FULLERENIC SYSTEMS FOR NANOSCIENCE:
COMPUTATIONAL SCREENING ILLUSTRATED ON X@C74 METALLOFULLERENES
ZdenÏk Slanina,[asteriskmath],a Filip Uhl´ ,b Shyi-Long Lee,c Ludwik Adamowiczd and Shigeru Nagasea
aDepartment of Theoretical Molecular Science, Institute for Molecular Science, Okazaki 444-8585, Japan
bSchool of Science, Charles University, 128 43 Prague 2, Czech Republic
cDepartment of Chemistry and Biochemistry, National Chung-Cheng University, Chia-Yi 62117, Taiwan
dDepartment of Chemistry, University of Arizona, Tucson, AZ 85721-0041, USA
ABSTRACT
The objects of fullerene science - fullerenes, metallo-
fullerenes & other fullerene endohedrals, and nan-
otubes - are discussed in a wider context of nanoscience
and nanotechnology applications for molecular memo-
ries and quantum computing. The emerging concepts
are illustrated on C74-based endohedrals, especially
Ca@C74, Ba@C74, and Yb@C74. A set of six C74 cages
is considered, namely one cage with isolated pentagons,
three isomers with a pentagon-pentagon junction, two
structures with one pentagon-pentagon pair and one
heptagon. Special interest is paid to the enthalpy-
entropy evaluations for estimations of the relative as
well as absolute populations.
1. INTRODUCTION
Although empty C74 fullerene [1] is not yet available
in solid form, several related endohedral species have
been known like Ca@C74 [2,3], Sr@C74 [4], Ba@C74 [5],
La@C74 [6-8], Eu@C74 [9], Yb@C74 [10], Sc2@C74 [11]
or Er3@C74 [12]. In the Yb@C74 case, two isomers were
in fact isolated [10]. This isomerism finding is particu-
larly interesting as there is just one [13] C74 cage that
obeys the isolated pentagon rule (IPR), namely of D3h
symmetry. The cage was experimentally confirmed in
Ca@C74 [2], Ba@C74 [4] and La@C74 [8]. Obviously,
with Yb@C74 a non-IPR cage should be involved as it
is the case of Ca@C72 [14] (empty C72 could also not
be isolated yet, possibly owing to solubility problems
[2,15-17]).
The metallofullerene family is naturally of com-
putational interest. First such computations were per-
formed for Ca@C74 with considerations of selected
non-IPR cages [2,16,18,19]. However, the non-IPR en-
capsulations are not significant with Ca@C74, in con-
trast to Ca@C72 [20,21]. The present paper surveys
the computations also for the Ba@C74 and Yb@C74
species. In order to respect high temperatures in
fullerene/metallofullerene preparations, the Gibbs en-
ergies are to be used [22,23] in relative stability consid-
erations rather than the mere potential energy terms.
2. COMPUTATIONS
The computations treat a set of six metallofullerene
isomers, using the carbon cages investigated with
Ca@C74, namely the three structures selected from di-
anion energetics [2,18], and three additional cages with
non-negligible populations as empty C74 cages [24,25].
In the computations [18,19,24] the cages have been la-
beled by some code numbers that are also used here,
combined with the symmetry of the complexes: 1/C2v,
4/C1, 52/C2, 103/C1, 368/C1, and 463/C1. The 1/C2v
endohedral is the species derived from the unique C74
IPR structure. The previously considered [16] two non-
IPR C74 cages are now labeled by 4/C1 and 103/C1.
A pair of connected pentagons is also present in the
52/C2 structure. The remaining two species, 368/C1
and 463/C1, contain a pentagon/pentagon pair and
one heptagon.
The present geometry optimizations were primar-
ily carried out using density-functional theory (DFT),
namely employing Becke’s three parameter functional
[26] with the non-local Lee-Yang-Parr correlation func-
tional [27] (B3LYP) in a combined basis set. In the
case of Ba@C74, the combined basis set consists of
the 3-21G basis for C atoms and a dz basis set [28]
with the effective core potential (ECP) on Ba (de-
noted here by 3-21Gsimilardz) while with Yb@C74 (where
the dz-type basis set [28] is not available for Yb) the
3-21G basis on C atoms is combined with the CEP-
4G basis set [29,30] employing the compact effective
(pseudo)potential (CEP) for Yb (denoted here by 3-
21GsimilarCEP-4G). The B3LYP/3-21Gsimilardz or B3LYP/3-
21GsimilarCEP-4G geometry optimizations were carried
out with the analytically constructed energy gradient.
The reported computations were performed with the
Gaussian 03 program package [31].
In the optimized B3LYP/3-21Gsimilardz or B3LYP/3-
21GsimilarCEP-4G geometries, the harmonic vibrational
analysis was carried out with the analytical force-
constant matrix. In the same optimized geometries,
higher-level single-point energy calculations were also
performed, using the standard 6-31G* basis set for C
atoms, i.e., the B3LYP/6-31Gasteriskmathsimilardz single-point treat-
ment for Ba@C74 and the B3LYP/6-31G*similarCEP-4G
level with Yb@C74. Moreover, in the latter case the
SDD (Stuttgart/Dresden) basis set [32,33] was also
employed (with the SDD ECP for Yb) for the single-
point calculations, and for the carbon atoms the SDD,
6-31G*, or 6-311G* basis set was stepwise used. In
addition, for the three lowest isomers, the geometry
optimizations were also carried out at the B3LYP/6-
31G*similarSDD level. The electronic excitation ener-
gies were evaluated by means of time-dependent (TD)
DFT response theory [34] at the B3LYP/3-21Gsimilardz or
B3LYP/3-21GsimilarCEP-4G level.
Relative concentrations (mole fractions) xi of m
isomers can be evaluated [35] through their partition
functions qi and the enthalpies at the absolute zero
temperature or ground-state energies deltaHo0,i (i.e., the
relative potential energies corrected for the vibrational
zero-point energies) by a compact formula:
xi = qiexp[-deltaH
o0,i/(RT)]
summationtextm
j=1 qjexp[-deltaH
o0,j/(RT)] , (1)
where R is the gas constant and T the absolute temper-
ature. Eq. (1) is an exact formula that can be directly
derived [35] from the standard Gibbs energies of the
isomers, supposing the conditions of the inter-isomeric
thermodynamic equilibrium. Rotational-vibrational
partition functions were constructed from the calcu-
lated structural and vibrational data using the rigid
rotator and harmonic oscillator (RRHO) approxima-
tion. No frequency scaling is applied as it is not signif-
icant [36] for the xi values at high temperatures. The
geometrical symmetries of the optimized cages were
determined not only by the Gaussian built-in proce-
dure [31], but primarily by a procedure [37] which
considers precision of the computed coordinates. The
electronic partition function was constructed by direct
summation of the TD B3LYP/3-21Gsimilardz or B3LYP/3-
21GsimilarCEP-4G electronic excitation energies. Finally,
the chirality contribution was included accordingly [38]
(for an enantiomeric pair its partition function qi is
doubled).
In addition to the conventional RRHO treatment
with eq. (1), also a modified approach to description of
the encapsulate motions can be considered [39], follow-
ing findings [14,16,40] that the encapsulated atoms can
exercise large amplitude motions, especially so at ele-
vated temperatures (unless the motions are restricted
by cage derivatizations [41]). One can expect that if
the encapsulate is relatively free then, at sufficiently
high temperatures, its behavior in different cages will
bring about the same contribution to the partition
functions. However, such uniform contributions would
then cancel out in eq. (1). This simplification is called
[39] free, fluctuating, or floating encapsulate model
(FEM) and requires two steps. In addition to removal
of the three lowest vibrational frequencies (belonging
to the metal motions in the cage), the symmetries of
the cages should be treated as the highest (topologi-
cally) possible, which reflects averaging effects of the
large amplitude motions. There are several systems
[39,42] where the FEM approach improves agreement
with experiment.
As for the temperature intervals to be considered,
it is true that the temperature region where fullerene
or metallofullerene electric-arc synthesis takes place is
not yet known, however, the new observations [43] sup-
ply some arguments to expect it around 1500 K. Very
low excited electronic states can be present in some
fullerenes like C80 [44] or even the C74 IPR cage [45]
which makes the electronic partition function partic-
ularly significant at such high temperatures. Inter-
estingly enough, there is a suggestion [25] that the
electronic partition function, based on the singlet elec-
tronic states only, could actually produce more re-
alistic results for fullerene relative concentrations in
the fullerenic soot. Incidentally, the electronic excita-
tion energies can in some cases (like empty fullerenes)
be evaluated by means of a simpler ZINDO method
[46,47].
Yb@C74 103/C1 Yb@C74 4/C1
Yb@C74 1/C2v Ba@C74 1/C2v
Fig. 1. B3LYP/3-21GsimilarCEP-4G optimized structures
of three Yb@C74 isomers and B3LYP/3-21Gsimilardz struc-
ture of the lowest Ba@C74 species.
3. RESULTS AND DISCUSSION
Let us first survey, for a more complete picture, the
empty C74 cages (B3LYP/6-31G*//B3LYP/3-21G en-
ergetics, ZINDO electronic partition functions). The
relative populations computed according to eq. (1)
show that the sole IPR cage (D3h) is prevailing. Shi-
nohara et al. [48] recently recorded electronic spectrum
of C74 anion and concluded that the cage could have
D3h symmetry. Moreover, it was observed by Achiba
et al. [3] that the only available IPR C74 cage is actu-
ally employed also in the Ca@C74 endohedral species.
At a temperature of 1500 K, the 1/C2v (related to the
C74 IPR species), 4/C1, and 103/C1 Ca@C74 isomeric
populations are computed [19] in the FEM scheme as
88.4, 8.0, 3.5 % , respectively.
Ba@C74 relative stability proportions differ from
those previously computed [19] for Ca@C74. For exam-
ple, at a temperature of 1500 K the 1/C2v, 4/C1, and
103/C1 species when evaluated with the conventional
RRHO treatment should form 99.5, 0.3, 0.2 % of the
equilibrium isomeric mixture, respectively. With the
more realistic FEM scheme, the relative concentration
are changed to 97.8, 1.2 and 1.0 % . The proportions
are in agreement with the observation of Reich et al. [5]
in which just one Ba@C74 species was isolated, namely
possessing the IPR carbon cage.
Yb@C74 is actually a more interesting system as
Xu et al. [10] isolated two isomers and even found
their production ratio as 100:3. In the computations
at the B3LYP/6-31G*similarSDD level the 1/C2v species
(see Fig. 1) is after about 13.14 kcal/mol followed by
the 4/C1 isomer, the 103/C1 structure is about 16.98
kcal/mol above the lowest isomer while the other en-
dohedrals are located more than 30 kcal/mol higher.
The still higher B3LYP/6-311G*similarSDD approach gives
about the some energetics as the the 4/C1 isomer is
placed 13.30 kcal/mol and the 103/C1 structure 16.99
kcal/mol above the 1/C2v species.
0
20
40
60
80
100
500 1000 1500 2000 2500 3000 3500 4000 4500
x (%)
T (K)
1/C2v
103/C1
4/C1
i
368/C1
463/C1
52/C2
103/C1
4/C1
1/C2v
Fig. 2. Relative concentrations of the Yb@C74 iso-
mers computed with the B3LYP/6-311G*similarSDD en-
ergetics, B3LYP/3-21GsimilarCEP-4G entropy, and FEM
treatment.
Fig. 2 converts the computed Yb@C74 energy
and entropy parts into the relative concentrations. In
order to reproduce the observed [10] production iso-
meric ratio (100:3) within the conventional RRHO ap-
proach, temperature should reach about 1850 K when
the 1/C2v, 4/C1, and 103/C1 species compose 95.7,
2.8, and 1.5 % of the equilibrium isomeric mixture,
respectively. The FEM treatment reduces the temper-
ature for the reproduction of the observed ratio [10] to
about 1200 K with 96.1, 3.2, and 0.7 % for the 1/C2v,
4/C1, and 103/C1 isomer, respectively. It should be
however realized that the observed relative populations
are just roughly estimated from chromatography peak
areas. The ratios at 1500 K would be changed to 88.4,
8.8, 2.8 % in the FEM treatment. Thus, the com-
putations support the experimental finding [10] of two
Yb@C74 isomers and point out that the major species
should have the IPR cage while the minor one should
contain one pentagon-pentagon junction in the carbon
cage. A similar situation should be met with Ca@C74
but rather not with Ba@C74.
There is a more general stability problem [49-52]
related to fullerenes and metallofullerenes, viz. the ab-
solute stability of the species or the relative stabilities
of clusters with different stoichiometries. We shall il-
lustrate the issue just on the most stable (i.e., 1/C2v)
structures of Ba@C74 and Yb@C74, thus ignoring the
remaining five isomers in each set. Let us consider for-
mation of a metallofullerene:
X(g) + Cn(g) = X@Cn(g). (2)
Under equilibrium conditions, we shall deal with the
encapsulation equilibrium constant KX@Cn,p:
KX@Cn,p = pX@Cnp
XpCn
, (3)
expressed in the terms of partial pressures of the com-
ponents. Temperature dependency of the encapsula-
tion equilibrium constant KX@Cn,p is described by the
van’t Hoff equation:
dlnKX@Cn,p
dT =
deltaHoX@Cn
RT2 (4)
where deltaHoX@Cn stands for the (negative) standard
change of enthalpy upon encapsulation. Let us fur-
ther suppose that the metal pressure is close to the
respective saturated pressure pX,sat. With this pre-
sumption, we shall deal with a special case of clus-
tering under saturation conditions [53,54]. While the
saturated pressures pX,sat for various metals are known
from observations [55,56], the partial pressure of Cn is
less clear as it is obviously influenced by a larger set of
processes (though, pCn should exhibit a temperature
maximum and then vanish). Therefore, we avoid the
latter pressure in our considerations at this stage. The
computed equilibrium constants KX@Cn,p show a tem-
perature decrease as it must be the case with respect
to the van’t Hoff equation (4) for the negative encapsu-
lation enthalpy. However, if we consider the combined
pX,satKX@Cn,p term:
pX@Cn similar pX,satKX@Cn,p, (5)
that directly controls the partial pressures of various
X@Cn encapsulates in an endohedral series (based on
one common Cn fullerene), we get a different pic-
ture. The considered pX,satKX@Cn,p term typically in-
creases with temperature which is the basic scenario of
the metallofullerene formation in the electric-arc tech-
nique. An optimal production temperature could be
evaluated in a more complex model that also includes
temperature development of the empty fullerene par-
tial pressure.
Table 1. The computeda products of the encapsulation
equilibrium constantb XiX = KX@C74,p with the metal
saturated-vapor pressure PsiX = pX,sat for Ba@C74 and
Yb@C74 at a temperature T = 1500 K
Species KX@C74,p pX,sat PsiXXiX PsiXXiXPsiBaXiBa
(atm-1) (atm)
Ba@C74 1332.6 0.0261 34.82 1.00
Yb@C74 81.77 1.42 116.13 3.34
a Ba@C74: the potential-energy change evaluated at
the B3LYP/6-31Gasteriskmathsimilardz level and the entropy part at
the B3LYP/3-21Gsimilardz level; Yb@C74: the potential-
energy change evaluated at the B3LYP/6-31GasteriskmathsimilarSDD
level and the entropy part at the B3LYP/3-21GsimilarCEP-
4G level.
b The standard state - ideal gas phase at 101325 Pa
pressure.
If we however want to evaluate production abun-
dances for two metallofullerenes like Ba@C74 and
Yb@C74, just the product pX,satKX@C74,p term can
straightforwardly be used. Let us consider a temper-
ature of 1500 K as the observations [43] suggest that
fullerene synthesis should happen in the temperature
region. The results in Table 1 show for 1500 K that the
pBa,satKBa@C74,p quotient is about three times smaller
than the pY b,satKY b@C74,p product term. The ratio
is enabled by a higher saturated pressure of Yb com-
pared to Ba though the equilibrium constants show
the reversed order. The B3LYP/6-31Gasteriskmathsimilardz potential-
energy change upon Ba encapsulation into the IPR
C74 cage is deltaE=-59.5 kcal/mol while the B3LYP/6-
31GasteriskmathsimilarSDD term for Yb encapsulation is computed at
-55.9 kcal/mol. Although the energy terms are likely
still not precise enough, their errors could be compara-
ble and thus they should cancel out in the relative term
pX,satKX@C74,p
pBa,satKBa@C74,p . Let us mention that the combined ba-
sis sets require in the Gaussian program specification
through a GEN keyword and for the sake of consistency
the GEN approach is to be used even with empty cages
(for example, the GEN-consistent approach gives for
the B3LYP/6-31Gasteriskmathsimilardz La@C60 encapsulation energy
[57] the value -54.7 kcal/mol). Let us also note that
the FEM treatment is not used in a full extent with
the product quotient pX,satKX@C74,p evaluation as the
three lowest vibrational frequencies are not removed in
contrast to the isomeric treatment by eq. (1), and also
the electronic partition functions were ignored in the
quotient evaluations. Finally, this new stability crite-
rion also suggests (as Yb@C74 should come in higher
yields than Ba@C74) that the conditions for the iso-
lation of a minor isomer are more convenient in the
Yb@C74 case (in addition to the computed higher frac-
tion of the non-IPR species in the case of Yb encapsu-
lation compared to Ba [58]).
Various endohedral cage compounds have been
suggested as possible candidate species for molecular
memories and other future nanotechnological applica-
tions. One approach is built on endohedral species
with two possible location sites of the encapsulated
atom [59], while another concept of quantum comput-
ing aims at a usage of the spin states of N@C60 [60],
and still another would employ fullerene-based molec-
ular transistors [61]. In the connection, low potential
barriers for a three-dimensional rotational motion of
encapsulates in the cages [14,16,40,62-64] or at least
large amplitude oscillations [65,66] can be a significant
factor. The low barriers are responsible for simplifica-
tions of the NMR patterns at room temperature. This
simplification is made possible by a fast, isotropic en-
dohedral motions inside the cages that yield a time-
averaged, equalizing environment [59,60] on the NMR
timescale. The internal motion can however be re-
stricted by a cage derivatization [41,67] thus in prin-
ciple allowing for a versatile control of the endohedral
positions needed, for example, in molecular memory
applications. In overall, a still deeper experimental and
computational knowledge of various molecular aspects
of the endohedral compounds is at present needed be-
fore tailoring of their nanoscience to future nanotech-
nology applications becomes possible.
ACKNOWLEDGMENTS
The reported research has been supported by a Grant-
in-aid for NAREGI Nanoscience Project, for Scientific
Research on Priority Area (A), and for the Next Gen-
eration Super Computing Project, Nanoscience Pro-
gram, MEXT, Japan, by the National Science Coun-
cil, Taiwan-ROC, and by the Czech National Re-
search Program ’Information Society’ (Czech Acad.
Sci. 1ET401110505).
REFERENCES
[asteriskmath] Corresponding author: zdenek@ims.ac.jp
[1] M. Buhl and A. Hirsch, ”Spherical aromaticity of fullerenes,”
Chem. Rev., 101, 1153 (2001).
[2] T. S. M. Wan, H. W. Zhang, T. Nakane, Z. D. Xu,
M. Inakuma, H. Shinohara, K. Kobayashi, and S. Nagase,
”Production, isolation, and electronic properties of missing
fullerenes: Ca@C72 and Ca@C74,” J. Am. Chem. Soc., 120,
6806 (1998).
[3] T. Kodama, R. Fujii, Y. Miyake, S. Suzuki, H. Nishikawa,
I. Ikemoto, K. Kikuchi, and Y. Achiba, ”C-13 NMR study
of Ca@C74: the cage structure and the site-hopping motion
of a Ca atom inside the cage,” Chem. Phys. Lett., 399, 94
(2004).
[4] O. Haufe, M. Hecht, A. Grupp, M. Mehring, and M. Jansen,
”Isolation and spectroscopic characterization of new endo-
hedral fullerenes in the size gap of C74 to C76,” Z. Anorg.
Allgem. Chem., 631, 126 (2005).
[5] A. Reich, M. Panthofer, H. Modrow, U. Wedig, and M.
Jansen, ”The structure of Ba@C74,” J. Am. Chem. Soc.,
126, 14428 (2004).
[6] Y. Chai, T. Guo, C. Jin, R. E. Haufler, L. P. F. Chibante, J.
Fure, L. Wang, J. M. Alford, and R. E. Smalley, ”Fullerenes
with metals inside,” J. Phys. Chem., 95, 7564 (1991).
[7] K. Sueki, K. Akiyama, T. Yamauchi, W. Sato, K. Kikuchi,
S. Suzuki, M. Katada, Y. Achiba, H. Nakahara, T. Akasaka,
and K. Tomura, ”New lanthanoid metallofullerenes and their
HPLC elution behavior,” Full. Sci. Technol., 5, 1435 (1997).
[8] H. Nikawa, T. Kikuchi, T. Wakahara, T. Nakahodo, T.
Tsuchiya, G. M. A. Rahman, T. Akasaka, Y. Maeda, K. Yoza,
E. Horn, K. Yamamoto, N. Mizorogi, and S. Nagase, ”Miss-
ing metallofullerene La@C74,” J. Am. Chem. Soc., 127, 9684
(2005).
[9] H. Matsuoka, N. Ozawa, T. Kodama, H. Nishikawa, I. Ike-
moto, K. Kikuchi, K. Furukawa, K. Sato, D. Shiomi, T.
Takui, and T. Kato, ”Multifrequency EPR study of metallo-
fullerenes: Eu@C-82 and Eu@C74,” J. Phys. Chem. B, 108,
13972 (2004).
[10] J. X. Xu, X. Lu, X. H. Zhou, X. R. He, Z. J. Shi, and Z.
N. Gu, ”Synthesis, isolation, and spectroscopic character-
ization of ytterbium-containing metallofullerenes,” Chem.
Mater., 16, 2959 (2004).
[11] S. Stevenson, H. C. Dorn, P. Burbank, K. Harich, J.
Haynes, C. H. Kiang, J. R. Salem, M. S. Devries, P. H.
M. Vanloosdrecht, R. D. Johnson, C. S. Yannoni, and D. S.
Bethune, ”Automated HPLC separation of endohedral met-
allofullerene Sc@C2n and Y@C2n fractions,” Anal. Chem.,
66, 2675 (1994).
[12] N. Tagmatarchis, E. Aslanis, K. Prassides, and H. Shi-
nohara, ”Mono-, di- and trierbium endohedral metallo-
fullerenes: Production, separation, isolation, and spectro-
scopic study,” Chem. Mater., 13, 2374 (2001).
[13] P. W. Fowler and D. E. Manolopoulos, An Atlas of
Fullerenes, Clarendon Press, Oxford, 1995.
[14] T. Ichikawa, T. Kodama, S. Suzuki, R. Fujii, H. Nishikawa,
I. Ikemoto, K. Kikuchi, and Y. Achiba, ”Isolation and char-
acterization of a new isomer of Ca@C72,” Chem. Lett., 33,
1008 (2004).
[15] M. D. Diener and J. M. Alford, ”Isolation and properties of
small-bandgap fullerenes,” Nature, 393, 668 (1998).
[16] K. Kobayashi and S. Nagase, ”Structures and electronic
properties of endohedral metallofullerenes; Theory and ex-
periment,” in Endofullerenes - A New Family of Carbon
Clusters, T. Akasaka, S. Nagase, eds. Kluwer Academic
Publishers, Dordrecht, 2002, p. 99.
[17] H. Kato, A. Taninaka, T. Sugai, and H. Shinohara, ”Struc-
ture of a missing-caged metallofullerene: La2@C72,” J.
Am. Chem. Soc., 125, 7782 (2003).
[18] S. Nagase, K. Kobayashi, and T. Akasaka, ”Unconventional
cage structures of endohedral metallofullerenes,” J. Mol.
Struct. (Theochem), 462, 97 (1999).
[19] Z. Slanina, K. Kobayashi, and S. Nagase, ”Ca@C74 isomers:
Relative concentrations at Higher Temperatures,” Chem.
Phys., 301, 153 (2004).
[20] K. Kobayashi, S. Nagase, M. Yoshida, and E. ¯sawa, ”En-
dohedral metallofullerenes. Are the isolated pentagon rule
and fullerene structures always satisfied?,” J. Am. Chem.
Soc., 119, 12693 (1997).
[21] Z. Slanina, K. Kobayashi, and S. Nagase, ”Ca@C72 IPR and
non-IPR structures: Computed temperature development
of their relative concentrations,” Chem. Phys. Lett., 372,
810 (2003).
[22] Z. Slanina, F. Uhlõk, X. Zhao, and E. ¯sawa, ”Enthalpy-
entropy interplay for C36 cages: B3LYP/6-31Gasteriskmath calcula-
tions,” J. Chem. Phys., 113, 4933 (2000).
[23] Z. Slanina, K. Kobayashi and S. Nagase, ”Computed tem-
perature development of the relative stabilities of La@C82
isomers,” Chem. Phys. Lett., 388, 74 (2004).
[24] X. Zhao, K. H. Lee, Z. Slanina, and E. ¯sawa, ”Evaluation of
the relative stabilities of the IPR and non-IPR structures of
C84,” in Recent Advances in the Chemistry and Physics of
Fullerenes and Related Materials, Vol. 7, P. V. Kamat, D.
M. Guldi, K. M. Kadish, eds. The Electrochemical Society,
Pennington, 1999, p. 711.
[25] Z. Slanina, F. Uhlõk, S.-L. Lee, L. Adamowicz, and S. Na-
gase, ”Enhancement of fullerene stabilities from excited
electronic states,” Comput. Lett., 1, 313 (2005).
[26] A. D. Becke, ”Density-functional thermochemistry. III. The
role of exact exchange,” J. Chem. Phys., 98, 5648 (1993).
[27] C. Lee, W. Yang, and R. G. Parr, ”Development of the
Colle-Salvetti correlation-energy formula into a functional
of the electron density,” Phys. Rev. B, 37, 785 (1988).
[28] P. J. Hay and W. R. Wadt, ”Ab initio effective core po-
tentials for molecular calculations. Potentials for K to Au
including the outermost core orbitals,” J. Chem. Phys., 82,
299 (1985).
[29] W. Stevens, H. Basch, and J. Krauss, ”Compact effective
potentials and efficient shared-exponent basis sets for the
first- and second-row atoms,” J. Chem. Phys., 81, 6026
(1984).
[30] T. R. Cundari and W. J. Stevens, ”Effective core potential
methods for the lanthanides,” J. Chem. Phys., 98, 5555
(1993).
[31] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuse-
ria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr.,
T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S.
S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi,
G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M.
Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M.
Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M.
Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross,
C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann,
O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W.
Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Sal-
vador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich,
A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A.
D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz,
Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Ste-
fanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L.
Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng,
A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. John-
son, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople,
Gaussian 03, Revision C.01, Gaussian, Inc., Wallingford,
CT, 2004.
[32] L. v. Szentpaly, P. Fuentealba, H. Preuss, and H. Stoll,
”Pseudopotential calculations on Rb+2 , Cs+2 , RbH+, CsH+
and the mixed alkali dimer ions,” Chem. Phys. Lett., 93,
555 (1982).
[33] X. Y. Cao and M. Dolg, ”Segmented contraction scheme for
small-core lanthanide pseudopotential basis sets,” J. Mol.
Struct. (Theochem), 581, 139 (2002).
[34] M. E. Casida, C. Jamorski, K. C. Casida, and D. R. Salahub,
”Molecular excitation energies to high-lying bound states
from time-dependent density-functional response theory:
Characterization and correction of the time-dependent lo-
cal density approximation ionization threshold,” J. Chem.
Phys., 108, 4439 (1998).
[35] Z. Slanina, ”Equilibrium isomeric mixtures: Potential en-
ergy hypersurfaces as originators of the description of the
overall thermodynamics and kinetics,” Int. Rev. Phys.
Chem., 6, 251 (1987).
[36] Z. Slanina, F. Uhlõk, and M. C. Zerner, ”C5H+3 isomeric
structures: Relative stabilities at high temperatures,” Rev.
Roum. Chim., 36, 965 (1991).
[37] M.-L. Sun, Z. Slanina, S.-L. Lee, F. Uhlõk, and L. Adamow-
icz, ”AM1 computations on seven isolated-pentagon-rule
isomers of C80,” Chem. Phys. Lett., 246, 66 (1995).
[38] Z. Slanina and L. Adamowicz, ”On relative stabilities of
dodecahedron-shaped and bowl-shaped structures of C20,”
Thermochim. Acta, 205, 299 (1992).
[39] Z. Slanina, L. Adamowicz, K. Kobayashi, and S. Na-
gase, ”Gibbs energy-based treatment of metallofullerenes:
Ca@C72, Ca@C74, Ca@C82, and La@C82,” Mol. Simul.,
31, 71 (2005).
[40] T. Akasaka, S. Nagase, K. Kobayashi, M. Walchli, K. Ya-
mamoto, H. Funasaka, M. Kako, T. Hoshino, and T. Erata,
”13C and 139La NMR studies of La2@C80: First evidence
for circular motion of metal atoms in endohedral dimet-
allofullerenes,” Angew. Chem., Intl. Ed. Engl., 36, 1643
(1997).
[41] K. Kobayashi, S. Nagase, Y. Maeda, T. Wakahara, and T.
Akasaka, ”La2@C80: Is the circular motion of two La atoms
controllable by exohedral addition?,” Chem. Phys. Lett.,
374, 562 (2003).
[42] Z. Slanina and S. Nagase, ”Sc3N@C80: Computations
on the two-isomer equilibrium at high temperatures,”
ChemPhysChem, 6, 2060 (2005).
[43] R. J. Cross and M. Saunders, ”Transmutation of fullerenes,”
J. Am. Chem. Soc., 127, 3044 (2005).
[44] F. Furche and R. Ahlrichs, ”Fullerene C80: Are there still
more isomers?,” J. Chem. Phys., 114, 10362 (2001).
[45] V. I. Kovalenko and A. R. Khamatgalimov, ”Open-shell
fullerene C-74: Phenalenyl-radical substructures,” Chem.
Phys. Lett., 377, 263 (2003).
[46] D. R. Kanis, M. A. Ratner, T. J. Marks, and M. C. Zerner,
”Nonlinear optical characteristics of novel inorganic chro-
mophores using the Zindo formalism,” Chem. Mater., 3,
19 (1991).
[47] R. D. Bendale and M. C. Zerner, ”Electronic structure
and spectroscopy of the five most stable isomers of C-78
fullerene,” J. Phys. Chem., 99, 13830 (1995).
[48] H. Moribe, T. Inoue, H. Kato, A. Taninaka, Y. Ito, T.
Okazaki, T. Sugai, R. Bolskar, J. M. Alford, and H.
Shinohara, ”Purification and electronic structure of C74
fullerene,” Paper 1P-1, The 25th Fullerene-Nanotubes Sym-
posium, Awaji, Japan, 2003.
[49] Z. Slanina, J. M. Rudzi´ski, and E. ¯sawa, ”C60(g) and
C70(g): A computational study of pressure and temper-
ature dependence of their populations,” Carbon, 25, 747
(1987).
[50] Z. Slanina, J. M. Rudzi´ski, and E. ¯sawa, ”C60(g), C70(g)
saturated carbon vapour and increase of cluster populations
with temperature: A combined AM1 quantum-chemical
and statistical-mechanical study,” Collect. Czech. Chem.
Commun., 52, 2381 1987.
[51] J. M. Rudzi´ski, Z. Slanina, M. Togasi, E. ¯sawa, and
T. Iizuka, ”Computational study of relative stabilities of
C60(Ih) and C70(D5h) gas-phase clusters,” Thermochim.
Acta, 125, 155 (1988).
[52] Z. Slanina, X. Zhao, N. Kurita, H. Gotoh, F. Uhlõk, J. M.
Rudzi´ski, K. H. Lee, and L. Adamowicz, ”Computing the
relative gas-phase populations of C60 and C70: Beyond the
traditional deltaHof,298 scale,” J. Mol. Graphics Mod., 19,
216 (2001).
[53] Z. Slanina, ”Clusters in a saturated vapor: Pressure-based
temperature enhancement of the cluster fraction,” Z. Phys.
Chem., 217, 1119 (2003).
[54] Z. Slanina, ”Temperature development of mono- and hetero-
clustering in saturated vapors,” J. Cluster Sci., 15, 3
(2004).
[55] W. T. Hicks, ”Evaluation of vapor-pressure data of mercury,
lithium, sodium, and potassium,” J. Chem. Phys., 38, 1873
(1963).
[56] CRC Handbook of Chemistry and Physics, 85th edition, D.
R. Lide, ed. CRC Press, Boca Raton, 2004.
[57] Z. Slanina, S.-L. Lee, L. Adamowicz, F. Uhlõk, and S. Na-
gase, ”Computed structure and energetics of La@C60,” Int.
J. Quantum Chem., 104, 272 (2005).
[58] Z. Slanina and S. Nagase, ”Stability computations for
Ba@C74,” Chem. Phys. Lett., 422, 133 (2006).
[59] J. K. Gimzewski, ”Scanning tunneling and local probe stud-
ies of fullerenes,” in The Chemical Physics of Fullerenes 10
(and 5) Years Later, W. Andreoni, ed. Kluwer Academic
Publishers, Dordrecht, 1996, p. 117.
[60] W. Harneit, M. Waiblinger, C. Meyer, K. Lips, and A. Wei-
dinger, ”Concept for quantum computing with N@C60,”
in Recent Advances in the Chemistry and Physics of
Fullerenes and Related Materials, Vol. 11, Fullerenes for
the New Millennium, K. M. Kadish, P. V. Kamat, D. Guldi,
eds. Electrochemical Society, Pennington, 2001, p. 358.
[61] N. Hiroshiba, K. Tanigaki, R. Kumashiro, H. Ohashi, T.
Wakahara, and T. Akasaka, ”C60 field effect transistor with
electrodes modified by La@C82,” Chem. Phys. Lett., 400,
235 (2004).
[62] J. M. Campanera, C. Bo, M. M. Olmstead, A. L.
Balch, and J. M. Poblet, ”Bonding within the endo-
hedral fullerenes Sc3N@C78 and Sc3N@C80 as deter-
mined by density functional calculations and reexamina-
tion of the crystal structure of {Sc3N@C78}·{Co(OEP)}·
1.5(C6H6)·0.3(CHCl3),” J. Phys. Chem. A, 106, 12356
(2002).
[63] T. Heine, K. Vietze, and G. Seifert, ”13C NMR fingerprint
characterizes long time-scale structure of Sc3N@C80 endo-
hedral fullerene,” Magn. Res. Chem., 42, S199 (2004).
[64] Z. Slanina, P. Pulay, and S. Nagase, ”H2, Ne, and N2 ener-
gies of encapsulation into C60 evaluated with the MPWB1K
functional,” J. Chem. Theory Comput., 2, 782 (2006).
[65] K. Kobayashi, S. Nagase, and T. Akasaka, ”Endohedral
dimetallofullerenes Sc2@C84 and La2@C80. Are the metal
atoms still inside the fullerence cages?,” Chem. Phys. Lett.,
261, 502 (1996).
[66] B. P. Cao, T. Wakahara, T. Tsuchiya, M. Kondo, Y. Maeda,
G. M. A. Rahman, T. Akasaka, K. Kobayashi, S. Nagase,
and K. Yamamoto, ”Isolation, characterization, and theo-
retical study of La2@C78,” J. Am. Chem. Soc., 126, 9164
(2004).
[67] T. Wakahara, Y. Iiduka, O. Ikenaga, T. Nakahodo, A.
Sakuraba, T. Tsuchiya, Y. Maeda, M. Kako, T. Akasaka,
K. Yoza, E. Horn, N. Mizorogi, and S. Nagase, ”Charac-
terization of the bis-silylated endofullerene Sc3N@C80,” J.
Am. Chem. Soc., 128, 9919 (2006).