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EFFECT OF HETEROATOMS ONPARTITIONING OF π-ELECTRONSIN RINGS OF CATAFUSENESAlexandru T. Balaban a , Ivan Gutman b & SonjaStanković ba Texas A&M University at Galveston , Galveston,Texas, USAb Faculty of Science , University of Kragujevac ,SerbiaPublished online: 23 Apr 2008.

To cite this article: Alexandru T. Balaban , Ivan Gutman & Sonja Stanković(2008) EFFECT OF HETEROATOMS ON PARTITIONING OF π-ELECTRONS INRINGS OF CATAFUSENES, Polycyclic Aromatic Compounds, 28:2, 85-97, DOI:10.1080/10406630801938427

To link to this article: http://dx.doi.org/10.1080/10406630801938427

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Polycyclic Aromatic Compounds, 28: 85–97, 2008

Copyright c© 2008 Taylor & Francis Group, LLC

ISSN: 1040-6638 print / 1563-5333 online

DOI: 10.1080/10406630801938427

EFFECT OF HETEROATOMS ONPARTITIONING OF π -ELECTRONS IN RINGSOF CATAFUSENES

Alexandru T. Balaban,1 Ivan Gutman,2

and Sonja Stankovic2

1Texas A&M University at Galveston, Galveston,Texas, USA2Faculty of Science, University of Kragujevac, Serbia

An earlier proposed method for assessing the π -electroncontent (EC) of rings of heteroatom–containing polycyclicconjugated molecules [Balaban et al., Polycyclic AromaticCompounds 27 (2007) 51] is modified so that the effects ofheteroatoms become additive. By means of this, relativelysimple rules for the changes of the EC-values could beformulated in the case of catafusenes.

Keywords π -electron content of rings, catafusenes, heteroatom-derivatives of benzenoid hydrocarbons, partition of π -electrons in ring

INTRODUCTION

A few years ago Randic and Balaban (1, 2) invented a method for par-titioning of π -electrons in rings of polycyclic molecules, that eventuallywas applied to a large variety of conjugated hydrocarbons, especiallybenzenoids (3–17). Recently this method was extended to heteroatom–containing benzenoid systems (18) and its applications to the simplestaza-derivatives of benzenoid molecules were reported (19, 20).

The introduction of heteroatoms into rings of benzenoid moleculescauses a displacement of electrons and, therefore, change of the π -electron content of rings. We illustrate this on the example of variousaza–derivatives of triphenylene.

Address correspondence to Ivan Gutman, Faculty of Science, P. O. Box 60, 34000 Kragujevac,Serbia. E-mail: gutman@kg.ac.yu

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86 A. T. Balaban et al.

FIGURE 1. (a) The numbering of the atoms and the labelling of the rings oftriphenylene. (b) The π -electron contents of the rings of triphenylene.

In Figure 1 is indicated the numbering (according to the IUPAC rules)of the carbon atoms of triphenylene, as well as the labelling of its rings.Also shown are the π -electron contents of the rings, as calculated ac-cording to the Randic–Balaban method (1, 2).

The π -electron content EC of the rings of heteroatom–containingbenzenoid molecules, calculated according to our method (18, 19), de-pends on an HMO–type parameter h, characteristic to the nature of theheteroatom. Recall, for instance, that benzene can be changed into pyri-dine, pyridinium or pyrylium salts (with varying properties according tothe nature of the heteroatom). Therefore, the computed EC-values de-pend on h, i.e., EC = EC(h). The nature of this dependence is illustratedin Figure 2.

FIGURE 2. Dependence of the π -electron content of the rings A, B, and C oftriphenylene (labelled as in Figure 1) on the parameter h of the heteroatom.(a) Heteroatom in position 1. (b) Heteroatom in position 2; note that EC(B) isalmost independent of h.

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Effect of Heteroatoms on Partitioning in Catafusenes 87

For the considerations in this work it is sufficient to observe the fol-lowing:

• EC(h) is either a monotonically decreasing or a monotonically in-creasing function of h. This holds for the chemically relevant valuesof h, say for 0 ≤ h ≤ 4.

• The dependence of EC(h) on h is not linear. However, for h lying ina relatively narrow interval, e.g., 0 ≤ h ≤ 0.5, the relation

EC(h) ≈ EC(0) + ah (1)

may be viewed as an acceptable approximation. Here EC(0) is theπ -electron content of the respective ring in the parent hydrocarbon.

In Table 1 are given the π -electron contents of the rings of various aza-derivatives of triphenylene, calculated according to the method describedin (18, 19), using the standard value h = 0.5 for the respective HMOparameter for pyridine–type nitrogen (21).

From the data in Table 1 it is easily seen that the EC-values are notadditive functions of the effects of individual N -atoms. For instance,a nitrogen atom in position 1 decreases the EC-value of the ring towhich it belongs by 0.034 electrons. Two nitrogen atoms in (mutuallyequivalent) positions 1 and 4 decrease the π -electron content by 0.037,instead of 2×0.0336 ≈ 0.07, what one would expect if the effect wouldbe additive. A nitrogen atom in position 2 increases the EC-value of thering to which it belongs by 0.032 electrons. Based on this, one mightexpect that the joint effect of two nitrogen atoms in positions 1 and 2

TABLE 1. The differences between the π -electron contents of the rings ofaza-derivatives of triphenylene and the π -electron contents of thecorresponding rings in the the parent hydrocarbon (see Figure 1 (b)). Thus,positive (resp. negative) values indicate an increase (resp. a decrease) of theπ -electron content, relative to the parent hydrocarbon. P. N. A. = position ofthe nitrogen atom(s), according to the numbering shown in Figure 1 (a). InFigure 1 (a) also the labelling of the rings (A,B,C,D) is indicated

P. N. A. A B C D

1 −0.0336 −0.0087 −0.0460 +0.08842 +0.0321 −0.0296 +0.0023 −0.00471,4 −0.0370 −0.0483 −0.0483 +0.13382,3 +0.0409 −0.0349 −0.0349 +0.02901,2 +0.0305 −0.0316 −0.0387 +0.03981,3 −0.0014 −0.0063 −0.0746 +0.0824

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88 A. T. Balaban et al.

would be nearly zero. In reality, two nitrogen atoms in positions 1 and 2increase the π -electron content of the ring by 0.030, which is nearly thesame as if nitrogen in position 1 would be absent.

Such multiple-heteroatom effects, which we are inclined to call “inter-ferences,” significantly complicate the analysis, understanding, and ra-tionalizing of the π -electron contents of rings of heteroatom-containingmolecules (20).

In what follows we offer a way out of this difficulty.

AN INTERFERENCE–FREE APPROACH TO THEπ-ELECTRON CONTENT OF RINGS OFHETEROATOM–CONTAINING BENZENOID MOLECULES

In the study of the effect of heteroatoms on partitioning of π -electronsin rings of polycyclic conjugated molecules it is purposeful to considerthe quantity (19)

�EC(R) = EC(R)h.c.m. − EC(R)p.h.

namely the difference between the π -electron content of the ring R,pertaining to the heteroatom–containing molecule (h.c.m.), and therespective π -electron content of the parent hydrocarbon (p.h.). Evi-dently, �EC(R) depends on the value of the parameter h (cf. Figure.2), and therefore we may write �EC(R) = �EC(R, h), noting that�EC(R, 0) = 0 for any ring R.

Our idea is to examine to effect of “infinitesimal” heteroatoms, thatis the effect of the parameter h when its values is near to zero. Formallyspeaking, we consider the limit value of

1

h

[EC(R)h.c.m. − EC(R)p.h.

] = 1

h�EC(R, h)

for h → 0. Recall that this limit value coincides with the multiplier a inEq. (1).

In what follows we denote

limh→0

�EC(R, h)

hby EC0 = EC0(R).∗

∗Note that the EC0-values reported in this work were obtained by evaluating �EC(R, h)/hat h = 0.00001.

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Effect of Heteroatoms on Partitioning in Catafusenes 89

The main (expected) property of EC0 is that it is additive with re-gard to the effects of several (mutually equal) heteroatoms present inthe molecule. Thus, if EC0(R)(i), EC0(R)( j), and EC0(R)(i, j) are theEC0-values of the ring R in the molecule possessing heteroatoms, re-spectively, in position i , in position j , and in both positions i and j ,then

EC0(R)(i, j) = EC0(R)(i) + EC0(R)( j) . (2)

As explained in the preceding section, nothing similar to this additivitycan be observed for ordinary EC-values.

Formula (2) can, of course, be extended to the case when there aremore than two heteroatoms, e.g.,

EC0(R)(i, j, k, �) = EC0(R)(i)+EC0(R)( j)+EC0(R)(k)+EC0(R)(�) . (3)

Examples illustrating formulas (2) and (3) are given in Table 2.As an immediate, but important, consequence of the absence of inter-

ference of several heteroatoms, it is sufficient to examine the EC0-valuesof rings of benzenoid molecules possessing a single heteroatom. In thatcase of several heteroatoms, EC0 can then be calculated by means ofEqs. (2) or (3), as exemplified in Table 2.

By examining the EC0-values of numerous catafusenes, we were ableto formulate the main regularities that govern the heteroatom–causedchanges of the π -electron contents of rings (relative to the parent hy-drocarbon). These rules are stated in the subsequent section. Analogousrules for perifusenes (that apparently will be much more complicated)await to be worked out in the future.

DEPENDENCE OF π-ELECTRON CONTENT OF RINGS ONTHE STRUCTURE OF HETEROATOM–CONTAININGCATAFUSENES

In order to be able to formulate the rules connecting molecular struc-ture and the EC0-values, we need to accept a few conventions and toadopt an appropriate notation.

As already explained, we are examining the EC0-values of cata-fusenes with a single “infinitesimal” heteroatom. The ring in which thisheteroatom is located will be denoted by R. A ring adjacent to R will bedenoted by S. With regard to S the heteroatom in R may be in position αor in position β, see Figure. 3. We say that the heteroatom is in position

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90 A. T. Balaban et al.

TABLE 2. The EC0-values of the rings of some aza-derivatives oftriphenylene; for labelling of atoms and rings see Figure 1. In the right columnis shown how the application of Eqs. (2) and (3) leads to results identical withthose obtained by direct calculation. Note that by symmetry, for EC0(A)(1) =EC0(A)(4) = EC0(B)(5) = EC0(B)(8) = EC0(C)(9) = EC0(C)(12),EC0(D) (1) = EC0(D)(4) = EC0(D)(5) = EC0(D)(8) = EC0(D)(9) =EC0(D)(12), etc

P. N. A. Ring EC0 Application of Eqs. (2) and (3)

1 A −0.0693 = EC0(A)(1)B −0.0176 = EC0(B)(1)C −0.0940 = EC0(C)(1)D +0.1808 = EC0(D)(1)

2 A +0.0651 = EC0(A)(2)B −0.0600 = EC0(B)(2)C +0.0046 = EC0(C)(2)D −0.0096 = EC0(D)(2)

1,4 A −0.1387 2EC0(A)(1) = −0.1386B −0.1114 EC0(B)(1) + EC0(C)(1) = −0.1116C −0.1114 EC0(B)(1) + EC0(C)(1) = −0.1116D +0.3616 2EC0(D)(1) = 0.3616

2,3 A +0.1302 2EC0(A)(2) = +0.1302B −0.0555 EC0(B)(2) + EC0(C)(2) = −0.0554C −0.0555 EC0(B)(2) + EC0(C)(2) = −0.0554D −0.0193 2EC0(D)(2) = −0.0192

1,2 A −0.0042 EC0(A)(1) + EC0(A)(2) = −0.0042B −0.0776 EC0(B)(1) + EC0(B)(2) = −0.0776C −0.0893 EC0(C)(1) + EC0(C)(2) = −0.0894D +0.1711 EC0(D)(1) + EC0(D)(2) = +0.1712

1,3 A −0.0042 EC0(A)(1) + EC0(A)(2) = −0.0042B −0.0130 EC0(B)(1) + EC0(C)(2) = −0.0130C −0.1539 EC0(B)(2) + EC0(C)(1) = −0.1540D +0.1712 EC0(D)(1) + EC0(D)(2) = +0.1712

1,6 A −0.0648 EC0(A)(1) + EC0(C)(2) = −0.0647B +0.0475 EC0(A)(2) + EC0(B)(1) = +0.0475C −0.1539 EC0(B)(2) + EC0(C)(1) = −0.1540D +0.1712 EC0(D)(1) + EC0(D)(2) = +0.1712

2,7,10 A −0.0550 EC0(A)(2) + 2EC0(B)(2) = −0.0549B +0.0096 EC0(A)(2) + EC0(B)(2) + EC0(C)(2) =

+0.0097C +0.0742 EC0(A)(2) + 2EC0(C)(2) = +0.0743D −0.0289 3EC0(D)(2) = −0.0288

1,4,6,11 A −0.1295 2EC0(A)(1) + 2EC0(C)(2) = −0.1294B −0.1064 EC0(B)(1) + EC0(C)(1) + EC0(A)(2)

+EC0(B)(2) = −0.1065C −0.1064 EC0(B)(1) + EC0(C)(1) + EC0(A)(2)

+EC0(B)(2) = −0.1065D +0.3423 2EC0(D)(1) + 2EC0(D)(2) = +0.3424

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Effect of Heteroatoms on Partitioning in Catafusenes 91

FIGURE 3. In diagram 1 are indicated the atoms in the ring R that (withregard to the neighboring ring S) are referred to as being in position α and β.In diagram 2 the atom marked by a heavy dot is in position α with regard tothe ring S, but in position β with regard to the ring S′. In diagram 3 are shownthe three ways in which a further ring can be attached to the system RS.

α if its distance to the ring S is unity. If its distance to S is two, then wespeak of a β position.

The second neighbor(s) of the ring R, that are first neighbors of S,will be denoted by T . A ring T can be attached to S in three differentways, as indicated by diagram 3 in Figure 3. Thus, in accordance withthe Balaban-Harary three-digit code (22–25), we speak of rings T1, T0,and T2, annelated to the system RS respectively in modes 1, 0, and 2,see Figure 4.

The next ring, annelated to the system RST will be denoted by U .Three of its nine possible arrangements are also shown in Figure 4. Ifwe need to consider additional rings, attached to R at a greater distancethan U , then these will be denoted consecutively by V , W , X , Y , . . . ,and supplied with an appropriate subscript 1, 0, or 2 (the three–digitcode (22–25)).

FIGURE 4. Three modes in which the ring T can be annelated to the systemRS, cf. diagram 3 in Figure 3, and three modes in which the ring U can beannelated to the system RST1.

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92 A. T. Balaban et al.

Structure–Dependency of EC0 in Case of Heteroatom in Position α

In what follows we assume that the “infinitesimal” heteroatom in thering R is in position 1, as indicated in diagram 1 in Figure 3.

Rule α0. A heteroatom in position α moves the π -electrons awayfrom the ring R, resulting in a negative EC0(R)-value. In the absence ofmode 0 annelation (see below) the π -electrons from ring R flow to theneighboring ring S, whose EC0-value is therefore increased.

The regularities stated here as Rule α0 have, for EC(R), been observedalready in our earlier works (19, 20).

Rule α1. If the T ring is annelated in mode 1, then also from this ringthe π -electrons flow into ring S, resulting in negative EC0(T1) and verylarge EC0(S). The π -electron contents of more distant rings (U , V , W ,. . . ) is only slightly influenced by the heteroatom.

Rule α2. If the ring T is annelated in mode 2, then the displacementof π -electrons is similar as in mode 1 annelation, just somewhat weaker.

Rule α3. If the rings T , U , V , . . . are annelated in mode 0, then theπ -electrons are shifted as far as such a linear segment goes. Then theEC0-values increase along the linear segment, becoming maximal atthe linearly annelated ring that is most distant from R. If after mode 0annelation there is a ring annelated in mode 1 or 2, then its EC0-valueobeys Rules α1 or α2, just the effect is less pronounced. The EC0-valuesof further rings (if any) are practically not affected by the heteroatom.

Examples illustrating the above four rules are given in Figure 5.

Structure–Dependency of EC0 in Case of Heteroatom in Position β

In what follows we assume that the “infinitesimal” heteroatom in thering R is in position 2, as indicated in diagram 1 in Figure 3.

Rule β0. A heteroatom in position β attracts the π -electrons intothe ring R, resulting in a positive EC0(R)-value. Except in the case ofmode 2 annelation (see below) the π -electrons into ring R flow from theneighboring ring S, whose EC0-value therefore becomes negative.

Rule β1. If the T ring is annelated in mode 1, then the change of theπ -electron contents in both this ring (T1) and in any additional rings (U ,V , . . . ) is negligible.

Rule β2. If the ring T is annelated in mode 2, then a significant lossof π -electrons from this ring happens, which flow into ring S. ThereforeEC0(T2) assumes large negative values. Because the π -electrons fromring S flow into ring R, the result is that the π -electron content of ringS is only slightly changed and remains near zero. The EC0-values offurther rings (if any) are practically not affected by the heteroatom.

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Effect of Heteroatoms on Partitioning in Catafusenes 93

FIGURE 5. Examples illustrating Rules α0 (all examples), α1 (first row), α2

(second row), and α3 (third and fourth rows). The EC0-vales, inscribed in thecorresponding hexagons, are rounded to two decimal places and multiplied by100. The position of the “infinitesimal” heteroatom is indicated by the heavydot.

A convincing example of the effects described in Rules β1 and β2 isseen in Figure 2 (b), where the curves A, B, C pertain to rings of the typeR, T1, and T2, respectively.

Rule β3. If the ring T is annelated in mode 0, then the displacementof π -electrons is similar as in mode 1 annelation.

Examples illustrating the above four rules are given in Figure 6.

DISCUSSION AND CONCLUSION

By means of the eight rules stated in the preceding section it is possi-ble, in a semiquantitative manner, to predict the flow of the π -electronsbetween rings (caused by a single heteroatom) in any catafusene.

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94 A. T. Balaban et al.

At this point it is necessary to mention that our considerations per-tain only to resonance–type effects, neglecting the inductive effect(s)of the heteroatom(s). In the case of real (i. e., not “infinitesimal”) het-eroatoms, these inductive effects may significantly alter the true flow ofπ -electrons. In particular, in both heterocycles such as quinoline (het-eroatom in position α) and isoquinoline (heteroatom in position β), cf.Figure 3, due to the higher electronegativity of nitrogen, the ring R holdsmore tightly its π -electrons than the ring S. In other words, the chemicalbehavior of quinoline and isoquinoline does not provide evidence for a“push” versus “pull” effect of π -electrons. Therefore, a degree of cautionis needed when the above rules are applied to real heteroatom containingpolycyclic conjugated molecules.

Being aware of the above limitations, in more complicated cases,namely when the catafusene is branched or when the ring containing the

FIGURE 6. Examples illustrating Rules β0–β3. Other details are same as inFigure 5.

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Effect of Heteroatoms on Partitioning in Catafusenes 95

FIGURE 7. The labelling of the rings of benzo[g]chrysene and theirEC0-values. The EC0-values and the position of the heteroatom are presentedin the same way as in Figures 5 and 6.

heteroatom has two neighbors, the rules stated in the preceding sectionshave to be combined.

Consider, for instance, the heteroatom–derivative of benzo[g] chry-sene, shown in Figure 7.

The heteroatom is in position α with regard to ring C, and in positionβ with regard to ring B. Therefore, by Rules α0 and β0, the heteroatomcauses the π -electrons flow from B to D, and simultaneously from D to

FIGURE 8. A diagrammatical summary of the rules for theheteroatom–caused displacements of π -electrons in rings of catafusenes. Notethat these are displacements caused only by resonance effect, whereasinductive effects have not been taken into account.

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96 A. T. Balaban et al.

C. As a consequence of this, EC0(B) and EC0(C) have large negativeand positive values, respectively. On the other hand, EC0(D) remainssmall.

Bearing in mind the position of the heteroatom, the ring E is annelatedin mode 1, and thus Rule α1 is applicable: EC0(E) has a relatively largenegative value. The ring A is annelated in mode 2, and it obeys Rule α2:its EC0-value is negative, but small.

The eight rules stated in the preceding section can be diagrammaticallyrepresented as in Figure 8. These rules describe the main features, but notthe fine details, of the displacements of the π -electrons in rings, causedby a heteroatom that is more electronegative than carbon. The rules wereobtained by studying a large number of examples, and only part of themcould be theoretically justified (19). Therefore additional research alongthese lines would be necessary.

The above formulated rules apply also in the case of perifusenes, butfor these benzenoid systems several additional constellations of ringsneed to be considered. Therefore the elaboration of the much more com-plicated case of perifusenes remains a task for the future.

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Effect of Heteroatoms on Partitioning in Catafusenes 97

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