Searching for Stable Hept-C62X2 (X 5 F, Cl, and Br):

Structures and Stabilities of Heptagon-Containing

C62 Halogenated Derivatives

LILI SUN, SHUWEI TANG, YINGFEI CHANG, ZHANLIANG WANG, RONGSHUN WANG*

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University,Changchun, Jilin 130024, China

Received 3 December 2007; Revised 9 March 2008; Accepted 24 March 2008DOI 10.1002/jcc.21017

Published online 16 May 2008 in Wiley InterScience (www.interscience.wiley.com).

Abstract: To determine the geometries of the most stable hept-C62X2 (X 5 F, Cl, and Br) isomers, all 967 possi-

ble hept-C62F2 isomers have been orderly optimized using AM1, HF/STO-3G, B3LYP/3-21G, and B3LYP/6-31G*

methods, and chlorofullerenes and bromofullerenes, which are isostructural with five most stable hept-C62F2 isomers,

were regarded as candidates of the most stable isomer, and optimized at the B3LYP/6-31G* level. The results reveal

that 2,9- and 9,62-hept-C62X2 (X 5 F, Cl, and Br) are the two most stable isomers with slight energy difference.

The halogenation releases strain energy of hept-C62, and all halogenated fullerenes are more chemically stable than

hept-C62 with lower EHOMO and higher ELUMO. All five most stable hept-C62X2 (X 5 F, Cl, and Br) isomers are en-

ergetically favorable, and their thermodynamic stability decreases along with the increase of sizes of addends. Only

hept-C62F2 isomers show high thermodynamic stability, and they are potentially synthesized in experiments. 59,62-

squ-C62X2 (X 5 F, Cl, and Br) were computed for comparison, and they are found to be more stable than their

heptagon-containing isomers.

q 2008 Wiley Periodicals, Inc. J Comput Chem 29: 2631–2635, 2008

Key words: C62; heptagon-containing; fullerenes; halogenation; stabilities

Introduction

Classical fullerenes are defined as spherical, polyhedral struc-

tures comprised of 12 pentagons and N (N � 0) hexagons, and

their geometries and stabilities are governed by the so-called iso-

lated-pentagon rule (IPR),1,2 which is possible for only C603,4

and C7012k (k � 0). Non-IPR fullerenes with adjacent pentagon–

pentagon fusions unavoidably suffer high strain energies and

show high lability, but they can be stabilized by forming endo-

hedral or exohedral derivatives with other groups. Numerous

non-IPR fullerene derivatives have been successfully synthesized

and characterized in this way, such as Sc2@C66, Sc3N@C68,

La2@C72, C50Cl10, C64H4,5–9 etc.

Fullerenes violating the classical definition, which contain

rings of other size, for example, 4 or 7, are expected to suffer

extra local strain or/and further loss of p delocalization,10 and

thus highly unstable. However, previous theoretical studies

revealed C40 cages containing one or more squares, or a hepta-

gon, were more stable than many classical isomers.10,11

Recently, nonclassical fullerenes derived from C60 by removing,

or adding, one or more adjacent carbon atoms have attracted

more and more attention, and were extensively studied.12–18 C58

is the most remarkable one due to the successful synthesis of

C58F18 and C58F17CF3,19 whose heptagon-containing structures

were supported by the spectroscopy data, and many endo- and

exohedral derivatives of C58 were theoretically studied.20–22

Nonclassical C62 fullerenes are also very attractive. A heptagon-

containing Cs symmetric C62, or square-containing C2v symmet-

ric C62, can be obtained by inserting two carbon atoms into C60

fullerene, and they are found to be more stable than all classical

C62 fullerenes. The heptagon-containing isomer is the most sta-

ble C62 isomer.17,18 In 2000, Qian et al. designed a synthetic

approach to the square-containing C62, and detected remarkable

intensity of the C62 radical anion in laser-desorption Fourier

transform mass spectrometry.23 In 2003, (4-Me-C6H4)2C62

was synthesized and characterized using X-ray, and it is the first

stable derivative of nonclassical fullerene incorporating a

four-membered ring.24

Additional Supporting Information may be found in the online version of

this article.

Correspondence to: R. Wang; e-mail: wangrs@nenu.edu.cn

Contract/grant sponsor: National Natural Science Foundation of China;

contract/grant number: 20773021

Contract/grant sponsor: Science Foundation for Young Teachers of

Northeast Normal University; contract/grant number: 20070311

q 2008 Wiley Periodicals, Inc.

However, as the most stable C62 isomer, the heptagon-con-

taining C62 or its derivatives are still unfound in experiments,

and derivatives of heptagon-containing C62 have never been the-

oretically studied up to now. Can the heptagon-containing C62

form stable exohedral derivatives, and which are the stabilizing

sites bearing the addends? To answer these questions, herein we

present a theoretical research to find the most stable heptagon-

containing C62X2 (X 5 F, Cl, and Br) derivatives, and compare

them with their square-containing isomers.

Calculation Details

Hept-C62 is used hereafter to denote the heptagon-containing Cs

C62, and squ-C62 refers the square-containing C2v C62.

Geometries of all 967 possible hept-C62F2 isomers were

firstly optimized with the semiempirical method AM1, and first

51 most stable isomers from AM1, with relative energies within

40 kcal/mol, were refined with HF/STO-3G. Geometries of first

15 most stable isomers from HF/STO-3G, with relative energies

within 30 kcal/mol, were refined with B3LYP method, 3-21G

and 6-31G* basis sets. The B3LYP/3-21G method was chosen

because of its good performance in C60 and C70 geometry opti-

mization in terms of computational efficiency and accuracy,25

and the B3LYP/6-31G* method was widely used in fullerene

computations,26–29 and its accuracy for predicting fullerenes

structures and total energies has been demonstrated by theoreti-

cal studies of C3630 and C50Cl10.

31,32 Hept-C62Cl62 and hept-

C62Br62, which are isostructural with five most stable hept-C62F2isomers from B3LYP/6-31G*, were assumed as candidates of

the most stable isomers, and optimized at the same level. 59,62-

squ-C62X2 (X 5 F, Cl, Br) were also computed for comparison.

All calculations were carried out using the Gaussian 98 quantum

chemical package.33 To measure the strain relaxation of hept-

C62 caused by halogenation, the pyramidalization angle (yp)34,35

was obtained by MOL2MOL.36

Results and Discussions

Structures and Relative Energies

The Cs hept-C62 has 34 nonidentical carbon atoms, which are la-

beled in Figure 1, and all 967 possible hept-C62F2 isomers were

orderly optimized using AM1, HF/STO-3G, B3LYP/3-21G, and

B3LYP/6-31G* methods as described in the ‘‘Calculation

Details’’ section (information about the first 15 most stable iso-

mers are provided in the Supplementary Table), and only first

five most stable hept-C62F2 isomers with relative energies within

10 kcal/mol are discussed here. As seen in Table 1, B3LYP/6-

31G* method predicts 2,9-hept-C62F2 to be the most stable iso-

mer, followed by 9,62-hept-C62F2 with rather small relative

energy. 61,62- and 2,10-hept-C62F2 are nearly isoenergetic (Erel

5 7.47 and 7.80 kcal/mol, respectively), followed by 9,10-hept-

C62F2 with relative energy of 9.96 kcal/mol. Moreover, carbon

sites bearing the addends of these five most stable isomers locate

on the chain of five pentagons (see Fig. 1), which contributes

large electron density to the HOMO and LUMO,18 indicating

the chemical reactivity of pentagon–pentagon fusions and penta-

gon–heptagon fusions.

Considering Cl and Br atoms are neighbors of F atoms in the

same group of the periodic table, it is reasonable to assume that

the stability order of hept-C62Cl2, or hept-C62Br2, is similar with

that of hept-C62F2. Therefore, 2,9-, 9,62-, 61,62-, 2,10-, and

9,10-hept-C62X2 (X 5 Cl, and Br), which are isostructural with

these five most stable hept-C62F2 isomers, were regarded as can-

didates of the most stable isomers, and optimized using B3LYP/

6-31G* method. The results are presented in Table 1.

As seen, the most stable isomers are 9,62-hept-C62X2 (X 5Cl, and Br), followed by 2,9-isomers with rather small relative

energies (1.25 kcal/mol for 2,9-hept-C62Cl2, and 1.59 kcal/mol

for 2,9-hept-C62Br2, respectively), and these two isomers can be

regarded as nearly isoenergetic, which is similar with situation

of fluorofullerenes. Stability order of other three hept-C62X2 (X

5 Cl and Br) isomers is different from that of fluorofullerenes.

As seen, 2,10-hept-C62X2 (X 5 Cl and Br) isomers are more

stable than the corresponding 61,62-hept-C62X2 (X 5 Cl and

Br), and the latter are the least stable ones among all investi-

gated isomers.

Fowler et al. provided a model for the pathways of radical

addition to fullerenes based on Huckel’s molecular orbital

(HMO) theory.37 They assumed the addends were attached to a

fullerene framework sequentially, and the first addend should be

attached to a position of maximum free-valence, and the second

addend should be attached to a position of maximum spin den-

sity. This model has been successfully applied to many sys-

tems.38–41 Herein, we first attach one addend to one of the two

most active sites C(9) (the other is C(10)) to obtain hept-C62X

(X 5 F, Cl, and Br), and then check the spin densities of all

atoms. The predicted spin densities show that the C(62) pos-

sesses the largest value (0.3531, 0.3488, and 0.3472 for hept-

C62F, hept-C62Cl, and hept-C62Br, respectively) of the atomic

spin density (the total spin density is 1.0000), followed by C(2)

(0.2658, 0.2599, and 0.2564 for hept-C62F, hept-C62Cl, and

Figure 1. The Schlegel diagram of hept-C62.

2632 Sun et al. • Vol. 29, No. 16 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

hept-C62Br, respectively). Therefore C(62) and C(2) should be

the two most favored sites bearing the second addend. Besides

that, spatial repulsion between the adjacent addends is significant

in 2,9-hept-C62X2 (X 5 Cl and Br) considering the large radii

of Cl and Br atoms, and it makes 2,9-hept-C62X2 (X 5 Cl and

Br) less stable than the 9,62-isomers. Therefore, stability order

of hept-C62X2 (X 5 Cl and Br) agrees with the prediction of

HMO’s free-valence/spin density model. However, in the 2,9-

hept-C62F2, spatial repulsion is replaced by nonbonded attrac-

tion42,43 between the adjacent F atoms with the distance of 2.6

A (the radius of F atom is 1.35 A), and thus 2,9-hept-C62F2 is

slightly more stable than the 9,62-isomer. That can also explains

the reason why 61,62-hept-C62F2 is the third most stable isomer,

but 61,62-hept-C62X2 (X 5 Cl or Br) is the least stable one

among five investigated isomers.

Strain Energies

The local strain of fullerenes can be assessed by the pyramidali-

zation angle (yp), and the B3LYP/6-31G* optimized geometries

of hept-C62 and halogenated fullerenes were analyzed by P-or-

bital axis vector (POAV) method. It is found that yp at C(61),

C(62), and C(2) (i.e., C(59)) are significantly larger than yp at

other carbon sites with values of 14.28, 16.47, and 15.878,respectively, indicating high strain. Table 1 lists yp at C(61),

C(62), C(2), and C(59) of five most stable hept-C62X2 (X 5 F,

Cl, and Br) isomers, and as seen, yp at these four sites are

smaller than those in hept-C62, indicating the release of strain.

According to the POAV method, the strain energy of mole-

cule corresponds toP

y2p, and thus the strain relaxation is meas-

ured byP

(Dy2p), which is the difference betweenP

y2p of the

hept-C62 and that of halogenated fullerene. As seen in Table 1,

strain energy of hept-C62 is indeed released by halogenation.

According toP

(Dy2p), the strain relaxation of 61,62-hept-C62X2

(X 5 F, Cl, and Br) is the most significant, and therefore, the

strain relaxation does not necessarily correlate with the relative

stability.

Frontier Orbital Analysis

EHOMO, ELUMO, and Eg of hept-C62 and the halogenated deriva-

tives from B3LYP/6-31G* are listed in Table 1. In agreement

with the literature,18 EHOMO and ELUMO of hept-C62 are 5.28

and 3.90 eV, respectively, and the Eg is 1.38 eV. As seen, the

five most stable hept-C62X2 (X 5 F, Cl, and Br) isomers have

lower EHOMO and higher ELUMO compared with hept-C62.

According to Koopman’s theorem, ionization potentials and

affinity potentials can be described by -EHOMO and -ELUMO,

respectively, and therefore, hept-C62X2 (X 5 F, Cl, and Br)

are not only more difficult to lose electrons, but also more dif-

ficult to obtain electrons compared with hept-C62. Moreover,

EHOMO and ELUMO of the isostructural hept-C62X2 (X 5 F, Cl,

and Br) are nearly equivalent, which means that chemical reac-

tivity of halogenated fullerenes is relevant with only the car-

bon sites bearing addends, but independent on addends them-

selves. Eg-values of hept-C62X2 (X 5 F, Cl, and Br) increase

accordingly, and they do not necessarily correlate with the rel-

ative stabilities.

Thermodynamic Stability

To measure the thermodynamic stability of halogenated fuller-

enes, the reaction energies of five most stable hept-C62X2 (X 5F, Cl, and Br) isomers were calculated. The additional reaction

is defined by eq. (1), and eq. (2) is used for calculation of reac-

tion energy, in which Er, E(hept-C62X2), E(hept-C62), and E(X2)

Table 1. B3LYP/6-31G* Relative Energies (Erel, in kcal/mol), Selected yp,P

y2p,P

(Dy2p), HOMO and

LUMO Energies, Energy Gaps (Eg, in eV), and Reaction Energies (Er, in kcal/mol) of Hept-C62, and

Five Most Stable Hept-C62X2 (X5 F, Cl, and Br) Isomers.

Attaching sites Erela

yp

Py2p

P(Dy2p) EHOMO ELUMO Eg ErC(61) C(62) C(2) C(59)

hept-C62 14.28 16.47 15.87 15.87 0.25776 25.28 23.90 1.38

hept-C62F2 2,9- 0.00(1) 10.42 12.81 14.13 0.2344 0.02336 25.90 23.78 2.12 2128.50

9,62- 2.15(2) 10.67 12.47 13.66 0.23254 0.02522 25.97 23.49 2.48 2126.35

61,62- 7.47(3) 12.68 12.68 0.232 0.02576 25.59 23.82 1.77 2121.03

2,10- 7.80(4) 9.43 13.70 13.92 0.23904 0.01872 25.74 23.66 2.08 2120.70

9,10- 9.96(5) 8.45 10.38 14.67 14.67 0.23426 0.0235 25.87 23.48 2.39 2118.54

hept-C62Cl2 2,9- 1.25(2) 9.98 13.06 14.11 0.23482 0.02294 25.91 23.81 2.10 247.96

9,62- 0.00(1) 10.40 12.52 13.75 0.2331 0.02466 26.02 23.55 2.47 249.21

61,62- 9.01(5) 12.93 12.93 0.23167 0.02609 25.56 23.86 1.70 240.20

2,10- 4.66(3) 10.26 12.95 13.58 0.23356 0.0242 25.78 23.72 2.06 244.55

9,10- 6.50(4) 7.88 10.76 14.51 14.51 0.2352 0.02256 25.92 23.52 2.40 242.71

hept-C62Br2 2,9- 1.59(2) 10.18 13.23 14.09 0.23457 0.02319 25.87 23.79 2.08 233.91

9,62- 0.00(1) 10.52 12.61 13.77 0.23372 0.02404 25.99 23.54 2.45 235.50

61,62- 9.65(5) 13.13 13.13 0.23238 0.02538 25.50 23.86 1.64 225.85

2,10- 4.85(3) 10.47 13.03 13.66 0.23442 0.02334 25.74 23.72 2.02 230.65

9,10- 5.81(4) 8.11 11.05 14.71 14.71 0.2354 0.02236 25.89 23.53 2.36 229.69

aStability order acquired by B3LYP/6-31G* method is given in parentheses.

2633Structures and Stabilities of Heptagon-Containing C62 Halogenated Derivatives

Journal of Computational Chemistry DOI 10.1002/jcc

stand for reaction energy of additional reaction, total energies of

hept-C62X2, hept-C62, and X2, respectively. The reaction energy

correlates with relative energy according to its definition, and

the results are presented in Table 1.

hept-C62 þ X2 ! hept-C62X2 (1)

Er ¼ Eðhept-C62X2Þ � Eðhept-C62Þ � EðX2Þ (2)

Thermodynamic stability is expected when a negative Er is

obtained, and the more negative the values of Er, the more sta-

ble is the halogenated fullerene. A positive Er represents ener-

getically unfavorable. As seen, all investigated halogenated full-

erenes are energetically favorable. Moreover, reaction energies

of all five most hept-C62F2 isomers are smaller than 2118 kcal/

mol, which indicates they are highly thermodynamically stable

and experimentally approachable. However, reaction energies of

hept-C62X2 (X 5 Cl, and Br) are larger than 250 kcal/mol,

which means hept-C62X2 (X 5 Cl and Br) are more difficult to

be synthesized than hept-C62F2. By comparing the isostructural

halogenated fullerenes, it is found that the reaction energies

increase along with the increase of radii of halogens, and the

thermodynamic stability decreases accordingly. Therefore,

the thermodynamic stability of hept-C62X2 (X 5 F, Cl, and Br)

correlates with the sizes of addends.

Although hept-C62F2 isomers show high thermodynamic sta-

bility, it is noteworthy that energy difference between hept-

C62F2 isomers is small, indicating that the hept-C62F2, if synthe-

sized, should be a mixture in which different isomers coexist,

and may be very difficult to purify.

Comparison with squ-C62X2 (X 5 F, Cl, and Br)

To the best of our knowledge, the square-containing (4-Me-

C6H4)2C6224 is the only C62 derivative successfully synthesized.

As the most stable C62 isomer, synthesis of hept-C62 or its deriv-

atives have never been reported in literature. Herein we have

applied the HMO’s free-valance/spin density model to the C2v

squ-C62 (see Fig. 2), and the four equivalent carbon sites around

the square, i.e., C(59), C(60), C(61), and C(62), are the best sites

of attaching the first addend. We add one halogen to the C(59)

to obtain squ-C62X (X 5 F, Cl, and Br), and the C(62) is found

to possess the largest value (0.3450, 0.3444, and 0.3436 for squ-

C62F, squ-C62Cl, and squ-C62Br, respectively) of the atomic spin

density (the total spin density is 1.0000). Therefore, the 59,62-

squ-C62X2 (X 5 F, Cl, and Br) should be the most stable halo-

genated derivatives. To study the relative stability of halogen-

ated derivatives of hept-C62 and squ-C62, we optimized the

59,62-squ-C62X2 (X 5 F, Cl, and Br) using B3LYP/6-31G*

method, and the results were presented in Table 2. As seen,

EHOMO of squ-C62 is lowered, and ELUMO is heightened due to

halogenation, and Eg-values increase accordingly. Strain energy

of squ-C62 is also released according toP

(Dy2p). All these indi-

cate that squ-C62 can be stabilized by halogenation. Moreover,

Erel and Er reveal that 59,62-squ-C62X2 (X 5 F, Cl, and Br) are

more stable than their heptagon-containing isomers, and show

thermodynamic stability, which means they are more easily syn-

thesized. That can explain why derivative of squ-C62 was al-

ready synthesized, but that of hept-C62 is still unfound.

Conclusion

In summary, B3LYP/6-31G* predicts that 2,9-, and 9,62-hept-

C62X2 (X 5 F, Cl, and Br) are two most stable isomers with

small energy differences, and stability order of chlorofullerenes

and bromofullerenes is slightly different from that of fluoroful-

lerenes. From the results of five most stable hept-C62X2 (X 5 F,

Cl, and Br) isomers, it is found that halogenation releases the

strain energy of hept-C62, and enhances its chemical stability.

Figure 2. The Schlegel diagram of squ-C62.

Table 2. Relative Energies (Erel, in kcal/mol), Reaction Energies (Er, in kcal/mol), HOMO and LUMO

Energies, Energy Gaps (Eg, in eV),P

y2p, andP

(Dy2p) of squ-C62 and Its Halogenated Derivatives.

Erela Er

Py2p

P(Dy2p) EHOMO ELUMO Eg

squ-C62 0.26436 25.43 23.59 1.84

61,62-squ-C62F2 25.44 2137.09 0.23403 0.03033 25.99 23.39 2.60

61,62-squ-C62Cl2 26.01 258.37 0.23274 0.03162 26.00 23.43 2.57

61,62-squ-C62Br2 25.10 243.74 0.23335 0.03101 25.96 23.42 2.54

aAcquired by comparing with the ground states of hept-C62X2 (X 5 F, Cl, and Br) isomer.

2634 Sun et al. • Vol. 29, No. 16 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

All five most stable halogenated fullerenes hept-C62X2 (X 5 F,

Cl, and Br) are energetically favorable, and their thermodynamic

stability decreases following with the increase of sizes of

addends. However, only hept-C62F2 isomers are potentially syn-

thesized in experiments with high thermodynamic stability. All

hept-C62X2 (X 5 F, Cl, and Br) isomers are less stable than

their square-containing isomers.

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2635Structures and Stabilities of Heptagon-Containing C62 Halogenated Derivatives

Journal of Computational Chemistry DOI 10.1002/jcc