Hirofumi Yajimac, Keiko Kitagishib, Seiji Tsuzukif a Chiba University, Chiba, Japan, b Otsuka Electronics Co. Ltd., Osaka, Japan, c Tokyo University of Science,.
Calculations of inter- and intramolecular vibrations of a perylene derivative to interpret observed absorption spectra of the crystal Toshiaki Osugaa, Yusuke Izutanib, Akira Itohc, Tetsuya Sakajirid, Shin-ichi Nagamatsue, Hirofumi Yajimac, Keiko Kitagishib, Seiji Tsuzukif a Chiba University, Chiba, Japan, b Otsuka Electronics Co. Ltd., Osaka, Japan, c Tokyo University of Science, Tokyo, Japan, d The University of Morioka, Iwate, Japan, e The University of Electro-Communications, Tokyo, Japan, f Advanced Industrial Science and Technology, Ibaraki, Japan
I. INTRODUCTION AND BACKGROUND
T
time-domain spectroscopy (THz-TDS) has recently become a valuable tool for identifying and characterizing materials since many compounds have a distinct terahertz (THz) absorption spectrum. While the infrared absorption spectra at frequencies over 6 THz can distinguish specific groups of atoms within molecules, THz-TDS under 6 THz can analyze lattice mode vibrations arising from the relative rotational and translational motions between molecules, and torsion and bending affected by crystal-packing interactions that cannot be detected in gas-phase molecular vibrational spectroscopy. In our previous study, we measured the THz-region absorption spectra of perylene and its derivatives used in organic electroluminescent devices and calculated the vibrational frequencies of isolated-molecules by density functional theory (DFT) [1]. Perylene 3,4,9,10-tetracarboxylic dianhydride (PTCDA, Figure 1) has many absorption peaks under 3.4 THz (Figure 2). DFT calculations using Gaussian 03 showed that the isolated-molecule has five absorption frequencies between 0.82 and 2.75 THz. The inclusion of the crystal-packing interactions in DFT calculations improved the agreement between the theory and experimental results [2,3]. In this study we performed DFT calculations for PTCDA in the isolated-molecule state and the solid-state to assign their lattice vibrational modes.
THz spectra of PTCDA were measured using a TR-1000 terahertz spectroscopic system (Otsuka Electronics, Japan) [1]. The cell parameters of PTCDA crystal are as follows: space group P21/c, a = 3.74 Å, b = 11.96 Å, c = 17.34 Å, α = γ = 90.0º, β = 98.8º [4]. Figures 3(a) and 3(b) show two PTCDA molecules in a crystal unit cell and a planar stack composed of PTCDA molecules, respectively. DFT calculations for the vibrations of PTCDA in the isolated-molecule state and in the solid-state including crystal-packing interactions were performed using Gaussian 03 at the B3LYP/6-31G(d,p) level and DMol3 (version 3.2) at the PBE/DNP level, where the DNP basis set is comparable to a 6-31G(d,p) Gaussian-type basis set and the density function of PBE is adequate for calculating intermolecular forces [2,3]. solid Cout Cinsolid
5
solid Bout Binsolid
4
solid Dout Dinsolid
3
solid Aout Ainsolid
2 1 0
AIRisolated inactive BIRisolated active 0.5
(a)
shifted and split isolated isolated isolated CIR inactive DIR inactive EIR inactive
1.5 2 2.5 Frequency(THz) (Hz) Frequency
3
crystal a axis
crystal b axis
(b)
Figure 1. Chemical structure of PTCDA showing (a) constitutional formula and (b) space-filling model.
1
solid Eout Einsolid
Figure 2. Absorption spectrum of PTCDA.
crystal c axis
ERAHETRZ
II. RESULTS AND DISCUSSION
Absorbance Absorbance
Abstract—Perylene 3,4,9,10-tetracarboxylic dianhydride (PTCDA), one of the perylene derivatives, has many absorption peaks in the THz region. Density functional theory (DFT) analysis of the crystal geometry elucidated that intermolecular vibrations of relative rotation and translation, and intramolecular vibrations of torsion and bending dominate below and above 2 THz, respectively. The frequency shifts relative to the frequencies obtained in isolated-molecule calculations and the frequency splitting of in- and out-of-phase vibrations of the two molecules in the crystal unit cell were caused by crystal-packing interactions. The higher absorption peaks of the PTCDA crystal originate from frequencies shifted and split from the IR-active intramolecular vibration mode in the isolated-molecule.
(a)
(b)
Figure 3. PTCDA showing (a) unit crystal cell and (b) stack.
3.5
The PTCDA crystal has three acoustic vibrations with frequencies below 0.5 THz and extremely low absorbance as shown in Figure. 2. Since a crystal unit cell containing M molecules causes 6M-3 intermolecular vibrations (relative translational and rotational motions) [2], the PTCDA crystal has nine intermolecular vibrations consisting of three optical translational motions (OT) and six optical rotational motions (OR). The three OT modes are suffixed as OT a, OTb and OTc since the displacements of the two PTCDA molecules in the unit crystal cell are in opposite directions along the crystal a, b a and c axes. The six OR modes are suffixed as ORina , ORout , ORbin , ORbout , c c ORin and OR out since the two PTCDA molecules in the unit crystal cell rotate in- phase and out-of- phase about the crystal a, b and c axes. The two PTCDA molecules rotate about the crystal a axis in the ORa modes. The rectangular molecule of PTCDA has two diagonals and rotates about these two diagonals. The two PTCDA molecules rotate about the diagonals whose directions are closed to the crystal b and c axes in the ORb and ORc modes, respectively. The intramolecular vibrations of an isolated-molecule of PTCDA have five frequencies under 3.5 THz of Ａisolated 0.819THz , isolated isolated isolated isolated Ｅ and [1]. Since the two PTCDA Ｂ1.14 , Ｃ , Ｄ 2.75THz THz 1.95THz 2.33THz molecules in the crystal unit cell vibrate in-phase and out-of-phase to each other under the crystal-packing interactions, frequency shifts relative to the isolated-molecule mode positions and frequency splitting into lower and higher positions occur. Therefore, the ten resultant intramolecular solid vibrations of solid- state PTCDA are suffixed as Ａ1.35 THz , solid solid solid solid solid solid solid Ｃ2.49 Ａ1.66 THz ,Ｃ2.88THz ,Ｄ2.97THz ,Ｄ3.05THz , THz ,Ｂ2.01THz ,Ｂ2.50THz ,
The displacement patterns of the inter- and intramolecular vibrations of the PTCDA crystal are displayed in Figures 4 and 5, respectively. The vibration frequencies are plotted in Figure 2, where higher absorption peaks in the solid-state originate from frequencies shifted and split from the B-mode IR-active intramolecular vibration in the isolated-molecule. IR-inactive vibrations in the isolated-molecule cause THz absorption according to the results of solid-state calculations. The large frequency shifts and splitting are related to the CH-O interaction between molecules [5,6]. REFERENCES [1] Y. Izutani, K. Kitagishi, T. Osuga, and S. Tsuzuki, “Spectroscopic measurements and DFT calculations of vibrational frequencies of perylene and its derivatives in THz region”, IRMMW-THz 2009, T3B04. [2] D.G.Allis, “Theoretical analysis of the terahertz spectrum of the high explosive PETN”, ChemPhysChem, 7, 2398-2408 (2006). [3] P. M. Hakey, M. R. Hudson, D. G. Allis, W. Ouellette, and T. M. Korter “Examination of phencyclidine hydrochloride via cryogenic terahertz spectroscopy, solid-state density functional theory, and X-ray diffraction”, J. Phys. Chem. 113, 13013-13022 (2009). [4]M. Möbus, N. Karl, and T. Kobayashi, “Structure of Perylenetetracarboxylic-dianhydride thin films on alkali halide crystal substrates”, J. Cryst. Growth, 116, 495-504 (1992). [5] Y.Gu, T.Kar and S.Schciner. “Fundamental properties of the CH・O interaction: Is it a true hydrogen bond?”, J. Am. Chem. Soc. 121, 9411-9423 (1999). [6] S.Tsuzuki, T.Uchimaru, K.Tanabe and T.Hisao, “Conformational analysis of 1,2-dimethoxyethane by ab initio molecular orbital and molecular mechanics calculations: stabilization of the TGG’ rotamer by the 1,5 CH3/O nonbonding attractive interaction”, J. Phys. Chem. 97, 1346-1350 (1993).
Aisolated 0.819THz
solid A1.66 THz
solid A1.35 THz
solid solid and Ｅ3.34 . Ｅ3.32 THz THz
1.60 THz
crystal c axis
crystal a axis
0.710 THz
1.67 THz
isolated
OTa (a) Optical translations ( OT a ,b,c ) 1.55 THz
ORain
OTb
isolated 2.02 THz
out-of-phase solid C2.49 THz
solid C2.88 THz
in-phase
out-of-phase solid D2.97 THz
solid D3.05 THz
Disolated 2.33THz
0.817 THz
1.24 THz isolated
Eisolated 2.75THz ORbout
in-phase
isolated C1.95 THz
isolated
ORcin
(b) Optical rotations in-phase ( ORina ,b ,c ) 1.39 THz
solid B2.01 THz
OTc
1.09 THz
ORbin
out-of-phase solid B2.50 THz
isolated B1.14 THz
crystal b axis
ORaout
in-phase
in-phase
out-of-phase solid E3.34 THz
solid E3.32 THz
ORcout
a ,b , c (c) Optical rotations out-of-phase ( ORout )
Figure 4. Intermolecular vibration modes of PTCDA crystal: OT and OR in-phase and OR out-of-phase, where and denote positive and negative displacements along the crystal a axis, respectively.
(a) isolated-molecule
(b) solid-state in-phase
(c) solid-state out-of-phase
Figure 5. Intramolecular vibration modes of PTCDA crystal: A, B, C, D and E, where the B-mode is IR-active in the isolated-molecule.
