Origin of Bistability in the Butyl-Substituted Spirobiphenalenyl-Based Neutral Radical Material

TL;DR: The results show that coupling a spin switch with a conformational switch in a molecular crystal provides a promising strategy in the design of new bistable materials.

Abstract: One of the most remarkable bistable materials reported so far is made of π dimers of a butyl-substituted spirobiphenalenyl boron radical (butyl-SBP). The phase transition of this material, which is accompanied by changes in its optical, conductive, and magnetic properties, occurs with a hysteretic loop 25 K wide centered at 335 K. Herein, a computational study is presented aimed at deciphering the origin of this hysteresis. The phase transition of butyl-SBP consists of a spin transition of the constituent π dimers coupled with an order-disorder transition involving the butyl chains linked to the nitrogen atoms of the superimposed phenalenyl rings of the π dimer. Below 335 K, the terminal methyl group of the butyl chains adopts a gauche conformation with respect to the methylene unit bonded to the nitrogen atom. Above 335 K, the methyl group is in an anti conformation and exhibits dynamic disorder. The gauche→anti conformational rearrangement triggers the spin transition of the π dimers and is responsible for the hysteretic behavior of butyl-SBP. Specifically, the onset of the phase transition in the heating mode, and thus, the width of the hysteresis loop, are governed by the high energy cost and strong structural cooperative effects associated with this conformational change. Our results show that coupling a spin switch with a conformational switch in a molecular crystal provides a promising strategy in the design of new bistable materials.

Summary

Introduction

• Therefore, the studies aimed at elucidating the origin of these barriers and at establishing the role of cooperative effects have the potential to offer most valuable hints on how to devise new bistable materials with improved properties.
• Below the spin transition temperature, the structures of the πdimers are governed by the potential energy surface (PES) of the ground singlet state (1Ag 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 .

1) Phase transition of butyl-SBP: a spin transition coupled with a conformational

• The optimized structures of the LT and HT polymorphs were obtained by means of variable-cell geometry relaxations, in which the atomic positions and the lattice parameters are optimized simultaneously.
• A constant number of plane waves imply no Pulay stress but a decreasing precision of the calculation as the volume of the cell increases.
• The large cutoff employed in these calculations ensures that the artifacts arising from this change of precision are negligible.
• The starting atomic positions and initial lattice parameters for the relaxation of the LS(gau) and HS (anti) polymorphs were taken from the X-ray resolved structures of the LT and HT phases of 2 at 100 and 360 K, respectively.
• The optimizations of the isolated π-dimers of 2 (carried out with the goal of evaluating the gas-phase ΔEadia values) were also done with plane wave pseudopotential calculations using Vanderbilt ultrasoft pseudopotentials.

3) Driving forces of the phase transition of butyl-SBP. Order-disorder transition

• 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 vibrational frequencies in the condensed phase were calculated by means of a finite-difference normal-mode analysis of the optimized structures.
• It thus follows that the computational strategy has been properly set up.
• All dynamic simulations were performed in the canonical ensemble using   23   the Nosé-Hoover chain thermostats100 in order to control the kinetic energy of the nuclei and the fictitious kinetic energy of the orbitals.
• In the simulations of the LT phase, the electronic structure of the π-dimers was that corresponding to their singlet ground state.

4) Origin of the hysteresis and the coupling between the spin transition and the

• Conformational change in the phase transition of butyl-SBP For the LS(gau) polymorph, in turn, five calculations were performed along the same rotation coordinate between the -107° and 0° values of the θ dihedral angle.
• To study the elementary steps of the LS(gau) à LS(anti) phase transition, the intermediate states connecting these two polymorphs (3gauche-1anti, 2gauche-2anti and 1gauche-3anti) were obtained by means of variable-cell geometry relaxations, in which the atomic positions and the lattice parameters are optimized simultaneously.
• 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.

Acknowledgments

• 83 The ΔEadia value between both gauche-IN LS and HS minima is ca. 1 kcal/mol larger than the ΔEadia value between anti polymorphs .
• Therefore, the large increase in vibrational entropy associated with the conformational switch explains why the system undergo first the conformational switch even if the energy gap that is cleared in this transition is larger than that of the spin switch.

Figures

Figure 1. Schemes of the ethyl-substituted (a) and the butyl-substituted (b) N- and Ofunctionalized spiro-bis(1,9-disubstitutedphenalenyl) boron radicals. The radical displayed on the left (right) is referred to as compound 1 (2) in the text.

Figure 2. X-ray crystal structures at 340 K of the LT (a) and HT (b) phases of the butyl-SBP πdimers. Hydrogen atoms are hidden for clarity.

Figure 3. Scheme of the relative energy of the different minimum energy configurations of compound 2 in gas phase (left) and solid-state (right). All adiabatic energy gaps are given, per π-dimer, in kcal/mol.

Figure 8. A short H···H contact between a hydrogen atom of the terminal methyl group of a butyl chain in an anti conformation and a hydrogen atom of a phenalenyl group of an adjacent SBP radical. The distance associated with this contact is shown for the LT-340 crystal structure (left) and for the optimized LS(gau) structure (right), i.e., the LT structure at 0 K. The values of the distances displayed in the Figure correspond to optimized structures. 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.

Figure 7. Potential energy profiles as a function of the θ dihedral angle of one butyl chain of the unit cell of 2. The three profiles were evaluated by means of constrained optimizations using three different sets of cell vectors: the cell vectors associated with the LT-340 crystal structure (red curve), the cell vectors of the HT-340 crystal structure (blue curve) and the cell vectors of LS(gau) polymorph (green curve), which were obtained upon variable-cell optimization (i.e., they correspond to the structure at 0 K). In all profiles, the energy of the gauche-IN conformation (θ = -107º) was taken as the reference energy.

Table 2. (a) Volume cell (V), CH···π distance, and interplanar distance between supPLYs (D) obtained for the butyl-SBP crystal at the optimized gauche-IN and anti structures in their 1Ag and 3Au states in solid-state conditions. All distances are given in Angstrom and the volume cell is given in bohr3. (b) Difference between the V, CH···π, and D values of various polymorphs of the butyl-SBP crystal.

Figure 6. Time-resolved evolution of the θ dihedral angle of the butyl-ligands attached to the sup-PLY (see Figure 5) for the four spiro-phenalenyl units included in the cell of the AIMD simulations. The values that correspond to the trajectory of the LT-340 (LS) phase are shown in (a), whereas (b) and (c) show the values for the HT-340 (HS) trajectories, starting from anti and gauche-IN polymorphs, respectively. Note that in our simulations 10000 steps amount to ca. 10 picoseconds.

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 1Ag and 3Au states in (b) solid-state and in (c) gas-phase conditions. All distances are given in Angstrom.

Figure 4. Temperature dependence of the difference in entropy (expressed as TΔST, where ΔST includes both the electronic and vibrational contributions of the entropy) between different configurations of the π-dimers of 2. The solid curves correspond to calculations carried out for isolated π-dimers, while the dashed curve corresponds to calculations in the solid state.

Figure 5. Scheme for the gauche-IN, anti and gauche-OUT conformations of the butyl chain of compound 2.

Figure 9. Scheme showing the energy changes (given in kcal/mol) involved in all the elementary steps of the LS(gau) à LS(anti) phase transition. In LS(gau), which is denoted by “4gauche” in the Figure, there are four butyl groups in the gauche-IN conformation in the simulation cell. In LS(anti), which is denoted by “4anti” in the Figure, all the butyl chains adopt an anti conformation. The name employed to define the intermediate states connecting these two polymorphs denote how many butyl groups of those four originally adopting a gauche-IN conformation are still in a gauche-IN conformation and how many of them have switched to an anti conformation. Note that the second intermediate state actually comprises three different states because there are three different configurations with two butyls in a gauche-IN conformation and two butyls in an anti conformation. All the energies are given relative to the optimized structure of the LS(gau) polymorph.

Full text

!
1!
The origin of bistability in the butyl-substituted spiro-
biphenalenyl-based neutral radical material
!
Maria Fumanal
¶
, Juan J. Novoa, Jordi Ribas-Arino*
Departament de Química Física and IQTCUB, Facultat de Química, Universitat
de Barcelona, Av. Diagonal 645, 08028-Barcelona (Spain)
* jordi.ribas.jr@gmail.com, j.ribas@ub.edu
¶
Present address: Laboratoire de Chimie Quantique, Institut de Chimie UMR7177
CNRS-Université de Strasbourg, 1 Rue Blaise Pascal BP 296/R8, F-67007 Strasbourg,
France
!
!

!
2!
!
Abstract
One of the most remarkable bistable materials so far reported is made of π-dimers of a
butyl-substituted spiro-biphenalenyl boron radical (butyl-SBP). The phase transition of
this material, which is accompanied by changes in its optical, conductive and magnetic
properties, occurs with a hysteretic loop 25-K wide and is centered at 335 K. Here, we
present a computational study aimed at deciphering the origin of this hysteresis. We
show that the phase transition of butyl-SBP consists of a spin transition of their
constituent π-dimers coupled with an order-disorder transition involving the butyl
chains linked to the N atoms of the superimposed phenalenyl rings of the π-dimer.
Below 335 K, the terminal methyl group of the butyl chains adopts a gauche
conformation with respect to the methylene unit bonded to the N atom. Above 335 K,
the methyl group is in an anti conformation and exhibits dynamic disorder. The gauche
! anti conformational rearrangement triggers the spin transition of the π-dimers and is
responsible for the hysteretic behavior of butyl-SBP. Specifically, the onset of the
phase transition in the heating mode and, thus, the width of the hysteresis loop, are
governed by the high energy cost and the strong structural cooperative effects
associated with this conformational change. Our results show that coupling a spin
switch with a conformational switch in a molecular crystal provides a promising strategy
in the design of new bistable materials.
!

!
3!
!
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. Molecule-
based 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
. The transition temperature and the hysteresis loop width
of a bistable material are crucial parameters in determining whether its bistability can
be harnessed in technological applications. These two parameters, in turn, depend on
the intermolecular interactions within the crystal and on the energy barriers associated
with the lattice reorganization upon phase transition. For most of the bistable
compounds reported so far, very little is known about either the origin of the energy
barriers associated with their phase transitions (i.e, whether the energy barrier of the
overall phase transition is dominated by a single molecular rearrangement or whether
the barrier is the result of the contributions of different reorganization events) nor the
role of structural cooperativity in promoting such phase transitions. It is clear that the
lack of this sort of information poses a major obstacle for the rational design of new
derivatives of a given bistable parent compound with the goal of fine tuning its
transition temperature and its hysteresis loop width. Therefore, the studies aimed at
elucidating the origin of these barriers and at establishing the role of cooperative
effects have the potential to offer most valuable hints on how to devise new bistable
materials with improved properties. Here, on the basis of a computational study, we
disclose the origin of the hysteretic phase transition of a phenalenyl-based butyl-
substituted neutral radical, which is one of the most prominent compounds within the
family of bistable materials.
Phenalenyl (PLY) is an odd-alternant hydrocarbon neutral radical arising from a
triangular fusion of three benzene rings. This open-shell molecule has emerged in the
past years as one of the most versatile building blocks for functional molecular devices

!
4!
and materials.
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 π-
dimers 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),

!
5!
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 π-
dimers 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.