Molecular Simulation of the Pressure-Induced Crystallographic Phase Transition ofp-Terphenyl

Bohdan Schatschneider‡ and Eric L. Chronister*,†

Department of Chemistry, UniVersity of California, RiVerside, RiVerside, California 92507, United States, andDepartment of Chemistry, The PennsylVania State UniVersity, The Eberly Campus, Uniontown,PennsylVania 15401, United States

ReceiVed: June 28, 2010; ReVised Manuscript ReceiVed: October 22, 2010

The pressure- and temperature-induced polymorphic crystal phase transitions of p-terphenyl (PTP) have beenmodeled using a modified PCFF interaction force field. Modifications of the interaction potential were necessaryto simultaneously model both the temperature-induced phase transition at ambient pressure and the pressure-induced phase transition at low temperature. Although the high-temperature and high-pressure phases areboth characterized by flattening of the PTP molecule, the mechanisms of the temperature- and pressure-induced phase transitions are different. At high temperature thermal energy exceeds the torsional barrier,resulting in a bimodal phenyl ring twist angle distribution that aVerages to zero. In contrast, compression ofPTP at high pressure results in a static planar structure. At high pressure the compression of the unit cell isalso characterized by large compression of the a lattice parameter and weak compression of c, but someexpansion of the b lattice parameter. The expansion of the b lattice parameter is likely associated with pressure-induced soft mode behavior of some lattice vibrations as well as soft mode behavior of pseudolocal phononsassociated with impurities in PTP. The crystallographic angles R, �, and γ also indicate a triclinic crystalphase above the critical phase transition pressure of Pc ∼ 0.5 GPa at low temperature, suggesting a distinctphase separate from the monoclinic high-pressure phase at high temperature.

1. Introduction

The strong coupling of molecular and intermolecular interac-tions in polyphenyls leads to interesting temperature- andpressure-induced polymorphic crystalline phase transitions.Structural phase transitions are often classified as “order-disorder”when the harmonic coupling is weak relative to the transitionbarrier height or as “displacive” in the strong coupling case.1

Crystalline p-terphenyl (PTP) is a particularly interesting systembecause there is strong coupling between molecular andintermolecular coordinates and because the interconversionbarrier height is comparable to the harmonic coupling strength.2

In addition, both order-disorder2,4 and displacive phasetransitions5,6 have been reported under various temperature andpressure conditions, respectively.

A number of experimental studies have focused on thecharacteristic electro-optic properties of polyphenyl materials.7-15

PTP in particular has been utilized as a host crystal for singlemolecule spectroscopy16-18 because of the unique dynamicsassociated with internal rotation of the central phenyl ring.19

Doped PTP has also recently been reported as a robust single-photon source, with the ability to emit >109 photons beforephotobleaching.20 Internal crystal defects have also been shownto permit micrometer scale molecular translations and photo-bleaching times that can differ by 2 orders of magnitudedepending on the orientation of the transition dipole relative tothe different crystallographic axes.21

Crystalline p-polyphenyls such as PTP can undergo uniquestructural phase transitions accompanied by a change of the

molecular conformation.6 Weak intermolecular interactions inthe crystal mediate the ortho-hydrogen repulsion and theπ-electron delocalization effects that control the libration of thecentral phenyl ring.22 Diffuse neutron scattering measurementsof the short-range ordering in low-temperature PTP show thatcentral phenyl ring twist angles alternate in sign for neighboringmolecules along the a and b crystallographic directions due tocooperative “ab” plane motions of neighboring molecules actingas molecular rods and levers.23

The polymorphic phase transitions of PTP under variabletemperature and pressure conditions have been studied viaX-ray,24-27 IR,28-30 Raman,6,31-33 optical absorption,66 neutronscattering,34-38 time-resolved THz39 and optical spectroscopy,40,61,65

NMR,41 and calorimetry.42,5 In addition, molecular dynamics(MD) simulations,43-46 pressure-dependent lattice dynamics,47

and ab initio calculations have been performed under highpressure.48

Modeling complex molecular crystals such as PTP are stilllargely beyond the scope of ab initio methods.49 However, forsmaller molecules DFT can be combined with empiricalmethods50,51 as well as perturbation theory52 to yield dispersioninteractions and crystal structure predictions.53 MD simulationsusing classical interaction potentials can provide an efficientand accurate method for modeling molecular crystals. Theprediction of molecular crystal structures requires accuratepotentials since most molecular solids can crystallize in differentcrystal polymorphs that may only differ in lattice energy byonly a few kJ/mol.49 Furthermore, finding a potential that cansimultaneously model temperature- and pressure-induced phasetransitions requires a potential that accurately capture both intra-and intermolecular interactions. This is particularly true for PTPbecause of the low torsional barrier of the central phenyl ring

* To whom correspondence should be addressed. E-mail: eric.chronister@ucr.edu.

† University of California, Riverside.‡ The Pennsylvania State University.

J. Phys. Chem. B 2011, 115, 407–413 407

10.1021/jp105973e 2011 American Chemical SocietyPublished on Web 12/23/2010

and the resulting coupling of this molecular motion to inter-molecular degrees of freedom.

Previous MD simulations of low-temperature PTP43 utilizeda modified Tsuzuki/Tanabe torsion potential54 with independentcharges on the 10 unique atom sites to reproduce the temper-ature-dependent phase transition.43 A Benkert-Heine-Simmons(BHS) intramolecular potential coupled with a modified Gavez-zotti/Filippini intermolecular potential55 has also been used toexplore the compression of the double-well torsion potentialinto a single-well potential at high pressure.44 That studydemonstrated the planarization of the molecule at elevatedpressures at room temperature, but phase transitions of the PTPcrystal were not reported. A “6-exp” intermolecular potential56

was coupled with a pressure-dependent intramolecular torsionpotential to model phonon dynamics associated with thepressure- and temperature-induced phase transitions in PTP.47

Lattice dynamics calculations have also been used to identifyunstable phonon modes associated with the order-disorderphase transition. Ab initio calculations have been used to explorethe effect of pressure on the electronic and optical propertiesof PTP.48

External high pressure can be used to tune the relative strengthof molecular and intermolecular interactions to affect thestructural and optical properties of materials.26,48,57 The goal ofthe present study has been to explore the ability of a modifiedstandard crystal potential to accurately model the moleculardynamics associated with both the temperature-induced phasetransition at ambient pressure and the pressure-induced phasetransition at low temperature (i.e., 20 K) in PTP. A force fieldis obtained by optimizing an intramolecular torsion potentialterm of the polymer consistent force field (PCFF)58,59 utilizingnonbonding Lennard-Jones parameters from the COMPASSforce field.60 A one-parameter optimization of the intramoleculartorsion potential term is found to be sufficient for obtaining acrystal potential that can accurately model both the criticaltemperature (at ambient pressure) and the critical pressure (atlow temperature).

PTP has an interesting phase diagram with at least threephases reported in the temperature and pressure regime ofinterest, as summarized in Figure 1. Under ambient pressureconditions there exists a monoclinic crystal phase at hightemperature34 and triclinic phase at low temperature.25 In thehigh-temperature P21/c monoclinic phase of PTP neutron and

X-ray diffraction studies have reported a bimodal probabilityfor the central ring libration angle,4,2 which has also beenobserved in MD simulation at high temperature.44,63 Pressure-dependent Raman6 and neutron diffraction5,37 measurementshave defined the triclinic/monoclinic phase boundary in the low-temperature and high-pressure regime, and optical studies ofimpurity molecules have been used to extend this phaseboundary to low temperature and high pressure.40,66 Neutronscattering studies37 reveal a Bragg peak associated with thetriclinic/triclinic phase boundary illustrated in Figure 1. Thehigh-pressure low-symmetry triclinic region of the phasediagram has been characterized by a critical wave vector37 thatindicates reorganization of the molecules, but without a changein either the space group or the number of molecules per unitcell. The soft phonon mode associated with this region6 indicatesthat the PTP phase transition evolves from an order-disordertransition at low pressure31,32 to a more displacive reconstructivetransition at high pressure6,37 (e.g., 0.3 GPa and 50 K). X-ray,neutron diffraction, and optical measurements all confirm fourunique molecular sites in the low-temperature low-pressuretriclinic phase, but only one optical site is observed in eitherthe high-temperature or the high-pressure phases.66

2. Experimental Section

MD calculations were performed using the Accelrys MaterialsStudio 4.2 on a Dell quad-core Linux machine (1.87 GHz) witha 64 bit memory extension. The starting configuration of thePTP triclinic phase for all simulations was taken from the low-temperature X-ray structure,25 illustrated in Figure 2a. Thetriclinic phase was modeled with a pseudo-monoclinic unit cellconsisting of eight PTP molecules with four unique crystal-lographic sites (M1, M2, M3, M4), each having a unique torsionangle (t1, t2, t3, t4) defined in Figure 2b, with values of 15.3°,

Figure 1. Summary of the phase diagram for p-terphenyl. The opensquares and open circles are from Raman measurements of p-terphenyland perdeuterated p-terphenyl, respectively.6 Small solid circles are fromneutron scattering measurements of deuterated p-terphenyl.5 Solidsquares are obtained from optical spectra of doped p-terphenyl.40,66

Figure 2. Triclinic unit cell and torsion angle used as the startingstructure for calculations.25 (a) Triclinic unit cell viewed along c. (b)Torsion angle defined for each molecule.

408 J. Phys. Chem. B, Vol. 115, No. 3, 2011 Schatschneider and Chronister

-26.9°, 18.3°, -23.4°, respectively. Calculations were per-formed on an expanded 2 × 2 × 2 supercell containing 64molecules.

The effect of computational sample size on the MD resultswas addresses by running sample calculations on larger 3 × 3× 3 (216 molecules) unit cell structures, which yieldedcomparable torsion angles and unit cell parameters to thoseobtained for simulations on 2 × 2 × 2 (64 molecule) structures.Comparable results were obtained for a variety of temperatureand pressure conditions (e.g., T ) 113 K, P ) 0 GPa and T )20 K, P ) 0.7 GPa). Given the correspondence with thedynamics of larger structures, the 2 × 2 × 2 lattice was chosento facilitate a more complete series of calculations under variablepressure and temperature conditions.

Pressure calculations were performed using an NPT ensemblewith a Berendsen thermostat.43 A Parrinello barostat was usedto permit reorganization of the unit cell parameters.60 An atom-based summation of the nonbonding interactions was used witha 9.5 Å cutoff. The simulations were compiled with 100 000,0.5 fs steps. No symmetry restrictions were imposed on thestructures during the simulations. The thermostat and barostatwere chosen for maximum thermalization and reorganizationof unit cell parameters without symmetry restrictions in orderto obtain a globally minimized structure.

Hysteresis has been reported for experimental pressure-induced phase transitions across the triclinic/triclinic phaseboundary37 (shown in Figure 1). To minimize the influence oflocal energy structures, each MD simulation was performedusing several different initial structures (e.g., triclinic structureat 113 K vs RT monoclinic structure), and consistent pressure-dependent results were obtained, independent of the startingstructure.

3. Results and Discussion

3.1. Force Field Optimization. A modified PCFF force fieldwas derived using the nonbond Lennard-Jones values from theCOMPASS force field. The “LJ-9-6 non-bond” values used forthe sp2 aromatic carbon (cp) and hydrogen bound to an aromaticcarbon (h1) were 3.915 and 2.878 Å for r0 and 0.068 and 0.023kcal/mol for ε0, respectively. A one-parameter optimization ofthe second-order torsion potential term (e.g., the cp-cp-cp-cpcoordinate shown in Figure 2b) was used to obtain a potentialwith a minimum torsion angle ∼40° and peak ratio of ∼1.9 forthe twisted barrier divided by the energy at the minimum, whichis consistent with modeling of the temperature-induced phasetransition.43

Two modified PCFF potentials are shown in Figure 3 in whichthe second-order torsional term was chosen to be 1.00 and 0.96kcal/mol, respectively. PCFFa reproduces the minimum-energyangle and relative energy extremes of ref 43.

The PCFFa force field was used to model the temperature-induced phase transition to confirm that the potential properlymodeled the known critical temperature for the triclinic/monoclinic phase transition, Tc ) 193 K.43,62 The temperature-induced phase transition is adequately modeled using eitherPCFFa or PCFFb, as shown in Figure 4. The dihedral anglevalues at 113 K reproduce the general trends observed in theexperimental X-ray data, as shown in Table 1. Force fieldoptimization involved three aspects: modeling Pc at lowtemperature, modeling Tc at ambient pressure, and reproductionof reported values of the M1-M4 torsion angles at lowtemperature and ambient pressure. Previous force fields usedto model the temperature-induced phase transition43 were ableto reproduce the published torsion angles to within about a

degree,2 as listed in Table 1. However, these potentials werenot as successful at simultaneously modeling the pressure-induced phase change at low temperature.62 Some force fieldsfailed to yield a well-defined critical pressure, while othersyielded a critical pressure well below the experimental value.Modern X-ray measurements also indicates the existence ofsome intrinsic disorder in the refinement of the PTP structure,in which case an exact fit to the torsion angles may not be asvaluable a metric. In the present study, greater significance wasplaced on minor force field modifications that could simulta-neously model the P and T phase transition boundaries whilepreserving the general features of the M1-M4 torsion angles.

3.2. Modeling the Pressure-Induced Phase Transition.Since PCFFa and PCFFb were both shown to adequatelyreproduce the temperature-induced phase transition at ambientpressure, they provided enough flexibility to optimize thepotential to simulate the pressure-induced solid-solid phasetransition at 20 K. Figure 5 shows the absolute values of theaverage dihedral angle as a function of pressure for PCFFa. Atlow pressure (0-0.3 GPa) four unique torsion angles areobtained as expected from the experimental triclinic structure.By ∼0.5 GPa the torsion angles for the four different sites haveall largely collapsed to zero, similar to the high-temperaturehigh-symmetry phase at high pressure.44 The high-pressure phasehas only one optical site,61 reminiscent of the high-temperaturemonoclinic phase, in which all of the molecules are planar.

Figure 3. Inter-ring torsion potential profiles for crystalline p-terphenylobtained with modified PCFF force fields.

Figure 4. Variation of dihedral angle as a function of temperature.Error bars were obtained by averaging ∼10 separate simulations withunique initial velocities.

Molecular Simulation of p-Terphenyl Phase Transitions J. Phys. Chem. B, Vol. 115, No. 3, 2011 409

The dihedral angle distributions provide insight into how thecollapse of the double-well potential eliminates the torsion angledifferences at high pressure. The angle distribution is narrowand localized at low pressures (0-0.3 GPa), in contrast to thebimodal distribution reported at higher temperature, since at 20K the thermal energy is well below the torsion barrier height.By P ∼ 0.5 GPa the increased intermolecular interaction isenough to force the molecules into a planar structure, as shownin Figure 6, with a torsion angle distribution centered around0°. Under high pressure the double-well potential is compressedinto a single-well torsion potential,44 and near the phasetransition pressure at low temperature (Pc ∼ 0.5 GPa) significantbroadening of the angular distribution is observed, as seen inFigure 6. Changes in the width of the torsion angle distributioncorroborated the critical pressure determined from changes inthe magnitude of the torsion angles. The broadening of thetorsion angle distribution observed near the phase transitionpressure was attributed to increased low-frequency motions atthe phase transition. The magnitude of the torsion angles wasfound to be a more sensitive measure of the phase transition.

Pressure-induced changes in the low-temperature absorptionspectra of pentacene impurities doped into PTP have beenreported.61 Simulations of the polarized single molecule spec-troscopy were able to correlate specific crystallographic sites(M1, M2, M3, M4) with the separate low-temperature optical sitesat ambient pressure (O1, O2, O3, O4).63 The crystallographic sitesassociated with larger torsion angles correlated with larger redshifts of pentacene occupying the corresponding photosite.63 Acrystallographic site associated with a large torsion angle causesa greater matrix shift for a pentacene molecule located in thatsite.64 The absorption spectrum of pentacene doped PTP at 15K shows four distinguishable photosites at low temperature, butonly one photosite at pressures above Pc > 0.65 GPa.61 Thecalculated coalescence of the different torsion angles at pressuregreater than 0.5 GPa correlates well with the pressure-inducedchanges in the optical spectroscopy.

3.3. Effect of Pressure on the Crystal Structure. Theexperimental and simulated unit cell parameters at ambientpressure are summarized in Table 2. Experimental studies27 andsimulations44 of PTP at high pressure and room temperature(RT) have shown that the a and c parameters experienced thelargest distortion, while the change in b was less than one-halfthat of a.27,44 The distortion of the unit cell was attributed torotation of the PTP molecules about their long molecular axis,resulting in an increase in the herringbone angle θ (defined inFigure 9b) and the set angle � (defined in Figure 9a), allowingfor “linear slip” and a tighter packing arrangement.

Although the high-temperature and high-pressure phases areboth characterized by flattening of the PTP molecule, themechanisms of the temperature- and pressure-induced phasetransitions are different. At high temperature thermal energycan exceed the torsional barrier, resulting in dynamic phenylring torsion that results in a symmetric bimodal twist angledistribution that aVerages to zero. In contrast, compression underpressure can yield a single-well potential, with a localized torsionangle distribution centered about a most probable planarstructure.44 Compression under high-temperature conditionsyields a monotonic change from an average planar structure toa most probable planar structure, i.e., conversion of a double-well torsion potential into a single-well potential.44 In contrast,compression at low temperature, e.g. 20 K, causes a shift inthe torsion angle distribution, as shown in Figure 6.

The aim of the present study has been to focus on modelingthe pressure-induced phase transition at low temperature. Thisfocus is motivated by a number of experimental pressure-dependent spectroscopic studies of the low-temperature phase

TABLE 1: Variation of Torsion Angles at 113 K for Two Similar PCFF Force Fields

universal force fields modified PCFF experimental simulations

site PCFF COMPASS PCFFb PCFFa X-ray25 ref 43

M1 1.02 1.6 21.5 22.5 15.2 16.5M2 -10.6 -0.9 -22.3 -23.7 -26.8 -25.5M3 2.04 -6.0 20.1 21.4 18.3 17.7M4 -1.7 -2.6 -23.8 -25.4 -23.4 -23.6

Figure 5. Variation of dihedral angle as a function of pressure usingPCFFa.

Figure 6. Variation of dihedral angle distributions of T2 as a functionof pressure using PCFFa at T ) 20 K.

TABLE 2: Comparison of Experimental and MD Unit CellParameters at 113 K and Ambient Pressure

cell parameters X-ray at 113 K from ref 25 PCFFa

a (Å) 16.01 16.63b (Å) 11.09 10.65c (Å) 13.53 13.38R (deg) 90.0 90.2� (deg) 92.0 95.8γ (deg) 90.0 90.7

410 J. Phys. Chem. B, Vol. 115, No. 3, 2011 Schatschneider and Chronister

boundary.61,65,66 The magnitude of the torsion angle provides aconvenient and sensitive metric for modeling this crystal-lographic phase transition in PTP.43,62

Compression of PTP at low temperature results in a localizedtorsion angle distribution with a most probable planar structure,in contrast to the bimodal distribution that aVerages to a planarstructure in the high-temperature monoclinic phase. When thelow-temperature system is placed under pressure, the moleculescooperatively flatten and rotate along the long molecular axis,to achieve the increase in θ and � associated with more efficientpacking of the molecules. The twisted molecular structure atlow temperature also has significant effects on pressure-inducedchanges in the lattice parameters (e.g., pressure-induced expan-sion of the b lattice parameter) compared with the hightemperature crystal, as shown in Figure 7.

The compression of unit cell parameters as a function ofpressure at low temperature (20 K) is shown in Figure 7. Thepressure-dependent lattice parameters reveal a phase transitionat ∼0.5. When pressure is increased from ambient pressure tothe high-pressure phase at 0.8 GPa, the length of a is found tocompress by ∆a ∼ 1.2 Å, while the corresponding compressionof c, ∆c ∼ 0.17 Å, is almost an order of magnitude smallerthan the change in a (e.g., ∆c , ∆a). Interestingly, b is observedto expand by ∼0.21 Å over the same pressure range. Thedominant compression of a is attributed to both intra- andintermolecular rearrangements, while the change in c mainlyinvolves intermolecular structural rearrangements. The flatteningof the PTP molecules is oriented mainly along the a direction,allowing for large compression along that axis. Compressionof the PTP crystal at room temperature has been shown to causesa “linear slip” in which aligned rows of PTP molecules slide inbetween each other to increase packing,27,44 quantified by adecrease in c, an increase in �, and an increase in the set angle�. Under the low-temperature conditions of this study linearslip is found not to be as significant, resulting in a relativelysmall compression of c.

The pressure-induced phase transition at low temperature ischaracterized by a flattening of the molecules and an increasein the herringbone angle θ (e.g., compression of a), as opposedto a “linear slip” (e.g., compression of c) of the molecular planesobserved for the high-temperature monoclinic phase under high-pressure conditions.27 An expansion of b at high pressure isobserved at the phase transition. Examination of the low-temperature triclinic crystal viewed down the a-b plane (Figure9b) illustrates that reduction of the molecular torsion angle athigh pressure increases intermolecular interactions with nearest

neighbors along the b direction (Figure 9d). Experimentalpressure-dependent crystallographic studies have not beenreported at very low temperature. However, the observation ofsoft vibrational modes6,65 at high pressure is consistent with alattice parameter expansion.

A soft phonon mode is observed at high pressure in the low-temperature phase,6 and a soft pseudolocal phonon mode hasalso been observed in the low-temperature phase of impurity-doped PTP.65 The observation of phonon frequencies thatdecrease with compression of the low-temperature lattice is alsoconsistent with the pressure-induced expansion of the b latticeparameter observed in the MD simulation, shown in Figure 7.

MD simulations44 and X-ray measurements27 under high-pressure at RT show that a linear slip mechanism is importantfor compression of the lattice. This is largely due to the factthat thermal motion yields an aVerage planar molecular structuresuch that compression occurs by an increase in the herringboneangle θ and increase in the set angle � (the angle made betweenthe long molecular axis and the c* axis) and a decrease in theunit cell height h, as illustrated in Figure 9. In contrast, at lowtemperature the dominant mechanism for compression is reduc-tion of the static molecular torsion angle, which occurs primarilyalong the a crystallographic direction. A pressure increase fromambient to 0.7 GPa at low temperature yields a reduction inthe unit cell height that is only one-third of that at hightemperature,27 confirming that the linear slip mechanism is lessimportant at low temperature. Nevertheless, some increase in� and � do occur at low temperature, as shown in Figure 9a,resulting in some increased molecular packing.

The effects of pressure on unit cell angles at low temperatureare shown in Figure 8. The phase transition pressure ∼0.5 GPais evident in the change observed in R, �, and γ. The crystal isoften modeled as pseudo-monoclinic at low temperature25

because � is the only angle that differs significantly from 90°.From 0 to 0.4 GPa � increases slightly with pressure (similarto RT experiments27) while the angles R and γ remainedunchanged over this pressure regime. At the critical phasetransition pressure Pc ∼ 0.5 GPa there is a rearrangement of allof the unit cell angles associated with planarization of the PTPmolecule. The fact that R and γ deviate significantly from 90°above the transition pressure suggests that the high-pressurephase at low temperature may not be monoclinic. This resultimplies another (as yet undetected) phase boundary separatingthe high-temperature high-pressure monoclinic phase and thelow-temperature high-pressure phase (see Figure 1). Althoughoptical spectroscopy shows that both of these phases possess a

Figure 7. Average unit cell parameters as a function of pressure for p-terphenyl at T ) 20 K using the PCFFa force field.

Molecular Simulation of p-Terphenyl Phase Transitions J. Phys. Chem. B, Vol. 115, No. 3, 2011 411

single optical photosite,61 the simulations suggest that they aredistinct crystallographic phases.

Neutron diffraction studies indicate the existence of a phaseboundary dividing the low-symmetry triclinic phase at highpressure,5,37 as illustrated in Figure 1. There are several reasonswhy the reconstructive phase transition is not observed in theMD study: (1) the torsion angle used to characterize theorder-disorder phase transition may not be sensitive to thereorganization associated with the neutron diffraction Bragg

peak; (2) the location of the phase boundary pressure is notknown at the 20 K temperature of this study; (3) studies of thetriclinic/triclinic reconstructive phase transition report increasedhysteresis at low temperature,37 so at 20 K the lower pressurephase may remain metastable until the higher pressure phaseboundary is crossed. The focus of the present study has beento model the phase transition region identified in Raman studiesof neat crystals6 and various optical studies of impurity dynamicsin PTP under pressure.40,61,65,66

Figure 9 illustrates the effect of pressure the crystallographicand molecular arrangements for a 64-molecule array at 20 K.The ambient pressure triclinic phase is illustrated in parts a andb of Figure 9 viewed along the b crystallographic axis and thelong molecular axis, respectively. At ambient pressure the a,clattice plane is fairly square, with a small set angle �, and thereare four unique out-of-plane torsional twist angles of the centralphenyl rings corresponding to the four distinct sites of thetriclinic crystal structure (colored as green, red, blue, and violet).Figure 9c,d shows corresponding projections for the high-pressure phase at a pressure P ) 0.7 GPa. The pressure-inducedincrease in � (previously plotted in Figure 7) resulting in anincreased slant of the a,c plane, the increase in the set angle �(i.e., an increase tilt of the long molecular axis relative to c*),and the decrease in the unit cell height along c* are all visuallyevident in Figure 9c. The increased set angle �, and correspond-ing displacement of end-to-end molecular contacts at highpressure, allows for some linear slip of molecules along theirlong axis. A comparison of Figure 9b,d illustrates the planar

Figure 8. Unit cell angles, R, �, and γ as a function of pressureobtained using the force field PCFFa.

Figure 9. Snapshots of the molecular network at 20 K at various pressures above and below the critical phase transition pressure Pc ∼ 0.5 GPa.(a) P ) 0 GPa viewed along b, where c* is perpendicular to the a axis, � is the angle between c* and the long molecular axis, and the height h isparallel to c*. (b) P ) 0 GPa viewed along the long molecular axis. The figure shows a view along the long molecular axis for one layer of PTPcrystal. The red lines pass through the center of the outer rings of translationally inequivalent molecules.48 These two lines define the correspondingherringbone angle θ. (c) P ) 0.7 GPa viewed along b. (d) P ) 0.7 GPa viewed along the long molecular axis.

412 J. Phys. Chem. B, Vol. 115, No. 3, 2011 Schatschneider and Chronister

PTP molecules in the high-pressure phase associated with thereduced torsion angles plotted in Figure 5. The static planarityof the molecules in the high-pressure phase at low temperature(20 K) is clear. The MD simulations provide a detailed pictureof the structure and dynamics associated with molecular andcrystallographic changes associated with the pressure-inducedphase transition.

4. Conclusions

The temperature-induced phase transition at ambient pressureand the pressure-induced phase transition at low temperaturehave been accurately modeled by a one-parameter optimizationof the intramolecular torsion potential combined with a PCFFintermolecular potential. The dihedral angle distributions of thecentral phenyl ring were probed as a function of pressure. Thefour torsion angles associated with the four unique sites ofthe triclinic phase were found to collapse to a nearly planarmolecule above 0.5 GPa at 20 K, in contrast to the dynamicallyaveraged planar structure at room temperature. The width ofthe torsion angle distributions also increased near the criticalpressure due to fluctuations near the phase boundary. Thecompression of the unit cell in the high-pressure phase wascharacterized primarily by compression of the a lattice param-eter, with weaker compression of c and some expansion of theb lattice parameter. The expansion of b is likely associated withpressure-induced soft mode behavior reported for lattice vibra-tions2 as well as soft mode behavior of pseudolocal phonons ofimpurities in PTP.65 The crystallographic angles R, �, and γalso indicate a triclinic crystal phase above the critical phasetransition pressure of Pc ∼ 0.5 GPa at low temperature,suggesting a distinct phase separate from the monoclinic high-pressure phase at higher temperature.44,27 The ability to suc-cessfully model the pressure-induced phase transition in PTPshould enable extended MD studies of pseudolocal phonondynamics in mixed PTP crystals near the high-pressure low-temperature polymorphic phase transition.65

Acknowledgment. This work was supported by the ACSPetroleum Research Fund (#37400-AC5) and the U.S. NationalScience Foundation (CHE-0612957).

References and Notes

(1) Aubry, S. J. Chem. Phys. 1975, 62, 3217.(2) Baudour, P. J. L.; Cailleau, H.; Yellon, W. B. Acta Crystallogr.

1977, B33, 1773.(3) Baudour, P. J. L.; Cailleau, H.; Yellon, W. B. Acta Crystallogr.

1977, B33, 1773.(4) Cailleau, H.; Girard, A.; Moussa, F.; Zeyen, C. M. C. Solid State

Commun. 1979, 29, 259.(5) Cailleau, H.; Baudour, J. L.; Meinnel, J.; Dworkin, A.; Moussa,

F.; Zeyen, C. Faraday Discuss. Chem. Soc. 1980, 69, 7.(6) Girard, A.; Delugeard, Y.; Cailleau, H. J. Phys. (Paris) 1987, 48,

1751.(7) Furumoto, H. W.; Ceccon, H. L. IEEE J. Quantum Electron. 1970,

6, 262.(8) Tang, C. W.; VanSlyke, S. A. Appl. Phys. Lett. 1987, 51, 913.(9) Era, M.; Tsutsui, T.; Saito, S. Appl. Phys. Lett. 1995, 67, 2436.

(10) Dimitrakopoulos, C. D.; Brown, A. R.; Pomp, A.; J. Appl. Phys1996, 80, 2501.

(11) Tasch, S.; Brandstatter, C.; Meghdadi, F.; Leisung, G.; Athouel,L.; Froyer, G. AdV. Mater. (Weinheim, Ger.) 1997, 9, 33.

(12) Gundlach, D. J.; Lin, Y.-Y.; Jackson, T. N.; Schlom, D. G. Appl.Phys. Lett. 1997, 71, 3853.

(13) Schoonveld, W. A.; Wildeman, J.; Fichou, D.; Bobbert, P. A.; vanWees, B. J.; Klapwijk, T. M. Nature (London) 2000, 404, 977.

(14) Eiras, C.; Foschini, M.; Faria, R. M.; Goncalves, D. Mol. Cryst.Liq. Cryst. Sci. Technol., Sect. A 2002, 374, 493.

(15) Jiang, F.; Zhou, Y. X.; Chen, H.; Note, R.; Mizuseki, H.; Kawazoe,Y. Los Alamos Nat. Lab., Preprint Archive, Condensed Matter, 2006.

(16) Orrit, M.; Bernard, J.; Personov, R. I. J. Phys. Chem. 1993, 97,10256.

(17) Moerner, W. E.; Kador, L. Phys. ReV. Lett. 1989, 62, 2535.(18) Orrit, M.; Bernard, J. Phys. ReV. Lett. 1990, 65, 2716.(19) Reilly, P. D.; Skinner, J. L. J. Chem. Phys. 1995, 102, 1540.(20) Moerner, W. E. New J. Phys 2004, 6, 88.(21) Werley, C. A.; Moerner, W. E. J. Phys. Chem. B 2006, 110, 18939.(22) Baudour, J. L. Acta Crystallogr. 1991, B47, 935.(23) Goosens, D. J.; Gutmann, M. J. Phys. ReV. Lett. 2009, 102, 015505.(24) Baudour, J. L.; Toupet, L.; Delugeard, Y.; Ghemid, S. Acta

Crystallogr. 1986, C42, 1211.(25) Baudor, J. L.; Delugeard, Y.; Cailleau, H. Acta Crystallogr. 1976,

B32, 150.(26) Heimel, G.; Puschnig, P.; Oehzelt, M.; Hummer, K.; Koppelhuber-

Bitschnau, B.; Porsch, F.; Ambrosch-Draxl, C.; Resel, R. J. Phys.: Condens.Matter 2003, 15, 3375.

(27) Puschnig, P.; Heimel, G.; Weinmeier, K.; Resel, R.; Ambrosch-Draxl, C. High Pressure Res. 2002, 22, 105.

(28) Zhuravlev, K. K.; McCluskey, M. D. J. Chem. Phys. 2004, 120,1841.

(29) Ghanem, A.; Bokobza, L.; Noel, C. J. Mol. Struct. 1987, 159, 47.(30) Schatschneider, B.; Chronister, E. L. J. Lumin. 2007, 127, 34.(31) Girard, A.; Cailleau, H.; Marqueton, Y.; Ecolivet, C. Chem. Phys.

Lett. 1978, 54, 479.(32) Girard, A.; Sanquer, M.; Delugeard, Y. Chem. Phys. 1985, 96, 427.(33) Amorim da Costa, A. M.; Amado, A. M. Solid State Ionics 1999,

125, 263.(34) Rietveld, H. M.; Maslen, E. N.; Clews, C. J. Acta Crystallogr. 1970,

B26, 693.(35) Rietveld, H. M.; Maslen, E. N.; Clews, C. J. Acta Crystallogr. 1970,

B26, 693.(36) Reynolds, P. A.; White, J. W. J. Chem. Soc., Faraday Trans. 1972,

68, 1434.(37) Toudic, B.; Launois, P.; Moussa, F.; Girard, A.; Cailleau, H.

Ferroelectrics 1998, 80, 241.(38) Toudic, B.; Cailleau, H.; Lechner, R. E. Phys. ReV. Lett. 1986, 56,

347.(39) Johnston, M. B.; Herz, L. M.; Khan, A. L. T.; Kohler, A.; Davies,

A. G.; Linfield, E. H. Chem. Phys. Lett. 2003, 377, 256.(40) Baer, B.; Chronister, E. L. High Pressure Res. 1994, 12, 101.(41) Toudic, B.; Cailleau, H.; Gallier, J.; Lechner, R. E. J. Phys. 1 1992,

2, 829.(42) Saito, K.; Atake, T.; Chihara, H. Bull. Chem. Soc. Jpn. 1988, 61,

2327.(43) Bordat, P.; Brown, R. Chem. Phys. 1999, 246, 323.(44) Murugan, N. A.; Yahonath, S. J. Phys. Chem. B 2005, 109, 1433.(45) Baranyai, A.; Welberry, T. R. Mol. Phys. 1992, 75, 867.(46) Bordat, P.; Brown, R.; Marbeuf, A. Mol. Simul. 2006, 32, 971.(47) Wasiutynski, T.; Cailleau, H. J. Phys.: Condens. Matter 1992, 4,

6241.(48) Puschnig, P.; Hummer, K.; Ambrosch-Draxl, C. Phys. ReV. B 2003,

67, 235321.(49) Stone, A. J. Science 2008, 321, 787.(50) Schwabe, T.; Grimme, S. Phys. Chem. Chem. Phys. 2007, 9, 3397.(51) Neumann, M. A.; Perrin, M. A. J. Phys. Chem. B 2005, 109, 15531.(52) Stone, A. J.; Misquitta, A. J. Int. ReV. Chem. 2007, 26, 193.(53) Misquitta, A. J.; Welch, G. W.; Stone, A. J.; Price, S. L. Chem.

Phys. Lett. 2008, 456, 105.(54) Tsuzuki, S.; Tanabe, K. J. Phys. Chem. 1991, 95, 139.(55) Filippini, G.; Gavezzotti, A. Acta Crystallogr. 1993, B49, 868.(56) Williams, D. E. J. Chem. Phys. 1966, 45, 3770.(57) Hummer, K.; Puschnig, P.; Ambrosch-Draxl, C. Phys. ReV. B 2003,

67, 184105.(58) Sun, H.; Mumby, S. J.; Maple, J. R.; Hagler, T. J. Am. Chem. Soc.

1994, 116, 2978.(59) Sun, H. J. Comput. Chem. 1994, 15, 752.(60) Sun, H. J. Phys. Chem. B 1998, 102, 7338.(61) Baer, B.; Chronister, E. L. J. Chem. Phys. 1994, 100, 23.(62) Schatschneider, B.; Chronister, E. L. Mol. Simul. 2008, 34, 1159.(63) Bordat, P.; Brown, R. Chem. Phys. Lett. 1998, 291, 153.(64) Fleischhauer, H.; Kryschi, C.; Wagner, B. J. Chem. Phys. 1992,

97, 1742.(65) Baer, B.; Chronister, E. L. J. Phys. Chem. 1995, 99, 7324.(66) Baer, B.; Chronister, E. L. J. Chem. Phys. 1993, 99, 3137.

JP105973E

Molecular Simulation of p-Terphenyl Phase Transitions J. Phys. Chem. B, Vol. 115, No. 3, 2011 413