Origin of Kinetic Instability of Fullerenes That Violate the Isolated

Subscriber access provided by UNIVERSITY OF TOLEDO LIBRARIES

Article

Origin of Kinetic Instability of Fullerenes That Violate the Isolated Pentagon Rule Jun-ichi Aihara J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b00112 • Publication Date (Web): 09 Mar 2015 Downloaded from http://pubs.acs.org on March 15, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 27

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

The Journal of Physical Chemistry

Origin of Kinetic Instability of Fullerenes That Violate the Isolated Pentagon Rule Jun-ichi Aihara* Department of Chemistry, Faculty of Science, Shizuoka University, Oya, Shizuoka 422-8529, Japan

ABSTRACT: The isolated pentagon rule (IPR) holds without exceptions for neutral fullerene molecules. Unlike those in non-IPR fullerenes, 5/5 bonds (i.e., π-bonds shared by two pentagons) in many planar polycyclic π-systems are kinetically rather stable with large positive bond resonance energies (BREs), where BRE is a graph-theoretically defined index of kinetic stability. Geometric conditions were explored for designing planar polycyclic π-systems with unstable 5/5 bonds. We then found that the kinetic instability of non-IPR fullerenes stems from the coexistence of pentalene substructures and nearby disjoint pentagons. Proper arrangements of fused pentagons and disjoint pentagons make the 5/5 bonds highly reactive with large negative BREs.

Keywords:

non-IPR

fullerene;

kinetic

instability;

bond

cyclopentahexacene: dicyclopentahexacene.

Received: January 5, 2015.

1 ACS Paragon Plus Environment

resonance

energy;


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

INTRODUCTION A spheroidal π-system of a fullerene molecule consists of a suitable number of hexagonal and 12 pentagonal rings.1-3 Although many different fullerenes are detectable during the laser vaporization of graphite4,5 or from the soot formed in the carbon arc reactor,6,7 most of them are not isolable in macroscopic amounts. This implies that many neutral fullerene molecules are rather comparable in thermodynamic stability but are markedly different in kinetic stability. As isolable fullerenes do not have abutting pentagons, it has been believed that pentagonal rings must be separated from each other in chemically stable or isolable fullerenes. This empirical rule is known as the isolated pentagon rule (IPR).1-3 It is very true that non-IPR or IPR-violating fullerenes are too reactive to isolate.8 Thus, the IPR is one of the necessary conditions for the isolability of neutral fullerene molecules. Kinetic instability of non-IPR fullerenes has been attributed to the antiaromaticity and local strain of the pentalene units.1,2,8 However, local strain seems not to be the main origin of kinetic stability, now that many metallofullerenes with non-IPR carbon cages have been isolated successfully.9-11 Thermodynamic stability of a fullerene cage almost monotonously increases as the size of the cage increases.12 In 1995, we defined graph-theoretically what is called bond resonance energy (BRE) as an indicator of kinetic stability and then found that a π-bond shared by two pentagons in a fullerene molecule has a large negative BRE, which seems to contribute significantly to the decrease in kinetic stability of the molecule.13-16 BRE for a given π-bond represents the aromatic contribution of all circuits that pass through the π-bond.13-17 As shown in Figure 1, π-bonds shared by two pentagons (i.e., 5/5 bonds) in non-IPR fullerenes, such as those in C50 (D5h, 1), exhibit large negative BREs. C60 (Ih,


Page 2 of 27

Page 3 of 27

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


2) and any IPR-satisfying fullerene do not have such reactive 5/5 bonds.13,14 It is the existence of such highly antiaromatic local structures that sharply distinguishes non-IPR fullerenes from IPR-satisfying isomers.13-16 A variety of exohedral non-IPR derivatives have indeed been prepared based on the remarkable reactivity of fused pentagons.8,9

Figure 1. BREs in units of |β| for two typical fullerenes. BRE for a 5/5 bond is given in red.

Like non-IPR fullerenes, planar polycyclic π-systems, such as pentalene (3), dibenzo[ed,gh]pentalene (4), and dibenzo[a,e]pentalene (5) in Figure 2, have 5/5 bonds. A serious problem then arose from the finding that, unlike those of non-PPR fullerenes, 5/5 bonds in these planar π-systems exhibit large positive BREs, stabilizing the antiaromatic framework of the π-system.17,18 This fact strongly suggests that the kinetic instability of non-IPR fullerenes cannot be attributed simply to the existence of 5/5 bonds in the pentalene moieties. In this paper, we examine whether or not planar polycyclic conjugated hydrocarbons with reactive 5/5 bonds can be designed and then attempt to explore in graph-theoretical terms the origin of kinetic instability of 5/5 bonds in non-IPR fullerenes.



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

Figure 2. BREs in units of |β| for pentalenes. BREs for 5/5 bonds are given in red.

THEORY In brief, bond resonance energy (BRE) is defined as follows.13-17 A hypothetical cyclic π-system, in which a given π-bond (e.g., a π-bond formed between the pth and qth carbon atoms) interrupts cyclic conjugation thereat, can be constructed simply by multiplying βpq by i and βqp by -i, where βpq is the resonance integral between the two conjugated atoms and i is the square root of -1. In this hypothetical π-system, no circulation of π-electrons is expected to occur along the circuits that pass through the p-q π-bond. Here, circuits stand for all possible cyclic or closed paths that can be chosen from a π-system. BRE for the p-q π-bond is given as a destabilization energy of this hypothetical π-system. In other words, BRE for a given π-bond represents the contribution of all circuits that pass through the bond to topological resonance energy (TRE).19-21 Peripheral π-bonds have the same BRE value if they belong to the same ring. A detailed procedure for calculating BRE has been reported previously.22 It is not easy to estimate the degree of kinetic stability of a cyclic π-system since innumerable chemical reactions are involved in it. We pay attention to the fact that the kinetic stability of a polycyclic π-system is primarily determined by the reactivity of the most reactive site. The most reactive site is often associated with the π-bond with the smallest or minimum BRE (min BRE) in the molecule. If min BRE in a molecule is


Page 4 of 27

Page 5 of 27

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


smaller than -0.100 |β|, it is highly probable that the molecule is kinetically very unstable.13-17 Hereafter, a π-bond shared by an m- and n-membered rings will be denoted by an m/n bond. Carbon-carbon π-bonds in fullerenes are then classified into three types: 6/6, 5/6, and 5/5 bonds. Most 6/6 bonds have large positive BREs. Every 5/6 bond has a small positive or negative BRE, suggesting that it is stabilized by the benzene ring to which the 5/6 bond belongs. In contrast, all 5/5 bonds in fullerenes have large negative BREs, at least almost all of which are smaller than -0.100 |β|.13-16 What we have seen so far is that abutting pentagons are never favorable to the stabilization of a fullerene π-system. TREs for polycyclic conjugated hydrocarbons to be dealt with in this paper are listed in Table 1, where the values in parentheses are the percentage TRE (% TRE), i.e., 100 times TRE, divided by the π-binding energy of the polyene reference.21,23 This quantity is useful when the degrees of aromaticity in different molecules are compared. For reference, TRE and %TRE for benzene, a prototype aromatic hydrocarbon, are 0.2726 |β| and 3.528, respectively.

Table 1. TREs for Polycyclic Conjugated Hydrocarbons Studied species

TREa / |β|

species

C50 (D5h, 1)

0.7078 (0.928) 1.6427 C60 (Ih, 2) (1.795) -0.2152 pentalene (3) (-2.017) 0.2222 dibenzo[ed,gh]pentalene (4) (1.158) 0.3102 dibenzo[a,e]pentalene (5) (1.418)

cyclopenta[fg]hexacene (25) cyclopenta[hi]hexacene (26) dicyclopenta[de,hi]hexaceene (27) dicyclopenta[de,jk]hexaceene (28) dicyclopenta[de,lm]hexaceene (29)


TREa / |β| 0.7515 (1.952) 0.7639 (1.984) 0.7660 (1.846) 0.7543 (1.818) 0.7112 (1.715)


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

triafulvene (6) fulvene (7) heptafulvene (8) triafulvalene (9) fulvalene (10) heptafulvalene (11) calicene (12) sesquifulvalene (13) extended fulvalene 1 (14) extended fulvalene 2 (15) extended fulvalene 3 (16) acenaphthylene (17) acephenanthrylene (18) cyclopenta[cd]pyrene (19) naphthalene (20) phenanthrene (21) pyrene (22) hexacene (23) cyclopenta[de]hexacene (24) a

0.0634 (1.294) 0.0200 (0.269) 0.0091 (0.091) -0.4607 (-5.813) -0.2992 (-2.284) -0.2182 (1.198) 0.4334 (4.125) 0.2716 (1.735) -0.1632 (-1.044) -0.0814 (-0.448) -0.0276 (-0.133) 0.3538 (2.175) 0.5085 (2.325) 0.5648 (2.269) 0.3888 (2.924) 0.5459 (2.888) 0.5978 (2.729) 0.7063 (1.992) 0.7075 (1.839)

dicyclopenta[de,qr]hexaceene (30) dicyclopenta[de,st]hexaceene (31) dicyclopenta[de,uv]hexaceene (32) dicyclopenta[de,wx]hexaceene (33) dicyclopenta[de,yz]hexaceene (34) dicyclopenta[fg,jk]hexaceene (35) dicyclopenta[fg,st]hexaceene (36) dicyclopenta[fg,uv]hexaceene (37) dicyclopenta[fg,vx]hexaceene (38) dicyclopenta[hi,uv]hexaceene (39) pyracylene (40) dicyclopenta[de,kl]anthracene (41) anthracene (42) C46H14 (61) C48H14 (62) C48H14 (63) C48H14 (64) C48H14 (65) C48H14 (66)

Page 6 of 27

0.6954 (1.677) 0.7202 (1.735) 0.7027 (1.692) 0.6421 (1.546) 0.3915 (0.942) 0.7925 (1.909) 0.7136 (1.717) 0.6494 (1.562) 0.3598 (0.864) 0.3520 (0.845) 0.1064 (0.551) 0.3739 (1.504) 0.4746 (2.519) 1.5639 (2.298) 1.5049 (2.165) 1.5380 (2.213) 1.5404 (2.216) 1.5028 (2.162) 1.3614 (1.956)

percentage TREs in parentheses.

RESULTS AND DISCUSSION We mainly consider the signs and magnitudes of BREs for planar polycyclic conjugated hydrocarbons that contain one or more five-membered rings. We then seek for


Page 7 of 27

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


geometric or graph-theoretical conditions for designing planar polycyclic π-systems with reactive 5/5 bonds and show that non-IPR fullerenes satisfy these conditions. Pentalenes. As can be seen from Figure 2, 5/5 bonds in pentalene (3) and dibenzo-fused pentalenes (4 and 5) all exhibit positive BREs. Pentalene itself is highly antiaromatic with a TRE of -0.2152 |β| and so is extremely reactive.17-22,24 The antiaromaticity of 3 has long been attributed to the fact that it is a bridged cyclooctateraene. Be that as it may, one should note that 3 is not consistent with the IPR, in that the 5/5 bond does not exhibit a negative BRE. It is interesting to see that large negative TRE of -0.5948 |β| for planar cyclooctatetraene19-21 is markedly reduced to -0.2152 |β| by introducing a 5/5 bond to form 3. Likewise, dibenzo-fused pentalenes, such as 4 and 5, have 5/5 bonds with large positive BREs, apparently indicating that the 5/5 bond is a stabilizing factor in these planar π-systems. If so, why is the 5/5 bond a destabilizing factor in non-IPR fullerenes? Conjugation Circuits. The origin of aromaticity/antiaromaticity in a polycyclic π-system is all possible circuits in it.19-21 A conjugation circuit is defined in the following manner.25,26 First, we remove all conjugated atoms that lie along one of the even-numbered-site circuits from the entire π-system. If one or more Kekulé structures can be written for the residual π-system, the even-numbered-site circuit will contribute significantly to the increase or decrease in TRE.25,26 Such a circuit has been called a conjugation circuit or a conjugated circuit in Randić’s terminology.25 Randić and Herndon noted that relatively small conjugation circuits are the main origin of aromaticity in neutral polycyclic conjugated hydrocarbons.25,26 In fact, the main origin of antiaromaticity in pentalene (3) is a peripheral eight-site circuit, which is the only conjugation circuit in 3. An analogous eight-site conjugation circuit is found in



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

Page 8 of 27

dibenzopentalenes 4 and 5. Here, an m-site circuit indicates a closed path that passes through m conjugated atoms. Hosoya et al. theoretically justified the importance of relatively small conjugation circuits in aromatic stabilization.27,28 Analyzing Hosoya’s own topological index27 for planar polycyclic π-systems, they proved that, as far as neutral hydrocarbons are concerned,

small

conjugation

circuits

contribute

significantly

to

global

aromaticity/antiaromaticity.27,28 Namely, small (4n+2)-site conjugation circuits tend to stabilize the π-system, while small 4n-site conjugation circuits tend to destabilize the π-system. This is rather a logical extension of Hückel’s 4n+2 rule to polycyclic π-systems. Note that Hückel’s original rule can be applied to monocyclic π-systems but not to polycyclic ones. When there is only one odd-membered ring as in fulvenes 6-8 (Figure 3), the corresponding circuit makes only a small contribution to global aromaticity. These fulvenes have no conjugation circuits. Next, suppose that there are two or more disjoint odd-numbered-site circuits (such as three-, five-, and seven-site circuits) in a π-system. We then remove all conjugated atoms that lie along any two of the disjoint odd-numbered-site circuits from the π-system. If one or more Kekulé structures can be written for the residual π-system, the pair of disjoint odd-numbered-site circuits may contribute appreciably to the TRE and the BREs for the π-bonds that lie along the circuits concerned.27,28 By analogy with the concept of a conjugation circuit, a pair of disjoint circuits that fulfill this requirement may be called a conjugated pair of disjoint circuits. Hosoya et al. found that conjugated pairs of disjoint circuits with 4n and 4n+2 carbon atoms in all contribute significantly to the global aromaticity and antiaromaticity, respectively.27,28 Some conjugated pairs of disjoint circuits will be exemplified later in Figures 7 and 11.


Page 9 of 27

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


Fulvalenes 9-16 in Figure 3 have two odd-numbered-site circuits. Symmetric fulvalenes 9-11 are highly antiaromatic with large negative TREs, although they have no conjugation circuits.19-21 In these species, antiaromaticity arises from a conjugated pair of disjoint circuits formed by 4n+2 atoms in all. For example, fulvalene 10 is antiaromatic with a negative TRE, because two disjoint circuits pass through ten carbon atoms in all. Likewise, calicene 12 and sesquifulvalene 13 in Figure 5 are aromatic with positive TREs.19-21 In these species, aromaticity arises from a conjugated pair of disjoint circuits formed by 4n atoms in all. In fact, TREs and BREs for nonalternant hydrocarbons, such as fulvalenes 9-16, are overestimated to varying degrees when simple Hückel theory is employed.17 Fortunately, this kind of overestimation can be suppressed by applying the ω-technique to them.29 As can be seen from Figure 3, BREs for the five-membered rings in extended fulvalenes (14-16) decrease as the distance between two five-membered rings increases. Fulvalene 10 and extended ones 14-16 are substructures of fullerene molecules.

Figure 3. BREs in units of |β| for fulvenes (6-8) and fulvalenes (9-16).

One comment may be needed when we analyze aromatic character of polycyclic antiaromatic π-systems. We learned that the 5/5 bond in 3 exhibits a large positive BRE,



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

Page 10 of 27

although aromatic conjugation circuits do not pass though this π-bond. The same is true for the 5/5 bonds in 4 and 5. We have often observed that the aromaticity of aromatic and non-aromatic circuits is greatly enhanced when they coexist with highly antiaromatic circuits.22,30 Enhanced aromaticity of aromatic and non-aromatic circuits seems to be a counterbalance to the antiaromaticity of antiaromatic conjugation circuits coexisting with them. As for pentalene (3), two five-site circuits are the only circuits besides the peripheral eight-site circuit. It naturally follows that these five-site circuits are greatly aromatized although they are odd-numbered-site circuits. Cyclopentahexacenes.

Acenaphthylene

(17),

acephenanthrylene

(18),

and

cyclopenta[cd]pyrene (19) in Figure 4 are among the benzene droplet combustion products.31 Five-membered rings in these cyclopenta-fused polycyclic aromatic hydrocarbons are slightly aromatic with small positive BREs. However, TREs for 17, 18, and 19 have a bit smaller than those for their respective parent PAHs 20, 21, and 22 (Table 1). It is true that an odd-membered ring contributes modestly to global aromaticity when it is located alone in the polycyclic benzenoid system.27,28,32

Figure 4. Three benzene droplet combustion products (17-19) and parent PAHs (20-22). BREs in units of |β| are given for the five-membered rings.


Page 11 of 27

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


Hexacene 23 in Figure 5 is a typical PAH consisting of six benzene rings. Three different cyclpenta-fused species 24-26 are imaginable for 23. As 24-26 have only one pentagonal ring, there are no conjugation circuits that enclose this ring. Like 17-19 in Figure 4, the pentagonal rings in 24-26 never contribute much to global aromaticity. The main origin of aromaticity in 24-26 is (4n+2)-site conjugation circuits enclosing one or more benzene rings. All of 23-26 are then of comparable aromaticity. BREs for outer π-bonds of the pentagonal ring in 24-26 exhibit small positive values. The BRE for such a cyclopenta-ring varies depending on the position of the cyclopenta-ring. Inner pentagonal rings exhibit larger BREs.

Figure 5. Hexacene (23) and cyclopentahexacenes (24-26). BREs in units of |β| are given for the five-membered rings.

Dicyclopentahexacenes. Let us go on to dicyclopenta-fused hexacenes. As has been seen, hexacene 23 has three different sites of cyclopenta-fusion. As a result, 13 isomers of dicyclopenta-fused hexacene are conceivable (27-39 in Figure 6). Major stabilizing factors in these species are still six- and ten-site conjugation circuits, whereas major destabilizing factors must be 12- and 16-site conjugation circuits, if any, and conjugated pairs of disjoint 5-site circuits, if any. Although every five-site circuit is never a conjugation one, two disjoint pentagons may form a conjugated pair of disjoint circuits.



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

Page 12 of 27

On this theoretical basis, BREs for 13 dicyclopenta-fused hexacenes are examined below.

Figure 6. Dicyclopentahexacene isomers (27-39) and related hydrocarbons (40-42). BREs in units of |β| are given for the five-membered rings. Dicyclopenta-fused hexacenes 27-39 in Figure 6 can be divided into two groups. The first group of dicyclopentahexacenes (27-29 and 35) are those without 4n-site conjugation

circuits

or

conjugated

pairs

of

five-site

circuits.

These

dicyclopentahexacene isomers have two cyclopenta-rings on the upper periphery. For these group-one isomers, BREs for the outer π-bonds of the cyclopenta-rings are fairly


Page 13 of 27

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


small, being comparable in magnitude with those for the corresponding π-bonds in monocyclopenta-fused hexacenes (24-26). For example, 27 belongs to this group; BREs for left and right cyclopenta-rings of this isomer are 0.0422 and 0.0759 |β|, respectively, which are close to those in 24 (0.0333 |β|) and 26 (0.0681 |β|), respectively. Dicyclopentahexacene isomers other than the first-group ones constitute the second-group ones, with a cyclopenta-ring on the upper periphery and another ring on the lower periphery. These second-group isomers (30-34 and 36-39) have a conjugated pair of disjoint pentagons, which are supposed to decrease more or less the BREs for the outer π-bonds of the two pentagons. As in the case of extended fulvalenes (Figure 3), these BREs take larger negative values when the two pentagons come closer to each other. As a result, 34, 38, and 39 exhibit BREs of less than -0.28 |β| for the outer π-bonds of the pentagons; they have not only a conjugated pair of pentagons but also 4n-site conjugation circuits. These structural factors are expected to cooperatively enhance the reactivity of the cyclopenta-rings. Conjugated pairs of isolated pentagons and 4n-site conjugation circuits in 30-34 and 36-39 are illustrated in Figure 7. It is worth noting that 37, which does not have 4n-site conjugation circuits but has a conjugated pair of disjoint five-site circuits, is also predicted to be very unstable with a min BRE of less than -0.100 |β|.



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

Figure 7. Selected conjugated pairs of disjoint pentagons (blue) and 4n-site conjugation circuits (red) in dicyclopentahexacenes. As has been seen, dicyclopentahexacene isomers 34 and 37-39 must be kinetically very unstable with min BREs of less than -0.100 |β|. Pyracylene (40) corresponds to the antiaromatic centers of isomers 34, 38, and 39, while dicyclopenta[de,kl]anthracene (41) is presumed to be the antiaromatic center of 37. BREs for the outer π-bonds of the cyclopenta-rings are –0.1818 |β| for 40 and –0.0576 |β| for 41 (Figure 6). It is interesting to see that the antiaromaticity of these antiaromaticity centers are enhanced when the π-systems of these π-systems are incorporated in the larger dicyclopentahexacene π-systems. TREs for 40 and 41 are much smaller than those for the parent PAHs 20 and 42, respectively. Fusion of Two Dicyclopentahexacene Molecules. We have seen that two pentagons in a polycyclic π-system are often coupled with each other to destabilize both


Page 14 of 27

Page 15 of 27

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


of them. We next fuse two molecules of the same dicyclopentahexacene isomer, in such a manner that they form a pentalene substructure in the fused dimer. Thirteen of the fused dicyclopentahexacene dimers thus formed are shown in Figure 8. We found that when two pentagons with large negative BREs are fused to form a pentalene substructure, the resulting 5/5 bond is very unstable with a large negative BRE. If a monomer has a conjugated pair of disjoint pentagons and/or one or more 4n-site conjugation circuits, these local geometries are all reserved in the fused dimer. Therefore, two pentagons with large negative BREs are fused to form a pentalene substructure, the 5/5 bond in the dimer is still very unstable with a large negative BRE. Conversely, when two pentagons with positive BREs are fused to form a pentalene substructure, the 5/5 bond in it is still stable with a positive BRE (see, e.g., 46, 47, 52, and 53).



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

Figure 8. Fused dicyclopentahexacene dimers. BREs in units of |β| are given for the five-membered rings of the dimers. Those for 5/5 bonds are given in red.

Some other fused cyclopentahexacene-based dimers (56, 57) and heterodimers 16 ACS Paragon Plus Environment

Page 16 of 27

Page 17 of 27

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


(58-60) are presented in Figure 9. BREs for the 5/5 bonds in these dimers can again roughly be predicted from the BREs for the cyclopenta-ring of the starting monomers. BREs for the pentagons of the cyclopentahexacene monomers and those for the 5/5 bonds of the fused dimers studied are listed in Table 2. By comparing 56 with 57-59 it is clear that a third pentagon is necessary in order to effectively destabilize the 5/5 bond.

Figure 9. Some other fused cyclopentahexacene-based dimers and heterodimers. BREs in units of |β| are given for the five-membered rings. Those for 5/5 bonds are given in red.



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

Page 18 of 27

Table 2. BREs for Selected π-Bonds in Cyclopenta-Rings of the Starting Monomers and Fused Dimers fused dimer

fused dimer

BRE / |β| pentagon of the lower monomer -0.2813

5/5 bond of the dimer

43

pentagon of the upper monomer -0.2813

-0.3038

44

-0.0886

-0.0886

45

-0.0280

46

BRE / |β| pentagon of the lower monomer 0.0294

5/5 bond of the dimer

52

pentagon of the upper monomer 0.0294

-0.1170

53

0.0061

0.0061

0.0278

-0.0280

-0.0314

54

-0.1120

-0.1120

-0.1058

0.0024

0.0024

0.0162

55

-0.4160

-0.4160

-0.2981

47

0.0215

0.0215

0.0464

56

0.0681

0.0681

0.1071

48

-0.0657

-0.0657

-0.0473

57

-0.1120

-0.1120

-0.1338

49

-0.3897

-0.3897

-0.2964

58

-0.1120

0.0681

0.0288

50

-0.1171

-0.1171

-0.1321

59

-0.4160

0.0681

-0.0797

51

-0.0244

-0.0244

-0.0162

60

-0.4160

0.0365

-0.1626

0.0570

Realistic Planar Models of non-IPR Fullerenes. Based on the above way of reasoning, realistic planar models of reactive non-IPR fullerenes, C48H14 (62-66), are proposed in Figure 10, in which a pentalene substructure is embedded in a polycyclic benzenoid π-system as in non-IPR fullerenes. These are cyclopenta-fused derivatives of the C46H14 molecule (61). Like pentalenes 3-5, BRE for the 5/5 bond in 61 is positive in sign, indicating that, as in the case of pentalenes 3-5 (Figure 2) and cyclopentahexacene dimer 56 (Figure 9), this π-bond serves as a stabilizer of the eight-site conjugation circuit. In contrast, BREs for 5/5 bonds in 62-66 are more or less smaller than that for the 5/5 bond in 61. These cyclopenta-fused derivatives of 61 have three pentagons, which are denoted as A, B, and C. As can be seen from Figure 10, the sign and magnitude of BRE for the 5/5 bond depends on the location of the third pentagon C.


Page 19 of 27

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


Figure 10. C46H14 (61) and the cyclopenta-fused derivatives (62-66). BREs in units of |β | are given for the five-membered rings; those for 5/5 bonds are given in red.

Isomers 63 and 64 have neither 4n-site conjugation circuits nor conjugated pairs of disjoint pentagons, so that the 5/5 bond exhibit a positive BRE ring as in 61; TREs for these three species indeed are comparable in magnitude to each other (Table 1). Outer π-bonds of ring C in 63 and 64 also exhibit positive BREs. In contrast, isomers 62, 65, and 66 have both 4n-site conjugation circuits and conjugated pairs of disjoint pentagons, so that the 5/5 bonds exhibit smaller positive or negative BREs. In particular, 66 exhibits a very large negative BRE of –0.1577 |β| for the 5/5 bond. Ring C participates in the formation of conjugated pairs of pentagons with rings A and B; rings B and C are a pair of the closest disjoint pentagons. Moreover, this isomer has four twelve-site conjugation circuits, all of which pass through the 5/5 bond. In this sense, 66 can be viewed as one of the best planar models of non-IPR fullerenes with reactive 5/5 bonds. In contrast, no and only one twelve-site circuit can be chosen from 62 and 65, respectively. Some conjugated pairs of disjoint pentagons (66a and 66b) and 4n-site



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

conjugation circuits (66c and 66d) found in 66 are shown in Figure 11. As in non-IPR fullerenes, eight-site circuits can be chosen from the pentalene substructures of 61-66. However, these circuits do not pass through the 5/5 bond and so do not contribute directly to the kinetic instability of the 5/5 bonds.

Figure 11. Conjugation pairs of isolated pentagons (blue) and twelve-site conjugation circuits (red) in the cyclopenta-fused derivative of C46H14 (61).

Non-IPR Fullerenes. Like those in some fused dicyclopentahexacene dimers (43, 44, 49, 50, 54, 55, 57, and 60) and one of the C48H14 isomers (66), large negative BREs for 5/5 bonds in non-IPR fullerenes must be related to the existence of disjoint pentagons in addition to the pentalene substructure. Since non-IPR fullerenes have ten more pentagons besides an arbitrarily chosen pentalene substructure, some of them must possibly participate in the formation of conjugated pairs with pentagons in the pentalene substructure and/or 4n-site conjugation circuits. In principle, 5/6 bonds in the pentalene substructure are never too unstable, because each of them is shared by a benzene ring. C50 (D5h, 1 in Figure 1) is one of the typical non-IPR fullerenes. With the above features of five-membered rings in mind, we can analyze in some detail the magnitudes of BREs for 5/5 bonds in this fullerene. Figure 11 shows the BREs calculated for the hemispheres of C50 (D5h). In the two hemispheres 67 and 68, outer π-bonds in the peripheral pentagons exhibit relatively large negative BREs, although they are not 20 ACS Paragon Plus Environment

Page 20 of 27

Page 21 of 27

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


smaller than –0.100 |β|. However, when these two hemispheres are fused to form C50 (1), much more 4n-site conjugation circuits and much more conjugated pairs of disjoint pentagons will occur in 1 than in the two separate hemispheres and the resulting 5/5 bonds must exhibit enhanced instability. In fact, as many as 22 twelve-site conjugation circuits pass through each 5/5 bond in 1. In addition, six conjugated pairs of the closest disjoint pentagons must further weaken each 5/5 bond. Thus, the kinetic instability of 1 can be attributed directly to the presence of reactive 5/5 bonds in the π-system. As shown in Figure 1, BREs for these 5/5 bonds are all –0.3083 |β|.14 As far as a fullerene cage is not too large, essentially the same principle of kinetic instability must be operative on it.13,14,16

Figure 12. BREs in units of |β| for 5/5 and 5/6 bonds in two hemispheres of C50 (1).

CONCLUDING REMARKS We suggested in 1995 that non-IPR fullerenes must have 4n-site conjugation circuits in addition to eight-site circuits.13 In the present study, we found that conjugated pairs of disjoint pentagons also enhance the kinetic instability of neutral polycyclic π-systems. Properly arranging such local structures, we can design planar polycyclic π-systems that reproduce the kinetic instability of neutral non-IPR fullerenes. In essence, 5/5 bonds in 21 ACS Paragon Plus Environment


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

non-IPR fullerenes must be destabilized by the presence of 4n-site conjugation circuits and conjugated pairs of nearby disjoint pentagons. The IPR never states that fullerene cages without 5/5 bonds are all kinetically stable.34 Conversely, some or many of very large non-IPR fullerenes might be kinetically stable with a large distance between the pentalene substructure and nearby pentagons.35 Again as pointed out in 1995, the IPR cannot be applied to charged fullerenes.11,12,14,16 The inapplicability of the IPR to charged fullerenes is due simply to the fact that fullerene molecules, including non-IPR ones, enhance aromatic character by acquiring negative charge. This is a characteristic of polycyclic π-systems with one or more five-membered rings, which tend to lower the low-lying vacant molecular orbitals. For example, the molecular dianion of highly reactive pentalene (3) is iso-π-electronic with naphthalene (20), both being highly aromatic with large positive TREs of 0.4638 and 0.3888 |β|, respectively.18 Fowler and Myrvold pointed out that non-IPR fullerenes with up to 118 carbon atoms do not have properly closed shells.35 That is, most of them have vacant bonding molecular orbitals.

ASSOCIATED CONTENT AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]


Page 22 of 27

Page 23 of 27

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


REFERENCES (1) Kroto, H. W. The Stability of the Fullerenes Cn (n=24, 28, 32, 50, 60 and 70). Nature 1987, 329, 529-531. (2) Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hife, G. E. Elemental Carbon Cages. J. Am. Chem. Soc. 1988, 110, 1113-1127. (3) Fowler, P.W.; Manolopoulos, D. E. An Atlas of Fullerenes; Oxford University Press: Oxford; 1995. (4) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. C60: Buckminsterfullerene. Nature 1985, 318, 162-163. (5) Kroto, H. W.; Allaf, A. W.; Balm, S. P. C60: Buckminsterfullerene. Chem. Rev. 1991, 91, 1213-1235. (6) Krätschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Solid C60: A New Form of Carbon. Nature 1990, 347, 354-358. (7) Diener, M. D.; Alford, J. M. Isolation and Properties of Small-Bandgap Fullerenes. Nature 1998, 393, 668-671. (8) Martin, N. Fullerene C72Cl4: The Exception That Prove the Rule? Angew. Chem., Int. Ed. 2011, 50, 5431-5433. (9) Tan, Y.-Z.; Xie, S.-Y.; Huang, R.-B.; Zhen, L.-S. The Stabilization of Fused-pentagon Fullerene Molecules. Nat. Chem. 2009, 1, 450-460 (10) Chaur, M. N.; Melin, F.; Ortiz, A.L.; Echegoyen, L. Chemical, Electrochemical, and Structural Properties of Endhedral Metallofullerenes. Angew. Chem., Int. Ed. 2009, 48, 7514-7538. (11) Popov, A. A.; Yang, S.; Dunisch, L. Endhedral Fullerenes. Chem. Rev. 2013, 113, 5989-6113.



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

(12) Chang, Y. F.; Zhang, J. P.; Sun, H.; Hong, B.; An, Z.; Wang, R. S. Geometry and Stability of Fullerene Cages: C24 to C70. Int. J. Quantum Chem. 2005, 105, 142-147. (13) Aihara, J. Bond Resonance Energy and Verification of the Isolated Pentagon Rule. J. Am. Chem. Soc. 1995, 117, 4130-4136. (14) Aihara, J. Bond Resonance Energies and Kinetic Stabilities of Charged Fullerenes. J. Phys. Chem. 1995, 99, 12739-12742. (15) Aihara, J.; Oe, S.; Yoshida, M.; Osawa, E. Further Test of the Isolated pentagon Rule: Thermodynamic and Kinetic Stabilities of C84 Fullerene Isomers. J. Comput. Chem. 1996, 17, 1387-1394. (16) Aihara, J. Kinetic Stability of Carbon Cages in Non-classical Metallofullerenes. Chem. Phys. Lett. 2001, 343, 465-469. (17) Aihara, J. Bond Resonance Energies of Polycyclic Benzenoid and Nonbenzenoid Hydrocarbons. J. Chem. Soc., Perkin Trans. 2 1996, 2185-2195. (18) Aihara, J. Incorrect NICS-Based Prediction on the Aromaticity of the Pentalene Dication. Bull. Chem. Soc. Jpn. 2004, 77, 101-102. (19) Aihara, J. A New Definition of Dewar-Type Resonance Energies. J. Am. Chem. Soc. 1976, 98, 2750-2758. (20) Gutman, I.; Milun, M.; Trinajstić, N. Graph Theory and Molecular Orbitals. 16. Nonparametric Resonance Energies Arbitrary Conjugated Systems. J. Am. Chem. Soc. 1977, 99, 1692-1704. (21) Aihara, J. Aromaticity and Diatropicity. Pure Appl. Chem. 1982, 54, 1115-1128. (22) Makino, M.; Aihara, J. Aromaticity and Magnetotropicity of Dicyclopenta-Fused Polyacened. Phys. Chem. Chem. Phys. 2008, 10, 591-599.


Page 24 of 27

Page 25 of 27

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


(23) Aihara, J. π-Electron Currents Induced in Polycyclic Benzenoid Hydrocarbons and Their Relevance to Clar Structures. J. Phys. Chem. A 2003, 107, 11553-11557. (24) Bally, T.; Chai, S.; Neuenschwander, M.; Zhu, Z. Pentalene: Formation, Electronic, and Vibrational Structure. J. Am. Chem. Soc. 1997, 119, 1869-1875. (25) Randić, M. Aromaticity and Conjugation. J. Am. Chem. Soc. 1977, 99, 444-450. (26) Herndon, W. C.; Ellzey, M. L., Jr. Resonance Theory. V. Resonance Energies of Benzenoid and Nonbenzenoid π Systems. J. Am. Chem. Soc. 1974, 96, 6631-6642. (27) Hosoya, H.; Hosoi, K.; Gutman, I. A Topological Index for the Total π-Electron Energy. Proof of a Generalised Hückel Rule for an Arbitrary Network. Theor. Chim. Acta 1975, 38, 37-47. (28) Hosoya, H. Aromaticity Index Can Predict and Explain the Stability of Polycyclic Conjugated Hydrocarbons. Monatsh. Chem. 2005, 136, 1037-1054. (29) Aihara, J. Improved Resonance Energies of Nonalternant Hydrocarbons. An

ω-Technique Approach. Bull. Chem. Soc. Jpn. 1980, 53, 2689-2694. (30) Ishida, T.; Kanno, H.; Aihara, J. Magnetic Responce Energies of Polycyclic Aromatic Hydrocarbon Molecular Ions. Polish J. Chem. 2007, 81, 699-710. (31) Marsh, N. D.; Wornat, M. J.; Scott, L. T.; Necula, A.; Lafleur, A. L.; Plummer, E. F. The Identification of Cyclopenta-Fused and Ethynyl-Substituted Polycyclic Aromatic Hydrocarbons in Benzene Droplet Combustion Products. Polycyclic Aromat. Compd. 2000, 13, 379-402. (32) Aihara, J. A Generalized Total π-Energy Index for a Conjugated Hydrocarbon. J. Org. Chem. 1976, 41, 2488-2490. (33) Havenith, R. W. A.; Jiao, H.; Jenneskens, L. W.; van Lenthe, J. H.; Sarobe, M.;



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

Schleyer, P. v. R.; Kataoka, M.; Necula, A.; Scott, L. W. Stability and Aromaticity of the Cyclopenta-Fused Pyrene Congeners. J. Am. Chem. Soc. 2002, 124, 2363-2370. (34) Aihara, J. Kinetic Stability of Metallofullerenes as Predicted by the Bond Resonance Energy Model. Phys. Chem. Chem. Phys. 2001, 3, 1427-1431. (35) Fowler, P. W.; Myrvold, W. Non-IPR Fullerenes with Properly Closed Shells. Phys. Chem. Chem. Phys. 2010, 12, 14822-14826.


Page 26 of 27

Page 27 of 27

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


TOC Image Origin of Kinetic Instability of Fullerenes That Violate the Isolated Pentagon Rule Jun-ichi Aihara


Origin of Kinetic Instability of Fullerenes That Violate the Isolated

Recommend Documents