both hysteretic and non-hysteretic spin transitions.

However, the existence of a PED process in a DTA compound is not sufficient to

determine whether a spin transition occurs with or without hysteresis.

In order to identify what controls the presence or absence of bistability in a spin

transition of a DTA crystal, we need to focus on the differences between 4-NCBDTA

and TTTA. The key difference between these two materials is that the former requires

only a single, intrastack stuctural transition (via PED), while the latter requires the

same intrastack change plus the addition of an interstack rearrangement (Figure 9).

The optimized, dimerized minimum potential energy structure of 4-NCBDTA at 0 K,

regardless of whether the optimization starts from the experimentally observed HT or

LT phase, corresponds to the experimentally observed LT phase. In the optimization

beginning from the observed, regular, HT phase, a barrierless, intrastack dimerization

process is observed. This requires only a change in the intrastack intermolecular

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distances and does not require a change in the interstack interactions; it is a fully

reversible process that leads to two degenerate structures. It is critical to note that the

potential energy surface relevant to the phase transition exhibits only two energetically

and topologically equivalent miniumum energy structures. Therefore, the spin transition

observed in 4-NCBDTA can be described based upon a temperature dependent

change in the free energy surface, resulting from an order/disorder transition as shown

in Figure 1d.

Conversely, in TTTA the scenario is more complex because it requires two distinct

types of structural transformations: an intrastack and an interstack (Figure 9a)

transformation. The optimized, dimerized structure of TTTA, beginning from the

observed LT, triclinic packing structure, corresponds to that experimentally observed

LT phase. In contrast, as shown in Ref. 34, the optimized, dimerized structure

beginning from the experimentally observed, regular, HT monoclinic phase, does not

correspond to the observed LT structure, nor to any experimentally observed phase of

TTTA. During the optimization beginning from the HT phase, a barrierless, intrastack

dimerization process is observed which again requires only a change in the

intermolecular, intrastack distances, exactly as was observed in the case of 4-

NCBDTA. Since this optimized, dimerized structure shows distinct interstack

interactions compared to the experimentally observed LT phase, we can conclude that

the interstack rearrangement upon phase transition of TTTA necessarily implies the

presence of an energetic barrier, which is the origin of the observed bistability.

Therefore, the critical observation in TTTA is the requirement for both the intrastack

transformation as observed previously in 4-NCBDTA and a non-degenerate interstack

rearrangment (Figure 9a). which connects two distinct crystal structure minima and is

responsible for the hysteresis and the first-order character of its phase transition.

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Conclusions

In the study herein presented, which is based on a joint effort between theory and

experiment, we have carried out an exhaustive analysis of the phase transitions of

prototypical examples of DTA radicals undergoing both hysteretic and non-hysteretic

spin transitions between LT diamagnetic and HT paramagnetic phases. The

mechanism of Pair Exchange Dynamics (PED), that is, the averaging of structures

arising from a dynamic interconversion between two equivalent dimerized

configurations, illustrated as (···A-A···A-A···)_n (-A···A-A···A-)_n, is operative in the

high temperature phases of these systems resulting in uniform spacing within the

radical stacks. At high temperatures, these uniform stacks constitute a minimum in the

free energy of the system as a result of entropy contributions, although they are not a

minimum in the potential energy surface. The theoretical results herein reported predict

that the phase transition that connects the HT and LT phases of 4-NCBDTA is gradual

and second order rather than abrupt and first order. Experimental results using DSC

and magnetic susceptibility analyses show that compound 1 does indeed undergo a

non-abrupt second-order phase transition as a result of the onset of a PED process.

The combination of the theoretical and experimental results demonstrates that the

entire transition can be described by a single potential energy surface.

The second-order transition of 4-NCBDTA is in contrast to what is observed for TTTA,

whose phase transition exhibits a large and abrupt heat change that is characteristic of

a first-order transition²⁶. In TTTA, the onset of an intrastack PED process is

accompanied by an interstack structural rearrangement resulting in a system which

crosses between two distinct minima with an associated energy barrier. This is

responsible for the observed hysteresis and accounts for the difference between the

behaviours of 4-NCBDTA and TTTA.

The fact that both compounds present the same kind of intra-stack thermal vibrations

(ie. PED) suggests that the PED process is a common feature in the DTA family of

radicals. The PED process will likely prove to be a key concept to rationalize not only

the properties of other DTA-based materials undergoing hysteretic spin transitions but

also the gradual variation of the magnetic susceptibility of other DTA radicals featuring

π-stacks (e.g. the quinoxaline-1,3,2-dithiazolyl radical³⁸and the  polymorph of the

pyridyl-1,3,2-dithiazolyl radical³⁹). Overall, it becomes now clear that the initiation of a

PED process and the concomitant gradual second-order phase transition is sufficient to

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endow DTA organic radicals with spin-switching properties. Notwithstanding the great

potential of the activation of a PED process as an effective tool to design new

switchable materials, it should be taken into account that this type of transition, that

occurs in isolated regions of the structure (i.e. within the stacks), does not suffice to

generate a region of bistability. The opening of a hysteresis loop calls for the presence

of two distinct energy minima and a barrier to the interconversion between them which

is required for the presence of bistability in the DTA family.

The potential application of these studies to the rational design and analysis of such

molecules, and switchable magnetic materials in general, is clear. Future studies

should explore how the onset of a PED process can be tuned by means of

intermolecular interactions (both intra- and inter-stack) to control the nature and

temperature of the spin transition. One of the main factors governing the onset of the

PED is the strength of the long, multicenter bond (alternatively called pancake bond⁴⁰)

between DTA radicals in the π-dimers. In this respect it should be mentioned that the

large impact of small geometrical changes on the strength of long, multicenter bonds

between planar organic radicals^24,41,42bodes well for the design of new switchable

DTA-based materials with a large variety of spin-transition temperatures. In addition,

investigations to determine how broadly applicable the initiation of a PED process may

be in related materials featuring stacks of planar organic radicals are in progress.

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Methods

The description of the methodology employed in this article is organized as follows. We

will first describe the computational methodology employed to obtain the results

presented in subsections 3.2, 3.3 and 3.4 of the Results and Discussion. After that, we

will detail the methodology employed in the experimental part of the work.

Computational Details

i) Evaluation of the magnetic exchange couplings (subsection 3.2 of Results and

Discussion)

The J values of the radical pairs of the X-ray crystal structures were computed at the

UB3LYP⁴³/6-31+G(d)⁴⁴level as implemented in Gaussian 09⁴⁵by using the isotropic

푁

퐴,퐵

̂

̂ ̂

퐽_퐴퐵· 푆_퐴· 푆_퐵. The Broken-Symmetry (BS)

∑

Heisenberg Hamiltonian, 퐻 = − 2

approach has been used to properly describe the open-shell low-spin (singlet) state

(퐽_퐴퐵= 퐸^퐵푆,푆− 퐸^푇).

ii) Optimum structure of the LT and HT polymorphs of 4-NCBDTA (subsection 3.3 of

Results and Discussion)

Plane wave pseudopotential calculations were employed for the variable-cell geometry

optimizations of 1. These calculations, in which the atomic positions and the lattice

parameters were optimized simultaneously, were carried out using the PBE exchange–

correlation functional⁴⁶within the spin unrestricted formalism, together with Vanderbilt

ultrasoft pseudopotentials ⁴⁷and gamma-point sampling of the Brillouin zone as

implemented in the QUANTUM ESPRESSO package⁴⁸. In these calculations, the

49

semiempirical dispersion potential introduced by Grimme

was added to the

conventional Kohn–Sham DFT energy in order to properly describe the van der Waals

interactions between the different 4-NCBDTA molecules. The parametrization

employed in our work is the so-called DFT-D2 parametrization. It is noted that a series

of recent benchmark calculations have shown that the use of PBE together with the

Grimme furnishes good predictions for the structure and cohesive energies of

molecular crystals.⁵⁰Indeed, the PBE-D2 scheme has already been shown to provide a

difference in cohesive energies between the two polymorphs of TTTA that is in good

accordance with the experimental data.³⁵The plane wave basis set was expanded at a

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kinetic energy cutoff of 70 Ry. The number of plane waves was kept constant

throughout the variable-cell relaxations. A constant number of plane waves implies no

Pulay stress but a decreasing precision of the calculation as the volume of the

supercell increases. The large cutoff employed in these calculations ensures that the

artefacts arising from this change of precision are negligible.

iii) Dynamics of the LT and HT polymorphs of 4-NCBDTA (subsection 3.4 of Results

and Discussion)

The Car-Parrinello molecular dynamics simulations of 4-NCBDTA were carried out with

the CPMD package⁵¹. These calculations were also done using the PBE exchange–

correlation functional⁴⁶within the spin unrestricted formalism, together with Vanderbilt

ultrasoft pseudopotentials⁴⁷and gamma-point sampling of the Brillouin zone. 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 Nose-Hoover chain of thermostats⁵²in order to control the

kinetic energy of the nuclei and the fictitious kinetic energy of the orbitals.

The potential energy profile displayed in Figure 7 has been computed with CPMD

using the same setup as that employed in the molecular dynamics simulations.

Experimental methodology

i) Magnetic Susceptibility Data

Magnetic susceptibility data were measured using a freshly sublimed batch of radical 1

on a Quantum Design MPMS-XL SQUID magnetometer. A sample of 1 was packed

into a #3 gelatin capsule and mounted in the SQUID. Susceptibility data were taken

over the temperature range from 290 K to 249 K and then back to 274 K in an applied

field of 5000 Oe. To ensure accuracy of the data, the sample's temperature was moved

towards each target temperature at a slow rate of 2 K/min and then allowed equilibrate

until it had stabilized within +/– 0.2 K of the target temperature before each data point

was collected. The data were corrected for the background signal of the sample holder,

and for the diamagnetic contributions of the constituent atoms (estimated using

Pascal’s constants, which were taken from Ref. 53).

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ii) Differential Scanning Calorimetry

DSC analysis of radical 1 was performed with freshly sublimed material with careful

exclusion of moisture. Data was collected on a Perkin Elmer DSC 7 with Pyris

9.0.2.0193 software.

Supporting Information

Crystal structure data in CIF format for the LT and HT phases of 4-NCBDTA (these

structures have been deposited in the CCDC with deposition numbers 1524306 and

1524307). The Supporting Information also includes: detailed information on the model

system employed in the computational studies, an extended analysis of the AIMD

trajectories, the synthetic procedure used to obtain 4-NCBDTA, analysis of the powder

diffraction X-ray data, an analysis of the single-crystal X-ray data, EPR data, magnetic

susceptibility data and differential scanning calorimetry data.

Acknowledgements

We acknowledge the Spanish Government for financial support (Projects MAT2011-

25972 and MAT2014-54025-P) and BSC and CSUC for the allocation of massive

computer time. S.V. is thankful to the LabEx-Chemistry of Complex Systems for a post-

doctoral grant (ANR-10-LABX-0026CSC). Funding for the experimental portions of this

work was provided by Clark University's faculty startup funds for CEJ. We would also

like to thank Professor Fred Greenaway for assistance with electron paramagnetic

resonance data collection, and Peter Müeller for assistance with powder diffraction X-

ray data collection. Finally, we are thankful to the Catalan DURSI (Grant

2014SGR1422).

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a)

b)

c)

d)

Figure 1. (a) Molecular structure of the TTTA radical and scheme of the main characteristics of

its phase transition. (b) Molecular structure of the 4-NCBDTA radical and scheme of the main

characteristics of its phase transition. (c) Molecular structure of the TBDTA radical, which does

not undergo any spin transition. (d) Scheme showing the temperature dependence of the free

energy profile of one column of TTTA radicals with respect to an intrastack dimerization

process.

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(a) 1-300K

(b) 1-180K

Figure 2. Top- and side-views of the experimental structure of the HT (a) and LT (b)

polymorphs of 1. The X-rays structure of HT was determined at 300 K, while that for LT was

obtained at 180 K. The distances displayed in the Figure correspond to the distances between

the N atoms of the S-N-S moieties of adjacent radicals.

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LT (1-180K)

HT (1-300K)

J = -342

J = -83

J = -342

J = -1723

J = -83

J = -342

Figure 3. Magnetic exchange couplings along the π-stacks of the LT and HT polymorphs of 1.

All the values of J are given in cm^-1.

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a)

b)

c)

d)

Figure 4. Structure of a stack of 1-0K after the variable-cell geometry optimization starting from

the 1-180K structure (a) and starting from the 1-300K structure (b). Average structure of a stack

along the AIMD trajectory at 180 K (c) and 300 K (d). The distances displayed in the Figure

correspond to the distances between the N atoms of the S-N-S moieties of adjacent radicals. In

the dimerized structures shown in (a), (b) and (c), the N-N distances marked in blue and red

correspond to the eclipsed and slipped pairs, respectively.

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(a) 180 K

(b) 300 K

Figure 5. Time-resolved evolution of the centroid-centroid distance (d_CM) between adjacent

molecules of 1 along the AIMD-trajectories at (a) 180 and (b) 300 K.

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Figure 6. 2D-PDF’s associated with the interplanar distance (d_ip) and the relative slippage (d_sl)

between adjacent molecules of 1 along the AIMD-trajectories at 180 K, 240 K, 260 K and 300 K

(from left to right)

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Figure 7. Potential energy profile of an isolated stack of 4-NCBDTA radicals along the reaction

coordinate . This reaction coordinate, which is defined in the left-most scheme, describes a

sliding motion of the radicals that preserves the interplanar distance between them. The profile

has been computed with periodic boundary conditions along the stacking direction. The regular

structure shown at =0 corresponds to the 1-300K crystal structure.

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Figure 8. Experimental analysis of radical 1's phase transition. (a) Molar magnetic susceptibility

data and (b) differential scanning calorimetry data at different heating and cooling rates. The

small differences observed between the cooling and heating curves are within normal

experimental error when measuring magnetization values near zero. In the raw data, the

magnetization transitions from positive to negative at 265 K.

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a)

b)

Figure 9. Cartoon depicting the differences between the phase transition of TTTA (a) and 4-

NCBDTA (b). While the phase transition of 4-NCBDTA involves only an intrastack order-

disorder transition, the phase transition of TTTA involves both an intrastack order-disorder

transition and an interstack transformation.

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Table 1. Magnetic exchange couplings (J) between selected radical pairs, extracted from the

experimentally reported 1-180-K and 1-300-K crystal structures. Pairs can be identified using

the N-N distance between the N atoms of their S-N-S moieties.

1-180K

1-300K

d(N-N)^a/ Å

3.286

J / cm^-1

−1723.1

−82.57

d(N-N) / Å

3.665

J / cm^-1

−341.9

−5.0

3.961

3.284 (Interstack)^b

^aThe different pairs of radicals have been identified using the distance between the N atoms of their S-N-S

moieties, since this N atom is the atom that formally holds the unpaired electron of the radical. These d(N-

N) distances are displayed in Figure 2.

^bThis distance corresponds to the closest pair of interstack radicals found in the 1-300K structure.

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References

¹O. Kahn, C.J. Martinez, Science 1998, 279, 44–48

²O. Sato, Nat. Chem. 2016, 8, 644-656.

³Spin Crossover in Transition Metal Compounds I-III, P. Gütlich, and H. A. Goodwin, Ed. Top.

Curr. Chem., Springer-Verlag, Berlin, 2004, vol. 233-235.

⁴Spin-Crossover Materials-Properties and Applications; M.A. Halcrow, Ed.; John Wiley & Sons:

Hoboken, NJ, 2013.

⁵S. Brooker, Chem. Soc. Rev. 2015, 44, 2880-2892.

⁶T.M. Barclay, A.W. Cordes, N.A. George, R.C. Haddon, M.E. Itkis, M.S. Mashuta, R.T. Oakley,

G.W. Patenaude, R.W. Reed, J.F. Richardson, H. Zhang, J. Am. Chem. Soc. 1998, 120, 352-

360.

⁷W. Fujita, K. Awaga, Science 1999, 286, 261-262.

⁸D.A. Shultz, R.M. Fico Jr., P.D. Boyle, J.W. Kampf, J. Am. Chem. Soc. 2001, 123, 10403-

10404.

⁹M.E. Itkis, X. Chi, A.W. Cordes, R.C. Haddon, Science 2002, 296, 1443-1445.

¹⁰J.L. Brusso, O.P. Clements, R.C. Haddon, M.E. Itkis, A.A. Leitch, R.T. Oakley, R.W. Reed

and J.F. Richardson, J. Am. Chem. Soc. 2004, 126, 8256-8265.

29

Article Doi

Bistability in Organic Magnetic Materials: A Comparative Study of the Key Differences between Hysteretic and Non-hysteretic Spin Transitions in Dithiazolyl Radicals

DOI: 10.1002/chem.201700021

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