Gauche–trans Conformational Equilibrium of Succinonitrile under

Feb 24, 2016 - Succinonitrile (C4H4N2) has been shown as an interesting material, which can dissolve many inorganic salts, form intricate self-assembl...
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Gauche-trans Conformational Equilibrium of Succinonitrile under High Pressure Yuxiang Dai, Kai Wang, Bo Zhou, Mingrun Du, Ran Liu, Bingbing Liu, and Bo Zou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b12341 • Publication Date (Web): 24 Feb 2016 Downloaded from http://pubs.acs.org on March 1, 2016

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Gauche-trans Conformational Equilibrium of Succinonitrile under High Pressure

Yuxiang Dai,† Kai Wang,*,† Bo Zhou,† Mingrun Du,† Ran Liu,† Bingbing Liu,† and Bo Zou,*,†



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State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China.

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Abstract Organic chain molecules have considerable importance because of their conformational stability, which is fundamental to their chemical stability. The phase behaviors and conformational equilibrium of simple hydrocarbons and their derivatives under extreme conditions are of interest to research because of their applications. In situ high-pressure Raman spectroscopy studies on succinonitrile up to 24 GPa at ambient temperature have been conducted to investigate its structural property and conformational equilibria. Succinonitrile has undergone a plastic-tocrystal phase transition around 0.7 GPa. A simultaneous conversion of gauche to trans conformation has been observed. A crystal-to-crystal phase transition has subsequently occurred around 2.9 GPa. The second high-pressure phase has remained stable up to 24 GPa. These two crystal structural transitions have also been confirmed by in situ high-pressure angle-dispersive X-ray diffraction experiments. Compared with the reported low-temperature phase, the new phases under high pressure have different molecular conformation and higher density, which can provide better understanding in paths of conformational transitions under different extreme conditions. The new phases under high pressure have different molecular conformations and higher densities compared with the reported low-temperature phase. This result helps clarify the paths of conformational transitions under different extreme conditions.

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Introduction The conformational equilibria are determined by the summation of intramolecular and intermolecular potentials as a central concept in the structural chemistry of biomolecules, polymers, and small flexible compounds in the condensed state.1–3 Applying pressure can reduce intermolecular distance, rearrange molecules, facilitate close molecular packing and efficiently enhance intermolecular interactions. These characters subsequently lead to transitions of crystal structures, which makes compression an efficient method of inducing conformational changes, structural transformations and polymerization.4 The phase behavior and the conformational equilibria of simple chain-shaped hydrocarbons and their derivatives under high pressure have attracted considerable attention.5–13 Succinonitrile (C4H4N2) has been shown as an interesting material, which can dissolve many inorganic salts, form intricate self-assembling network coordination compounds, and act as a potential base for solid electrolytes for lithium battery materials.14–17 Succinonitrile is a solidstate plastic crystal at ambient conditions, with molecules that have well-defined positions and disordered orientation in a crystal lattice.18,19 The properties arising from the low energy barrier for rotation around the C–C bond of the two methylene groups allow the isomerization transition of succinonitrile molecules between the synclinal and antiperiplanar conformers.20 The roomtemperature plastic–crystal phase (phase I) of succinonitrile crystallizes into a bcc-structure that belongs to the Im͞3m space group.18 Both the gauche and trans conformers exist in the roomtemperature phase (~ 20%, trans; 80%, gauche).21 The purification of the conformational mixture by physical stimuli is important in biochemistry.2 Several groups have explored to obtain a sole conformation. They have found that succinonitrile molecules crystallize into the P21/a

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space group containing only gauche conformers at temperatures below 230 K (Scheme 1 and Figure S1).18,21–24 However, pure trans-succinonitrile conformers have not been reported. No detailed high-pressure investigations are reported for succinonitrile although many diffraction, spectroscopic measurements, and computational theories are available at ambient pressure. Investigating the crystal structure and molecular behavior of succinonitrile under high pressure is necessary because the low-temperature phase transition has a collapse of volume, and pressure is also an efficient factor in increasing substance density. The present study performs an in situ high-pressure Raman spectroscopy of succinonitrile by diamond anvil cell (DAC) and sapphire anvil cell to investigate structure transition and molecular conformation in succinonitrile under extreme pressure conditions. Subsequently, in situ angle-dispersive X-ray diffraction (ADXRD) experiments have been performed to further analyze of the crystal structure of succinonitrile under compression. This study will provide basic information on applying succinonitrile under high pressure. This work also helps in understanding the pressureinduced conformational transition of chain-shaped organic molecules. Pre-assembled unsaturated molecules usually favor polymerization reactions under high pressure.25–32 Unsaturated molecules that have not been pre-assembled are difficult to react under compression. Succinonitrile molecules are not pre-assembled by π-stacking or hydrogen bonding at ambient conditions. Through the study of this system, we can explore whether unsaturated molecules, which are not pre-assembled, are difficult to polymerize by compression.

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Experimental Section Succinonitrile with 98% purity was purchased from Alfa Aesar and used as received without further purification. A symmetric DAC with 400 µm diameter culet diamonds was utilized in high-pressure Raman and ADXRD experiments. A T301 steel gasket was placed between the parallel diamonds and pre-indented to a thickness of about 40 µm. A 130 µm diameter hole was manually drilled in the center of the gasket and used as the sample compartment. Partial data were collected by using a sapphire anvil cell to avoid the diamond’s first-order Raman peak. The sapphire anvil cell was furnished with 500-µm-diameter culet sapphires to obtain high-pressure Raman spectra near 1333 cm−1.The DAC was applied to collect the Raman spectra over the 50−1200 and 1400−3400 cm−1 range, obtain high pressures and avoid the sapphire interferences. Subsequently, succinonitrile was loaded in the gasket hole together with a small ruby ball to measure the pressure by using the standard ruby-fluorescence method.33 Argon was used as a pressure transmitting medium (PTM) in partial high-pressure Raman experiments (Figures S2−S4) because succinonitrile dissolves in many kinds of PTM (e.g., 4:1 mixture of methanol and ethanol). Now that succinonitrile is sticky and soft as a solid-state plastic crystal at room temperature, it can create a quasi-hydrostatic pressure environment at ambient conditions. We found the results of this work were not affected by PTM (Figures 1, 2, 5 and 6). The quasihydrostatic pressure conditions were ensured by monitoring the separation and width of ruby R1 and R2 lines. All of the high-pressure experiments were conducted at room temperature. The high-pressure Raman spectra were collected by using an Acton SpectraPro 2500i spectrometer with liquid nitrogen-cooled CCD camera (Pylon, 100B). The 532 nm line from the diode pumped solid state laser with 10 mW power was applied for excitation source. The integration time of each Raman spectrum was kept at 60 s. The spectra were collected through

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backscattering geometry with the spectral resolution set to 1 cm−1. Some vibrations were decomposed by combining Gaussian and Lorentzian line shapes if it is necessary to fit Raman profiles. In situ high-pressure ADXRD experiments were conducted on a 4W2 beamline at the High Pressure Station of Beijing Synchrotron Radiation Facility (BSRF). The monochromatic beam wavelength used for data collection was 0.6199 Å with a 20 × 30 µm2 size. The distance of the sample detector and the geometric parameters were calibrated by a CeO2 standard. An imageplate area detector (Mar345) was utilized to collect the typical Bragg diffraction rings. The average exposure time for each spectrum was set to 500 s to maintain sufficient intensity, considering the light atoms (i.e., C, H, and N) in succinonitrile. Fit2D software was utilized to yield plots of intensity versus 2θ as recorded 2D data.34 Further analysis of the ADXRD spectra was undertaken using commercial Materials Studio 5.0 to gain more information on the crystal structure of succinonitrile under high pressure.

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Results and Discussion The observed succinonitrile Raman spectrum at ambient pressure agrees well with that reported in literature. Therefore, Raman peaks are assigned based on the results reported in literature (Table S1).35–38 In this work, the Raman spectra of succinonitrile were measured at pressure up to 24 GPa. The succinonitrile Raman spectra at the selected pressures are presented in Figures 1, 3 and 5, respectively. The simultaneous changes in many of the Raman modes demonstrate that succinonitrile underwent two structural transitions at 0.7 and 2.9 GPa. The second new phase is stable and did not undergo any further abrupt changes at all higher pressures tested. The frequency shifts in the Raman modes demonstrate the existence of the high-pressure phases (Figures 2, 4, and 6). The shifts of several vibrational modes around 0.7 and 2.9 GPa are discontinuous, whereas the other modes suddenly change in their slopes. These phenomena are also accompanied by the appearance of several new modes and the disappearance of initial modes. The observed spectra provide some insights into the structural features and molecular conformation of high-pressure phases although no crystal structure information can be determined from the high-pressure Raman data. The external modes of the organic crystal are very sensitive to pressure-induced phase transition. The broad peak at about 87 cm−1 is assigned as the external mode at ambient conditions. Figure 1a shows the persistence of this broad Raman mode below 0.7 GPa. This is because succinonitrile existed in the plastic phase (phase I). However, the replacement of this broad Raman modes by three sharper ones (i.e., 71, 105, and 116 cm−1) at pressures higher than 0.7 GPa indicates the formation of a solid crystal structure (phase II). Figure 2 shows the evolution of these low-frequency modes at elevated pressures. All external modes exhibit significant blue shifts at higher pressures, which is caused by the reduction in the intermolecular

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distances that results from a stronger interaction among adjacent molecules. The spectrum shape abruptly changed at 2.9 GPa, which serves as evidence for the phase transition induced by increasing pressure. Three new Raman peaks gradually appeared with high intensity at 128, 158, and 171 cm−1. The intensity of the original peaks distinctly decreased or disappeared. These phenomena indicate the transition of phase II into another new phase (i.e., phase III). The frequency increase in the new Raman peak pattern is preserved up to 24 GPa (Figure S5), which indicates that phase III is stable under 24 GPa. All results of the external modes provide strong evidence for the occurrence of pressure-induced phase transitions at about 0.7 and 2.9 GPa. The changes in internal vibration modes ranging from 200 to 1200 cm−1 also reveal the existence of these two phase transitions (Figure 1). Reported literature

35–38

indicate that among

all the CCN bending modes at 187, 230, 359, 389, 481, and 514 cm−1, the modes at 359 and 514 cm−1 are stronger in the trans conformation (trans band). The modes at 389 and 481 cm−1 are stronger in the gauche form (gauche band). The CH2 rocking mode at 812 cm−1 is related to the gauche conformers, whereas the CCN stretching mode at 952 cm−1 is related to the trans conformers. Most of the internal modes started to gradually shift to higher frequencies of up to 0.7 GPa with increasing pressure. These frequencies show blue shifts because of the reduction in the interatomic distances. Figure 1b shows that trans and gauche bands coexisted at ambient conditions, whereas the initial gauche bands were dominant below 0.7 GPa. On the one hand, the Raman modes at 0.7 GPa, which correspond to the gauche conformers at 389, 481, and 812 cm−1, suddenly disappeared. On the other hand, the related intensity of the other modes enhanced. The absence of the gauche bands and the enhancement of the trans bands suggest that the high-pressure phases were stabilized to trans conformation above 0.7 GPa (Figures 1b and S6). The disappearance of the methylene rocking mode (about 812 cm−1) also suggests random

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freezing of the methylene group in the dense state of succinonitrile over 0.7 GPa. Considering the discontinuities of the external modes, these changes suggest that succinonitrile favors trans conformation for achieving denser packing to facilitate volume reduction. The Raman modes at 0.7 GPa showed normal blue shifts all the way up to 2.9 GPa, which implies that phase II is stable in the 0.7–2.9 GPa range. The two CCN bending modes at 240 and 274 cm−1 were abruptly replaced by one mode at 255 cm−1 when the pressure reached 2.9 GPa. Moreover, an intensity exchange among the CH2 rocking bands appeared at about 1015 and 1036 cm−1. These spectral features indicate that the phase II–phase III transition occurred at 2.9 GPa. Furthermore, phase III of the succinonitrile also only contains trans conformation. A sapphire anvil cell was used to acquire high-pressure Raman spectra near 1332 cm−1 (Figure 3) and analyze the bands covered by the diamond band at 1332 cm−1. Figure 4 shows the evolution of Raman modes from 1100 to 1600 cm−1. The bands of CH2 twisting and CH2 wagging in the gauche conformation suddenly disappeared at 0.7 GPa. Meanwhile, the relative intensity of the CH2 wagging bands in the trans conformation obviously increased at 0.7 GPa. All these phenomena indicate that only the trans conformation survived in phase II, which is consistent with the results acquired by DAC in Figure 1. Such changes in the CH2 bands also indicate that the rotation and the compression of methylene groups occurred during the phase I– phase II transition at 0.7 GPa. All the Raman modes retained regular shifting under further compression until the pressure reached 2.7 GPa. The two new Raman modes at 1276 and 1434 cm−1 emerged, whereas the three original Raman modes largely weakened at about 1290, 1413, and 1458 cm−1 at 2.7 GPa. The shifts of the CH2 wagging at 1354 cm−1 and the Raman mode at 1300 cm−1 became discontinuous. All these abrupt changes indicate that a phase II transition happened

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scissoring/twisting/stretching modes in the 2.7 GPa spectrum indicate that the environment around the methylene groups changed during the crystal structural transition from phase II to phase III. Figures 5a and 5b depict the selected Raman spectra representing the internal modes of succinonitrile in the 2200−2450 and 2800−3300 cm−1 range. Figure 6 shows the pressure dependence of the corresponding modes. From ambient pressure to 0.7 GPa, all the observed internal modes displayed normal blue shifts arising from the contraction of the interatomic distances with increasing pressure. All the Raman modes became sharper at 0.7 GPa (Figure 5). This result is consistent with the phenomena shown in Figures 1 and 3, which indicate that the plastic–crystal structure changed to a crystal structure. The abrupt changes of the C≡N stretching mode evolution at about 2253 cm−1 at 0.7 and 2.9 GPa (Figure 6) indicate the presence of two phase transitions at these two pressure levels. The two CH stretching modes in Figure 5b revealed blue shifts caused by the repulsive nature of the chemical environment around the methylene groups below 0.7 GPa. The CH stretching modes exhibited abrupt red shifts at 0.7 GPa, which implies that the length of the C−H bonds enhanced in transition from the plastic phase (phase I) to the crystalline phase (phase II). This phenomenon occurred at the same time with the conformational transition from gauche to trans. Combined with the changes of the CH2 twisting/wagging/scissoring modes, the discontinuities of the CH stretching modes at 0.7 GPa indicate that succinonitrile molecules have been rearranged. The methylene groups are rotated during the phase transition. Therefore, the phase transition of succinonitrile at 0.7 GPa may involve the crystallization process. Conformational changes are also expected to facilitate the rearrangement of succinonitrile molecules in phase II. The abrupt movement of the CH stretching mode from 2993 to 3001 cm−1 at 2.9 GPa is traced in Figure 6. The other CH

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stretching modes slightly changed. The rotation of the methylene groups is dampened. Furthermore, the C–H bonds were shortened in the second phase transition. The CH stretching modes above 2.9 GPa showed regular shifts of up to 24 GPa (Figure S7), which indicates the stability of phase III over this pressure range. Conclusively, the first phase transition is reconstructive with the rotation of the CH2 groups. The second one is associated with the local distortions of the CH2−CH2 skeleton based on the abovementioned comments. Additionally, the trans conformation is preferred in the two condensed phases under high pressure. The related intensity of the C≡N stretching mode did not abruptly decrease in Figures 5a and S8. The polymerization reactions of succinonitrile were not observed up to 24 GPa. This is because the succinonitrile molecules are not pre-assembled by hydrogen bonding or π-stacking interactions. Moreover, the intermolecular interactions are not strong enough to make the reactive sites close enough to react under high pressure.25–32 A comparison of the Raman spectra of the recovered sample and succinonitrile at 1 atm (Figure S9) indicates that the observed transitions are also completely reversible. A high-pressure ADXRD measurement was performed to further confirm the two phase transitions induced by elevating pressure. Figure 7 shows the X-ray diffraction patterns of succinonitrile with increasing pressure. The emergence of several sharp peaks at 0.7 GPa indicates that the transition from phase I to phase II is a transition of succinonitrile from the plastic state to the crystal state. The diffraction peaks shifted to higher angles with increasing pressure, which indicates that the unit cell volume is decreasing and the crystal structure tends to achieve close packing at high pressures. Many new peaks (marked by arrows) emerged above 2.9 GPa, whereas some initial peaks weakened and subsequently vanished. This phenomenon indicates that the crystal structure of succinonitrile was again changed by compression. All the

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high-pressure ADXRD experiment results provide direct evidence of these two phase transitions, which is consistent with the Raman results. The Pawley refinement of the diffraction pattern at 0.7 and 4.1 GPa was conducted based on rigid body approximation to obtain more information on phases II and III (Figures S10 and S11). Much background and insufficient signal-to-noise in the diffraction pattern were found in the polycrystalline samples of organic molecules inside a DAC, which is challenging. The refinement results indicate that phases II and III might both be indexed to a monoclinic symmetry with possible space groups P21/m and Pm, respectively. Figure 8 shows the pressure dependence of the unit cell volume. The volume collapse is ~10.6% from phase I to phase II at 0.7 GPa. Phase II then underwent a solid–solid transition at 2.9 GPa, which is marked by a 6.3% volume jump. Volume reduction in the first phase transition is much bigger than that in the second phase transition because succinonitrile changed from a plastic state to a crystal state from phase I to phase II, with gauche conformers transferring to trans conformers. Succinonitrile underwent another transition from phase II to phase III between two crystal states with the same molecular conformation (only trans conformers). The molecular interactions could not support the increased Gibbs free energy when the pressures reached 0.7 and 2.9 GPa. Therefore, the molecular interactions change to reduce the free energy, thereby resulting in phase transition. Interestingly, all the gauche characteristic bands disappeared in the first high-pressure phase transition. This experimental result indicates that pressure selected trans conformers, which have a higher molecular symmetry and a smaller volume than the gauche conformers, to adapt to the denser space under high pressure conditions. These changes in the isomer population are affected by the transition from the plastic to the crystalline state, which is different from our previous study on pressure-dependent tautomerization.39 Accordingly, pressure can result in more planar

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molecules, as shown in other reports.40,41 These phenomena show that high pressure favors quasi-2D structure in a denser arrangement of succinonitrile molecules. Closely packed molecules adopt energetically unfavored conformation to accommodate strains in their crystal environment at high pressure because the energy of the gauche isomer is lower than the trans isomer by 0.36 kcal mole−1.37 The greater stability in phases II and III of succinonitrile is attributed to the higher dielectric constant and the greater dipole moment of this structure compared with phase I. From phase I to phase II, succinonitrile selected more efficient crystal packing with energy compensating the difference between gauche–trans conformers, which can be written in the following form: phase I phase I phase II phase II Einter +Econf = Einter +Econf + ∆E

∆E, as the transition latent heat, is supposed to be a small positive value. Meanwhile, phase II phase I Einter − Econf ≅ 0.8 × 0.36 kcal mole −1 = 0.288 kcal mole −1

The intermolecular interactions of the rearrangement constitute the main energetic contribution driving this transformation.6,42,43 The release of the lattice-packing interactions in the first phase transition around 0.7 GPa might compensate for a big outcome of the conversion energy, whereas the latent heat of the transition contributes a small part to the energy transfer of the structure. This phase transition yielded succinonitrile phase II with the molecules in the trans conformation located in ordered orientations. An analogous energy balance between the intra- and intermolecular contributions can also be applied to much more complex systems, such as the protein folding and reversing handedness of DNA turns controlled by compression.2,3,44 The first high-pressure polymorph (phase II) of succinonitrile with a higher molecular symmetry should be characterized by a melting point higher than the polymorph at ambient conditions (phase I). Pressure increases the melting point

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and induces conversion to the more symmetrical conformation (trans conformation). The volume relations and the molecular symmetry relation between phases I and II are also consistent with the Carnelley rule.45 The transition path of the conformational equilibrium at 0.7 GPa is exactly opposite to the low-temperature transition of succinonitrile (Figures 1b, 3 and S1). According to reported literature,21 the volume collapse of the conversion from the room-temperature phase (phase I) to the low-temperature phase is less than 7%. Whereas our ADXRD results shows that the volume jump of the first high-pressure transition (10.6%) is larger than that of the lowtemperature phase transition, which indicates that the first high-pressure polymorph (phase II) may have a higher density than the low-temperature phase. Corresponding to the Wallach rule,46 the higher-density phase favors a centrosymmetric structure. Coincidentally, the high-pressure phases only comprise centrosymmetric achiral conformers (trans conformers), whereas the room-temperature and low-temperature phases contain non-centrosymmetric chiral conformers (gauche conformers). The two phase transitions under high pressure are totally reversible, which is because only weak molecular interactions such as van der Waals interactions are involved and the small energy barriers of these transitions are easily overcome when pressure is released.

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Conclusion In summary, we have studied the structure and property of succinonitrile up to 24 GPa. Highpressure Raman and ADXRD spectra have shown two phase transitions. The plastic phase (phase I) changed to a crystal phase (phase II) when the pressure exceeded 0.7 GPa. The phase transition corresponded to an orientational disorder–order transition. The original equilibrium of the molecular conformation was broken. The initial coexistence of the gauche and trans conformers transferred to only the trans conformers in phase II. This phenomenon is exactly opposite to the low-temperature phase transition of succinonitrile because phase II had centrosymmetric achiral conformers (trans conformers) that accommodated the higher density. Phase II then changed into another crystal phase (phase III) at 2.9 GPa. The succinonitrile molecules were rearranged and changed to denser trans conformers in the crystal structure of phase III. All the observed transitions were completely reversible upon release to ambient conditions. Moreover, phase III was stable up to 24 GPa without the occurrence of polymerization. This result demonstrates that unsaturated molecules that have not been preassembled are difficult to react under compression. The molecular behavior of succinonitrile under compression may elucidate the conformational equilibrium of organic molecules. Moreover, pressure is supposedly an efficient factor in obtaining sole conformation from the conformational mixture.

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Scheme 1. Newman's projections of the succinonitrile conformers.

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Figure 1. Raman spectra of succinonitrile at selected pressures: (a.) 50−300, (b.) 300−1200 cm−1. g denotes gauche, while t represents trans.

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Figure 2. Pressure dependence of the Raman shifts of succinonitrile (50−1200 cm−1).

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Figure 3. Raman spectra of succinonitrile at selected pressures (1100−1600 cm−1). g denotes gauche; while t represents trans.

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Figure 4. Pressure dependence of the Raman shifts of succinonitrile (1100−1600 cm−1).

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Figure 5. Raman spectra of succinonitrile at selected pressures: (a.) 2200−2500 cm−1, (b.) 2800−3300 cm−1.

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Figure 6. Pressure dependence of the Raman shifts of succinonitrile (2200−3060 cm−1).

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Figure 7. Representative synchrotron X-ray diffraction patterns of succinonitrile at high pressures.

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Figure 8. Unit cell volume as a function of pressure.

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Supporting Information Experimental detail information about Raman spectroscopy and X-ray diffraction cited in manuscript. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author *E−mail: [email protected]. Tel: 86-431-85168882 *E−mail: [email protected]. Notes The authors declare no competing financial interests. Acknowledgments This work is supported by NSFC (Nos. 91227202, and 11204101), RFDP (No. 20120061130006), Changbai Mountain Scholars Program (No. 2013007). Angle-dispersive XRD measurement was performed at 4W2 beamline, Beijing Synchrotron Radiation Facility (BSRF) which is supported by Chinese Academy of Sciences (No. KJCX2-SW-N20, KJCX2SW-N03).

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Scheme 1. Newman's projections of the succinonitrile conformers. 76x30mm (300 x 300 DPI)

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Figure 1. Raman spectra of succinonitrile at selected pressures: (a.) 50−300, (b.) 300−1200 cm−1. g denotes gauche, while t represents trans. 152x117mm (300 x 300 DPI)

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Figure 2. Pressure dependence of the Raman shifts of succinonitrile (50−1200 cm−1). 76x87mm (300 x 300 DPI)

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Figure 3. Raman spectra of succinonitrile at selected pressures (1100−1600 cm−1). g denotes gauche; while t represents trans. 76x101mm (300 x 300 DPI)

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Figure 4. Pressure dependence of the Raman shifts of succinonitrile (1100−1600 cm−1). 76x87mm (300 x 300 DPI)

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Figure 5. Raman spectra of succinonitrile at selected pressures: (a.) 2200−2500 cm−1, (b.) 2800−3300 cm−1. 152x152mm (300 x 300 DPI)

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Figure 6. Pressure dependence of the Raman shifts of succinonitrile (2200−3060 cm−1). 76x87mm (300 x 300 DPI)

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Figure 7. Representative synchrotron X-ray diffraction patterns of succinonitrile at high pressures. 76x114mm (300 x 300 DPI)

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Figure 8. Unit cell volume as a function of pressure. 76x57mm (300 x 300 DPI)

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Table of Contents Graph 76x29mm (300 x 300 DPI)

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