the far-infrared spectroscopy of very large neutral ... - IOPscience

The Astrophysical Journal, 709:42–52, 2010 January 20 C 2010.

doi:10.1088/0004-637X/709/1/42

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

THE FAR-INFRARED SPECTROSCOPY OF VERY LARGE NEUTRAL POLYCYCLIC AROMATIC HYDROCARBONS Alessandra Ricca1 , Charles W. Bauschlicher, Jr.2 , Andrew L. Mattioda3 , Christiaan Boersma3 , and Louis J. Allamandola3 1

Carl Sagan Center, SETI Institute, 515 N. Whisman Road, Mountain View, CA 94043, USA; [email protected] 2 Space Technology Division, Mail Stop 230-3, NASA Ames Research Center, Moffett Field, CA 94035, USA 3 Space Science Division, Mail Stop 245-6, NASA Ames Research Center, Moffett Field, CA 94035, USA Received 2010 June 13; accepted 2009 December 1; published 2009 December 24

ABSTRACT Here we report the computed far-infrared (FIR) spectra of neutral polycyclic aromatic hydrocarbon (PAH) molecules containing at least 82 carbons up to 130 carbons and with shapes going from compact round and oval-type structures to rectangular and to trapezoidal. The effects of size and shape on the FIR band positions and intensities are discussed. Using FIR data from the NASA Ames PAH IR Spectroscopic Database Version 1.1, we generate synthetic spectra that support the suggestion that the 16.4, 17.4, and 17.8 μm bands arise from PAHs. Key words: astrochemistry – infrared: ISM – ISM: molecules – methods: numerical Online-only material: color figures

frequencies as a function of molecular shape and size are discussed and guidance is provided for future FIR observations. Recently, Boersma et al. (2010) studied the 15–20 μm range in detail using an earlier version of the database that does not include the molecules studied in this work. Since there are known interstellar emission features at 15.8, 16.4, 17.4, 17.8, and 18.9 μm, we reconsider this region using the results of the present study.

1. INTRODUCTION The mid-infrared (MIR) spectra of a large majority of astronomical sources are dominated by a family of emission features falling near 3.3, 6.2, 7.7, and 11.2 μm (Gillett et al. 1973; Spitzer First Observations Special Edition 2004). These features are now generally thought to originate in polycyclic aromatic hydrocarbons (PAHs) and closely related species. Thus, they are now often referred to as the PAH bands or features (Spitzer First Observations Special Edition 2004). Infrared Space Observatory and recent Spitzer observations show that PAHs dominate the MIR emission from late circumstellar outflows, the local diffuse ISM, reflection nebulae, and PDR/star formation regions in our own Galaxy, as well as that of other nearby normal galaxies and more distant starburst galaxies and ultraluminous infrared galaxies (ULIRGs; Spitzer First Observations Special Edition 2004; Genzel et al. 1998). The upcoming Herschel and SOFIA observatories will extend observations of these objects deep into the far-infrared (FIR). Given their importance in the MIR, PAHs are expected to contribute to the observed FIR spectra. Indeed, recent laboratory FIR matrix-isolated spectra of isolated, cold, and moderately sized neutral PAHs (coronene, ovalene, and dicoronylene; Mattioda et al. 2009) have shown that PAH molecules have bands in the FIR. Such findings have been confirmed by density functional theory (DFT) calculations (Mattioda et al. 2009). Beyond 20 μm, the bands become very dependent on molecular size and structure as they involve the motion of the entire PAH molecule, so-called drumhead modes. Investigation of these wavelengths will be useful in the interpretation of new observations and in the identification of specific PAH molecules, which in turn will provide more information about the chemical and physical environments of different sources where PAHs are observed. In this work, we extend our previous DFT study of the FIR spectra of neutral PAHs coronene (C24 H12 ), ovalene (C32 H14 ), and dicoronylene (C48 H20 ) to much larger PAHs containing at least 82 carbons and up to 130 carbons, which are more relevant to astronomical conditions (Allamandola et al. 1989). In order to assess the nature of the drumhead modes, several kinds of molecular shapes are considered. Trends in vibrational

2. MODEL AND METHODS The molecules studied in this work are shown in Figure 1. The more symmetric C96 H24 and C130 H28 have been studied previously (Bauschlicher et al. 2008). The structures were fully optimized and the harmonic frequencies computed using DFT. We used the hybrid B3LYP (Becke 1993; Stephens et al. 1994) functional in conjunction with the 4-31G basis set (Frisch et al. 1984). Previous work (Bauschlicher & Langhoff 1997) has shown that the computed B3LYP/4-31G harmonic frequencies scaled by a single scale factor of 0.958 are in excellent agreement with the matrix isolation MIR fundamental frequencies of the PAH molecules. An FIR study of neutral coronene, ovalene, and dicoronylene (Mattioda et al. 2009) has shown that the scale factor of 0.958 can also be applied to the FIR spectral region as it brings the computed B3LYP/4-31G harmonic frequencies in excellent agreement with the experimental FIR frequencies. The scale factor to bring the computed bands in the 15–20 μm range for 13 large molecules into the best agreement with experiment is essentially 0.958 as well (Boersma et al. 2010). Joblin et al. (2002) and Mulas et al. (2006b) also concluded that the MIR scale factor was reasonable for the FIR bands. Therefore, in the present work we use the scale factor of 0.958 for all bands. Previous work has shown that the band intensities are in good agreement with experiment in the 5.8–20 μm range (Mattioda et al. 2009, and references therein). Therefore, the computed intensities are used without any modification. All the calculations were performed using the Gaussian 03 computer code (Frisch et al. 2003). Most of the allowed FIR bands are given in Table 1. However, due to the very large number of bands present, we will make 42

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absorption and emission from hot molecules. The choice of 15 cm−1 is discussed in detail in Bauschlicher et al. (2009). Note, however, that when we are not comparing the theoretical spectra with observations no shift is utilized. The interactive molecular graphics tool MOLEKEL (Flükiger et al. 2000) was used to aid the analysis and illustrate the vibrational modes. The modes are shown in the figures using the computed displacement vectors. 3. RESULTS AND DISCUSSION

Figure 1. Structures of the PAHs studied in this paper.

all of the band positions and intensities available on the NASA Ames PAH IR Spectroscopic Database Version 1.1. In order to compare with experiment or astronomical observations, synthetic spectra are generated with the full width at halfmaximum (FWHM) taken to be 5 cm−1 from 15 to 20 μm. This choice is consistent with the observations that line widths in this region are 4–8 cm−1 (e.g., van Kerckhoven et al. 2000; Moutou et al. 1998). For 20–1000 μm, we expect the FWHM to decrease with increasing wavelength, and we assume a linear scaling in wavenumber space from 5 cm−1 for 500 cm−1 (20 μm) to 0.5 cm−1 for 1 cm−1 (1000 μm). Mulas et al. (2006a) showed that naphthalene’s and anthracene’s out-of-plane modes are sharper than the in-plane modes because of their pronounced Q branch. This is probably true for the larger molecules as well, and, while we broaden the in-plane and out-of-plane modes similarly, we indicate which bands correspond to out-of-plane motions, and hence might be easier to observe. The computational studies yield integrated band intensities in km mol−1 , which we broaden in wavenumber space because it is linear in energy. Thus, the units in our synthetic spectra are cm−1 for the x-axis and km (mol cm−1 )−1 for the y-axis. The units on the y-axis are more commonly given as a cross section, which would have units of 105 × cm2 mol−1 . We then convert the x-axis to μm to be consistent with how observational results are commonly reported. Typically, the astronomical PAHs are observed as the emission of hot molecules. Hence when comparing with observations in the 15–20 μm range, we shift our computed 0 K absorption spectra 15 cm−1 to the red to account for the difference between

As previously stated, the molecules studied in this work are shown in Figure 1. These molecules are similar in size to those studied previously (Bauschlicher et al. 2008, 2009), but with lower symmetry. Thus, the combination of these calculations and previous work allows us to explore the effect of size and shape on the FIR spectra of these large PAH molecules. As shown in Figure 1, the molecules range in size from C82 H24 to C130 H28 with the shapes going from round and oval-type structures to rectangular and to trapezoidal. The Appendix contains a detailed description of the modes of the molecules studied in this work, while in this section an overview of the FIR vibrational modes is discussed. Typical FIR vibrational modes are shown in Figure 2 and the band positions and intensities are summarized in Table 1. Figures 3 and 4 show how the drumhead and “jumping-jacks” modes change with increase in molecular size for similar shaped molecules. Namely, the position of drumhead mode scales with the number of carbons, while the “jumping-jacks” scale more slowly. The individual spectra are shown in Figures 5–7 and it is clear that the shape of the molecule complicates the picture dramatically. As discussed in the Appendix, there are many cases where bands in two molecules are at similar positions, but arise from very different modes, making the spectra even more complex than they initially appear. Thus, unlike the MIR where similar type bands fall in the same region, the FIR bands vary greatly from molecule to molecule. It is for this reason that the PAH FIR spectra may make it possible to identify a specific molecule. 3.1. An Overview of the Mid-infrared Spectra A full analysis of the MIR spectra of these molecules will be given in another publication, where the results will be compared and contrasted with our previous work on the large PAHs. However, before beginning a discussion of the FIR spectra of these species, a few comments about their MIR properties seems appropriate. In previous work on large PAHs, we noted that the peak position for the non-bay C–H stretch for the neutrals was between 3.256 and 3.272 μm and the bay C–H stretch fell between 3.213 and 3.231 μm (Bauschlicher et al. 2009). The results for the current set of molecules are consistent with the earlier data. The C–C stretching and C–H in-plane bending vibrations (6–9 μm) are weak, as expected for neutral molecules. Only the spectra of the two C98 H28 species look a bit strange in that the two strongest bands in this region are at about 7.1 and 8.95 μm. However, upon ionization, even the spectra of these two species are consistent with the other larger PAHs. The C–H out-of-plane bending vibrations (9–15 μm) of the species are similar to the other large species, but also show some differences. For C82 H24 and C98 H28 A the solo H peak splits into two peaks, one band at the typical position, 11 μm (without any redshift to correct for emission) and a second at 11.18 μm. A band near 11.2 μm was previously (Bauschlicher et al. 2009) observed for C84 H24 , which has only duo hydrogens, and

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Table 1 Summary of the Band Positions (in μm) and Integrated Intensities, Given in Parentheses (in km mol−1 ) Drumhead*

Jumping-Jacks

Butterfly*

NoNa

Nodes

Short

76.7(12.15)

39.6(5.06) 31.5(3.87) 23.7(31.37) 20.4(28.24)

466.6(0.18) 169.8(0.30) 103.4(0.64)

84.7(2.70)

763.8(0.14) 84.6(1.21) 48.7(2.05) 37.3(12.70)

C–H

E/Cc

Scissor

Other

18.7(26.14) 17.0(24.22) 15.0(34.09)

49.0(39.93) 44.8(3.68)∗ 36.8(4.57) 23.1(8.38) 18.3(30.49)

Long

OOP∗b

C82 H24 248.7(0.48)

17.4(7.87)

34.5(4.52) 30.8(35.62)

18.0(9.69) 17.4(11.68)

37.9(31.78)

C94 H26 223.6(1.41)

21.7(8.04) 15.8(27.43) 15.4(26.80)

C96 H24 319.9(1.38) 76.5(3.72) 32.9(7.90)

49.3(14.00)

24.8(9.36)

17.5(21.16) 16.8(11.32)

265.4(1.32) 58.9(5.32) 26.1(6.79)

79.5(0.83)

26.8(3.12)

739.2(0.13)

116.4(5.05)

46.5(15.94)

928.2(0.14) 206.8(0.34) 136.1(1.08)

112.7(8.61)

42.1(5.08)

701.2(0.11)

93.4(9.60)

30.0(17.50)

645.3(0.15) 76.2(1.76) 42.8(1.59) 36.4(1.66)

61.8(6.26) 53.0(10.99)

28.4(4.05) 22.3(3.13) 21.8(2.16)

599.7(0.18)

16.9(18.23)

23.4(1.95) 19.9(2.10)

C96 H26

C98 H28 A 163.2(1.37) 31.3(7.30) C98 H28 B 172.3(0.32) 150.4(2.43) 31.2(5.12) C126 H30 431.2(0.37)

16.8(15.78)

37.7(45.30) 20.0(21.89)

16.8(18.94)

21.7(7.04)

16.2(18.19)

38.8(12.20) 31.3(7.30) 22.0(12.49)

19.0(17.92)

31.1(7.64) 23.8(7.41) 15.7(11.53)

16.2(21.00)

36.8(3.07) 31.2(5.12) 24.4(7.35)

22.5(3.10) 21.5(3.80) 18.5(16.57) 17.5(12.66)

17.8(10.53) 15.8(4.99)

17.5(11.42)

63.2(7.42) 36.4(7.14) 34.5(16.13) 24.0(4.33) 23.0(5.07) 16.4(24.53)

15.7(6.29)

67.2(11.32) 24.6(5.05) 21.4(14.07)

16.9(25.28)

28.4(3.38) 27.4(1.89) 26.7(0.41) 25.1(2.31)

C130 H28 421.4(0.87) 97.3(2.10) 40.8(4.91) 28.2(1.61) 23.9(3.59)

Notes. The out-of-plane nodes are indicated with an asterisk. a NoN indicates no nodes. b OOP indicates out of plane. c E/C indicates elongation/compression.

for C120 H36 , which has only solo and quartet hydrogens. An interesting difference with previous work is that for C82 H24 the band at 11.18 μm is the stronger of the two. C126 H30 also shows a splitting of the solo band, but the splitting is larger than found previously, with the longer wavelength band falling at 11.30 μm. It is interesting that this is at an even longer wavelength than the “all duo” molecule C82 H24 . An inspection of the modes suggests that some solo–trio coupling could be responsible for the shift in the mostly solo bands. We should also note that C94 H26 has a shoulder on the 11 μm band, but it is an in-plane C–C deformation mode. C96 H26 has a strong band at 11.53 μm with about half the intensity of the 11 μm band. This might appear to be a strong duo band for a molecule with only two duo groups, but, in fact, it is an inplane deformation of the two C6 rings with the trio hydrogen on both sides of the molecule. If one replaces the C3 H3 unit

with two H atoms on both sides of the molecule, this band is eliminated. A mostly in-plane deformation of the rings with the trio hydrogens in C126 H30 is responsible for a band at 12.2 μm, which falls at what is expected to be a duo out-of-plane bending region. Overall, the MIR spectra of these molecules appear consistent with the other large PAHs and with astrophysical observations, however, they suggest that the out-of-plane bending region may be more complicated than believed; the solo bands seem to be shifted in some species and in-plane C deformations can produce bands that fall in the out-of-plane bending region. 3.2. Summary of the Far-infrared Features The FIR features reported here will be discussed in three separate regions: the 130–1000 μm, 20–130 μm, and 15–20 μm regions. The modes that fall at the longest wavelengths involve

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Figure 2. Typical vibrational modes in the FIR. (A color version of this figure is available in the online journal.)

Figure 3. Theoretical FIR spectra of circumcircumcoronene (C96 H24 ) and coronene (C24 H12 ). Note the increasing complexity of the C96 H24 spectrum as well as the shift of the drumhead modes. (A color version of this figure is available in the online journal.)

the entire molecule and have no nodes. Going toward shorter wavelengths, more and more nodes appear. In Figures 8–11, we show the sum of the spectra for all the molecules studied in this work (the individual spectra are presented in Figures 5–7). The 130–1000 μm region is shown in Figures 8 and 9. The peaks in this range correspond to the easiest way of bending the molecules out of the molecular plane. These modes are sensitive to molecular size and shape and can potentially be used as indicators of degree of compactness and molecular size. For a given molecular shape, the lowest drumhead or

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Figure 4. Jumping-jacks modes along the C2 axis for coronene and circumcircumcoronene. Despite the size difference, these are nearly identical vibrational motions. (A color version of this figure is available in the online journal.)

Figure 5. Synthetic absorption spectra in the 200–1000 μm region for the neutral PAHs shown in Figure 1.

butterfly peak will shift to longer wavelengths as the number of carbons increases (compare the butterfly modes for C82 H24 with C126 H30 ). Compact and symmetric molecules, such as C130 H28 , are more rigid than trapezoidal molecules, such as C126 H30 , which, in turn, are more rigid than elongated rectangular ones (C98 H28 B). This is reflected in the lowest butterfly mode shifting to longer wavelengths going from C130 H28 to C98 H28 A despite a decrease in the number of carbons. The 200–450 μm region (see Figure 8) shows much stronger peaks compared with the 450–1000 μm region. These peaks

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Figure 8. Sum of the synthetic absorption spectra in the 200–1000 μm region for the eight neutral PAHs studied in this work. All the spectra have equal weights. All of the labeled peaks are due to out-of-plane modes and are marked with an asterisk in Table 1. The FWHM scales linearly (in wavenumber space) from 5 cm−1 for 20 μm to 0.5 cm−1 for 1000 μm.


correspond to out-of-plane motions for compact structures, such as C94 H26 , C96 H24 , C96 H26 , and C126 H30 . The weak bands all arise from short axis butterfly modes. The 130–200 μm range, shown in Figure 9, shows weak features that correspond to outof-plane motions for elongated, flexible, rectangular shapes, C98 H28 A and C98 H28 B. The 20–130 μm region, shown in Figures 9 and 10, contains both in-plane and out-of-plane modes. In-plane bands are significantly stronger (10 times) than out-of-plane modes. The in-plane modes fall into two main categories: elongation/ compressions and “jumping-jacks”/twisting. More bands are present compared with the 130–1000 μm region and the number of bands increases going from 130 to 20 μm. The peaks for the trapezoidal molecules, C82 H24 and C126 H30 , carry most of the intensities. The elongated rectangular molecules C98 H28 A and C98 H28 B have a characteristic “jumping-jack” mode around 115 μm. The compact, parallelogram shaped C94 H26 and C96 H26 have a very characteristic peak between 37.3 and 37.9 μm, which corresponds to an in-plane elongation/ compression mode. The 15–20 μm region, shown in Figure 11, is sensitive to the degree of compactness and size. Large compact structures have

Figure 9. Sum of the synthetic absorption spectra in the 60–200 μm region for the eight neutral PAHs studied in this work. All the spectra have equal weights. The labeled peaks that are due to out-of-plane modes are marked with an asterisk.

fewer bands centered around 17 μm with the out-of-plane C–H becoming predominant as the size gets larger than 100 carbons. For our largest compact structure, C130 H28 , the C–H out-ofplane becomes predominant at around 17 μm. C96 H24 follows a similar trend with two major bands around 17 μm, one C–H outof-plane with the largest intensity and one in-plane mode. As the structures get more elongated, the number of bands increases significantly with most of them corresponding to in-plane H–C–C–H scissoring and elongation/compressions. A few modes corresponding to C–H out-of-plane motions are also present. 3.3. Astrophysical Implications As illustrated in Figures 5 and 6, the peaks in the 60–200 μm spectral range vary significantly from molecule to molecule.

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Figure 10. Sum of the synthetic absorption spectra in the 20–60 μm region for the eight neutral PAHs shown in Figure 1. All the spectra have equal weights. The labeled peaks that are due to out-of-plane modes are marked with an asterisk.

Clearly any one peak would not allow an identification of a specific PAH. If there are only a few PAHs present, using the positions and relative intensities of several bands, it might be possible to identify a specific PAH molecule. On the other hand, if there are many PAH species present, there will be many bands, some of which will overlap, making a positive identification almost impossible. Thus, the utility of this region in identifying specific PAHs depends greatly on the number of different PAHs present in the emission region. Boersma et al. (2010) recently analyzed the 15–20 μm region using an earlier version of the NASA Ames PAH IR Spectroscopic database. They used a simple emission model that included a single photon absorption, the thermal approximation, and radiative relaxation to compare the computed spectra with astronomical spectra. This simple model yielded an emission spectrum that is in qualitative agreement with the observations for NGC 7023 for the 10–20 μm region. The agreement for the 6–10 μm region is also reasonable, but not quite as good, which probably reflects the difference in size of molecules that dominate the emission in these two wavelength regions (Schutte et al. 1993) more than any limitations in the model or in the PAH data. Given that the new species considered here are of a size comparable to those likely to dominate the emission from the 5–20 μm region, we compare the results of the molecules studied in this work with all of the pure PAH containing more than 50 carbons, as the smaller ones are not representative of the species emitting in this spectral range. (We should note that we exclude C90 H30 , which is circumcircumcoronene with a hole in the center as this is probably not a representative PAH, but we should note that its inclusion does not significantly affect the results.) Because we are interested in such a limited region of the spectra, we simply average the computed absorption spectra. We also decompose the bands into in- and out-of-plane, because, as discussed by Mulas et al. (2006a), the out-of-plane bands could be shaper than the in-plane bands. Before beginning, a few words of caution are probably worthwhile. We have commonly found that our computed bands agree with matrix isolation experiments to about 1–5 cm−1 , with a few bands off by 10 cm−1 , and in the worst case, we have found a few bands, out of hundreds, that have differed by as much as

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Figure 11. Sum of the synthetic absorption spectra in the 15–20 μm region for the eight neutral PAHs studied in this work. All the spectra have equal weights and the frequencies have been shifted to the red by 15 cm−1 to account for the emission process and facilitate a comparison with the astronomical emission features. The vertical lines at 15.8, 16.4, 17.4, 17.8, and 18.9 μm correspond to the emission features observed in many objects.

30 cm−1 . In the MIR such errors are small, but in the 15– 20 μm region, a 10 cm−1 error would shift a 15(20) μm band to 15.23(20.41) μm. We should note, however, that for three moderately sized PAHs we found (Mattioda et al. 2009) that a better estimate of the error in the computed positions in the 15– 20 μm region would be 0.1 μm. In addition, the magnitude of the redshift to account for the difference between emission and absorption, which we take to be 15 cm−1 , is probably uncertain to within a few cm−1 . Finally, we should note that our PAHs contain between 54 and 130 carbon atoms, which could be smaller than the size of the PAHs emitting in the 15–20 μm range (Schutte et al. 1993). Given these limitations, while one should not expect the computed spectra to line up directly with the observed, these calculations reveal insights into the PAH populations that account for the trends in the observational data. In order to compare our features with the emission features observed in the 15–20 μm region, we shift all the spectra to the red by 15 cm−1 and we sum all the spectra with equal weights (see Figure 11). The vertical lines correspond to the observed emission features at 15.8, 16.4, 17.4, 17.8, and 18.9 μm (see Boersma et al. 2010). The four peaks at 15.4, 16.2, 17.4, and 17.9 μm have the largest intensities. In Figure 12, we show a stack plot of all the in-plane and outof-plane frequencies shifted by 15 cm−1 and with integrated intensities larger than 2 km mol−1 . Figure 12 shows that the band at 17.9 μm corresponds to an out-of-plane C–H mode with some contribution from a C–C–C skeletal out-of-plane mode. Almost every neutral molecule considered in this study contributes to this mode, making this a molecule-independent PAH feature, like those found in the MIR. The other bands have only contributions from a subset of molecules. The band centered around 17.4 μm has in-plane and out-of-plane (see Figure 12) contributions, with compact molecules, such as C96 H24 , C96 H26 , and C130 H28 , having peaks with the largest intensities. The peak at 16.2 μm is somewhat shifted with respect to the observed peak at 16.4 μm and is mostly due to inplane elongation/compression modes for parallelogram-shaped

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Figure 12. Stack plot of the out-of-plane (top) and in-plane (bottom) band positions with intensities greater than 2 km mol−1 in the 15–20 μm region for the eight neutral PAHs shown in Figure 1. The frequencies have been shifted to the red by 15 cm−1 .

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structures, such as C94 H26 and C96 H26 . The peak at 15.4 μm is considerably shifted compared to the observed peak at 15.8 μm and has contributions from a small subset of molecules, such as C82 H24 and C98 H28 A, with peaks having sizeable intensities and corresponding to in-plane modes. The peak at 18.9 μm has a smaller intensity and in-plane contributions from C82 H24 , C94 H26 , and C98 H28 B. Using the full database, the results for all three charge states show peaks near 16.2, 17.4, and 17.8 μm. The anions show a peak near 19.4 μm and the neutrals something near 15.4 μm. Considering the uncertainties associated with our calculations and the fact that the 16.4 μm band is observed in more sources than the 15.8 μm band, we speculate that our band at 16.2 μm is associated with the observed band at 16.4 μm. This is interesting to note that the position and relative intensities of the three bands vary somewhat with charge state, which could result in these features varying from source to source. Our work seems to find the 17.4 and 17.8 μm bands to have similar intensity implying a correlation, while the 17.8 μm band is not observed in all astronomical sources. Perhaps the 17.8 μm feature is actually broader than we find, and hence contributes to the broad feature centered at 17 μm and is not always observed as a separate band. If the peak at 18.9 μm is associated with PAHs, our best suggestion would be that it is due to anions and that our computed band has a larger error than expected. We have no suggestions for the origin of the 15.8 μm band. It is clear from Figure 13 that the band at about 18.0 μm is mostly an out-of-plane motion that appears in many of the molecules. An inspection of this mode shows that it is a combination of a C–H out-of-plane bend and a skeletal motion where C–C groups vibrate in and out of the plane; this band is best described as a cross between C–H out-ofplane bend and a drumhead with many nodes. It is weak for the smaller molecules and its position varies somewhat with the size of the molecule that makes this band broad. The band near 16.2 μm is mostly in-plane in character. A comparison of the two bottom plots helps to illustrate that there are two in-plane components. The component at the longer wavelength comes from the molecules studied in this work, while the shorter

Figure 13. Sum of the synthetic absorption spectra in the 15–20 μm region for the molecules studied in this work and for all the pure PAHs (with only C and H atoms) in the NASA Ames PAH IR Spectroscopic Database containing more than 50 carbons. The FWHM is 5 cm−1 . For the species in the full database, the cations, anions, and neutrals are plotted separately. The spectra are decomposed in to the in-plane (dashed) and out-of-plane (dotted) modes. All the spectra have equal weights and the frequencies have been shifted to the red by 15 cm−1 . The vertical lines at 15.8, 16.4, 17.4, 17.8, and 18.9 μm correspond to the emission features observed in many objects.

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wavelength component comes from C120 H26 . The vibrational motion for C120 H26 involves the pendant rings and might be typical of molecules with pendant rings with quartet hydrogens. The other component is found for three molecules, C94 H26 , C96 H26 , and C98 H28 A, and are very complex skeletal motions that are not easy to describe. For C94 H26 , some C6 groups are twisting, while in others, two of the carbons on opposite sides of a C6 ring are vibrating in sync. For C96 H26 and C98 H28 A, the motion seems to be an out-of-sync breathing motion on opposite sides of the molecule. It has been previously suggested that the 16.4 μm band was due to pendant rings (van Kerckhoven et al. 2000); this work supports the notion that the band does not arise from highly symmetric molecules, but suggests that the class of molecules be broadened to include those with some points on their edges. In this regard, we note that Peeters et al. (2004) noted pendant rings would be expected to also result in emission near 14 μm, which is weak. Boersma et al. (2010) found that emission near 13.5 μm was weaker than expected if pendant rings were responsible for the 16.4 μm band. They suggested that perhaps preferential dehydrogenation of the pendant rings enhanced the 16.4 to 13.5 μm ratio. They also noted that a coupling of the out-of-plane C–H bending modes with the C– C–C modes in some cases shifts the 13.5 μm mode to 15.6 μm, which would also enhanced the 16.4 to 13.5 μm ratio. However, the present work suggests that the 16.4 μm band does not arise solely from pendant rings and hence the connection between the 16.4 and 13.5 μm bands is weaker than assumed previously. While we have more than 10 molecules for each charge state, clearly more molecules, larger molecules, and PAH derivatives would need to be considered to be more definitive about the origin of the bands in the 15–20 μm region. Despite the limitations of our data, we feel that some of the bands that have been suggested to arise from PAHs, do in fact arise from PAHs, namely, the 16.4, 17.4, and 17.8 μm bands. 4. CONCLUSIONS The FIR spectra of large neutral PAHs, containing at least 82 carbons up to 130 carbons and with shapes ranging from round/oval-type structures to rectangular and to trapezoidal, have been computed in the 15–1000 μm range. The 130– 1000 μm region corresponds to weak out-of-plane modes. For round, highly symmetric molecules, such as C96 H24 , peaks in this range shift as a function of the number of carbons. For example, going from C24 H12 to C96 H24 the drumhead modes shift by a factor of 4, which is consistent with the C96 /C24 ratio. Using such a shift one can potentially predict the peak position of the drumhead modes for round and highly symmetric PAHs. Less symmetric molecules have at least one butterfly mode in the 700–1000 μm region, which reflects the molecular shape. Elongated, flexible molecules will have the butterfly mode at the longest wavelength. The 20– 130 μm range shows both in-plane and out-of-plane modes. The in-plane modes are 10 times stronger than the out-of-plane ones. Elongated rectangular molecules with about 100 carbons (C98 H28 ) have a characteristic “jumping-jacks” mode at 115 μm and parallelogram-shaped molecules (C94 H26 and C96 H26 ) have a characteristic elongation/compression peak around 37.5 μm. The position of these characteristic peaks will shift for a different number of carbons. A plot of the average spectrum (shifted by 15 cm−1 to the red) in the 15–20 μm range for the neutral PAHs considered in this work shows four main peaks at 15.4, 16.2, 17.4, and 17.8 μm and smaller features, including a peak at 19.4 μm. A

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comparison of the average spectrum mentioned above to the average spectra of all the pure PAHs containing more than 50 carbons in the NASA Ames PAH IR Spectroscopic Database for neutral, cations, and anions shows that the peak at 15.4 μm gets significantly smaller for the larger PAH set, the peak at 16.2 μm becomes stronger for cations, whereas the peak at 17.4 μm gets stronger for anions. The peak at 17.8 μm has similar intensities for all the charge states and the anions show a peak at 19.4 μm. Despite the limitations of our data set, our work supports the suggestion that the bands at 16.4, 17.4, and 17.8 μm arise from PAHs. We thank NASA’s Astronomy and Physics Research and Analysis (APRA) (NNX07AH02G), Spitzer Archival, Laboratory Astrophysics, Astrobiology, and Herschel Laboratory Astrophysics Programs for their generous support of this work. APPENDIX DETAILED ANALYSIS OF THE FAR-INFRARED SPECTRA In this appendix, we consider the FIR molecular vibrations in detail. The modes are discussed in terms of the types of modes, shown in Figure 2 and the description of the modes is relative to the molecular orientation shown in Figure 1, that is, top, bottom, left, and right refer to the orientation of the molecule in Figure 1. A.1. Effect of Molecular Size We first want to focus on the effect of molecular size and compare two molecules that have very similar molecular shape and the same symmetry (D6h ), namely coronene (C24 H12 ; see the inset in Figure 3) and circumcircumcoronene (C96 H24 ; see Figure 1). Circumcircumcoronene can be described as a coronene surrounded by two rings made up of benzene molecules. We have measured and computed the FIR spectrum of coronene (Mattioda et al. 2009; see Figure 3) from 15.4 μm (650 cm−1 ) to 100 μm (100 cm−1 ). Coronene’s spectrum is fairly simple and consists of only three bands around 18.2 μm (549 cm−1 ), 26.5 μm (378 cm−1 ), and 80.6 μm (124 cm−1 ). The band at 80.6 μm, shown in Figure 3, is a “drumhead” or out-ofplane breathing motion and corresponds to the (0,1) mode of an ideal membrane. The degenerate band at 26.5 μm corresponds to an in-plane C–C–C bending mode, which can be described as a “jumping-jacks” movement along the C2 axis passing through two C–C bonds and to another in-plane “jumpingjacks” movement along the C2 axis that is rotated by 90 degrees (see Figure 4). The drumhead motion at 18.2 μm corresponds to the (0,2) mode of an ideal membrane (see Figure 3). The circumcircumcoronene (0,1) drumhead mode shifts to much longer wavelengths, i.e., 319.9 μm (see Figure 3), compared to the 80.6 μm band for coronene. The shift by a factor of 4 reflects the change in the number of carbons going from C24 to C96 . The circumcircumcoronene (0,2) drumhead mode at 76.5 μm is also shifted by approximately a factor of 4 compared with coronene (18.2 μm). Two peaks, somewhat reminiscent of a (0,3) mode in a circular membrane, are present at 32.9 μm and 27.2 μm (see Figure 3). The vibrational mode at 32.9 μm has all the C–H bonds moving in unison in and out of the molecular plane, whereas the mode at 27.2 μm has pairs of adjacent C–H bonds moving out-of-phase in and out of the molecular plane. The mode at 17.5 μm is mostly an out-of-plane C–H bending mode that is coupled with a C-skeletal out-of-plane bending mode. Given the band shifts and increasing complexity of the FIR

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spectrum on going from a small to large PAH, clearly, the outof-plane drumhead modes are good indicators of the molecular size, shape, and flexibility. The degenerate “jumping-jacks” band at 26.5 μm for coronene shifts by approximately a factor of 2 to 49.3 μm for C96 H24 . The coronene “jumping-jacks” motion, shown in Figure 4, involves two halves of the molecular skeleton with all the displacement vectors in each half lining up along the outer ridge of the molecule (reminiscent of the magnetic field lines of a bar magnet). Because of its larger size, C96 H24 has more in-plane and out-of-plane skeletal modes than does coronene. Most of these modes build up by adding an increasing number of nodes to the in-plane “jumping-jacks” and to the out-of-plane drumhead modes. The vibrational mode at 24.8 μm is a degenerate “jumping-jacks” band, which contains nodes compared with the band at 49.3 μm. The vibrational mode at 23.4 μm is a degenerate in-plane breathing motion along the C2 axis passing through the C–C bonds coupled with ring twisting at the two corners on each side of the C2 axis and along the C2 axis that is rotated by 90 degrees. The vibrational mode at 19.9 μm is a degenerate mode that consists mostly of four in-plane ring twisting motions with adjacent H–C–C–H scissorings. The degenerate band at 16.9 μm can be described as mostly in-plane H–C–C–H scissorings. Finally, the band at 16.8 μm corresponds to C–H out-of-plane motions coupled with an out-of-plane ring component. A.2. Effect of Molecular Shape We now turn our attention to the effect of molecular shape on the FIR spectra. The FIR spectra reported here span the region from 15 μm to 1000 μm; the spectra are shown in Figures 5– 7, while the band positions and integrated intensities are given in Table 1. A quick glance at the spectra tells us that both molecular shape and size affect the peak position and intensity. We first focus on low-frequency drumhead motions in the 200– 1000 μm spectral range (see Figure 5 and Table 1). C82 H24 , C94 H26 , C96 H24 , and C96 H26 have a strong peak in the 200– 400 μm range. The intensities are small and the peaks are slightly shifted with respect to each other, which reflects the geometrical differences. Interestingly, for C98 H28 A and C98 H28 B (see Figure 1), which have very elongated shapes, the peak is shifted to lower wavelengths and carries almost no intensity. C130 H28 , a compact structure which has an additional row of benzene rings as compared to C96 H24 , has a feature centered around 421.4 μm that corresponds to an out-of-plane (0,1) drumhead motion. This feature is shifted by a factor of 1.3 compared with the drumhead mode at 320 μm for C96 H24 . This shift is consistent with the C130 /C96 ratio. C94 H26 , C96 H26 , and C98 H28 A are parallelograms and C98 H28 B is almost rectangular in shape (see Figure 1). Their geometries vary in the number of benzene rings per length and width. C94 H26 is seven benzenes long and five benzenes wide, C96 H26 is six benzenes long and six benzenes wide. C98 H28 A and C98 H28 B are both nine benzenes long and four benzenes wide. C82 H24 and C126 H30 are isosceles trapezoids. C82 H24 has one base consisting of four benzene rings and another base consisting of eight benzene rings. C126 H30 has one base consisting of four benzene rings and another base consisting of 10 benzene rings. The changes in shape affect the molecular flexibility, which in turn modifies the out-of-plane vibrational frequencies. The mode at the longest wavelength corresponds to the easiest way of bending the molecule. For all the molecules shaped

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as parallelograms or rectangles, this mode can be described as a butterfly motion along the shortest diagonal. C98 H28 A is the easiest molecule to bend with the butterfly mode along the shortest diagonal at 928.2 μm. C98 H28 B is more compact and is stiffer than C98 H28 A, which is reflected by a butterfly mode along the shortest diagonal at 701.2 μm. C94 H26 and C96 H26 have similar lowest frequency butterfly modes along the short diagonal at 763.8 μm and 739.2 μm, respectively. For the trapezoids C82 H24 and C126 H30 , the mode at the longest wavelength corresponds to a butterfly motion along the short C2 axis. This mode is at 466.6 μm for C82 H24 and at 645.3 μm for C126 H30 . Finally, for the more compact C130 H28 , the lowest frequency mode shifts to 599.7 μm despite its largest number of carbons. Overall, this lowest frequency butterfly mode is a good indicator of the molecular shape. Elongated molecules shaped as long parallelograms are the most flexible followed by the trapezoidal molecules. Compact and symmetric molecules are more rigid and have their lowest-energy butterfly modes at shorter wavelengths, see Table 1. For all the molecules considered in this study, this mode carries almost no intensity. In the 200–400 μm range (Figure 5), peaks with larger intensities are present for C94 H26 , C96 H24 , and C96 H26 . C82 H24 and C98 H28 A have peaks carrying much lower intensities, which are centered around 248.7 μm for C82 H24 , and at 206.8 μm for C98 H28 A. For the parallelogram-shaped molecule C94 H26 , the peak at 223.6 μm corresponds to a butterfly motion very similar to that at the longer wavelengths, but along the long diagonal. For C96 H26 , which is more compact, the peak at 265.4 μm corresponds to an out-of-plane (0,1) drumhead mode. For the compact C96 H24 molecule, the vibrational mode at 319.9 μm corresponds to a (0,1) drumhead motion, as discussed before. C82 H24 has a vibrational mode at 248.7 μm, which can be described as a butterfly motion along the long molecular axis, which is perpendicular to the short C2 axis. The mode at 206.8 μm for C98 H28 A is a butterfly mode along the short axis with one additional node compared with the mode at 928.2 μm. In the 60–200 μm range (Figure 6) groups of molecules show similarities in their spectra. C82 H24 , C94 H26 , C96 H24 , and to a lesser extent C96 H26 have a peak in the 70–90 μm region. C98 H28 A and C98 H28 B have comparable spectra. C126 H30 and C130 H28 have reasonably similar spectra. For C82 H24 two peaks with low intensities are visible. The peak at 169.8 μm corresponds to an out-of-plane butterfly motion along the short C2 axis with the two upper corners moving in one direction and the two lower corners moving in the opposite direction. The peak at 103.4 μm can be described as an out-of-plane butterfly motion with an additional node as compared with the vibrational mode at 169.8 μm. The four corners now move out-of-plane in phase. The two upper corners are separated by two adjacent C–H bonds, which move in opposite directions. The two lower corners are separated by three pairs of adjacent C–H bonds and they move out-of-phase with respect to each other. C98 H28 A has a weak peak at 163.2 μm that corresponds to an out-of-plane butterfly motion along the long molecular axis. Similarly, C98 H28 B has two peaks at 172.3 μm and 150.4 μm, which correspond to an out-of-plane butterfly motion along the long molecular axis with one and two nodes, respectively. C98 H28 A and C98 H28 B have both a peak around 115 μm. The vibrational mode at 116.4 μm for C98 H28 A is similar to the vibrational mode at 112.7 μm and corresponds to a “jumping-jacks” motion along the short axis. A close inspection at the vibrational spectra of C82 H24 and C126 H30 reveals that the two features at 67.2 μm and 93.4 μm for C126 H30 correspond to the two features at 49.0 μm and 76.7 μm

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for C82 H24 shifted by 17 μm to longer wavelengths due to the increase in the number of carbons. The vibrational modes at 76.7 μm and 93.4 μm correspond to “jumping-jacks” along the short C2 axis, and the 67.2 μm and 49.0 μm correspond to an in-plane C–C–C twisting. The vibrational mode at 76.2 μm for C126 H30 corresponds to a butterfly mode along the short axis with one node. Although C82 H24 and C96 H24 both exhibit a peak around 76.5 μm, this peak corresponds to completely different vibrational motions in the two molecules. For C96 H24 it is an outof-plane (0,2) drumhead motion, whereas for C82 H24 it is an in-plane “jumping-jacks.” For C94 H26 the peak at 84.7 μm has two components: the major component is an in-plane twisting motion along the short diagonal similar to the “jumping-jacks” shown on the right-hand side of Figure 4. The minor component is an out-of-plane mode with groups of atoms opposite to each other with respect to the center of inversion moving in phase in and out of the molecular plane. For C96 H26 , there is a weak mode at 79.5 μm, which corresponds to a “jumping-jacks” with the two pointy corners moving in-sync along the short C2 axis and a peak at 58.9 μm, which corresponds to an out-of-plane (0,2) drumhead mode. Finally, the vibrational mode at 61.8 μm for C130 H28 corresponds to an in-plane “jumping-jacks” along the short C2 axis and the mode at 97.3 μm corresponds to a (0,2) drumhead motion similar to the (0,2) drumhead motion at 76.5 μm for C96 H24 . The vibrational mode at 53.0 μm for C130 H28 corresponds to an in-plane “jumping-jacks” along the long axis. The degenerate “jumping-jacks” mode at 49.2 μm in C96 H24 loses its degeneracy in C130 H28 splitting into two peaks at 61.8 μm and 53.0 μm. The 15–60 μm range (Figure 7) shows two distinct regions: the 15–20 μm region contains a large number of peaks for molecules shaped as a parallelogram and the 20–60 μm region has fewer peaks. We first consider the 20–60 μm range. The peaks at 49 μm for C82 H24 and C96 H24 , and at 53 μm for C130 H28 have already been discussed. For C98 H28 A, the vibrational mode at 46.5 μm corresponds to a “jumping-jacks” with one more node compared with the mode at 116.4 μm. The vibrational mode at 38.8 μm involves an elongation/compression motion along the long axis. For C98 H28 B, the two weak peaks at 42.1 μm and 36.8 μm are equivalent to the two peaks for C98 H28 A at 46.5 μm and 38.8 μm, respectively. The vibrational mode at 31.3 μm for C98 H28 A and the vibrational mode at 31.2 μm for C98 H28 B correspond to a butterfly mode along the long axis with one node. This creates a zigzag pattern along the long axis of the molecule. The two other peaks on each side of the peak at 31.3 μm correspond mostly to an inplane elongation/compression (33.1 μm) and to an in-plane twisting mode (31.1 μm). The peak at 23.8 μm for C98 H28 A is an in-plane twisting motion and the peak at 22.0 μm is an in-plane elongation/compression. C98 H28 B has similar peaks at 24.4 μm and 22.5 μm, respectively. C94 H26 has peak around 37.9 μm and C94 H26 has a peak at 37.7 μm. Both peaks correspond to an elongation/compression mode along the long diagonal. C82 H24 has a sizable peak at 31 μm, which has two components: one small component at 31.5 μm, which corresponds to “jumping-jacks” with more nodes, and a larger component at 30.8 μm, which corresponds to an elongation/compression of the top and bottom parts of the molecule. Four additional small features are present. The vibrational mode at 34.5 μm corresponds to an in-plane elongation/compression mode, the vibrational mode at 36.8 μm corresponds to an in-plane twisting,

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the mode at 39.6 μm corresponds to “jumping-jacks” along the short C2 axis. Finally, the vibrational mode at 44.8 μm is an out-of-plane vibrational mode with the central hexacene moiety moving in and out of the molecular plane. C126 H30 has several peaks in the region from 30 to 40 μm. The vibrational mode at 30.0 μm is a “jumping-jacks” with nodes along the C2 axis, which resembles the mode at 24.8 μm for C96 H24 and at 23.7 μm for C82 H24 . The vibrational mode at 34.5 μm is an in-plane elongation/compression mode. The peak at 36 μm includes an elongation/compression mode at 36.4 μm and an out-of-plane mode at 36.4 μm, corresponds to a butterfly mode along the short axis with three nodes. C130 H28 has peaks at 40.8 μm and 28.4 μm that are similar in nature to the peaks at 32.9 μm and 24.8 μm for C96 H24 . The out-of-plane vibrational mode at 40.8 μm corresponds to a (0,3) drumhead mode. The peak at 28.4 μm is actually two modes that are accidentally degenerate. One vibration with B2u symmetry corresponds to an in-plane elongation/compression along the short molecular axis and the other vibration has B1u symmetry and corresponds to an in-plane “jumping-jacks” with nodes along the long axis. Under the peak at 28.4 μm, there is another out-of-plane (0,4) drumhead feature at 28.2 μm, which is symmetric with respect to the long axis. At 27.4 μm and 26.7 μm, there are two in-plane elongation/compression modes. The first is along the long axis and the second is along the short axis. In the 20–25 μm spectral region, two sizeable peaks are visible for C82 H24 and minor peaks are present for the rest of the molecules. C82 H24 has one peak at 20.4 μm and two peaks at 23.1 μm and 23.7 μm. The two vibrational modes at 23.7 μm and 20.4 μm can be described as “jumping-jacks” along the short C2 axis. The mode at 23.7 μm is equivalent to the mode at 24.8 μm for C96 H24 . The mode at 23.1 μm is an in-plane twisting mode. C94 H26 has a peak at 21.7 μm which can be described as an in-plane twisting motion. C96 H26 has two peaks very close to each other. One feature at 26.8 μm corresponds to an in-plane “jumping-jacks” with nodes and the other feature at 26.1 μm can be described as an out-of-plane (0,3) drumhead mode. C96 H26 has a sizeable peak at 20.0 μm which corresponds mostly to an elongation/compression mode along the long diagonal. The smaller peak at 21.7 μm corresponds to an in-plane twisting motion. C98 H28 A has two peaks between 20 and 25 μm. The vibrational mode at 22.0 μm corresponds to an elongation/ compression along the long diagonal and the peak at 23.8 μm can be described as an in-plane twisting motion. C98 H28 B has three weak peaks between 20 and 25 μm. The vibrational mode at 24.4 μm can be described as an elongation/compression along the long axis passing through nine benzenes. The mode at 22.5 μm can be described as H–C–C–H scissors, and the mode at 21.5 μm can be described as H–C–C–H scissors plus some elongation/compression motions. C126 H30 has four peaks in the 20–25 μm range. The vibrational mode at 24.6 μm is an in-plane twisting mode. The mode at 24.0 μm can be described as an in-plane elongation/compression along the short C2 axis. The mode at 23.0 μm is an in-plane elongation/compression breathing mode along the C2 axis. Finally, the mode at 21.4 μm involves the top row (four benzenes) with the two central benzenes “rocking” in the opposite direction of the two corner benzenes. C130 H28 has four peaks in the 20–25 μm region. The vibrational mode at 25.1 μm can be described as an in-plane elongation/compression along the short C2 axis. The left and right sides of the molecule elongate/compress out-of-sync. The peak at 23.9 μm is the (0,4) drumhead mode. The two modes

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at 22.3 μm and 21.8 μm are derived from the “jumping-jacks” along the long axis and have many more nodes. The 15–20 μm region is somewhat different than the 20– 1000 μm as it shows significantly more peaks. The modes in this region become very complex and have often several components. We classify them using the major component. The vibrational motions in this region belong to five types: inplane H–C–C–H scissors, in-plane “jumping-jacks,” in-plane elongations/compressions, C–H out-of-plane bending motions, and in-plane rocking/twisting. The rocking/twisting motions are very complex and appear in the column denoted “others” in Table 1. For C82 H24 , the in-plane vibrational motions carry the most intensity. There are four main peaks. The vibrational mode at 18.7 μm can be described as in-plane H–C–C–H scissors. The peak at 18.3 μm corresponds to an in-plane rocking/ twisting motion. The vibrational mode at 17.0 μm corresponds mostly to in-plane scissors. Finally, the peak at 15.0 μm is mostly in-plane scissors. The out-of-plane C–H bending mode with the strongest intensity is at 17.4 μm. For C94 H26 many peaks are present, which are mainly due to in-plane H–C–C– H scissoring, in-plane elongation/compressions, and C–H outof-plane motions. Two peaks carry most of the intensity: one is centered around 15.8 μm and the other is centered around 15.4 μm. Both vibrational modes correspond mostly to in-plane C-skeletal elongations/compressions with minor contributions from H–C–C–H scissors. The two C–H out-of-plane peaks with the largest intensities are at 18.0 μm and 17.4 μm. C96 H24 due to its high-symmetry has only three peaks in the 15–20 μm region. One mode at 16.9 μm is a degenerate mode and probably best described as a scissors mode, but might also be viewed as a “jumping-jacks” mode with many nodes. The other two modes at 17.5 μm and 16.8 μm correspond to C–H out-of-plane vibrational motions. For C96 H26 , three peaks carry most of the intensity. The vibrational mode at 16.8 μm can be described as an in-plane H–C–C–H scissoring and the vibrational mode at 16.78 μm corresponds to a C–H out-of-plane along the long diagonal. Finally, the vibrational mode at 15.8 μm corresponds to an in-plane elongation/compression along the long diagonal. C98 H28 A has many peaks with similar intensities (see Figure 7). Almost all of them correspond to in-plane H–C– C–H scissors and elongation/compression motions. The out-ofplane mode that carries the largest intensity is at 16.2 μm. It can be described as mostly a C–H out-of-plane mode along the long axis coupled with C-skeletal out-of-plane motions with alternating rows of carbons moving in opposite directions.

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C98 H28 B has a similar profile with somewhat broader features. As for C98 H28 A, most of the peaks correspond to in-plane H–C– C–H scissors and elongation/compressions. The out-of-plane mode that carries the largest intensity is at 16.2 μm. It consists mostly of C–H out-of-plane motions along the long axis. C126 H30 shows several small peaks mostly due to in-plane H–C– C–H scissors and in-plane elongation/compression modes. Two features have larger intensities. One peak at 17.50 μm can be described as an out-of-plane C–H motion mostly concentrated on the three bottom rows. For C82 H24 , the C–H out-of-plane was at 17.4 μm, a very similar peak position. The second vibrational mode at 16.4 μm can be described as an in-plane elongation/ compression mode. For C130 H28 , one larger peak emerges at 16.9 μm. The largest out-of-plane C–H motions are for the four sides containing the largest number of benzenes (five benzenes). All the C–Hs move in unison and all the dipoles contribute to create this large intensity. REFERENCES Allamandola, L. J., Tielens, A. G. G. M., & Barker, J. R. 1989, ApJS, 71, 733 Bauschlicher, C. W., & Langhoff, S. R. 1997, Spectrochim. Acta A, 53, 1225 Bauschlicher, C. W., Peeters, E., & Allamandola, L. J. 2008, ApJ, 678, 316 Bauschlicher, C. W., Peeters, E., & Allamandola, L. J. 2009, ApJ, 697, 311 Becke, A. D. 1993, J. Chem. Phys., 98, 5648 Boersma, C., Bauschlicher, C. W., Allamandola, L. J., Ricca, A., Peeters, E., & Tielens, A. G. G. M. 2010, A&A, in press Flükiger, P., Lüthi, H. P., Portmann, S., & Weber, J. 2000, MOLEKEL 4.2 (Manno, Switzerland: Swiss Center for Scientific Computing), 2000–2002 Frisch, M. J., Pople, J. A., & Binkley, J. S. 1984, J. Chem. Phys., 80, 3265 (and references therein) Frisch, M. J., et al. 2003, Gaussian 03 (Revision B.05; Pittsburgh PA: Gaussian, Inc.) Genzel, R., et al. 1998, ApJ, 498, 579 Gillett, F. C., Forrest, W. J., & Merrill, K. M. 1973, ApJ, 183, 87 Joblin, C., Toublanc, D., Boissel, P., & Tielens, A. G. G. M. 2002, Mol. Phys., 100, 3595 Mattioda, A. L., Ricca, A., Tucker, J., Bauschlicher, C. W., & Allamandola, L. J. 2009, AJ, 137, 4054 Moutou, C., et al. 1998, in ASP Conf. Ser. 132, Star Formation with the Infrared Space Observatory, ed. J. Yun & L. Liseau (San Francisco, CA: ASP), 47 Mulas, G., Malloci, G., Joblin, C., & Toublanc, D. 2006a, A&A, 456, 161 Mulas, G., Malloci, G., Joblin, C., & Toublanc, D. 2006b, A&A, 460, 93 Peeters, E., Mattioda, A. L., Hudgins, D. M., & Allamandola, L. J. 2004, ApJ, 617, L65 Schutte, W. A., Tielens, A. G. G. M., & Allamandola, L. J. 1993, ApJ, 415, 397 Spitzer First Observations Special Edition. 2004, ApJS, 154 Stephens, P. J., Devlin, F. J., Chabalowski, C. F., & Frisch, M. J. 1994, J. Phys. Chem., 98, 11623 Van Kerckhoven, C., et al. 2000, A&A, 357, 1013