closed-shell polycyclic aromatic hydrocarbon cations: a ... · density functional theory has been...

Spectrochimica Acta Part A 57 (2001) 907ndash930 wwwelseviernllocatesaa

Closed-shell polycyclic aromatic hydrocarbon cations a new category of interstellar polycyclic aromatic hydrocarbons

Douglas M Hudgins Charles W Bauschlicher Jr Louis J Allamandola NASA Ames Research Center MS 230-3 Moffett Field CA 94035 USA

Received 11 July 2000 received in revised form 14 September 2000 accepted 18 September 2000

Abstract

Density functional theory has been employed to calculate the harmonic frequencies and intensities of a range of polycyclic aromatic hydrocarbon (PAH) cations that explore both size and electronic structure effects on the infrared spectroscopic properties of these species The sample extends the size range of PAH species considered to more than 50 carbon atoms and includes several representatives from each of two heretofore unexplored categories of PAH cations (1) fully benzenoid PAH cations whose carbon skeleton is composed of an odd number of carbon atoms (Codd PAHs) and (2) protonated PAH cations (HPAH+) Unlike the radical electronic structures of the PAH cations that have been the subject of previous theoretical and experimental work the species in these two classes have a lsquoclosedrsquo-shell electronic configuration The calculated spectra of circumcoronene C54H18 in both neutral and (radical) cationic form are also reported and compared with those of the other species Overall the Codd PAHs spectra are dominated by strong CC stretching modes near 1600 cmminus1 and display spectra that are remarkably insensitive to molecular size The HPAH+ species evince a more complex spectrum consistent with the added contributions of aliphatic modes and their generally lower symmetry Finally for both classes of closed-shell cations the intensity of the aromatic CH stretching modes is found to increase with molecular size far out of proportion with the number of CH groups approaching a value more typical of neutral PAHs for the largest species studied copy 2001 Published by Elsevier Science BV

Keywords Infrared spectroscopy Polycyclic aromatic hydrocarbon Harmonic frequencies and intensities Interstellar molecules

1 Introduction

The discovery of an unexpected infrared emisshysion feature from two planetary nebulae by Gillett Forrest and Merrill in 1973 marked the

Corresponding author Tel +1-650-6046231 Fax +1shy650-6045244

E-mail address bauschlipegasusarcnasagov (CW Bauschlicher Jr)

1386-142501$ - see front matter copy 2001 Elsevier Science BV

PII S1 386-1425 (00 )00453 -4

beginning of an exciting chapter of modern astroshyphysics [1] Gillett et al recognized that this band near 885 cmminus1 (113 microm) was associated with interstellar dust and that its identification could give important insight into dust formation and evolution through the latter stages of the stellar life cycle Moreover this feature could not be associated with graphite grains long thought to be produced in intense circumstellar outflows

908 DM Hudgins et al Spectrochimica Acta Part A 57 (2001) 907ndash930

from late-type carbon-rich stars Subsequent pioshyneering observations showed this was just one part of a now well-known spectrum of features emitted from a wide variety of very different astronomical objects (for example see Refs [2ndash 5]) This spectrum is characterized by dominant features near 3030 1610 1280 1150 and 890 cmminus1 (33 62 77 86 and 112 microm) as well as a number of minor bands and underlying continua The brightest emission is observed from dusty regions exposed to intense ultraviolet radiation Surprisingly the age and history of the material seem to be relatively unimportant Similar emisshysion spectra are observed from objects that span the lifecycle of matter in the interstellar medium (ISM) mdash from objects only a few thousand years in age (late carbon star ejecta and planetary nebushylae shells) to those millions of years in age (H II regions reflection nebulae and the diffuse ISM) [6ndash11] Understanding the source of this unexshypected yet widespread phenomenon has become an important problem in astrophysics

The idea now gaining acceptance that stochasshytically heated gas-phase polycyclic aromatic hyshydrocarbons (PAHs) are the band carriers was first put forth over a decade ago [1213] This attribushytion is based on several pieces of lsquocircumstantialrsquo evidence that point to these species First the interstellar emission is non-thermal in nature The banded (rather than continuous) nature of the spectrum the typically large featurecontinuum ratio and the close association with ultraviolet radiation all indicate that the emission is due to infrared fluorescence from gas-phase molecules excited by the absorption of single ultraviolet and visible photons rather than thermal emission from a solid material [14] Second careful observations of planetary nebulae have established that the fraction of the total infrared energy that is emitshyted through these features is closely correlated with the amount of available carbon [15] indicatshying that the gas-phase molecular carriers are carshybon rich Third since the carbon-rich carriers must survive under remarkably harsh conditions they must also be extremely stable Finally alshythough there are variations among the relative band intensities the features are correlated [1617] implying that a single class of chemical

species is responsible Of course any proposed carrier must have an IR spectrum consistent with the positions and intensities of these bands As a molecular class PAHs readily accommodate all these constraints

Originally the principal reason for the assignshyment to PAHs was the suggestive but far from perfect resemblance of the interstellar lsquoemissionrsquo spectra to the then-available infrared lsquoabsorptionrsquo spectra primarily those of PAH clusters dispersed in KBr pellets or soot particles Unfortunately although rich this spectral database was not adeshyquate to squarely address the astronomical quesshytions since such laboratory conditions strongly perturb the spectrum and are far from those in the interstellar emission zones Moreover if PAHs are indeed present in the highly energetic emission zones they are likely to be ionized [13] and until recently there was no spectroscopic data available on the infrared properties of PAH ions Thus the spectral database initially available was not suffishycient for a critical test of the PAH hypothesis nor if the hypothesis held up to close scrutiny was it up to the task of exploiting PAHs as probes of the emission zones To truly test the PAH hypothesis special techniques for studying individual PAHs and PAH ions under astrophysically relevant conshyditions were required

Motivated in no small part by their emerging interstellar importance the past decade has seen a renaissance in experimental and theoretical methshyods aimed at determining the physical [18ndash20] chemical [21ndash25] and spectroscopic [26ndash38] imshypact of PAHs in the interstellar medium Particushylarly relevant to the problem of the interstellar infrared emission these efforts have produced a large and growing database of the infrared specshytroscopic properties of PAHs and PAH ions that are directly relevant to the astrophysical problem [39ndash55] These studies have included PAHs in neutral cationic and anionic forms and encomshypass species ranging in size from ten to 32 carbon atoms Nevertheless to date both experimental and theoretical studies in this area have focused primarily on the determination of the spectroshyscopic properties of the sorts of conventional structures that characterize terrestrially stable commercially available PAHs Such PAHs in their

DM Hudgins et al Spectrochimica Acta Part A 57 (2001) 907ndash930 909

neutral forms (indeed virtually all stable chemical compounds) have a lsquoclosed-shellrsquo electronic strucshyture mdash one having only paired electrons This necessarily implies that their daughter cations all have the alternative lsquofree-radicalrsquo or lsquoopen-shellrsquo electronic structure carrying one unpaired electron Regardless of their ionization state due to their incomplete electronic structure open-shell species are inherently less stable and more reactive than their closed-shell counterparts Despite the focus on PAH radical cations PAH cations that have a closed-shell configuration are not unknown Two classes of these are of particular interest to astroshyphysics (1) fully benzenoid PAH cations with an odd number of carbon atoms (Codd PAH cations) and (2) protonated PAHs (HPAH+) Representashytive structures from each of these classes are shown

Fig 1 The structures of the Codd PAH cations considered in this work The species all have a fully benzenoid skeleton composed of an odd number of carbon atoms The open circles represent carbon atoms

Fig 2 The structures of the protonated PAH cations HPAH+ considered in this work Note the aliphatic -CH2-groups that replace one aromatic CH in each case Large circles carbon atoms small circles hydrogen atoms

in Figs 1 and 2 respectively For such closed-shell cations it is the corresponding neutral species that have the highly reactive radical electron configurashytion and are not isolatable The lack of a suitable precursor presents serious practical difficulties that have yet to be overcome with the current experishymental techniques Thus these classes of closed-shell PAH cations make excellent subjects for a theoretical investigation of their infrared spectroshyscopic properties

An additional noteworthy aspect of the compushytational results presented in the following is the molecular size range of the PAH species that are considered To date most studies (experimental and theoretical alike) have focused on PAH molecules containing only up to about 30 carbon atoms In the theoretical studies this limitation was imposed largely by the significant amounts of CPU time required for calculations of larger speshycies However the latest experimental and theoshyretical studies suggest that while molecules containing as few as 20ndash30 carbon atoms may contribute to the interstellar infrared emission


spectrum the strongest interstellar emission feashytures in the 1600ndash1100 cmminus1 (6ndash9 microm) region are dominated by species comprised of 50ndash100 carshybon atoms [183556] It is therefore important to the astrophysical problem that studies of PAH cations be extended to species of this size In this manuscript with the benefit of several key adshyvances [57] in the calculation of analytic second derivatives (which have been implemented in the GAUSSIAN 98 package of programs) we report computed IR spectra of PAH cations as large as 59 carbon atoms

This paper is laid out as follows The computashytional methods are described in Section 2 In Section 3 the calculated harmonic frequencies and intensities for the two classes of closed-shell PAH cations are presented and discussed accordshying to class with the Codd PAH cations considered in Section 31 and the protonated PAH cations considered in Section 32 Finally the astrophysishycal implications of the results are considered in Section 4

2 Computational methods

The geometries are optimized and the harshymonic frequencies and infrared intensities are computed using the B3LYP [58] hybrid [59] funcshytional in conjunction with the 4-31G basis sets

[60] Calibration calculations which have been carried out for selected systems [36] show that a single scale factor of 0958 brings the B3LYP harmonic frequencies computed using the 4-31G basis set into excellent agreement with the experishymental fundamentals for example in naphthashylene the average absolute error is 44 cmminus1 and the maximum error is 124 cmminus1 To calibrate the intensities we have performed B3LYP calculashytions on naphthalene and the naphthalene and 1shyand 2-hydronaphthalene cations as well as pyrene and the pyrene and 1- 2- and 4-hydropyshyrene cations using the 6-31+G and 6-31+ + G basis sets The computed ratios of the intensities obtained using these higher level basis sets to those obtained using the 4-31G basis set are presented in Table 1 Excluding the naphthashylene cation in the 6-31+ +G basis set improvshying the basis set generally reduces the aromatic C-H stretching intensity For the pyrene species considered this reduction is found to be as large as two- to fourfold While the impact of the higher level basis sets is more ambiguous for the naphthalene species it should be noted that the absolute intensities of the aromatic CH stretching modes in these species are very small tending to exaggerate the relative impact of any variations in the calculations For example in the naphthalene cation the aromatic C-H stretch intensity changes from 145 kmmol in the 4-31G basis set

Table 1 The basis set dependence of the calculated total aromatic and aliphatic CH stretching intensities for the naphthalene and pyrene species considered in Section 32 compared with that of the remaining non-CH stretching modes in those species

Species 6-31+G4-31G 6-31++G4-31G

CH stretching modes All other modes CH stretching modes All other modes

Aromatic Aliphatic Aromatic Aliphatic

C10H8 087 083 071 112 +C10H8 083 092 198 095 +aC10H9 068 095 094 098 108 096

C16H10 086 085 071 106 C16H10

+ 056 092 027 095 +bC16H11 061 093 094 039 113 097

a Average for two possible hydronaphthalene cation structures b Average for three possible hydropyrene cation structures


to 286 kmmol for the 6-31+ +G basis set so while the ratio is much larger than 1 the absolute change is small Thus the calibration data proshyvided by the pyrene system is expected to provide a more realistic assessment of the accuracy of the calculations for PAH species as a whole

Interestingly unlike the aromatic C-H stretchshying intensity the aliphatic C-H stretching intensishyties and the total non-C-H stretching intensities are relatively independent of the basis set used Thus this work along with previous work [3643] indicates that while the 4-31G intensities of non-C-H stretching modes in PAHs are reasonably accurate the aromatic C-H stretching intensities are too large by some two- to threefold The current work also shows that unlike their aroshymatic counterparts the accuracy of the computed aliphatic C-H stretching intensities is comparable with that of the non-C-H stretching modes Thus the overestimation of the intensities with the 4shy31G basis set appears to be limited specifically to the aromatic C-H stretching modes Therefore since this effect is variable in magnitude and limited to only a single class of modes we report the 4-31G intensities as computed for all bands with the stipulation that the aromatic CH stretchshying intensities probably represent an overestimate of their actual intensities We should also note that regardless of their composition when two modes of the same symmetry are close in energy their relative intensities are sensitive to the level of theory but the sum of their intensities is very reliable

The B3LYP calculations were performed using the GAUSSIAN 98 computer codes [61] The comshyplete harmonic frequencies and intensities includshying those obtained with the higher level basis sets can be found at lthttpccfarcnasagov cbauschlclosed-shelldata)

3 Results

The results of our theoretical analyses of closed-shell PAH cations are presented next orgashynized according to class with the infrared spectra of the Codd PAH cations considered first followed by that of the protonated PAH cations

31 Fully benzenoid PAH cations containing an odd number of carbon atoms (Codd PAH cations)

These closed-shell PAH cations are fully benshyzenoid (ie composed only of fused six-membered rings) species whose skeleton is composed of an odd number of carbon atoms This investigation was motivated by the work of Weilmunster Keller and Homann [62] who have analyzed the PAH cation structures that are produced in comshybustion processes the processes considered most likely involved in the production of interstellar PAHs [6364] Employing time-of-flight mass spectrometry to monitor the formation and growth of PAH cations in flames Weilmunster et al found that the PAH cations exhibit their own unique growth chemistry involving species and structures that differ significantly from those found in the neutral PAH population Not surshyprisingly small PAH cations appear first early in the combustion region with sequentially larger species becoming important with increasing depths into the combustion region What is surshyprising is the distribution of the structures in the flame PAH cation population They report that for cations up to about 50 carbon atoms strucshytures with an odd number of carbon atoms actushyally dominate the population Furthermore the authors determined that these odd carbon number species were not simply species that incorporated a five-membered ring in their structures but were instead fully benzenoid structures Such strucshytures are illustrated in Fig 1 which shows the structures of the species considered in this work As one approaches 50 carbon atoms the populashytions of the species with even and odd numbers of carbon atoms converge and above this size apshypear in roughly equal proportions Considering the energetic conditions in many of the infrared emission zones and the inherent stability of the closed-shell Codd PAH cations if interstellar PAHs are indeed produced under combustion-like conditions in carbon-rich circumstellar shells such species may well represent important memshybers of the smaller PAH population in these regions

The results of the aforementioned combustion experiments can be understood in terms of the


electronic structures of the ions involved Quite simply Ceven PAH cations necessarily have an open-shell radical structure while the Codd PAHs have the chemically more favorable closed-shell structure and are therefore preferred Presumably by the time one reaches 50 carbon atoms stability provided by electron delocalization over the exshytensive aromatic framework dilutes the energetic cost associated with maintaining the odd electron to the point that there is no longer any significant preference for closed-shell over open-shell structures

Synthetic representations of the theoretically calculated infrared spectra of several Codd PAH

+ +cations ranging from C13H9 to C59H19 are preshysented in Fig 3 These simulations were generated by assigning each calculated band a 20 cmminus1

full-width at half-height (FWHH) gaussian profile of the appropriate intensity Such a profile is consistent with that expected from molecules emitting under the conditions of the interstellar problem [26] Abbreviated tabulations of the calshyculated band positions symmetries and intensishyties can be found in Tables 2 and 3 In those tables the data at frequencies below 2000 cmminus1

have been truncated at the 10 level The infrared active modes in the 3200ndash2800 cmminus1 CH stretchshying region are presented in their entirety in accorshydance with their more diminutive nature and their role in the following discussion Complete tabulashytions of the calculated data (including both IR active and inactive modes) have been posted on the Internet at lthttpccfarcnasagov cbauschlclosed-shelldata) Inspection of these data reveals that each of the spectra are domishynated by three strong features in the 1600ndash1100 cmminus1 (625ndash91 microm) region which is characterisshytic of aromatic CC stretching and CH in-plane wagging vibrations In some cases these features represent a single very strong band while in othshyers they reflect an overlapping of two or more features that fall close to each other (see Tables 2 and 3) The band near 1600 cmminus1 (a strong doublet in the spectrum of C13H9

+) is consistently the strongest of these The other two typically fall in the mid-1300 cmminus1 (75 microm) and the low 1200 cmminus1 (83 microm) regions While it is well established that the strongest infrared bands of PAH cations

tend to fall in the 1600ndash1100 cmminus1 region it is unusual to find the band near 1600 cmminus1 to be the strongest in the spectrum (see for example Figs 6ndash9) It is also unusual to see such a similarshyity in the pattern of these strong bands over such a large range of molecular sizes Indeed comparishyson of the spectra in Fig 3 with the data currently available in the literature [39ndash55] shows that throughout the infrared the spectral variations of Codd PAHs over a wide range of molecular sizes are more subtle than those of neutral PAHs and PAH radical cations They are also more subtle than those found for the closed-shell protonated PAH cations that are discussed in Section 32 (for reference compare also the spectra of the naphshythalene radical cation and the circumcoronene radical cation in Fig 6a and Fig 9b respectively) At this stage it is unclear whether this is a characteristic of the particular series of molecules studied or whether this is a general feature of this class of PAH cation Another interesting aspect of this region of the spectrum is the size dependence of the dominant band positions Specifically highest frequency features in this region all tend to cluster between 1595 and 1575 cmminus1 and show little dependence on molecular size The positions of the other two dominant bands on the other hand shift steadily toward lower frequencies with increasing molecular size from 1361 and 1259

minus1 +cm (74 and 794 microm) in the C13H9 cation to 1318 and 1189 cmminus1 (76 and 84 microm) in the

+C59H19 cation This behavior stands in marked contrast to that of PAH radical cations [56] where it is the bands near 1600 cmminus1 that shift to higher frequencies with increasing molecular size while the bands near 1300 cmminus1 remain more or less static In both cases however the net effect is an increase in the spacing between these features

A final noteworthy aspect of this series of specshytra is the molecular size dependence of the aroshymatic CH stretching features in the 3100ndash3050 cmminus1 (323ndash328 microm) range First inspection of the data in Tables 2 and 3 shows that the position of the dominant CH stretching feature undergoes a distinct red shift with increasing molecular size decreasing from a maximum of 3106 cmminus1 (322

+ minus1microm) in the C13H9 cation down to 3078 cm(325 microm) for the C59H19

+ cation At the same time

Tab

le 2

+

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

C1

3H

9

+

and

C27H

13 ca

tion

sa+

C

19H

11

+

++

C

13H

9

C1

9H

11

C

27H

13

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

187

4 A

2 12

39

005

5 86

44

A

786

8 0

169

872

6 B

1

778

00

286

750

7 A

267

08

029

6 12

264

A

158

49

034

0 92

42

B1

803

70

296

855

3 A

2 73

70

032

6 13

511

A

10

877

0

233

1188

3

A1

331

50

122

1120

6

E

496

80

219

1364

8A

50

86

010

9 12

152

A

1

140

850

518

1206

7

E

333

2 0

147

1396

3

A

120

77

025

9 12

161

B

2

103

13

038

012

595

E

16

604

073

315

466

A

535

6 0

115

1267

4

A1

439

70

162

1361

1

E

170

86

075

5 15

668

A

61

16

013

1 13

496

B

2

148

440

546

1543

6

E

158

040

698

1594

9A

46

681

1

00

1354

3

A1

221

440

815

1581

8

E

226

42

100

1460

3

A1

556

4 0

205

1548

0

B2

331

7 0

122

1571

7

B2

154

66

056

9 15

805

A

1

271

72

100

15

977

A

1

232

25

085

5

3072

9

E

038

0

002

3061

7

A

054

0

001

3061

5

B2

190

000

730

768

E

0

500

002

3072

0A

0

77

000

2 30

616

A

1

019

000

131

057

E

1

72

000

830

755

A

1

62

000

3 30

661

B

2

045

0

002

3087

1

A

222

0

005

3067

2

A1

066

000

230

888

A

9

25

002

0 30

682

A

1

029

0

001

3101

3

A

738

0

016

3070

3

A1

065

0

002

3101

4

A

125

0

003

3073

3

B2

196

000

730

836

A

1

643

0

024

3085

1

B2

305

5 0

112

3085

6

A1

140

4 0

052

3099

9

A1

837

0

031

a T

he d

ata

for

020

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)



Fig 3 Representations of the B3LYP computed IR spectra of (a) C13H9 + (b) C19H+

11 (c) C27H13 + and (e) C59H19

+ (d) C47H17 + These

simulations were generated by assigning each calculated band a 20 cmminus1 FWHH gaussian profile of the appropriate intensity

the intrinsic intensity per CH group of these tion that is reflected in these numbers should be modes increases from 030 kmmolmiddotCH group for independent of that correction (the same correcshy

+C13H9 (26 kmmol-9 CH groups) to 153 km tion likely applies to all the numbers) Although +molmiddotCH group for C59H19 (290 kmmol-19 CH some increase in the intensity of the CH stretching

groups) Note that while the absolute intensities features is expected simply on the basis of the of these modes have not been corrected for the increasing number of aromatic CH groups in the expected computational overestimate the varia- molecule the observed magnitude of this effect is


Table 3 + +Calculated frequencies symmetries and intensities for the infrared active modes of the C47H17 and C59H19 cationsa

C47H17 + C59H19

+

0 (cmminus1) Symmetry Intensity (kmmol) Irel 0 (cmminus1) Symmetry Intensity (kmmol) Irel

8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204

11889 B2 14336 0250 9327 B1 12300 0347 11908 A1 14230 0249 11845 A1 18327 0517 11921 B2 12724 0222 11899 B2 10356 0292 12750 A1 6017 0105 11928 B2 9141 0258 13175 B2 17804 0311 11937 A1 11640 0328 13317 A1 17337 0303 12542 A1 4658 0131 13319 B2 25921 0453 12701 A1 8302 0234 14831 A1 5942 0104 12863 A1 5094 0144 15327 B2 17233 0301 13064 A1 7364 0208 15801 A1 23510 0411 13141 B2 29725 0838 15834 B2 10208 0178 13235 A1 19973 0563 15893 B2 57248 100 13310 A1 12128 0342

13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134

30573 A1 219 0004 30553 A1 098 0003 30573 B2 573 0010 30558 A1 302 0009 30597 A1 684 0012 30571 B2 343 0010 30601 A1 534 0009 30573 A1 1106 0031 30616 B2 098 0002 30582 B2 1734 0049 30626 A1 667 0012 30584 A1 023 0001 30630 B2 183 0003 30595 B2 1198 0034 30631 A1 093 0002 30600 A1 471 0013 30795 B2 690 0012 30607 B2 138 0004 30798 A1 2076 0036 30608 A1 137 0004 30800 B2 1977 0035 30629 B2 349 0010 30801 A1 3434 0060 30773 B2 604 0017 30821 B2 7129 0125 30776 A1 4576 0129 30823 A1 19 0033 30781 B2 9084 0256

30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167

a The data for 0 2000 cmminus1 have been truncated at the 10 level The complete data are tabulated at lthttpccfarcnasagov cbauschlclosed-shelldata)


greater than can be explained by this factor alone This trend is understandable in terms of the variashytions in the charge distribution within the cations and the localized nature of the CH stretching modes In general extensive electron delocalization within these species leads to an effective distribushytion of the positive charge throughout the molecule Consequently the charge density across the cation decreases in proportion to the area of the PAH structure The CH bonds (and their associated stretching modes) on the other hand are confined to the periphery of the structure and therefore increase in number only in proportion to the circumference of the molecule Thus as the size of the cation increases the increase in the number of CH groups cannot completely compensate for the reduced charge density and there is a steady deshycrease in the net oscillating charge associated with the CH stretching vibrations This implies that the character of the CH stretching vibrations in the cation should approach that of the neutral species with increasing molecular size This is exactly what is reflected in the spectrum in the form of a substantial relaxation of the dramatic suppression that these modes experience upon ionization [27353639ndash55]

It should be noted that this effect is not expected to appreciably impact the other classes of vibrashytions within the molecule The CC stretching modes for example typically involve the entire carbon skeleton of the molecule Thus the region associated with these modes scales as the area of the molecule neutralizing the effect of the charge dilution Furthermore despite the fact that the CH in-plane bends in principle depend on the number of CH groups these modes mix much more effecshytively with the CC stretches and again the effect of charge dilution is largely nullified Finally the intensities of the CH out-of-plane modes are similar between the cation and the neutral species and consequently little variation would be expected to accompany a transition from cation to quasi-neushytral character in the CH groups

32 Protonated PAH Cations (HPAH+)

In recent selected-ion flow tube experiments Le Page et al [23] and Snow et al [24] explored the

reactivity of ionized PAH structures with various simple atomic and molecular species of interstellar relevance Of particular interest they found that the radical cations of benzene naphthalene and pyrene reacted readily with atomic hydrogen but were relatively unreactive toward molecular hydroshygen Furthermore the HPAH+ species thus formed were found to be relatively unreactive toward additional H atoms Note that while reaction with a hydrogen atom is not strictly a protonation reaction (ie the addition of H+) the product in this case (HPAH+) is identical to that obtained from the addition of a proton to a neutral PAH molecule and thus is referred to here as a lsquoprotoshynatedrsquo PAH These results are consistent with the studies of Weilmunster et al described in Section 31 which also bear on this issue In those studies in contrast to the Codd PAH cations the PAH cations containing an even number of carbon atoms were found to exist predominantly in the protonated form Together these experiments indishycate that PAH radical cations readily add an H atom while closed-shell ion structures do not

These results are again understandable in terms of the electronic structures of the ions involved The radical cations with their highly reactive open-shell structures readily add a hydrogen atom (also having a single unpaired electron) to produce a cation with a more favorable closed-shell electron configuration The resultant protonated cation is far less reactive with H atoms because it already has the preferred closed-shell electronic structure and addition of another H atom would thus disrupt this favorable configuration The theoretical calculashytions carried out here are consistent with this interpretation For example consider the sequenshytial addition of H atoms to the naphthalene radical

degcation (C10H8

+ ) While calculations at the B3LYP 4-31G level reveal no barrier to the addition of an H atom to the naphthalene radical cation they do qualitatively indicate the presence of a barrier to the addition of a second hydrogen atom (forming

degC10H9

+ respectively) The experimenshy+ and C10H10

tal results indicate that this barrier must be of sufficient magnitude to measurably affect the reacshytivity of these species even at large thermal energies (ie in a flame) The calculations further indicate that while there is no barrier to the addition of a


Fig 4 An illustration of the reaction of the naphthalene radical cation (C10H8

+ deg ) with atomic hydrogen showing the two possible structural isomers of the hydronaphthalene cation product

third H atom there is once again a barrier to the addition of a fourth (forming C10H11

+ + and C10H12 deg

respectively) Again this is presumably a reflecshytion of the inherently greater reactivity of the open-shell electronic structure Thus in general once formed the closed-shell protonated PAH structure represents a bottleneck in the further hydrogenation of interstellar PAH cations modshyerating the degree of hydrogenation achieved by the interstellar PAH population and favoring those HnPAH+ species in which n is odd Nevershytheless given the great interstellar abundance of hydrogen the formation of hydrogenated PAH cations with some modest loss of aromatic characshyter is expected to be a natural consequence of the presence of PAH ions in the ISM

Consider again the reaction between the naphshy

thalene radical cation C10H8 + deg and an H atom

This reaction and the topology of its associated potential energy surface are illustrated in Figs 4 and 5 respectively The calculations indicate that

+ deg the C10H8 +H reaction is exothermic by 259 kJmol Thus in the absence of a reaction barrier the rapid reaction observed in the laboratory is understandable [232462] As already discussed the primary driving force for this reaction lies in the pairing of the parent radical cationrsquos odd electron It should be emphasized that these and the other protonated PAH cations discussed later do not arise merely from an electrostatic attracshytion between the H atom and the PAH cation but are in fact fully covalently bound ions Conseshyquently the adsdition reaction results in the forshymation of an aliphatic sp3-hybridized carbon atom that no longer participates in the delocalized n molecular orbital of the aromatic carbon skeleshyton reducing the aromaticity of the parent PAH Inspection of Fig 4 reveals that for naphthalene there are two chemically distinct products of H atom addition 1-and 2-hydronaphthalene cation with the former more stable by 134 kJmol The calculations indicate that there is no significant barrier to H-atom addition at either of the two possible sites and that the barrier to isomerizashytion between the two structures (71 kJmol) is small compared with the energy liberated in the H addition reaction (see Fig 5) Together these results imply that the two isomers would probably be formed in roughly the statistical ratio (11)

deg +H deg reaction All numerical values were obtained using DFT at theFig 5 A potential energy diagram for the C10H8

+

B3LYP4-31G level


Fig 6 The B3LYP computed IR spectra of the (b) 1-hydronaphthalene and (c) 2-hydronaphthalene cations (both C10H9 +) compared

with that of the naphthalene radical cation C10H8 + deg (a) Full-width at half-maximum (FWHM) 20 cmminus1

under interstellar conditions The sequential addishytion of a second hydrogen atom to form the 12-dihydronaphthalene cation is exothermic by another 178 kJmol but as already discussed faces a significant reaction barrier and proceeds at a rate some two orders of magnitude less at room temperature [2324]

Analogous calculations have been performed for the pyrene coronene and circumcoronene

deg deg deg + + +radical cations (C16H10 C24H12 and C54H18 respectively) with similar results As was the case for the naphthalene radical cation hydrogen atom addition to these cations is exothermic by 251 229 and 234 kJmol respectively Examples of the types of structures found in the resulting protonated PAH species are presented in Fig 2 The pyrene cation has three non-equivalent sites for H atom addition yielding three unique prodshy

ucts 1-hydropyrene 2-hydropyrene and 4-hyshydropyrene (C16H11

+) The most stable product is the 1-hydropyrene with the 2- and 4-hydropyreshynes lying 632 and 452 kJmol higher in energy respectively For the coronene cation all the posishytions for H atom addition are equivalent yielding only one chemically unique protonated cation

(C24H13structure +) For the circumcoronene cation there are again two possible non-equivashylent products 1- and 3-hydrocircumcoronene (C54H19

+) In this case the 3-hydrocircumcoronene is calculated to be the lower energy structure with the 1-hydrocircumcoronene lying 523 kJmol higher in energy

Representations of the calculated infrared specshytra of the 1- and 2-hydronaphthalene cations are shown in Fig 6 and the salient band positions and intensities are tabulated in Table 4 For refershy


ence the spectrum of the naphthalene cation is also shown in the figure The spectra of the 1- 2- and 4-hydropyrene cations are shown together with that of the parent pyrene cation in Fig 7 The prominent band positions and intensities for the protonated species are presented in Table 5 The spectrum of the 1-hydrocoronene cation is shown referenced to that of the parent coronene cation in Fig 8 and tabulated in Table 6 The spectra of the 1- and 3-hydrocircumcoronene cations are shown in Fig 9 and the positions of the prominent bands in these spectra are reported in Table 7 The spectra of neutral circumcoronene and the circumcoronene radical cation have not been reported previously and are also included in Fig 9 The salient bands of these species are summarized Table 8 In all cases spectral simulashytions were generated by assigning each calculated band a 20 cmminus1 FWHH gaussian profile of the appropriate intensity In addition in accordance with space limitations the data for 0 2000 cmminus1

have been truncated at the 10 level in the tables However the infrared active modes in the 3200ndash 2800 cmminus1 region are reported in their entirety Complete tabulations of the calculated data (inshycluding both IR active and inactive modes) have been posted on the Internet at lthttp ccfarcnasagov cbauschlclosed-shelldata)

Again as has been the case for PAH radical cations and the Codd cations already presented these spectra are all dominated by the aromatic CC stretching and CH in-plane wagging modes in the 1600ndash1200 cmminus1 region Inspection of Figs 6ndash9 shows that in general the spectra of the protonated PAHs considered here are substanshytially more complicated than those of the Codd

cations discussed in Section 31 Indeed comparishyson of the spectra of the protonated species with that of their parent radical cation indicates that H atom addition is accompanied by a marked inshycrease in spectral complexity through this region This is not surprising since H atom addition

Table 4 Calculated frequencies symmetries and intensities for the infrared active modes of the 1-hydronaphthalene and 2-hydronaphthalene

+acations C10H9

1-Hydronaphthalene 2-Hydronaphthalene


7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198

11871 A 2661 0118 12908 A 3243 0136 12715 A 2803 0125 13342 A 17950 0755 13362 A 9112 0406 13775 A 9448 0398 13512 A 8974 0399 14578 A 14120 0594 13618 A 3468 0154 14919 A 3105 0131 14164 A 5041 0224 15869 A 3602 0152 14530 A 10628 0473 16069 A 23763 100 15001 A 22469 100 15589 A 8012 0357 15999 A 7908 0352

28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)


+Fig 7 The B3LYP computed IR spectra of the pyrene radical cation C16H10

deg (a) is shown together with the spectra of (b) the

1-hydropyrene cation (c) the 2-hydropyrene cation and (d) the 4-hydropyrene cation (all C16H11 +) FWHM 20 cmminus1

reduces the molecular symmetry thereby increasshying the number of infrared active modes andor enhancing the IR activity of previously weak modes in the region In addition the characterisshytic deformation modes of the aliphatic -CH2 -group in the protonated species also contribute in this region although these modes mix effectively with the aromatic modes such that there is not a clear distinction between lsquoaromaticrsquo and lsquoaliphaticrsquo modes This increase in spectral complexity is also

accompanied by an appreciable redistribution of the total intensity amongst the modes in this region For example while the total intensities of both the 1-hydro- and 3-hydrocircumcoronene cations (both 3500 kmmol) are similar to that of the parent circumcoronene radical cation ( 3700 kmmol) the intensity of the strongest indishyvidual band in the spectrum of the 1- and 3-hydrocircumcoronene cations (15760 cmminus1 1965 kmmol and 15779 cmminus13276 kmmol


respectively Table 7) are three- to fivefold weaker than the strongest band in the spectrum of the circumcoronene radical cation (15712 cmminus1 9581 kmmol Table 8) Clearly a significant fraction of the intensity that is concentrated in the 15712 cmminus1 mode of the circumcoronene radical cation has been redistributed over the manifold of new infrared active modes in the hydrocircumshycoroenene cations Similar behavior is also found between the 1-hydrocoronene cation and the coroshynene radical cation

For those species that have more than one chemically unique site the spectral structure in the 1600ndash1200 cmminus1 region is quite sensitive to the position of the added H atom This effect is greatest for the smaller hydronaphthalene and hydropyrene cations where the added H atom has a relatively greater impact of on the vibrational modes Nevertheless the differences between the spectra of the two hydrocircumcoronene cations are not inconsequential Furthermore it should be emphasized that this effect is not simply due to differences in the symmetry of the species in quesshytion For example the 1- and 2-hydronaphthalene cations share the same Cs symmetry yet their

spectra (Fig 6bc) are widely disparate through the 1600ndash1200 cmminus1 region The same is also true for the 1- and 4-hydropyrene cations whose specshytra are shown in Fig 7bd

Another aspect of the infrared spectra of protoshynated PAHs that warrants discussion is the CH stretching region between 3200 and 2800 cmminus1 Comparison of this region of the spectra in Figs 6ndash9 shows that there is a marked increase in the relative strength in the aromatic CH stretching feature near 3100 cmminus1 (323 microm) compared with the aliphatic CH stretching feature near 2850 cmminus1 (351 microm) with increasing molecular size In the spectra of the 1- and 2-hydronaphthalene cations the CH stretching region is dominated by the aliphatic feature of the single -CH2 - group near 2850 cmminus1 (35 microm) while the aromatic CH stretching feature near 3050 cmminus1 (328 microm) is so weak as to be all but invisible However the relative intensity of the aromatic feature increases relative to the aliphatic feature in the hydropyreshynes and actually dominates the aliphatic feature in the spectra of the hydrocoronene and hydrocirshycumcoronene cations Indeed such a trend is exshypected simply on the basis of the steady increase

Fig 8 The B3LYP computed IR spectra of the 1-hydrocoronene cation C24H13deg + (b) is shown compared with that of the coronene

+cation C24H12 (a) FWHM 20 cmminus1 The coronene radical cation spectrum has been scaled by 05 to facilitate its presentation on the same scale as the hydrocoronene cation


Table 6 Calculated frequencies symmetries and intensities for the

+ainfrared active modes of the 1-hydrocoronene cation C24H13

1-Hydrocoronene

0 (cmminus1) Symmetry Intensity (kmmol) Irel

5483 A 2468 0155 8801 A 15927 100

10010 A 2258 0142 12095 A 2112 0133 12183 A 7047 0442 12209 A 2958 0186 13357 A 13744 0863 13495 A 6775 0425 13561 A 11210 0704 13677 A 4863 0305 13727 A 8928 0561 13884 A 2150 0135 14044 A 1873 0118 15038 A 13925 0874 15384 A 6941 0436 15668 A 13045 0819 15799 A 6232 0391 15892 A 12954 0813 15963 A 1819 0114 16066 A 10772 0676

28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

a The data for 0 2000 cmminus1 have been truncated at the 10 level The complete data are tabulated at lthttp ccfarcnasagov cbauschlclosed-shelldata)

in the ratio of aromatic CH groups to aliphatic CH groups (hydronaphthalene 72 hydropyrene 92 hydrocoronene 112 hydrocircumcoronene 172 see Fig 2) However the data in Tables 4ndash7 shows that the magnitude of the observed spectral change far exceeds that expected simply on the basis of the increase in the relative number of

aromatic CH groups In going from hydronaphshythalene to hydrocircumcoronene the ratio of the number of aromatic CH groups to the number of aliphatic CH groups increases by a factor of 24 (from 35 to 85) Over this same range the calcushylated ratio of the total aromatic CH stretching intensity ((3110ndash3040 cmminus1)) to the aliphatic CH stretching intensity ((2900ndash2840 cmminus1)) inshycreases from an average of 007 for the hyshydronaphthalenes to 110 for the hydrocircumcoronenes an increase of nearly 1600-fold This dramatic shift arises through a combination of two concurrent effects (1) a reshyduction in the total intrinsic aliphatic CH stretchshying intensity by a factor of about 20 (hydronaphthalenes Aaliphatic 44 kmmol hyshydrocircumcoronenes Aaliphatic 23 kmmol) coushypled with (2) an increase in the total intrinsic aromatic CH stretching intensity by a factor of nearly 100 (hydronaphthalenes Aaromatic 3 km mol hydrocircumcoronenes Aaromatic 250 km mol) The enhancement in the intensity of the aromatic CH stretching feature is very similar to that observed in the Codd PAH cations discussed in Section 31 and presumably shares the same origin The suppression of the aliphatic CH stretching intensity is on the other hand more unexpected and not clearly understood at this point

Finally it should be noted that the spectrum of neutral circumcoronene has also been calculated as part of this work and is presented along with the cation spectra in Fig 9 The spectrum of neutral circumcoronene has not been published previously and it is included here for both its intrinsic merit and as a benchmark for comparishyson with the various related cationic species As is typical of neutral PAHs the spectrum is domishynated by the strong aromatic CH stretching feashyture near 3060 cmminus1 and the aromatic CH out-of-plane bending mode near 900 cmminus1 Both of these features are substantially more intense than any of the CC stretching and CH in-plane bending modes in the 1600ndash1100 cmminus1 region Thus the significantly increased CH ratio of the larger PAH molecule (circumcoronene CH=3 coronene CH=2 naphthalene CH=125) is


not in and of itself sufficient to bring the ratios between the bands in these two regions into agreeshyment with their typical interstellar values This is consistent with the conclusion that the pattern of band intensities observed in the interstellar specshytrum is indicative of a dominant contribution from lsquoionizedrsquo PAHs

4 Astrophysical implications

Based on the data already presented the presshyence of closed-shell PAH cations in the interstellar infrared emission zones will impact the spectrum in several ways These are now considered accordshying to spectral region

Fig 9 The B3LYP computed IR spectra of (a) neutral circumcoronene (C54H18) and (b) the circumcoronene radical cation (C54H18

+) FWHM +deg ) are compared with those of (c) the 1-hydrocircumcoronene and (d) the 3-hydrocircumcoronene cations (C54H19

20 cmminus1 The circumcoronene radical cation spectrum has been scaled by 05 to facilitate its presentation on the same scale as the hydrocircumcoronene cations


Table 7 Calculated frequencies symmetries and intensities for the infrared active modes of the 1-hydrocircumcoronene and 3-hydrocircumshy

+ acoronene cations C54H19

1-Hydrocircumcoronene 3-Hydrocircumcoronene


7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192

10419 A 3125 0140 9281 B1 8662 0231 11703 A 2305 0103 11768 B2 12453 0332 11737 A 5661 0253 11929 A1 11037 0294 11841 A 7024 0314 11960 B2 4818 0129 11925 A 12698 0568 12735 A1 4081 0109 12500 A 2368 0106 12764 A1 8298 0221 12577 A 5563 0249 12802 A1 5854 0156 12737 A 6892 0308 13034 B2 12619 0337 12907 A 2975 0133 13150 B2 37485 100 13051 A 2812 0126 13298 A1 18478 0493 13075 A 8581 0384 13459 B2 4132 0110 13170 A 20960 0938 13528 A1 6997 0187 13203 A 9365 0419 13889 A1 4331 0116 13345 A 10722 0480 15113 A1 4599 0123 13475 A 2535 0113 15409 B2 20238 0540 13541 A 4250 0190 15526 A1 5230 0140 13759 A 2259 0101 15562 B2 4417 0118 13878 A 4918 0220 15720 B2 9362 0250 13937 A 5079 0227 15779 A1 32763 0874 13959 A 2264 0101 15824 B2 11268 0301 13990 A 2244 0100 15874 A1 9966 0266 14446 A 2333 0104 15965 A1 11393 0304 14561 A 4047 0181 16068 B2 6394 0171 14656 A 7815 0350 14742 A 2303 0103 14858 A 3489 0156 15048 A 4840 0217 15129 A 14530 0650 15279 A 2260 0101 15442 A 4645 0208 15507 A 22351 100 15665 A 5187 0232 15760 A 19649 0879 15839 A 3453 0155 15870 A 4568 0204 15900 A 19243 0861 15932 A 2648 0118 15982 A 3303 0148 16069 A 5435 0243

28541 A 291 0013 28763 A1 030 0001 28664 A 027 0001 28970 B1 101 0003 30482 A 1474 0066 30567 A1 455 0012 30546 A 574 0026 30576 B2 198 0005 30559 A 403 0018 30577 A1 555 0015 30567 A 1375 0062 30587 B2 1424 0038 30580 A 749 0033 30589 A1 124 0003 30595 A 279 0013 30599 B2 195 0005


Table 7 (Continued)



30603 A 391 0018 30601 A1 991 0026 30607 A 530 0024 30610 B2 434 0012 30617 A 456 0020 30613 A1 138 0004 30631 A 069 0003 30620 B2 402 0011 30777 A 1493 0067 30772 B2 838 0022 30781 A 4782 0214 30773 A1 3756 0100 30783 A 5300 0237 30789 B2 025 0001 30790 A 3763 0168 30790 A1 2430 0065 30808 A 3337 0149 30793 B2 9688 0258

30795 A1 2981 0080


41 The 1600 cmminus1 (62 microm) region cmminus1 close to the prominent 62ndash63 microm intershystellar feature are strongly enhanced in the

Consistent with the behavior of PAH radical closed-shell cations compared with the neutral cations reported previously [2739ndash55] the aro- species In fact in the spectra of the closed-shell matic CC stretching modes that fall near 1600 species this is consistently the strongest band in

Table 8 Calculated frequencies symmetries and intensities for for the infrared active modes of neutral circumcoronene C54H18 and the

+deg circumcoronene radical cation C54H18 a

C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112



the spectrum Of further interest these features consistently fall at higher frequencies in the closed PAH structures than in the corresponding open-shell species For example for circumcoronene (Fig 9 and Table 8) the most prominent band of the closed-shell neutral species falls at 1608 cmminus1

(6219 microm) while that of the radical cation falls at 1572 cmminus1 (6361 microm) Coronene also exhibits such a trend (neutral 1602 cmminus1 6242 microm radical cation 1554 cmminus1 6435 microm) [274044] Although this general trend holds for both the Codd and protonated PAH cations considered here the corresponding vibration falls between 1590 and 1580 cmminus1 (629 and 633 microm) still somewhat red-shifted from the band position in the parent neutral While this falls in the red wing of the canonical 1610 cmminus1 (62 microm) interstellar feature it is close to the newly discovered 1590 cmminus1 (629 microm) emission component recently reshysolved in the high-resolution spectra of a number of objects by the ISO satellite [65] Overall given the prominence of the features in this region in the spectra of the closed-shell PAH cations if a significant population of such species is indeed present in the interstellar medium they would certainly be expected to dominate the emission at this position

42 The 1500ndash1100 cmminus1 (67ndash9 microm) region

In the interstellar spectrum this region is domishynated by the strong broad 77 microm emission envelshyope and its prominent shoulder near 86 microm Careful observations [66] have shown that this band is actually a composite of a number of overlapping features dominated by two composhynents falling near 76 and 78 microm This spectral region is diagnostic of aromatic CC stretching and CH in-plane bending motions in PAHs Previous studies of PAH radical cations have established that these modes are strongly enhanced by ionizashytion [2739ndash55] and not surprisingly the results already presented confirm that this effect also holds for closed-shell cations Unlike the consisshytent behavior of the bands in the 1600 cmminus1

region already discussed the direction of the ionshyization shift experienced by the PAH bands in this range is less predictable For example in the

circumcoronene radical cation the most promishynent band in this region falls at 1256 cmminus1 (7962 microm) red-shifted by 30 cmminus1 from its position in neutral circumcoronene (1286 cmminus1 7776 microm see Table 8) Compare this with coronene where the most prominent band of the radical cation in this region is blue-shifted by 38 cmminus1 (cation 1350 cmminus1 7407 microm neutral 1312 cmminus1 7622 microm) [4044] Nonetheless there is an underlying consistency with the interstellar emission specshytrum In each case the dominant bands tend to fall within the envelope of the interstellar 76 microm (1315 cmminus1) component that dominates the 77 microm emission envelope in HII regions and reflecshytion nebula [66] Indeed inspection of the tables show that in general for both the Codd-PAH and HPAH+ cations considered here the dominant features in this region typically fall between 1350 and 1314 cmminus1 (741 and 761 microm) most consisshytent with the position of the interstellar 76 microm component The detailed origin of the strong 78 microm component therefore remains unclear

In addition to the aromatic modes that fall in this region the HPAH+ species have an addishytional unique contribution in this region of the spectrum The aliphatic CH2 deformation modes of these species are expected to fall in the midshy1400 cmminus1 ( 7 microm) range [67] Indeed the greater spectral complexity that is observed throughout this region in the protonated PAH cations is no doubt partially attributable to the contributions of the aliphatic modes As with the aromatic modes in this region the aliphatic deforshymation modes are enhanced by ionization and are actually more intense than the strong aliphatic CH stretching bands (see Tables 4ndash7) that domishynate the spectra of neutral hydrogenated PAHs However as already noted these modes mix with the aromatic CC stretching and CH in-plane bending modes to such a degree that it is not possible to distinguish between lsquoaliphaticrsquo and lsquoaromaticrsquo modes in this region

A final consistent aspect of the spectra of these species with the interstellar emission spectra is the presence of a prominent band in the 1214ndash1140 cmminus1 (824ndash877 microm) range that corresponds most closely to the interstellar 86 microm (1165 cmminus1) component of the interstellar emission


spectrum For the closed-shell cations considered here the intensities of these bands relative to the dominant 1300 cmminus1 bands also echos that of the interstellar emission


The other region in which closed-shell cations potentially impact the interstellar emission specshytrum is in the CH stretching region between 3200 and 2800 cmminus1 (31 and 36 microm) While all of the species considered here would certainly contribute to the well-known 33 microm emission band (aromatic CH stretching modes) of particular interest is the contribution of the HPAH+ species to the variable emission complex that falls on the red wing of the aromatic feature between 34 and 35 microm This range is diagnostic of aliphatic CH stretching modes and as expected inspection of Figs 6ndash9 shows that protonation is accompanied by the appearance of a feature that is attributable to these modes In each of the HPAH+ considered here the aliphatic CH stretching region displays a pair of bands that are typically separated by 5ndash20 cmminus1

and centered near 2860 cmminus1 (35 microm) The distrishybution of intensity between these bands is variable but in all but one case it is the lower frequency band that dominates the pair (see Tables 4ndash7)

The dominance of the 33 microm aromatic CH stretching feature over the aliphatic CH stretching feature in the typical interstellar emission specshytrum despite the markedly greater intrinsic strength of the latter modes indicates that the interstellar emitting population is predominantly aromatic with only a modest degree of aliphatic character Given the great abundance of hydrogen in the interstellar medium and the inherent favor-ability of the closed-shell HPAH+ species it is tempting to posit that simple protonation across the PAH cation population might contribute suffishycient aliphatic character to account for the intershystellar 34ndash35 microm emission This idea is however not borne out by the data presented in this article As already mentioned the protonated species disshycussed in Section 32 consistently display only a single noteworthy feature near 2860 cmminus1 (350 microm) Thus while such species likely contribute to the interstellar emission in this region they cannot

in-and-of-themselves explain the spectral complexshyity that is observed in that spectrum Instead that complexity implies a modest subpopulation of more highly hydrogenated species (Hn PAHs and or their associated ions) [22]


Finally it is interesting to note that although there are twice as many doubly-adjacent CH groups as non-adjacent CH groups in C59H19

+ the circumcoronene radical cation and the hydroshygenated circumcoronene cations the 900ndash700 cmminus1 (11ndash14 microm) CH out-of-plane bending region is dominated by only one band That band consisshytently falls near 930ndash920 cmminus1 (1075ndash1087 microm) close to the position of non-adjacent CH groups on open shell PAH cations that have previously been proposed as a tracer of the ionized interstellar PAH component [68]

5 Conclusions

Prompted by recent experimental studies that indicate such species may play an important role in the interstellar medium we have carried out B3LYP431G calculations to determine the harshymonic frequencies and intensities for a variety of closed-shell PAH cations The set of species conshysidered extends over a wide range of molecular sizes and includes both Codd PAH cations mdash fully benzenoid species composed of an odd number of carbon atoms mdash and protonated PAHs

Overall the spectra of closed-shell PAH cations are consistent with previously reported theoretical and experimental spectra of PAH radical cations and with the global pattern of band positions and intensities in the interstellar emission spectrum The spectra do however display some distinctive features that distinguish them from the PAH speshycies considered previously The Codd PAH cation spectra for example display a notably weaker dependence on molecular size than is typical of either the protonated PAHs considered here or of the PAH radical cations that can be found the literature Furthermore the spectra of these species are dominated by several strong features in the


1600ndash1100 cmminus1 region the strongest of which is consistently the highest frequency band falling near 1600 cmminus1 Thus if these species are indeed common in the interstellar medium they would be expected to make a disproportionate contribushytion to the 62 microm infrared emission band

The protonated PAHs tend to display a greater degree of spectral complexity compared with their parent radical cation This is due both to a lowershying of the symmetry of the cation as well as to the contributions of the characteristic aliphatic modes of the associated CH2 group

Finally for both classes of closed-shell PAH cations increasing molecular size is found to be accompanied by a strong increase in the intensity of the aromatic CH stretching features Analysis of the Mulliken populations indicates that this is a consequence of the decrease in charge density within the molecule as the positive charge is smeared over a larger and larger molecular skeleshyton Consequently the character of these modes which are in general strongly suppressed in PAH cations gradually approaches the dominant charshyacter of the analogous modes in neutral PAHs In contrast the aliphatic CH stretching modes of the protonated PAHs are increasingly suppressed with increasing molecular size The origin of this effect is not yet clearly understood and will reshyquire further study

Acknowledgements

Two of the authors (DMH LJA) would like to thank the editors of this issue for conshytributing their time and effort to organize this special journal edition We also gratefully acshyknowledge support under NASArsquos Long Term Space Astrophysics Program (Grant 399-20-01)

References

[1] FC Gillett WJ Forrest KM Merrill Astrophys J 183 (1973) 87

[2] RW Russell BT Soifer SP Willner Astrophys J 217 (1977) L149

[3] DK Aitken in CG Wynn-Williams DP Cruikshank (Eds) Infrared Astronomy Reidel Dordrecht 1981 p 207

[4] SP Willner in MF Kessler JP Phillips (Eds) Galacshytic and Extragalactic Infrared Spectroscopy Reidel Dorshydrecht 1984 p 37

[5] MM Phillips DK Aitken PF Roche Mon Not R Astron Soc 207 (1984) 25

[6] TR Geballe AGGM Tielens S Kwok BJ Hrivnak Astrophys J 387 (1992) L89

[7] PR Roelfsema et al Astron Astrophys 315 (1996) L289

[8] RJ Laureijs et al Astron Astrophys 315 (1996) L313 [9] T Onaka I Yamamura T Tanabe TL Roellig L

Yuen Pub Astron Soc Jpn 48 (1996) L59 [10] K Matilla et al Astron Astrophys 315 (1996) L353 [11] GC Sloan JD Bregman TR Geballe LJ Allamanshy

dola CE Woodward Astrophys J 474 (1997) 735 [12] A Leger JL Puget Astron Astrophys 137 (1984) L5 [13] LJ Allamandola AGGM Tielens JR Barker Astroshy

phys J 290 (1985) L25 [14] K Sellgren Astrophys J 277 (1984) 627 [15] M Cohen AGGM Tielens LJ Allamandola Astroshy

phys J 299 (1985) L93 [16] M Cohen LJ Allamandola AGGM Tielens J Bregshy

man JP Simpson FC Witteborn D Wooden D Rank Astrophys J 302 (1986) 737

[17] M Cohen AGGM Tielens J Bregman FC Witshyteborn D Rank LJ Allamandola D Wooden M DeMuizon Astrophys J 341 (1989) 246

[18] W Schutte AGGM Tielens LJ Allamandola Astroshyphys J 415 (1993) 397

[19] ELO Bakes AGGM Tielens Astrophys J 427 (1994) 822

[20] F Salama ELO Bakes LJ Allamandola AGGM Tielens Astrophys J 458 (1996) 621

[21] HW Jochims E Ruhl H Baumgartel S Tobita S Leach Astrophys J 420 (1994) 307

[22] MP Bernstein SA Sandford LJ Allamandola Astroshyphys J 472 (1996) L127

[23] V LePage Y Keheyan V Bierbaum T Snow J Am Chem Soc 119 (1997) 8373

[24] T Snow V Le Page Y Keheyan V Bierbaum Nature 391 (1997) 259


[26] LJ Allamandola AGGM Tielens JR Barker Astroshyphys J Suppl Ser 71 (1989) 733

[27] DJ DeFrees MD Miller in LJ Allamandola AGGM Tielens (Eds) Interstellar Dust Contributed Papers NASA CP 3036 1989 p 173

[28] JD Brenner JR Barker Astrophys J 388 (1992) L39 [29] F Pauzat D Talbi MD Miller DJ DeFrees Y

Ellinger J Phys Chem 96 (1992) 7882 [30] DJ DeFrees MD Miller D Talbi F Pauzat YJ

Ellinger Astrophys J 408 (1993) 530 [31] J Szczepanski M Vala Nature 363 (1993) 699 [32] F Salama C Joblin LJ Allamandola J Chem Phys

101 (1994) 10252


[33] D Hudgins SA Sandford LJ Allamandola J Phys Chem 98 (1994) 4243

[34] S Schlemmer DJ Cook JA Harrison B Wurfel W Chapman RJ Saykally Science 265 (1994) 1686

[35] SR Langhoff J Phys Chem 100 (1996) 2819 [36] CW Bauschlicher Jr SR Langhoff Spectrochim Acta

A 53 (1997) 1225 [37] DJ Cook RJ Saykally Astrophys J 493 (1998) 793 [38] H Piest G von Helden G Meijer Astrophys J 520

(1999) L75 [39] DM Hudgins SA Sandford LJ Allamandola J Phys

Chem 98 (1994) 4243 [40] DM Hudgins LJ Allamandola J Phys Chem 99

(1995) 3033 [41] DM Hudgins LJ Allamandola J Phys Chem 99

(1995) 8978 [42] DM Hudgins LJ Allamandola J Phys Chem A 101

(1997) 3472 [43] DM Hudgins SA Sandford J Phys Chem A 102



(1998) 353 [46] DM Hudgins LJ Allamandola CW Bauschlicher Jr

J Fetzer J Phys Chem A 104 (2000) 3655 [47] J Szczepanski M Vala D Talbi O Parisel Y Ellinger

J Chem Phys 98 (1993) 4494 [48] J Szczepanski C Chapo M Vala Chem Phys Lett 205

(1993) 434 [49] J Szczepanski M Vala Astrophys J 414 (1993) 179 [50] M Vala J Szczepanski F Pauzat O Parisel D Talbi

Y Ellinger J Phys Chem 98 (1994) 9187 [51] J Szczepanski C Wehlberg M Vala Chem Phys Lett

232 (1995) 221 [52] J Szczepanski J Drawdy C Wehlburg M Vala Chem

Phys Lett 245 (1995) 539 [53] CW Bauschlicher SR Langhoff SA Sandford DM

Hudgins J Phys Chem A 101 (1997) 2414 [54] SR Langhoff CW Bauschlicher Jr DM Hudgins

SA Sandford LJ Allamandola J Phys Chem A 102 (1998) 1632

[55] CW Bauschlicher Jr DM Hudgins LJ Allamandola Theor Chem Acc 103 (1999) 154

[56] DM Hudgins LJ Allamandola Astrophys J 513 (1999) L69

[57] RE Stratmann GE Scuseria MJ Frisch Chem Phys Lett 257 (1996) 213

[58] PJ Stephens FJ Devlin CF Chabalowski MJ Frisch J Phys Chem 98 (1994) 11623

[59] AD Becke J Chem Phys 98 (1993) 5648 [60] MJ Frisch JA Pople JS Binkley J Chem Phys 80

(1984) 3265 [61] MJ Frisch GW Trucks HB Schlegel GE Scuseria

MA Robb JR Cheeseman VG Zakrzewski JA Montgomery Jr RE Stratmann JC Burant S Dapshyprich JM Millam AD Daniels KN Kudin MC Strain O Farkas J Tomasi V Barone M Cossi R Cammi B Mennucci C Pomelli C Adamo S Clifford J Ochterski GA Petersson PY Ayala Q Cui K Morokuma DK Malick AD Rabuck K Raghavachari JB Foresman J Cioslowski JV Ortiz AG Baboul BB Stefanov G Liu A Liashenko P Piskorz I Komaromi R Gomperts RL Martin DJ Fox T Keith MA Al-Laham CY Peng A Nanayakshykara C Gonzalez M Challacombe PMW Gill B Johnson W Chen MW Wong JL Andres C Gonzashylez M Head-Gordon ES Replogle JA Pople GAUSshy

SIAN 98 Revision A7 Gaussian Inc Pittsburgh PA 1998

[62] P Weilmunster A Keller K-H Homann Comb Flame 116 (1998) 62

[63] M Franklach ED Feigelson Astrophys J 341 (1989) 372

[64] I Cherchneff JR Barker AGGM Tielens Astrophys J 401 (1992) 269

[65] E Peeters S Hony C Van Kerckhoven AGGM Tielens LJ Allamandola DM Hudgins Astron Astroshyphys (in preparation)

[66] JD Bregman in LJ Allamandola AGGM Tielens (Eds) Interstellar Dust Kluwer Dordrecht 1989 p 109

[67] LJ Bellamy The Infrared Spectra of Complex Organic Molecules Wiley New York 1958



from late-type carbon-rich stars Subsequent pioshyneering observations showed this was just one part of a now well-known spectrum of features emitted from a wide variety of very different astronomical objects (for example see Refs [2ndash 5]) This spectrum is characterized by dominant features near 3030 1610 1280 1150 and 890 cmminus1 (33 62 77 86 and 112 microm) as well as a number of minor bands and underlying continua The brightest emission is observed from dusty regions exposed to intense ultraviolet radiation Surprisingly the age and history of the material seem to be relatively unimportant Similar emisshysion spectra are observed from objects that span the lifecycle of matter in the interstellar medium (ISM) mdash from objects only a few thousand years in age (late carbon star ejecta and planetary nebushylae shells) to those millions of years in age (H II regions reflection nebulae and the diffuse ISM) [6ndash11] Understanding the source of this unexshypected yet widespread phenomenon has become an important problem in astrophysics

The idea now gaining acceptance that stochasshytically heated gas-phase polycyclic aromatic hyshydrocarbons (PAHs) are the band carriers was first put forth over a decade ago [1213] This attribushytion is based on several pieces of lsquocircumstantialrsquo evidence that point to these species First the interstellar emission is non-thermal in nature The banded (rather than continuous) nature of the spectrum the typically large featurecontinuum ratio and the close association with ultraviolet radiation all indicate that the emission is due to infrared fluorescence from gas-phase molecules excited by the absorption of single ultraviolet and visible photons rather than thermal emission from a solid material [14] Second careful observations of planetary nebulae have established that the fraction of the total infrared energy that is emitshyted through these features is closely correlated with the amount of available carbon [15] indicatshying that the gas-phase molecular carriers are carshybon rich Third since the carbon-rich carriers must survive under remarkably harsh conditions they must also be extremely stable Finally alshythough there are variations among the relative band intensities the features are correlated [1617] implying that a single class of chemical

species is responsible Of course any proposed carrier must have an IR spectrum consistent with the positions and intensities of these bands As a molecular class PAHs readily accommodate all these constraints

Originally the principal reason for the assignshyment to PAHs was the suggestive but far from perfect resemblance of the interstellar lsquoemissionrsquo spectra to the then-available infrared lsquoabsorptionrsquo spectra primarily those of PAH clusters dispersed in KBr pellets or soot particles Unfortunately although rich this spectral database was not adeshyquate to squarely address the astronomical quesshytions since such laboratory conditions strongly perturb the spectrum and are far from those in the interstellar emission zones Moreover if PAHs are indeed present in the highly energetic emission zones they are likely to be ionized [13] and until recently there was no spectroscopic data available on the infrared properties of PAH ions Thus the spectral database initially available was not suffishycient for a critical test of the PAH hypothesis nor if the hypothesis held up to close scrutiny was it up to the task of exploiting PAHs as probes of the emission zones To truly test the PAH hypothesis special techniques for studying individual PAHs and PAH ions under astrophysically relevant conshyditions were required

Motivated in no small part by their emerging interstellar importance the past decade has seen a renaissance in experimental and theoretical methshyods aimed at determining the physical [18ndash20] chemical [21ndash25] and spectroscopic [26ndash38] imshypact of PAHs in the interstellar medium Particushylarly relevant to the problem of the interstellar infrared emission these efforts have produced a large and growing database of the infrared specshytroscopic properties of PAHs and PAH ions that are directly relevant to the astrophysical problem [39ndash55] These studies have included PAHs in neutral cationic and anionic forms and encomshypass species ranging in size from ten to 32 carbon atoms Nevertheless to date both experimental and theoretical studies in this area have focused primarily on the determination of the spectroshyscopic properties of the sorts of conventional structures that characterize terrestrially stable commercially available PAHs Such PAHs in their














Species 6-31+G4-31G 6-31++G4-31G



C10H8 087 083 071 112 +C10H8 083 092 198 095 +aC10H9 068 095 094 098 108 096

C16H10 086 085 071 106 C16H10

+ 056 092 027 095 +bC16H11 061 093 094 039 113 097






3 Results


















Tab

le 2

+

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

C1

3H

9

+

and

C27H

13 ca

tion

sa+

C

19H

11

+

++

C

13H

9

C1

9H

11

C

27H

13

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

187

4 A

2 12

39

005

5 86

44

A

786

8 0

169

872

6 B

1

778

00

286

750

7 A

267

08

029

6 12

264

A

158

49

034

0 92

42

B1

803

70

296

855

3 A

2 73

70

032

6 13

511

A

10

877

0

233

1188

3

A1

331

50

122

1120

6

E

496

80

219

1364

8A

50

86

010

9 12

152

A

1

140

850

518

1206

7

E

333

2 0

147

1396

3

A

120

77

025

9 12

161

B

2

103

13

038

012

595

E

16

604

073

315

466

A

535

6 0

115

1267

4

A1

439

70

162

1361

1

E

170

86

075

5 15

668

A

61

16

013

1 13

496

B

2

148

440

546

1543

6

E

158

040

698

1594

9A

46

681

1

00

1354

3

A1

221

440

815

1581

8

E

226

42

100

1460

3

A1

556

4 0

205

1548

0

B2

331

7 0

122

1571

7

B2

154

66

056

9 15

805

A

1

271

72

100

15

977

A

1

232

25

085

5

3072

9

E

038

0

002

3061

7

A

054

0

001

3061

5

B2

190

000

730

768

E

0

500

002

3072

0A

0

77

000

2 30

616

A

1

019

000

131

057

E

1

72

000

830

755

A

1

62

000

3 30

661

B

2

045

0

002

3087

1

A

222

0

005

3067

2

A1

066

000

230

888

A

9

25

002

0 30

682

A

1

029

0

001

3101

3

A

738

0

016

3070

3

A1

065

0

002

3101

4

A

125

0

003

3073

3

B2

196

000

730

836

A

1

643

0

024

3085

1

B2

305

5 0

112

3085

6

A1

140

4 0

052

3099

9

A1

837

0

031

a T

he d

ata

for

020

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)




11 (c) C27H13 + and (e) C59H19








C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252


















































Species 6-31+G4-31G 6-31++G4-31G



C10H8 087 083 071 112 +C10H8 083 092 198 095 +aC10H9 068 095 094 098 108 096

C16H10 086 085 071 106 C16H10

+ 056 092 027 095 +bC16H11 061 093 094 039 113 097






3 Results


















Tab

le 2

+

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

C1

3H

9

+

and

C27H

13 ca

tion

sa+

C

19H

11

+

++

C

13H

9

C1

9H

11

C

27H

13

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

187

4 A

2 12

39

005

5 86

44

A

786

8 0

169

872

6 B

1

778

00

286

750

7 A

267

08

029

6 12

264

A

158

49

034

0 92

42

B1

803

70

296

855

3 A

2 73

70

032

6 13

511

A

10

877

0

233

1188

3

A1

331

50

122

1120

6

E

496

80

219

1364

8A

50

86

010

9 12

152

A

1

140

850

518

1206

7

E

333

2 0

147

1396

3

A

120

77

025

9 12

161

B

2

103

13

038

012

595

E

16

604

073

315

466

A

535

6 0

115

1267

4

A1

439

70

162

1361

1

E

170

86

075

5 15

668

A

61

16

013

1 13

496

B

2

148

440

546

1543

6

E

158

040

698

1594

9A

46

681

1

00

1354

3

A1

221

440

815

1581

8

E

226

42

100

1460

3

A1

556

4 0

205

1548

0

B2

331

7 0

122

1571

7

B2

154

66

056

9 15

805

A

1

271

72

100

15

977

A

1

232

25

085

5

3072

9

E

038

0

002

3061

7

A

054

0

001

3061

5

B2

190

000

730

768

E

0

500

002

3072

0A

0

77

000

2 30

616

A

1

019

000

131

057

E

1

72

000

830

755

A

1

62

000

3 30

661

B

2

045

0

002

3087

1

A

222

0

005

3067

2

A1

066

000

230

888

A

9

25

002

0 30

682

A

1

029

0

001

3101

3

A

738

0

016

3070

3

A1

065

0

002

3101

4

A

125

0

003

3073

3

B2

196

000

730

836

A

1

643

0

024

3085

1

B2

305

5 0

112

3085

6

A1

140

4 0

052

3099

9

A1

837

0

031

a T

he d

ata

for

020

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)




11 (c) C27H13 + and (e) C59H19








C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252









































3 Results


















Tab

le 2

+

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

C1

3H

9

+

and

C27H

13 ca

tion

sa+

C

19H

11

+

++

C

13H

9

C1

9H

11

C

27H

13

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

187

4 A

2 12

39

005

5 86

44

A

786

8 0

169

872

6 B

1

778

00

286

750

7 A

267

08

029

6 12

264

A

158

49

034

0 92

42

B1

803

70

296

855

3 A

2 73

70

032

6 13

511

A

10

877

0

233

1188

3

A1

331

50

122

1120

6

E

496

80

219

1364

8A

50

86

010

9 12

152

A

1

140

850

518

1206

7

E

333

2 0

147

1396

3

A

120

77

025

9 12

161

B

2

103

13

038

012

595

E

16

604

073

315

466

A

535

6 0

115

1267

4

A1

439

70

162

1361

1

E

170

86

075

5 15

668

A

61

16

013

1 13

496

B

2

148

440

546

1543

6

E

158

040

698

1594

9A

46

681

1

00

1354

3

A1

221

440

815

1581

8

E

226

42

100

1460

3

A1

556

4 0

205

1548

0

B2

331

7 0

122

1571

7

B2

154

66

056

9 15

805

A

1

271

72

100

15

977

A

1

232

25

085

5

3072

9

E

038

0

002

3061

7

A

054

0

001

3061

5

B2

190

000

730

768

E

0

500

002

3072

0A

0

77

000

2 30

616

A

1

019

000

131

057

E

1

72

000

830

755

A

1

62

000

3 30

661

B

2

045

0

002

3087

1

A

222

0

005

3067

2

A1

066

000

230

888

A

9

25

002

0 30

682

A

1

029

0

001

3101

3

A

738

0

016

3070

3

A1

065

0

002

3101

4

A

125

0

003

3073

3

B2

196

000

730

836

A

1

643

0

024

3085

1

B2

305

5 0

112

3085

6

A1

140

4 0

052

3099

9

A1

837

0

031

a T

he d

ata

for

020

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)




11 (c) C27H13 + and (e) C59H19








C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252


















































Tab

le 2

+

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

C1

3H

9

+

and

C27H

13 ca

tion

sa+

C

19H

11

+

++

C

13H

9

C1

9H

11

C

27H

13

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

187

4 A

2 12

39

005

5 86

44

A

786

8 0

169

872

6 B

1

778

00

286

750

7 A

267

08

029

6 12

264

A

158

49

034

0 92

42

B1

803

70

296

855

3 A

2 73

70

032

6 13

511

A

10

877

0

233

1188

3

A1

331

50

122

1120

6

E

496

80

219

1364

8A

50

86

010

9 12

152

A

1

140

850

518

1206

7

E

333

2 0

147

1396

3

A

120

77

025

9 12

161

B

2

103

13

038

012

595

E

16

604

073

315

466

A

535

6 0

115

1267

4

A1

439

70

162

1361

1

E

170

86

075

5 15

668

A

61

16

013

1 13

496

B

2

148

440

546

1543

6

E

158

040

698

1594

9A

46

681

1

00

1354

3

A1

221

440

815

1581

8

E

226

42

100

1460

3

A1

556

4 0

205

1548

0

B2

331

7 0

122

1571

7

B2

154

66

056

9 15

805

A

1

271

72

100

15

977

A

1

232

25

085

5

3072

9

E

038

0

002

3061

7

A

054

0

001

3061

5

B2

190

000

730

768

E

0

500

002

3072

0A

0

77

000

2 30

616

A

1

019

000

131

057

E

1

72

000

830

755

A

1

62

000

3 30

661

B

2

045

0

002

3087

1

A

222

0

005

3067

2

A1

066

000

230

888

A

9

25

002

0 30

682

A

1

029

0

001

3101

3

A

738

0

016

3070

3

A1

065

0

002

3101

4

A

125

0

003

3073

3

B2

196

000

730

836

A

1

643

0

024

3085

1

B2

305

5 0

112

3085

6

A1

140

4 0

052

3099

9

A1

837

0

031

a T

he d

ata

for

020

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)




11 (c) C27H13 + and (e) C59H19








C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252







































11 (c) C27H13 + and (e) C59H19








C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252







































C47H17 + C59H19

+


8504 B1 6164 0108 7922 B1 3557 0100 9204 B1 10342 0181 8453 B1 4192 0118 9385 B1 6400 0112 9190 B1 7239 0204


13400 B2 5295 0149 13510 A1 4038 0114 14749 B2 7274 0205 14771 A1 4308 0121 15036 B2 6438 0181 15539 A1 21163 0597 15754 A1 11348 0320 15813 B2 30642 0864 15851 A1 35475 100 15926 A1 9004 0254 16042 B2 4738 0134


30782 A1 2184 0062 30802 B2 734 0021 30820 A1 5918 0167









degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252












































degcation (C10H8


degC10H9







+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252









































+ + and C10H12 deg







+

B3LYP4-31G level


















+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252






















































+acations C10H9



7299 A 2871 0128 7668 A 3009 0127 7763 A 7353 0327 7941 A 4694 0198


28542 A 2401 0107 28395 A 4662 0196 28657 A 636 0028 28440 A 1013 0043 30750 A 039 0002 30627 A 033 0001 30790 A 100 0004 30790 A 139 0006 30801 A 015 0001 30938 A 033 0001 30913 A 065 0003 30971 A 052 0002 31073 A 076 0003 31078 A 019 0001


Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252





































Tab

le 5

+a

Cal

cula

ted

freq

uenc

ies

sym

met

ries

an

d in

tens

itie

s fo

r th

e in

frar

ed a

ctiv

e m

odes

of

the

1-hy

drop

yren

e 2

-hyd

ropy

rene

an

d 4-

hydr

opyr

ene

cati

ons

C16H

11

1-H

ydro

pyre

ne

2-H

ydro

pyre

ne4-

Hyd

ropy

rene

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

yI r

el

0 (c

mminus

1)

Sym

met

ry

Inte

nsit

y (k

mm

ol)

I rel

(km

mol

) (k

mm

ol)

869

4 A

10

333

0

398

737

7 B

1

391

1 0

247

702

3 A

35

49

021

812

081

A

40

95

015

8 85

06

B1

97

81

061

7 84

80

A

102

560

631

1230

7

A

139

91

053

9 93

68

A1

15

97

010

1 12

063

A

21

01

012

912

411

A

45

68

017

695

32

B1

27

81

017

6 12

375

A

24

56

015

113

526

A

38

58

014

9 99

85

A1

20

34

012

8 12

429

A

21

63

013

313

569

A

48

09

018

510

747

B2

20

36

012

8 13

149

A

60

08

037

013

716

A

99

28

038

2 11

894

B

2

243

6 0

154

1358

2

A

382

80

236

1381

9

A

943

70

363

1328

8A

1

158

42

100

13

594

A

81

09

049

914

762

A

58

87

022

7 13

314

B

2

760

9 0

480

1372

1

A

143

390

882

1522

2

A

144

99

055

8 13

470

B2

47

50

030

0 14

123

A

60

49

037

215

540

A

98

76

038

0 13

993

A

1

253

6 0

160

1437

0

A

276

80

170

1562

8

A

127

230

490

1414

0A

1

885

9 0

559

1466

3

A

550

60

339

1587

1

A

259

64

100

14

622

B

2

814

8 0

514

1499

1

A

413

7 0

255

1613

7

A

459

4 0

177

1498

2B

2

351

0 0

222

1541

6

A

336

90

207

1546

8

A1

11

956

0

755

1575

8

A

615

1 0

379

1589

3

B2

51

53

032

5 15

846

A

48

54

029

916

039

A

1

753

3 0

475

1607

5

A

162

51

100

2865

1

A16

62

006

428

436

A

1

391

2 0

247

2848

1

A

268

10

165

2879

3

A

060

0

002

2848

9

B1

7

69

004

9 28

583

A

2

80

001

730

730

A

0

33

000

1 30

747

B

2

016

0

001

3066

8

A

252

0

016

3074

5

A

054

000

230

759

A1

0

59

000

4 30

717

A

0

230

001

3077

4

A

077

0

003

3076

4

A1

0

81

000

5 30

736

A

0

260

002

3085

2

A

322

001

230

826

B2

1

92

001

2 30

781

A

1

750

011

3089

3

A

139

0

005

3090

2

B2

9

340

059

3089

9

A

545

0

034

3091

6

A

596

0

023

3097

2A

1

555

0

035

3096

1

A

676

004

231

027

A

3

47

001

3 31

056

A

1

04

000

6


a T

he d

ata

for

0 20

00 c

mminus

1 ha

ve b

een

trun

cate

d at

the

10

lev

el

The

com

plet

e da

ta a

re t

abul

ated

at lth

ttp

cc

far

cna

sag

ov

cbau

schl

clo

sed-

shel

ldat

a)

















1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252





















































1-Hydrocoronene


5483 A 2468 0155 8801 A 15927 100


28575 A 1393 0087 28699 A 077 0005 30627 A 020 0001 30635 A 166 0010 30667 A 030 0002 30677 A 036 0002 30688 A 056 0004 30799 A 692 0043 30838 A 215 0014 30848 A 1016 0064 30858 A 1918 0120 30884 A 1002 0063

















7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252

















































7905 A 3591 0161 7915 B1 4831 0129 9191 A 18900 0846 9215 B1 7202 0192




Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252






































Table 7 (Continued)




30795 A1 2981 0080






C54H18 C54H18 + deg


7820 9041

12865 12866 16079 16083

B3u

B3u

B1u

B2u

B2u

B1u

4330 22023 3437 3469 2617 2609

0188 0954 0149 0150 0113 0113

9190 12461 12569 13148 13511 14836 14934 15700 15712

Au

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

21685 11278 35064 28699 16405 23283 10050 14143 95813

0226 0118 0366 0300 0171 0243 0105 0148 100

30418 30420 30455 30460 30470 30628 30634 30637

B2u

B1u

B1u

B2u

B1u

B2u

B1u

B2u

052 050

5658 5191 243 531

22917 23088

0002 0002 0245 0225 0011 0023 0993 100

30584 30593 30604 30625 30633 30798 30805 30807

Bu

Bu

Bu

Bu

Bu

Bu

Bu

Bu

919 1171 2079 1145

961 3487 8122

10691

0010 0012 0022 0012 0010 0036 0085 0112





















5 Conclusions







Acknowledgements


References




























101 (1994) 10252
























































5 Conclusions







Acknowledgements


References




























101 (1994) 10252









































Acknowledgements


References




























101 (1994) 10252





































closed-shell polycyclic aromatic hydrocarbon cations: a ... · density functional theory has been...

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