Eur. Phys. J. D (2013) 67: 13DOI: 10.1140/epjd/e2012-30535-0

Regular Article

THE EUROPEANPHYSICAL JOURNAL D

Isomer-separated photodissociation of large sized siliconand carbon cluster ions: Drift tube experiment combinedwith a tandem reflectron mass spectrometer for Si+24– Si+27

and C+32–C+

38�

Ryoichi Moriyama, Tomohiro Ohtaki, Jun Hosoya, Kiichirou Koyasu, and Fuminori Misaizua

Department of Chemistry, Graduate School of Science, Tohoku University, 6–3 Aoba, Aramaki, Aoba-ku,980–8578 Sendai, Japan

Received 28 August 2012 / Received in final form 25 October 2012Published online 5 February 2013 – c© EDP Sciences, Societa Italiana di Fisica, Springer-Verlag 2013

Abstract. Isomer-resolved multiphoton dissociations (PDs) with 4.66-eV laser photons were applied tocarbon and silicon cluster cations, C+

n (n = 32, 34, 36, and 38) and Si+m (m = 24–27), in order toinvestigate correlations between the isomer structures and dissociation reactions. Cyclic and fullerenestructures of C+

n and prolate and spherical isomers of Si+m, which are the coexisting isomers in these sizeranges, were separated by ion mobility spectrometry, followed by photolysis using a tandem reflectron massspectrometer. Photofragment ion distributions were revealed to depend on the parent isomer structures.Dissociation mechanisms were discussed from the fragment ion distributions.

1 Introduction

Ion mobility spectrometry, IMS, is a gas phase elec-trophoretic technique which is known as one of the pow-erful methods to identify conformations of isomer ions.IMS has been utilized for separations of isomer ions of gasphase clusters and large molecules [1–3], and it has re-cently been applied in wide fields such as military andsecurity [4]. In the IMS measurements, the structural dif-ferences are distinguished by collision cross sections of theions with buffer gas atoms filled in a drift cell, in whichan electrostatic field is applied to guide ions forward [5].

Covalent clusters, such as carbon and silicon clusters,have been revealed to have many isomers by IMS measure-ments. This technique showed that carbon cluster ions,C+

n , consist of linear isomers, several kinds of cyclic iso-mers, and fullerene isomers, and that the isomers coexistat some transition sizes [6,7]. For silicon cluster ions, Si+m,structural transformation was found to occur at aroundm = 25 from prolate to more spherical structures [8], andthe two isomers coexist in the size range of m = 24–30.

Photodissociation (PD) spectroscopy was, on the otherhand, applied so far for size-selected C+

n and Si+m clus-ters. Laser-induced fragmentation of C+

n , 34 � n � 80,showed that such large even-sized clusters lose C2 unitssequentially from internally high energy species [9]. The

� ISSPIC 16 - 16th International Symposium on Small Par-ticles and Inorganic Clusters, edited by Kristiaan Temst,Margriet J. Van Bael, Ewald Janssens, H.-G. Boyen andFrancoise Remacle.

a e-mail: misaizu@m.tohoku.ac.jp

C2-loss mechanism was extensively investigated for sucheven-sized clusters, which have fullerene structures [10].

In addition, fragment-ion species were found to dependsensitively upon the cluster size. It was reported that C+

n

with n � 31, which mainly have mono- and multi-cyclicstructures, showed photofragmentations with the loss ofneutral C3 [9–12]. Photofragment ions other than C3-losswere also observed [13]: for example, fragment ions of C+

15,C+

19, and C+23 were observed from C+

29, corresponding toC14-loss, C10-loss, and C6-loss products, respectively. C10-and C14-losses were also observed in metastable dissocia-tion reactions of C+

n , n � 30 [14].Ultraviolet PD measurements of Si+m were also ex-

amined by several groups for m = 2–12 [15] andm = 10–80 [16]. In these experiments, two different dis-tributions of photofragment ions were observed: one wasm = 6–11, and another was neutral Si10-loss and Si7-loss.Collision induced dissociation of Si+m, m = 6–26, were alsomeasured with argon at a collision energy of 5 eV [17].Main products observed for m = 19–29 were again Si10-loss as well as Si7-loss.

As mentioned above, PD of C+n around n = 30 and Si+m

around m = 25 showed various photofragment ions, im-plying that these PD involve complicated processes. Al-though the variety of photofragment distributions couldbe ascribed to the coexistence of different parent isomers,it is still unclear what isomer dissociates into what size offragment ions.

In order to distinguish fragmentation products ofeach isomer, spectroscopic measurements should be ex-amined after isomer separation. Anion photoelectron

Page 2 of 5 Eur. Phys. J. D (2013) 67: 13

Fig. 1. Schematic drawing of our experimental setup for isomer-resolved photodissociation.

spectroscopy has so far been reported on the separatedisomers of C−

n , n = 10–12 [18], and DNA oligonucleoti-des [19]. These investigations successfully revealed dif-ferent electronic structures depending on their structuralisomers. We applied isomer-resolved multiphoton dissoci-ation at 3.49 eV and collision-induced dissociation to C+

n ,n = 7–10, in which size the linear and cyclic isomers co-exist. We observed isomer-dependent mass distributionsof fragment-ions [20]; from the linear isomers, C3-loss re-actions were predominantly observed, whereas cyclic iso-mers produced C2-loss fragment ions in addition to C3-lossproducts.

In this study, we have examined isomer-resolved PDexperiments at 4.66 eV with a tandem reflectron setupon the larger size covalent clusters of C+

n , n = 32, 34, 36,and 38, and Si+m, m = 24–27. In this size range, mono- andmulti-cyclic isomers and fullerene isomers coexist for C+

n ,and prolate and spherical isomers coexist for Si+m. Wehave found the isomer-dependent fragment-ion distribu-tions for C+

n , while little isomer-dependence was observedfor Si+m. We discuss the isomer-dependent fragmentationand isomerization reaction mechanisms.

2 Experimental procedure

We have developed a home-built tandem reflectron massspectrometer combined with an ion drift cell [21] forisomer-selected PD measurements. Details of the exper-imental procedures for isomer- and mass-separation werereported already [22], and the schematic view of the ap-paratus is shown in Figure 1. Here, we briefly describethe experimental setup and conditions for the isomer- andmass-selected PDs. Carbon or silicon cluster ions wereproduced by laser vaporization of a graphite disk or asilicon rod with the second harmonic of a Nd:YAG laser,532 nm. These cluster ions were introduced into the driftcell through an ion-gate electrode, on which a pulsed elec-tric field of 75–300 V cm−1 was applied at a given time,t = t0. The ions were then separated depending on thecollision cross section in the drift cell, of which the tem-perature ranged between 170–300 K, the pressure was

varied between 0.01–0.8 Torr, and the drift electric fieldwas set at 7–15 V cm−1. After running through the cell,the ions with a certain collision cross section were accel-erated with 2.1 kV by a second pulsed electric field at atime, t = t0 + Δt in a time-of-flight mass spectrometer(TOFMS). We hereafter denote the delay time from theion gate pulse Δt as “arrival time”. The accelerated ionswere mass-separated in the tandem reflectron TOFMS,and a mass spectrum was measured with a given Δt. Weobtained a series of TOF mass spectra sequentially bychanging the arrival time, and obtained a plot of arrivaltime distribution (ATD), in which the total ion intensityof a certain TOF peak was shown as a function of thearrival time. The peak of the ATD plot corresponds to arepresentative arrival time of a certain isomer in the se-lected ion species.

After determining the representative arrival time andmass-separation conditions for each isomer, we examinedPDs of C+

n and Si+m. With the tandem reflectron setup,isomass ion packets were temporally and spatially fo-cused at a certain point between the first and the sec-ond reflectrons. We set this point as an interaction regionwith a dissociation laser so as to obtain optimal PD effi-ciency [23–25]. Just before the interaction region, we useda mass gate [26] in which a pulsed electric field of around400 V cm−1 was applied perpendicular to the direction ofthe ion beam to extract only a target ion. At the interac-tion region, isomer- and mass-selected ions were irradiatedwith a photolysis laser of the fourth harmonic (266 nm,4.66 eV) of a pulsed Nd:YAG laser (Spectra Physics,GCR150). The parent and daughter ions were then mass-separated in the second reflection region and detected af-ter passing through the following field free region.

3 Results and discussion

3.1 Isomer-resolved photodissociations of C+n , n = 32,

34, 36, and 38

In order to apply the isomer-resolved photodissocia-tions (PDs) of even-numbered cluster ions, C+

32, C+34,

Eur. Phys. J. D (2013) 67: 13 Page 3 of 5

Fig. 2. Photofragment ion mass spectra from (a)–(d) cyclic isomers and (e)–(h) fullerene isomers of C+n , n = 32, 34, 36, and 38,

measured at 266 nm. A peak marked by * represents signals of parent C+35 which were not completely eliminated by mass gate.

C+36, and C+

38, these ions were separated by IMS un-der the condition that the He pressure inside the cell of0.01–0.04 Torr and at room temperature, correspondingto E/N = 760–3000 Td. In the drift cell, ions run fasterwith increasing drift electric field, E, and with decreasingnumber density of buffer gas, N due to the decrease ofcollision frequency. Thus, the ratio E/N is an importantparameter to control separation conditions of isomers. Inexperiments with “low-field condition” on carbon clusters,E/N were in general in the range of 1.5–10 Td [27,28],where Td is the unit representing to 10−17 Vcm2. Evenif the collision frequencies of the cluster ions with He areinsufficient to thermalize the clusters in such a high E/N -condition, the cyclic and the fullerene isomers were sepa-rated enough for isomer-resolved PD. The obtained arrivaltime distributions, ATDs, of C+

n isomers were consistentwith the previous reports [6]; in even numbered clusters,two peaks of fullerene and cyclic isomers were observed,while odd numbered clusters showed almost single peak ofcyclic isomers in our separation conditions.

From the photolysis measurements under this isomer-separation condition, we have found the isomer-dependentphotofragment distributions of C+

n , as shown in Figure 2.From the cyclic C+

n isomers, we have mainly observedC3-loss and C14-loss in addition to C+

15, C+19, and C+

23photofragment ions irrespective of the size of parent C+

n

(Figs. 2a–2d). These fragment ions, along with the neu-tral C14 fragments, were shown to be stable cyclic clus-ters with (4n+2)π electrons, corresponding to the Huckelrule from the previous annealing measurements [29,30].The C14-loss products from the cyclic isomers were alsoreported in PD [13] and metastable dissociation [14] ofC+

25–C+29 without isomer separation.

By contrast, successive loss of neutral C2 units wasmainly observed from the fullerene isomers (Figs. 2e–2h).This observation is similar to the previous results in thesize selected dissociation of large C+

n ions; the C2-loss pro-cess was observed from C+

n with n > 34 [9], in which sizerange the fullerene isomers become more stable than cyclicisomers [6]. Furthermore, it was also reported that the C+

60ion, which was vaporized and ionized from the isolated C60

sample, exhibited C2-loss fragment ions [10].By von Helden et al. [29] and by Hunter et al. [30,31],

fragment-ion structures in CID of C+n , n = 30–50, were

investigated by annealing measurements using an iondrift cell with an ion injection energy of 150 eV. It was

concluded that there were two dissociation pathways fromcollisionally excited C+

n , 30 � n � 40, that is, monocyclic-ion formation with loss of C10, C14, C18, or C22, andthe formation of fullerenes by losing C1, C2, or C3 [29].The fragment ions from C+

34 was mainly monocyclic iso-mers, while fullerene fragment ions which were formedby C2-loss process was observed comparably with mono-cyclic fragment ions from C+

36 and C+38. Although Bowers

et al. proposed the dissociation pathways from the even-numbered C+

n polycyclic ring isomers to fullerene frag-ments by C2 loss, little such fragments was observed inthe present PD results on cyclic C+

n . We observed muchless intensity of C2-loss fragments than C14-loss fragments(monocyclic fragments) from cyclic C+

n , n = 34–38.The above difference of C2-loss probability may be due

to the different excitation methods used; photoexcitationin the present study and the collisional excitation in CIDexperiments. However, it is also necessary to consider theexcitation energies for the two experiments. Activation en-ergy for dissociation into the fullerene fragments and thecyclic fragments was estimated by Jarrold et al. the energyto obtain fullerene fragments ranged from 2.8 eV for C+

34

to 2.5 eV for C+60, while the energy for cyclic fragments

amounts to 4.4 eV for C+34 and 3.7 eV for C+

60 [30]. Al-though this energy range is in the same order with thephoton energy used in the present study, the dissociationprocesses are expected to be governed by multiphotonabsorption and relaxation into the vibrationally excitedstates in the electronic ground state by internal conver-sion, as was already discussed in a previous study [32] andalso mentioned in the following section. Thus the isomer-ization reaction between fullerene and cyclic isomers maybe possible also in the present photoexcitation. However,we concluded that the isomerization hardly proceeds inthe photoinduced dissociation of C+

n , although the reasonis unclear at present.

3.2 Isomer-resolved photodissociations of Si+m ,m = 24–27

Quite a few studies were also reported so far about thedissociation of size-selected Si+m ions. Si10-loss was signif-icantly observed in PD of m = 23–29 and also in CID ofm = 33. Meanwhile, PD of the larger Si+m, m > 30, andCID of m = 38, 48, and 67 showed Si+6 –Si+11 fragmentions and no intermediate fragments of Si10-loss [33,34].

Page 4 of 5 Eur. Phys. J. D (2013) 67: 13

Fig. 3. Photofragment ion mass spectra from (a) prolate iso-mers and (b) spherical isomers of Si+25 measured at 266 nm.Only the fragment ions appear in these mass spectra. Arrivaltime distributions of Si+m, m = 24–27, are also shown in (c)–(f).The arrows in the figures indicate the peaks of separated iso-mer ions of Si+m.

In this size range, the stable geometry of Si+m changesfrom prolate to spherical structures [35]. Therefore it issuggested that the photofragment ion distributions fromSi+m are different between the two different isomers.

There is a characteristic structural motif in the pro-late Si+m isomer [36,37]; theoretical calculation predictedthat the ground state structures of the neutral Si25 pro-late isomer consists of three stable subunits, Si10, Si6 andSi9 [36], as shown in the inset of Figure 3. The stable unitssuch as Si10 in the prolate isomer can be dissociated withlow excitation energy [37]. By contrast, the spherical iso-mers have more stuffed structures and therefore, dissocia-tion with the Si10-loss appear to be less efficient than theother process such as generating Si+6 –Si+11 [37]. Thus, it isexpected that the Si+25 prolate isomer dissociates predom-inantly with the loss of neutral Si10, whereas the sphericalisomer hardly produces the Si10-loss photofragment.

Prior to apply the isomer-resolved PD of Si+m, the iso-mer ions were separated under the cell condition thatthe drift electric field of 13.4 V cm−1, cell temperatureof 180 K, and He pressure of 0.5 Torr for m = 25 and0.3 Torr for m = 24, 26, and 27. The field to number den-sity ratio, E/N , amounted to 50 Td for m = 25 and 84 Tdfor other sizes. Although our experimental condition wasinsufficient to completely separate the isomers as shown inFigures 3c–3f, the He pressure was kept low to suppressthe decreasing of ion intensity for the following PD ex-periments. The obtained ATDs showed two distributionscorresponding to the prolate and spherical isomers in thissize range, which was almost consistent with the previousreport [35] except for the relative intensity of each isomer;prolate isomers had less intensity compared with spheri-cal ones under our condition, whereas the prolates wereproduced with a comparable intensity with the spheres ina previous study [35].

Photodissociation mass spectra were measured with aphotolysis energy of 4.66 eV for the two separated isomers

Fig. 4. Bar graph of the branching fractions of observed frag-ment ions, Si+6 –Si+11 and Si10-loss fragment ions from each iso-mers of Si+m, m = 24–27. Error bars for Si+25 and Si+26 wereestimated from the standard deviation of the results of threeindependent measurements, and thus these error bars do notinclude the effect of isomer-separation incompleteness.

of Si+25, prolate and spherical, as shown in Figure 3. As aresult, the mass distributions of fragment ions from bothisomers were found to be similar: Si+6 –Si+11 and Si+15 frag-ment ions were observed. The obtained distributions wereconsistent with the previously reported one which wasmeasured without isomer separation [33]. It is well knownfrom theoretical calculation that the Si+m fragments withm = 6, 7, 10, and 11 have higher stability than others [38],while the Si+15 fragment corresponds to loss of stable neu-tral Si10. As observed in the Si+25 PD, the photofragmention distributions from prolate and spherical isomers ofSi+m, m = 24, 26, and 27, showed no significant differ-ence each other. In addition, the fragment ion distribu-tions were also independent of photon energy for PD. Thedistributions obtained by the 3rd harmonic of a Nd:YAGlaser showed similar distributions obtained by the 4th har-monic.

In order to focus on the Si10-loss process from eachisomer, the branching ratios of Si10-loss and Si+6 –Si+11 ob-tained from each size and isomer were plotted in Figure 4as a bar graph. The smaller sized clusters such as Si+24and Si+25 dissociated into Si+m−10 with higher branchingratio than the larger sized ones, Si+26 and Si+27. This size de-pendence agrees with the trends observed in the previousreports [33,34]. However, it was found that these branch-ing ratios were little dependent on the Si+m isomer, al-though all of the prolate isomers produced slightly higheramount of Si10-loss fragments. The little difference in PDof Si+m shows that the two different isomers have similarPD pathways.

One plausible explanation for the observation of theirsimilar PD pathways is isomerization of Si+m before frag-mentation. It is difficult to distinguish whether Si+m dis-sociated via electronically or vibrationally excited state.However, it is expected that the cluster ion dissociatesafter multiphoton absorption and following relaxation byinternal conversion, as was already expected for the pho-todissociation of C+

n , from the fact that the fragment iondistribution is almost independent of the photolysis energyand also it is similar to that observed by CID of Si+m [34].

Eur. Phys. J. D (2013) 67: 13 Page 5 of 5

Hence, we observed dissociations of Si+m from vibrationallyexcited states in the ground electronic state. The activa-tion energy for the isomerization of vibrationally excitedSi+m was experimentally [39,40] and theoretically [41,42]estimated to be 0.8–1.5 eV. Dissociation energy was alsodetermined to be from 2 to 4 eV up to Si+70 [29]. Becausethe isomerization energy is lower than the dissociation en-ergy [39], we have probably observed similar fragment-iondistributions from prolate and spherical Si+m isomers. Itwas concluded that such a low activation energy of Si+m cancause a significant difference with the isomer-dependentresults obtained for C+

n .

4 Conclusions

We have applied isomer-resolved multiphoton dissocia-tions (PDs) with 4.66 eV to carbon and silicon clustercations, C+

n (n = 32–38) and Si+m (m = 24–27), in order toinvestigate correlations between the isomer structures anddissociation reactions. We have found that photofragment-ion distributions obtained from PDs of C+

n depended onthe structure of parent isomers; fullerene isomers mainlydissociated by C2-loss, while cyclic isomers dissociatedby C3-loss and into other small fragment ions includingC14-loss process. On the other hand, PDs of Si+m showedisomer-independent photofragment-ion distributions. Thelittle difference in PD of Si+m shows that the two differ-ent isomers have similar photodissociation pathways. Itmay be ascribed to the lower isomerization energy for Si+mthan dissociation energy. Such a low activation energyof Si+m can cause a significant difference with the isomer-dependent results obtained for C+

n .

This work was supported by Yamada Science Foundation,Sumitomo Foundation, and in part by a Grant-in-Aid for Scien-tific Research from the Japan Society for the Promotion of Sci-ence (JSPS). The authors are grateful to Mr. Naoya Norimasafor his assistance of the measurement.

References

1. M.T. Bowers, P.R. Kemper, G. von Helden, P.A.M. VanKoppen, Science 260, 1446 (1993)

2. G.A. Eiceman, Z. Karpas, Ion Mobility Spectrometry(CRC Press, Boca Raton, 2005)

3. E. Oger, R. Kelting, P. Weis, A. Lechtken, D. Schooss,N.R.M. Crawford, R. Ahlrichs, M.M. Kappes, J. Chem.Phys. 130, 124305 (2009)

4. C.S. Creaser, J.R. Griffiths, C.J. Bramwell, S. Noreen,C.A. Hill, C.L.P. Thomas, Analyst 129, 984 (2004)

5. H.E. Revercomb, E.A. Mason, Anal. Chem. 47, 970 (1975)6. G. von Helden, M.-T. Hsu, N. Gotts, M.T. Bowers, J. Phys.

Chem. 97, 8182 (1993)7. G. von Helden, M.-T. Hsu, P.R. Kemper, M.T. Bowers, J.

Chem. Phys. 95, 3835 (1991)8. R.R. Hudgins, M. Imai, M.F. Jarrold, P. Dugourd, J.

Chem. Phys. 111, 7865 (1999)9. S.C. O’Brien, J.R. Heath, R.F. Curl, R.E. Smalley, J.

Chem. Phys. 88, 220 (1988)

10. H. Hohmann, C. Callegari, S. Furrer, D. Grosenick, E.E.B.Campbell, I.V. Hertel, Phys. Rev. Lett. 73, 1919 (1994)

11. M.E. Geusic, M.F. Jarrold, T.J. Mcllrath, R.R. Freeman,W.L. Brown, J. Chem. Phys. 86, 3862 (1987)

12. R. Bouyer, F. Roussel, P. Monchicourt, M. Perdrix, P.Pradel, J. Chem. Phys. 100, 8912 (1994)

13. R. Bouyer, P. Monchicourt, M. Perdrix, P. Pradel, F.Roussel, J. Phys. B: At. Mol. Opt. Phys. 30, 135 (1997)

14. P.P. Radi, T.L. Bunn, P.R. Kemper, M.E. Molchan, M.T.Bowers, J. Chem. Phys. 88, 2809 (1988)

15. L.A. Bloomfield, R.R. Freeman, W.L. Brown, Phys. Rev.Lett. 54, 2246 (1985)

16. Q.-L. Zhang, Y. Liu, R.F. Curl, F.K. Tittel, R.E. Smalley,J. Chem. Phys. 88, 1670 (1988)

17. M.F. Jarrold, J.E. Bower, J. Phys. Chem. 92, 5702 (1988)18. R. Fromherz, G. Gantefor, A.A. Shvartsburg, Phys. Rev.

Lett. 89, 083001 (2002)19. M. Vonderach, O.T. Ehrler, K. Matheis, P. Weis, M.M.

Kappes, J. Am. Chem. Soc. 134, 7830 (2012)20. K. Koyasu, T. Ohtaki, N. Hori, F. Misaizu, Chem. Phys.

Lett. 523, 54 (2012)21. F. Misaizu, N. Hori, H. Tanaka, K. Komatsu, A. Furuya,

K. Ohno, Eur. Phys. J. D 52, 59 (2009)22. K. Koyasu, T. Ohtaki, F. Misaizu, Bull. Chem. Soc. Jpn

84, 1342 (2011)23. M.A. Seeterlin, P.R. Vlasak, D.J. Beussman, R.D.

McLane, C.G. Enke, J. Am. Soc. Mass Spectrom. 4, 751(1993)

24. D.J. Beussman, P.R. Vlasak, R.D. McLane, M.A.Seeterlin, C.G. Enke, Anal. Chem. 67, 3952 (1995)

25. A.E. Giannakopulos, B. Thomas, A.W. Colburn, D.J.Reynolds, E.N. Raptakis, A.A. Makarov, P.J. Derrick, Rev.Sci. Instrum. 73, 2115 (2002)

26. P. Weis, S. Gilb, P. Gerhardt, M.M. Kappes, Int. J. MassSpectrom. 216, 59 (2002)

27. M.F. Mesleh, J.M. Hunter, A.A. Shvartsburg, G.C. Schatz,M.F. Jarrold, J. Phys. Chem. 100, 16082 (1996)

28. T. Wyttenbach, G. von Helden, J.J. Batka Jr., D. Carlat,M.T. Bowers, J. Am. Soc. Mass Spectrom. 8, 275 (1997)

29. G. von Helden, N.G. Gotts, M.T. Bowers, J. Am. Chem.Soc. 115, 4363 (1993)

30. J.M. Hunter, J.L. Fye, M.F. Jarrold, J. Chem. Phys. 99,1785 (1993)

31. J.M. Hunter, J.L. Fye, E.J. Roskamp, M.F. Jarrold, J.Phys. Chem. 98, 1810 (1994)

32. R. Bouyer, F. Roussel, P. Monchicourt, M. Perdrix, P.Pradel, J. Chem. Phys. 100, 8912 (1994)

33. Q.-L. Zhang, Y. Liu, R.F. Curl, F.K. Tittel, R.E. Smalley,J. Chem. Phys. 88, 1670 (1988)

34. M.F. Jarrold, J.E. Bower, J. Phys. Chem. 92, 5702 (1988)35. R.R. Hudgins, M. Imai, M.F. Jarrold, P. Dugourd, J.

Chem. Phys. 111, 7865 (1999)36. S. Yoo, X.C. Zeng, J. Chem. Phys. 124, 054304 (2006)37. W. Qin, W.-C. Lu, L.-Z. Zhao, Q.-J. Zang, C.Z. Wang,

K.M. Ho, J. Phys.: Condens. Matter 21, 455501 (2009)38. K. Raghavachari, C.M. Rohlfing, J. Chem. Phys. 89, 2219

(1988)39. M.F. Jarrold, E.C. Honea, J. Am. Chem. Soc. 114, 459

(1992)40. M. Rosemeyer, J.A. Becker, R. Schafer, Z. Phys. Chem.

216, 857 (2002)41. L. Mitas, J.C. Grossman, I. Stich, J. Tobik, Phys. Rev.

Lett. 84, 1479 (2000)42. L. Tsetseris, G. Hadjisavvas, S.T. Pantelides, Phys. Rev.

B 76, 045330 (2007)