Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76

Contents lists available at ScienceDirect

Journal of Molecular Structure: THEOCHEM

journal homepage: www.elsevier .com/locate / theochem

A study on the electronic and structural properties of fullerene C30

and azafullerene C18N12

Jie Song a,*, Mathew Parker a, George Schoendorff a, Andrew Kus a, Mojtaba Vaziri b

a Department of Chemistry and Biochemistry, University of Michigan-Flint, Flint, MI 48502, USAb Department of Computer Science, Engineering Science, and Physics, University of Michigan-Flint, Flint, MI 48502, USA

a r t i c l e i n f o

Article history:Received 13 May 2009Received in revised form 26 November 2009Accepted 27 November 2009Available online 6 December 2009

Keywords:FullereneAzafullereneStabilization

0166-1280/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.theochem.2009.11.040

* Corresponding author. Tel.: +1 810 762 3275; faxE-mail address: jiesong@umich.edu (J. Song).

a b s t r a c t

The structures and electronic properties of both fullerene C30 and the azafullerene C18N12 are studied byab initio methods. The result demonstrates that the substitution of carbon atoms by nitrogen atoms in C30

can strengthen C–C bonds surrounded by nitrogen atoms and increase the p character. Therefore, aza-fullerene C18N12 is expected to be more stable. The structure of the most stable C18N12 isomer and itsinfrared spectroscopy are predicted for the future experimental work.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

With the discovery of C60, the structure and stability of smallerfullerenes with less than 60 carbons have been studied experimen-tally and theoretically [1–13]. A set of small fullerenes has been de-tected with the mass spectroscopic method and among them, onlyC20 [14] and C36 [15] have been observed.

Fullerenes are closed-cage molecules composed of twelve pen-tagonal and several hexagonal rings. The stability of fullerenes isdetermined by the isolated pentagon rule (IPR) [16], which statesthat none of the twelve pentagons touches each other and ensuresa minimum curvature of the fullerene cage. C60 is the smalleststructure to follow IPR and exceptions to this rule have only beensuggested for some endohedral and charged fullerenes. For smallerfullerenes Cn (n < 60), it is impossible to build a cage with all pen-tagons isolated and thus neighboring pentagons in a carbon net-work are energetically unstable. It has been established thatthese non-IPR fullerenes follow the pentagon adjacency penaltyrule (PAPR) [17], which states that the most stable structure corre-sponds to the minimum number of adjacent pentagons (APs) or thenumber of C–C bonds shared between pentagons.

It is important to recognize that stable small fullerenes open thedoor to a new family of azafullerene molecules containing pairedpentagon structures. Paired pentagons allow the formation ofsmaller fullerenes, new isomers with sharper surface angles, andunusual morphologies in nitrogen-doped carbon nanostructures.

ll rights reserved.

: +1 810 766 6693.

It has been shown that in the presence of N2 and He, electric arcdischarge from high purity graphite electrodes produces carbon-nitride materials. These materials contain small carbon-nitrideheterofullerene molecules that are N-substituted Cn (n = 40–50[6] and n = 28–32 [18]). Although efforts have been made to isolatethese azafullerenes, only small amounts of C16N12 have been ob-tained for infrared spectroscopy studies. The result of IR study withfurther theoretical investigation confirms the structure of C16N12 asthe N-substituted C28 carbon-cage [13].

Both the decorated and nitrogen-substituted fullerenes havepotential in many types of applications such as molecular electron-ics and nonlinear optics. Yet the search for these materials is ham-pered by inability to isolate them and the lack of understanding ofthe formation of these molecules.

In this study, ab initio calculations of the structures and elec-tronic properties of both fullerene C30 and the azafullereneC18N12 are presented. The relative stability is predicted based onthe theoretical data. In addition, vibrational spectra of proposedstable neutral species, as well as the infrared intensities are calcu-lated. The effects of N-substitution are discussed and comparedwith similar phenomena in C28.

2. Computational details

For both C30 and C18N12 the following procedure was used. Thegeometries were optimized at the HF level in the correspondingsymmetry group, and then, at the hybrid HF/DFT level. Anunrestricted open shell wavefunction was used to describe theHF/DFT quintet states. In the hybrid HF/DFT calculations, a B3LYP

Fig. 1. Structures of C30.

Table 3Bond lengths (in ÅA

0

) and bond orders of C–C bonds in C30 structures calculated at the

72 J. Song et al. / Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76

functional (Becke 3-parameter Lee–Yang–Parr) which combinesfive functionals, namely Becke + Slater + HF exchange andLYP + VWN5 correlations was used [19–21]. Energy correctionswere done at the 2nd order Møller Plesset Perturbation Theory le-vel [22], using optimized geometries at the B3LYP level. In all cal-culations Dunning’s cc-pVDZ basis set [23] was used, as shown inprevious studies [24–28]. The GAMESS suite of programs was usedfor all calculations [29–31] and MacMolPlt was used for visualiza-tion [32].

3. Results and discussion

3.1. Fullerene C30

Since C60 is the smallest possible structure that keeps everypentagon well separated from each other, the number of C–Cbonds shared between pentagons (N55) is zero. As shown inFig. 1, structures of three C30 [5,6] isomers 1–3 (with C2v, C2v,and D5h, respectively) all have 12 pentagons and five hexagonsbut separations between pentagons and hexagons are different.Compared to large fullerenes, smaller fullerenes usually have alarge piece of fused pentagons, which are energetically unfavor-able. In order to get the location of pentagons in a simple way,the modified (n � Fm) nomenclature based on the small numberof hexagons is applied. In this approach F is the number of thefused hexagons, m is the shared C–C bonds among the fused hexa-gons, and n is the number of the Fm combination. The sum of n� Fm

Table 2Relative energies and HOMO–LUMO gap (DE in kcal/mol and DEHOMO–LUMO in eV) for C30

# Symmetry DE

Singlet Triplet

1 C2v – [5,6] 0.0a (0.0b) 5.6 (15.1)2 C2v – [5,6] 4.4 (12.0) 20.5 (36.8)3 D5h – [5,6] – 55.8 (99.7)

a Calculated at the B3LYP/cc-pVDZ//B3LYP/cc-pVDZ level.b The value in parentheses are the energy correction at MP2/cc-pVDZ//B3LYP/cc-pVDZ

Table 1The structure characters of C30 cluster isomers.

# Symmetry Sum (n � Fm) N66 N56 N55

1 C2v – [5,6] (2 � 21) + (1 � 10) 2 26 172 C2v – [5,6] (1 � 32) + (1 � 21) 3 24 183 D5h – [5,6] (1 � 55) 5 20 20

is equal to the number of the shared hexagonal C–C bonds (N66).For the C30 [5,6] isomers, N55, the number of C–C bonds shared be-tween two pentagons, can be obtained by calculating the differ-ence between the total number of C–C bonds in C30 isomers,which is equal to 45, and N66. For example, structure 1 has two setsof two fused hexagons sharing one C–C bond (2 � 21), and one iso-lated hexagon without shared C–C bonds (1 � 10). The nomencla-ture for 1 is (2 � 21) + (1 � 10), and the number of the C–C bondssharing fused hexagons is two (N66 = 2). The number of the C–Cbonds shared between pentagons and hexagons is 26 (N56 = 26) be-cause all hexagons are surrounded by pentagons. For all C30 [5,6]structures, there are 45 shared C–C bonds and, therefore, the num-ber of the C–C bonds shared between pentagons (N55) is 17 (45-N66–N56). The nomenclature for all three structures is given in Ta-ble 1. It can be seen that structure 1 has the smallest N55 = 17 andstructure 2 has the largest N55 = 20.

Relative energies of these isomers are listed in Table 2. Thegeometries are optimized at the B3LYP/cc-pVDZ level and thenthe energy corrections are done at the MP2/cc-pVDZ level. Relativeenergies at the MP2 level are different from those at the B3LYPlevel and may imply the need to include more electron correla-tions. Results at both theory levels demonstrate the same tendencythat isomer 1 with N55 = 17 is the most stable isomer at both levels.Both 1 and 2 have the same relative stability: quintet > trip-

cluster isomers.

DEHOMO–LUMO

Quintet Singlet Triplet Quintet

23.3 (40.5) 1.3 2.6 2.739.5 (70.4) 2.3 1.9 2.4– – 1.5 –

level.

B3LYP/cc-pVDZ level.

Structure Singlet Triplet Quintet

1 C–C bond length (Å) 1.363–1.529 1.375–1.502 1.401–1.505C–C bond order 1.0–1.5 1.1–1.4 1.1–1.4

2 C–C bond length (Å) 1.396–1.512 1.378–1.503 1.400–1.485C–C bond order 1.0–1.4 1.1–1.4 1.1–1.4

3 C–C bond length (Å) – 1.399–1.478 –C–C bond order – 1.1–1.4 –

J. Song et al. / Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76 73

let > singlet. Although the singlet and quintet of 3 are not con-verged (i.e. they tend to break the cage structure), the triplet of 3is the least stable triplet. The singlet 1 is more stable than the sin-

Fig. 2. Structure

glet 2 and triplet 1 by 4.4 and 5.6 kcal/mol at the B3LYP level (12.0and 15.1 kcal/mol at the MP2 level), respectively. Therefore, thepotential energy surface might be dominated by the singlet state,

s of C18N12.

Table 5Bond lengths (in ÅA

0

) and bond orders of C–C and C–N bonds in C18N12 structurescalculated at the B3LYP/cc-pVDZ level.

Structure Singlet Triplet Quintet

1a C–C bond length (Å) 1.348–1.432 1.343–1.419 1.338–1.426C–C bond order 1.2–1.6 1.3–1.6 1.3–1.6C–N bond length (Å) 1.413–1.501 1.395–1.503 1.408–1.496C–N bond order 1.0–1.1 1.0–1.2 1.0–1.1

1b C–C bond length (Å) 1.338–1.444 1.337–1.445 1.337–1.446C–C bond order 1.1–1.6 1.1–1.6 1.1–1.6C–N bond length (Å) 1.421–1.479 1.421–1.477 1.423–1.477C–N bond order 1.0–1.1 1.0–1.1 1.0–1.1

1c C–C bond length (Å) 1.338–1.441 1.339–1.440 1.339–1.439C–C bond order 1.2–1.6 1.2–1.6 1.2–1.6C–N bond length (Å) 1.405–1.485 1.408–1.502 1.408–1.499C–N bond order 1.0–1.1 1.0–1.1 1.0–1.1

1d C–C bond length (Å) 1.339–1.443 1.339–1.445 1.339–1.469C–C bond order 1.2–1.7 1.2–1.7 1.2–1.7C–N bond length (Å) 1.334–1.539 1.334–1.539 1.340–1.535C–N bond order 0.9–1.4 0.9–1.4 0.9–1.4

1e C–C bond length (Å) 1.338–1.343 1.343–1.485 1.345–1.485C–C bond order 1.6 1.0–1.6 1.0–1.6C–N bond length (Å) 1.415–1.475 1.414–1.476 1.411–1.480C–N bond order 1.0–1.1 1.0–1.1 1.0–1.1

74 J. Song et al. / Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76

which is in agreement with previous theoretical studies. The agree-ment on the order of relative energies between two theory levelsimplies that B3LYP should be able to supply, at least, semi-quanti-tatively accurate results.

Optimized bond lengths and bond orders of C30 are listed inTable 3. Compared to previous calculations of C28 at the theoreticallevel, the C–C bonds in C30 are slightly shorter than those in C28.Both the bond length values and the bond order analysis imply thatmost C–C bonds are still normal single bonds.

3.2. Azafullerene C18N12

As indicated before, substituting some C atoms by N atoms inthe fullerene shell can stabilize the structures of smaller fullerenes.Due to the tendency of N–N multiple bonds to break the shellstructure, no two N atoms could be adjacent to each other. Basedon three C30 [5,6] isomers, there are only five C18N12 azafullerenes(see 1a�1e in Fig. 2) with certain symmetry types (other than C1)that can be visualized. These are all generated from the structure 1.This structure has three fused hexagons and separate pentagons asopposed to structure 2, which has only two fused hexagons. Addi-tionally, there are only up to eleven carbons that can be replaced instructure 2. For structure 3, there is only one fused hexagon andtwo fused pentagons (each with six pentagons and 10 shared C–C bonds). In order to satisfy both requirements of the substitution,up to 10 carbons can be replaced. Thus, N-substitution for struc-tures 2 and 3 can be C19N11 and C20N10. However, the previousmass-spectroscopy data [18] does not suggest the formation ofthese molecules, therefore, they will not be considered in thispaper.

The relative energies and the HOMO–LUMO gaps are summa-rized in Table 4. The singlet of structure 1b is the most stable iso-mer at the B3LYP level, followed by 1c and 1e (11.7 and 11.9 kcal/mol higher at the B3LYP level and 15.6 and 18.9 kcal/mol at theMP2 level, respectively). 1a seems the least stable one and is38.6 kcal/mol higher in energy at the B3LYP level (49.4 kcal/molat the MP2 level). High spin states are considered as well. As givenin Table 4, the relative energies of the triplet states (1b > 1c> 1e > 1d > 1a) and the quintet states (1b > 1c > 1a > 1e > 1d)slightly differ from those of the singlets (1b > 1c > 1e > 1d > 1a).1b and 1c are always candidates of the stable structures, especiallyat the high-spin electronic states. The relative energies of 1c areonly 1.3 and 0.7 kcal/mol higher for triplet and quintet at theB3LYP level (2.8 and 2.7 kcal/mol at the MP2 level), respectively,compared to 11.7 kcal/mol of the singlet state at the B3LYP level(15.6 kcal/mol at the MP2 level). The HOMO–LUMO energy gapshave been used to predict the relative stabilities of larger fullereneswith more than 60 carbons. In this study, HOMO–LUMO gaps ofazafullerene C18N12, similar to those of C30, do not show a clearrelationship with the relative stability.

In previous studies of C28, it was found that the C–C bonds be-tween two carbon atoms from two separate hexagons were greatlyshortened after being surrounded by nitrogen atoms and the bond

Table 4Relative energies and HOMO–LUMO gap (DE in kcal/mol and DEHOMO–LUMO in eV) for C18N

# Symmetry DE

Singlet Triplet

1a C2v – [5,6] 38.6a (49.4b) 27.4 (35.2)1b Cs – [5,6] 0.0 (0.0) 0.4 (4.8)1c Cs – [5,6] 11.7 (15.6) 1.7 (7.6)1d Cs – [5,6] 25.2 (38.9) 24.9 (37.8)1e Cs – [5,6] 11.9 (18.9) 24.4 (34.6)

a Calculated at the B3LYP/cc-pVDZ//B3LYP/cc-pVDZ level.b The value in parentheses are the energy correction at the MP2/cc-pVDZ//B3LYP/cc-p

order increased from 1.0 to 1.6. The increasing sum of bond angleson each carbon atom indicates more flattened structures, relievesthe bent sp2 orbitals, and helps the side-to-side overlap to formstronger C–C bonds. The detailed information of bond lengths inC18N12 and orders can be found in Table 5 and the bond anglesare listed in Fig. 3.

Unlike C16N12, C18N12 has more flexibility to substitute carbonatoms with nitrogen atoms but there are still nine C–C bonds thatare under different environments. A C–C bond can be shared be-tween pentagon/pentagon or between pentagon/hexagon, whilecarbon atoms in this C–C bond may be from two separate penta-gons, two separate hexagons, or one hexagon and one pentagon.Additionally, it can be surrounded by only two or three nitrogenatoms rather than four. From Fig. 3, a shortening of C–C bonds isoften observed in the cases where both carbons are from two hexa-gons or one hexagon and one pentagon and these C–C bonds areshared between pentagon/pentagon. It is accompanied by theincreasing sum of the bond angles around both carbon atomsand the subsequent flattened structures. Although previous theo-retical models demonstrated that the four nitrogen atoms maypush carbon atoms together to form a stronger bond, calculationsin this study do not show any significant difference if carbon atomsare surrounded by three nitrogen atoms. When there are only twonitrogen atoms surrounding a carbon atom, one nitrogen atom oneach carbon is preferred. Accompanied with the shorter C–C bondlength in C18N12, the stretching of the strengthened C–C bond is ex-pected to shift to the region 1600–1700 cm�1, the range for a C@Cbond, from the region 1200–1400 cm�1 for a C–C bond. Previoustheoretical investigations of C16N12 already showed that the exis-

12 cluster isomers.

DEHOMO–LUMO

Quintet Singlet Triplet Quintet

12.6 (21.3) 1.2 3.0 3.20.8 (4.2) 2.7 3.0 3.21.5 (7.9) 2.2 3.0 3.030.5 (42.6) 1.9 3.0 2.822.6 (33.4) 2.5 3.2 3.5

VDZ level.

N

NN

NN

NN

NC

CN

N

120.3(120.7)

110.9(108.2)107.5(108.2)107.5(108.2)110.9(108.2)

120.3(120.7)

124.2(120.7)

124.2(120.7)

116.7(108.2)116.7(108.2)

111.2(108.2)111.7(108.2)

126.4(121.4)

123.7(120.4)

108.7(107.3)107.6(106.3)

115.5(110.7)115.5(107.3)

1c-1 1c-2 1c-3

N

NN

N N

CN

N N

CN

N

113.8(109.0)

122.5(118.5)

111.6(112.6)109.3(105.9)

111.6(112.6)109.3(105.9)

108.9(108.0)

110.9(109.0)

120.8(121.4)120.3(120.7)

108.6(106.3)107.5(108.2)

108.6(106.3)

118.7(117.5)

120.8(121.4)120.0(121.4)

108.9(108.0)111.1(108.0)

1c-4 1c-5 1c-6

N

NN

N N

NN

N C

NN

N

123.9(120.7)

112.2(108.2)111.7(106.9)

123.9(120.7)

124.1(120.7) 124.5(117.5)

122.7(120.4)124.1(120.7)

112.6(108.2)112.6(106.9)112.6(108.2)112.6(106.9)

110.4(105.2)111.4(107.3)

109.4(108.8)110.5(106.7)112.2(108.2)111.7(106.9)

1d-1 1d-2 1d-3

N

NN

N N

NN

N C

NN

C

104.5(110.9)

104.4(110.9) 125.6(118.5) 116.8(118.5)

109.7(109.0)113.6(113.6)

110.2(112.6)110.2(112.6)110.4(105.9)110.4(105.9)

108.8(112.6)106.1(105.9)

108.8(112.6)106.1(105.9)

106.5(109.2)106.0(109.2)

106.5(109.2)106.0(109.2)

1d-4 1d-5 1d-6

N

NN

N N

NN

N N

NN

C

105.4(110.9)

103.0(109.2)

122.2(120.7)

111.5(108.2)

123.6(121.4)

110.8(110.7)

1a-1 1a-2 1a-3

N

NN

N C

CN

N

125.4(120.7)

112.1(108.2)

120.1(120.7)

110.6(106.9)

120.1(120.7)

113.4(108.2)

N

NN

N

127.7(121.4)

111.4(109.9) 112.2(110.7)

124.7(120.4)

111.3(107.3)112.7(106.7)112.1(108.2)113.4(108.2)

125.4(120.7)

110.6(106.9)107.9(108.2)107.9(108.2)

N

NN

N N

CN

N

114.0(108.4)

109.4(112.6)109.4(112.6)111.4(105.9) 111.4(105.9)

123.5(118.5)

108.1(106.3)

109.2(108.0)110.2(105.4)

119.9(121.4)123.5(117.5)

120.5(117.5)

1b-1 1b-2 1b-3 1b-4 1b-5

N

NN

N C

NN

N N

NN

N N

NC

C

125.7(120.7)

125.7(120.7)

124.5(121.4)

125.7(120.4)

112.6(106.9)112.6(106.9)

112.4(108.2)112.4(108.2)

111.5(109.3)110.4(110.7)110.6(106.7)107.0(107.3)

114.2(110.9)

114.2(110.9)

110.6(109.2)110.5(109.2)

110.6(109.2)110.5(109.2)

125.6(120.4)125.6(120.4)

110.6(106.7)

107.0(107.3)107.0(107.3)

110.6(106.4)

1e-1 1e-2 1e-3 1e-4

Fig. 3. Bond angles (in degrees) in C18N12 (Values in parentheses are bond angles in C30) calculated at the B3LYP/cc-pVDZ level.

J. Song et al. / Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76 75

tence of absorption in the region of 1600–1700 cm�1 can be con-sidered as the enhanced C–C bond and is in good agreement with

the experimental data. Fig. 4 shows the calculated infrared spec-troscopy of the most stable C18N12 isomer, singlet 1b. As expected,

Fig. 4. Calculated infrared spectroscopy of the most stable isomer of C18N12 at theB3LYP/cc-pVDZ level.

76 J. Song et al. / Journal of Molecular Structure: THEOCHEM 942 (2010) 71–76

many absorptions between 1600 and 1700 cm�1 contribute to theC@C stretching [33]. Such information is very helpful to determinethe structure of C18N12 experimentally in the future.

4. Conclusion

In summary, electronic and geometric properties of azafullereneC18N12 are studied and compared with the parent structure, thefullerene C30. This study shows that the substitution of carbon bynitrogen atoms in C30 can increase the C–C bond strength whenthey are surrounded by two or more nitrogen atoms. With theincreasing p character in those enhanced C–C bonds, the curvedC30 structure becomes more flattened, which is similar to the pre-vious observation of C16N12 and C28. To provide the guidance toexperimental work in the future, the most stable isomer ofC18N12 is predicted and its infrared spectroscopy is calculated forthe structural determination.

Acknowledgments

M.V. and J.S. acknowledge the supports from Research and Cre-ative Activity Award of the University of Michigan-Flint. J.S. alsoappreciates the support of computer time via National Center forSupercomputing Applications (NCSA) at University of Illinois at

Urbana-Champaign (CHE060036). M.P., G.S., and A.K. are thankfulthe financial support from Undergraduate Research OpportunityProgram (UROP) at University of Michigan-Flint.

References

[1] H.W. Kroto, Nature 329 (1987) 529.[2] T. Guo, M.D. Diener, Y. Chai, A.J. Alford, R.E. Haufler, S.M. McClure, T. Ohno, J.H.

Weaver, G.E. Scuseria, R.E. Smally, Science 257 (1992) 161.[3] R.K. Mishra, Y.Y. Lin, S.L. Lee, Chem. Phys. Lett. 313 (1999) 437.[4] Yu.N. Makurin, A.A. Sofronov, A.I. Gusev, A.L. Ivanovsky, Chem. Phys. 270

(2001) 293.[5] J.C. Grossman, M. Cote, S.G. Louie, M.L. Cohen, Chem. Phys. Lett. 284 (1998)

344.[6] D. Schultz, R. Droppa, F. Alvarez, M.C. dos Santos, Phys. Rev. Lett. 90 (2003)

15501.[7] N. Breda, R.A. Broglia, G. Colo, G. Onida, D. Provasi, E. Vigezzi, Phys. Rev. B62

(2000) 130.[8] L. Gan, J. Liu, Q. Hui, S. Shao, Z. Liu, Chem. Phys. Lett. 472 (2009) 224.[9] E. Malolepsza, Y. Lee, H.A. Witek, S. Irle, C. Lin, H. Hsieh, Inter. J. Quantum

Chem. 109 (2009) 1999.[10] L. Shi, B. Chen, J. Zhou, T. Zhang, Q. Kang, M. Chen, J. Phys. Chem. A 112 (2008)

11724.[11] G. Sun, M.C. Nicklaus, R. Xie, J. Phys. Chem. A 109 (2005) 4617.[12] J. Pattanayak, T. Kar, S. Scheiner, J. Phys. Chem. A 108 (2004) 7681.[13] J. Song, M. Vaziri, Mol. Phys. 104 (2006) 319.[14] H. Prinzbach, A. Weiler, P. Landenberger, F. Wahl, J. Wörth, L.T. Scott, M.

Gelmont, D. Olevano, B.V. Issendorff, Nature 407 (2000) 60.[15] C. Piskoti, J. Yarger, A. Zettle, Nature 393 (1998) 771.[16] T.G. Schmalz, W.A. Seitz, D.J. Klein, G.E. Hite, J. Am. Chem. Soc. 110 (1988)

1113.[17] S. Diaz-Tendero, F. Martin, M. Alcami, ChemPhysChem 6 (2005) 92.[18] M. Vaziri, Mater. Lett. 60 (2006) 926.[19] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.[20] P.J. Stephens, F.J. Devlin, D.F. Chablowski, M.J. Frisch, J. Phys. Chem. 98 (1994)

11623.[21] R.H. Hertwig, W. Koch, Chem. Phys. Lett. 268 (1997) 345.[22] C. Moller, M.S. Plesset, Phys. Rev. 46 (1934) 618.[23] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.[24] J.M.L. Martin, J. El-Yazal, J.P. Francois, Chem. Phys. Lett. 248 (1996) 345.[25] J.M.L. Martin, J. El-Yazal, J.P. Francois, Chem. Phys. Lett. 242 (1995) 570.[26] J.M.L. Martin, J. El-Yazal, J.P. Francois, Chem. Phys. Lett. 244 (1995) 120.[27] J.M.L. Martin, J. Chem. Phys. 100 (1994) 8186.[28] J.M.L. Martin, J. El-Yazal, J.P. Francois, Mol. Phys. 86 (1995) 1437.[29] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S.

Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A.Montgometry, J. Comp. Chem. 14 (1993) 1347.

[30] G.D. Fletcher, M.W. Schmidt, M.S. Gordon, Adv. Chem. Phys. 110 (1999) 267.[31] G.D. Fletcher, M.W. Schmidt, B.M. Bode, M.S. Gordon, Comput. Phys. Commun.

128 (2000) 190.[32] B.M. Bode, M.S. Gordon, J. Mol. Graph. Model. 16 (1998) 133.[33] R.M. Silverstein, G.C. Bassler, T.C. Morrill, Spectrometric Identification of

Organic Compounds, John Wiley & Sons, New York, 1991.