Article pubs.acs.org/JPCC
New Insights on Vibrational Dynamics of Corannulene Rozenn Le Parc,*,† Patrick Hermet,‡,§ Stéphane Rols,∥ David Maurin,† Laurent Alvarez,† Alexandre Ivanov,∥ Jennifer M. Quimby,⊥ Caitlin, G. Hanley,⊥ Lawrence T. Scott,⊥ and Jean-Louis Bantignies† †
Université Montpellier 2, Laboratoire Charles Coulomb (UMR CNRS 5521), 34095 Montpellier Cedex 5, France Research Center in Physics of Matter and Radiation (PMR), University of Namur-FUNDP, Rue de Bruxelles 61, 5000 Namur, Belgium § Institut Charles Gerhardt Montpellier, UMR5253 CNRS-UM2-ENSCM-UM1, C2M, UMII, CC1504, Place E. Bataillon, 34095 Montpellier Cedex 5, France ∥ Institut Max von Laue-Paul Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble, Cedex 9, France ⊥ Merkert Chemistry Center, Department of Chemistry, Boston College, Chestnut Hill, Massachusetts, United States ‡
ABSTRACT: Vibrational dynamics in the corannulene crystal is exhaustively studied through Raman scattering, infrared spectroscopy, and inelastic neutron scattering. Experimental data are coupled to simulations of the phonon modes performed in the framework of first principle calculations. Intermolecular vibrations (libration and translation) are assigned in the low frequency domain (10−200 cm−1). These modes exhibit specific temperature dependence in the far-infrared.
interest in them for possible interstellar identification,7−9 these bucky bowls appear as promising new materials for different applications: luminescence,10−13 hydrogen storage,14 molecular containers or receptors,15−18 or building block for macromolecular structures.19,20 Their specific physical properties lie in their curvature and the associated charge distribution9 that involves particular intermolecular interactions. These interactions have been widely studied in planar PAHs and involve πstacking or/and CH−π interactions.21 In the case of bowl shaped molecules, different packing has been observed depending on the molecule curvature, size, and symmetry.22−25 H···π stacking in the crystal directs the relative orientation of the two crystallographically independent corannulene molecules. The positively charged rim region of one molecule is oriented almost perpendicular to the negative potential region at the bottom of a second molecule.22 Differences between flat and curved PAHs can be attributed to the electrostatic dipole− dipole attraction in bowls which is absent in “planar” dimers. Eclipsed conformations are preferred for the curved corannulene dimers while a staggered conformation is preferred for planar dimers.25
1. INTRODUCTION Corannulene is a bowl shaped polycyclic aromatic hydrocarbon (PAH). The introduction of the central pentagon induces curvature (Figure 1), and the whole molecule is puckered in the shape of a cap so-called bucky bowl.1−6 Beyond fundamental
Received: July 30, 2012 Revised: October 26, 2012 Published: November 2, 2012
Figure 1. Primitive unit cell of corannulene. C and H atoms are gray and white, respectively. © 2012 American Chemical Society
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dx.doi.org/10.1021/jp307536d | J. Phys. Chem. C 2012, 116, 25089−25096
The Journal of Physical Chemistry C
Article
2.3. Infrared Spectroscopy. IR experiments have been performed on a Bruker IFS 66 V spectrometer using a mercury cadmium telluride detector in the mid-IR domain (600−4000 cm−1), and a Si-bolometer detector cooled at 10 K was used to probe the far-IR (40−600 cm−1). The sample was ground with polyethylene (far-IR) or KBr (mid-IR) and compressed under 8 tons to form isotropic pellets of 12 mm diameter. The spectral resolution was 2 cm−1 and 64 scans were coadded for each spectrum. Low temperature measurements between room temperature and 10 K have been performed using a helium cooled cryostat.
Low frequencies vibrations are particularly sensitive to the intermolecular interactions.26,27 Vibrational modes of corannulene have been intensively investigated theoretically in the literature using density functional theory (DFT).7,28−32 In all these studies, the authors use an isolated molecule based model to assign the phonon modes measured on a corannulene crystalline phase. Ball and bowl shaped carbon molecules (0 dimension system, 0D), in contrast to the 1D and 2D carbon nanostructures where the infrared activity is weak,33,34 show significant information in the infrared domain. Comparison between main experimental intramolecular infrared bands obtained in the gas phase and those calculated on isolated molecules has recently been performed.6 Surprisingly, no significant difference between features in crystalline and gas phase are reported in the middle infrared domain (MIR, between 400 and 4000 cm−1). Thus, although there has been tremendous effort to understand the vibrational dynamics in corannulene crystals theoretically and experimentally,7,1 discussion on the intermolecular domain below 400 cm−1 and an exhaustive description of the intramolecular range are still lacking. In this work, we report a detailed experimental lattice dynamics investigation of corannulene using inelastic neutron scattering (INS), infrared absorption spectroscopy (IR), and Raman scattering coupled to DFT calculations in the crystal phase. Our principal aim is to conduct an extensive study of vibrational properties of corannulene crystal to indentify intermolecular vibrations of corannulene.
3. THEORETICAL SECTION AND COMPUTATIONAL DETAILS Calculations of the relaxed structure, Hellmann−Feynman (HF) forces, and Born effective charge tensors (Z*) of corannulene were performed by using the Vienna ab initio simulation package35 and the generalized gradient approximation to the exchange correlation functional as proposed by Perdew, Burke and Ernzerhof.36−38 Interactions between ions and electrons were described by the projector augmented wave method39 in the real space representation. Experimental lattice parameters were fixed in the calculation to the experimental ones and only the atomic positions were relaxed by using a fine integration grid until the maximum residual forces on each atoms were less than 5.10−3 eV/Å. Calculations of the dynamical matrix (and therefore normal modes of vibrations) were calculated at the Γ-point in the harmonic approximation, via the knowledge of the HF forces, using the direct method.35 Molekel software40,41 was used to display the normal modes. Linear response was used to compute Z*. A plane-wave energy cutoff of 400 eV and a 4 × 4 × 4 Monkhorst-Pack42 k-points mesh over the Brillouin zone were found to provide sufficient precision in the geometry optimization of corannulene, and in the calculation of its HF forces and Z*. The CLIMAX43 program was used to calculate the INS spectrum of corannulene from its Γ-point normal modes. Overtones and combinations were included in the calculations. IR absorption coefficient, ε(ω), of an isotropic material is directly related to the imaginary part of the dielectric susceptibility tensor χ (q = 0,ω) as
2. EXPERIMENTAL SECTION 2.1. Synthesis. A pure corannulene crystalline sample has been synthetized by flash vacuum pyrolysis by the group of Scott.2,3 2.2. Inelastic Neutron Scattering. The generalized phonon density of state (GDOS) can be derived using inelastic neutron scattering (INS). The molecular nature of corannulene crystal, together with the presence of strong covalent C−H bonds at the bowl edges imply that the GDOS extends from a few cm−1 up to 4000 cm−1. To measure the GDOS in a wide energy range, we used two INS apparatus at the Institut LaueLangevin: the filter analyzer spectrometer IN1BeF and the time-of-flight spectrometer IN4. The former is installed on a hot neutron source and allows measurements from 200 cm−1 up to several thousands of cm−1. The latter is installed on a thermal beam, thus allowing energy transfer in the 20−500 cm−1 range. For both experiments, 102 mg of corannulene wrapped in an aluminum foil were used. INS were performed on IN4 in the 20−500 cm−1 range to probe lattice dynamics. In this experiment, the monochromator selects the incident neutron wavelengths 1.1 Å at 10 K and 2.4 Å from 300 to 10 K. Rotating Fermi chopper produces monochromatic pulses that hit the sample at precise time interval. The scattered neutrons are detected by detectors at 2 m from the sample. The energy of the neutrons can be determined by time-of-flight. The scattering function S(Q,ω) can be determined from the neutron count in all detectors and all time channels. Measurement above 400 cm−1 were performed on IN1BeF, where a beryllium filter scatters out all neutrons with energies higher than 5.2 meV (beryllium cutoff) thus permitting recording of only low-energy neutrons scattered by the sample. Measurements have been performed at 13 K. The scattered intensity measured for a fixed monitor is directly proportional to S(Q,ω).
ε(ω) =
ω 3κc
∑ 0χαα α
where the sum is over the three Cartesian directions and κ and c are respectively the index of refraction of the material and the speed of light. For harmonic systems, the imaginary part of the dielectric susceptibility is correlated to the displacement autocorrelation function. It can be defined as a function of the eigenvalues and eigenvectors of the dynamical matrix according to44−46 Iχαα
1 = ε0V
∑ j
1 2ωj
∑ β ,n
Z*α , β (n) mn
2
eβ(n , j)
[δ(ω − ωj) − δ(ω + ωj)]
where ε0 is the vacuum permittivity, mn is the mass of the nth atom, V is the unit cell volume, and eβ(n,j) and ωj are respectively the βn-component of the eigenvector and the frequency of the mode j. 25090
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4. RESULTS AND DISCUSSION Corannulene molecules crystallize in the monoclinic P21/c (C52h) space group with Z = 8 molecules inside the unit cell (Figure 1).1,47,48 The molecule packing is different from the columnar one observed in many PAHs. According to the group theory analysis, the 720 zone-center phonon modes are decomposed as, 180 Ag ⊕ 180 Bg ⊕ 180 Au ⊕ 180 Bu, where one Au mode and two Bu modes are acoustic modes. As the structure of corannulene is centrosymmetric, a phonon mode is either Raman (Ag and Bg) or IR (Au and Bu) active. No silent mode is expected. A comparison of the vibrational features obtained by INS, IR and Raman in the low frequency domain is given to illustrate the complementarity of the different spectroscopic approaches (Figure 2). When phonons of corannulene are probed over the
Furthermore, comparison between state of art DFT calculations and experimental IR and Raman features allows precise assignment of the lattice vibrations in the low frequency domain. The results will be discussed in the following parts. Our results are presented in three different sections. In the first section, INS study on corannulene is presented. It gets exhaustive results on its low-frequency lattice dynamics. In the second section, a detailed study of the IR active features is given. Finally in the last section, Raman active lines are discussed thanks to the DFT calculations. 4.1. Inelastic Neutron Scattering. The experimental vibrational density of states of corannulene and the calculated one from Γ-point normal modes are reported for the first time. A full calculation of the vibrational density of states requires the calculation of the dynamical matrix for numerous wavevectors. Such a calculation is too time-consuming to be performed on corannulene due to the important number of atoms in its primitive unit cell. Nevertheless, assuming a small dispersion of the high frequency modes, it is possible to estimate the density of states only from the Γ-point normal modes. We show the GDOS in the low frequency range below 250 cm−1 (Figure 3a) and in the high frequency range up to 3500 cm−1 (Figure 3b) measured at 10 K respectively using the spectrometers IN4 and IN1BeF, together with the simulated GDOS. The molecular nature of the crystal is suggested by the observation of sharp peaks in the frequency range above 120 cm−1 (Figure 3b), this hypothesis will be confirmed through simulations of the IR active modes in part 2. In the following, we discussed first the domain below 150 cm−1, where the spectrum is composed of lattice modes, the latter involving either displacements of the center of mass of the molecules (acoustic and optical phonons), periodic rotations of the rigid molecule, or a mixture of both. These modes are usually much more dispersive than molecular vibrations, which results in broader features in the GDOS, as observed in Figure 3a. The lattice modes are dominated by an intense contribution at 30 cm−1, with a shoulder at 40 cm−1. A double peak structure, with contributions at 70 and 90 cm−1, completes the spectrum. In a molecular crystal packed via soft
Figure 2. Low frequency INS (a), IR absorbance (b), and Raman (c) spectra of corannulene respectively measured at 13, 10, and 20 K.
whole Brillouin zone, the vibrational features are shown to be broad and assignment of the lattice vibration modes in the low energy domain is not straightforward. In this case, it is interesting to perform complementary studies restricted to IR and Raman active modes evidencing more resolved features.
Figure 3. (a) Low frequency part of the GDOS highlighting the lattice modes (
