Differences in thermal expansion and motion ability for herringbone and face-to-face π-stacked solids

A series of halogenated compounds with motion-capable moieties were designed and synthesized, and they exhibit different π-stacking arrangements. The thermal expansion behaviors are influenced by crystal packing, halogen-bond strength and pedal motion ability.


Introduction
Thermal expansion (TE) is a fundamental property of materials, and it describes the response to temperature change (Yao et al., 2019;Saha, 2017). An increase in the size or dimension of a material upon heating is positive thermal expansion (PTE) (Das et al., 2010;Bhattacharya & Saha, 2014). Negative thermal expansion (NTE) or zero thermal expansion (ZTE) are rarer behaviors, which correspond to a decrease or nearly no change in size upon heating, respectively (Chen et al., 2015;Wu et al., 2016a;Zhu et al., 2018). TE is capable of controlling phase transitions and mechanical properties of organic crystals and has potential applications in thermally responsive materials (Naumov et al., 2015;Reddy et al., 2010). Moreover, understanding TE in materials such as organic semiconductors is important because it influences bandwidth narrowing (Li et al., 2012;van der Lee et al., 2018) and performance can be reduced if TE properties in a device are mismatched (Mei et al., 2017;Wu et al., 2016b).
One aspect that affects the TE of a solid material is the strength of the interactions holding it together. Stronger interactions are less affected by temperature and lead to smaller expansion when compared with weaker interactions (Saraswatula et al., 2018). Halogen bonding is quickly becoming a widely utilized interaction in materials science (Cavallo et al., 2016;Saccone & Catalano, 2019). Recently, halogen bonds have been used to control solid-state packing in organic semiconductor-based materials and improve device performance (Wilson et al., 2015;Weldeab et al., 2018;Zhang & Wang, 2021;Li et al., 2018). HalogenÁ Á Áhalogen interactions are a subset of halogen bonds and can be classified into two distinct types based on the angles () between the halogens [C-XÁ Á ÁX, Fig. 1(a)] (Mukherjee et al., 2014). Saraswatula and Saha have studied the TE behavior of halogenÁ Á Áhalogen interactions within a series of isostructural organic molecules (Saraswatula & Saha, 2014). The TE responses of the solids correlated with the strength of the inter-halogen interactions, and the trend was IÁ Á ÁI < BrÁ Á ÁBr < ClÁ Á ÁCl (where < refers to a smaller distance change). However, bond strength is not the only parameter that influences TE.
A continued interest in our group is to investigate the effect of molecular pedal motion (Harada & Ogawa, 2009) on TE behaviors [ Fig. 1(c)]. Recently, our group demonstrated that dynamic pedal motion leads to large PTE in organic solids (Hutchins et al., 2018;Juneja et al., 2019;Ding et al., 2020). The most widely studied motion-capable moieties are olefin (C C) and azo (N N) groups (Harada & Ogawa, 2001;Peedikakkal, 2017). Imine (C N) groups are also capable of pedal motion, and though imines have been well studied in Schiff base chemistry (Kiefer et al., 2019;Hadjoudis et al., , 2011, pedal motion of imines has been investigated to a lesser extent (Harada et al., 2004a,b). To date, our group has only investigated TE properties for motion-capable moieties substituted with pyridine rings (Juneja et al., 2019;Ding et al., 2020).
Here, we designed and synthesized a series of aromatic, dihalogenated molecules functionalized with one or two olefin, azo and imine groups [Figs. 2(a) and 2(b)]. The compounds outlined in Fig. 2 were chosen to systematically tune three features and investigate the impact on TE: motion group identity, number of motion groups and halogen-bond strength. We demonstrate that the molecules crystallize into packing arrangements analogous to those frequently observed in organic semiconductor materials, herringbone or face-to-face -stacked [ Fig. 1(b)]. We show that herringbone packing supports solid-state pedal motion, yet face-to-face stacking does not. Furthermore, the herringbone and face-to-face -   Geometries of (a) type-I and type-II halogenÁ Á Áhalogen interactions and (b) herringbone and offset face-to-face -stacking. (c) Pedal motion in a diphenyl molecule with a motion-capable group. stacked solids undergo different degrees of TE along two directions. Surprisingly, the TE along the -stacked direction is similar even though the interactions and packing along the direction are clearly different. Overall, we demonstrate the comprehensive influence of crystal packing motion and noncovalent interaction strength on TE behaviors instacked solids.

Experimental
The 16 compounds in Figs. 2(a) and 2(b) were synthesized using literature or modified-literature procedures and characterized by variable-temperature single-crystal X-ray diffraction (VT SCXRD) and 1 H NMR spectroscopy (pages S2-S9, Tables S1-S34 and Figs. S18-S36 of the supporting information). The diolefin compounds were not soluble in common deuterated solvents, so powder X-ray diffraction was used to characterize these three compounds in place of NMR (Figs. S37-S39). VT SCXRD studies were performed in the range 290-190 K, and full crystallographic datasets were collected at 20 K intervals. Each crystal was mounted at 190 K and warmed to collect additional datasets. The morphology and color of each crystal was characterized using a Leica DM2700M microscope equipped with a camera. TE coefficients were calculated using the software PASCal (Cliffe & Goodwin, 2012).
A search of the Cambridge Structural Database (CSD; version 5.42 + 2 updates) demonstrated that the single-crystal structures of imine-Br (Bernstein & Izak, 1975;Marin et al., 2013;Ashokkumar et al., 2021), azo-I (Grebel-Koehler et al., 2003 and azo-Br (Amit & Hope, 1966;Howard et al., 1994;Karanam & Choudhury, 2013) have been previously published at one temperature. For imine-Br and azo-I, we obtained crystals that are identical to the published structures (Marin et al., 2013;Grebel-Koehler et al., 2003) and conducted VT SCXRD studies here. Azo-Br has been reported to crystallize as two polymorphs (a and b) (Amit & Hope, 1966;Howard et al., 1994;Karanam & Choudhury, 2013), and we conducted VT SCXRD experiments for both. The polymorph azo-Br(a) crystallizes in the face-to-face packing arrangement (isostructural to others) and is discussed below. The polymorph azo-Br(b) crystallizes in an arrangement that differs from the other 16 solids discussed here; thus, it is not a focus of this work and full details are given in the supporting information (pages S86-S87).

Results and discussion
We incorporated three different motion groups to systematically investigate if one motion group undergoes dynamic motion more readily than another, if the number of motion groups impacts motion ability, and to study the influence of motion on TE. In total, 12 of the 16 halogenated molecules are symmetrical (olefin-I, olefin-Br, imine-I, imine-Br, azo-I, azo-Br, diolefin-I, diolefin-Br, diimine-I, diimine-Br, diazo-I and diazo-Br) and four are unsymmetrical (olefin-I Br, azo-I Br, diolefin-I Br and diazo-I Br). The two unsymmetrical imine compounds are not included in this manuscript. The unsymmetrical nature of the single-imine molecule was not distin-guishable by X-ray diffraction due to an inversion center in the imine, and the iodine and bromine occupying the same crystallographic site. The synthesis of the unsymmetrical double-imine molecule was unsuccessful due to competing reactions that afford the symmetrical products.
In the solid state, the halogenated molecules are expected to assemble into an extended structure through XÁ Á ÁX forces. The symmetrical compounds were chosen to include two iodo or two bromo groups. We expected the stronger IÁ Á ÁI interactions to be less affected by temperature changes, while BrÁ Á ÁBr interactions are weaker and should be more affected. The unsymmetrical donor molecules feature one iodo and one bromo group and offer a subtle interplay between the two symmetrical systems.
Single-crystal analysis revealed the three single olefin compounds (olefin-I, olefin-Br and olefin-I Br), imine-I, azo-I (Grebel-Koehler et al., 2003) and three diolefin compounds (diolefin-I, diolefin-Br and diolefin-I Br) to crystallize in the orthorhombic space group Pccn. Imine-Br (Marin et al., 2013), azo-Br(a) (Amit & Hope, 1966), azo-I Br, the two diimine compounds (diimine-I and diimine-Br) and diazo-I crystallized in the monoclinic space group P2 1 /c. The other two diazo compounds diazo-Br and diazo-I Br crystallized in the monoclinic space group P2 1 /n. The asymmetric units of diimine-I, diimine-Br and diazo-I contain one-half of two unique molecules, while in the other 13 crystals, the asymmetric units contain one-half of the molecule. In the unsymmetrical iodobromo compounds, olefin-I Br, azo-I Br, diolefin-I Br and diazo-I Br, the iodine and bromine atoms sit at nearly identical crystallographic positions. The site occupancy for each atom was constrained at 0.5 with SIMU restraints being used primarily to maintain reasonable ADP values for the two atoms. For the single imine compounds, imine-I and imine-Br, an inversion center lies at the center of the bridge group; thus, the carbon and nitrogen atoms occupy the same crystallographic space. The halogenÁ Á Áhalogen interaction distances and angles for each solid are shown in Table S36. Of the 16 solids, 11 self-assembled into herringbone packed structures and five into face-to-face -stacked structures. The morphology and color of each crystal are shown below (Fig. 3).

Molecular motion
Motion was characterized using VT SCXRD and observed through disorder of the motion-capable molecule. If disorder is present, the site occupancies of the major and minor sites are quantified. If the site occupancies change with temperature, the motion is dynamic, and if the occupancies remain nearly constant, the disorder is static (Harada & Ogawa, 2001, 2009). The molecules imine-I, azo-I, diolefin-Br, diolefin-I Br and diazo-I exhibited disorder during the variable-temperature experiments. The site occupancies of each orientation were allowed to freely refine in the five compounds, and the sum of the two site occupancies was set to a total of one. VT SCXRD experiments demonstrated that all five compounds undergo dynamic pedal motion as confirmed by changes in the site occupancies as a function of temperature (Table 1). The overall change in the site occupancies between 190 and 290 K ranged from 3 to 27% for the five solids. Imine-I and azo-I undergo dynamic pedal motion over the entire temperature range studied Figs. 4(a)

Compounds with herringbone crystal packing
In total, 11 of the 16 solids crystallize with the extended packing sustained by herringbone -stacking. The molecules described below self-assemble into 2D sheets through type-II halogenÁ Á Áhalogen forces. The sheets assemble into herringbone-packed layers that interact through C-HÁ Á Á interactions, type-I halogenÁ Á Áhalogen bonds and C-HÁ Á ÁX forces.  Table 1 Site occupancies of the major conformations within molecules that undergo dynamic pedal motion.

Figure 3
Images of each crystal with the corresponding molecular structure for (a) herringbone and (b) face-to-face -stacked arrangements. The three single-olefin compounds, olefin-I, olefin-Br and olefin-I Br, are isostructural (IUCr Online Dictionary of Crystallography, 2019) and do not exhibit pedal motion. The molecules self-assemble into 2D sheets, which extend in the bc plane [Figs. 5(a), 5(c) and 5(e)]. The sheets further assemble into layers that stack along the crystallographic a axis [Figs. 5(b), 5(d) and 5( f)].
Unlike the single motion group olefin series, the single imine and azo compounds are not isostructural within a series. Two of the molecules that undergo dynamic pedal motion, imine-I and azo-I, crystallize in the same space group as the three single-olefin molecules and exhibit crystal packing that is isostructural to the olefins (Fig. 6). Single-crystal X-ray structures showing 2D halogen-bonded sheets, layers and TE axes for (a) and (b) olefin-I, (c) and (d) olefin-Br, and (e) and ( f ) olefin-I Br. Type-II halogen bonds are shown with yellow dashed lines, type-I halogen bonds are shown with blue dashed lines and C-HÁ Á ÁX forces are shown with green dashed lines. Structures are shown at 290 K for olefin-Br and olefin-I Br, and 270 K for olefin-I (due to poor data quality at 290 K).

Figure 6
Single-crystal X-ray structures at 290 K showing 2D halogen-bonded sheets, layers and TE axes for (a) and (b) imine-I, and (c) and (d) azo-I. Disorder in the aromatic rings and halogens has been omitted for clarity. Type-II halogen bonds are shown with yellow dashed lines, type-I halogen bonds are shown with blue dashed lines and C-HÁ Á ÁI forces are shown with green dashed lines.
The three diolefin molecules diolefin-I, diolefin-Br and diolefin-I Br crystallize in the same space group as the molecules above and exhibit isostructural crystal packing. The 2D sheets extend in the bc plane [Figs. 7(a), 7(c) and 7(e)] and further stack into herringbone-packed layers along the crystallographic a axis [Figs. 7(b), 7(d) and 7(f )].
The two diimine compounds diimine-I and diimine-Br crystallize in a different space group than all the molecules above; however, the crystal packing is still isostructural. The 2D halogen-bonded sheets self-assemble in the bc plane [Figs. 8(a) and 8(c)] and then stack into herringbone-packed layers along the crystallographic a axis [Figs. 8(b) and 8(d)].
The three diazo molecules are not isostructural within a series. The compound diazo-I, which undergoes pedal motion over the entire temperature range, crystallizes in the same space group as the two diimine molecules and exhibits crystal packing that is isostructural with all the compounds outlined above [Figs. 9(a) and 9(b)]. Diazo-I contains two crystallographically unique molecules and, as outlined in the molecular motion section, one molecule is fully ordered from 190-250 K and exhibits disorder at 270 and 290 K. The second molecule is disordered at all the temperatures studied; however, between 250 and 270 K the positions of major and minor conformations switch [Figs. 9(c) and 9(d)]. The conformational change is accompanied by a 0.13 Å increase in the b axis between 250 and 270 K, while the angle decreases by 0.58 and approaches 90 (Table S29).  Single-crystal X-ray structures at 290 K showing 2D halogen-bonded sheets, layers and TE axes for (a) and (b) diolefin-I, (c) and (d) diolefin-Br, and (e) and ( f ) diolefin-I Br. Type-II halogenÁ Á Áhalogen bonds are shown with yellow dashed lines, type-I bonds are shown with blue dashed lines and C-HÁ Á ÁX forces are shown with green dashed lines.

Figure 8
Single-crystal X-ray structures at 290 K, highlighting the 2D halogen-bonded sheets, layers and TE axes for (a) and (b) diimine-I, and (c) and (d) diimine-Br. Type-II halogenÁ Á Áhalogen bonds are shown with yellow dashed lines, type-I bonds are shown with blue dashed lines and C-HÁ Á ÁX bonds are shown with green dashed lines.

Compounds with face-to-face p-stacked crystal packing
Out of the 16 solids, 5 crystallize with the extended packing sustained by face-to-face -stacking. The five structures described below also self-assemble into 2D sheets through type-II halogenÁ Á Áhalogen forces, similar to the structures discussed above. However, the sheets in the structures described below assemble into face-to-face -stacked layers that interact through C-HÁ Á ÁX forces, rather than herringbone-packed layers.
The three molecules imine-Br, azo-Br(a) and azo-I Br crystallize in the same space group and exhibit isostructural crystal packing. The 2D sheets extend approximately in the bc plane [Figs. 10(a), 10(c) and 10(e)] and then pack into face-toface -stacked layers along the crystallographic a axis [Figs. 10(b), 10(d) and 10( f )]. However, the arrangement of the molecules within the 2D sheets differs from the previous structures. Within the sheet, neighboring halogen-bonded molecules are twisted from planarity by $55 , whereas in the all the previously described structures, the molecules are much closer to planarity (deviation by 19-32 ).
The two diazo compounds diazo-Br and diazo-I Br crystallize in a different space group than imine-Br, azo-Br(a) and azo-I Br; however, all five solids exhibit isostructural crystal packing. Within the 2D sheets, which extend approximately in

Influence of packing and motion group on pedal motion
As highlighted above, 5 of the 16 single-component solids undergo pedal motion and all five compounds exhibit herringbone crystal packing. Thus, solid-state packing has a clear influence on motion ability.
In the single motion group series, zero of three olefin molecules, one of three azo structures and one of two imine molecules undergo pedal motion in the solid state. In the double-motion group series, two of three double-olefin molecules, one of three double-azo molecules and zero of two double-imine molecules undergo pedal motion in the solid state. At first glance, the identity of the motion group does not appear to significantly impact the occurrence of pedal motion in these single-component halogenated solids. However, examination of the five solids that undergo motion suggests that the degree of motion is influenced by identity. The overall change of the site occupancy between 290 and 190 K reveals that azo groups undergo larger changes (azo-I = 20%, diazo-I = 27 and 24%), the imine lies in the middle (imine-I = 9%) and the olefins undergo the smallest overall changes (diolefin-Br = 3%, diolefin-I Br = 7%).
The pedal motion behaviors in four of the five solids (imine-I, azo-I, diolefin-I Br and diazo-I) were further analyzed by a van't Hoff plot analysis (Harada & Ogawa, 2004, 2009Harada et al., 2004b;Vande Velde et al., 2015) (Figs. S57-S60). Analysis for diolefin-Br was not performed because disorder is only present at two temperatures. The natural logarithm of the ratio between occupancies of major and minor sites was plotted against the reciprocal of temperature. For the disordered solids imine-I, azo-I and diolefin-I Br, the plots are linear, so the entropic and enthalpic differences between the two sites remain constant during the temperature range and the pedal motion reaches thermodynamic equilibrium. For one of the two unique molecules in diazo-I, the plot is linear in the lower temperature range from 190 to 250 K. On reaching 270 K, the minor conformation of the molecule switches to the major conformation and remains the major site at 290 K. Nonlinearity in van't Hoff plots has been observed in cases where the enthalpy and entropy are different at high and low temperatures, which can indicate a phase transition (Vande Velde et al., 2011). In diazo-I, the conformational switching of the major and minor sites corresponds to a phase transition and is the cause of nonlinearity.

Thermal expansion analysis
In order to determine the TE behaviors of these halogenated molecules and the impact of crystal packing and motion on TE, PASCal (Cliffe & Goodwin, 2012) was used to calculate the principal axes (X 1 , X 2 and X 3 ) and TE coefficients ( X 1 and X 2 , X 3 ) for each crystal using the VT SCXRD data (Table 2, Figs. S1-S17). The single-crystal data at 290 K for olefin-I were excluded because the crystal began to disintegrate and data quality was low. Since diazo-I undergoes a phase transition, only the VT SCXRD data between 190 and 250 K was used for the TE calculations. The crystal packing of diazo-I at 250 K is shown in Fig. S62, which is identical to the packing at 290 K [Figs. 9(a) and 9(b)]. The principal axes for each solid are highlighted in Figs. 5-11. As a benchmark, a TE coefficient ! 100 MK À1 has been termed 'colossal' TE (Goodwin et al., 2008).
On average, the solids with herringbone packing exhibit different TE behaviors from the face-to-face packed solids along the X 1 and X 2 axes, while the behavior along the X 3 axis is similar. The herringbone solids undergo minimal TE along the X 1 axis, appreciable PTE along the X 2 axis and colossal PTE along X 3 (average: X 1 = À2, X 2 = 73, X 3 = 124 MK À1 ). The face-to-face packed solids undergo PTE along the X 1 and X 2 axes and colossal PTE along X 3 (average: X 1 = 9, X 2 = 46, X 3 = 130 MK À1 ). The key differences in TE behavior of the solids arise from differences in halogen-bond strength, crystal packing and motion occurrence. Single-crystal X-ray structures at 290 K highlighting 2D halogen-bonded sheets, layered packing and TE axes for (a) and (b) diazo-Br, and (c) and (d) diazo-I Br. Type-II halogenÁ Á Áhalogen bonds are shown with yellow dashed lines and C-HÁ Á ÁX bonds are shown with green dashed lines.
For the solids with herringbone crystal packing, the X 1 axis lies along the direction of the 2D halogen-bonded sheet. The X 1 axis corresponds to the crystallographic b axis, and the TE coefficients range from À18 to 24 MK À1 (Table 2). Specifically, the molecules with a single motion group exhibit nearly ZTE or PTE, whereas the molecules with two motion groups all exhibit NTE along X 1 . The ZTE in olefin-I and olefin-I Br arises from minimal changes along the crystallographic b axis (in the third decimal place) as a function of temperature (Tables S1, S2, S5 and S6). The solids olefin-Br, imine-I and azo-I undergo slight to moderate PTE along X 1 , and the length of the crystallographic b axis increases gradually with increasing temperature in each case. The NTE in diolefin-Br, diolefin-I Br, diimine-I and diimine-Br arises from a decrease in the length of the crystallographic b axis as the temperature is increased. For diolefin-I, the length of the b axis also decreases upon heating overall to afford NTE, but there is a slight increase in length between 230 and 250 K (Tables S19 and S20).
The influence of molecular width on TE has been investigated by Saha and coworkers who showed that the direction of longer molecular width experiences less TE (Rather et al., 2019). The direction of longer molecular width contains more covalent bonds and less intermolecular interactions; thus, the covalent bonds within the molecule are stronger and will expand less than noncovalent bonds between molecules. In the herringbone structures, the b axis corresponds to the longest width of the molecules and does indeed exhibit the smallest expansion. Perhaps more interesting is that when comparing the shorter (one motion group) to the longer (two motion group) molecules, the longer molecules exhibit less expansion along X 1 .
The intermolecular interactions that contribute to TE along X 1 are primarily type-II halogenÁ Á Áhalogen bonds (Table S37). In the symmetrical single-and double-olefin molecules, the type-II IÁ Á ÁI distances increase by 0.03 Å in both olefin-I and diolefin-I, whereas the type-II BrÁ Á ÁBr bond lengths increase by 0.04 Å in both olefin-Br and diolefin-Br on heating. In the two diimine compounds, the type-II bond lengths increase on heating by 0.03 Å on average for diimine-I and 0.04 Å on average for diimine-Br. The larger increase in the BrÁ Á ÁBr bond lengths is expected since they are weaker than IÁ Á ÁI bonds. In imine-I and azo-I, the type-II IÁ Á ÁI separations increase by ca 0.06 Å on warming. The larger increase in bond length for these iodinated solids could be due to appreciable pedal motion over the entire temperature range, which includes a small repositioning of the iodine atoms. For the unsymmetrical solids, the iodine and bromine atoms sit at nearly identical crystallographic positions with site occupancies of 0.5 and 0.5. This prevented a clear comparison of bond length changes between the symmetrical and unsymmetrical solids because, at any point, the contact could be IÁ Á ÁI, BrÁ Á ÁBr or IÁ Á ÁBr (see Table S37 for all three values). We also calculated the centroid of the I/Br atoms on each side of the type-II bond and measured the distance between the centroids. For olefin-I Br, the centroid separation decreases by 0.01 Å on heating, and the separation increases by 0.03 Å for diolefin-I Br on heating. The type-I halogenÁ Á Áhalogen interactions also contribute slightly to the expansion along research papers IUCrJ (2022). 9, 31-42 Xiaodan Ding et al. Thermal expansion and motion ability for -stacked solids 39 Table 2 TE coefficients for crystals with errors denoted in parentheses and approximate crystallographic axes denoted in brackets.
The solids are divided into sections based on crystal packing. The average values for solids with the same packing are provided at the bottom of each section. Crystal X 1 in the herringbone-packed compounds, and the distances increase by ca 0.03-0.09 Å on warming.
Diazo-I exhibits slightly larger PTE along X 1 than the other herringbone solids, but the temperature range used for the calculation only includes data from 190-250 K due to the conformational change at 270 K. The PTE arises from an increase in the length of the b axis with increasing temperature, the type-II IÁ Á ÁI bonds increase by an average of 0.02 Å , and the type-I IÁ Á ÁI bonds increase by 0.05 Å .
In the isostructural molecules that exhibit face-to-facestacked crystal packing, imine-Br exhibits ZTE and the other four molecules undergo slight PTE along X 1 . The ZTE in imine-Br arises from minimal changes along the crystallographic c axis (in the third decimal place) as a function of temperature (Tables S9 and S10). Unlike the herringbone solids, expansion along X 1 for the face-to-face -stacked solids encompasses the a and/or c crystallographic axes (Table 2). In all five solids, the direction of the X 1 axis includes the C-HÁ Á ÁX forces, which increase by ca 0.03-0.06 Å on warming (Table S37). In imine-Br, diazo-Br and diazo-I Br, the Á Á Ástacking interactions also contribute to X 1 and increase by ca 0.05-0.07 Å on warming. In one case, namely azo-I Br, the type-II halogenÁ Á Áhalogen bonds lie along X 1 , akin to the herringbone structures, and the centroid I/Br distance increases by 0.03 Å on heating. The difference in the direction of the X 1 axis and included intermolecular forces for the faceto-face solids with respect to the structure results in larger average TE coefficients compared with the herringbone solids.
The X 2 axis corresponds to the c axis in the herringbone solids and the b axis for the face-to-face -stacked solids. Importantly, in both the herringbone and the face-to-facestacked solids, the direction of X 2 with respect to the structure is nearly identical. The X 2 axis lies along the vertical direction of the 2D halogen-bonded sheet and includes the type-II halogenÁ Á Áhalogen contacts [Figs. 12(a) and 12(c); Table S38]. The difference in the two structure types arises in the arrangement of neighboring molecules within the 2D sheet. In the herringbone structures, molecules within a sheet are parallel, but lie edge-to-face between the sheets [ Fig. 12(b)]. In the face-to-face structures, molecules within a sheet and between sheets are parallel [ Fig. 12(d)]. On heating, the solids in the herringbone arrangement twist further from coplanarity, and for solids that undergo pedal motion, the conformational interconversion affects the X 2 axis [ Fig. 12(b)]. On the other hand, molecules in the face-to-face structures remain coplanar and do not undergo motion. This structural difference results in a difference in TE behaviors; thus, the solids with herringbone packing exhibit larger PTE along X 2 . Additionally, on average, the c-axis length in the herringbone solids experiences a larger increase on heating than the b axis length in the face-to-face -stacked molecules.
All 16 solids in the herringbone and face-to-face categories exhibit colossal (Goodwin et al., 2008) PTE along X 3 , and on average, the solids exhibit similar TE coefficients ( Table 2). The X 3 axis in both types of solids lies along the -stacking direction. For the herringbone solids, this encompasses the C-HÁ Á Á interactions, whereas in the face-to-face stacked solids, this includes Á Á Á interactions. On heating, the C-HÁ Á Á distances increase by ca 0.04-0.05 Å on average in the herringbone solids, whereas the Á Á Á distances increase by ca 0.05-0.07 Å on average in the face-to-face stacked solids (Table S39). These differences in interaction type and distance change over the temperature range afford a slightly higher TE average for the face-to-face -stacked solids. The solid imine-Br exhibits the largest PTE along X 3 ( X 3 = 162 MK À1 ) due to the largest increase in Á Á Á distance (0.07 Å ).
The volumetric TE coefficient for all 16 solids is also colossal and ranges from 166 to 212 MK À1 . The volume of each crystal increases gradually on warming (Figs. S40-S56) and the volume increases by ca 1.5-2.1% on heating. On average, the solids with herringbone packing exhibit slightly larger volumetric TE (average V = 197 MK À1 ) than the solids with face-to-face -stacking (average V = 187 MK À1 ), owing to the significantly larger expansion along X 2 .

Unsymmetrical olefins
The unsymmetrical IÁ Á ÁBr systems were designed to offer an interplay between the symmetrical IÁ Á ÁI and BrÁ Á ÁBr solids with regard to bond strength and TE along the halogenbonding direction. All six olefins crystallized in the herringbone packing motif, and the type-II halogenÁ Á Áhalogen interactions contribute to TE along the X 1 and X 2 axes. Gratifyingly, the solid olefin-I Br exhibits a TE coefficient between olefin-I and olefin-Br for both X 1 and X 2 . The solid diolefin-I Br exhibits a TE coefficient between diolefin-I and diolefin-Br for X 1 ; however, the TE coefficient of diolefin-I Br along X 2 is within the error of diolefin-Br.

Conclusions
Here, we report the TE behaviors and the impact of crystal packing and pedal motion on TE in 16 di-halogenated molecules with one or two motion-capable moieties, which selfassemble into herringbone or face-to-face -stacked structures. Dynamic pedal motion was successfully achieved in five Single-crystal X-ray structures highlighting X 2 axes for representative (a) and (b) herringbone structures (imine-I), and (c) and (d) face-to-facestacked structures (imine-Br). The X 2 planes are shown in red and going into the page. solids, which all exhibit herringbone packing; thus, crystal packing influences motion ability. Moreover, the degree of pedal motion is affected by the identity of the motion group, and the azo groups undergo the largest changes. Halogen bonds contribute to TE along X 1 in the herringbone solids and X 2 in all 16 solids. The type-II IÁ Á ÁI bonds are stronger and undergo less expansion than the BrÁ Á ÁBr bonds. On average, herringbone-packed solids exhibit larger TE along one direction of the 2D halogen-bonded sheet and larger volumetric expansion, which results from twisting within the herringbone arrangement and pedal motion. The TE along X 3 corresponds to the -stacking direction. The degree of TE is similar in both types of molecules, but face-to-face packed solids experience slightly more TE along X 3 due to the larger increase in the Á Á Á distances. Solid-state packing arrangements and noncovalent interaction strengths both contribute to TE in aromatic based solids, which are important in the field of organic electronics. We are continuing to investigate TE properties of aromatic and halogen-bonded solids.

Related literature
The following references are cited in the supporting information: Wang et al. (2012Wang et al. ( , 2018

Funding information
Financial support from the National Science Foundation (grant No.DMR-2045506 awarded to KMH) and the American Chemical Society Petroleum Research Fund (grant No. 61912-DNI10 awarded to KMH) is gratefully acknowledged. EZ acknowledges the Welch Summer Scholar program for financial support.