Simultaneous Orientational and Conformational Molecular Dynamics in Solid (1,1,2)-Trichloroethane

The molecular dynamics in the ambient-pressure solid phase of (1,1,2)-trichloroethane is studied by means of broadband dielectric spectroscopy and molecular dynamics simulations. The dielectric spectra of polycrystalline samples obtained by crystallization from the liquid phase exhibit, besides a space-charge relaxation associated with accumulation of charges at crystalline domain boundaries, two loss features arising from dipolar molecular relaxations. The most prominent and slower of the two loss features is identified as a configurational leap of the molecules which involves a simultaneous change in spatial orientation and structural conformation, namely between two isomeric forms (gauche$^+$ and gauche$^-$) of opposite chirality. In this peculiar dynamic process, the positions of the three chlorine atoms in the crystal lattice remain unchanged, while those of the carbon and hydrogen atoms are modified. This dynamic process is responsible for the disorder observed in an earlier x-ray diffraction study and confirmed by our simulation, which is present only at temperatures relatively close to the melting point, starting 40 K below. The onset of the disorder is visible as an anomaly in the temperature dependence of the dc conductivity of the sample at exactly the same temperature. While the slower relaxation dynamics (combined isomerization/reorientation) becomes increasingly more intense on approaching the melting point, the faster dynamics exhibits significantly lower but constant dielectric strength. Based on our molecular dynamics simulations, we assign the faster relaxation to large fluctuations of the molecular dipole moments, partly due to large-angle librations of the chloroethane species.


Introduction
Ethane derivatives are the smallest organic molecules undergoing conformational conversions which modify the molecular chirality. Modified ethanes are therefore the simplest systems where properties such as dynamic chiral isomerism and torsional flexibility can be investigated. In this respect, halogenated ethanes are a particularly interesting model system. Compared to other ethane derivatives such as ethanol, ethylamine or ethanolamine, for example, the intermolecular coupling and molecular dynamics of halogenated ethanes are expected to be simpler due to the lack of directional hydrogen-bond interactions, so that self-aggregation and networking are not expected to occur. Nonetheless, due to their delicate conformational equilibrium, halogenated ethanes such as chloroethanes display very fascinating and rich conformational phase diagrams, [1][2][3][4][5][6][7][8][9] which include in some cases dynamic orientational or conformational disorder. [10][11][12][13][14][15] While some chloroethanes exhibit, as pristine ethane, only one possible conformation (e.g. monochloroethane), others, such as (1,2)-dichloroethane, (1,1,2)-trichloroethane, and (1,1,2,2)tetrachloroethane, exhibit three different conformations, namely gauche + , gaucheand transoid, depending on the relative positions of the chlorines linked to either carbon atom (in the transoid isomer of (1,1,2,2)-tetrachloroethane, it is actually the hydrogen on carbon 1 and the chlorine on carbon 2 that are in a trans configuration with respect to each another). The occurrence and relative concentration of conformers varies according to the nature of the system, and depends on the subtle balance of intramolecular strains and the effects of the molecular environment. 14, [16][17][18] We focus here on (1,1,2)-trichloroethane (hereafter TCE), of molecular formula C 2 H 3 Cl 3 . At ambient pressure, TCE is liquid at room temperature and below 237 K it displays a monoclinic phase, referred to as phase α, characterized by the simultaneous presence of distinct molecular conformers and orientations, accompanied by site disorder close to the melting point. 14 At high pressure, a different monoclinic solid phase is observed (referred to as phase ߚ), which at room temperature is stable above 0.82 GPa. Different conformers are present in the different phases of TCE. The gauche conformer is energetically more stable in isolation and by far the most abundant in the gas phase, 19,20 where intermolecular interactions are negligible. Vibrational and NMR studies on the pure solvent have shown instead that in the liquid phase the C 2 H 3 Cl 3 molecules exist in both gauche and transoid conformations, with comparable concentrations. [21][22][23][24] In the ߚ crystalline phase (at high pressure) only transoid conformers are observed. The α solid phase is arguably the most interesting one: only gauche conformers are present, but of both chirality, namely gauche + and gauche -. The simultaneous presence of two conformers has been reported also in 1:1 stoichiometric cocrystals of (1,1,2)-trichloroethane with Buckminsterfullerene. 18 The disorder in phase α is particularly intriguing. While at low temperature the gauche + and gaucheconformers each occupy distinct crystallographic sites related by an inversion center, close to the melting point of this phase (237 K) all sites exhibit orientational and conformational disorder, with the molecules in one of two possible configurations. At 220 K, the observed occupancies of the majority and minority conformer at each site are 0.85 and 0.15, respectively. 14 An interesting aspect of this disorder is that the bulky halogen atoms occupy always the same crystallographic positions, while the carbon positions, C-C orientation, and molecular chirality (conformation), change between the two orientations. A similar type of disorder, with the halogens occupying the same lattice position and disorder in the backbone orientation, has been observed also in other halogenated ethanes. 6,7 The authors of Ref. 14 observe a gradual reduction of this disorder as the temperature is lowered, and suggest that this may indicate a dynamic nature of such disorder, that is, that the ethane derivatives may undergo dynamic conformational changes. For this to happen, however, the TCE molecules should undergo a simultaneous orientational and configurational jump between the two different chiral states of the gauche conformation.
In this contribution, we employ broadband dielectric spectroscopy and molecular dynamic simulations to investigate the reorientational motions in the solid α phase of TCE. Our dielectric study shows that the peculiar disorder observed in Ref. 14 has indeed a dynamic character. We moreover detect a less intense relaxation process at lower temperature in the same phase. Based on our molecular dynamics simulations, we show that the main dynamic process is a simultaneous orientational-conformational jump of the TCE molecules involving gauche +gaucheisomerization, and assign the other relaxation to short-lived fluctuations into nonequilibrium configurations, partially ascribable to large-angle librations of the molecules. The presence of two relaxations was reported also in the disordered solid phase of the related (1,1,2,2)-tetrachloroethane derivative, 25 but neither involved a simultaneous change in conformational and orientational degrees of freedom. Conformational molecular dynamics are not uncommon in gaseous or liquid molecular phases, and they have also been also reported in some plastic crystals. [26][27][28] However, the α phase of TCE is, to the best of our knowledge, the only ordered small-molecule crystal phase that exhibits such kind of dynamic isomerism, which moreover involves a change in chirality.

Materials and Methods
(1,1,2)-Trichloroethane (TCE) was purchased from a commercial supplier (Aldrich, 98%) and distilled twice at 385 K. For the dielectric measurements, the distilled TCE was inserted in its liquid phase inside a home-made stainless steel parallel-plate capacitor especially designed for liquid samples, with the two plates separated by needle-like cylindrical silica spacers of 50 µm diameter. The capacitor was then loaded within a nitrogen-gas flow Quatro cryostat for temperature control. The α crystal phase was obtained by slow cooling of the sample directly in the capacitor cell, and isothermal measurements were taken both upon decreasing and increasing the temperature. Isothermal dielectric spectra were acquired using a Novocontrol Alpha analyzer in the frequency (f) range between 10 -2 and 5·10 6 Hz. Dielectric measurements yield the complex impedance of the sample, from which the complex relative permittivity ε*(ω), complex dielectric modulus M*(ω) = ε*(ω) -1 , and complex conductivity σ*(ω) = iωε 0 (1 -ε*) of the material can be retrieved. These frequency-dependent quantities carry information on the dipolar molecular dynamics processes as well as about the dc conductivity and space-charge relaxations of the sample. In particular, dipolar and conductivity-related features can be observed either in the imaginary part of the permittivity ε"(f), called loss spectrum, or in the imaginary part of the modulus M"(f), called modulus spectrum (f = ω/2π).
The value of dc conductivity, σ dc , was obtained as the low-frequency plateau value of the ac conductivity spectrum, given by σ'(f) = 2πf ε 0 ε"(f). We found that the loss spectra are dominated at low frequency by a conductivity-related space-charge loss, which made impossible a direct fit of the loss spectra. Instead, in the modulus spectra three clearly separated contributions are observed. We therefore determined the frequency maxima of each component from a fit of the modulus spectrum. For this purpose, each component was modeled as a separate peak described with a Havriliak-Negami (HN) function, whose analytical expression in the modulus representation is: 29,30 (Eq. 1) ‫ܯ‬ ுே ሺ݂ሻ = ൫ଵାሺଶπఛ ಹಿ ሻ ഁ ൯ ം .
Here, A represents the intensity of the process, and the exponents β and γ are shape parameters related to the low-and high-frequency tails of the imaginary spectrum M"(f), and τ HN is a fitting parameter from which the characteristic time τ max at which the imaginary part of the modulus is maximum is obtained as: Two of the components turned out to be characterized by a symmetric peak and well described Starting from this knowledge of the relaxation times of all three relaxations, we were able to reproduce the loss spectra ε"(f) as the imaginary part of the following Eq. (3), which takes into account the presence of three relaxation processes as well as of a conductivity background: The parameter Δε is the dielectric strength (intensity) of each process.
Molecular dynamics simulations of (1,1,2)-trichloroethane were performed using the Gromacs v5.0.2 package 31 in the NPT ensemble, using a system of 960 molecules. Total run times were between 100 to 1000 nanoseconds. Flexible molecules were considered, including harmonic atom-atom forces, harmonic angle potentials and dihedral potential, 32,33 together with a time with time step of 0.5 fs, to allow for conformational changes. The intermolecular interactions were described by Lennard-Jones (L-J) and Coulombic potentials, [32][33][34][35][36] with parameters deduced from liquid-and gas-phase properties obtained from Ref. 32. As initial configuration, we used the experimental volume and the crystalline structure of the perfectly ordered α phase at 100 K, as determined by X-ray diffraction. 14 In order to allow a comparison with dielectric experiments, we have determined the time self-correlation function of the molecular dipole moment p of single molecule, defined as: Here N is the number of molecules considered in the calculation, i is the molecule number, and the average is carried out over times ζ. The dipole moment correlation function was found to vary slowly, so that extremely long simulation times would be needed to obtain a reliable fit of the correlation decay. For this reason, we also calculated the bond-orientation self-correlation functions given by: Here the index j indicates a particular C-Cl bond of the TCE molecule. Obviously, any molecular dynamics such as a reorientation motion or a conformational change involves the simultaneous change of the C-C and C-Cl bond directions, so that the time dependence of the latter contains all the information about molecular dynamic processes. The so-obtained selfcorrelation functions were then fitted as the sum of two exponential decays to mimic the effect of the two dipolar relaxations observed in the modulus spectra. The comparison is meaningful because the dipole time correlation function and the imaginary part of the permittivity are related by the fluctuation-dissipation theorem of linear response theory.

Results and Discussion
In the molecular dynamic simulation, the solid phase α is observed to be stable up to approximately 240 K, i.e., only few degrees higher than the experimental melting point T m (237 K). Our simulations show that the populations of gauche + and gaucheconformers in phase α are both of 50%, independent of temperature. At low enough temperature, namely, for temperatures lower than T m -30 K, each conformer occupies two distinct crystallographic sites in the unit cell (which contains four molecules). The two sites for the gauche + conformer and those for the gaucheconformer are related by an inversion operation. 14 As the temperature is increased from T m -30 K, the sites that are initially occupied only by gauche + conformers become partially occupied by gaucheones and viceversa, in agreement with an earlier x-ray diffraction study. 14 In these simulation runs the initial configuration reproduced the equilibrium situation at low temperature, where all molecules are in the majority orientation at each site and conformational disorder is absent. The system is then allowed to evolve freely from this starting condition. Figure 1(a) shows, as a function of simulation time and for four different temperatures, the fraction of sites that remain occupied by the same conformer that occupies them in the starting condition (i.e., the fraction of sites that are still occupied by the low-T equilibrium conformer). It is seen that for simulation temperatures of T m -30 K, the fraction of sites occupied by the majority conformer is virtually unchanged from its initial value of 1. For higher simulation temperatures (approaching the melting point), it is observed that after an initial transient the same fraction is reduced from 1 to a lower value, which remains more or less stationary at long simulation times. Figure 1(b) shows, for the highest simulation temperatures, the final fraction of "disordered" molecules in the new equilibrium configuration, i.e., the steady-state fraction of molecules that have changed their initial orientation. The number of steady-state disordered molecules increases exponentially with temperature, indicating an activated population of nonequilibrium conformers at a given site. Close to the melting temperature (T m ), this fraction is as high as 20%. At T m -10 K it is close to 15%, in agreement with Ref. 14. It is interesting to note that, although the interconversion rate and the population of a given site depend on temperature, the total percentages of each conformer (gauche + and gauche -) in the simulation always remain equal to 50%. Assuming that the population of the minority conformers follows an activated temperature dependence, as suggested by the linear fit displayed in Figure 1(b), an activation energy of ~ 4.1 kcal/mol is obtained. This value is close to the calculated potential barrier between gauche + and gaucheconformers in the gas phase (between 4 and 5 kcal/mol depending on the calculation level 19 ) and of the same order of magnitude as the potential barrier in solution (between 3 and 7 kcal/mol depending on the solvent and the method used to estimate the energy barrier 19,37 ). This comparison suggests that the rotational barrier between the energetically equivalent gauche + and gaucheconformations is mainly determined by intramolecular effects, in contrast with the energy and thus the relative stability of the gauche and transoid conformers, which are instead strongly dependent on the environment, as mentioned in the introduction.
We next turn to our dielectric spectroscopy data acquired on the α phase of TCE upon heating.
Panel (a) of Figure 2 displays the isothermal dielectric loss spectra (ε"(f)) at selected temperatures between 115 and 235 K (just below the melting point). The corresponding modulus and ac conductivity spectra are shown in panels (b) and (c), respectively. The σ' spectra display at low frequency a dc conductivity plateau, which corresponds to the linear decrease towards low frequency in the ε" spectra of panel (a). Two separate spectral features can be clearly discerned in the loss spectra, namely, a low-intensity peak visible at low-temperature, labeled as process II, and a more intense loss feature that becomes clearly visible only at high temperature, close to the melting point, and labeled as process I. Besides these two processes, the loss spectra actually comprise also a third loss, labeled as "pre-peak". To highlight the presence of such pre-peak, in the inset to Figure 2(a) we show the so-called derivative loss spectrum, defined as -(π/2) dε'/d(Logf), 38 for the permittivity data at 224 K. The derivation procedure allows enhancing the visibility of the dipolar loss features. The maximum of the modulus (panel (b)) corresponds to the so-called "conductivity loss" peak, 39 and it can be seen in the inset to panel (a) that its frequency position matches roughly that of the pre-peak in the permittivity representation.
Besides this contribution, two more features are observed in the modulus, at frequencies that match those of processes I and II in the ε" spectra.
In panels (a), (b) and (c) of Figure 2, markers represent experimental spectra and solid lines are fits. In (b), solid lines are fits of the modulus spectra as the sum of three contributions, each described as the imaginary part of a HN function (Eq. (1)). While process II exhibited both shape parameters (HN exponents) different from 1, the conductivity loss could be modeled as a Cole-Cole function and process I with a Cole-Davidson function (see Methods Section). In panels (a) and (c), continuous lines are fits of the loss and ac spectra using Eq. (3) and maintaining the same relaxation times found in the modulus fits.
The plateau value of the σ', which is the dc limit of the conductivity, σ dc , is displayed as Arrhenius plot in Figure 2 that it exhibits the same temperature dependence as σ dc (or more accurately, as the resistivity 1/σ dc ). This confirms the identification of the M"(f) maximum as the conductivity loss, and thus of the pre-peak in ε"(f), which is visible at almost the same frequency, as a conductivity-related space-charge relaxation. While the peak in the modulus representation arises mostly from the σ dc contribution, that is, from the drift of charge carriers under an applied quasi-dc field, in the permittivity representation the σ dc contribution is the linear background, while the weak loss feature (pre-peak) is actually a space-charge relaxation due to the accumulation of charge carriers at sample's heterogeneities such as grain boundaries. 41 Having discussed the conductivity-related features, we now focus on relaxations I and II, which stem from molecular dynamic processes. Figure 3(a) shows the Arrhenius plot of the relaxation times τ max,ε of both relaxations, obtained from the fit of the loss spectra by means of Eq. (3). For comparison, the value of τ max,M of process II is also shown, as obtained from the fit of the corresponding portion of the modulus spectra with Eq. (1). It may be observed that for process II the values of τ max,M and τ max,ε are virtually identical, as expected because the two quantities are related 42 as τ max,ε /τ max,M = ε s /ε ∞ (where ε s and ε ∞ are respectively the low-and highfrequency limits of the real part of the permittivity above and below the characteristic frequency of relaxation II), and such ratio is close to one because the dielectric strength Δε of relaxation II, which is equal to the difference ε s -ε ∞ , is relatively low. For the same reason, the ratio τ max,ε /τ max,M for relaxation I may be expected to deviate from 1 because of the larger dielectric strength of relaxation I; nonetheless, for simplicity in our model of the loss spectra with Eq. (3) we took τ max,ε = τ max,M at all temperatures for relaxation I.
The inset to Figure 3(a) shows the dielectric strength Δε I of process I close to the melting point.
The strength of relaxation I exhibits an increase up to the melting temperature, where the relaxation ceases to exist. Such increase is consistent with the observed behavior of the raw loss spectra (Figure 2(a)), where process I is observed to be smeared out below 180 K while it becomes increasingly visible with increasing temperature. In contrast, the dielectric strength of process II decreases slowly with temperature, as it is normally expected for a dipolar relaxation (not shown). The increase of relaxation I in the modulus representation is reminiscent of the increase of disordered sites discussed in relation with Figure 1(b), and matches the observations of an earlier x-ray diffraction study of solid TCE, 14 which reported dynamic orientational disorder near the melting point. The substantial increase of Δε for process I near the melting temperature is a strong indication that it stems from a molecular dynamic process associated with the conformational site-occupancy disorder. Since such disorder involves conformational changes between gauche + and gaucheisomers with distinct spatial orientation of the C-C bond, we are lead to assign process I to a simultaneous orientational and conformational motion of the TCE molecules. This assignment is corroborated by our molecular dynamics study, as detailed in the following. The temperature dependence of the relaxation times of process I could be modeled with a simply activated (Arrhenius) behavior, with activation energy of 39.3 kJ/mol and hightemperature relaxation time τ ∞ = 0.68 · 10 -14 s, which is consistent with a dipolar dynamics. 43 Process II displayed a more pronounced dependence on temperature, well described by the Vogel-Fulcher-Tamman (VFT) equation, which is given by: Here the prefactor τ ∞ , the fragility parameter D and the so-called Vogel-Fulcher temperature T VF are phenomenological parameters, with values τ ∞ = 6.31 · 10 -12 s, D = 11, and T VF = 87.2 K).
The fit of the relaxation times with an Arrhenius equation or with Eq. (6) also allows determining the vitrification point of both processes, defined as the temperature at which their relaxation time approaches 100 s (see dotted horizontal line in Figure 3(a)) -in other words, the vitrification temperature is defined as to coincide with the glass transition temperature (T g ) if the processes were the main cooperative dynamics in a glass-forming system. The estimated vitrification temperatures are 127 ± 1 K and 119 ± 1 K for process I and II, respectively. It is interesting to note that the two vitrification temperatures are not far from one another.
The behavior of relaxation II is the expected one for a cooperative reorientational process: it is observed at all temperatures, displays VFT behavior and a dielectric strength that decreases slowly with temperature. In this sense, this relaxation is the intrinsic relaxation of the α phase, and it is reminiscent of the observed dynamics in the solid phase of another halogenated ethane derivative, (1,1,2,2)-tetrachloroethane. 25,44 On the other hand, process I has, as mentioned, a strength that increases strongly with increasing temperature. Moreover, the disorder with which it is associated is absent far below the melting point. In this respect, process I has features that make it unique to the solid phase of TCE.
To compare experiment with simulation, we carried out a statistical analysis, in terms of selfcorrelation functions, of our molecular dynamic simulation data. The time self-correlation function of the single-molecule dipole moment p (Eq. (4)) is shown with a dotted line in Figure   3(b). Since the decay of the correlation is too slow in time to allow a reliable analysis, we focus on the C-Cl bond correlation defined by Eq. (5), which is shown for one C-Cl bond of each carbon atom of a TCE molecule in the same Figure 3(b), at three different temperatures. For each temperature, the bond self-correlation function was fitted as the sum of two exponential functions, with the same time constant for all C-Cl bonds of the same molecule. The existence of two decay constants is indicative of the presence of two main dynamic ranges, one at lower frequency, corresponding to molecular dynamic processes that occur more seldom, and the other at higher frequency, corresponding to processes that occur more often. The obtained characteristic self-correlation times are shown as empty squares in Figure 3   It is natural to assign the observation of two clearly separate relaxation times to the presence of two distinct types of dynamics. In view of the similarity of experimental and simulation relaxation times, and in view of the fact that the jumps between equilibrium configurations involve a simultaneous orientational and conformational change, just as required for the dynamic disorder of Figure 1 and observed by x-ray diffraction, 14 we assign dielectric relaxation I to the interconversion dynamics between equilibrium conformers, such as that depicted in the left-hand side of Figure 4. This assignment is corroborated also by the analysis of the mean waiting time between successive equilibrium jumps: as we did in a previous work, 45   It should be remarked that, according to our molecular dynamics and the consequent interpretation of dielectric spectroscopy results, both macroscopic relaxations (I and II) actually correspond to more than one possible microscopic (molecular) dynamics: as exemplified in

Conclusions
We employ molecular dynamics simulations and dielectric spectroscopy to study the ambientpressure stable crystal phase of (1,1,2)-trichloroethane (TCE). Our simulations show that both gauche + and gaucheconformers are present in this solid phase, occupying preferently specific crystallographic sites. While the total population of each conformer phase α is always 50%, independent of temperature, between the melting point T m and T m -40 K a considerable fraction of crystallographic sites are occupied by the minority conformer, in agreement with previous xray diffraction results (Ref. 14). The onset of this disorder is signaled by an anomalous temperature dependence of the (ionic) dc conductivity and of the space-charge relaxation frequency in a ten degree range around approximately T m -30 K.
Two macroscopic relaxations of the sample's polarization are observed by means of dielectric spectroscopy, which stem from distinct molecular dynamic processes. Our MD simulations show that the slower molecular dynamics (relaxation I) involves a simultaneous reorientational and conformational change of the TCE molecules, namely between gauche + and gaucheconformers of well-defined and distinct orientation. The observation of this process both in dielectric experiments and molecular simulations confirms the idea of Ref. 14 that the disorder in solid TCE is dynamic in nature and involves simultaneous orientational/conformational leaps. Our simulations also unveil the existence of short-lived (few ps) molecular fluctuations that are undetectable by x-ray diffraction, and whose existence and frequency are able to account for the experimental observation of the faster molecular relaxation process (relaxation II). The simulation results indicate that such macroscopic relaxation stems both from conformational fluctuations and large-angle librations of the TCE molecules, which are short-lived because the intermediate state in both cases is a non-equilibrium, high-energy configuration with enhanced steric repulsion between the chlorine atoms of next-neighbor molecules.
Our study confirms once more the vast richness of molecular dynamics of ethane derivatives in the solid state. In particular, simultaneous orientational-conformational dynamics are quite rare in solid phases, and it is therefore interesting that the TCE molecules exhibit more than one local dynamics where both changes take place simultaneously. Our results show that the combination of molecular dynamics simulation with a sensitive probe such as dielectric spectroscopy is required to fully unravel the dynamic disorder of small-molecule organic solids.