The Predictive Power of the Annellation Theory: The Case of the

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The Predictive Power of the Annellation Theory: The Case of the C H Benzenoid Polycyclic Aromatic Hydrocarbons 32

16

Jorge O Oña-Ruales, and Yosadara Ruiz-Morales J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 20 Jun 2014 Downloaded from http://pubs.acs.org on June 25, 2014

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The Journal of Physical Chemistry

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The Predictive Power of the Annellation Theory: The Case of the C32H16 Benzenoid Polycyclic Aromatic Hydrocarbons. Jorge O. Oña-Ruales1* and Yosadara Ruiz-Morales2

1

National Institute of Standards and Technology, NIST, Gaithersburg, Maryland 20899

2

Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, Mexico City 07730,

Mexico

ACS Paragon Plus Environment


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ABSTRACT

The positions of maximum absorbance for the p and β bands of the UV-Vis Spectra of the Benzenoid Polycyclic Aromatic Hydrocarbons, PAHs, with molecular formula C32H16 have been predicted by means of the Annellation Theory. In the C32H16 PAH group there are 46 isomers, 39 of which have not been synthesized so far, thus their characterization and possible presence in the environment remains unknown. The methodology has been validated using literature information for 7 isomers in this PAH group. The results have been satisfactorily substantiated by means of semi-empirical calculations using the ZINDO/S approach. It has been concluded that the Annellation Theory is a powerful tool for the prediction of the positions of maximum absorbance of aromatic compounds with unknown UV-Vis spectra. It is the first time that the UV-Vis spectral information of these 39 benzenoid C32H16 PAHs has been predicted.

KEYWORDS

Polycyclic Aromatic Hydrocarbons, Ultraviolet-Visible Spectrum, Annellation Theory, ZINDO/S Calculations, C32H16 compounds


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1. INTRODUCTION Erich Clar postulated the Annellation Theory in the 1940’s when he evidenced ultraviolet-visible (UV-Vis) effects in the absorption spectra due to the addition of one or more hydrocarbon rings to the molecules of polycyclic aromatic hydrocarbons, PAHs.1,2 The fusing of a new ring, or rings, to a PAH molecule (a.k.a. Annellation), modifies the electronic distribution (in sextets and isolated double bonds), and therefore, the UV-Vis absorption spectra. Clar stated that the observed effects comprised foreseeable wavelength shifts of the para (p) and beta (β) spectral bands.1 These spectral shifts are noticeable in the series of pericondensed and catacondensed PAHs.2 The β bands are the most intense bands in the absorption spectrum. These bands are not in general superimposed by other bands, as in some cases it can occur that the α bands be hidden by the p bands. In general in pericondensed and catacondesed PAHs the annellation effect can be observed in the α, β, and p bands of the UV-Vis absorption spectrum. The fusion of a ring to a PAH can occur either onto a ring with a sextet or onto a ring with a localized double bond or localized double bonds. The annellation effect, on the spectral p bands due to these two types of fusions, is different. When a ring is fused to a localized (fixed) double bond it causes either no shift at all or a very small shift towards shorter wavelength whilst a considerable shift to the red is observed if the annellation takes place onto a sextet and if the fusion produces aromatic conjugation, i.e., sextet migration (superaromaticity).2 Also a shift to the red occurs if the fusion causes the formation of a sextet or sextets and if there is possibility for sextet migration to take place. If there is no formation of new sextet, after the annellation process, but it produces sextet migration, then a shift of the bands to the red is also observed.



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Considering the pericondensed case, Figure 1 analyzes the positions of maximum absorbance for the p and β bands of pyrene (I) and benzo[e]pyrene (II) and the positions of maximum absorbance for the p and β bands of dibenzo[cd,lm]perylene (III) and tribenzo[a,cd,lm]perylene (IV). Figure 1 shows (in red) the structural resemblance between pyrene (I) and dibenzo[cd,lm]perylene (III) that includes the same locations of the sextets and the same locations of the isolated double bonds.2 Due to this resemblance, the Annellation Theory predicts that changes applied to pyrene (I) and dibenzo[cd,lm]perylene (III) (in this red region) will produce similar effects in the positions of maximum absorbance for the p and β bands. The fusion of one ring to one of the isolated double bonds of pyrene (I) in going to benzo[e]pyrene (II) produces the same effect, in the position of maximum absorbance for the p and β bands, as for the case of the fusion of one ring to an isolated double bond of dibenzo[cd,lm]perylene (III) in going to tribenzo[a,cd,lm]perylene (IV). This annellation change has both structural and spectral effects. On the structural side, it increases the aromatic behavior of the molecule due to the increase in the number of sextets, and on the spectral side, it retains the positions of maximum absorbance for the p bands3 and produces the same wavelength shift for the positions of maximum absorbance for the β bands. Consequently, it is anticipated that the wavelength shifts of the positions of maximum absorbance for the p bands and for the β bands will have approximately the same magnitude for the passage from pyrene (I) to benzo[e]pyrene (II) and for the passage from dibenzo[cd,lm]perylene (III) to tribenzo[a,cd,lm]perylene (IV). Consistent with this reasoning, Figure 1 shows that the absolute shifts of the positions of maximum absorbance for the transit pyrene (I) - benzo[e]pyrene (II) have average magnitudes of 1 nm for the p bands and 16 nm for the β bands, and the absolute shifts of the positions of maximum absorbance for the transit dibenzo[cd,lm]perylene (III) - tribenzo[a,cd,lm]perylene (IV) have


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average magnitudes of 2 nm for the p bands and 14 nm for the β bands. These spectral changes are minor due to the fact that the fusion occurs onto a ring with a localized double bond and in the resulting PAHs there is no sextet migration. Transit 1: pyrene – benzo[e]pyrene

I

II

UV-Vis Bands Positions1


λp, nm

λβ, nm

λp, nm

λβ, nm

334 318 305

272 262 251

332 317 304

289 278 267

Absolute Shifts of Spectral Bands nm Δλp, nm Δλβ, nm 2 17 1 16 1 16

Transit 2: dibenzo[cd,lm]perylene – tribenzo[a,cd,lm]perylene

III

IV



λp, nm

λβ, nm

λp, nm

λβ, nm

440 413 388

328 313 296

437 412 389

342 327

Absolute Shifts of Spectral Bands nm Δλp, nm Δλβ, nm 3 1 1

14 14

Figure 1. UV-Vis spectral analysis of the positions of maximum absorbance for the p and β bands of pyrene (I) and benzo[e]pyrene (II),

and of dibenzo[cd,lm]perylene (III) and

tribenzo[a,cd,lm]perylene (IV).



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Regarding the catacondensed case, Figure 2 examines the positions of maximum absorbance for the p and β bands of chrysene (V), benzo[b]chrysene (VI), picene (VII), and benzo[b]picene (VIII). As it is observed in Figure 2, the annellation change for the transit chrysene (V) benzo[b]chrysene (VI), and the transit picene (VII) - benzo[b]picene (VIII) involves the linear fusion of one ring to chrysene (V) and picene (VII) in going to benzo[b]chrysene (VI) and benzo[b]picene (VIII), respectively. This annellation does not increase the number of sextets but it takes place on a ring with a sextet and prolongs the path for linear movement of one of the terminal sextets (sextet migration), as shown by the arrow in Figure 2.2 Consequently, it is anticipated that the wavelength shifts of the positions of maximum absorbance for the p bands and for the β bands will have approximately the same magnitude for the transit chrysene (V) benzo[b]chrysene (VI) and for the transit picene (VII) - benzo[b]picene (VIII),2 and as the Annellation Theory predicts, the shift will be strong and to the red (longer wavelength). In agreement with this reasoning, Figure 2 shows that the absolute shifts of the positions of maximum absorbance for the p bands for the transits chrysene (V) - benzo[b]chrysene (VI) and picene (VII) - benzo[b]picene (VIII) have average values of 41 nm and 48 nm, respectively, and the absolute shifts of the positions of maximum absorbance for the β bands for the transits chrysene (V) - benzo[b]chrysene (VI) and picene (VII) - benzo[b]picene (VIII) have average values of 34 nm and 38 nm, respectively. Also, the observed wavelength differences between the p bands and between the β bands are explained due to the solvent effect that produces a shift of the solute spectral bands depending on the solvent refractive index.4


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Transit 3: chrysene – benzo[b]chrysene

V UV-Vis Bands Positions1

VI UV-Vis Bands Positions1

λp, nm

λβ, nm

λp, nm

λβ, nm

319 306 295

267 259

365 347 331

305 288 280


38 29

Transit 4: picene – benzo[b]picene

VII

VIII



λp, nm

λβ, nm

329 315 304

287 274 256

λp, nm 382 363 347

λβ, nm 325 311 296


38 37 40

Figure 2. Analysis of the positions of maximum absorbance for the p and β bands of chrysene (V) and benzo[b]crhysene (VI) and the positions of maximum absorbance for the p and β bands of picene (VII) and benzo[b]picene (VIII).

Besides the examples mentioned above, many other comparisons are described in the books and articles of Clar and co-workers that explain the insights and applications of the Annellation Theory applied to PAHs.1,2,5-9



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1.1. Localization of Sextets and the Y-Rule. To be able to understand the red shift of the p band, it is necessary to elucidate the π-electronic distribution in sextets and localized double bonds. When the annellation (either symmetric or asymmetric) takes place onto a ring with localized or fixed double bonds, there will be almost no effect in the β and p bands. While there will be a considerable red shift of the p bands (more than in the β bands, which are also shift to the red) if the annellation takes place onto a ring with a sextet and if there is sextet migration as a consequence of the annellation process. The Y-rule10-14 was used to find the π-electronic distribution in all the systems except those in Figure 2. In both the original formulation of the Clar theory2 and its several later variants,15 sextets of π-electrons are located in particular hexagons of the benzenoid molecule, indicating domains of increased π-electron contents and/or local aromaticity. The Y-rule offers a new, original and easy-to-apply, criterion for locating aromatic sextets in pericondensed benzenoids. The Y-rule applies to benzenoid hydrocarbons possessing carbon atoms that simultaneously belong to three hexagons. Such carbon atoms are named Y-carbons -because they are located at the vertex of what looks like a Y-letter. The Y-rule is not applicable to catafusenes. The Y-rule enunciates as follows:10-14 (a) The aromatic sextets are to be located so as to cover all internal Y-carbons. If not all Ycarbon atoms can be covered by aromatic sextets, then the highest possible Y-carbons must be covered. (b) The number of aromatic sextets must be as large as possible.


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(c) If several Clar-type structures satisfy conditions (a) and (b), then the one with the highest symmetry (provided such exists) is chosen, i.e., considered as most important. (d) If the Clar-type structure obtained by means of requirements (a), (b), and (c) is unique, then it represents the basic features of the π-electronic distribution, local aromaticity, and similar. (e) If there are several Clar-type structures obeying the requirements (a), (b), and (c), then the conclusions about π-electronic distribution, local aromaticity, and similar are drawn from their superposition. 1.2. The UV-Vis Spectra of PAH and the HOMO-LUMO Gap. In addition to the Annellation Theory, another method to determine the position of maximum absorbance for the last p band (λ0-0), from left to right, in the UV-Vis absorption spectra of PAHs is the calculation of the HOMO-LUMO gap wavelength by means of semi-empirical calculations.10,11 In asymmetric and symmetric annellation, onto a sextet and with resulting aromatic conjugation, the p bands shift more to the red than the α and β bands, as shown in Figure 2. The p band, which is associated to the HOMO-LUMO gap (energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital), represents a measure of the stability of the final PAH obtained by the annellation process. The HOMO-LUMO gap is used as a direct indicator of kinetic stability.10 A large HOMOLUMO gap implies high kinetic stability and low chemical reactivity because it is energetically unfavorable to add electrons to a high-lying LUMO or to extract electrons from a low-lying HOMO. Clar1,2 observed that the more highly colored a PAH is (high wavelengths in the visible



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spectrum), the less kinetically stable it is. Thus, he related kinetic instability to a small HOMOLUMO gap. It has been shown that for benzenoid PAHs there is a correlation between the HOMO-LUMO gap and the Hess-Schaad resonance energy per π electron, which is a measure of thermodynamic stability due to cyclic conjugation.16-19 This correlation indicates that, in general, thermodynamically stable PAHs are kinetically stable. 1.3. The C32H16 Nonradical Benzenoid PAHs. Table 1 shows the 46 nonradical benzenoid isomers with the formula C32H16 (9FAR, 9 fused aromatic rings, PAH group). The C32H16 PAH group has particular importance because only 7 benzenoid isomers (shown in Table 2), compounds IX, X, XIII, XXII, XLVI, XLIX, and L have been synthesized so far;1,20,21 in consequence, there is a lack of spectral data for the potential detection of the other 39 members. The C32H16 benzenoid PAH group is also important because

16 compounds, XI, XII, XV, XVII, XX, XXI, XXIII, XXVI, XXVIII, XXIX,

XXXVI, XXXVIII, XLIV, XLVI, LI, and LII have molecular structures that include the same fjord

region

present

in

the

well-known

non-planar

carcinogenic

compound,

dibenzo[def,p]chrysene (LV) shown in Figure 3. Until further analysis, this resemblance tentatively categorizes them as potential carcinogenic entities. Furthermore, 37 members of the C32H16 benzenoid PAHs, IX, X, XI, XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX, XXI, XXII, XXIII, XXIV, XXV, XXVI, XXVII, XXVIII, XXIX, XXX, XXXI, XXXII, XXXIII, XXXIV, XXXV, XXXVI, XXXVII, XXXVIII, XXXIX, XL, XLI, XLII, XLIII, XLIV, and XLV, are structurally similar to the C28H14 benzenoid PAHs, with a molecular mass of 350 g/mol (8FAR), which are shown in Table 3, where the only difference is one more ring in the structures. Since 6 members of the 8 nonionic isomers of the C28H14 benzenoid PAHs, see Table 3, compounds LVII, LVIII, LIX, LX, LXI, and LXII, have been identified in several


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environments,22,23 the presence of C32H16 benzenoid PAHs in modified and non-modified atmospheres is feasible and highly probable.

C32H16 benzenoid PAH

Structure


dibenzo[a,g]coronene IX

dibenzo[a,ghi]naphtho[8,1,2-klm]perylene XVII

dibenzo[a,j]coronene X

dibenzo[fg,ij]naphtho[7,8,1,2,3-pqrst]pentaphene XVIII

dibenzo[a,d]coronene XI

anthra[2,1,9,8,7-defghi]benzo[st]pentacene XIX

naphtho[1,2-a]coronene XII

benzo[e]phenanthro[2,3,4,5-pqrab]perylene XX benzo[4,10]anthra[3,2,1,9,8-rstuva]pentaphene XXI

naphtho[2,3-a]coronene XIII

dibenzo[ij,rst]naphtho[2,1,8,7-defg]pentaphene XIV

dibenzo[cd,n]naphtho[3,2,1,8-pqra]perylene XXII

dibenzo[a,ghi]naphtho[2,1,8-cde]perylene XV

dibenzo[a,cd]naphtho[8,1,2,3-fghi]perylene XXIII

dinaphtho[2,1,8-fgh:3’,2’,1’,8’,7’-rstuv]pentaphene XXIV

dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-qrst]pentacene XVI

Table 1. C32 H16 benzenoid PAH structures.


Structure


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Structure

C32H16 benzenoid PAH dibenzo[ghi,n]naphtho[8,1,2-bcd]perylene XXXIII

anthra[2,1,9,8-defgh]benzo[rst]pentaphene XXV

benz[5,10]anthra[3,2,1,9,8-rstuva]pentaphene XXXIV

pyreno[5,4,3,2,1-pqrst]pentaphene XXVI

dibenzo[cd,k]naphtho[3,2,1,8-pqra]perylene XXVII

anthra[2,1,9,8,7-defghi]benzo[uv]pentacene XXXV

benzo[de]phenaleno[1,2,3,4,5-rstuv]pentaphene XXVIII

dibenzo[a,ghi]naphtho[2,1,8-lmn]perylene XXXVI

anthra[3,2,1,9-pqra]benzo[cd]perylene XXIX

benzo[h]phenanthro[2,1,10,9,8,7-pqrstuv]pentaphene XXXVII

dibenzo[de,ij]naphtho[3,2,1,8,7-rstuv]pentaphene XXX

benzo[3,4]phenanthro[2,1,10,9,8,7-pqrstuv]pentaphene XXXVIII

anthra[2,1,9,8,7-defghi]benzo[qr]pentacene XXXI

benzo[def]pyranthrene XXXIX

dinaphtho[2,1,8-fgh:7’,8’,1’,2’,3’-pqrst]pentaphene XXXII

phenanthro[2,1,10,9,8,7tuvwxyz]hexaphene XL

Table 1. C32 H16 benzenoid PAH structures (continued).


Structure

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Structure


anthra[3,2,1,9,8-rstuva]benzo[ij]pentaphene XLI

dibenzo[de,ij]naphtho[7,8,1,2,3-pqrst]pentaphene XLVIII

anthra[7,8,9,1,2,3rstuvwx]hexaphene XLII

dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-opqr]pentacene XLIX

naphthaceno[2,1,12,11,10qrstuva]pentacene XLIII

dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-ijkl]pentaphene L

benzo[fg]phenaleno[1,2,3,4,5-rstuv]pentaphene XLIV

dinaphtho[1,8-ab: 8’,1’,2’,3’-fghi]perylene LI

benzo[e]phenanthro[1,10,9,8-opqra]perylene XLV

dibenzo[ghi,lm]naphtho[1,8-ab]perylene LII

benzo[lm]phenanthro[5,4,3-abcd]perylene XLVI

dinaphtho[8,1,2-cde:7’,8’,1’,2’,3’-pqrst]pentaphene LIII

dibenzo[kl,rst]naphtho[2,1,8,7-defg]pentaphene XLVII

anthra[2,1,9,8,7-defghi]benzo[op]pentacene LIV

Table 1. C32 H16 benzenoid PAH structures (continued).


Structure


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λp, nm

λβ, nm

Reference

XXII

453 423 399

329 313

UV-Vis20

XLVI

468 438 414

345 332

UV-Vis21

495 462 435

323

XLIX

L

520 482 450

343 328 302

X

401 381 363

330 316

XIII

423 400 379

341 326 310

IX

379 360 349

328 314


UV-Vis1

UV-Vis1

UV-Vis1

UV-Vis1

UV-Vis1

Table 2. Positions of maximum absorbance for the p and β Bands of the 7 C 32 H16 PAH with UVVis spectra available in the literature.


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fjord region

dibenzo[def,p]chrysene LV

Figure 3. The structure of dibenzo[def,p]chrysene (LV) showing the characteristic fjord region.


Structure

phenanthro[1,10,9,8-opqra] perylene LVI benzo[cd]naphtho[3,2,1,8-pqra]perylene LVII benzo[a]coronene LVIII phenanthro[5,4,3,2-abcde]perylene LIX benzo[lmn]naphtho[2,1,8-qra]perylene LX benzo[pqr]naphtho[8,1,2-bcd]perylene LXI phenanthro[2,1,10,9,8,7pqrstuv]pentaphene LXII peri-naphthacenonaphthacene LXIII

Table 3. C28 H14 benzenoid PAH structures.



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1.4. Objective. The objective of this paper is to report the prediction of the wavelength positions of maximum absorbance for the p and β spectral bands of the 39 benzenoid PAH isomers with the formula C32H16, and with molecular mass 400 g/mol, which have not been synthesized and their UV-Vis spectra are unknown. With this aim, the positions of maximum absorbance for the p and β bands are inferred from quantitative analyses using the Annellation Theory. To substantiate the results, the UV-Vis spectral information obtained by means of the Annellation Theory for this PAH group are compared with the results of the HOMO-LUMO gap wavelength obtained from semiempirical calculations. It is the first time that the Annellation Theory is applied to the prediction of the UV-Vis absorption spectra of benzenoid PAHs with a molecular mass greater than 350 g/mol. The analysis presented here constitutes a fundamental spectroscopic methodology for the prediction of unknown UV-Vis absorption spectra of benzenoid PAHs, and it can be applied for both the prediction of the UV-Vis spectra of benzenoid, and non-benzenoid compounds with aromatic rings in their structures – for example in the case of linear and bent biphenylene derivatives.15 2. THEORETICAL METHODS 2.1. Annellation Theory Methodology. The Annellation Theory Analysis followed for the prediction of the positions of maximum absorbance for the p and β bands of the C32H16 benzenoid PAHs is described in Figure 4.


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17

Aromatic and Structural

PAH #1

PAH #2

Relationship Aromatic and Structural Enclosure

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Spectral Bands Positions λp, nm

λβ, nm

x2 y2 z2

Aromatic and Structural

PAH #3

Relationship

Spectral Bands Positions

x3 y3 z3

λp, nm

u1 v1 w1

x1 y1 z1

λp, nm


λβ, nm u2 v2 w2

PAH #4


λβ, nm

λp, nm

λβ, nm

u3 v3 w3

x4=x3+(x2-x1) y4=y3+(y2-y1) z4=z3+(z2-z1)

u4=u3+(u2-u1) v4=v3+(v2-v1) w4=w3+(w2-w1)

Figure 4. Annellation Theory analysis for the prediction of the positions of maximum absorbance for the p and β bands of the C32H16 benzenoid PAH.

On one hand, PAH #1, PAH #2, and PAH #3 are the reference PAH with known UV-Vis spectra, and on the other hand, PAH #4 is the PAH with unknown UV-Vis spectrum whose positions of maximum absorbance for the p and β bands are going to be predicted. In order to apply the Annellation Theory approach, the aromatic relationship, given by the positions of the sextets and double bonds, and the structural relationship, given by the shape of the molecules, between PAH #1 and PAH #2 should be equivalent to the respective aromatic-structural relationship between PAH #3 and PAH #4. Also, PAH #1 should be enclosed aromatically and



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structurally in PAH #3 so as to connect the top and the bottom part of the scheme. Once these structures are recognized, the numerical calculations can be performed. To do so, the differences between the positions of maximum absorbance for the p and β bands of PAH #1 and PAH #2 are mathematically added to the positions of maximum absorbance for the p and β bands of PAH #3. As a basis of calculation, only the positions of the three most important p bands and the positions of the three most important β bands (when enough data are available) are used. The results of these calculations are the predicted values of the positions of maximum absorbance for the p and β bands of PAH #4. The methodology mentioned above has been validated by means of the prediction of the positions of maximum absorbance of 7 C32H16 PAHs, XXII, XLVI, XLIX, L, X, XIII, and IX, a group of PAHs with UV-Vis spectral information available in the literature. Table 2 shows the structures of these 7 PAHs, the positions of the sextets were obtained by application of the YRule10-14 (see the Introduction section), and the positions of maximum absorbance for the p and β bands from literature information. 2.2. Theoretical Semi-empirical ZINDO/S Calculation Methodology. To calculate the HOMO-LUMO gap wavelength, the geometry optimization of the PAH systems was first carried out by performing force field-based minimization using the energy minimization panel in Cerius 2 program24 and the COMPASS (Condensed-Phase Optimized Molecular Potentials for Atomistic Simulation Studies)25,26 consistent force field as it is provided in the Cerius 2 package.24 The excited electronic states for the PAH systems were calculated using the ZINDO/S27 approach, which is a semi-empirical electronic structure method calibrated for calculating excited states, as implemented in the Cerius 2 program,24 using the COMPASS


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forcefield geometry optimized structures. Previously, this method has been proven to provide a good agreement with experimental values for the calculation of optical properties of PAHs.10,11,28 The theoretical estimates are derived from a single “frozen” molecule in the gas phase at 0 K without corrections for thermal motions and solvent effects. The difference between the theoretical and experimental data could be due to the Stokes shift, which involves the reconfiguration of the solvent cage for the ground electronic state once the excited molecule of PAH undergoes photoemission.29-31 The Stokes shift to the red is reported to be around 10-45 nm for solvents with low polarity.30,32 3. RESULTS AND DISCUSSION 3.1. Validation of the Methodology for the Annellation Theory Analysis. 3.1.1 Calculation of the Positions of Maximum Absorbance for the p and β Bands of dibenzo[cd,n]naphtho[3,2,1,8-pqra]perylene (XXII). The positions of maximum absorbance for the p and β bands of dibenzo[cd,n]naphtho[3,2,1,8pqra]perylene (XXII) are obtained by application of the Annellation Theory using benzo[e]pyrene (II), dibenzo[fg,op]naphthacene (LXIV), and benzo[cd]naphtho[3,2,1,8pqra]perylene (LVII), three reference PAHs with UV-Vis spectral bands available in the literature,1,33 as it is described in Figure 5a. Figure 5a shows (in red) the structural resemblance between compound II and compound LVII that includes the same locations of the 3 sextets and the same location of the isolated double bond.



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20

Annellation Theory Analysis Compound

Structure

Compound

II

Structure

LXIV


λp, nm 332 317 304


λβ, nm 289 278 267

λp, nm 328 315

LVII

λβ, nm 288 278

XXII


Predicted UV-Vis Bands Positions

λp, nm

λβ, nm

λp, nm

λβ, nm

460 430 407

326 312 300

456 428

325 312

UV-Vis Absorption Spectrum of Compound XXII20

329

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

240

313 453 423 399

290

340

390 440 Wavelength (nm)

490

540

Figure 5a. Top: Prediction of the positions of maximum absorbance for the p and β bands of dibenzo[cd,n]naphtho[3,2,1,8-pqra]perylene (XXII). Bottom: Experimental UV-Vis absorption spectrum of dibenzo[cd,n]naphtho[3,2,1,8-pqra]perylene (XXII).

Due to this similarity, annellation changes applied to compound II and compound LVII, in this red region, will produce similar effects in the positions of maximum absorbance for the p and β bands. Following this comment, the addition of one ring to one of the isolated double


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bonds in compound II, to form compound LXIV, produces the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of a ring to an isolated double bond of compound LVII to form compound XXII. Based on this analysis, the predicted positions of maximum absorbance for the p and β bands of compound XXII will be equal to the positions of maximum absorbance for the p and β bands of compound LVII plus the difference between the positions of maximum absorbance for the p and β bands of compound LXIV and compound II. Consequently, the predicted positions for the p bands of compound XXII are equal to 456 nm and 428 nm, and the predicted positions for the β bands of compound XXII are equal to 325 nm and 312 nm. The UV-Vis absorption spectrum of compound XXII published in the literature20 is presented at the bottom of Figure 5a. The published positions of maximum absorbance for the p bands are equal to 453 nm, 423 nm, and 399 nm, and the published positions of maximum absorbance for the β bands are equal to 329 nm and 313 nm. The absolute error between the predicted and the published values does not exceed 1%. In

the

upper

portion

of

Figure

5b

the

experimental

UV-Vis

spectrum

of

dibenzo[cd,n]naphtho[3,2,1,8-pqra]perylene (XXII) is shown,20 while in the lower portion of Figure 5b the calculated UV-Vis spectrum using the ZINDO/S methodology is presented. It can be seen that the ZINDO/S method cannot reproduce all the spectral features but it does have a good agreement for the case of the most intense p band and β bands. Among the p bands, only the p band corresponding to the HOMO-LUMO gap was calculated with ZINDO/S. The theoretical ZINDO/S estimates are derived from a single “frozen” molecule in the gas phase at 0 K without corrections for thermal motions and solvent effects. The Stokes shift to the red is reported to be around 10-45 nm for solvents with low polarity.



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22

UV-Vis Absorbance20

329

1.2

XXII

313

453 423 399

240

Normalized Oscillator Strength

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

290

340


490

540

(268.5, 0.46405) (300.9, 0.90183)

1

(307.6, 1.00000) 0.8 0.6 (436.5, 0.41937) 0.4 (340.9, 0.11362)

0.2 0 240

290

340


490

540

Figure 5b. Top: Experimental UV-Vis absorption spectrum of dibenzo[cd,n]naphtho[3,2,1,8pqra]perylene (XXII). Bottom: Calculated ZINDO/S spectrum of dibenzo[cd,n]naphtho[3,2,1,8-

pqra]perylene (XXII).

3.1.2. Calculation of the Positions of Maximum Absorbance for the p and β Bands of benzo[lm]phenanthro[5,4,3-abcd]perylene (XLVI).


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The positions of maximum absorbance for the p and β bands of benzo[lm]phenanthro[5,4,3abcd]perylene (XLVI) are obtained by application of the Annellation Theory using naphtho[1,2,3,4-pqr]picene (LXV), tribenzo[a,cd,lm]perylene (IV), and benzo[ghi]naphtho[1,2b]perylene (LXVI), three reference PAHs with UV-Vis spectral bands available in the literature,3,34,35 as it is described in Figure 6a. Figure 6a shows (in red) the structural similarity between compound LXV and compound LXVI that includes the same locations of the 4 sextets and the same locations of the 2 isolated double bonds. Due to this analogy, annellation changes applied to compound LXV and compound LXVI, in this red region, will produce similar effects in the positions of maximum absorbance for the p and β bands. Following this argument, the addition of one ring to the bay region A of compound LXV to form compound IV produces the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of a ring to the bay region A’ of compound LXVI to form compound XLVI. Based on this behavior, the predicted positions of maximum absorbance for the p and β bands of compound XLVI will be equal to the positions of maximum absorbance for the p and β bands of compound LXVI plus the difference between the positions of maximum absorbance for the p and β bands of compound IV and compound LXV. As a result, the predicted positions for the p bands of compound XLVI are equal to 471 nm, 442 nm, and 414 nm, and the predicted positions for the β bands of compound XLVI are equal to 351 nm and 337 nm. The UV-Vis absorption spectrum of compound XLVI published in the literature21 is also present in Figure 6a. The published positions of maximum absorbance for the p bands are equal to 468 nm, 438 nm, and 414 nm, and the published positions of maximum absorbance for the β bands are equal to 345 nm and 332 nm. The absolute error between the predicted and the published values does not exceed 2%.



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24


Structure

Compound

Structure

A

LXV

IV

UV-Vis Bands Positions34 λp, nm


λβ, nm 318 304 292

377 358 342

λβ, nm 342 327

437 412 389

A’

LXVI

XLVI


λp, nm 411 388 367


λβ, nm 327 314 301

λp, nm 471 442 414

λβ, nm 351 337

UV-Vis Absorption Spectrum of Compound XLVI21

468

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

250

438

345 332 414

300


450

500

Figure 6a. Top: Prediction of the positions of maximum absorbance for the p and β bands of

benzo[lm]phenanthro[5,4,3-abcd]perylene (XLVI). Bottom: Experimental UV-Vis absorption spectrum of benzo[lm]phenanthro[5,4,3-abcd]perylene (XLVI).

In Figure 6b there is a comparison of the experimental absorption spectrum for XLVI21 and the calculated theoretical spectrum using the ZINDO/S method. The calculated spectrum shows a


Page 25 of 61


25

good agreement only for the case of the highest p and β bands. The differences in values are due to the fact that solvent is not considered in the calculation.

UV-Vis Absorbance21

XLVI

468 438

345 332 414

250

300


450

500

1.2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(480.4, 1.00000)

(292.9, 0.50451)

1

(318.8, 0.81365) 0.8 0.6 0.4

(345.2, 0.21340)

0.2 0 250

300


450

500

Figure 6b. Top: Experimental UV-Vis absorption spectrum of benzo[lm]phenanthro[5,4,3-

abcd]perylene (XLVI). Bottom: Calculated ZINDO/S spectrum of benzo[lm]phenanthro[5,4,3abcd]perylene (XLVI).

3.1.3. Calculation of the Positions for the p and β Bands of dinaphtho[2,1,8,7defg:2’,1’,8’,7’-opqr]pentacene (XLIX).



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26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The positions of maximum absorbance for the p and β bands of dinaphtho[2,1,8,7defg:2’,1’,8’,7’-opqr]pentacene

(XLIX)

are

calculated

using

perylene

(LXVII)

and

naphtho[8,1,2-bcd]perylene (LXVIII), two reference PAHs with UV-Vis spectral bands available in the literature,1 as it is described in Figure 7a. Figure 7a shows (in red) the structural analogy between compound LXVII and compound LXVIII that includes sextet migration (shown with the arrow in Figure 7a).2 Consequently, annellation changes applied to compound LXVII and compound LXVIII, in this red region, will produce similar effects in the positions of maximum absorbance for the p and β bands. Following this condition, the addition of two rings to the red region of compound LXVII to form compound LXVIII produces the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of two rings to the red region of compound LXVIII to form compound XLIX. Based on this behavior, the predicted positions of maximum absorbance for the p and β bands of compound XLIX will be equal to the positions of maximum absorbance for the p and β bands of compound LXVIII plus the difference between the positions of maximum absorbance for the p and β bands of compound LXVIII and compound LXVII. Thus, the predicted positions for the p bands of compound XLIX are equal to 506 nm, 474 nm, and 433 nm, and the predicted position for the β band of compound XLIX is equal to 337 nm. The UV-Vis absorption spectrum of compound XLIX published in the literature1 is also present in Figure 7a. The published positions of maximum absorbance for the p bands are equal to 495 nm, 462 nm, and 435 nm, and the published position of maximum absorbance for the β band is equal to 323 nm. The absolute error between the predicted and the published values does not exceed 4%.


Page 27 of 61


27


Structure

Compound

LXVII

Structure

LXVIII



λp, nm

λβ, nm

λp, nm

λβ, nm

434 406 387

251 245

470 440 410

294

LXVIII

XLIX



λp, nm

λβ, nm

λp, nm

λβ, nm

470 440 410

294

506 474 433

337

UV-Vis Absorption Spectrum of Compound XLIX1

495

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

300

462

435

323

350


500

550

Figure 7a. Top: Prediction of the positions of maximum absorbance for the p and β bands of

dinahptho[2,1,8,7-defg:2’,1’,8’,7’-opqr]pentacene

(XLIX).

Bottom:

Experimental

UV-Vis

absorption spectrum of dinahptho[2,1,8,7-defg:2’,1’,8’,7’-opqr]pentacene (XLIX).

In Figure 7b there is a comparison of the experimental absorption spectrum for XLIX1 and the calculated theoretical spectrum using the ZINDO/S method. The calculated spectrum shows a



Page 28 of 61

28

good agreement; however, as in the former examples, only for the case of the highest p band. The differences are also due to the lack of solvent in the calculation.

495

UV-Vis Absorbance1

XLIX

462

435

323

300

350


0.80


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

500

550

(494.2, 0.67417)

0.60

0.40 (312.1, 0.06411) 0.20 (394.8, 0.01671) 0.00 300

Figure

7b.

350

Top:


Experimental

defg:2’,1’,8’,7’-opqr]pentacene

UV-Vis

(XLIX).

absorption

Bottom:

500

spectrum

Calculated

dinahptho[2,1,8,7-defg:2’,1’,8’,7’-opqr]pentacene (XLIX).


550

of

dinahptho[2,1,8,7-

ZINDO/S

spectrum

of

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29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.1.4. Calculation of the Positions of Maximum Absorbance for the p and β Bands of dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-ijkl]pentaphene (L). The positions of maximum absorbance for the p and β bands of dinaphtho[2,1,8,7defg:2’,1’,8’,7’-ijkl]pentaphene (L) are calculated using tribenzo[b,n,pqr]perylene (LXIX), dibenzo[fg,ij]pentaphene

(LXX),

and

benzo[pqr]dinaphtho[8,1,2-bcd:2’,1’,8’-lmn]perylene

(LXXI), three reference PAHs with UV-Vis spectral bands available in the literature,1 as it is described in Figure 8a. Figure 8a shows (in red) the structural resemblance between compound LXIX and compound LXXI that includes the same locations of the 5 sextets. For that reason, annellation changes applied to compound LXIX and compound LXXI, in this red region, will produce similar effects in the positions of maximum absorbance for the p and β bands. Following this argument, the subtraction of the ring located in position B of compound LXIX to form compound LXX produces the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the subtraction of a ring to the bay region B’ of compound LXXI to form compound L. Based on this analysis, the predicted positions of maximum absorbance for the p and β bands of compound L will be equal to the positions of maximum absorbance for the p and β bands of compound LXXI plus the difference between the positions of maximum absorbance for the p and β bands of compound LXX and compound LXIX. As a result, the predicted positions for the p bands of compound L are equal to 512 nm, 480 nm, and 449 nm, and the predicted position for the β band of compound L is equal to 333 nm. The UV-Vis absorption spectrum of compound L published in the literature1 is also present in Figure 8a. The published positions of maximum absorbance for the p bands are equal to 520 nm, 482 nm, and 450 nm, and the published positions of maximum absorbance for the β bands are equal to 343 nm, 328 nm,



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30

and 302 nm. The absolute error between the predicted and the published values does not exceed 3%.


Structure

Compound

Structure

B

LXIX

LXX

UV-Vis Bands Positions1 λp, nm 374 354 338

λβ, nm 300 288


λβ, nm 302 288

B’

LXXI

L


λβ, nm 331

Predicted UV-Vis Bands Positions λp, nm 512 480 449

λβ, nm 333

UV-Vis Absorption Spectrum of Compound L1

520 343

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

302

250

300

482 328 450

350


500

550

Figure 8a. Top: Prediction of the positions of maximum absorbance for the p and β bands of dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-ijkl]pentaphene (L). Bottom: Experimental UV-Vis absorption spectrum of dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-ijkl]pentaphene (L).


Page 31 of 61


31 In Figure 8b the experimental spectrum of L1 is compared with the calculated spectrum obtained using the ZINDO/S methodology. As it can be seen there is a relative good agreement mainly with the highest p band and some of the β bands.

520

L

UV-Vis Absorbance1

343 482

328 302

250

450

300

350


500

550

0.70


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(514.0, 0.57136)

0.60 (296.3, 0.15333)

0.50

(328.9, 0.29193)

0.40 0.30

(343.2, 0.20627)

0.20 0.10 0.00 250

Figure

8b.

Top:

300

350

Experimental

defg:2’,1’,8’,7’-ijkl]pentaphene

(L).


UV-Vis

absorption

Bottom:

500

spectrum

Calculated

dinaphtho[2,1,8,7-defg:2’,1’,8’,7’-ijkl]pentaphene (L).


of

ZINDO/S

550

dinaphtho[2,1,8,7spectrum

of


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3.1.5. Calculation of the Positions of Maximum Absorbance for the p and β Bands of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII). The positions of maximum absorbance for the p and β bands of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII) are calculated using coronene (LXXII) and benzo[a]coronene (LVIII), two reference PAHs with UV-Vis spectral bands available in the literature,1 as it is described in Figure 9a. Figure 9a shows (in red) the structural correlation between compound LXXII, compound LVIII, compound X, and compound XIII and the sextet migration shown by the arrows. As it can be evidenced in Figure 9a, the addition of one ring to compound LXXII, to form compound LVIII, causes the ceasing of the sextet migration in compound LVIII. Even though compound LVIII presents one more sextet in the structure, than compound LXXII, it has a HOMO-LUMO gap which is smaller (redder last p band) and therefore less stable. Compound LXXII has only three sextets in the structure but these sextets are moving or migrating, and in circular motion, as the arrows show, thus creating a sextet ring current or superaromaticity2 (see introduction) which confers an extra-stability to the system. Annellation changes applied to compound LXXII, compound LVIII, compound X, and compound XIII will have, in general, the same effect in the positions of maximum absorbance for the p and β bands if the presence or absence of superaromatic current is preserved. Using this assertion, the addition of one ring to compound LXXII to form compound LVIII would produce the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of one ring to compound LVIII to form compound X. Analogously, the addition of one ring to compound LXXII to form compound LVIII would produce the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of one ring to compound LVIII to form compound XIII.


Page 33 of 61


33


Structure

Compound

LXXII

Structure

LVIII



λp, nm

λβ, nm

λp, nm

λβ, nm

342 336 326

305 290

376 358 343

320 308

X

XIII

Predicted UV-Vis Bands Positions λp, nm

λβ, nm

410 380 360

335 326

UV-Vis Absorption Spectra of Compound XIII1 and Compound X1 341

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

310 326 XIII 330

363 381 401

X 215

423

379 400

UV-Vis Abs + 80%

316

265


UV-Vis Abs + 0%

415

Figure 9a. Top: Prediction of the positions of maximum absorbance for the p and β bands of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII). Bottom: Experimental UV-Vis absorption spectrum of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII).

Based on this reasoning, the predicted positions of maximum absorbance for the p and β bands of compound X and compound XIII will be equal to the positions of maximum



Page 34 of 61

34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

absorbance for the p and β bands of compound LVIII plus the difference between the positions of maximum absorbance for the p and β bands of compounds LVIII and compound LXXII. Consequently, the predicted positions for the p bands of compound X and compound XIII are equal to 410 nm, 380 nm, and 360 nm, and the predicted positions for the β bands of compound X and compound XIII are equal to 335 nm and 326 nm. The UV-Vis absorption spectra of compound X and compound XIII published in the literature1 is present at the bottom of Figure 9a. Regarding compound X, the published positions of maximum absorbance for the p bands are equal to 401 nm, 381 nm, and 363 nm, and the published positions of maximum absorbance for the β bands are equal to 330 nm and 316 nm. Thus, the absolute error between the predicted and the published values does not exceed 3%. With respect to compound XIII, the published positions of maximum absorbance for the p bands are equal to 423 nm, 400 nm, and 379 nm, and the published positions of maximum absorbance for the β bands are equal to 341 nm, 326 nm, and 310 nm. The absolute error between the predicted and the published values does not exceed 5%. The annellation process going from LXXII to LVIII causes the sextet migration to stop – because the migration of any of the sextets, in LVIII, would increase the valence of some of the carbon atoms. Then the annellation of LVIII to transit to X causes the occurrence of sextet migration, as shown by the arrows in X, see Figure 9a, but the sextet migration is not circular. On the other hand, the annealing of LVIII to transit to XIII causes also the occurrence of sextet migration -depicted by the arrow in XIII, see Figure 9a. While Annellation Theory predicts the same spectral band positions for X and XIII, the experimental spectra (bottom section in Figure 9a) shows that X is more stable (bluer) than XIII (redder) due to the fact that there is more sextet migration in X than in XIII, as explained above.


Page 35 of 61


35 In Figure 9b there is a comparison between the experimental spectra of X1 and XIII1 with the calculated spectra using the theoretical semi-empirical ZINDO/S method.

X

XIII

UV-Vis Absorbance1

341 310 326 330

400 423

379

215

1.20

265

(267.8, 0.08989) 0.80

401


(292.5, 0.35853) (249.7, 0.18285)

1.00

UV-Vis Abs + 80%

316 363 381


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

UV-Vis Abs + 0%

415

(309.4, 1.00000) (321.0, 1.00000)

(288.1, 0.43622)

0.60

(395.6, 0.08658)

0.40 0.20 (399.1, 0.07810) 0.00 215

265


415

465

Figure 9b. Top: Experimental UV-Vis absorption spectrum of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII). Bottom: Calculated ZINDO/S spectrum of dibenzo[a,j]coronene (X) and naphtho[2,3-a]coronene (XIII).



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36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

As it can be seen the predicted spectra present the main characteristics, where X is bluer than XIII, and also where XIII presents more bands in the UV-Vis region than X. Among the p bands, only the p band corresponding to the HOMO-LUMO gap was calculated with ZINDO/S. 3.1.6. Calculation of the Positions of Maximum Absorbance for the p and β Bands of dibenzo[a,g]coronene (IX). The positions of maximum absorbance for the p and β bands of dibenzo[a,g]coronene, IX, are calculated using benzo[ghi]perylene (LXXIII), dibenzo[b,pqr]perylene (LXXIV), and benzo[a]coronene (LVIII), three reference PAHs with UV-Vis spectral bands available in the literature,1 as it is described in Figure 10a. Figure 10a shows (in red) the structural correlation between compound LXXIII and compound LVIII, which includes the same location of the 3 sextets and the same location of the isolated double bond. Due to this correlation, annellation changes applied to compound LXXIII and compound LVIII, in this red region, will produce similar effects in the positions of maximum absorbance for the p and β bands. Applying this observation, the addition of one ring to compound LXXIII to form compound LXXIV produces the same shifts in the positions of maximum absorbance for the p and β bands as the shifts produced due to the addition of a ring to compound LVIII to form compound IX. Thus, the predicted positions of maximum absorbance for the p and β bands of compound IX will be equal to the positions of maximum absorbance for the p and β bands of compound LVIII plus the difference between the positions of maximum absorbance for the p and β bands of compound LXXIV and compound LXXIII. As a result, the predicted positions for the p bands of compound IX are equal to 366 nm, 350 nm, and 338 nm, and the predicted positions for the β bands of compound IX are equal to 327 nm and 313 nm. The UV-Vis absorption spectrum of compound IX published in the literature1 is also present in Figure 10a. The published positions


Page 37 of 61


37

of maximum absorbance for the p bands are equal to 379 nm, 360 nm, and 349 nm, and the published positions of maximum absorbance for the β bands are equal to 328 nm and 314 nm.


Structure

Compound

Structure

LXXIII

LXXIV



λp, nm

λβ, nm

λp, nm

λβ, nm

388 367 348

303 292

378 359 343

310 297

LVIII

IX



λβ, nm 320 308

376 358 343

λp, nm 366 350 338

λβ, nm 327 313

UV-Vis Absorption Spectrum of Compound IX1 328

UV-Vis Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

300

314 349 360

320

340

379


400

420

440

Figure 10a. Top: Prediction of the positions of maximum absorbance for the p and β bands of dibenzo[a,g]coronene

(IX).

Bottom:

Experimental

UV-Vis

dibenzo[a,g]coronene (IX).


absorption

spectrum

of


Page 38 of 61

38

The absolute error between the predicted and the published values does not exceed 3%. In Figure 10b there is a comparison between the experimental spectrum of IX1 and the calculated spectrum using the theoretical semi-empirical ZINDO/S method.

UV-Vis Absorbance1

328

300

1.20 Normalized Oscillator Strength

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

IX

314 349

320

340

360

379


400

420

440

420

440

(305.2, 0.83674) (310.2, 1.00000)

1.00 0.80 0.60 0.40

(377.5, 0.04931)

0.20 0.00 300

320

340


400

Figure 10b. Top: Experimental UV-Vis absorption spectrum of dibenzo[a,g]coronene (IX). Bottom: Calculated ZINDO/S spectrum of dibenzo[a,g]coronene (IX).


Page 39 of 61


39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

As it can be seen the predicted spectrum presents the strongest p and β bands. Among the p bands, only the p band corresponding to the HOMO-LUMO gap was calculated with ZINDO/S. The differences in values are due to the fact that solvent is not considered in the calculation. 3.2. Calculation of the Positions of Maximum Absorbance for the p and β Bands of the C32H16 Benzenoid PAHs with Unknown UV-Vis Spectra. In the former section (see Validation of the Methodology for the Annellation Theory Analysis) the predictive power and methodology of the Annellation Theory has been proven and validated by comparing the Annellation Theory-predicted maximum absorbance for the p and β bands of seven C32H16 PAH isomers (XXII, XLVI, XLIX, L, X, XIII, and IX) with their respective reported experimental spectra.1,20,21 In this section the Annellation Theory has been used for the prediction of the positions of maximum absorbance for the p and β bands of the 39 C32H16 benzenoid PAHs with unknown UV-Vis spectra. Figure 11 presents the structures and the positions of maximum absorbance for the p and β bands of the reference PAHs, used in the Annellation Theory analysis, and the predicted positions of maximum absorbance for the p and β bands of the 39 C32H16 benzenoid PAH isomers with unknown UV-Vis spectra. With the exception of the catacondensed PAHs, the positions of the sextets have been obtained by the application of the Y-Rule for pericondensed PAHs (see the Introduction).



Page 40 of 61

λp, nm λβ, nm

λp, nm λβ, nm

289 278 267

UV-Vis

332 317 304

λp, nm λβ, nm 297 290 269

395 374 355

385 364 347

297 284 274

UV-Vis36

B. UV-Vis Bands Prediction of XII

UV-Vis1

A. UV-Vis Bands Prediction of XI

λp, nm λβ, nm 439 415 394

328 320

λp, nm λβ, nm 376 358 343

320 308

UV-Vis

320 308

λp, nm λβ, nm 383 363 347

308 297

XII

UV-Vis1

376 358 343

UV-Vis

λp, nm λβ, nm

λp, nm λβ, nm 374 357 343

331 321

λp, nm λβ, nm

λp, nm λβ, nm

332 317 304

289 278 267

λp, nm λβ, nm 328 315

288 278

332 317 304

289 278 267

UV-Vis1

D. UV-Vis Bands Prediction of XV

UV-Vis1

C. UV-Vis Bands Prediction of XIV

UV-Vis1

UV-Vis1

UV-Vis1

XI

322 308 293

λp, nm λβ, nm 402 383

321 308

λp, nm λβ, nm 406 385 364

322 308 293

UV-Vis

406 385 364

λp, nm λβ, nm 378 360 343

307 295

XV

UV-Vis1

λp, nm λβ, nm

UV-Vis

XIV

UV-Vis1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

UV-Vis1

40

λp, nm λβ, nm 452 428 403

340 325

Figure 11. Prediction of the positions of maximum absorbance for the p and β bands of the 39

C32 H16 benzenoid PAH with unknown UV-Vis spectra.


Page 41 of 61


λp, nm λβ, nm

λp, nm λβ, nm

289 278 267

λp, nm λβ, nm 378 360 343

307 295

332 317 304

289 278 267

λp, nm λβ, nm

UV-Vis

332 317 304

UV-Vis1

F. UV-Vis Bands Prediction of XVII

UV-Vis1

E. UV-Vis Bands Prediction of XVI

λp, nm λβ, nm 452 428 403

340 325

λp, nm λβ, nm 374 354 338

300 288

UV-Vis1

310 297

UV-Vis1

UV-Vis1

378 359 343

406 385 364

322 308 293

λp, nm λβ, nm 328 315

288 278

363

334 318

λp, nm λβ, nm 367

344 327 313

UV-Vis

λp, nm λβ, nm

UV-Vis3

344 327 313

UV-Vis

367

λp, nm λβ, nm 469 442 415

330 320 295

λp, nm λβ, nm 350 340

316 302

XIX

XVIII λp, nm λβ, nm

297 290 269

H. UV-Vis Bands Prediction of XIX

G. UV-Vis Bands Prediction of XVIII

λp, nm λβ, nm

λp, nm λβ, nm

UV-Vis

322 308 293

UV-Vis1

406 385 364

395 374 355

XVII

UV-Vis1

λp, nm λβ, nm

UV-Vis

UV-Vis1

XVI

UV-Vis3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

UV-Vis1

41


372 351

Figure 11. Prediction of the positions of maximum absorbance for the p and β bands of the 39 C32 H16 benzenoid PAH with unknown UV-Vis spectra (continued).



Page 42 of 61

λp, nm λβ, nm

332 317 304

289 278 267

λp, nm λβ, nm 378 360 343

307 295

328 315

288 278

UV-Vis34

λp, nm λβ, nm

UV-Vis1

J. UV-Vis Bands Prediction of XXI

UV-Vis1

I. UV-Vis Bands Prediction of XX

413

362 344

λp, nm λβ, nm 395 374 355

297 290 269

UV-Vis1

297 284 274

UV-Vis

UV-Vis1

385 364 347

367

344 327 313

λp, nm λβ, nm 434 406 387

251 245

λp, nm λβ, nm 470 440 415

326 318 295

λp, nm λβ, nm 460 430 407

326 312 300

UV-Vis

326 312 300

312 298 285


368 347

λp, nm λβ, nm 435 408 385

260 230

XXIV

UV-Vis33

460 430 407

UV-Vis

XXIII λp, nm λβ, nm

395 386 370

L. UV-Vis Bands Prediction of XXIV

K. UV-Vis Bands Prediction of XXIII

λp, nm λβ, nm

λp, nm λβ, nm

UV-Vis

λp, nm λβ, nm

UV-Vis1

367

344 327 313

λp, nm λβ, nm

XXI

UV-Vis3

λp, nm λβ, nm

UV-Vis

UV-Vis3

XX

UV-Vis33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

UV-Vis1

42

λp, nm λβ, nm 461 432 405

335 297



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43

251 245

λp, nm λβ, nm 435 408 385

260 230

λp, nm λβ, nm 385 364 347

297 284 274

UV-Vis1

434 406 387

N. UV-Vis Bands Prediction of XXVI

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

M. UV-Vis Bands Prediction of XXV

335 297

λp, nm λβ, nm 418 394 373

311 298 272

UV-Vis1

UV-Vis1

O. UV-Vis Bands Prediction of XXVII

λp, nm λβ, nm 458 430 406

315 302

460 430 407

326 312 300

UV-Vis

461 432 405

λp, nm λβ, nm

λp, nm λβ, nm 385 364 347

297 284 274

λp, nm λβ, nm 500 466 440

330 316

λp, nm λβ, nm 460 430 407

326 312 300

UV-Vis

326 312 300

297 285 272

λp, nm λβ, nm 472 441 417

326 313 298

λp, nm λβ, nm 451 424 401

314 301 290

XXVIII

UV-Vis33

460 430 407

UV-Vis

XXVII λp, nm λβ, nm

397 375 357

P. UV-Vis Bands Prediction of XXVIII

UV-Vis1

326 312 300

λp, nm λβ, nm

UV-Vis33

460 430 407

λp, nm λβ, nm

XXVI

UV-Vis1

λp, nm λβ, nm

UV-Vis

UV-Vis33

XXV

UV-Vis33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 526 490 461

343 329 316




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44

251 245

λp, nm λβ, nm 503 473 445

276

λp, nm λβ, nm 385 364 347

297 284 274

UV-Vis1

434 406 387

R. UV-Vis Bands Prediction of XXX

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

Q. UV-Vis Bands Prediction of XXIX

λp, nm λβ, nm 529 497 465

351

λp, nm λβ, nm 402 392 363

329 316 303

UV-Vis1

333 318 305

UV-Vis1

UV-Vis38

407 384 364

449 423 402

343 327 313

λp, nm λβ, nm 385 364 347

297 284 274

λp, nm λβ, nm 444 431 401

339 325 311

λp, nm λβ, nm 449 423 402

343 327 313

UV-Vis

343 327 313

307 295

λp, nm λβ, nm 442 419 398

353 338

λp, nm λβ, nm 381 362 345

308 295

XXXII

UV-Vis22

449 423 402

UV-Vis

XXXI λp, nm λβ, nm

378 360 343

T. UV-Vis Bands Prediction of XXXII

S. UV-Vis Bands Prediction of XXXI

λp, nm λβ, nm

λp, nm λβ, nm

UV-Vis

326 312 300

UV-Vis37

460 430 407

λp, nm λβ, nm

XXX

UV-Vis22

λp, nm λβ, nm

UV-Vis

UV-Vis33

XXIX

UV-Vis22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 445 421 400

354 338

Figure 11. Prediction of the positions of maximum absorbance for the p and β bands of the 39 C32H16 benzenoid PAH with unknown UV-Vis spectra (continued).


Page 45 of 61


45

281 272

λp, nm λβ, nm 321 306

293 281 261

λp, nm λβ, nm 385 364 347

297 284 274

UV-Vis1

315 303 296

V. UV-Vis Bands Prediction of XXXIV

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

U. UV-Vis Bands Prediction of XXXIII

355 336

λp, nm λβ, nm 407 384 364

333 318 305

UV-Vis38

UV-Vis38

W. UV-Vis Bands Prediction of XXXV

λp, nm λβ, nm 450 426 402

369 350 333

449 423 402

343 327 313

UV-Vis

455 426

λp, nm λβ, nm

λp, nm λβ, nm 315 303 296

281 272

λp, nm λβ, nm 492 465 440

379 359 341

λp, nm λβ, nm 449 423 402

343 327 313

UV-Vis

343 327 313

297 285 272

λp, nm λβ, nm 461 434 412

343 328 311

λp, nm λβ, nm 372 354 338

308 295 284

XXXVI

UV-Vis22

449 423 402

UV-Vis

XXXV λp, nm λβ, nm

397 375 357

X. UV-Vis Bands Prediction of XXXVI

UV-Vis1

343 327 313

λp, nm λβ, nm

UV-Vis22

449 423 402

λp, nm λβ, nm

XXXIV

UV-Vis1

λp, nm λβ, nm

UV-Vis

UV-Vis22

XXXIII

UV-Vis22

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 506 474 444

370 350




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46

297 285 272

λp, nm λβ, nm 297 285 268

385 364 347

λp, nm λβ, nm 444 416 392

326 312 299

UV-Vis3

397 375 357

Z. UV-Vis Bands Prediction of XXXVIII

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

Y. UV-Vis Bands Prediction of XXXVII

λp, nm λβ, nm 465 434 405

330 317 300

λp, nm λβ, nm 475 443 416

354 337 318

UV-Vis1

326 312 299

UV-Vis3

UV-Vis1

444 416 392

437 412 389

477 445 415

330 317 304

λp, nm λβ, nm 470 441 412

λp, nm λβ, nm 444 416 392

326 312 299

475 443 416

358 342 323

λp, nm λβ, nm 477 445 415

330 317 304

UV-Vis

λp, nm λβ, nm 508 472 439

354 337 318

XL

UV-Vis23

330 317 304

UV-Vis

477 445 415

346 332

λp, nm λβ, nm

XXXIX λp, nm λβ, nm

342 327

AB. UV-Vis Bands Prediction of XL

AA. UV-Vis Bands Prediction of XXXIX

λp, nm λβ, nm

λp, nm λβ, nm

UV-Vis

330 317 304

UV-Vis3

477 445 415

λp, nm λβ, nm

XXXVIII

UV-Vis23

λp, nm λβ, nm

UV-Vis

UV-Vis23

XXXVII

UV-Vis23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 508 472 439

358 342 323



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47

335 320

446 420 397

327 317

λp, nm λβ, nm 359 344 329

290 280 267

UV-Vis3

458 431 406

λp, nm λβ, nm

AD. UV-Vis Bands Prediction of XLII

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

AC. UV-Vis Bands Prediction of XLI

520 487 456

340 329

λp, nm λβ, nm 359 344 329

290 280 267

UV-Vis1

UV-Vis1

AE. UV-Vis Bands Prediction of XLIII

λp, nm λβ, nm 516 480 450

325 311 290

λp, nm λβ, nm 433 408 385

310 297 287

UV-Vis

λp, nm λβ, nm

λp, nm λβ, nm 503 473 445

276

λp, nm λβ, nm 590 544 506

345 328 310

λp, nm λβ, nm 663 603 556

312 301 290

UV-Vis

310 297 287

362 345 328

λp, nm λβ, nm 512 479 449

382 362 348

λp, nm λβ, nm 589 545 509

294

XLIV

UV-Vis1

433 408 385

UV-Vis

XLIII λp, nm λβ, nm

438 415 393

AF. UV-Vis Bands Prediction of XLIV

UV-Vis39

348 332 323

UV-Vis1

532 498 465

λp, nm λβ, nm

XLII

UV-Vis1

λp, nm λβ, nm

UV-Vis

UV-Vis

XLI

UV-Vis1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 749 675 620

330




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48

251 245

λp, nm λβ, nm 435 408 385

260 230

λp, nm λβ, nm 406 385 364

322 308 293

UV-Vis1

434 406 387

AH. UV-Vis Bands Prediction of XLVII

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

AG. UV-Vis Bands Prediction of XLV

664 605 554

321 286

λp, nm λβ, nm 388 367 348

303 292

UV-Vis1

272 262 251

UV-Vis1

UV-Vis1

334 318 305

470 440 410

446 420 395

331

λp, nm λβ, nm 510 475 441

λp, nm λβ, nm 334 318 305

272 262 251

λβ, nm

433 408 385

310 297 287

λp, nm λβ, nm 524 489 453

325

λp, nm λβ, nm 470 440 410

294

UV-Vis

LI

UV-Vis1

294

UV-Vis

470 440 410

303

λp, nm

XLVIII λp, nm λβ, nm

294

AJ. UV-Vis Bands Prediction of LI

AI. UV-Vis Bands Prediction of XLVIII

λp, nm λβ, nm

λp, nm λβ, nm

UV-Vis

312 301 290

λp, nm λβ, nm

UV-Vis1

663 603 556

λp, nm λβ, nm

XLVII

UV-Vis1

λp, nm λβ, nm

UV-Vis

UV-Vis1

XLV

UV-Vis1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 569 530 490

332



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49

221

λp, nm λβ, nm 251 245

434 406 387

λp, nm λβ, nm 385 364 347

297 284 274

UV-Vis1

285 275 266

AL. UV-Vis Bands Prediction of LIII

UV-Vis1

λp, nm λβ, nm

UV-Vis1

UV-Vis1

AK. UV-Vis Bands Prediction of LII

582 539 506

340

λp, nm λβ, nm 475 443 416

354 337 318

UV-Vis

310 297 287

λp, nm λβ, nm

UV-Vis3

433 408 385

UV-Vis

UV-Vis1

λp, nm λβ, nm

λp, nm λβ, nm 433 408 385

310 297 287

LIII

LII

λp, nm λβ, nm 523 487 454

367 350 331

λp, nm λβ, nm 334 318 305

272 262 251

UV-Vis1

UV-Vis1

AM. UV-Vis Bands Prediction of LIV

λp, nm λβ, nm 433 408 385

310 297 287

λp, nm λβ, nm 470 440 410

294

UV-Vis

LIV

UV-Vis1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

λp, nm λβ, nm 569 530 490

332




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50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The positions of maximum absorbance for the p and β bands of XI and XII involve the fusion onto a ring of benzo[a]coronene (LVIII), see bottom part of the frames A and B in Figure 11. In the case of PAH XI the fusion occurs onto a ring, of benzo[a]coronene (LVIII), with sextet carbon, to form compound XI. The annellation effect produces a considerable red shift of the bands in compound XI. For the case of compound XII a “lesser” Clar structure2,12 is shown for benzo[a]coronene (LVIII) where only three resonant sextets are depicted, see bottom part of the frame B in Figure 11, instead of four resonant sextets. The higher the number of resonant sextets are present in a PAH structure, the higher its kinetic stability is;10 therefore, LVIII has four resonant sextets. However, the “lesser” Clar structure is shown in the analysis of the frame B in Figure 11 exclusively to be clear on how the upper part of this analysis correlates with the bottom part. There is sextet migration in both cases of the frame B (bottom part) in Figure 11 that encloses the four sextets in the benzo[a]coronene region of XII. The positions of maximum absorbance for the p and β bands of the reference PAH LXIII, peri-naphthacenonaphthacene (see PAH with 8 fused aromatic rings, 8 FAR, at the left and bottom part of the frame AC in Figure 11) have been deduced following the same procedure applied by McClaine, et.al.22 to predict the position of maximum absorbance for the last p band of peri-naphthacenonaphthacene. 3.3. Comparison between the Wavelength of the Last p Band, predicted with the Annellation Theory, and the calculated HOMO-LUMO Gap Wavelength obtained with the Semi-empirical ZINDO/S Methodology.. The positions of maximum absorbance obtained by application of the Annellation Theory for the last p band of the UV-Vis spectra of the 39 C32H16 benzenoid PAHs present in Figures 5a-10a


Page 51 of 61


51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

and in Figure 11 have been compared with the theoretical HOMO-LUMO gap wavelength calculated with the semi-empirical ZINDO/S method. In Table 4 the ZINDO/S HOMO-LUMO gap energy is tabulated for all the systems.

System IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII

λ(nm) 377.5 395.6 400.0 386.4 399.1 396.4 450.3 420.5 452.6 375.1 400.8 410.4 413.3 436.5 456.5 452.1 448.2 429.0 489.4 497.4 516.4 428.5 439.7 459.3 443.0 464.1 484.4 488.1 488.2 499.7 506.3 534.7 500.7 513.2 555.8

Oscillator Strength (arbitrary units, au) 0.12491 0.28576 0.21718 0.05207 0.23289 0.92365 0.84790 0.99503 1.01468 0.08917 0.25751 0.14960 0.21362 0.64788 0.77133 0.90554 0.71537 0.60394 0.72477 0.65876 0.71211 0.77698 0.99219 1.00381 0.80626 1.18215 0.95136 0.73726 1.50671 1.37571 1.72180 1.83442 0.95933 1.40614 0.94909

Table 4. Calculated ZINDO/S HOMO-LUMO for C32 H16 benzenoid PAHs.



Page 52 of 61

52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

System XLIV XLV XLVI XLVII XLVIII XLIX L LI LII LIII LIV

λ(nm) 688.2 602.9 480.4 491.6 441.1 494.2 514.0 557.6 580.4 514.6 526.3

Oscillator Strength (arbitrary units, au) 0.84583 0.94278 1.13114 1.39704 0.87006 1.69339 1.24619 1.02759 1.33836 1.77384 1.41226

Table 4. Calculated ZINDO/S HOMO-LUMO for C32 H16 benzenoid PAHs (continued).

In Figure 12 the comparison between the Annellation Theory predictions and the HOMOLUMO gap wavelength calculations for the last p band of the spectrum is shown. As it can be seen in general there is a satisfactory agreement between the prediction of the Annellation Theory and the calculated HOMO-LUMO gaps with an average wavelength difference of 18 nm. The difference between the Annellation Theory predictions and the HOMO-LUMO calculated gaps stems mainly from the fact that in the Annellation Theory experimental data is used which includes solvent while the theoretical semi-empirical calculations were carried out without the inclusion of solvent. The difference between the theoretical and experimental data could be due to the Stokes shift, which involves the reconfiguration of the solvent cage for the ground electronic state once the excited molecule of PAH undergoes photoemission. The Stokes shift to the red is reported to be around 10-45 nm for solvents with low polarity.


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53

LIV LIII LII LI L XLIX XLVIII XLVII XLVI XLV XLIV

XLIII XLII XLI XL XXXIX

XXXVIII XXXVII XXXVI XXXV XXXIV

Compound

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

XXXIII XXXII XXXI XXX XXIX XXVIII XXVII XXVI XXV XXIV XXIII

XXII XXI XX XIX XVIII XVII XVI XV XIV XIII XII XI X IX

0

100

200

300 400 500 Wavelength (nm)

600

700

800

Figure 12. Comparison between the Annellation Theory predictions of the positions of maximum absorbance for the last p band, denoted with blue bars, and the ZINDO/S HOMOLUMO gap wavelength calculations, denoted with red bars, of the C32 H16 benzenoid PAHs.



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4. CONCLUSIONS. The results obtained here demonstrate the usefulness of the Annellation Theory methodology for the prediction of the positions of maximum absorbance for the p and β bands of the 46 benzenoid C32H16 PAHs. Initially, the methodology has been validated using the 7 C32H16 PAHs with experimental UV-Vis spectra published in the literature. The results indicate that the difference between the predicted and the experimental values is lower than 5%. Knowing the exactness of the Annellation Theory calculations for these 7 PAHs, the methodology has been extended to the prediction of the positions of maximum absorbance for the p and β bands of the other 39 PAH isomers with unknown UV-Vis spectra. As a way to evaluate the consistency of these predictions, the values calculated by means of the Annellation Theory of the positions of maximum absorbance for the last p band of the 39 PAHs with unknown UV-Vis spectra have been compared with the corresponding HOMO-LUMO gap wavelength calculated at the ZINDO/S semi-empirical level. The comparison indicates a satisfactory agreement between the Annellation Theory approach and the semi-empirical point of view with an average wavelength difference of 18 nm, which is equivalent to the stokes shift due to solvent, which has not been considered in the ZINDO/S calculations. The semi-empirical ZINDO/S method is not able to reproduce all of the p and β bands, as it can be seen in the calculated absorption spectra presented in Figures 5b-10b. The ZINDO/S method can only predict the most intense p and β bands. To calculate all the bands, it would be necessary to perform singlet and triplet high level DFT-TD (time dependent density functional theory) calculations with a hybrid functional, which becomes computationally expensive. Due to the novel and reliable results obtained in this study, it is concluded that the Annellation Theory is a useful and powerful tool for the prediction of the positions of maximum absorbance of aromatic compounds with unknown UV-Vis spectra,


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allowing this, among others, the potential identification of PAHs in samples. To the best of our knowledge, it is the first time that the UV-Vis spectral information of the 39 benzenoid C32H16 PAHs with unknown UV-Vis has been predicted. 5. AUTHOR INFORMATION Corresponding Author *Guest Researcher, National Institute of Standards and Technology, NIST, 100 Bureau Drive, Mail Stop 8390, Gaithersburg, Maryland 20899, Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. 6. ABBREVIATIONS UV-Vis, Ultraviolet-Visible; PAH, Polycyclic Aromatic Hydrocarbons; AT, Annellation Theory; FAR, Fused Aromatic Rings 7. REFERENCES (1) Clar, E. Polycyclic Hydrocarbons; Academic Press: New York, 1964. (2) Clar, E. The Aromatic Sextet; Wiley-Interscience: New York, 1972. (3) Fetzer, J. C. Large (C >= 24) Polycyclic Aromatic Hydrocarbons: Chemistry and Analysis; Wiley-Interscience: New York, 2000. (4) Oña, J. O.; Wornat, M. J. The Influence of Solvents on the Ultraviolet-Visible Absorption Spectra of Polycyclic Hydrocarbons: Applications in the Identification of Fuel Products by HPLC/UV/MS. Polycyclic Aromat. Compd. 2008, 28, 15-38.



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TABLE OF CONTENTS GRAPHIC


The Predictive Power of the Annellation Theory: The Case of the

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