Anharmonic IR absorption spectra of the prototypical interstellar PAHs phenanthrene, pyrene, and pentacene in their neutral and cation states

Combination band and overtone transitions of polycyclic aromatic hydrocarbon (PAH) cations in the 2000–2900 cm-1 (5-3.5 µm) region are implicated as carriers of the ‘quasi-continuum’ observed in the near-infrared (IR) emission spectra of many astronomical objects. In neutral PAHs, the strongest absorption features are concentrated in the 700–900 cm-1 (14–11 µm) range, which are associated with CH out-of-plane bending motions. Upon ionization, this shifts to the 1000–1600 cm-1 (10–6 µm) range, where bands are associated with C=C stretches and CH in-plane bends. Anharmonicity is required to accurately characterize the IR absorption spectrum of PAHs, indicated herein by the ability to directly assign the bands in high-resolution experimental absorption spectra of neutral and cationic phenanthrene, pyrene, and pentacene. Neutral PAHs are indicated as the source of the strong 3.3 and 11.2 µm astronomical PAH features, while the broad features in the 6–10 µm region and the ‘quasi-continuum’ from 3.5–5 µm stem from PAH cations. This study reinforces the need for including anharmonicity in the computation of IR absorption and emission spectra of larger and more complex PAHs. This is particularly pertinent to the interpretation of data returned by JWST. GRAPHICAL ABSTRACT


Introduction
The mid-infrared (IR) emission features that are now generally attributed to fluorescence from vibrationally excited polycyclic aromatic hydrocarbons (PAHs) were discovered in the late 1970s and early 1980s.Today, thanks to decades of observations from ground-based, airborne, and space-based telescopes, the initial handful of spectra has grown to thousands.Interstellar PAH emission is now clearly associated with many, if not most, galactic and extragalactic objects and that PAHs play essential roles in key astronomical processes [1][2][3].Their unique properties, coupled with their spectroscopic response to changing astrophysical and astrochemical conditions, makes them important players in CONTACT Vincent J. Esposito vincent.j.esposito@nasa.govNASA Ames Research Center, MS 245-6, Moffett Field, CA 94035-1000, USA and powerful probes of their astronomical environment.For example, PAHs account for roughly 15-20% of interstellar carbon, and their emission is responsible for up to 20% of the IR power of the Milky Way and entire star-forming galaxies [1,2,4].They dominate cloud cooling, thereby influencing star and planet formation, and are efficient catalysts for H 2 formation [5,6].As probes, PAH IR band positions, profiles, and relative strengths reveal the composition of the underlying PAH population in terms of size, charge distribution, edge structure, and chemistry; and that composition reflects the interplay of PAHs with their astrophysical environment.Despite the continuous advancements made with the astronomical PAH model over the years, significant questions and uncertainties remain and new ones continue to arise.These uncertainties severely limit fundamental understanding of how the PAH population responds to and affects the local physical and chemical conditions in different astronomical environments.The recent launch of the James Webb Space Telescope (JWST) will make it possible, for the first time, to overcome many of these uncertainties.JWST's unprecedented combination of spatial-spectral resolution and sensitivity across the entire near-to mid-IR region is revolutionizing understanding of the PAH population makeup and how it drives the astrophysics and chemistry of their astronomical environments.
In many ways, the quality of available PAH spectroscopic data and associated models used to interpret astronomical observations exceeds the capabilities of earlier IR observatories.However, JWST is able to resolve peak positions and profiles with a precision that far surpasses the previous generation, requiring a commensurate improvement in the quality of the laboratorymeasured as well as computationally-modeled spectroscopic data.Current density functional theory (DFT) quantum chemical methods rely on the harmonic approximation in which all vibrational levels in a particular vibrational mode are evenly spaced and band profiles (Gaussian, Lorentzian, etc.) are simply chosen.In reality, proper predictions of vibrational levels should be done anharmonically with the spacing between levels either increasing or decreasing with each increasing level.As one would expect, including anharmonicity notably affects DFT computed spectra across the entire IR range.Observationally, anharmonicity is responsible for the extended red wings on the 6.2 and 11.2 μm (1613 and 893 cm −1 ) PAH bands, much of the broadband continuum underlying the features, the distinct 5.25 and 5.75 μm (1905 and 1740 cm −1 ) bands, and similar subtle features [7].Emission models are used to reproduce these aspects of the astronomical spectra since none of these features are treated by the anharmonic approximation.
Anharmonicity has not been possible to include in quantum chemically computing IR spectra for molecules as large as PAHs until recently.Thanks to increases in computational power and the development of novel computational techniques, anharmonic spectra for PAHs containing up to 30 carbon atoms with an accuracy and precision commensurate with JWST capabilities can now be computed [8][9][10][11][12].Here, using these techniques, the computed 300-3200 cm −1 (33.3-3.13 μm) anharmonic absorption spectra of the neutral and cation forms of the PAHs phenanthrene (C 14 H 10 ), pyrene (C 16 H 10 ), and pentacene (C 22 H 14 ) are presented as examples of how the state-of-the-art quantum chemical computations can inform IR observations.These PAHs are chosen for the following reasons: 1)-their experimental neutral and cation spectra are available in order to benchmark the computations, 2)-phenanthrene and pyrene are the first two members of the most thermodynamically favourable, high temperature PAH growth route [13] and likely are important in circumstellar regions where PAHs are produced, 3)-different H-adjacency classes are represented in this sample because of their very different edge structures (solo through quartet), and 4)-the pentacene structure provides a long, straight-edged structure of solo hydrogens, a dominant characteristic of interstellar PAHs.
This work starts to lay the foundation required to develop the techniques to compute the complete IR anharmonic spectra of very large PAHs needed to interpret properly the astronomical PAH spectrum.Earlier studies have detailed the importance of including anharmonicity in order to properly predict the IR absorption spectrum of PAHs in the CH stretch region [14,15]; that work is expanded here.The data generated here will be included in a new spectral library of the NASA Ames PAH IR Spectroscopic Database (PAHdb) 1 [16][17][18][19].

Methods
The methods utilised in this study have been described in detail elsewhere [8,14,[20][21][22][23]; therefore, only an abbreviated description is included here.Geometry optimisation, harmonic frequency analysis, and computation of the quartic force field (QFF, quadratic, cubic, and quartic force constants) for the PAHs phenanthrene, pyrene, and pentacene are performed at the B3LYP [24]/N07D [25] level of theory using Gaussian 16 [26].The N07D basis set is based on the 6-31G(d) basis with additional diffuse and polarisation functions added that have been shown to improve the anharmonic treatment for large PAH molecules [27].A QFF is a group of force constants derived from a fourth order Taylor expansion of the potential around the equilibrium geometry.These force constants are computed through small displacements of atoms along predefined coordinates [28,29].
Following this, 2 nd order vibrational perturbation theory (VPT2) is employed to predict anharmonic vibrational frequencies with a locally modified version of SPECTRO.This allows for direct control over the treatment of resonances via polyad matrices, increasing accuracy and computational efficiency.The maximum energy separation of the states to include in the resonance treatment ( ) is set to 200 cm −1 , while the minimum magnitude of the interaction strength between states (W) is chosen to be 10 cm −1 as has been shown to be effective in previous work [20].The redistribution of intensity throughout the entire spectrum is contained within this polyad treatment, which is not included in the Gaussian VPT2 implementation.This intensity redistribution has been shown to be critical for providing proper intensity predictions, especially when used in comparison with experimental results [20,30].Lastly, the spectra of the neutral and cation molecules are then convolved with a Lorentzian line profile having a full-width-athalf-maximum (FWHM) of 8.0 and 1.0 cm −1 , respective of the charge states, in order to create continuous spectra.

The aromatic CH stretch region (3200-2900 cm −1 ; 3.10-3.50 µm)
Figure 1 presents the IR absorption spectra of phenanthrene (left), pyrene (middle), and pentacene (right) in the aromatic CH stretch region.The top frame (a) shows the experimental, matrix-isolated IR absorption spectra of the neutral species.Lower frames (b) and (c) show the computed anharmonic theoretical IR absorption spectra of the corresponding neutral and cation species, respectively.
These three cases serve two purposes: to provide an accurate theoretical basis for analyzing current and future PAH experimental data and to validate the chosen methodology in order to calculate novel anharmonic spectra of PAH cations.As discussed in the following, the results from frames (a) and (b) accomplish these two goals and allow for the analysis of the PAH cation spectra, which are quite different from the neutral species in the CH stretching region.

Neutral phenanthrene, pyrene, and pentacene
Phenanthrene (symmetry C 2v ): Excellent agreement between experiment (a) and anharmonically computed (b) spectra is demonstrated in the central peak position, width, and satellite peak structure of neutral phenanthrene (left panel, Figure 1).Note that no shift or scaling factor is applied to the theoretical spectrum.Quantum chemistry reproduces the base width of the structure from approximately 3000-3150 cm −1 (3.30-3.17μm).When considering the overall band structure, the triple peak main band, low intensity dip at 3042 cm −1 (3.29 μm), peak at 3026 cm −1 (3.30 μm), and high energy shoulder are all well-matched between theory and experiment.
Pyrene (symmetry D 2h ): Moving to the slightly larger, more symmetric pyrene (middle panel, Figure 1), similar good agreement is found between the experimental and anharmonic, quantum chemical spectrum.In this case, a small 10 cm −1 bathochromic (red) shift is applied to the theoretical spectrum in order to match the central peak position.This lies well within the normal range of dispersive shifts associated with matrix isolation experiments.The central feature in the experimental pyrene spectrum is narrow with a FWHM of 24.4 cm −1 and a base width from 3015 to 3080 cm −1 (3.32-3.25 μm).The anharmonically computed spectrum matches the width reasonably well and predicts the high and low energy shoulders.On both sides of the central feature in the experiment, small peaks above the noise arise from the combination bands and overtones.These features are predicted by the anharmonic theory and even extend beyond the frequencies captured by the experiment providing additional spectroscopic characterisation.
Pentacene (symmetry D 2h ) For pentacene, the largest PAH and third case examined in this study, a moderate bathochromic shift of 30 cm −1 is required to match the matrix-isolation peak position (right panel, Figure 1).The overall structure observed in the laboratory-measured spectrum is reproduced reasonably well in the anharmonic computed spectrum, including the tall, narrow central peak, the high and low energy shoulders, and in additional small peaks surrounding the central peak.While there are minor to moderate intensity ratio differences in some of the smaller shoulder peaks, the frequency predictions match quite well.
As these test cases demonstrate, all the spectroscopic detail and the overall width of these features arise from the inclusion of anharmonicity.The overtones and combination bands of lower energy modes have appreciable intensity in the aromatic CH stretching region.

Cationic phenanthrene, pyrene, and pentacene
The computed spectra for the cation forms of these PAHs are shown in the lower three frames (c) in Figure 1.To the best of our knowledge, experimental spectra for PAH cations in the CH stretch region are not available.Comparing the spectra of the neutral PAHs shown in the (b)-frames and the corresponding cation spectra in the (c)-frames illustrates the profound change that occurs upon ionization.When ionized, PAHs lose nearly all of their intensity in the aromatic CH stretching frequencies but gain intensity in the fundamental C = C stretching and bending frequencies from 1000 to 1600 cm −1 (10-6.2μm) [31,32,[38][39][40][41][42][43][44].Taken together, weak combination and overtone bands are predicted across the entire 2900-3200 cm −1 (3.5-3.1 μm) CH stretching range, but nothing with intensities comparable to neutral molecules.To compensate for this for the purpose of visualizing the results, the intensity of the cation bands shown in the c-frames have been multiplied by the factors shown in Figure 1.

3.2.
The 300-2900 cm −1 ; 33.0-3.50µm region Subsections 3.2.1,3.2.3, and 3.2.5 present the experimental and computed neutral anharmonic 300-2900 cm −1 (33.0-3.50 μm) IR absorption spectra of phenanthrene, pyrene, and pentacene, respectively, while Subsections 3.2.2,3.2.4,and 3.2.6 discuss their counterpart computed cation anharmonic IR spectra in the same frequency range.Unlike the pyrene and pentacene spectra in the 2900-3200 cm −1 range that required a small overall frequency shift to match the experiment, the forthcoming spectra of the neutral and cation PAHs in the 300-2900 cm −1 range have not been shifted.The computed anharmonic frequencies that are directly assigned to experiment are labelled and identified in Tables 1-6.Some of these features are comprised of a mixture of various modes due to Fermi resonance coupling.Although there is agreement throughout the entire spectral range, some minor experimental features may be missed in the computational spectra due to higher-order (three-quanta and above) transitions not considered in the anharmonic calculations.Even so, these will be minimal and will not affect any characterisation save for the most fine-grained  [36] and pentacene from Ref. [37].
Table 1.Neutral Phenanthrene band identifications (ID), matrix-isolation (MI) and gas-phase (GP) experimental line positions (cm −1 ), normalised relative experimental intensities, computed anharmonic frequencies (cm −1 ), mode assignments, intrinsic computed intensities (km/mol) and normalised anharmonic relative intensities for the spectra shown in Figure 2. The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.[36] b Gas-phase data from Ref. [35] analysis.The matrix-isolated and gas-phase experimental data for these PAHs in their neutral state as well as anharmonic frequencies conjoined to the intrinsic and relative intensities have been identified and assigned according to the anharmonic computed frequencies.Due to experimental limitations, the IR cation spectra are incomplete, making this the first report of the complete mid-IR spectra of phenanthrene, pyrene, and pentacene cations.While cation experimental relative intensities are included in the tables below and compared to computed anharmonic relative intensities, experimental limitations on the precise measurement of these intensities make extensive comparisons impossible.However, the agreement between the experimental and computational frequencies, where possible, is noteworthy.

Neutral phenanthrene
The spectra of neutral phenanthrene in Figure 2 and spectroscopic details listed in Table 1 show excellent agreement between the (top) experimental and the (bottom) anharmonic, quantum chemical results.
Throughout the entire 500-2000cm −1 (20-5 μm) range, each major feature in the experimental spectrum is reproduced by the quantum chemical computations.The maximum difference between the experimental and anharmonic frequencies is a remarkable 6.3 cm −1 , with an outlier of 14.3 cm −1 for the feature labelled as 'q'.The relative intensities, scaled to 1.0 relative to the most intense feature, are in good agreement between the experiment and theory as well, with a maximum difference of 0.25 for the second strongest peak labelled 'h'.The two strongest features, 'g' and 'h', are associated with the CH out-of-plane (CHoop) bending modes for the quartet and duo adjacent hydrogens on the outer and central rings, respectively.Again, there are many weak features in the 1500-2000cm −1 (6.70-5.00μm) range of the experimental spectrum that are well predicted by theory solely due to the inclusion of anharmonicity in the computations.For example, the weak to moderate features labelled 'v' and 'w' in the spectrum of neutral phenanthrene are assigned to combination bands that arise from anharmonicity and have near exact matches with their computed frequencies and relative intensities.Many of these are associated with combinations involving the strong neutral CHoop modes [45,46].Interestingly, the spectrum of the phenanthrene cation shows no significant absorption in this region (Table 2).Comparison of the anharmonic theory and experiment, again, validates the theoretical methodology utilised here.

Phenanthrene cation
Moving to the phenanthrene cation spectrum in Figure 3 and data presented in Table 2, a major shift in intensity is predicted.As discussed in the previous sections, upon ionization, intensity decreases in the aromatic CH stretching region, as well as in the out-of-plane CH wag (CHoop) region from 700 to 900 cm −1 (14.0-11.0μm), which are the most intense bands in the neutral molecule.In the cation, the most intense transitions occur between 1000 and 1600 cm −1 (10-6.25 μm) and represent various in-plane CH wagging (bending) motions as well as C = C stretch and associated skeletal deformations.IR absorption spectra obtained in matrix-isolation and gas-phase experiments are also included in Table 2.The experimental data agree well for all observed matrix experiments [31], and the gas-phase experiment [35] detects a host of additional features that remained unassigned due to the lack of available anharmonic computational data, until now.
Throughout the spectrum, the assigned features correspond to various fundamental and combination band transitions.For example, the band labelled 'a' is assigned to the ν 59 +ν 66 combination band while the feature labelled 'c' is assigned to the ν 51 fundamental.Sixteen transitions observed in the gas-phase experiment from 855 to 1231 cm −1 (11.7-8.1 μm) were unassigned in the original report [35] due to a lack of anharmonic data.In this work, direct assignment is difficult due to the presence of many computed transitions exhibiting intrinsic intensity in a close energy range.However, all these features, computed here at high-resolution in Figure 3, will contribute to the band shape and intensity observed in the experiment after convolution to the lower-resolution detection.
Moving to higher frequency, a greater density of vibrational states arising from combination bands and overtones results in resonances and resonance chaining, The large unlabeled peaks in the experimental spectrum slightly above 1600 cm −1 and the weak gas phase envelope centered at 2340 cm −1 are due to water in the matrix and uncanceled CO 2 gas, respectively, and thus do not show up in the theoretical spectrum.Experimental data from Hudgins and Sandford [36].
Table 2. Phenanthrene cation band identification (ID), matrix-isolation (MI) and gas-phase (Ph-Ar, Ph-Ne) experimental line positions (cm −1 ), computed anharmonic frequencies (cm −1 ), mode assignments, experimental and computed anharmonic relative intensities, and anharmonic computed intrinsic intensities (km/mol) for the spectra shown in Figure 3.The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.o a Matrix-isolation data from Ref. [31] b Gas-phase data from Ref. [35] which causes the assignments in this region to include a high degree of mode mixing as well as various transitions located close together.An example of this is the feature labelled 'g' detected at 1264.7 cm −1 (7.9 μm), which could be assigned to the anharmonic transitions at 1261.4 and/or 1262.4 cm −1 .Both transitions could possibly contribute to the feature when experimental broadening is considered.Each of these transitions are highly mixed, with large-percentage contributions coming from two different combination bands.The intrinsic intensity of the strongest transitions in the phenanthrene cation absorption spectrum are larger than those in the neutral phenanthrene spectrum.PAH cations have previously been suggested to be the strongest contributors of the 6.2 μm band and 7.7 μm band complex in the astronomical spectra [42,47], which the results of this study continue to support.
Examination of the 1600-2900 cm −1 (6.25-3.5 μm) region of the neutral and cation spectra shows that there are significantly more numerous, minor features with appreciable intensity in the cation spectrum.In contrast, the neutral spectrum is relatively flat from 2000 to 2900 cm −1 (5-3.5 μm).While the intrinsic intensities of these cation bands are roughly an order of magnitude weaker than the very strong fundamentals between 1000 and 1600 cm −1 (10-6.25 μm), they are quite strong in relative terms when compared to the average intensity of the fundamentals.An intriguing observation of the band assignments listed in Tables 1 and 2 is that the neutral phenanthrene spectrum is comprised of an almost equal number of fundamental transitions (14 fundamentals, 7 combinations), whereas the cation spectrum includes 4 fundamentals and 14 combination bands.

Neutral pyrene
Figure 4 depicts the (top) experimental and (bottom) computational spectra of pyrene in the 300-2900 cm −1 (33.0-3.40 μm) region with the corresponding spectroscopic details listed in Table 3. Pyrene's higher degree of symmetry (D 2h ) compared to phenanthrene results in fewer IR active modes, making its experimental and theoretical spectrum sparser.
The anharmonic theory for neutral pyrene, one more time reproduces every major and minor feature in the 500-2000cm −1 (20-5 µm) range.The largest difference in frequency is 13.7 cm −1 for the feature labelled 'p', the feature dominated by the combination band v 46 + v 61 .Otherwise, most features are predicted to within 5 cm −1 of their experimental assignment.The relative intensities The insets are expanded regions of the spectrum to show assignments in spectrally-congested areas.The intensity of the spectrum from 1600 to 2900 cm −1 has been multiplied by a factor of 10 relative to the more intense 300-1600 cm −1 region.Table 3. Neutral pyrene band identification (ID), matrix-isolation (MI) experimental line positions (cm −1 ), normalised relative experimental intensities, computed anharmonic frequencies (cm −1 ), mode assignments, anharmonic computed intrinsic intensities (km/mol), and normalised anharmonic relative intensities obtained for the spectra shown in Figure 4.The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.[36] are predicted even more accurately than for phenanthrene, with an average difference of 0.05.There is only a single large deviation of 0.41 for the minor feature labelled 'l' that likely stems from the overlapping nature of the transitions in that region.The two strongest features, 'd' and 'g' are associated with the CHoop bending modes for the trio and duo adjacent hydrogens, respectively.As with phenanthrene, the neutral pyrene spectrum from 2000 to 2900 cm −1 (5-3.5 μm) is relatively flat, having only some weak bumps with absolute intrinsic intensities averaging about 0.14 km/mol.

Pyrene cation
Figure 5 shows the 300-2900 cm −1 (33.0-3.40 μm) computational spectrum of the pyrene cation.The spectrum and spectroscopic details in Table 4, once again, show that there is excellent agreement between the experimental and the anharmonic theoretical results.In addition to the expected intensity drop of the strong neutral pyrene bands in the CHoop region (700-900 cm −1 ; 4.0-11.0μm) and dramatic intensity increase in the C = C stretching and in-plane CH wagging (bending) region (1000-1600 cm −1 ; 10-6.25 μm), comparing the spectra shown in Figures 4 and 5 and data listed in Tables 3 and 4 shows that an equally significant difference between the neutral pyrene spectrum with that of the cation is again, the richness of new weak features that span the entire 2000-2900 cm −1 (5-3.5 μm) range.
The pyrene cation spectrum is characterised by the same increase in intensity to higher energy transitions as reported for phenanthrene, though, with still some appreciable intensity in the two lowerenergy, CHoop bending modes.Starting in the CHoop region (700-900 cm −1 , 4.0-11.0μm), transition 'a' at 868.7 cm −1 (11.5 μm) corresponds to v 45 , the duo CHoop bend.Upon ionization, the transition blueshifts by ∼ 22 cm −1 , and its intensity (90 km/mol) drops some 20% compared to that of its neutral counterpart, band 'g' (115.9 km/mol), the largest feature in the neutral spectrum.The strongest intensity transition is v 14 , which is a C = C stretch and associated skeletal deformation mode that includes in-plane CH wagging motions.This transition is labelled ' * ' and is predicted to occur at 1549.8 cm −1 (6.50 μm) with an intensity of 144.9 km/mol.
Many small features are predicted between 1600 cm −1 (6.25 μm) and 2900 cm −1 (3.5 μm) that are produced by first order combinations and overtones of the strong fundamental transitions below 1600 cm −1 .A plethora of these features have intensities between 0.3 and 2% of the intensity of the very strong band at 1549.8 cm −1 (144.9 km/mol) marked with a ' * ' in Figure 5.Most have intensities of about 0.5 km/mol, some ten have intensities roughly at 1.5 km/mol and a handful have intensities around 3 km/mol.Although weak, the richness of these features produces astronomically observable bands and a continuum that will appear in telescopic observation.The transitions in this region and many other weaker features that are unlabeled stem from 2 quanta combination bands with small intensities that are only possible to predict via the inclusion of anharmonicity in the computations.

Neutral pentacene
The spectra of pentacene, the sole acene (linear PAH, symmetry D 2h ) studied here, shows some notable differences from the spectra of phenanthrene and pyrene across the 300-2900 cm −1 (33.0-3.40 μm) range.These spectra are depicted in Figure 6, with the corresponding spectroscopic data listed in Table 5.First, the (top) experimental and (bottom) computed anharmonic spectra of neutral pentacene produce seemingly equivalent peaks throughout the entire spectral range with no spectral shift required.All major features have been assigned.The most intense feature is, again, the feature labelled 'g' at an experimental frequency of 899.9 cm −1 (11.1 μm) assigned to v 56 , the CHoop bending mode of the solo hydrogens on the long side of the structure.The second most intense feature, the band labelled 'e' at 731.5 cm −1 (13.7 μm), is dominated by the CHoop bending modes Table 4. Pyrene cation band identification (ID), matrix-isolation (MI) experimental line positions (cm −1 ), computed anharmonic frequencies (cm −1 ), mode assignments, experimental and computed anharmonic relative intensities, and anharmonic computed intrinsic intensities (km/mol) for the spectra shown in Figure 5.The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.19.9 a Matrix-isolated data from Ref. [31] b Matrix-isolated data from Ref. [48] c Gas-phase data from Ref. [34] of the quartet hydrogens on the end rings.The anharmonic computed and experimental band positions up to 1300 cm −1 show differences of less than 10 cm −1 .However, above this frequency the anharmonic computations show absolute peak differences of 51.4 and 25.6 cm −1 for features 'o' and 'q', respectively.The differences could have various causes, including matrix effects in the experiment and limits of the level of theory, e.g. an incorrect characterisation of the QFF.Feature 'o' has the largest deviation.This combination band includes v 99 , a low frequency rocking motion.Low frequency transitions, particularly those with frequencies below 200 cm −1 are challenging to characterise with both harmonic and anharmonic DFT methods due to their possible flat potential energy surface surrounding the minimum structure and less precise energy values.Despite this, the anharmonic computations appear to perform well in predicting the major features in the neutral pentacene experimental IR absorption spectrum.

Pentacene cation
As with the other two molecules, ionization of pentacene, shown in Figure 7, shifts intensity to the higher energy modes with the intensity clustered closer to 1500 cm −1 (6.6 μm).There is less intensity remaining in the lower energy intense features such as the CHoop modes of the quartet and solo hydrogens, whereas in phenanthrene and pyrene there are many modes with larger intensity at lower frequencies.Direct assignments for the main contributing transitions are possible for the lowest frequency modes of pentacene, as given in Table 6.The features labelled 'a' and 'b' arise from CHoop bending fundamentals.From there, the remaining assigned features contain a mixture of coupled combination bands and fundamentals.Beginning with the experimental feature at 1384.0 cm 1 (7.3 μm), the anharmonic computational spectrum becomes densely populated, hampering direct assignment.Examples of the many transitions surrounding each experimental feature are included in Table 6.As with phenanthrene, these neighbouring features computed here with a narrow bandwidth blend together in the experimental spectrum and contribute to the broad bands observed in the experiment.
Again, there are small bumps all along the 1600-2900 cm −1 range with a few noticeable features.Compared to the phenanthrene and pyrene cations, there are fewer features with appreciable intensity throughout this entire range for pentacene.However, the intensity of the weak features in the pentacene cation are an order of magnitude more intense than those found in the phenanthrene and pyrene cations.This is due to a much larger intrinsic intensity in the very strong bands of the pentacene cation between 1350 and 1600 cm −1 (7.4-6.25 μm).

Astrophysical implications
Consistent with past experiments and DFT predictions, the computed spectra presented here confirm that ionization state plays a critical role in determining the overall appearance of the 3-20 μm (3200-500 cm −1 ) astronomical PAH emission spectrum [42,47].While emission from both neutral and cationic PAHs contribute across the entire range, neutral species are the main contributors in the CHoop bending and CH stretching regions (for example, the 11.2 and 3.3 μm; 893 and 3030 cm −1 bands) and PAH cations the main carriers in the CHip bending and C = C stretching region (e.g. the 8.6, 7.7, and 6.2 μm; 1163, 1300, and 1610 cm −1 bands).Because of the inclusion of anharmonicity in the DFT computations, this work shows that dozens of weak, but significant, first-order PAH cation combination and overtone bands produce a quasi-continuum between 5 and 3.5 μm (2000-2900 cm −1 ; Figures 3, 5, and 7) that can explain some, if not all of, the excess emission seen in astronomical spectra [50].
The unique insight into the specific vibrational modes involved in the bands afforded by anharmonicity promises to deepen understanding of the astronomical PAH spectrum by tightening constraints on PAH Table 5. Neutral pentacene band identifications (ID), matrix-isolation (MI) experimental line positions (cm −1 ), normalised relative intensities, computed anharmonic frequencies (cm −1 ), mode assignments, computed intrinsic intensities (km/mol) and normalised anharmonic relative intensities for the spectra shown in Figure 6.The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.[37] b Matrix-isolated data from Ref. [49] charge balance, size, and structure.This work, in conjunction with the foundational work previously done on small PAHs [8,20,21,23] demonstrates the necessity of including anharmonicity in the computation of PAH spectra.Anharmonicity has also been shown to be the driver behind the extended red wings observed on the astronomical 6.2 and 11.2 μm (1613 and 893 cm −1 ) PAH bands [23], and not, as previously speculated, due to emission from PAH anions [51] or different PAH mixtures.Likewise, the congestion of features shown here between 6.25 and 9 μm (1600-1100 cm −1 ) for the cations (upper frames, Figures 3, 5, and 7) and between 3.2 and 3.5 μm (3175-2900 cm −1 ) for the neutrals ((b)-frames, Figure 1), suggest that the plateaus and small satellite bands accompanying the strong astronomical features are a consequence of anharmonicity.
Turning to specific modes, the pentacene data shown in Figures 6 and 7 and listed in Tables 5 and 6 illustrate how the very strong neutral pentacene 'g' band at 905.1 cm −1 (11.1 μm) is due to the fundamental CHoop bending mode (v 56 ) of the solo hydrogens.Upon electron loss, this band weakens and redshifts to 936.0 cm −1 (10.68 μm; v 55 ).This is congruent to the behaviour observed for the astronomical 11.2 and 11.0 μm PAH bands, which have been assigned to neutral and ionized solo hydrogen fundamental modes [52].However, this is not the case for the quartet hydrogen bending modes in pentacene.Here, the strong 'e' band, which falls at 730.6 cm −1 (13.7 μm) in neutral pentacene, would normally be attributed to the quartet hydrogen bending fundamental.Rather, the mode assignment in Table 5 shows its nature is mixed with 68% of its intensity arising from the pure fundamental and 31% from a resonance with a combination band involving two other fundamentals.This band, designated by ' * ' in Figure 7, is blue-shifted by 10 cm −1 and falls at about 740 cm −1 (13.5 μm).
After the initial discovery of the near-IR excess in 1984 [53], subsequent observations revealed a 6-3.5 μm (1660-2900 cm −1 ) continuum that is an integral part of the astronomical PAH spectrum [50,[54][55][56] but whose origin is yet to be settled.The anharmonic computations presented here support an interpretation where this 'continuum' is produced by the vast array of combination and overtone bands in PAH cations.This is similar to how neutral PAHs produce the 5.25 and 5.75 μm (1905 and 1740cm −1 ) bands [45,46].The first order overtones and combinations of strong fundamentals largely produce the PAH-continuum shown in Figure 8 [50].Here, again, the significant number of combination and overtone bands from various PAHs along the line-of-sight blend, adding to the undulating structure shown in the figure .Anharmonic computations are required to interpret laboratory experiments.Likewise, the high-fidelity data returned by JWST will provide ready discernment for the types of features predicted here.As such, anharmonic computations are now required to analyze and interpret astronomical observations.Observational access to these weaker anharmonic bands provides a new handle for determining the make-up of the astronomical PAH population with a deeper precision than previously possible, with the promise to [45,46] to break degeneracies between factors like PAH size, charge, edge structure, and composition [57][58][59].

Conclusions
The results in this study implicate combination bands in PAH cations as the potential origin of the quasicontinuum shown in Figure 8. Upon ionization, IR absorption intensity shifts from the CH stretching region (3200-2900 cm −1 ; 3.1-3.5 μm) and out-of-plan CH bends (800-700 cm −1 ; 12.5-14.2μm) to the C = C stretches and in-plane CH bends in the 1600-1000 cm −1 (6-10 μm) region.Additionally, the large intensity of these higher frequency modes leads to appreciable intensity growing in in the 2900-1600 cm −1 (3.4-6 μm) range Figure 6.Absorption spectra of pentacene in the 300-2900 cm −1 (33.0-3.40 μm) range: (top) neutral, argon matrix-isolated experimental spectrum and(bottom) neutral, anharmonic theoretical spectrum.The two sharp, unlabeled peaks in the experimental spectrum slightly above 1600 cm −1 and the two near 2340 cm −1 are due to water and CO 2 in the matrix, respectively, and thus do not show up in the theoretical spectrum.Experimental data from Hudgins and Sandford [37].Table 6.Pentacene cation band identifications (ID), matrix-isolation (MI) experimental line positions (cm −1 ), computed anharmonic frequencies (cm −1 ), mode assignments, experimental and computed anharmonic relative intensities, and computed intrinsic intensities (km/mol) for the spectra shown in Figure 7.The mode number in parenthesis for the anharmonic intrinsic intensity is the mode where the intensity of the dark state is derived from the resonance coupling if different from the mode assignment.[32] b Matrix-isolated data from Ref. [49] due to combination bands that include these strong inplane CH bending modes.This region has been dubbed the 'quasi-continuum' in the astronomical literature, where spectra show an appreciable increase in strength after the dominant 3.3 μm feature.
The anharmonic IR absorption spectrum of neutral and cationic phenanthrene, pyrene, and pentacene have been provided herein giving the first complete computational or experimental mid-IR characterisation of these molecules.Comparison of the computed neutral spectra to available gas-phase and matrix-isolated experiments covering the range from 500 to 3100 cm −1 obtained through the PAHdb provides a benchmark for the accuracy of the chosen methodology.The anharmonic computations on the neutral species agree well with the experimental results with all major features reproduced by the anharmonic predictions.For phenanthrene and pyrene, the anharmonic computations show frequency differences of < 10 cm −1 for all features besides one.In both cases, the relative intensities exhibit good agreement with experiment.For pentacene, agreement is slightly less favourable, potentially due to the presence of low frequency transitions from combination bands; although, overall, the spectrum is well-matched.
Taken together, the work presented here adds to the existing literature and continues to provide validation of the chosen methodology in predicting genuine PAH IR absorption spectra.Quantum chemical computation is currently the best means of obtaining complete, PAH cation IR spectra for large numbers of molecules, and these results provide solid ground for expanding the use of this methodology for predicting the anharmonic IR absorption spectra of PAH cations.In addition, these methods scale within the availability of modern, contemporary computational resources and ongoing work will show the application of these methods to larger systems in forthcoming publications.
Although the molecules studied here are 'small' relative to the expected average size of cosmic PAHs, the results from this study suggest the need for the computation of anharmonic PAH cation absorption spectra in order to fully understand their role in the origin of the quasi-continuum.Additionally, future studies are required to realize how anharmonicity impacts the resultant full-cascade emission profiles of the cation compared to the well-studied neutral species.developed the methods utilised here.He was an integral and central member of the Astrophysics Team at NASA Ames, both scientifically, and more importantly, personally, as a friend, mentor, and inspiration.He is, and will always be, missed by us all.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Figure 1 .
Figure 1.Absorption spectrum of phenanthrene (left), pyrene (middle), and pentacene (right) in the CH stretching region.(a) The argon matrix-isolated experimental spectrum, (b) the theoretical spectrum of the neutral species including anharmonicity and resonance effects, and (c) the theoretical spectrum of the cation species including anharmonicity and resonance effects.The theoretical data for the neutral species have been normalised to match the maximum intensity of the experimental peak.The intensities of the much weaker computed cation bands have been multiplied by factors of 5, 2, and 10 as indicated.Phenanthrene and pyrene data from Ref.[36] and pentacene from Ref.[37].

Figure 2 .
Figure 2.Absorption spectra of phenanthrene in the 300-2900 cm −1 (33.0-3.40 μm) range: (top) neutral, argon matrix-isolated experimental spectrum and (bottom) neutral, anharmonic theoretical spectrum.The large unlabeled peaks in the experimental spectrum slightly above 1600 cm −1 and the weak gas phase envelope centered at 2340 cm −1 are due to water in the matrix and uncanceled CO 2 gas, respectively, and thus do not show up in the theoretical spectrum.Experimental data from Hudgins and Sandford[36].

Figure 3 .
Figure 3. Anharmonic computational absorption spectrum of the phenanthrene cation in the 300-2900 cm −1 (33.0-3.40 μm) range.The insets are expanded regions of the spectrum to show assignments in spectrally-congested areas.The intensity of the spectrum from 1600 to 2900 cm −1 has been multiplied by a factor of 10 relative to the more intense 300-1600 cm −1 region.

Figure 4 .
Figure 4. Absorption spectra of pyrene in the 300-2900 cm −1 (33.0-3.40 μm) range: (top) neutral, Argon matrix-isolated experimental spectrum and (bottom) neutral, anharmonic theoretical spectrum.The two sharp, unlabeled peaks directly to the right of feature labelled 's' and blended with 's', and the barely noticeable absorption near 2340 cm −1 in the experimental spectrum are due to water in the matrix and uncanceled CO 2 , respectively.Experimental data from Hudgins and Sandford [36].

Figure 5 .
Figure 5. Anharmonic computational absorption spectrum of the pyrene cation in the 300-2900 cm −1 (33.0-3.40 μm) range.The insets are expanded regions of the spectrum to show assignments in spectrally-congested areas.The intensity of the spectrum from 1600 to 2900 cm −1 has been multiplied by a factor of 20 relative to the more intense 300-1600 cm −1 region.

Figure 7 .
Figure 7. Anharmonic computational absorption spectrum of the pentacene cation in the 300-2900 cm −1 (33.0-3.40 μm) range.The insets are expanded regions of the spectrum to show assignments in spectrally-congested areas.The intensity of the spectrum from 1600 to 2900 cm −1 has been multiplied by a factor of 10 relative to the more intense 300-1600 cm −1 region.