Assessing the Extent of Ï-Electron Delocalization in Naphtho

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Assessing the Extent of #-Electron Delocalization in NaphthoAnnelated Fluoranthenes by Means of Topological Ring-Currents Timothy K Dickens, Roger B Mallion, and Slavko Radenkovi# J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b12068 • Publication Date (Web): 22 Jan 2019 Downloaded from http://pubs.acs.org on January 26, 2019

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The Journal of Physical Chemistry

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Assessing the Extent of π-Electron Delocalization in Naphtho-Annelated Fluoranthenes by means of Topological Ring-Currents Timothy K. Dickens*†, Roger B. Mallion‡, and Slavko Radenković§

University Chemical Laboratory, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England, United Kingdom

School of Physical Sciences, University of Kent, Canterbury CT2 7NH, England, United Kingdom Faculty of Science, University of Kragujevac, 12 Radoja Domanovića, 34000 Kragujevac, Serbia

Abstract The extent of π-electron delocalization in the five-membered rings of 14 naphtho-annelated fluoranthenes has recently been assessed by means of several approaches, including application of the following indices: the energy effect (ef), bond resonance-energy (BRE), multi-center delocalizationenergies (MCI), the index arising from the harmonic-oscillator model of aromaticity (HOMA), and nucleus-independent chemical shifts (NICS). The calculated Hückel–London–Pople–McWeeny (HLPM) (“topological”) ring-current intensities (TRC) for the five-membered rings of these same structures are here compared with the above-named indices in order to assess how well TRC parallels these other criteria. The indices ef and BRE are the ones that correlate best with TRC and it is suggested that this is because all three approaches are founded on the Hückel model. TRC does not, however, confirm the proposal that cyclic delocalization in the five-membered rings can be greater than in any of the six-membered rings in this series of conjugated systems. Certain ostensible shortcomings of the

* Corresponding author. E-Mail: [email protected]. Phone: +44 1223 763 811 †

University Chemical Laboratory, University of Cambridge

‡

School of Physical Sciences, University of Kent

§

Faculty of Science, University of Kragujevac

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2 NICS approach are discussed and some doubts are emphasized regarding the legitimacy of associating “ring currents” with “aromaticity”.

Introduction One of us (SR), and collaborators,1 recently examined the extent of π-electron conjugation in the five-membered rings of fluoranthene (the structure labeled “1” in Figure 1) and the 14 naphtho-annelated fluoranthenes illustrated in Figures 1 and 2. This was done by applying the following indices (often described1 as “indices of aromaticity” — see also ref 2): the energy effect (ef),3–7 bond resonance-energy (BRE),8,9 multi-center delocalizationenergies (MCI),10,11 the index arising from the harmonic-oscillator model of aromaticity (HOMA),12,13 nucleus-independent chemical shifts (NICS),14,15 and current-density maps.1 It was found1 that, according to the first four criteria in the above list, the pentagonal rings in certain naphtho-annelated fluoranthenes appear to participate more in the conjugation of the molecule as a whole than do some of the hexagonal rings, and that, of those listed above, the magnetic indices do not in general support the results obtained by the energetic, electrondelocalization, and geometrical indices.

F

C

D

D

A

A

A

B

B

C

1 (Fluoranthene)

E

N-a1-1

N-a3-1

H

H

G

D A

A B

C

E

G

N-a1a2-1

E

F

G

D A C

H

J

I

D

I

H

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C

G

D A

A B

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N-a1a4-1

J

E

E

B

C

N-a1a3-1 F

H

D A

B

C

F

H

G

D

B

C

F

E

B

E

F


C

B

E

F

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3

N-a3a4-1

N-a1a2a3-1

N-a1a3a4-1 J

L K

I

D A

G

H

C

B

F

E

N-a1a2a3a4-1 Figure 1. The carbon–carbon connectivities (“molecular graphs”16) and ring labelings for fluoranthene and nine angularly naphtho-annelated fluoranthenes introduced in ref 1 and studied in this Article.

C

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D

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E

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N-l1l3-1

B E F

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N-l1l2l3-1


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4 Figure 2. Carbon–carbon connectivities (“molecular graphs”16) and ring labelings for five linearly naphthalene-annelated fluoranthenes introduced in ref 1 and studied in this Article.

Two of us (TKD and RBM), together with Balaban and Gutman,7 had earlier studied energy-effects in the five-membered rings of benzo-annelated fluoranthenes by comparing these with an application of the notion of so-called “topological” ring-currents.17 This is a formalized, quasi graph-theoretical16 approach, based on the traditional methods of Hückel,18 London,19 Pople20 and McWeeny21 (HLPM); the so-called “topological ring-currents” 7,17 (TRC) that arise from these formalisms depend only on the connectivity of the carbon atoms in the molecular graph16 representing the conjugated hydrocarbon under study, and on the geometrical areas of its constituent rings. The HLPM model7,17 has been extensively reviewed.22–25 In this communication we subject the 15 structures considered by Radenković et al.1 (depicted in Figures 1 and 2) to an investigation based on the calculated HLPM “topological” ring-currents,7,17 in order to find how, for these structures, the latter correlate with the various indices already reported in ref 1 and referred to in our opening paragraph.

Calculations Values of the several indices referred to in the Introduction had already been calculated in ref 1 and their mode of computation was fully described there. The HLPM calculations were effected according to the standard assumptions exhaustively described in, for example, refs 7, 17 & 22–25. The areas of all the five-membered rings were taken to be (5 tan( / 5)) / (6 tan( / 6)) times the area of a standard benzene hexagon20 — that is, in practice, ca. 66% of that latter area. The topological ring-current intensities calculated for the various rings (labeled with letters A–L, as indicated in Figures 1 and 2 and in the corresponding Figures of ref 1) are presented in Table 1 (for rings A–D) and in Table 2 (for rings E–L). The HLPM topological ring-currents are dimensionless quantities expressed, as they are, as a ratio to the benzene value calculated by the same method. Ring currents in all rings are documented here for completeness but our discussion will largely be confined to those in Table 1 — namely, rings B–D and especially the rings A, which constitute the lone five-membered ring in all of these structures. The nomenclature of these 15 structures is also as defined in Figures 1 and 2 and in ref 1. (“a” denotes an angular annelation of a naphthalenic moiety, as in Figure 1, and “l” denotes a linear one, as in Figure 2.) Table 1. Topological Ring-Currents in Rings A–D of the 15 Conjugated Systems 1 to N-l1-l2-l3-1 (with Rings and Structures Labeled as in Figures 1 & 2). Structure 1 N-a1-1 N-a3-1 N-a1a2-1

Ring A 0.050 0.117 0.064 0.321

Ring B 0.987 1.133 0.952 1.093

Ring C 0.860 0.961 0.963 1.093


Ring D – 0.848 0.917 0.881

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5 N-a1a3-1 N-a1a4-1 N-a3a4-1 N-a1a2a3-1 N-a1a3a4-1 N-a1a2a3a4-1 N-l1-1 N-l3-1 N-l1l2-1 N-l1l3-1 N-l1l2l3-1

0.157 0.161 0.070 0.424 0.174 0.442 0.050 0.030 0.040 0.029 0.024

1.061 1.080 0.941 0.985 1.036 0.939 0.810 0.983 0.946 0.807 0.940

0.932 0.922 0.941 1.002 0.905 0.939 1.033 0.983 0.946 1.027 0.940

0.874 0.881 0.647 0.848 0.609 0.565 0.858 0.939 0.854 0.936 0.933

Table 2. Topological Ring-Currents in Rings E–L of the 15 Conjugated Systems 1–N-l1-l2-l3-1 (with Rings and Structures Labeled as in Figures 1 & 2).

Structure 1 N-a1-1 N-a3-1 N-a1a2-1 N-a1a3-1 N-a1a4-1 N-a3a4-1 N-a1a2a31 N-a1a3a41 Na1a2a3a41 N-l1-1 N-l3-1 N-l1l2-1 N-l1l3-1 N-l1l2l3-1

Ring E

Ring F

Ring G

Ring H

Ring I

– 1.253 1.221 1.211 1.222 1.229 1.184 1.168 1.210 1.148 1.219 1.200 1.257 1.217 1.254

– 1.058 1.070 1.038 1.050 1.051 1.098 1.029 1.047 1.024 1.097 1.055 1.100 1.096 1.098

– – – 1.211 1.207 1.205 1.184 1.174 1.172 1.148 – – 1.257 1.198 1.254

– – – 1.038 1.069 1.067 1.098 1.030 1.096 1.024 – – 1.100 1.055 1.098

– – – – – – – 1.206 1.159 1.150 – – – – 1.197

Ring J

Ring K

Ring L

– – – – – – – – – – – – – – – – – – – – – 1.077 – – 1.088 – – 1.089 1.150 1.089 – – – – – – – – – – – – 1.054 – –

Trends in the Topological Ring-Currents and Comparison with the Other Indices Considered (a) Assessment of the Ring-Current Data in Tables 1 & 2 It is immediately seen from Table 1 that the topological ring-current in the “empty rings”1 (A) is less variable amongst the “linear” annelations (with values not dissimilar to that of fluoranthene (1) itself (0.05)26–29 — indicated in the last five rows of Table 1) than amongst the “angular” ones (rows 2–10). The point was not emphasized in ref 1 but it is 5 ACS Paragon Plus Environment


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evident from that account that the effect of linear naphthalenic annelations (Figure 2) is significantly weaker than the effect of the corresponding angular annelations (Figure 1). The same holds for the benzo-annelations that were studied in ref 7. The five-membered rings (labeled “A”) in the structures shown in Figures 1 and 2 are, in ref 1, described as “empty” because the unshared bonds in those rings never appear other than as single bonds in any Kekulé structure that can be devized for the structure as a whole.30 This fact intuitively suggests that the extent of participation of such “empty” rings in the conjugation that is extant within the entire structure is minimal — literally, in fact, zero. As Radenković et al.1 put it: all methods based on Kekulé structures “. . . predict that in an ‘empty’ ring there would be no π-electron cyclic conjugation and that this ring would be nonaromatic.” It is also evident from Table 1 that the ring currents in Rings B and C vary very little (ca. 0.86–1.13) throughout the whole series, all being within 15% of the benzene value. With exception of ring D in N-a1a2a3a4-1 and ring D in N-a3a4-1 there is also very little variation in the topological ring-current in the rings D, all being within the range 0.84– 0.94. This consistency in most of the rings B, C and D is in contrast to what was observed with all the indices that were employed in the earlier work1 being considered here. In their paper that motivated this work, Radenković et al.1 rhetorically asked “Can the five-membered rings be more aromatic than the six-membered rings?” and they answered that “An empty five-membered ring can be even more aromatic than some hexagonal rings in the same structure.” This occurred in the structure that they called Na1a2a3a41 in Figure 2 of ref 1 and in Figure 1 of the present paper. If it be conceded that diamagnetic ring-current is an intuitive indication of “aromaticity” — and this is indeed a controversial matter (see, for example, refs 31–42) that we shall refer to again, later in this paper — then the tabulated topological ring-currents presented in Table 1 do not support that conclusion. The nearest that the topological ring-currents come to this state of affairs is in this structure N-a1a2a3a4-1 in which the “empty” ring (ring A) has associated with it a topological ring-current intensity of 0.442, whilst the smallest ringcurrent among the six-membered rings in this molecule is a little larger, at 0.565. (See Figure 3). Even though the central five-membered ring’s current is exceeded by those in the six-membered rings, it does nevertheless appear from Table 1 that the larger the structure in the angularly annelated series, the larger the topological ring-current in the central five-membered ring (A) seems to be. A similar, and more pronounced, phenomenon regarding strong topological ring-currents in the centers of larger structures was noted in ref 43, in the middle regions of large, fully benzenoid hydrocarbons. It is in any case clear44 that in the five-membered rings of angularly Naphtho-annelated fluoranthene derivatives there can be a significant extent of cyclic π-electron conjugation (albeit — when judged by the criteria of topological ring-currents — smaller than that encountered in the six-membered rings) that cannot be anticipated from Kekulé structures (according to which the five-membered ring is an “empty”1,29,20,44 ring). 6 ACS Paragon Plus Environment

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1.089

1.089 1.150

1.150 0.565

0.442

1.024

1.148

0.939

0.939

1.024

1.148

Figure 3. Map of (diamagnetic) HLPM topological ring-currents24,25 for the structure N-a1a2a3a41. The currents are dimensionless because they are expressed as a ratio to the HLPM topological ring-current calculated, by the same method, for benzene.

(b) Comparison with other Indices of π-Electron Conjugation The topological ring-current (TRC) intensities displayed in column 2 of Table 1 for the Rings A in all of the 15 structures considered here and in ref 1 were regressed against each of the six indices for which numerical (as distinct from pictorial) information is available from ref 1. In each case, TRC was plotted along the ordinate and each of the six indices, in turn, was plotted as the abscissa. Such plots of TRC versus ef and TRC versus BRE are illustrated in Figures 4 and 5, respectively. The correlation coefficients of all six of the regression lines constructed in this way are listed in Table 3. 0.60 0.50

TRC

0.40 0.30 0.20 0.10 0.00 0.000

0.005

0.010

0.015

0.020

0.025

ef


0.030

0.035

0.040

0.045


8 Figure 4. Straight-line regression of Topological Ring-Current (TRC)24,25 in Rings A of the 15 structures studied versus Energy Effect (ef).3–7 TRC is dimensionless25 and ef is expressed in units of the standard Hückel18 carbon–carbon resonance-integral, β, whose recommended value is

≈137 kJmol–1.

0.60 0.50 0.40

TRC

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

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0.30 0.20 0.10 0.00 0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

BRE

Figure 5. Straight-line regression of Topological Ring-Current (TRC)24,25 in Rings A of the 15 structures studied in ref 1 versus Bond Resonance Energy (BRE).8,9 TRC is dimensionless25 and BRE8,9 is expressed in units of the standard Hückel18 carbon–carbon resonance-integral, β.

Table 3. Correlation Coefficients of Regression Lines Confronting Topological Ring-Currents (as the Ordinate) with the Six Different Indices Indicated (Plotted as the Abscissa)a Index Correlation Coefficientb with TRC

Ef3–7

BRE8,9

MCI10,11

0.974

0.994

0.825

HOMA12,13 NICS(0)14,15 NICS(1)14,15 0.869

0.886

0.878

a

In all cases the correlation coefficients (R-values) of these plots are for unconstrained correlations — that is, lines that are not forced to go through the origin. b For

the correlation between topological ring-current (TRC)24,25 in rings A and (in turn) each of the six indices indicated. For possible insight, the regression lines in Figures 4 and 5 were repeated but this time constraining the lines to go through the origin. The regression corresponding to Figure 4 (TRC versus ef) had an R2-value of 0.9377; (this is equivalent to a correlation coefficient, R, 8 ACS Paragon Plus Environment

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of approximately 0.968, compared with 0.974 for the unrestricted plot.) The regression analogous to Figure 5 (TRC versus BRE) had an R2-value of 0.9867 (correlation coefficient, R, approximately 0.993, compared with ca. 0.994 for the unrestricted plot.) These regressions in which the lines were forced to go through their respective origins are thus seen to have negligibly different correlation coefficients from the corresponding unrestricted plots. It is seen from Figures 4 and 5 and Table 3 that TRC24,25 correlates with ef3–7 and BRE8,9 with high correlation coefficients — approximately 0.97 and 0.99, respectively. However, Table 3 shows that the correlation of TRC with the other four indices adopted in ref 1 (MCI,10,11 HOMA12,13 and NICS(0) & (1)14,15) is considerably weaker — correlation coefficients being in the range ca. 0.82 – 0.88. It may be the case that the concordance of TRC with ef and with BRE arises because all three approaches are based on the Hückel model.18 Indeed, when the ef and the BRE data used to compile Figures 4 and 5 and Table 3 are freely regressed against each other, a very high correlation coefficient of ca. 0.99 is obtained. Furthermore, as has already been pointed out,25 adopting, as it does, a graphtheoretical16 approach to ring currents,45 Aihara’s ‘circuit’ formalism46,47 is entirely equivalent, numerically, to the HLPM method,24,25 when identical Hückel assumptions are invoked and the two sets of calculations are based on the same molecular geometry. It was observed in ref 1 that the magnetic indices do not support the results obtained by examining the energetic, electron delocalization and geometrical indices — thereby confirming a so-called “multi-dimensional” 2 aspect of indices such as those under consideration. Here, we do not further examine the current-density maps presented in ref 1 as they do not immediately provide quantitative data with which to compare the TRC reported in Tables 1 and 2. We do note in passing, however, that the quality of the correlations of TRC with computations effected by NICS(0) and NICS(1),14,15 though not as good as those for ef and BRE, are similar to those found for MCI and HOMA (Table 3). It should be noted that the NICS idea as a measure of the “aromaticity” of a given ring in a polycyclic structure14,15 has been criticized — see for example pp 20–21 of ref 48, pp 1366–1369 of ref 23, pp 1945–1947 of ref 49, and pp 6602–6606 of ref 50. Furthermore, it should be borne in mind that the single-point NICS index14,15 measures the shielding calculated at the center of a given ring (NICS(0)) (or — NICS(1) — at some distance above that ring-centre), as a result of the ring currents in all the rings of the molecule under study. Such a shielding is thus a single number associated with that given ring in a polycyclic structure (with, say, n rings) which depends on (a) the ring-current in that ring and (to a smaller extent) the ring currents in all the other (n – 1) rings in the conjugated system, and (b) the geometrical relation of that ring center (or point above the ring) to its own ring and to each and every one of the other (n – 1) rings. That single calculated shielding thus in general depends on 2n independent quantities. Now, since the topological ring-current intensity in a given ring is a calculated property only of that particular, single, ring, it is perhaps not surprising that the correlation between NICS(0) and NICS(1) values on the one hand, and topological ring-currents on the other, is not strong (as is indicated by the data in the sixth and seventh columns of Table 3). Similar, though much stronger, reservations about NICS have also been expressed on several occasions by Stanger et al.,49,50 including the ostensibly censorious remark (on p 6604 of ref 9 ACS Paragon Plus Environment


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50) that “. . . the NICS value of one ring in a conjugated polycyclic system is practically worthless for understanding the system. . .”50 In addition to single-point NICS indices such as NICS(0) and NICS(1),14, 15 there are, however, more-advanced NICS-related approaches — such as the NICS scans introduced by Stanger and Gershoni-Poranne51,52 and the calculation of NICS iso-chemical-shielding surfaces53, 54 — that are much more general and are likely to produce significantly morereliable results for conjugated polycyclic compounds such as those studied here. Finally, it would perhaps also be appropriate to mention Sundholm’s55 approach of gauge-including magnetically induced currents (GIMIC), as it would possibly be relatively straightforward to carry out Hartree-Fock or density-functional theory GIMIC calculations for the polycyclic conjugated structures investigated here. It would, for example, be of interest to see whether there might be significant differences from the CTOCD-DZ55 current-density maps reported in ref 1.

“Ring-Currents” and “Aromaticity”23 We conclude by making some comments and historical observations on the vexed question as to whether “ring currents” — and, here, we consider explicitly only HLPM “topological” 7, 17, 25 ring-currents — may be considered to be some measure of, or even a definition of, “aromaticity”. The idea was first put forward in 1961 and was subsequently evaluated in the early 1960s31–34 and much discussed in the 1970s (e.g., ref 35). The suggestion from Elvidge et al.31–34 was that ring currents become “. . . a new criterion of aromaticity rather than those then extant.”35 Furthermore, Elvidge et al.31–34 always made it clear — at least, in the first instance — that they were dealing only with mono-cycles. When, at about the same time, Pople and Untch36 declared [4n]-π-electron conjugated systems to be paramagnetic and similar [4n+2]-systems to be diamagnetic, they, too, restricted themselves to consideration of moncyclic annulenes. Like the famous Hückel Rule for Aromaticity,18 this rule strictly applies only to monocycles. Now, as long ago as 1969, Jung37 pointed out the difficulties that arise from the ringcurrent criterion for the overall aromaticity of polycyclic structures when some rings in the given structure bear diamagnetic currents and others bear paramagnetic ones — a situation that does not, however, arise in the structures being dealt with in the present Article, in which all calculated ring-currents in all rings of the 15 structures studied are diamagnetic. One of us (RBM)38 tried to circumvent this problem by suggesting that the overall calculated “London” (“ring-current”) magnetic susceptibility of a given structure, (expressed as a ratio, π-London (  )  χ Structure   π-London ( )  , to the similarly calculated benzene value) should be used instead, because this  χ Benzene  yields a single number for a given conjugated molecule. This is shown by an application of (for example) equation (5) of ref 56:


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11 π-London (  ) r  χ Structure   Si   J i    π-London ( )     , S Benzene   J Benzene   χ Benzene  (rings)  i =1

where Si is the area of the ith ring in the conjugated system in question (which, in all, is comprised of r rings), SBenzene is the area of a standard benzene hexagon, Ji is the HLPM topological ring-current intensity in the ith ring, and JBenzene is the topological ring-current in benzene itself, calculated by the same method. It is evident, therefore, that “London” magnetic susceptibilities — denoted by the  χ π-London ( )  symbol  Structure for a given structure in refs 22, 24, 25, and 56 and elsewhere — may be π-London (  )   χ Benzene  calculated by means of the above expression by simple arithmetic, purely from a knowledge of (a) the HLPM “topological” ring-currents in each of the several rings and (b) the areas of the individual rings which comprize the conjugated structure in question. However, this strategy gave rise to the difficulty38 that paramagnetic systems, especially, were extremely sensitive to the sophistication of the method (and especially of the wavefunction) that was used to calculate them.38–42

To a certain extent, these concerns regarding “aromaticity” and “ring currents” have since been superseded by developments, over the last decades, in the field of ab initio calculations such as those mentioned at the end of the previous section — see, however, a reviewer’s remarks at the end of ref 57 concerning the conceptual value of more simpleminded non-ab-initio approaches such as the HLPM one being advocated here. We nevertheless maintain that there are still unsatisfactory aspects of regarding “ring currents” as a measure or diagnosis of “aromaticity”.

Conclusion Of the six indices invoked in ref 1 in order to assess the extent of π-electron cyclic delocalization in the five-membered rings of fluoranthene and 14 naphtho-annelated fluoranthenes, those which correlate best with HLPM “topological ring-currents” (TRC)7,17,24,25 are Energy Effect (ef)3–7 and Bond Resonance Energy (BRE8,9). Having a very high correlation coefficient between themselves (ca. 0.99), ef and BRE are the very entities considered here that, like the TRC index itself, are based on the Hückel model.18 This, therefore, is likely to be the reason for the concordance that arises amongst these three criteria for π-electron delocalization.

Acknowledgement SR thanks the Serbian Ministry of Education, Science, and Technological Development for support through Grant # 174033.



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