Chemical Physics 394 (2012) 52–55

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Chemical Physics

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Stability of functionalized C60 paramagnetic dimers and monomers

Michael Miller a, Frank J. Owens b,⇑a Armament Research Development and Engineering Center, Picatinny, NJ 07806-5000, United Statesb Department of Physics, Hunter College, City University of New York, 695 Park Ave., NY 10065, United States

a r t i c l e i n f o

Article history:Received 20 October 2011In final form 19 December 2011Available online 28 December 2011

Keywords:C60

C60 dimersFerromagnetismBond dissociation energyDensity functional theory

0301-0104/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.chemphys.2011.12.013

⇑ Corresponding author.E-mail addresses: owensfj@gmail.com, fowens@hu

a b s t r a c t

Density functional theory is used to calculate the bond dissociation energy to cleave the C60@C60 bond of theparamagnetic X–C60@C60–X and X–C60@C60 dimers where X is F, OH, O and H. The results show that thesedimers would not be stable much above room temperature and therefore cannot constitute the paramag-netic phase needed to form the observed ferromagnetism which has been shown to be stable up to 800 K.The calculated bond dissociation energies to remove an F, OH or H from a single C60 are large suggesting thatthey could be the source of the unpaired spin needed for the high temperature ferromagnetism.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

There have been a number of reports of ferromagnetism in C60

subjected to various treatments. Stable ferromagnetism has beenreported in C60 photolyzed in the presence of oxygen [1,2]. The fer-romagnetism has been suggested to arise from oligomers, mostlydimers of C60 having the form ON–C60@C60–ON. It is argued thatthe epoxide is formed in the presence of oxygen by photolyticdecomposition of O2 followed by atomic oxygen bonding to C60.A solution of C60 in dimethylformamide (DMF) ultrasonically dis-persed in a solution of polyvinyl difluoride (PVDF) was shown toproduce a ferromagnetic C60 suggested to be a F–C60@C60–F dimer[3]. More recently further evidence for ferromagnetism in fluori-nated C60 has been reported [4]. Ferromagnetism has also been re-ported in C60 treated with iodine and IBr [5–8]. In the case of IBrtreatment X-ray diffraction indicated the ferromagnetism was aris-ing from a body centered cubic structure of C60. Subjecting C60 tohydrogen gas under pressure has also been shown to produce fer-romagnetism at room temperature [9]. The crystal structure of thismaterial was also determined to be body-centered cubic.

The possibility that the ferromagnetism is due to functionalizeddimers of C60 having the form X–C60@C60–X where X may be O, F,OH, or H raises a number of questions. Firstly, since such dimersare singlets, where does the needed unpaired spin come from toform the ferromagnetic state? Secondly, there is the issue of thethermal stability of the dimers. The C60 dimer has been shownfrom Raman spectroscopy to dissociate into two C60s at 450 K[10]. However, the ferromagnetism in the treated C60 has been ob-

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nter.cuny.edu (F.J. Owens).

served up to 800 K implying that the functionalized dimers areconsiderable more stable than the non functionalized dimers.

The purpose of this work is to use density functional theory(DFT) to determine the stability of the various proposed C60 func-tionalized dimers as well as X–C60 monomers and to address thequestion of the origin of the unpaired electron spin.

2. Methods

The minimum energy structures of various functionalized di-mers having the forms X–C60@C60–X, X–C60@C60 and monomersX–C60 where X is O, OH, H, and F are obtained using density func-tional theory at the B3LYP/6-31G� level.

The calculations are performed on a Cray XE6 super computerusing the Gaussian 09 software [11]. The frequencies of the minimumenergy structures were also calculated to verify there were no imag-inary frequencies indicating that the calculated structures were at aminimum on the potential energy surface. The frequency calculationalso enabled a calculation of the zero point vibrational energy (ZPE)which is needed to calculate the bond dissociation energy. In orderto assess the stability of the various dimers and monomers the bonddissociation energy to dissociate the dimers into two C60 moleculeswas calculated. Specifically the dissociations considered are

X—C60@C60—X! 2ðX—C60Þ ð1Þ

X—C60@C60 ! X—C60 þ C60 ð2Þ

X—C60 ! C60 þ X ð3Þ

For example the bond dissociation energy (BDE) for reaction 1 is gi-ven by,

Table 1Total calculated energy of minimum energy structure of neutral and negativelycharged C60 monomers and dimers.

Molecule E(e) + E(ZPE) eV

M. Miller, F.J. Owens / Chemical Physics 394 (2012) 52–55 53

BDE ¼ ½EðeÞdimer þ EðZPEÞdimer� � 2½EðeÞx—c60þ EðZPEÞx—c60

� ð4Þ

where E(e) is the total electronic energy of the structure and E(ZPE)the zero point energy.

C60 �84.0009C�60 �84.0039C60–O �86.7775C60–O� �86.7805C60@C60 �168.0004(C60@C60)� �168.0042O–C60@C60–O �173.5259(O–C60@C60–O)� �173.5298

3. Results

3.1. Origin of paramagnetism

Previous calculations have shown that the C�60 anion is more sta-ble than the neutral C60 [12]. This has been experimentally verifiedby electron paramagnetic resonance which shows the presence ofthe anion in synthesized batches of C60 [13]. If the (C60–O)� is morestable than the neutral (C60–O) a possible source of the unpairedspin is the formation of the negatively charged dimer, (O–C60@C60–O)�. It is known from NMR and XRD studies that atomicoxygen bonds to C60 by a bridge across C@C double bond sharedby two adjacent carbons [14,15]. Fig. 1 shows the calculated min-imum energy structure of C60–O showing the bridged bond. Table 1gives the total energy of the calculated minimum energy structuresof C60, C�60, O–C60 and O–C�60 and the dimers formed from them. It isseen that the negatively charged dimers have a slightly lower totalenergy than the neutral dimers. Thus incorporation of the nega-tively charged epoxide of C60 could provide the spin needed forthe ferromagnetism.

Another possibility for the origin of the unpaired spin, sug-gested by previous calculations, is that the triplet states of thefunctionalized dimers, X–C60@C60–X, have a lower energy thanthe singlet states [16]. Using DFT at the B3LYP/6-31G� level theminimum energy structures of the singlet and triplet states offunctionalized dimers have been obtained. Fig. 2 shows the calcu-lated minimum energy structure of the fluorinated dimer, F–C60@C60–F. Table 2 gives the calculated energy difference, ES–Et

of the minimum energy structures between the singlet and tripletstates. The results indicate that the fluorine, hydrogen and hydro-xyl functionalized dimers have ground state triplets but not theneutral dimers or the oxygenated dimers. The calculated valuesof Es–Et are smaller than a previous calculation using a smaller ba-sis set, 3-21G [16]. These results suggest another possibility for theorigin of spin in the functionalized dimers.

Another possibility is that only one of the C60 molecules in thedimer is functionalized with OH, H or F which would give the di-mer an unpaired electron. Fig. 3 shows the optimized structureof a dimer in which only one C60 is fluorinated. Table 3 presentsthe energy of the minimum energy structures for such dimers.There are no calculated imaginary frequencies in all the structures

Fig. 1. DFT calculated minimum energy structure of epoxide of C60 showing thebridged oxygen carbon bond.

discussed above indicating they are at a minimum on the potentialenergy surface.

It is also possible that the ferromagnetism is not arising fromC60 dimers but from a cubic phase of C60. XRD measurements ofIBr, I and H doped C60 which have been reported to be ferromag-netic indicate the presence of a body centered cubic phase. Theseresults indicate that the ferromagnetism is arising from a cubicphase in which the halogen is intercalated into the cubic structureor bonded to a C60 in the structure.

3.2. Stability

The stability of the various functionalized dimers and mono-mers of C60 discussed in the previous section which have unpairedelectrons is examined. The ferromagnetism in the photolyzed C60

has been observed up to 800 K meaning the ferromagnetic phaseis quite stable [1]. The stability is assessed by calculating the bonddissociation energy (BDE) to dissociate the dimers into two C60

molecules or to remove the functional group from C60 i.e. C60–X ? C60 + X.

The calculated BDEs for the various functionalized dimers arepresented in Table 3. There are a number of points to make aboutthe results in this table. Firstly, the calculated BDE for the neutraldimer C60@C60 is in reasonable agreement with the estimate ofthe activation energy from the temperature dependence of the Ra-man frequency of the pentagonal pinch mode of C60 [10]. Secondly,the negatively charged dimers have smaller BDEs than the neutraldimers. All of these dimers would be stable at room temperature;however, the most stable dimers having BDEs slightly greater than1.0 eV would not be stable at 800 K. From Boltzman statistics thefraction of the initial number of dimers existing at room tempera-ture would be about 5 � 10�7 which would result in too small amagnetization to be measured. These calculations suggest thatthe dimers discussed above having a net electron spin are notthe source of the observed ferromagnetism.

It has been reported that MO62X hybrid meta functional betterpredicts the BDE particularly where dispersion forces are present[17,18]. To investigate this BDE has been calculated using thisfunctional for the C60@C60 neutral dimer because there is an exper-imental measurement of the activation energy available to enable acomparison [10]. The calculated BDE for this dimer to break thebond between the two C60 entities using the M062X functionalyields 0.51 eV. The B3LYP/6-31G� calculated value is 1.10 eV whichis in better agreement with the experimental value of 1.25 eV.

Since the basis sets used in determination of the BDEs were notat the HF limit, some of the energy in the dimer will be essentiallyused to help stabilize the individual components of the dimer in-stead of stabilizing the dimer itself. Therefore the as-calculated en-ergy could be too low. In order to correct for this basis setsuperposition error (BSSE) the Boys–Bernardi counterpoise (cp)method was implemented. The results indicate the cp correctionterm is quite small for these systems. For example, for the

Fig. 2. Calculated structure of fluorinated C60 dimer, F–C60@C60–F.

Table 2Calculated difference in energy of singlet and triplet states, Es–Et of the minimumenergy structures of C60 dimersa.

DIMER Es–Et (eV)

C60@C60 �0.508O–C60@C60–O �0.519F–C60@C60–F +0.550H–C60@C60–H +0.510OH–C60@C60–HO +0.540

a Plus sign means triplet state has lower energy than singlet.

54 M. Miller, F.J. Owens / Chemical Physics 394 (2012) 52–55

F–C60@C60–F the BSSE correction to the BDE is 0.0035 eV repre-senting a third of a percent of the uncorrected value

Table 4 gives the BDEs to remove an OH, H or F from a single C60.Provided that the decomposition of C60–X involves removal of theX, these values are sufficiently high to suggest that the unpairedspin needed to form the ferromagnetism arises from single crystalsof C60–X. The other possible decomposition route removal of a Catom from the C60 frame work has previously been shown to have

Fig. 3. Structure of dimer where

a much higher binding energy, in the order of 7.0 eV [19]. Furtherthe presence of a C vacancy in the C60–X, would still leave it withan unpaired electron. Since ferromagnetism is observed in H, I andIBr treated C60 which has been shown to have a body centered cu-bic unit cell, it is likely that this is the structure of the C60–F andC60–OH ferromagnetic phases. However further work is neededto confirm this possibility.

4. Conclusion

The possibility that dimers of C60 having a net spin are thesource of the observed ferromagnetism is considered. It is shownthat [O–C60@C60–O]�, F–C60@C60, OH–C60@C60 and H–C60@C60 arestable structures having a net magnetic moment. The calculationsindicate that the minimum energy structures of X– C60@C60–Xwhere X is F, OH or H have ground state triplets and therefore amagnetic moment.

However, calculations of the bond dissociation energy to breakthe intra C60 bond where the C60 is functionalized by a H or halogen

only one C60 is fluorinated.

Table 3Calculated bond dissociation energy (BDE) to dissociated C60 dimers into theirmonomers for various charged and functionalized dimers.

Dimer Products BDE (eV)

C60@C60 2 C60 1.10[C60@C60]� C60, C�60 0.28O–C60@C60–O 2 (O–C60) 1.04[O–C60@C60–O]� O–C60, O–C�60 0.43OH–C60@C60–HO 2(OH–C60) 1.02H–C60@C60–H 2(H–C60) 1.04F–C60@C60–F 2(F–C60) 1.00F–C60@C60 F–C60,C60 0.82OH–C60@C60 OH–C60,C60 0.83H–C60@C60 H–C60,C60 0.84

Table 4Calculated bond dissociation energy to remove an F, OH and H from a single C60

molecule.

Molecule Products BDE (eV)

F–C60 F, C60 4.36OH–C60 OH, C60 1.65H–C60 H, C60 9.90

M. Miller, F.J. Owens / Chemical Physics 394 (2012) 52–55 55

atoms indicate that none of these dimers would be sufficiently sta-ble to produce magnetism observed at high temperature. These re-sults suggest that the various dimers considered are not the sourceof the ferromagnetism as has been proposed.

Because X-ray diffraction studies of ferromagnetic H and IBrtreated C60 indicate a body centered structure, it is likely that theferromagnetism is arising from this phase. It is shown that thebond dissociation energy to remove the functionalized entity froma single C60 is sufficiently high to allow for the existence of ferro-magnetism at high temperature.

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