extended y rule method for the characterization of the

Extended Y‑Rule Method for the Characterization of the AromaticSextets in Cata-Condensed Polycyclic Aromatic HydrocarbonsJorge O. Ona-Ruales*,† and Yosadara Ruiz-Morales‡

†National Institute of Standards and Technology, NIST, Gaithersburg, Maryland 20899, United States‡Instituto Mexicano del Petroleo, Eje Central Lazaro Cardenas Norte 152, Mexico City 07730, Mexico

ABSTRACT: The location, number, and migrating behavior of the sextets in the cata-condensed benzenoid polycyclic aromatic hydrocarbons with available bay regionshave been determined by a new proposed topological methodology called theextended Y-rule. The precursor of this rule is the well-known Y-rule method fordetermining sextets in peri-condensed polycyclic aromatic hydrocarbons. The newmethodology has been successfully validated by means of literature information and bytheoretical nucleus independent chemical shift (NICS) calculations. Even though thefamilies of polycyclic aromatic hydrocarbons analyzed here comprise the C14H10,C18H12, C22H14, and C26H16 isomers, the procedure can practically be extended to thefamilies C(10+4x)H(8+2x), where x = 1, ..., ∞. It is the first time that a straightforwardprocedure, easy to apply, has been proposed to obtain the sextets arrangement andbehavior in the group of cata-condensed benzenoid polycyclic aromatic hydrocarbons.

1. INTRODUCTION

The complete characterization of the sextets inside of polycyclicaromatic hydrocarbons, PAHs, in terms of arrangement andmigrating behavior is important in order to recognize the PAHchemical stability and reactivity1−3 and to understand thespectral absorption responses that provide an unambiguousidentity of each PAH molecule.3−5

Several theoretical methods have been applied to evaluatequalitatively and quantitatively the aromatic character of PAHsin general and cata-condensed PAHs, also known as ortho-fused PAHs in IUPAC notation, in particular. The methodsinclude the para-delocalization index, PDI; the harmonicoscillator model of aromaticity, HOMA; and the nucleusindependent chemical shift, NICS. Although PDI, HOMA, andNICS are consistent with the information obtained from Clarstructures,6 all of these methods require quantum chemistrycalculations that involve computationally expensive procedures.Randic and co-workers considered partitions of π-electrons

associated with CC bonds of Kekule valence structures toindividual rings,7−11 mainly for cata-condensed PAHs, whileGutman and co-workers considered partition the Pauling bondorders to individual rings.12 In both studies the contributionsfrom bonds adjacent to two rings were divided between the tworings. Later on, Randic made the distinction where thecontributing Pauling bond orders are not partitioned betweenthe neighboring rings, allowing the numerical characterizationof individual benzene rings as fully aromatic, intermediate, andweakly aromatics.13 A limitation for these methods is that allthe Kekule structures have to be found for a given PAH, whichis not an easy task in many cases and in particular for large PAHsystems.An approach for the characterization of the aromatic sextets

in cata-condensed PAHs based on a graphical manipulation of

the molecular structure has been reported by Klavzar et al.14

According to these authors, the number of sextets in a cata-condensed PAH is given by the minimum number of segmentlines that cross all of the benzenoid rings. However, thismethod does not give information about the position of thesextets. Randic has mentioned in several papers,11,15,16 withrespect to Klavzar paper, that the line segments should bedrawn so that the number of crossings of lines is maximal. Theplacing of the aromatic sextet then is done in any of the ringsthat have no crossing of lines where there will be “migrating”sextets. However, as far as we know, these statements have notbeen developed further in a publication and neither have theybeen validated.An easy to apply qualitative methodology for the

determination of the locations, number, and migrating directionof the aromatic sextets, i.e., π-electronic distribution inpericondensed PAHs, involves the application of the Y-rule17−19 which produces Clar-type-structures4,20 and that hasbeen widely validated by means of NICS values.21−25 Scheme 1shows the methodology followed by the Y-rule, the simplestapproach, so as to establish the arrangement and behavior ofthe aromatic sextets in peri-condensed PAHs.17−19

The Y-rule details are outlined and widely exemplified in refs17−19. The method presented in Scheme 1 is only applicableto peri-condensed PAHs because it requires the presence of Y-carbons (internal carbons arranged in the vertex of a Y shape)which are physically absent in cata-condensed PAHs.17

Therefore, a method to extend the approach of the Y-rulebeyond the group of peri-condensed PAHs is needed in order

Received: October 8, 2014Revised: November 20, 2014Published: December 2, 2014

Article

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to obtain the sextets arrangement and behavior in the group ofcata-condensed PAHs. The Y-rule method has been success-fully used to determine the structure of the peri-condensedPAHs that are part of the aromatic region in oil asphaltenes,which are very problematic compounds in the oil indus-try,3,26−28 in the identification of a new C28H14 polycyclicaromatic hydrocarbon as a product of supercritical fuelpyrolysis,29 in the analysis of carbon K-edge X-ray Ramanspectroscopy of oil asphaltene studies,30 and in the determi-nation of the aromaticity of cyclopenta-fused PAHs.19

It is the purpose of this work to elucidate the locations,number, and migrating direction of the aromatic sextets in thecata-condensed benzenoid PAHs with one or more availablebay regions (cata-PAHs). With that aim, the locations, number,and migrating direction of the sextets in the structurallyanalogous peri-condensed benzenoid PAHs (peri-PAHs) areused. The π-electronic distribution in the cata-PAHs then isobtained by means of a new proposed methodology thatinvolves the Y-rule; therefore, named the extended Y-rulemethod.The results of the proposed methodology are validated with

published information1,4,16,20 concerning the π-electronicdistribution in low molecular mass cata-PAHs, e.g., C14H10,C18H12, and C22H14, and with calculations of the aromaticityinside of the hexagonal rings using the NICS approach inrepresentative high molecular mass cata-PAHs, e.g., C26H16cata-PAHs.The NICS is defined21 as the negative value of the absolute

isotropic magnetic shielding at some selected point in space,e.g., at the center of a ring that is being probed, NICS(0), orone angstrom above the geometrical center of the ring that isbeing probed, NICS(1). Significant negative NICS values insideof the rings indicates the presence of “aromaticity” whereaspositive values denotes “antiaromaticity”.21,31 Ab initio anddensity functional studies have demonstrated17,19,32 that NICSis a useful indicator of aromaticity and generally correlates wellwith the energetic, geometric, and magnetic criteria foraromaticity.33

It is the first time that a method to connect the peri-condensed PAHs and the cata-condensed PAHs through thearomatic character of the molecules has been proposed. Since

the π-electronic distribution in PAHs is related to the positionof the UV−vis absorption spectral bands,3,4,20,34 this method-ology constitutes the initial step toward the unequivocalidentification of cata-PAHs with unknown synthetic protocolsin a variety of natural and modified environments.

2. COMPUTATIONAL DETAILS

The optimization of the PAH structures was carried out byperforming force-field-based minimization using the energyminimization panel in Materials Studio35 and the COMPASSconsistent force field as embedded in the Material Studiopackage. The COMPASS (condensed-phase optimized molec-ular potentials for atomistic simulation studies)36,37 force fieldwas used in all the optimizations because it has been tested andvalidated extensively against experiment for many organicmolecules.The geometry optimization (structure relaxation) for systems

I and XXVIII was carried out using the high level quantumdensity functional theory (DFT) approach with the self-consistent generalized-gradient GGA and the Perdew−Wang91 (PW91) exchange-correlation potential (DFT GGA-PW91).38 The DNP basis set (double-ζ plus polarizationfunction basis set)39 with a radial cut off of 3.0 Å was used, asimplemented in the DMol3 code,39−41 and instrumented in theinterface of Materials Studio.35

The NICS calculations were carried out using the GIAO−DFT42,43 method as implemented in the Gaussian 0944

package. A dummy atom was located one angstrom abovethe geometrical center of each hexagon in the PAH structuresto calculate the NICS(1). The Becke 1988 functional,45 whichincludes the Slater exchange along with corrections involvingthe gradient of the density was used together with thecorrelation functional of Lee, Yang, and Parr,46 which includesboth local and nonlocal terms, i.e., the B3LYP hybrid functionalwas used. A basis set that is augmented with two sets ofpolarization functions, i.e., the 6-31G(d, p) or 6-31G** basisset,44 was used.NICS(1) has been chosen instead of NICS(0) because in the

calculated NICS(1), at 1 Å above the molecular plane, the π-electron ring current effects are dominant and the σ-bondingcontributions are diminished.47,48

3. RESULTS AND DISCUSSION

In the present study, we present and validate theoretically theperformance of a qualitative heuristic rule to determine thearomaticity of each hexagonal ring in cata-condensed benzenoidpolycyclic aromatic hydrocarbons with available bay regions(cata-PAHs). We have named this rule the extended Y-rulebecause in one of the steps of its methodology of application itmakes use of the Y-rule,17,18 which determines the relativearomaticity in peri-condensed PAHs or peri-PAHs.

3.1. Extended Y-Rule Methodology. The extended Y-rule method is useful exclusively for cata-PAHs which canaccommodate by addition C2H2 units, in a bay region or bayregions, to form peri-PAHs. This excludes several classes ofcata-condensed PAHs such as the linear polyacenes, thehelicenes, and the nonlinear cata-condensed PAHs with onlycove and fjord regions. These distinctive classes of cata-condensed PAHs generate, upon C2H2 addition, peri-PAHs(with five- or seven-sided rings) that do not satisfy the fullybenzenoid requirement for the application of the extended Y-rule method stated in the introduction; thus, they are

Scheme 1. Methodology of the Y-Rule for Establishing theLocations, Number, and Migrating Direction of the Sextetsin Pericondensed Polycyclic Aromatic Hydrocarbons17,18

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unsuitable for the proposed methodology. The suitability andunsuitability of the extended Y-rule method for the character-ization of the aromatic sextets in several cata-condensed PAHsis described in Figure 1.The extended Y-rule method consists of the following steps:Step 1. The known structure of the cata-PAH under analysis

is used to elucidate the parent structure of the peri-PAH byadding n C2H2 units to all of the available n single bay regionsin the σ-backbone of the cata-PAH. The σ-backbone is used inthis step to make the explanation unambiguous.Step 2. The Y-rule method described in Scheme 117−19 is

applied to obtain the locations, number, and migrating behaviorof the sextets in the parent peri-PAH molecule.Step 3. The n C2H2 units, added in step 1, are removed from

the peri-PAH so as to obtain the π-electronic distribution thatindicates the final locations, number, and migrating behavior ofthe sextets in the cata-PAH under analysis.3.2. Electronic Rearrangement during the Conversion

from peri-PAH to cata-PAH. Two scenarios are possible byelectronic rearrangement during the conversion from peri-PAH

to cata-PAH after the removal of n C2H2 units in step 3 (seesection 3.1.).Scenario 1. When in the formed hexagon or hexagons in the

peri-PAH created by the addition of a C2H2 unit or units in step1, and elucidated by application of the Y-rule, in step 2, there isan isolated double bond or a migrating sextet. No changes inthe locations or number of the adjacent sextets are expected instep 3 due to the removal of the C2H2 unit, in the transitionfrom a peri-PAH to a cata-PAH. Concerning the sextetmigrating behavior variations, no changes are anticipated forthe case of the isolated double bond removal, but observabledifferences are predicted for the case of the C2H2 unit removalfrom a migrating sextet that consists in the reduction of thesextet linear path either to a shorter path or to a stationarysextet.The following examples, presented in Figure 2, are given

exclusively to exemplify step 3-scenario 1. They are notexhaustive and are provided as guidance regarding possiblesituations that can be encountered during the application of theextended Y-rule methodology. The electronic rearrangement

Figure 1. Suitability of the extended Y-rule method for cata-condensed PAHs with one or more bay regions and unuitability of the extended Y-rulemethod for cata-condensed PAHs with no bay regions. The σ-backbone is used for clarity.

Figure 2. Two examples of step 3-scenario 1 depicting the change of the positions, number, and migrating behavior in the transitions from coroneneto triphenylene and from benzo[de]naphtho[1,2,3-qr]naphthacene to naphtho[2,3-g]chrysene. See text for details.



based on scenario 1 during the conversion from peri-PAH tocata-PAH is exemplified in Figure 2, cases 1 and 2. Case 1describes the transition from coronene (peri-PAH) totriphenylene (cata-PAH). This transition comprises theremoval of three C2H2 units from three single-bay regionswith hexagons in sextet migrating paths. Coronene has threelinear sextet paths with two hexagons from the addition of threeC2H2 units to three single-bay regions performed in step 1. Asobserved in Figure 2, case 1, the removal of the three C2H2units in step 3 does not modify the final sextet locations andnumber but generates a reduction in the linear sextet path fromtwo hexagons to one hexagon with one stationary sextet.Case 2 denotes the transition from benzo[de]naphtho[1,2,3-

qr]naphthacene (peri-PAH) to naphtho[2,3-g]chrysene (cata-PAH). This transition involves the removal of one isolateddouble bond from a single-bay region. Benzo[de]naphtho-[1,2,3-qr]naphthacene has one isolated double bond from theaddition of one C2H2 unit to a single-bay region performed instep 1. As described in Figure 2, case 2, in the transition frombenzo[de]naphtho[1,2,3-qr]naphthacene to naphtho[2,3-g]-chrysene, the removal of the C2H2 unit in step 3 does notalter the final sextet locations, number, and migrating behavior.Scenario 2. When in the formed hexagon or hexagons in the

peri-PAH created by the addition of a C2H2 unit or units in step

1, and elucidated by application of the Y-rule, in step 2, there isa stationary sextet.The opening of this sextet to remove the C2H2 unit in step 3,

in the transition from the peri-PAH to the cata-PAH will leavebehind two double bonds whose electrons will be distributed inthe adjacent hexagons where new sextets can be formed if thereis enough electronic density. This new sextet would bestationary or it would migrate if in any of the adjacenthexagons there is a linear path of hexagons with less densitythan in sextets, i.e., a linear path of hexagons with two doublebonds or one double bond (like sextet migration in coronene)but not three double bonds because there cannot be adjacentsextets without exceeding the carbon atoms valence of four.The examples described in Figure 3 are given solely to

illustrate step 3-scenario 2. They are not exhaustive and areprovided as guidance regarding possible situations than can beencountered during the application of the extended Y-rulemethodology. The electronic rearrangement based on scenario2 during the conversion from peri-PAH to cata-PAH isexemplified in Figure 3, cases 1−3.Case 1 describes the transition from benzo[vwx]hexaphene

(peri-PAH) to hexaphene (cata-PAH). This transition involvesthe opening of one sextet in a single-bay region. Benzo[vwx]-hexaphene has one stationary sextet S1 from the addition of

Figure 3. Three examples of step 3-scenario 2 depicting the change of the positions, number, and migrating behavior in the transitions frombenzo[vwx]hexaphene to hexaphene, naphtho[2,3-a]coronene to dibenzo[a,c]tetracene, and naphtho[1,2-a]coronene to dibenzo[f,k]tetraphene. Seetext for details.



one C2H2 unit to a single-bay region performed in step 1, oneadditional stationary sextet S2, and one sextet S3 with a linearpath of two hexagons. The opening of the stationary sextet S1to remove the C2H2 unit in step 3 leaves behind two doublebonds whose electrons will be distributed into two of theadjacent hexagons. As represented in Figure 3, case 1, in thetransition from benzo[vwx]hexaphene to hexaphene, thiselectronic distribution, on one hand, gives rise to a linearpath of two hexagons where the stationary sextet S2 is present,and, on the other hand, causes an increase of the linear path ofthe sextet S3 from two to three hexagons.Case 2 describes the transition from naphtho[2,3-a]coronene

(peri-PAH) to dibenzo[a,c]tetracene (cata-PAH) that involvesthe opening of three sextets in three single-bay regions.Naphtho[2,3-a]coronene has three stationary sextets S4, S5,and S6 from the addition of three C2H2 units to three single-bay regions performed in step 1 and one sextet S7 with a linearpath of two hexagons.The opening of the three stationary sextets S4, S5, and S6 to

remove the three C2H2 units in step 3 leaves behind six doublebonds (two double bonds from each opened sextet) whoseelectrons will be distributed in three of the adjacent hexagons.As described in Figure 3, case 2, in the transition fromnaphtho[2,3-a]coronene to dibenzo[a,c]tetracene, the firsteffect of this electronic distribution is the formation of twostationary sextets S8 and S9 due to the absence of a linear pathwhere isolated double bonds were present, and the secondeffect is an increase of the linear path of the sextet S7 from twoto three hexagons. Finally, case 3 describes the transition fromnaphtho[1,2-a]coronene (peri-PAH) to dibenzo[f,k]tetraphene(cata-PAH) that involves the opening of two sextets in twosingle-bay regions and the opening of one sextet in a double-bay region. Naphtho[1,2-a]coronene has three stationarysextets S10, S11, and S12 from the addition of two C2H2units to two single-bay regions and from the addition of oneC2H2 unit to one double-bay region performed in step 1, andone sextet S13 with a linear path of two hexagons. The openingof the three stationary sextets S10, S11, and S12 to remove thethree C2H2 units in step 3 leaves behind six double bonds (twodouble bonds from each opened sextet) whose electrons will bedistributed in three of the adjacent hexagons. As described inFigure 3, case 3, in the transition from naphtho[1,2-a]coroneneto dibenzo[f,k]tetraphene, and due to the absence of linearpaths for sextet migration, this electronic distribution givesorigin to four stationary sextets S14, S15, S16, and S17.3.3. Cata-PAHs with m (2 ≤ m ≤ 6) Number of Bay

Regions in Series. A special case takes place for systems withdouble, triple, quadruple, quintuple, or sextuple bay regions inseries, which are not single-bay regions, as described in Figure4. For such cases, step 1 of the extended Y-rule methodologyshould start with the addition of the C2H2 unit to one of thebay regions in the series (one C2H2 unit per series) and to all of

the other single-bay regions. The choice of the bay region in theseries for the addition of the C2H2 unit is arbitrary and will notaffect the final locations, number, or migrating behavior of thesextets in the cata-PAH.

3.4. Application of the Extended Y-Rule Method forthe Characterization of the Sextets in the C14H10, C18H12,and C22H14 Cata-PAHs. Using the three-step proceduredescribed above for the extended Y-rule method, thecharacterization of the sextets in the C14H10, C18H12, andC22H14 cata-PAHs has been achieved by means of the parentperi-PAHs. Figure 5 shows the establishment of the sextetlocations, number, and migrating behavior in the C14H10,C18H12, and C22H14 cata-PAHs. The results shown in Figure 5about the characterization of the aromatic sextets in the C14H10,C18H12, and C22H14 cata-PAHs, obtained with the extended Y-rule methodology, are in agreement with the available literatureinformation.1,4,16,20

3.5. Application of the Extended Y-Rule Method forthe Characterization of the Sextets in the C26H16 Cata-PAHs and Validation with NICS Calculations. Theextended Y-rule method for the characterization of the sextetshas also been applied to the C26H16 cata-PAHs. The C26H16cata-PAHs group, i.e., C26H16 benzenoid PAHs with one ormore available bay regions, comprises 28 structures as shown inFigure 6. Figure 6 enumerates the C26H16 cata-PAHs, theirsteric strain5 based on the number of bay, cove, and fjordregions, and their length-to-breadth ratios (L/B),49−51 aparameter extensively used in chromatographic analysis todefine the shape of PAHs. The use of a steric strain argumentand a shape descriptive parameter gives a viable criterion for theselection of suitable C26H16 cata-PAHs that can be used as thesubject of analysis for the extended Y-rule method in lieu of theentire class of compounds.For the application of the extended Y-rule and the validation

by means of the NICS values ten C26H16 cata-PAHs have beenselected. The structures selected comprise dibenzo[g,p]-chrysene (I), naphtho[1,2-g]chrysene (III), dibenzo[a,c]-naphthacene (VIII), dibenzo[b,p]chrysene (X), hexaphene(XI), dibenzo[a,j]naphthacene (XIII), dibenzo[b,k]chrysene(XX), naphtho[2,3-c]chrysene (XXII), benzo[f ]picene(XXVII), and benzo[c]picene (XXVIII). These structureshave been chosen due to their diverse number of bay (1 to4), cove (0 to 2), and fjord (0 to 1) regions and due to thevariety of L/B values, as described in Figure 6.Both the number of bay, cove, and fjord regions, and the L/B

values49−51 of the 10 C26H16 cata-PAHs span the entire range ofsteric strain and L/B that characterize the C26H16 cata-PAHs.Figure 7 shows the application of the extended Y-rule

method for the establishment of the locations, number, andmigrating behavior of the sextets in the 10 C26H16 cata-PAHsselected for this analysis. Due to the limited literatureinformation1,4,16,20 so as to completely validate the results of

Figure 4. Examples of structures with single (1), double (2), triple (3), quadruple (4), quintuple (5), and sextuple (6) bay regions in series. The σ-backbone is used for clarity.



the extended Y-rule method for the characterization of thearomatic sextets elucidated in Figure 7, the validation has beencarried out by comparison with the characterization of thesextets provided by NICS calculations.The establishment of the location, number, and migrating

behavior of the sextets in the 10 C26H16 cata-PAHs by means ofthe NICS21 values is depicted in Table 1 and explained belowwhere the most representative cases are discussed. For thecharacterization of the sextets, it is applied the criteria proposedby Ruiz-Morales,17,19 that relates the highest negative NICS(1)value in each structure to the presence of a sextet in that givenring.

3.5.1. Cases in which the Aromatic Character of a cata-PAH Is Elucidated Using Only the Total NICS Analysis. Forcompound VIII, Table 1 shows that the π-electronic density islocated mainly in ring D and there is sextet migration along therings E-D-C because the NICS(1) values are close. Also, thereare sextets in rings A and F but these sextets do not migratebecause the ring labeled B has a very small NICS(1) value =−3.33, which indicates no presence of π-electronic density.For compound XI, which contains 26 π-electrons and a total

of six fused rings (6FAR), Table 1 shows that the sextets arelocated in the rings B and E, NICS(1) = −11.36 and −12.29,respectively, giving a total of two resonant sextets that comprise12 π-electrons. Thus, the remaining 14 π-electrons are locatedin the rings A, C, D, and F, taking care of not exceeding thevalence of any of the carbon atoms. Due to the fact that theNICS(1) values of rings A and B, and rings D, E, and F are nottoo different, it is considered that there is sextet migration alongthe rings A-B and along the rings D-E-F.For compound XIII, the NICS(1) values in Table 1 suggest

that the π-electronic density is located in rings A and C. Bymolecular symmetry is established that the same π-electronicdensity present in rings A and C is present in rings F and D,respectively. Thus, rings C and D, which have the same π-electronic density, are bonded together. Since two sextetscannot be at adjacent hexagons, due to the violation of thecarbon atoms valence, it is expected the presence of sextetmigration in rings C and D.For compound XX, Table 1 shows that the π-electronic

density is located mainly in rings B and E and there is sextetmigration between rings A and B, and between rings E and F.

3.5.2. Cases in which the Aromatic Character of a cata-PAH is Elucidated Using the Total NICS Analysis Coupledwith the Perpendicular Diamagnetic Shielding Analysis. Thedetermination of the π-electronic distribution (characterizationof the sextets) based on the NICS calculation presentslimitations. The most important constraint has to do with thefact that the NICS value of a particular ring is significantlyinfluenced not only by the higher order circuits (ring currents)encircling the ring at which it is evaluated but also by the localaromaticity of the surrounding rings (as it is stated in Figure 8),and occasionally, the NICS values are even influenced bycurrents farther away in the molecule.17,22,52−57 In the samesense, Fias et al.54,55 have shown that there is a lack of a goodcorrelation between the NICS and the multicenter delocaliza-tion indices. These authors have shown through a thoroughstatistical analysis that the NICS values arise not only from localaromaticity of the benzenoid rings in PAHs but also from othercircuits of current. As it is asserted by these authors, the NICSindex does not reveal the individual aromatic nature of aspecific ring, contrary to the delocalization indices. The lack ofcorrelation between NICS and multicenter aromaticity indicesappears when molecules contain several aromatic rings, wheredifferent circuits of ring currents are contributors to the totalring current and the effect of NICS, as a local aromaticity index,may be seen to reflect, at a chosen point, all ring currents in themolecule. Therefore, NICS cannot be used to assess a degree ofbenzenoid character for a specific ring in a PAH, because NICSnot solely contain the ring current of the particular benzenoidcircuit, NICS contain superimposed ring currents in allhexagons in the molecule. However, if only one circuit ispresent, there are good correlations between NICS andmulticenter delocalization indices.

Figure 5. Application of the extended Y-rule method for thedetermination of the locations, number, and migrating directions ofthe aromatic sextets in the C14H10, C18H12, and C22H14 cata-PAHsusing the peri-PAHs as parent molecules. Each determination involvesthe addition of n C2H2 units (step 1), the application of the Y-rulemethod (step 2), and the removal of n C2H2 units (step 3). In the caseof the PAHs where the arrows of the migrating sextets end in adjacenthexagons, the sextets cannot occupy at the same time these adjacenthexagons. The symbol n corresponds to the number of bay regions inthe cata-PAHs. The blue arrows indicate the direction of the migrationof the sextets.



In cases where the total NICS analysis does not provide thefull location of the aromatic sextets in a cata-PAH, theperpendicular diamagnetic shielding values could be used.17

The relation between the NICS and the diamagnetic shieldingis obtained through the following analysis.The NICS is defined as the negative value of the absolute

isotropic magnetic shielding according to eq 1.

σ

σ σ

= −

= − +

= +

⊥

⊥

⎜ ⎟⎛⎝

⎞⎠

NICS

13

23

13

NICS23

NICS

isotropic

(1)

where σ⊥ and σ∥ are the perpendicular and parallelcomponents, respectively. In the case of benzene σ⊥ isindicative of the π-induced ring current. The component ofthe isotropic chemical shielding perpendicular to the molecularplane, σ⊥ (eq 1), can be written as a sum of a diamagneticcontribution, σ⊥

d , and a paramagnetic contribution, σ⊥p ,

according to eq 2.

σ σ σ= − = − + = +⊥ ⊥ ⊥ ⊥ ⊥ ⊥NICS ( ) NICS NICSd p d p(2)

In benzene, where there is an ideal ring current in the π-system,the paramagnetic contribution in eq 2 vanishes, for symmetryreasons.17,58 Thus, for benzene the π-contribution to σ⊥consists of the diamagnetic part only according to eq 3.

σ= −π− ⊥NICS densityd

(3)

When a molecule is placed into a homogeneous static magneticfield, a current density is induced. This current density inducesadditional fields at the position of the nuclei being tested. Thesituation is presented in Figure 8. The perpendiculardiamagnetic shielding, σ⊥

d (eq 2) stems from a circulation ofthe ground state density (Jd) around the dummy probe inducedby the applied magnetic field, Bo. The circulation results in aninduced magnetic field, Bind

d , which is opposite in direction toBo. The corresponding shielding, σ⊥

d , is as a consequencepositive and NICS⊥

d is negative (see eqs 1 and 2). However, theresulting magnetic field, Bind

d , is parallel to Bo “outside” the loopof the current density Jd and the corresponding shielding σ⊥

d

outside the hexagon been tested, is as a consequence negative(paratropic) and NICS⊥

d is positive (see eqs 1−3).Therefore, the effect of a diatropic π-current, due to the

presence of a resonant sextet in a hexagon of a PAH, is toproduce an induced magnetic field that has a positivecontribution (diatropic) to the total shielding of that hexagonand, thus, a negative NICS; however, the effect of that samediatropic π-current outside the hexagon, where it is located, isto produce a negative (paratropic) contribution to the totalshielding, outside the tested hexagon, and consequently, apositive NICS outside the diatropic ring current.A factor that affects the calculated NICS value at several

hexagons in PAHs is that ring currents induced in a PAH are asuperposition of currents induced in all hexagons in themolecule. Thus, the analysis of local aromaticity in PAHs usingNICS calculations becomes complicated in terms of all thepossible contributions.

Figure 6. C26H16 cata-PAHs represented by the steric strain based on the number of bay (b), cove (c), and fjord (f) regions, and by the values of thelength-to-breadth ratio (L/B).49−51 The σ-backbone is used for clarity.



Once the relation between the NICS and the diamagneticshielding has been illustrated, the locations, number, andmigrating behavior of the sextets in cata-PAHs can bedeciphered by means of a combination of these twoapproaches, NICS plus diamagnetic shielding calculations.For compound XXII, which contains 26 π-electrons, Table 1

indicates that the highest total NICS in the moleculecorrespond to the hexagons labeled B, A, and F, in thatorder. Therefore, there is a resonant sextet in ring B. However,there cannot be a resonant sextet in ring A, at the same time,without overcoming the valence of four for some carbon atoms.Thus, there is a sextet migration between hexagons B and Athat comprises one resonant sextet and two double bonds, andthere is another resonant sextet in ring F. Ring E has the lowest

NICS value, therefore, not resonant sextet is located in this ringbut there is a localized double bond. There are 8 π-electrons leftto be accommodated in rings C and D. These two rings have avery similar NICS value, and to verify how the electronicdensity is distributed in these rings, the diamagnetic shieldingvalues in the perpendicular direction, σ⊥

d , which correspondsmainly to the NICSπ‑density,

17,58 are used, and shown in Table 1.Ring C presents a very high (116.66) positive paratropicdiamagnetic shielding which is indicative that there is noresonant sextet located in this ring. Also, this high paratropicshielding cannot arise only from the electronic distribution inthat ring which confirms that ring C is surrounded by tworesonant sextets present in the adjacent rings B and D. Thepresence of these two resonant sextets, adjacent to ring C,

Figure 7. Application of the extended Y-rule method for the determination of the locations, number, and migrating directions of the aromatic sextetsin 10 representative C26H16 cata-PAHs using the peri-PAHs as parent molecules. Each determination involves the addition of n C2H2 units (step 1),the application of the Y-rule method (step 2), and the removal of n C2H2 units (step 3). In the case of the PAHs where the arrows of the migratingsextets end in adjacent hexagons, the sextets cannot occupy at the same time these adjacent hexagons. The symbol n corresponds to the number ofbay regions in the cata-PAHs. The blue arrows indicate the direction of the migration of the sextets.



produces magnetic fields that are opposite in direction to theapplied external magnetic field at the position of the C ring;

therefore, its NICS is highly positive, i.e., paratropic (see Figure8 and related text). The final electronic distribution for PAHXXII, from the NICS analysis, is presented in Table 1.For compound XXVII, which contains 26 π-electrons, Table

1 indicates that the calculated highest NICS value correspondsto hexagons A and E; therefore, there are resonant sextetslocated there. The lowest NICS value corresponds to hexagonD; therefore, there is no resonant sextet in this hexagon. Thereare 14 π-electrons to be distributed in rings B, C, and F.Hexagon B has the highest NICS value of the three hexagons,but there cannot be adjacent sextets without overcoming thevalence of some carbon atoms, and there is already a sextet inhexagon A. Thus, there could be a sextet in hexagons C and F,without overcoming any carbon atom valence and a doublebond in hexagon B. The diamagnetic shielding values in theperpendicular direction, σ⊥

d , for rings B and C are −24.74 and−54.35, respectively, which indicates that there is a sextet inring C.

Table 1. Locations, Number, and Migrating Directions (π-Electronic Distribution) of the Ten Representative C26H16 cata-PAHsby Means of NICS(1) Calculations and Comparison with the Correspondent Results Using the Extended Y-Rule Methoda

aThe blue arrows indicate direction of the migration of the sextets. The symbols * and ** indicate that the NICS(1) value in the ring has beendetermined using the equivalent symmetrical ring in the molecule.

Figure 8. Effect of an induced magnetic field inside and outside thebenzene ring.17 Reproduced with permission from J. Phys. Chem. A2004, 108, 10873−10896. Copyright 2004 American ChemicalSociety.



Compound XXVIII has a C2h symmetry (based on thegeometry optimization procedure described in section 2 andbased on literature information59) and contains 26 π-electrons.It can be concluded that the resonant sextets are located in thesymmetry related hexagons labeled A and F, which present thehighest NICS(1) value, and equal to −11.00, see Table 1.Hexagons B and E, also related by symmetry, present thelowest NICS(1) value; therefore, there are no resonant sextetsin these hexagons but they contain at least one double bondeach. There are left 10 π-electrons to be distributed in thesymmetry related hexagons C and D, which have anintermediate NICS(1) value of −9.98. It could be consideredthat there is a resonant sextet and two double bonds in thesehexagons, and there is a sextet migration between these twohexagons. In Table 1 the diamagnetic shielding values in theperpendicular direction are presented. Hexagons B, C, D, and Epresent almost the same value of −44, see Table 1, which onlywould occur if these four hexagons present a similar electronicdistribution and this is only possible by considering sextetmigration. Based on this analysis, the electronic distributiongiven by NICS for compound XXVIII is presented in Table 1.In this electronic distribution, the sextet migration is alternatedin a way that there are no adjacent resonant sextets at the sametime; otherwise the valence of four of some carbon atomswould be overcome. The electronic distribution obtained withNICS(1) and the extended Y-rule method are in agreement.As demonstrated in Table 1, the results from the application

of the postulated extended Y-rule method match correctly withthe results obtained using only the NICS methodology for thecata-PAHs I, III, VIII, X, XI, XIII, and XX, and with the resultsobtained using the NICS methodology plus the diamagneticshielding calculations for the cata-PAHs XXII, XXVII, andXXVIII. The same sextet characterization strategy applied tothe 10 cata-PAHs can be applied to the other 18 cata-PAHs inthe family C26H16 and to the other cata-PAHs in the isomerfamilies C(10+4x)H(8+2x), where x = 5, 6, 7, ..., ∞.3.6. Application of the Extended Y-rule Method

during the Estimation of the UV−vis Spectral Featuresof cata-PAHs. As it was stated in the Introduction, theextended Y-rule method for the characterization of the aromaticsextets explained here is a cornerstone for the estimation of theUV−vis spectral band positions of cata-PAH using theAnnellation Theory4,20 procedure described by Ona-Rualesand Ruiz-Morales.34 Since the predictive procedure explainedby Ona-Ruales and Ruiz-Morales34 is based on the knowledgeof the location, number, and migrating behavior of the sextetsin the peri-PAHs and cata-PAHs involved, the Y-rule methodexplained elsewhere17,18 and the extended Y-rule methodproposed here has been respectively used to accomplish thisspectral estimation. Following the predictive procedure,34 theestimation of the UV−vis spectral band positions of dibenzo-[g,p]chrysene, cata-PAH I in Figure 6, has been carried outusing three reference PAHs, naphtho[8,1,2-ghi]chrysene XXX,benzo[g]chrysene XXXI, and benzo[p]naphtho[1,8,7-ghi]-chrysene XXXII, with experimental UV−vis absorption spectralpositions available from reference standards and from literaturesources, as it is described in Figure 9. Benzo[g]chrysene XXXIhas a sextet migrating behavior and distribution alreadyestablished in Figure 5, and dibenzo[g,p]chrysene I hasstationary sextets as it is already established in Figure 7. Onthe other hand, the characterization of the sextets for the peri-PAHs, naphtho[8,1,2-ghi]chrysene XXX and benzo[p]naphtho-[1,8,7-ghi]chrysene XXXII, has been obtained by means of the

Y-rule method.17 Using these PAH structures and theirrespective sextets characterizations, a figure similar to theAnnellation Theory figures mentioned by Ona-Ruales andRuiz-Morales34 has been applied so as to predict the positionsof the UV−vis spectral p and β bands for the cata-PAHdibenzo[g,p]chrysene I (see Figure 9). The referred theoreticalprocedure states34 that the position of the UV−vis spectralbands of the PAH under investigation, e.g., PAH I located atthe bottom right corner of Figure 9, can be deciphered using atwo-step approach. Taking as a reference PAH I in Figure 9, thefirst step consists in subtracting the wavelength values of thespectral bands positions of the PAH located at the top rightcorner, PAH XXXI, and the PAH located at the top left corner,PAH XXX. The second step, afterward, consists in adding thisresult to the spectral band positions of the PAH located at thebottom left corner, PAH XXXII. The predicted p and β UV−visspectral band positions of PAH I calculated using this methodsatisfactorily agree (showing an average difference lower than2%) with the experimental p and β UV−vis spectral bandspositions reported in the literature20 for PAH I, dibenzo[g,p]-chrysene, as it is mentioned in Figure 10.

4. CONCLUSIONSThe extended Y-rule method has been proposed for thecharacterization of the sextets in the cata-PAHs C(10+4x)H(8+2x),where x = 1, ...,∞, where the methodology based exclusively on

Figure 9. Prediction of the UV−vis spectral band positions of the cata-PAH I, dibenzo[g;p]chrysene by means of the experimental UV−visspectral band positions of naphtho[8,1,2-ghi]chrysene XXX, benzo-[g]chrysene XXXI,20 and benzo[p]naphtho[1,8,7-ghi]chryseneXXXII.60

Figure 10. Experimental UV−vis spectral band positions of the cata-PAH I, dibenzo[g,p]chrysene.20



the Y-rule17,18 is not sufficient to achieve this objective becausethe Y-rule was designed to be applied in peri-condensed PAHs.The results of the application of the extended Y-rule method tocata-PAHs C(10+4x)H(8+2x), where x = 1, 2, 3, and 4, werecompared and successfully validated with literature informa-tion1,4,16,20 and with the results of the π-electronic distributionobtained by NICS(1) calculations. It is concluded that theextended Y-rule method is a straightforward heuristic andtopological method, easy to apply, for the determination of theπ-electronic distribution, i.e., location, number, and migratingdirection of the sextets, for cata-condensed benzenoid PAHswith one or more available bay regions (also known as cata-PAHs).The published methods to determine the electronic

distribution in cata-condensed PAHs are difficult to applybecause they require either computational theoretical chemistrycalculations or the knowledge of all the Kekule representations,which in many cases are not easy to establish. The method byKlavzar et al.,14 although easy to apply, does not provideinformation on the location of the resonant sextets.The link between the cata-condensed structures and the peri-

condensed structures, one of the steps of the extended Y-rulemethod, gives a broader scope to the methodology hereproposed. By means of this link, not only the aromaticcharacter of the peri-PAH can be related to the respectivearomatic character of the cata-PAH but also the UV−visspectral behavior, which is dependent on the sextet distributioninside of the molecule, can be deciphered by means of this peri-cata relationship. In this sense, a successful illustration of thisapproach has been presented for the prediction of the UV−visspectral features of dibenzo[g,p]chrysene. More importantly,the usage of computational techniques to characterize thearomatic sextets is unnecessary in the extended Y-rule methoddue to its easy approach that demands the usage of only a penand a paper.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest. Certaincommercial equipment, instruments, or materials (or suppliers,or software, ...) are identified in this paper to fosterunderstanding. Such identification does not imply recommen-dation or endorsement by the National Institute of Standardsand Technology, NIST, nor does it imply that the materials orequipment identified are necessarily the best available for thepurpose.

■ ACKNOWLEDGMENTSY.R.-M. acknowledges the support under Projects D.60019 andY.61000 (CONACYT-SENER 177007) of the InstitutoMexicano del Petroleo.

■ ABBREVIATIONSIUPAC, International Union of Pure and Applied Chemistry;PAH, polycyclic aromatic hydrocarbons; PDI, para-delocaliza-tion index; HOMA, harmonic oscillator model of aromaticity;

NICS, nucleus-independent chemical shift; UV−vis, ultra-violet−visible; FAR, fused aromatic rings

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extended y rule method for the characterization of the

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