A valence bond approach to explaining fullerene stabilities

0040-4039/91 $3.cxl+ .oo PergamonPressplc

TetrahedronLetters,Vo1.32,No.30, pp 3731-3734, 1991 Printedin GreatBritain

A Valence

Bond Approach

to Explaining

Fullerene

Stabilities

Roger Taylor School of Chemistry and Molecular Sciences, University of Sussex, Brighton BNl 9QJ, Sussex

, UK.

Abstract: Considemtionof valencebondstructures aidsunderstanding of therelativestkbilitiesof the closedcage carbonmoleculesknownas fukenes.

The isolation

and structural determination

and C70 (Falmerene),

which are comprised

of the eventual isolation twelve pentagonal from juxtaposition contributory

of a whole range of fullerenes,

rings) are known.3 However,

for such molecules,‘l considerations,

of the closed cage carbon molecules C60 (Buckminsterfullerene) entirely of sp2 hybtidised

and these differences

as molecules

mass spectroscopic

readily seen by consideration

of this type (each of which contains

studies have indicated differing stabilities

have thus far been attributed to strain effects arising in particular

rings. 3 It is suggested

of pentagonal

carbon atoms. lt2 has raised the prospect

here that aromaticity

of Valence Bond (canonical)

and bond localisation

structures may also be an important

feature. In this approach, principles to be considered arc:

1. The H&kc1 rule. The validity of the application COO, C6(), C70, Qo,

of this rule to three-dimensional

and Cg4, only C5o and C70 are predicted

structures is unclear. Of

by the rule to be aromatic,

and presumably

the more stable, whereas in fact the stability of C60 appears to far exceed that of all other fullerenes. the H&kel rule is difficult to apply even in planar systems in which benzenoid membered

rings. Thus according

electrophilic

aromatic substitutions,

be the minimisation isolated aromatic

molecules.7v8

(I) nor fluoranthene

5 and important here in making these compounds

of double bond character in the central rings, so that the hexagonal systems.

RandiE has emphasized

aromatic would seem to rings tend to behave as

the view that the nature of the smallest

the canonicals (I) and (II), respectively, For example in fluoranthene,

(II) are

In fact they are both typical aromatics and undergo normal

molecule rather than the molecular perimeter governs its overall classification and fluomnthene

rings are joined by four- or Iive-

to the Huckel rule, overall neither biphenylene

aromatic, being 12x and 16x systems, respectively.

However

circuit within a

and behaviour. 6 For biphenylene

come closest to describing the actual structures of the

the average bond lengths in the pentagonal

ring are 1.44 x, but

only 1.38 A for the bonds exocyclic to it.8 It is reasonable to assume therefore that fullerenes will seek to attain the ideal bond localisation such a~ is found in fluoranthene and corannulenc (III) ,9 and for C60 at least,calculations confirm this. lOApplication of the Hcckel rule alone as a guide to stability will be unsatisfactory.

3731

3732

(II)

(I) 2. Juxtaposition previously

noted.3

and stable molecules substitution.12 different,

of five-membered However,

rings gives rise to structures

similar strain is accommodated

such as thienothiophenes

The major difference

(III)

(Via, b) which for example

is that although

pentalene (IV) is antiaromatic

such as (IV) which are strained,

without difficulty

the geometries

as

in the stable dianion (v),l 1

undergo

normal electrophilic

of (IV), (V),and

whereas (V and Va, b) are aromatic. Furthermore,

(Via, b) are little molecules such as

oo.cQ (W

(VI

(VII) comprised of five- and six-membered (4n + 2)7r circuits if the r-electrons and seven-membered isopyrene

(VI4

WIb)

rings, with adjacent pentagonal rings are unable to contain aromatic

of the pentagonal

rings are fused together,

the central double bond is not involved

rings are involved. This only becomes possible if five-

and a classic example in conjugation

of this is isopyrcnc

with the 147r perimeter,

(VIII).13

molecule is planar and shows aromatic behaviour.

wm

(VIII)

For

so that the whole

(IX)

3733

Molecules

such as (VII) have no possibility

thus differ from the case of fluoranthene tricyclodecapentaene antiaromatic fullerenes

of avoiding having double bonds in the pentagonal

and biphenylene,

(IX), apart from the previously

circuits,6 containing

present, a pentagonal

thereby also contributing adjacent

etc. If three pentagonal

noted increased

strain,3

to the reduced stability.

five- and seven-membered

rings and

rings are fused as in the this provides

for three 8x

(It should be noted however

rings are feasible,

and for every heptagonal

that ring

ring additional to the minimum of twelve is required. For example, a C3v isomer of C76

with an apex comprised of three pentagonal rings as in (IX), but with three adjacent heptagonal

rings is feasible

and relatively strain free.) 3. The high stability of t&o has been attributed to it being the smallest fullerene in which all of the required twelve pentagons

are isolated from each other and so is the iirst fullerene formed during clustering

in which

strain in minimised as described in (2) above.3 The question then arises as to why higher fullerenes are less stable. The answer would seem to lie in the fact that on]n in C6u is it possible (using the Valence Bond method) to locate &l of the double bonds in six-membered

rings and none in the five-membered

minimum

rings This is because any two pentagonal

bond orders will be found in the five-membered

fused to a hexagonal pentagonal requirement

ring are in a ‘meta’ relationship,

and this permits

rings as in (X). By contrast, when the pentagonal

minimisation

rings i.e. rings

of bond orders in the

rings are in a ‘paxa’ relationship

as in (XI), this

cannot be satisfied and a degree of instability will result, [The same is also true if the pentagonal

rings are in an ‘ortho’ relationship

(XII) and this factor here also reinforces the argument in (2) above.]

(W It is significant

(XII)

(XI) therefore

that C70, which is less stable than C60, contains five arrangements

whilst the D6h isomer of C84 (a less stable fullerene than C70 14 ) has six such arrangements yet confirmed which of this and others isomers such as Td and D2 are present).

of type (XI),

(though it is not

It is significant

too that mass

spectral data indicate that C&o is less stable than many other fullerenes in this mass range.4 Both icosahedral isomer and D5h isomers are, like C&o, perfectly non-equivalent

spherical but being larger are h

carbons in the ratios of 3: 1, and 2: 2:2: 1:I, respectively.

the fact that the former isomer

has some sixty hexagonal/pentagonal

has twenty; this would seem to be the major destabilising

strained; they consist of

A key difference

arrangements

from C60 however is

of type (X), whilst the latter

feature here.

An indication that the stabilities of the fullerenes is a balance between strain and aromaticity factors is nicely indicated by the case of C72 which the mass spectrometric studies indicate to be one of the less stable molecules.

The D6b isomer has the ideal bond disposition

proposed

in this paper and it is thus able to have

3734

minimum bond orders in the pentagonal

rings. {This arrangement

also requires minimum

bond orders in the

central hexagonal ring of the coronene-like polar caps. Since this is the preferred bond disposition in coronene itselfI5 it is unlikely to be a destabilising feature.) The D6h isomer is however very strained being very flat (flatter even than $0 ) to the extent also that transannular strain appears to be the destabilising

n-cloud interactions

may become significant.

This

factor here.

4. For giant fullerenes the disposition

of the twelve pentagonal

rings in relation to the hexagonal

rings will

become less important, and strain effects will diminish with increasing size. Likewise the number of benzenoid rings will be a small proportion

of the total hexagons,

as is the case for large planar polycyclic

the stability should tend towards that of the latter and of graphite,

though increased

aromatics,

and

of course through the

absence of either C-H or dangling bonds. In summary, it is suggested contribute to determining

that bond fixation and aromaticity

considerations,

in addition to strain effects,

the relative stabilities of fullerenes.

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