Extended Y-Rule Method for the Characterization of the Aromatic

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Extended Y-Rule Method for the Characterization of the Aromatic Sextets in Cata-Condensed Polycyclic Aromatic Hydrocarbons. Jorge O Oña-Ruales, and Yosadara Ruiz-Morales J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp510180j • Publication Date (Web): 02 Dec 2014 Downloaded from http://pubs.acs.org on December 6, 2014

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The Journal of Physical Chemistry

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Extended Y-Rule Method for the Characterization of the Aromatic Sextets in Cata-condensed* Polycyclic Aromatic Hydrocarbons. Jorge O. Oña-Ruales1* and Yosadara Ruiz-Morales2

1

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

States 2

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

Mexico

* The descriptive name "cata-condensed" has been used in this article due to its widespread presence in the scientific literature; however, the formal IUPAC name is "ortho-fused".

ACS Paragon Plus Environment


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ABSTRACT The location, number, and migrating behavior of the sextets in the cata-condensed benzenoid polycyclic aromatic hydrocarbons with available bay regions have been determined by a new proposed topological methodology called the extended Y-rule. The precursor of this rule is the well-known Y-rule method for determining sextets in peri-condensed polycyclic aromatic hydrocarbons. The new methodology has been successfully validated by means of literature information and by theoretical Nucleus Independent Chemical Shift (NICS) calculations. Even though the families of polycyclic aromatic hydrocarbons analyzed here comprise the C14H10, C18H12, C22H14, and C26H16 isomers; the procedure can practically be extended to the families C(10+4x)H(8+2x), where x=1, … , ∞. It is the first time that a straightforward procedure, easy to apply, has been proposed to obtain the sextets arrangement and behavior in the group of catacondensed benzenoid polycyclic aromatic hydrocarbons. KEYWORDS Polycyclic Aromatic Hydrocarbons, Cata-condensed, Aromaticity, Sextets, Y-rule


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1. INTRODUCTION The complete characterization of the sextets inside of polycyclic aromatic hydrocarbons, PAHs, in terms of arrangement and migrating behavior is important in order to recognize the PAH chemical stability and reactivity,1-3 and to understand the spectral absorption responses that provide an unambiguous identity of each PAH molecule.3-5 Several theoretical methods have been applied to evaluate qualitatively and quantitatively the aromatic character of PAHs in general and cata-condensed PAHs in particular. The methods include the para-delocalization index, PDI; the harmonic oscillator model of aromaticity, HOMA; and the nucleus independent chemical shift, NICS. Although PDI, HOMA, and NICS are consistent with the information obtained from Clar structures,6 all of these methods require quantum chemistry calculations that involve computationally expensive procedures. Randić and coworkers considered partitions of π-electrons associated with C=C bonds of Kekulé valence structures to individual rings,7-11 mainly for cata-condensed PAHs; while Gutman and coworkers considered partition the Pauling bond orders to individual rings.12 In both studies the contributions from bonds adjacent to two rings were divided between the two rings. Later on, Randić made the distinction where the contributing Pauling bond orders are not partitioned between the neighboring rings, allowing this the numerical characterization of individual benzene rings as fully aromatic, intermediate, and weakly aromatics.13 A limitation for these methods is that all the Kekulé structures have to be found for a given PAH, which is not an easy task in many cases and in particular for large PAH systems. 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 Klavžar et al.14



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According to these authors, the number of sextets in a cata-condensed PAH is given by the minimum number of segment lines that cross all of the benzenoid rings. However, this method does not give information about the position of the sextets. Randić has mentioned in several papers,11,15,16 with respect to Klavžar paper, that the line segments should be drawn so that the number of crossings of lines is maximal. The placing of the aromatic sextet then is done in any of the rings that have no crossing of lines where there will be “migrating” sextets. However, as far as we know, these statements have not been developed further in a publication neither have been validated. An easy to apply qualitative methodology for the determination of the locations, number, and migrating direction of the aromatic sextets, i.e., π-electronic distribution in pericondensed PAHs, involves the application of the Y-rule17-19 which produces Clar-Type-Structures4,20 and that has been widely validated by means of NICS values.21-25 Scheme 1 shows the methodology followed by the Y-rule, the simplest approach, so as to establish the arrangement and behavior of the aromatic sextets in peri-condensed PAHs.17-19 The Y-rule details are outlined and widely exemplified in references 17, 18, and 19. The method presented in Scheme 1 is only applicable to 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-rule beyond the group of peri-condensed PAHs is needed in order to obtain the sextets arrangement and behavior in the group of cata-condensed PAHs. The Y-rule method has been successfully used to determine the structure of the peri-condensed PAHs that are part of the aromatic region in oil asphaltenes, which are very problematic compounds in the oil industry,3,26,27,28 in the identification of a new C28H14 polycyclic aromatic hydrocarbon as a


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product of supercritical fuel pyrolysis,29 in the analysis of Carbon K-edge X-ray Raman spectroscopy of oil asphaltene studies,30 and in the determination of the aromaticity of cyclopenta-fused PAHs.19

Postulate the positions of the sextets COVERING the Y internal carbons (Y-carbons)

Several Possible Structures

Are the sextets covering the MAXIMUM number of Y internal carbons ?

Is there only ONE Clartype structure with the highest level of symmetry ? Structure Selected

If Necessary

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SUPERIMPOSE the Clartype structures to obtain the position of the sextets

Scheme 1. The methodology of the Y-rule for establishing the locations, number, and migrating direction of the sextets in pericondensed polycyclic aromatic hydrocarbons.17,18

It is the purpose of this work to elucidate the locations, number, and migrating direction of the aromatic sextets in the cata-condensed benzenoid PAHs with one or more available bay regions (cata-PAHs). With that aim, the locations, number, and migrating direction of the sextets in the structurally analogous peri-condensed benzenoid PAHs (peri-PAHs) are used. The πelectronic distribution in the cata-PAHs then is obtained by means of a new proposed methodology that involves the Y-rule; therefore, named the extended Y-rule method. The results of the proposed methodology are validated with published information1,4,16,20 concerning the π-electronic distribution in low molecular mass cata-PAHs, e.g., C14H10, C18H12,



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C22H14, and with calculations of the aromaticity inside of the hexagonal rings using the NICS approach in representative high molecular mass cata-PAHs, e.g., C26H16 cata-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), or one angstrom above the geometrical center of the ring that is being probed, NICS(1). Significant negative NICS values inside of the rings indicates the presence of “aromaticity” whereas positive values denotes “antiaromaticity”.21,31 Ab initio and density functional studies have demonstrated17,19,32 that NICS is a useful indicator of aromaticity and generally correlates well with the energetic, geometric and magnetic criteria for aromaticity.33 It is the first time that a method to connect the peri-condensed PAHs and the cata-condensed PAHs through the aromatic character of the molecules has been proposed. Since the π-electronic distribution in PAHs is related to the position of the UV-Vis absorption spectral bands,3,4,20,34 this methodology constitutes the initial step toward the unequivocal identification of cata-PAHs with unknown synthetic protocols in a variety of natural and modified environments. 2. COMPUTATIONAL DETAILS The optimization of the PAH structures was carried out by performing force-field-based minimization using the energy minimization panel in Materials Studio35 and the COMPASS consistent force field as embedded in the Material Studio package. The COMPASS (condensedphase optimized molecular potentials for atomistic simulation studies)36,37 force field was used in all the optimizations because it has been tested and validated extensively against experiment for many organic molecules.


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The geometry optimization (structure relaxation) for systems I and XXVIII was carried out using the high level quantum density functional theory (DFT) approach with the self-consistent generalized-gradient GGA and the Perdew-Wang 91 (PW91) exchange-correlation potential (DFT GGA-PW91).38 The DNP basis set (double zeta plus polarization function basis set)39 with a radial cut off of 3.0 Å was used, as implemented in the DMol3 code,39-41 and instrumented in the interface 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 above the geometrical center of each hexagon in the PAH structures to calculate the NICS(1). The Becke 1988 functional,45 which includes the Slater exchange along with corrections involving the gradient of the density was used together with the correlation functional of Lee, Yang, and Parr, 46 which includes both local and non-local terms, i.e. the B3LYP hybrid functional was used. A basis set that is augmented with two sets of polarization functions, i.e. the 6-31G(d, p) or 6-31G** basis set44 was used. NICS(1) has been chosen instead of NICS(0) because in the calculated NICS(1), at 1Å above the molecular plane, the π-electron ring current effects are dominant and the σ bonding contributions are diminished.47,48 3. RESULTS AND DISCUSSION In the present study, we present and validate theoretically the performance of a qualitative heuristic rule to determine the aromaticity of each hexagonal ring in cata-condensed benzenoid polycyclic aromatic hydrocarbons with available bay regions (cata-PAHs). We have named this rule the extended Y-rule because in one of the steps of its methodology of application it makes



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use of the Y-rule,17,18 which determines the relative aromaticity in peri-condensed PAHs or periPAHs. 3.1. Extended Y-Rule Methodology The extended Y-rule method is useful exclusively for cata-PAHs which can accommodate by addition C2H2 units, in a bay region or bay regions, to form peri-PAHs. This excludes several classes of cata-condensed PAHs such as the linear polyacenes, the helicenes, and the non-linear cata-condensed PAHs with only cove and fjord regions. These distinctive classes of catacondensed PAHs generate, upon C2H2 addition, peri-PAHs (with five- or seven-sided rings) that do not satisfy the fully-benzenoid requirement for the application of the extended Y-rule method stated in the introduction; thus, they are unsuitable for the proposed methodology. The suitability and unsuitability of the extended Y-rule method for the characterization of the aromatic sextets in several cata-condensed PAHs is described in Figure 1.

1. Suitable pattern: Addition of a C H

1. Suitable pattern: Addition of a C22H22 unit benzenoid unit toto aa cata-condensed cata-condensed benzenoid PAH with a bay region and successful PAH (cata-PAH) with a bay region and formation a peri-condensed successful of formation of a peribenzenoid PAH. condensed benzenoid PAH (peri-PAH).

2. Unsuitable pattern: Addition of a C2H2 2. Unsuitable pattern: Addition of a unit to a cata-condensed benzenoid C2H2 unit to a cata-condensed PAH (cata-PAH) with no bay regions benzenoid PAH with no bay and unsuccessful formation of regions a periand unsuccessful formation of a pericondensed benzenoid PAH (peri-PAH).

condensed benzenoid PAH.

Figure 1. Suitability of the extended Y-rule method for cata-condensed PAHs with one or more bay regions Figure 1. Suitability of the extended Y-rule method cata-PAHs with one or more andThe σand unsuitability of the extended Y-rule method forfor cata-condensed PAHs with nobay bayregions regions. unsuitability of for the clarity. extended Y-rule method for cata-PAHs with no bay regions. The σ-backbone is backbone is used used for clarity.


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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 by adding n C2H2 units to all of the available n single bay regions in the σ-backbone of the cata-PAH. The σ-backbone is used in this step to make the explanation unambiguous. Step 2. The Y-rule method described in Scheme 117,18,19 is applied to obtain the locations, number, and migrating behavior of 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 that indicates the final locations, number, and migrating behavior of the sextets in the cata-PAH under analysis. 3.2. Electronic Rearrangement during the Conversion from Peri-PAH to Cata-PAH Two scenarios are possible by electronic rearrangement during the conversion from peri-PAH to cata-PAH after the removal of n C2H2 units in Step 3 (see section 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 Step 1, and elucidated by application of the Y-rule, in Step 2, there is an isolated double bond or a migrating sextet. No changes in the locations or number of the adjacent sextets are expected in Step 3 due to the removal of the C2H2 unit, in the transition from a peri-PAH to a cata-PAH. Concerning the sextet migrating behavior variations, no changes are anticipated for the case of the isolated double bond removal, but observable differences are predicted for the case of the C2H2 unit removal from a migrating sextet that consists in the reduction of the sextet linear path either to a shorter path or to a stationary sextet.



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The following examples, presented in Figure 2, are given exclusively to exemplify Step 3Scenario 1. They are not exhaustive and are provided as guidance regarding possible situations that can be encountered during the application of the extended Y-rule methodology. The electronic rearrangement based on Scenario 1 during the conversion from peri-PAH to cata-PAH is exemplified in Figure 2, Cases 1 and 2. Case 1 describes the transition from coronene (periPAH) to triphenylene (cata-PAH). This transition comprises the removal of three C2H2 units from three single-bay regions with hexagons in sextet migrating paths. Coronene has three linear sextet paths with two hexagons from the addition of three C2H2 units to three single-bay regions performed in Step 1. As observed in Figure 2, Case 1, the removal of the three C2H2 units in Step 3 does not modify the final sextet locations and number but generates a reduction in the linear sextet path from two 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 isolated double bond from a single-bay region. Benzo[de]naphtho[1,2,3-qr]naphthacene has one isolated double bond from the addition of one C2H2 unit to a single-bay region performed in Step 1. As described in Figure 2, Case 2, in the transition from benzo[de]naphtho[1,2,3-qr]naphthacene to naphtho[2,3-g]chrysene, the removal of the C2H2 unit in Step 3 does not alter 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 is a stationary sextet.


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1. Removal of three C2H2 units from three single-bay regions with hexagons in sextet migrating paths.

-3C2H2

Coronene Peri-PAH

Triphenylene Cata-PAH

2. Removal of one isolated C2H2 unit from a single bay region.

-C2H2

benzo[de]naphtho[1,2,3-qr]naphthacene Peri-PAH

naphtho[2,3-g]chrysene Cata-PAH

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

The opening of this sextet to remove the C2H2 unit in Step 3, in the transition from the periPAH to the cata-PAH will leave behind two double bonds whose electrons will be distributed in the adjacent hexagons where new sextets can be formed if there is enough electronic density. This new sextet would be stationary or it would migrate if in any of the adjacent hexagons there is a linear path of hexagons with less density than in sextets, i.e., a linear path of hexagons with two double bonds or one double bond (like sextet migration in coronene) but not three double bonds because there cannot be adjacent sextets without exceeding the carbon atoms valence of four.



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The examples described in Figure 3 are given solely to illustrate Step 3-Scenario 2. They are not exhaustive and are provided as guidance regarding possible situations than can be encountered during the application of the extended Y-rule methodology. The electronic rearrangement based on Scenario 2 during the conversion from peri-PAH to cata-PAH is exemplified in Figure 3, Cases 1, 2, and 3. Case 1 describes the transition from benzo[vwx]hexaphene (peri-PAH) to hexaphene (cataPAH). This transition involves the opening of one sextet in a single-bay region. Benzo[vwx]hexaphene has one stationary sextet S1 from the addition of one C2H2 unit to a single-bay region performed in Step 1, one additional stationary sextet S2, and one sextet S3 with a linear path of two hexagons. The opening of the stationary sextet S1 to remove the C2H2 unit in Step 3 leaves behind two double bonds whose electrons will be distributed into two of the adjacent

hexagons.

As

represented

in

Figure

3-Case

1,

in

the

transition

from

benzo[vwx]hexaphene to hexaphene, this electronic distribution, on one hand, gives rise to a linear path of two hexagons where the stationary sextet S2 is present, and, on the other hand, causes an increase of the linear path of the 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 involves the 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 linear path of two hexagons.


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1. Opening of one stationary sextet, S1, by removal of one C2H2 unit in a single-bay region. S2

S2

S1

-C2H2

S3

S3

benzo[vwx]hexaphene Peri-PAH

hexaphene Cata-PAH

2. Opening of three stationary sextets, S4, S5, and S6, by removal of three C2H2 units in three single-bay regions. S5 S4

S8

S7

S7

-3C2H2

S6

S9

naphtho[2,3-a]coronene Peri-PAH

dibenzo[a,c]tetracene Cata-PAH

3. Opening of two stationary sextets, S10 and S11, by removal of two C2H2 units in two single bay-regions and opening of one stationary sextet, S12, by removal of one C2H2 unit in a double-bay region. S17

S12

S13 S11

S16

-C2H2 S14

S15

S10 naphtho[1,2-a]coronene Peri-PAH

dibenzo[f,k]tetraphene Cata-PAH

Figure 3. Three examples of Step 3-Scenario 2 depicting the change of the positions, number, and migrating behavior in the transitions from benzo[vwx]hexaphene to hexaphene, naphtho[2,3a]coronene to dibenzo[a,c]tetracene, and naphtho[1,2-a]coronene to dibenzo[f,k]tetraphene. See text for details.



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The opening of the three stationary sextets S4, S5, and S6 to remove the three C2H2 units in Step 3 leaves behind six double bonds (two double bonds from each opened sextet) whose electrons will be distributed in three of the adjacent hexagons. As described in Figure 3-Case 2, in the transition from naphtho[2,3-a]coronene to dibenzo[a,c]tetracene, the first effect of this electronic distribution is the formation of two stationary sextets S8 and S9 due to the absence of a linear path where isolated double bonds were present, and the second effect is an increase of the linear path of the sextet S7 from two to three hexagons. Finally, Case 3 describes the transition from naphtho[1,2-a]coronene (peri-PAH) to dibenzo[f,k]tetraphene (cata-PAH) that involves the opening of two sextets in two single-bay regions and the opening of one sextet in a double-bay region. Naphtho[1,2-a]coronene has three stationary sextets S10, S11, and S12 from the addition of two C2H2 units to two single-bay regions and from the addition of one C2H2 unit to one double-bay region performed in Step 1, and one sextet S13 with a linear path of two hexagons. The opening of the three stationary sextets S10, S11, and S12 to remove the three C2H2 units in Step 3 leaves behind six double bonds (two double bonds from each opened sextet) whose electrons will be distributed in three of the adjacent hexagons. As described in Figure 3Case 3, in the transition from naphtho[1,2-a]coronene to dibenzo[f,k]tetraphene, and due to the absence of linear paths for sextet migration, this electronic distribution gives origin 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 with double, triple, quadruple, quintuple, or sextuple bay regions in series, which are not single-bay regions, as described in Figure 4. For such cases, Step 1 of the extended Y-rule methodology should start with the addition of the C2H2 unit to one of the bay regions in the series (one C2H2 unit per series) and to all of the other single-bay regions.


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The choice of the bay region in the series for the addition of the C2H2 unit is arbitrary and will not affect the final locations, number, or migrating behavior of the sextets in the cata-PAH.

1 bay region

2 bay regions

3 bay regions

4 bay regions

5 bay regions

6 bay regions

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.

3.4. Application of the Extended Y-Rule Method for the Characterization of the Sextets in the C14H10, C18H12, and C22H14 Cata-PAHs Using the three-step procedure described above for the extended Y-rule method, the characterization of the sextets in the C14H10, C18H12, and C22H14 cata-PAHs has been achieved by means of the parent peri-PAHs. Figure 5 shows the establishment of the sextet locations, number, and migrating behavior in the C14H10, C18H12, and C22H14 cata-PAHs. The results shown in Figure 5 about 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 literature information.1,4,16,20 3.5. Application of the Extended Y-Rule Method for the Characterization of the Sextets in the C26H16 Cata-PAHs and Validation with NICS Calculations The extended Y-rule method for the characterization of the sextets has also been applied to the C26H16 cata-PAHs. The C26H16 cata-PAHs group, i.e., C26H16 benzenoid PAHs with one or more



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available bay regions, comprises 28 structures as shown in Figure 6. Figure 6 enumerates the C26H16 cata-PAHs, their steric strain5 based on the number of bay, cove, and fjord regions, and their length-to-breadth ratios (L/B),49-51 a parameter extensively used in chromatographic analysis to define the shape of PAHs. The use of a steric strain argument and a shape descriptive parameter gives a viable criterion for the selection of suitable C26H16 cata-PAHs that can be used as the subject of analysis for the extended Y-rule method in lieu of the entire 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 been selected. 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[2,3c]chrysene (XXII), benzo[f]picene (XXVII), and benzo[c]picene (XXVIII). These structures have been chosen due to their diverse number of bay (1 to 4), cove (0 to 2), and fjord (0 to 1) regions and due to the variety 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 of steric 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, and migrating behavior of the sextets in the 10 C26H16 cata-PAHs selected for this analysis. Due to the limited literature information1,4,16,20 so as to completely validate the results of the extended Y-rule method for the characterization of the aromatic sextets elucidated in Figure 7, the validation has been carried out by comparison with the characterization of the sextets provided by NICS calculations.


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17

cata-PAH

Extended Y-rule Method Step 1

Step 2

Step 3

C14H10 phenanthrene

+n C2H2

Y-rule

-n C2H2

C18H12 triphenylene

+n C2H2

C18H12 chrysene

+n C2H2

n=1

n=1 Y-rule

n=3

n=3 Y-rule

n=2 C18H12 benz[a]anthracene

+n C2H2

C22H14 benzo[g]chrysene

+n C2H2

Y-rule

C22H14 benzo[c]chrysene

+n C2H2

C22H14 dibenz[a,j]anthracene

+n C2H2

C22H14 benzo[a]naphthacene

+n C2H2

Y-rule

Y-rule

Y-rule

Y-rule

C22H14 dibenz[a,h]anthracene

+n C2H2

-n C2H2 n=1

Y-rule

n=1

+n C2H2

-n C2H2 n=1

n=1

C22H14 picene

-n C2H2 n=3

n=1

+n C2H2

-n C2H2 n=2

n=3

C22H14 benzo[b]chrysene

-n C2H2 n=1

n=2 +n C2H2

-n C2H2 n=2

n=1

C22H14 benzo[b]triphenylene

-n C2H2

-n C2H2 n=1

Y-rule

-n C2H2 n=2

n=2

Y-rule

n=3

-n C2H2 n=3

Y-rule

n=2

-n C2H2 n=2

Figure 5. Application of the extended Y-rule method for the determination of the locations, number, and migrating directions of the aromatic sextets in the C14H10, C18H12, and C22H14 cata-PAHs using the periPAHs 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 migrating sextets end in adjacent hexagons, the sextets cannot occupy at the same time these adjacent hexagons. The symbol n corresponds to the number of bay regions in the cata-PAHs. The blue arrows indicate the direction of the migration of the sextets.



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18

I

Steric Strain

b 2

L/B

II

c f 2 0 1.095

b 2

VIII

Steric Strain

b 3

L/B

b 1

L/B

c f 0 0 1.410

b 4

L/B

b 1

c f 1 0 1.635

c 1 1.516

b 2

b 2

c f 0 0 1.414

b 2

b 1

b 1

c f 1 0 1.442

c f 1 0 1.636

b 2

c f 0 0 2.034

c f 1 0 1.761

b 1

c f 0 0 2.048

b 1

b 3

c f 0 0 1.853

b 2

c f 0 0 1.777

c 0

b 2

c f 1 0 1.522

b 1

c f 1 0 1.786

b 2

b 3

2.059

c f 0 0 2.086

b 3

c f 0 0 2.010

b 2

c f 0 0 2.126

b 1

c f 1 0 1.523

c f 2 0 1.528 XXI

b 2

XXVII

b 3

c f 0 0 1.359 XIV

XX

XXVI

f 0

c f 0 1 1.334

VII

XIII

XIX

XXV

b 2

c f 0 1 1.292

VI

XII

XVIII

XXIV

b 3

c f 2 0 1.215 XI

XVII

XXIII

f 0

c f 0 1 1.184

V

IV

X

XVI

XXII

Steric Strain

c f 1 0 1.107 IX

XV

Steric Strain

III

c f 0 0 1.985 XXVIII

b 4

c f 0 0 2.274

Figure 6. The 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 the length-to-breadth ratio (L/B).49-51 The σ-backbone is used for clarity.

The establishment of the location, number, and migrating behavior of the sextets in the 10 C26H16 cata-PAHs by means of the NICS21 values is depicted in Table 1 and explained below where the most representative cases are discussed. For the characterization of the sextets, it is applied the criteria proposed by Ruiz-Morales,17,19 that relates the highest negative NICS(1) value in each structure to the presence of a sextet in that given ring.


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19

C26H16 cata-PAH I

Extended Y-rule Method Step 1

Step 2

Step 3

+n C2H2

Y-rule

-n C2H2

n=2

III

+n C2H2

n=2 Y-rule

VIII

+n C2H2

Y-rule

n=3

X

+n C2H2

+n C2H2

Y-rule

+n C2H2

Y-rule

+n C2H2

Y-rule

+n C2H2

XXVII

Y-rule

Y-rule

+n C2H2

-n C2H2 n=1

Y-rule

n=3

XXVIII

-n C2H2 n=2

n=1

+n C2H2

-n C2H2 n=2

n=2

XXII

-n C2H2 n=1

n=2

XX

-n C2H2 n=2

n=1

XIII

-n C2H2 n=3

n=2

XI

-n C2H2 n=2

n=2

-n C2H2 n=3

Y-rule

n=4

-n C2H2 n=4

Figure 7. Application of the extended Y-rule method for the determination of the locations, number, and migrating directions of the aromatic sextets in 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 Yrule method (step 2), and the removal of n C2H2 units (step 3). In the case of the PAHs where the arrows of the migrating sextets end in adjacent hexagons, the sextets cannot occupy at the same time these adjacent hexagons. The symbol n corresponds to the number of bay regions in the cata-PAHs. The blue arrows indicate the direction of the migration of the sextets.



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20

3.5.1. Cases in which the aromatic character of a cata-PAH is elucidated using only the total NICS analysis For compound VIII, Table 1 shows that the -electronic density is located mainly in ring D and there is sextet migration along the rings E-D-C because the NICS(1) values are close. Also, there are sextets in rings A and F but these sextets do not migrate because the ring labeled B has a very small NICS(1) value=-3.33, which indicates no presence of -electronic density. For compound XI, which contains 26 -electrons and a total of six fused rings (6FAR), Table 1 shows that the sextets are located in the rings B and E, NICS(1)= -11.36 and -12.29, respectively, giving a total of two resonant sextets that comprise 12 -electrons. Thus, the remaining 14 -electrons are located in the rings A, C, D, and F; taking care of not exceeding the valence of any of the carbon atoms. Due to the fact that the NICS(1) values of rings A and B, and rings D, E, and F are not too different, it is considered that there is sextet migration along the rings A-B and along the rings D-E-F. For compound XIII, the NICS(1) values in Table 1 suggest that the -electronic density is located in rings A and C. By molecular symmetry is established that the same π-electronic density 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 sextets cannot be at adjacent hexagons, due to the violation of the carbon atoms valence, it is expected the presence of sextet migration in rings C and D. For compound XX, Table 1 shows that the -electronic density is located mainly in rings B and E and there is sextet migration between rings A and B, and E and F.


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21

C26H16 PAH

PAH σ-backbone with ring labels

NICS(1) in each ring A

B

C

D

E

F

D B E F

-10.00

-5.90

-10.00

-10.00 *

-5.90 **

-10.00 *

III

A B C D E F

-10.27

-7.84

-7.08

-10.90

-10.27 *

-7.84 *

VIII

A B C D E F

-9.16

-3.33

-10.77

-11.98

-10.34

-9.16 *

-10.80

-11.33

-4.96

-8.71

-10.30

-9.40

-9.84

-11.36

-4.42

-11.01

-12.29

-10.33

A

I

C

π-electronic distribution based on NICS(1)

π-electronic distribution based on the extended Y-rule

D F

X

A B C E

XI

A

B

C

D

E

F

XIII

F B C D E A

-10.31

-6.99

-11.72

-11.72 *

-6.99 *

-10.31 *

XX

D E F A B C

-10.69

-11.85

-7.84

-7.84 *

-11.85 *

-10.69 *

-11.05

-13.02

-8.80

-8.92

-7.91

-10.74

-5.30

-10.70

-8.49

-9.98

-8.88

-11.00

XXII

A B C D E F

A

XXVII

B

C

(+116.7) (-13.54)

D F

E

-10.32

-11.00

XXVIII

A

B

C

D

E

-9.73

-9.24

(-24.74)

(-54.35)

-8.88

-9.98

F (-18.78) (-44.12) (-44.05) (-44.05) (-44.12) (-18.78) * * *

Table 1. Locations, number, and migrating directions (π-electronic distribution) of the ten representative C26H16 cata-PAHs by means of NICS(1) calculations and comparison with the correspondent results using the extended Y-rule method. The blue arrows indicate direction of the migration of the sextets. The symbols * and ** indicate that the NICS(1) value in the ring has been determined using the equivalent symmetrical ring in the molecule.

3.5.2. Cases in which the aromatic character of a cata-PAH is elucidated using the total NICS analysis coupled with the perpendicular diamagnetic shielding analysis The determination of the π-electronic distribution (characterization of the sextets) based on the NICS calculation presents limitations. The most important constraint has to do with the fact



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Page 22 of 40

22

that the NICS value of a particular ring is significantly influenced not only by the higher order circuits (ring currents) encircling the ring at which it is evaluated but also by the local aromaticity of the surrounding rings (as it is stated in Figure 8), and occasionally, the NICS values are even influenced by currents farther away in the molecule.17,22,52-57 In the same sense, Fias et al

54,55

have shown that there is a lack of a good correlation between the NICS and the

multicenter delocalization indices. These authors have shown through a thorough statistical analysis that the NICS values arise not only from local aromaticity of the benzenoid rings in PAHs but also from other circuits of current. As it is asserted by these authors, the NICS index does not reveal the individual aromatic nature of a specific ring, contrary to the delocalization indices. The lack of correlation between NICS and multicenter aromaticity indices appears when molecules contain several aromatic rings, where different circuits of ring currents are contributors to the total ring current and the effect of NICS, as a local aromaticity index, may be seen to reflect, at a chosen point, all ring currents in the molecule. Therefore, NICS cannot be used to assess a degree of benzenoid character for a specific ring in a PAH, because NICS not solely contain the ring current of the particular benzenoid circuit, NICS contain superimposed ring currents in all hexagons in the molecule. However, if only one circuit is present, there are good correlations between NICS and multicenter delocalization indices. In cases where the total NICS analysis does not provide the full location of the aromatic sextets in a cata-PAH, the perpendicular diamagnetic shielding values could be used17. The relation between the NICS and the diamagnetic shielding is obtained through the following analysis:


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23 The NICS is defined as the negative value of the absolute isotropic magnetic shielding according to Equation 1. 1

2

1

2

3

3

3

3

NICS = −σisotropic = − ( σ⊥ + σ∥ ) = NICS⊥ + NICS∥

(1)

Where σ⊥ and σ∥ are the perpendicular and parallel components, respectively. In the case of benzene σ⊥ is indicative of the π-induced ring current. The component of the isotropic chemical shielding perpendicular to the molecular plane, σ⊥ (Equation 1), can be written as a sum of a p

diamagnetic contribution, σd⊥ , and a paramagnetic contribution, σ⊥ , according to Equation 2. p

p

NICS⊥ = −σ⊥ = −(σd⊥ + σ⊥ ) = NICS⊥d + NICS⊥

(2)

In benzene, where there is an ideal ring current in the π-system, the paramagnetic contribution in Equation 2 vanishes, for symmetry reasons.17,58 Thus, for benzene the π-contribution to σ⊥ consists of the diamagnetic part only according to Equation 3. NICSπ−density = −σd⊥

(3)

When a molecule is placed into a homogeneous static magnetic field, a current density is induced. This current density induces additional fields at the position of the nuclei being tested. The situation is presented in Figure 8. The perpendicular diamagnetic shielding, σd⊥ (Equation 2) stems from a circulation of the ground state density (J⃗d ) around the dummy probe induced by the applied d ⃗⃗o . The circulation results in an induced magnetic field, B ⃗⃗ind magnetic field, B , which is opposite in

⃗⃗o . The corresponding shielding, σd⊥ , is as a consequence positive and NICS⊥d is direction to B d negative (see Equation 1 and Equation 2). However, the resulting magnetic field, ⃗B⃗ind , is parallel

⃗⃗o ‘outside’ the loop of the current density ⃗Jd and the corresponding shielding σd⊥ outside the to B hexagon been tested, is as a consequence negative (paratropic) and NICS⊥d is positive (see Equation 1, Equation 2, and Equation 3).



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24

inside outside

outside

Figure 8. Effect of an induced magnetic field inside and outside the benzene ring. 17 Reproduced with permission from J. Phys. Chem. A, 2004, 108, 10873-10896. Copyright 2004 Am. Chem. Soc.

Therefore, the effect of a diatropic π-current, due to the presence of a resonant sextet in a hexagon of a PAH, is to produce an induced magnetic field that has a positive contribution (diatropic) to the total shielding of that hexagon and, thus, a negative NICS; however, the effect of that same diatropic π-current outside the hexagon, where is located, is to produce a negative (paratropic) contribution to the total shielding, outside the tested hexagon, and consequently, a positive 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 a superposition of currents induced in all hexagons in the molecule. Thus, the analysis of local aromaticity in PAHs using NICS calculations becomes complicated in terms of all the possible contributions.


Page 25 of 40

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25

Once the relation between the NICS and the diamagnetic shielding has been illustrated, the locations, number, and migrating behavior of the sextets in cata-PAHs can be deciphered by means of a combination of these two approaches, NICS plus diamagnetic shielding calculations. For compound XXII, which contains 26 π-electrons; Table 1 indicates that the highest total NICS in the molecule correspond to the hexagons labeled B, A, and F; in that order. 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 A that comprises one resonant sextet and two double bonds, and there is another resonant sextet in ring F. Ring E has the lowest NICS value, therefore, not resonant sextet is located in this ring but there is a localized double bond. There are 8 -electrons left to be accommodated in rings C and D. These two rings have a very similar NICS value, and to verify how the electronic density is distributed in these rings, the diamagnetic shielding values in the perpendicular direction, 𝜎⊥𝑑 , which corresponds mainly to the NICSdensity,

17,58

are used, and shown in Table 1. Ring C presents a very high (116.66) positive

paratropic diamagnetic shielding which is indicative that there is no resonant sextet located in this ring. Also, this high paratropic shielding cannot arise only from the electronic distribution in that ring which confirms that ring C is surrounded by two resonant sextets present in the adjacent rings B and D. The presence of these two resonant sextets, adjacent to ring C, produces magnetic fields that are opposite in direction to the applied external magnetic field at the position of the C ring, therefore, its NICS is highly positive, i.e. paratropic (see Figure 8 and related text). The final electronic distribution for PAH XXII, from the NICS analysis, is presented in Table 1.



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Page 26 of 40

26

For compound XXVII, which contains 26 -electrons; Table 1 indicates that the calculated highest NICS value corresponds to hexagons A and E, therefore there are resonant sextets located there. The lowest NICS value corresponds to hexagon D, therefore, there is no resonant sextet in this hexagon. There are 14 -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 the valence of some carbon atoms, and there is already a sextet in hexagon A. Thus, there could be a sextet in hexagons C and F, without overcoming any carbon atom valence and a double bond in hexagon B. The diamagnetic shielding values in the perpendicular direction, 𝜎⊥𝑑 , for rings B and C are -24.74, -54.35, respectively, which indicates that there is a sextet in ring C. Compound XXVIII has a C2h symmetry (based on the geometry optimization procedure described in Section 2 and based on literature information59) and contains 26 π-electrons. It can be concluded that the resonant sextets are located in the symmetry related hexagons labeled A and F, which present the highest NICS(1) value, and equal to -11.00, see Table 1. Hexagons B and E, also related by symmetry, present the lowest NICS(1) value; therefore, there are no resonant sextets in these hexagons but they contain at least one double bond each. There are left 10 π-electrons to be distributed in the symmetry related hexagons C and D, which have an intermediate NICS(1) value of -9.98. It could be considered that there is a resonant sextet and two double bonds in these hexagons, and there is a sextet migration between these two hexagons. In Table 1 the diamagnetic shielding values in the perpendicular direction are presented. Hexagons B, C, D, and E present almost the same value of -44, see Table 1, which only would occur if these four hexagons present a similar electronic distribution and this is only possible by considering sextet migration. Based on this analysis, the electronic distribution given by NICS for compound XXVIII is presented in Table 1. In this electronic distribution, the sextet


Page 27 of 40

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27

migration is alternated in a way that there are no adjacent resonant sextets at the same time; otherwise the valence of four of some carbon atoms would be overcome. The electronic distribution obtained with NICS(1) and the extended Y-rule method are in agreement. As demonstrated in Table 1, the results from the application of the postulated extended Yrule method match correctly with the results obtained using only the NICS methodology for the cata-PAHs I, III, VIII, X, XI, XIII, and XX, and with the results obtained using the NICS methodology plus the diamagnetic shielding calculations for the cata-PAHs XXII, XXVII, and XXVIII. The same sextet characterization strategy applied to the 10 cata-PAHs can be applied to the other 18 cata-PAHs in the family C26H16 and to the other cata-PAHs in the isomer families 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 Features of Cata-PAHs. As it was stated in the introduction, the extended Y-rule method for the characterization of the aromatic sextets explained here is a cornerstone for the estimation of the UV-Vis spectral band positions of cata-PAH using the Annellation Theory4,20 procedure described by Oña-Ruales and Ruiz-Morales34. Since the predictive procedure explained by Oña-Ruales and Ruiz-Morales34 is based on the knowledge of the location, number, and migrating behavior of the sextets in the peri-PAHs and cata-PAHs involved, the Y-rule method explained elsewhere17,18 and the extended Y-rule method proposed here has been respectively used to accomplish this spectral estimation. Following the predictive procedure,34 the estimation of the UV-Vis spectral band positions of dibenzo[g,p]chrysene, cata-PAH I in Figure 6, has been carried out using three reference PAHs, naphtho[8,1,2-ghi]chrysene XXX, benzo[g]chrysene XXXI, and benzo[p]



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Page 28 of 40

28

naphtho[1,8,7-ghi]chrysene XXXII, with experimental UV-Vis absorption spectral positions available from reference standards and from literature sources, as it is described in Figure 9. Benzo[g]chrysene XXXI has a sextet migrating behavior and distribution already established in Figure 5, and dibenzo[g,p]chrysene I has stationary sextets as it is already established in Figure 7. On the other hand, the characterization of the sextets for the peri-PAHs, naphtho[8,1,2ghi]chrysene XXX and benzo[p]naphtho[1,8,7-ghi]chrysene XXXII, has been obtained by means of the Y-rule method17. Using these PAH structures and their respective sextets characterizations, a figure similar to the Annellation Theory figures mentioned by Oña-Ruales and Ruiz-Morales34 has been applied so as to predict the positions of the UV-Vis spectral p and β bands for the cata-PAH dibenzo[g,p]chrysene I (see Figure 9). The referred theoretical procedure states34 that the position of the UV-Vis spectral bands of the PAH under investigation, e.g., PAH I located at the bottom right corner of Figure 9, can be deciphered using a two-step approach. Taking as a reference PAH I in Figure 9, the first step consists in subtracting the wavelength values of the spectral bands positions of the PAH located at the top right corner, PAH XXXI, and the PAH located at the top left corner, PAH XXX. The second step, afterwards, consists in adding this result to the spectral band positions of the PAH located at the bottom left corner, PAH XXXII. The predicted p and β UV-Vis spectral band positions of PAH I calculated using this method satisfactorily agree (showing an average difference lower than 2%) with the experimental p and β UV-Vis spectral bands positions reported in the literature20 for PAH I, dibenzo[g,p]chrysene, as it is mention in Figure 10.


Page 29 of 40

29

UV-Vis Bands Prediction of I

XXXI

XXX 357 342 327

λp, nm λβ, nm

UV-Vis

UV-Vis

λp, nm λβ, nm 306 295

UV-Vis

λp, nm λβ, nm

374 360

334 321 308

286 277

I

XXXII

UV-Vis

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


314 301 290

λp, nm λβ, nm

351 339

294 283

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-Vis spectral band positions of naphtho[8,1,2-ghi]chrysene XXX, benzo[g]chrysene XXXI,20 and benzo[p]naphtho[1,8,7-ghi]chrysene XXXII.60

I

λp, nm 351 336

λβ, nm 301 288

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



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4. CONCLUSIONS The extended Y-rule method has been proposed for the characterization of the sextets in the cata-PAHs C(10+4x)H(8+2x), where x=1, … , ∞, where the methodology based exclusively on the Yrule17,18 is not sufficient to achieve this objective because the Y-rule was designed to be applied in peri-condensed PAHs. The results of the application of the extended Y-rule method to cataPAHs C(10+4x)H(8+2x), where x=1, 2, 3, 4, were compared and successfully validated with literature information1,4,16,20 and with the results of the π-electronic distribution obtained by NICS(1) calculations. It is concluded that the extended Y-rule method is a straightforward heuristic and topological method, easy to apply, for the determination of the π-electronic distribution, i.e., location, number, and migrating direction of the sextets, for cata-condensed benzenoid PAHs with 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 apply because they require either computational theoretical chemistry calculations or the knowledge of all the Kekulé representations, which in many cases are not easy to establish. The method by Klavžar et al14, although easy to apply, does not provide information 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-rule method, gives a broader scope to the methodology here proposed. By means of this link, not only the aromatic character of the peri-PAH can be related to the respective aromatic character of the cata-PAH but also the UV-Vis spectral behavior, which is dependent on the sextet distribution inside of the molecule, can be deciphered by means of this peri-cata relationship. In this sense, a successful illustration of this approach has been presented


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for the prediction of the UV-Vis spectral features of dibenzo[g,p]chrysene. More importantly, the usage of computational techniques to characterize the aromatic sextets is unnecessary in the extended Y-rule method due to its easy approach that demands the usage of only a pen and a paper. 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. Notes Certain commercial equipment, instruments, or materials (or suppliers, or software, ...) are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. 6. ACKNOWLEDGMENT Y.R.-M. acknowledges the support under projects D.60019 and Y.61000 (CONACYT-SENER 177007) of the Instituto Mexicano del Petróleo.



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7. ABBREVIATIONS IUPAC, International Union of Pure and Applied Chemistry; PAH, Polycyclic Aromatic Hydrocarbons; PDI, Para-delocalization Index; HOMA, Harmonic Oscillator Model of Aromaticity; NICS, Nucleus-Independent Chemical Shift; UV-Vis, Ultraviolet-Visible; FAR, Fused Aromatic Rings. 8. REFERENCES (1) Zhang, L.; Fonari, A.; Liu, Y.; Hoyt, A-L. M.; Lee, H.; Granger, D.; Parkin, S.; Russell, T. P.; Anthony, J. E.; Bredas, J-L.; et al. Bistetracene: An Air-Stable, High-Mobility Organic Semiconductor with Extended Conjugation. J. Am. Chem. Soc. 2014, 136, 9248-9251. (2) Jiang, D. F.; Dai, S. Circumacenes versus Periacenes: HOMO–LUMO Gap and Transition from Nonmagnetic to Magnetic Ground State with Size. Chem. Phys. Lett. 2008, 466, 72-75. (3) Ruiz-Morales, Y. HOMO−LUMO Gap as an Index of Molecular Size and Structure for Polycyclic Aromatic Hydrocarbons (PAHs) and Asphaltenes: A Theoretical Study. I. J. Phys. Chem. A 2002, 106, 11283-11308. (4) Clar, E. The Aromatic Sextet; Wiley-Interscience: New York, 1972. (5) Fetzer, J. C. Large (C >= 24) Polycyclic Aromatic Hydrocarbons: Chemistry and Analysis; Wiley-Interscience: New York, 2000. (6) Solà, M. Forty years of Clar's aromatic π-sextet rule. Front. Chem. 2013, 1-22. (7) Randić, M. Algebraic Kekulé Formulas for Benzenoid Hydrocarbons. J. Chem. Inf. Comput. Sci., 2004, 44, 365–372.


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40 TABLE OF CONTENTS GRAPHIC


Extended Y-Rule Method for the Characterization of the Aromatic

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