electronic, energetic, and geometric properties of methylene-functionalized c60

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Journal of Cluster ScienceIncluding Nanoclusters andNanoparticles ISSN 1040-7278Volume 24Number 3 J Clust Sci (2013) 24:669-678DOI 10.1007/s10876-013-0563-6

Electronic, Energetic, and GeometricProperties of Methylene-Functionalized C60

Mohammad T. Baei, Ali AhmadiPeyghan & Zargham Bagheri

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ORI GIN AL PA PER

Electronic, Energetic, and Geometric Propertiesof Methylene-Functionalized C60

Mohammad T. Baei • Ali Ahmadi Peyghan • Zargham Bagheri

Received: 10 January 2013 / Published online: 2 February 2013

� Springer Science+Business Media New York 2013

Abstract Chemical functionalization of C60 fullerene with one to six carbene

(CH2) molecule(s) has been investigated using density functional theory. We have

found that the reaction is regioselective so that a CH2 molecule prefers to be

adsorbed atop a C–C bond which is shared between two hexagonal rings of the C60,

releasing energy of -3.95 eV. Singly occupied molecular orbital (SOMO) of the

CH2 interacts with LUMO of the C60 via a [2 ? 1] cycloaddition reaction. Energy

of the reaction and work function of the system are decreased by increasing the

number of adsorbed CH2 molecules. The HOMO/LUMO energy gap of C60 is

slightly changed and the electron emission from its surface is facilitated upon the

functionalization.

Keywords Fullerene � DFT � C60 � Adsorption

Introduction

Nanomaterials have attracted great interest in recent years due to their excellent

mechanical, electrical, optical, magnetic, and surface properties [1–6]. Since the

discovery of C60 fullerene [7], several studies on different nanostructures such as

fullerene-like clusters, nanotubes, nanocapsules, nanopolyhedra, cones, cubes, and

M. T. Baei

Department of Chemistry, Azadshahr Branch, Islamic Azad University, Azadshahr, Golestan, Iran

A. A. Peyghan (&)

Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

e-mail: [email protected]

Z. Bagheri

Physics Group, Science Department, Islamic Azad University, Islamshahr Branch,

P.O. Box: 33135-369, Islamshahr, Tehran, Iran

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J Clust Sci (2013) 24:669–678

DOI 10.1007/s10876-013-0563-6

Author's personal copy

onions have been reported [8–10]. Being interesting candidates for constructing

units of new materials, increasing variety of species have been utilized for

functionalization of the fullerenes [11]. These derivatives have also enhanced

stability of the endohedral fullerenes [12], which might be very interesting for

applications in medicinal chemistry, materials science, and nanotechnology [13].

Several types of functionalized fullerenes have been recently synthesized for

possible applications in electronics and optical devices as well as for developing

possible applications in biology and medicine [14]. Exploration of the reactivity in

addition reactions of the fullerenes has motivated special interest for preparation of

specific fullerene derivatives by exohedral functionalization [15]. Synthesis of

uniformly exohedrally monofunctionalized fullerene derivatives in preparative

quantities has been explored with success by a variety of addition reactions [16, 17],

most notably by a range of cycloaddition [18, 19] and organometallic addition

reactions [20]. The preparation of specific multiply functionalized derivatives of C60

with organic addends has been taken up in several research groups [21], exploiting

the regioselectivity of the cycloaddition step.

In the present work, [2 ? 1] cycloaddition reactions of one to six carbene(s) with

a C60 molecule have been theoretically investigated in terms of geometry, energies,

electronic structures, stability, etc. using density functional theory (DFT). Carbenes

have played an important role as transient intermediates over the past five decades

[22]. Introduced by Doering into organic chemistry in the 1950s [23] and by Fischer

into organometallic chemistry in 1964 [24], these fascinating species are involved in

many reactions of high synthetic interest. The [2 ? 1] cycloaddition of carbene to

nanotubes was reported for the first time by Haddon et al. and coworkers in 1998

[25]. It was proposed initially that the [2 ? 1] cycloaddition on the nanotube

sidewall gave rise to the formation of three-membered-ring species [26]. However,

our results may be useful for further studies in functionalization of C60 and

construction of nanodevices.

Computational Methods

Geometry optimizations and density of states (DOS) analysis have been performed

on a C60 fullerene and different n CH2/C60 complexes using B3LYP functional with

6–31G (d) basis sets as implemented in GAMESS suite of program [27]. GaussSum

program [28] has been used to obtain DOS results. The B3LYP has been

demonstrated to be a reliable and commonly used functional for study of different

nanostructures [29–33]. Vibrational frequencies were also calculated at the same

level to confirm that all the stationary points correspond to true minima on the

potential energy surface. All frequency calculations were performed using

numerical second derivatives and verified that all of the structures are true minima

by frequency analysis and obtained positive Hessian eigenvalues. We used B3PW91

functional to study the electronic properties of the systems. Xiao et al. [34] have

shown that for several studied semiconductors, B3PW91 predicts gaps substantially

better than all modern hybrid functionals. Reaction energy (Er) of the CH2 molecule

with the C60 has been calculated using the following equation:

670 M. T. Baei et al.

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Er ¼ H n CH2=C60ð Þ � H C60ð Þ � nH CH2ð Þ; n ¼ 1� 6 ð1Þ

where H (n CH2/C60) is the enthalpy of the complex of n CH2 adsorbed on the C60

and H (CH2) refers to the enthalpies of an isolated CH2 molecule at 298 K and 1

atom. The H (C60) is the enthalpy of the pristine C60. The negative value of Er

indicates the exothermic character of the adsorption process.

Results and Discussion

In the optimized C60 molecule (Fig. 1), the carbon nuclei reside on a sphere with the

diameter of about 7.10 A. More precisely, the atoms are positioned at 60 vertices of

a truncated icosahedron structure with 90 edges, comprised of 12 pentagons and 20

hexagons. Two different C–C bonds exist within the C60 structure which they have

been calculated to be about 1.40 and 1.46 A, being in complete agreement with the

previous reported experimental values of 1.40 and 1.46 A, respectively [35]. The 30

short bonds are nearly double bonds and lie on the edges that are shared by two

hexagons (B66). The longer ones, that are single bonds, lie at the 60 edges shared by

a hexagon and a pentagon (B65). In Fig. 1a, the double and single bonds are depicted

in black and green, respectively.

Carbenes are neutral compounds featuring a divalent carbon atom with only six

electrons in its valence shell. Two electronic configurations can be envisaged for

carbenes as singlet and triplet [36]. Carter et al. indicated that triplet CH2 with bent

configuration has more stability than other configurations. Thus, in order to

investigate chemical functionalization of the exterior surface of the C60 by CH2

molecule, we have put the bent carbene atop the B66 and B65 bonds of the C60,

assuming that a reaction is occurred. As shown in Table 1, Er values corresponding

to the adsorption of CH2 have been calculated to be -85.1 and -82.4 kcal/mol for

B66 and B65 bond additions, respectively (Fig. 2). The reaction is a [2 ? 1]

cycloaddition of the molecule and C60. The driving force of the reaction is the

formation of new r-bonds, which are energetically more stable than the p-bonds.

Fig. 1 Geometrical parameters of the optimized C60 and its DOS. Distances are in A

Electronic, Energetic, and Geometric Properties 671

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Experimental work has indicated that in cycloadditions the molecule prefers to

attack the B66 bond (double bond) of the fullerene over the B65 bond [37].

Therefore, it can be concluded that the Er of the CH2 interaction with the B66 bond is

higher than that with the B65 which is in good agreement with the experimental

results. Subsequently, kinetic favorability of reactions was explored. As shown in

Fig. 3, barrier energy must be overcome to get into a final configuration in each

reaction. The barrier energies for the configurations B66 and B65 are about 10.3 and

56.7 kcal/mol, respectively. It can be inferred that barrier energy for configuration

B65 is large that the reaction process may not overcome that at the room

temperature. Thus, the CH2 addition on C60 through C66 bond is both kinetically and

energetically more favorable than that on the B65 one.

As shown in panel (a) of Fig. 2, the carbon atom of CH2 is bonded to the carbon

atoms of a B66 bond so that the lengths of the newly formed C–C bonds are about

1.50 A, with a charge transfer of 0.071 e from the adsorbate to the fullerene.

Furthermore, the reaction induces a locally structural deformation to the C60. For

example, one of the angles of the pentagonal ring is decreased from 108� to 105�,

and the adsorbing B66 bond is pulled outward from the fullerene surface with the

bond length increasing from 1.40 A (in the pristine C60) to 1.62 A. On the other

hand, when the CH2 is attached to the C60, significant out-of-place displacement of

the H atoms is observed, where H–C–H angle is reduced from 133� in the free

molecule to 115� due to the intramolecular steric repulsion.

The energy difference between the highest occupied molecular orbital (HOMO)

and the lowest unoccupied molecular orbital (LUMO), Eg, has been calculated from

the DOS (Fig. 1) results, indicating that the C60 is a semi-conductive material with

an Eg of 2.72 eV which is in good agreement with the results obtained by Lee et al.

[38]. Calculated DOS plots show that the electronic properties of the C60 have

changed upon the addition of CH2 molecules (Fig. 2). In the most stable

Table 1 Calculated reaction energy (Er, kcal/mol), HOMO energies (EHOMO), LUMO energies (ELUMO),

HOMO–LUMO energy gap (Eg) Fermi level energy (EFL) of systems

System Er QT (e)a EHOMO EFL ELUMO Eg DEg (%)b

C60 – – -6.18 -4.6 -3.46 2.72 –

B66-attached -85.1 0.071 -5.9 -4.61 -3.33 2.57 -5.5

B65-attached -82.4 -0.025 -5.84 -4.48 -3.13 2.71 -0.3

(1) 2CH2/C60 -78.3 0.062 -5.76 -4.44 -3.12 2.64 -2.9

(2) 2CH2/C60 -77.9 0.068 -5.57 -4.5 -3.43 2.14 -21.3

(3) 2CH2/C60 -73.4 0.054 -5.33 -4.29 -3.25 2.08 -23.5

(4) 2CH2/C60 -76.9 0.06 -5.87 -4.58 -3.29 2.58 -5.1

(5) 2CH2/C60 -80.9 0.065 -5.73 -4.41 -3.1 2.63 -3.3

Energies are in eVa QT is defined as the total Mulliken charge per CH2 molecule, and positive values mean charge transfer

from the molecule to the fullereneb The change of HOMO–LUMO gap of C60 after functionalization with CH2


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configuration (B66 addition), the Eg of the C60 is decreased from 2.72 to 2.57 eV (by

about 5.5 % changes). This can result in a change in the corresponding electrical

conductivity since it is well known that the Eg (or the band gap in bulk materials) is

a major factor determining the electrical conductivity of the material and a classic

relation between them is as follows [39]:

r / exp�Eg

2kT

� �ð2Þ

where r is the electrical conductance and k is the Boltzmann’s constant. According

to the equation, smaller Eg values lead to higher conductance at a given temperature.

Therefore, the observed substantial decrement of Eg of the C60 leads to the change in

electrical conductivity of the fullerene after adsorption process.

Fig. 2 Models for two different CH2 molecule adsorbed on the C60 and their DOS plots


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With each B66 bond on the C60 being a potential chemisorption site, the

possibility of multiple adsorption is interesting to evaluate CH2 concentration on the

C60. Thus, it seems evident that the formation of a symmetric hexakisadduct will

proceed through multiple cycloadditions to B66 bonds. For the addition of a second

CH2, five different reaction sites were considered, with the two CH2 molecule

bonded to B66 bonds, in which three unique symmetry were found namely Cs

(compounds 1 and 2), C2 (compounds 3 and 4) and D2h (compound 5). All of the

optimized structures of the regioisomeric bis-adducts of CH2/C60 are shown in

Fig. 4. The Er of these compounds ranged between -73.4 and -80.9 kcal/mol per

each CH2, which is slightly lower than that of one CH2 interaction. The most stable

configuration (compound 5) is that two CH2 are located on the top of two B66 bond

as far as possible, in such a way that the steric repulsion between these molecules

would be minimum. The lengths of newly formed C–C bonds are close to those that

obtained for CH2 -attached C60 with individual addends discussed above.

Why is the second addition of CH2 to the C60 slightly less favorable than that of

the first one? To answer this question, we have performed frontier molecular orbital

(FMO) analysis. The obtained results have been summarized in Table 2. Overlap-

ping between singly occupied molecular orbital (SOMO) of the CH2 and LUMO of

the C60 is energetically allowed in the reaction, providing the orbitals with similar

energies. Herein, our results reveal that the SOMO of the CH2 interacts with the

LUMO of the C60. This can be attributed to the fact that the LUMO energy of the

C60 is increased (Table 2) upon its reaction with the first CH2 and some charges are

transferred from the CH2 to the C60. Therefore, the Er of the second CH2 is

decreased.

Fig. 3 Energy diagram for CH2

adsorption on B66 and B65 bondof C60. Energies are in kcal/mol.The energies of reactants havebeen taken as the reference pointwith energy equal to zero. TS istransition state and B56 and B66

indicated the kind of C60 bondwhich carbene has beenattached. Units are in kcal/mol


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Subsequently, we have explored functionalization of the C60 with more carbenes

up to six (Fig. 5). Each CH2 is adsorbed successively to a B66 bond far away relative

to the previous CH2 on the surface of the fullerene. It can be seen from Table 2 that

the Er per CH2 molecule decreases gradually (from -85.1 to -71.0 kcal/mol) by

increasing the number of the adsorbed molecules. This phenomenon can be

explained by FMO analysis. As it has been mentioned before, one of the most

Fig. 4 Models for five different isomers of bis-adducts of CH2 molecule on the C60. Distances are in A

Table 2 Calculated reaction energy (Er, kcal/mol), HOMO energies (EHOMO), LUMO energies (ELUMO),

HOMO–LUMO energy gap (Eg) Fermi level energy (EFL) of systems

System Er QT (e)a EHOMO EFL ELUMO Eg DEg (%)b

C60 – – -6.18 -4.6 -3.46 2.72 –

2CH2/C60 -80.9 0.065 -5.73 -4.41 -3.1 2.63 -3.3

3CH2/C60 -76.4 0.06 -5.35 -3.98 -2.61 2.74 0.7

4CH2/C60 -74.7 0.057 -5.11 -3.69 -2.27 2.84 4.4

5CH2/C60 -71 0.052 -4.98 -3.5 -2.02 2.96 8.8

6CH2/C60 -68.3 0.049 -4.79 -3.23 -1.68 3.11 14.3

Energies are in eVa QT is defined as the total Mulliken charge per CH2 molecule, and positive values mean charge transfer

from the molecule to the fullereneb The change of HOMO–LUMO gap of C60 after functionalization with CH2


123


important factors in SOMO/LUMO interactions is the energy difference between

the SOMO and LUMO of the reactants. The FMO analysis shows that the SOMO

energy of the nucleophile agent (CH2) is about -6.61 eV and that of the LUMO of

the pristine C60 is about -3.46 eV which is gradually increased by increasing the

number of attached CH2 (Table 1) species. It suggests that the Er decrement by

increasing the number of carbenes is due to the larger difference between the SOMO

energy of the CH2 and the LUMO energy of the adsorbent.

Total electronic DOSs for the CH2/C60 complexes are shown in Fig. 6, indicating

that their Eg have changed about 0.7–14.3 % after the functionalization with two or

more carbenes. It is noteworthy to say that as shown in Table 2, not also the Eg of

the C60 is changed but also the Fermi level energy (EFL) is gradually increased by

increasing the number of the adsorbed CH2. The canonical assumption for Fermi

level is that in a molecule (at T = 0 K) it lies approximately in the middle of the Eg.

In fact, what lies in the middle of the Eg is the chemical potential, and since the

chemical potential of a free gas of electrons is equal to its Fermi level as

traditionally defined, herein, the Fermi level of the considered systems is at the

middle of the Eg.

When one or two CH2 molecules are adsorbed on the fullerene, the EFL obviously

increases by 0.21–0.38 eV. When six CH2 molecules are adsorbed on the C60, the

EFL is increased from -4.82 eV in the pristine fullerene to -3.23 eV in the

adsorbed form. This phenomenon leads to a decrement in the work function that is

important in field emission applications. The work function can be found using the

standard procedure by calculating the potential energy difference between the

vacuum level and the Fermi level, which is the minimum energy required for one

electron to be removed from the Fermi level to the vacuum. The decrement in the

work function indicates that the field emission properties of the C60 are facilitated

upon the adsorption of CH2 molecules. Furthermore, this results in reduced potential

barrier of the electron emission for the fullerene, facilitating the electron emission

Fig. 5 Model for a 4CH2 and b 6CH2 fucntionalized-C60


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from the C60 surface. All of the above calculations suggest that the CH2 adsorption

has an advantageous effect on the field emission properties of C60 fullerene.

Conclusion

The reaction of C60 with one to six carbene (CH2) molecule(s), resulting in a

functionalized-C60 adduct through [2 ? 1] cycloaddition has been investigated

using density functional theory. We have found that the reaction is regioselective

and the CH2 molecule prefers to be adsorbed atop a B66 bond of the C60 with

reaction energy of -85.1 kcal/mol (for one CH2). The SOMO of the CH2 interacts

with the LUMO of the C60 via a cycloaddition reaction. The energy of the reaction

and work function of the system are decreased by increasing the number of the

Fig. 6 Calculated density of states for different models of nCH2/C60 complexes


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adsorbed CH2 molecules. The Eg of the C60 is slightly changed and the electron

emission from its surface is facilitated upon the reaction.

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electronic, energetic, and geometric properties of methylene-functionalized c60

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