Article
Pocket and Antipocket conformations for the CH4@C84 endohedral
fullerene
MOUGHAL SHAHI, Abdul Rehaman, GAGLIARDI, Laura, PYYKKÖ, Pekka
Abstract
The endohedral fullerene CH4@C84 has been studied using density functional theory (DFT)
and second-order Møller-Plesset perturbation theory (MP2). In addition to the structure with a
CH bond of CH4 in a tetrahedral pocket conformation, we find an alternative minimum, very
close in energy (6.3-9.5 kJ/mol higher according to the level of theory), with the methane
inverted, which we call the antipocket conformation. Computed IR spectra are reported for
CH4@C84 and also for the reference system CH4@C60. The calculated vibrational levels, in
a harmonic approximation, reveal close-lying translational, librational, and shell-vibrational
modes. The results are also presented for the isoelectronic species NH@C60.
Reference
MOUGHAL SHAHI, Abdul Rehaman, GAGLIARDI, Laura, PYYKKÖ, Pekka. Pocket and
Antipocket conformations for the CH4@C84 endohedral fullerene. International Journal of
Quantum Chemistry, 2007, vol. 107, no. 5, p. 1162-1169
DOI : 10.1002/qua.21230
Available at:
http://archive-ouverte.unige.ch/unige:3200
Disclaimer: layout of this document may differ from the published version.
Pocket and Antipocket Conformations
for the CH4@C84 Endohedral Fullerene
ABDUL REHAMAN,1 LAURA GAGLIARDI,1 PEKKA PYYKKÖ2
1
Department of Physical Chemistry, University of Geneva 30, Quai Ernest Ansermet,
CH-1211 Geneva 4, Switzerland
2
Department of Chemistry, University of Helsinki, P. O. Box 55, University of Helsinki,
Helsinki FIN-00014, Finland
Received 2 August 2006; accepted 31 August 2006
Published online 27 October 2006 in Wiley InterScience (www.interscience.wiley.com).
DOI 10.1002/qua.21230
ABSTRACT: The endohedral fullerene CH4@C84 has been studied using density
functional theory (DFT) and second-order Møller–Plesset perturbation theory (MP2). In
addition to the structure with a COH bond of CH4 in a tetrahedral pocket
conformation, we find an alternative minimum, very close in energy (6.3–9.5 kJ/mol
higher according to the level of theory), with the methane inverted, which we call the
antipocket conformation. Computed IR spectra are reported for CH4@C84 and also for
the reference system CH4@C60. The calculated vibrational levels, in a harmonic
approximation, reveal close-lying translational, librational, and shell-vibrational modes.
The results are also presented for the isoelectronic species NH⫹
© 2006 Wiley
4 @C60.
Periodicals, Inc. Int J Quantum Chem 107: 1162–1169, 2007
Key words: endohedral fullerene chemistry; methane; DFT
Introduction
W
hen putting a hand in a glove, we normally
expect the fingers to enter the pockets provided for them. It would be rather surprising if a
stable configuration were also found with the finCorrespondence
chiphy.unige.ch
Contract grant
Contract grant
Contract grant
Contract grant
lecular Science.
to: L. Gagliardi; e-mail: laura.gagliardi@
sponsor: Swiss National Science Foundation.
sponsor: Academy of Finland.
numbers: 200903; 206102.
sponsor: Finnish CoE of Computational Mo-
gers positioned between the pockets. In this work
we report a theoretical study of methane in a tetrahedral fullerene, where both possibilities form stable minima, at least within the theoretical models
applied.
Endohedral fullerenes [1] are no longer new.
Both atomic and molecular species have been experimentally enclosed inside a Cn shell. The first
one, He@C60, was discovered in 1992 [2, 3]. For
methane in C60, both molecular mechanics [4],
semiempirical [5], and ab initio [6, 7] studies on
CH4@C60 already exist. Also, methane in the higher
tetrahedral fullerene C84 was studied by Charkin et
al. [7], who furthermore considered the valence
International Journal of Quantum Chemistry, Vol 107, 1162–1169 (2007)
© 2006 Wiley Periodicals, Inc.
POCKET AND ANTIPOCKET CONFORMATIONS FOR CH4@C60 ENDOHEDRAL FULLERENE
⫹
⫺
isoelectronic species BH⫺
4 , CH4, NH4 , AlH4 , SiH4,
⫹
and PH4 in the same cage [6, 7].
Recently, the possibility of putting metal hydride
molecules inside the cage, MH4@C60; MASc, Ti,
and Zr was considered by one of us [8]. This work
predicted bound systems, but they were rather
crowded and the cage was strongly deformed. In
the ZrH4@C60 case, for example, the energy of the
system was ⬃400 kJ/mol above that of the components, ZrH4 and C60. The possibility of forming
metal-hydrides inside a nanotube was also considered and such compounds turned out to be energetically more favorable. Even more crowded is the
case of neopentane inside C60, recently considered
by Huntley et al. [9].
Our interest in the present species was to study
them as a less strained alternative to endohedral
XH4 hydrides. During the course of the work, we
arrived at the two title conformations, namely two
isomers of CH4@C84. They correspond to two different orientations of CH4 with respect to the C84
cage. We call them the pocket and antipocket orientations, meaning that the methane COH bonds
are directed toward a shell protuberance, or opposite to one, respectively.
Several isomers of C84 alone exist [10]. We have
chosen the one with tetrahedral symmetry because
we wanted to study a tetrahedral model case. To
facilitate the possible identification, we provide
synthetic infrared (IR) spectra. Those are also given
for the CH4@C60 reference system.
Finally, we note that there are experiments with
CH4 trapped in solid C60, but in those samples the
methane is in the interstitial spaces between the
icosahedra, not inside the icosahedra [11–13]. Comparative results are also presented for the isoelectronic species NH⫹
4 @C60. We shall describe the
methods used in the calculations, and we shall then
present and discuss our results.
Methods
The program turbomole [14, 15] was employed. The calculations were performed using
DFT, with the Becke–Perdew BP86 exchange-correlation functional. For H and C, a split-valence
plus polarization basis set, contracted to 2s1p and
3s2p1d, respectively, was used. Equilibrium geometries and harmonic frequencies were computed for all species at the BP86/DFT level of
theory, using the resolution-of-the-identity (RI)
variant available in the turbomole package [14,
VOL. 107, NO. 5
DOI 10.1002/qua
FIGURE 1. Structure of CH4@C60.
15] to make the calculations feasible. The auxiliary basis sets of split-valence plus polarization
type, available in the TURBOMOLE library, were
used for all atoms.
Comparative equilibrium geometry calculations
on some selected structures were performed at the
second-order Møller–Plesset perturbation theory
(MP2) level with the RI variant, MP2, in order to
check whether possible weak interactions between
the H atoms and the fullerene cage would imply a
substantial rearrangement of the structures. The
energy difference between the supersystem and its
constituents was computed at both the BP86/DFT
and MP2 levels of theory. Correction for the basis
set superposition error (BSSE) was included in the
MP2 calculations of the energetics.
Harmonic frequency calculations were performed for all systems at the DFT/BP86 level, and
for the two isomers of CH4@C84, also at the MP2
level of theory, to check that the presence of two
almost degenerate minima was not an artifact of
DFT. We are aware of the fact that the harmonic
model may be just an approximation, but for much
smaller systems with a few vibrational quanta, the
density of vibrational states becomes prohibitively
large.
Results and Discussion
In CH4@C60 (Fig. 1) both parts of the complex
survive almost undeformed on complex formation. The deformations of the C60 shell are a couple of picometers (pm) and the compression of
the COH bond ⬍1 pm. Note that T d is not a
subgroup of I h . The minimum that was obtained
has C 2 symmetry, only. The most significant
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1163
REHAMAN, GAGLIARDI, AND PYYKKÖ
TABLE I ______________________________________
Typical DFT/BP86 and MP2 bond distances (pm)
in CH4@C60 and in the pocket isomer of CH4@C84
and NH4ⴙ@C84 and their constituents.*
BP86a
Distance
MP2a
C(CH4)OC(C60)
Free C60 (COX)
356.9–357.8 354.6–355.7
358.8
C(CH4)OC(C84)
N(NH4⫹)OC(C84)
Free C84 (COX)
396.3–443.3 348.0–486.3
395.8–443.6
396.3–443.3
C(CH4)OH (in C60)
C(CH4)OH (in C84)
N(NH4⫹)OH (in C84)
Free CH4
Free NH4⫹
110.3
111.1
104.8
111.0
104.4
B3LYPb
110.1
110.6
110.2
110.1
* When two values are reported, they represent the smallest
and largest distance for that bond parameter. X is the center
of a bare C60 (C84) molecule. See Fig. 1 for a description of
the structure. The nonbonding HOC distance varies from
180.0 to 263.6 pm.
a
This work.
b
Ref. [6].
structural parameters of CH4@C60 are reported in
Table I. The interaction energies for CH4@C60 are
reported in Table II.
It should be noted that the energy difference
between CH4@C60 and the two moieties, CH4 and
C60, has been computed including the zero-point
energy (ZPE) correction at the BP86 level of theory,
since, at this level of theory, all the structures have
been characterized by harmonic frequency calculations. CH4@C60 is 46 kJ/mol higher in energy than
separated CH4 and C60. This compound is thus
indeed less endothermic for decomposition than
the corresponding group 4 metal hydride compounds [8]. In contrast, MP2 theory predicts
CH4@C60 to be 29 kJ/mol more stable than its constituents, with the inclusion of the BSSE correction.
The MP2 results are likely to be more reliable than
the BP86 results, since they include also the weak
interaction effects, and we thus conclude that the
supersystem is energetically lower than the two
constituents. (It is known that the MP2 method
rather exaggerates the dispersion energies, compared to a CCSD(T) limit for the same basis [16,
17].) A larger basis, which cannot be used at
present, would be expected to strengthen the interaction [16]. Concerning the zero-point vibrational
energy (ZPVE) corrections to the interaction energy, they were found to be negligible (0.4 kJ/mol)
at the BP86 level. This effect will hence probably be
negligible at the MP2 level as well. We consider the
difference of ⫺29 kJ/mol between the supersystem
CH4@C60 and its constituents as our best current
estimate.
Table III presents the harmonic vibrational
modes of CH4@C60 together with the experimental
and calculated frequencies for empty C60. Because
of the harmonic approximation used in the frequency calculation, the overtones of the lowest
modes are not now visible. Because of the low
symmetry of the complex, it is not surprising that
the librational mode is strongly split.
A further aspect is that of the nuclear-spin functions for CH4 or CD4. These hydrogen isotopes will
span a spin space of dimension 16 or 81, respec-
TABLE II ______________________________________________________________________________________________
CH4@C60: Total energies (a.u) and energy differences (kJ/mol) with [ⴙE(ZPE)] and without zero-point
energy correction (ZPE).*
System
ET (DFT)/a.u.
ET (DFT)/a.u. ⫹ E (ZPE)
ET (MP2)(BSSE corr)
CH4
C60
CH4@C60
a
ECH
@C60OECH4OEC60
4
b
ECH
@C60OECH4OEC60
4
⫺40.4747
⫺2284.7902
⫺2325.2461
⫹49.4
⫹62.4
⫺40.4314
⫺2284.4215
⫺2324.8340
⫹49.8
⫹71.2
⫺40.3000
⫺2278.0265
⫺2318.3372
⫺28.1
⫺51.9
⫺64.1c
* Our MP2 values include the basis-set superposition energy (BSSE) correction, but no ZPE.
a
This work: DFT ⫽ BP86.
b
Ref. [6]: DFT ⫽ B3LYP 6-31G*.
c
Ref. [6]: MP2 without BSSE correction 6-31G**.
1164 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
DOI 10.1002/qua
VOL. 107, NO. 5
POCKET AND ANTIPOCKET CONFORMATIONS FOR CH4@C60 ENDOHEDRAL FULLERENE
TABLE III _____________________________________
TABLE IV _____________________________________
Calculated (DFT/B86) harmonic frequencies (in
cmⴚ1) for CH4@C60 and empty C60, together with
a
experimental frequencies for C60
.*
Calculated (DFT/B86) harmonic frequencies (in
cmⴚ1) for CH4@C60 and empty C60.*
CH4@C60
124 (L)
143 (L)
188 (L)
152 (L, av.)
209 (PIB)
217 (PIB)
220 (PIB)
261
338
350
395
423
474
488
515–519 (98)
520–521 (2)
546–547
547–548
558
577 (61)
654
688
693–699
706–710
711–714
719
723
738
770
775
807
920
a
C60
(exp)
—
—
—
—
—
—
272
342
353
403
433
485
496
CH4@C60
C60 (calc)
C60 (calc)
260 (hg)
339 (t2u)
349 (gu)
399 (hu)
426 (hg)
474 (gg)
487 (ag)
525 (100) (t1u)
522 (hu)
551 (t2g)
556 (t1g)
565 (gg)
580 (66) (t1u)
661 (hu)
683 (t2g)
696 (hg)
701 (t2u)
705 (gu)
714 (hu)
724 (gg)
744 (gu)
776 (hg)
782 (t2g)
814 (t1g)
929 (au)
960–961
968
1092
1102
1195 (37)
1197
1214
1257
1273
1292–1301 (5)b
1304
1312
1339
1340
1434
1437
1444 (46)
1482
1500
1511b
1517b
1526
1559
1569
3028b
3171–3173b
965 (gu)
975 (t2u)
1097 (gg)
1111 (hg)
1202 (38) (t1u)
1203 (t2u)
1223 (hu)
1266 (hg)
1282 (t1g)
1313 (gg)
1320 (gu)
1347 (hu)
1347 (t2g)
1443 (hg)
1445 (gu)
1453 (46) (t1u)
1492 (ag)
1509 (gg)
1536 (t2u)
1569 (hu)
1578 (hg)
* The shell-deformation modes are identified by their Ih labels. The sizable IR intensities (km/mol) are reported in parentheses. See also Table III.
a
Menendéz, J.; Page, J. B. as quoted by Schettino et al. [21].
b
Methane-based modes, see Table VI.
L, libration; PIB, particle-in-box translational mode.
* The shell-deformation modes are identified by their Ih labels. The sizable IR intensities (km/mol) are reported in parentheses. See also Table IV.
a
Menendéz, J.; Page, J. B. as quoted by Schettino et al. [21].
tively. These spin states will couple with the various tunneling or rotational states of the system.
The vibrational spectrum of the system showed
unexpectedly that three different modes have comparable frequencies: the translations (particle-in-aspherical box), the librations (hindered rotations of
methane inside the deformed C60), and the deformations of the C60 shell, beginning with the lowest,
hg, mode. Table III and IV also shows the splittings
of the COH stretching modes.
VOL. 107, NO. 5
DOI 10.1002/qua
FIGURE 2. Structure of the pocket isomer of
CH4@C84.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1165
REHAMAN, GAGLIARDI, AND PYYKKÖ
FIGURE 3. Structure of the antipocket isomer of
CH4@C84.
Two isomers of CH4@C84 were found to be stable, with all frequencies real. As noted in the Introduction, we call them the pocket and antipocket
orientations, meaning that the methane COH
bonds are directed towards a shell protuberance, or
opposite to one, respectively. The structures of the
two isomers are shown in Figures 2 and 3. To make
more clear the structural differences between the
two isomers, we show the two isomers projected
into a plane orthogonal to one of the threefold
symmetry axes (Figs. 4 and 5). The COH bonds of
methane point toward the vertexes of the triangle in
the pocket isomer, while they point toward the
sides of the triangle in the antipocket isomer.
They differ in energy by only 6.3 kJ/mol at the
BP86 level of theory and 9.6 kJ/mol at the MP2
level of theory (the pocket isomer is predicted to be
lower in energy than the antipocket isomer with
both methods). The most significant bond distances
FIGURE 5. Planar projection of the structure of the
antipocket isomer of CH4@C84.
of the pocket CH4@C84 isomer are reported in Table
I. We do not report the structural parameters for the
antipocket isomer because they are almost identical
to those of the pocket isomer. The structures of the
two components CH4 and C84 hardly change in the
supersystem. The same holds for NH⫹
4 @C84 (see
Table I).
TABLE V ______________________________________
CH4@C84 total energies (a.u) and energy
difference (kJ/mol) with zero-point energy
correction for the pocket isomer (lowest energy
isomer).
System
ET (DFT)/a.u
CH4
C84
CH4@C84
ECH4@C84–ECH4–EC84
⫺40.4314
⫺3198.3629
⫺3238.7855
⫹23.0
TABLE VI _____________________________________
Calculated harmonic frequencies (in cmⴚ1) for
CH4 in CH4@C60, in CH4@C84, and for free CH4,
respectively, together with their assignments (in
Td symmetry) and experimental frequencies.
CH4@C84
CH4@C60
FIGURE 4. Planar projection of the structure of the
pocket isomer of CH4@C84.
1292–1301
1511, 1517
3028
3171–3173
1166 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
CH4
Pocket Antipocket This work
1289
1486
2939
3076
1298
1529
2953
3085
DOI 10.1002/qua
1286 (t2)
1497 (e)
2938 (a1)
3073 (t2)
Ref.
[6]
Exp
[22]
1410
1610
3085
3213
1306
1526
2914
3020
VOL. 107, NO. 5
POCKET AND ANTIPOCKET CONFORMATIONS FOR CH4@C60 ENDOHEDRAL FULLERENE
TABLE VII ____________________________________________________________________________________________
BP86 and MP2 harmonic frequencies (in cmⴚ1) for the pocket and antipocket isomers of CH4@C84 (Td
symmetry), respectively, and for C84 (BP86 only), together with their assignments.*
Pocket/BP86
70 (t2) PIB
210 (t2)
210 (e)
270 (t2)
281 (t1)
282 (a1)
323 (t1)
328 (e)
344 (a1)
350 (t1)
359 (t2) (1)
372 (e)
381 (t1) L
409 (a1)
419 (t2)
434 (t1)
437 (e)
464 (t2) (1)
468 (a2)
469 (t2) (7)
484 (e)
487 (t1)
506 (t2) (1)
513 (t1)
513 (t2) (28)
527 (a2)
539 (t1)
586
590
600
606
639
645
657
669
671
(e)
(t2) (0)
(a2)
(t1)
(t2) (1)
(e)
(t1)
(a2)
(t2) (5)
Antipocket/BP86
196 PIB
215
215
276
284
284
324
328
350
356
363
376
C84/BP86
206
211
270
278
276
322
326
345
348
355 (2)
370
Ref. [6]
143
222
225
289
302
290
181
411
425
440
443
466 (1)
473
471 (5)
490
490
508 (5)
515
521 (24)
532
546
548 (t1) L
586
591 (0)
602
607
640 (1)
651
664
695
673 (5)
410
417
432
434
460 (2)
467
469 (26)
481
485
506 (4)
511
512 (100)
528
537
585
590 (1)
600
606
631 (3)
641
653
664
671 (19)
511
614 (57)
15
Pocket/MP2
Antipocket/MP2
89
232
235
307
315
320
359
364
401
392
414 (1)
421
406
434
491 (1)
498
511
504 (4)
532
528
561
553
545 (4)
585
614 (57)
599
642
123
234
236
307
316
322
359
364
401
374
415 (1)
421
407
434
492 (1)
497
512
504 (4)
531
529 (1)
561
552
545 (3)
585
648
656 (0)
672
676
717 (2)
723
730
690
735 (5)
648
656 (0)
671
676
717 (2)
723
728
688
736 (5)
598
642
L, libration; PIB, particle-in-box translational mode.
* The sizable IR intensities (km/mol) are reported in parentheses.
The energy difference between the pocket and
antipocket isomers is quite small. It is not unlikely that a slightly hindered or quasi-free rotation of methane molecule inside the C84 cage will
occur at conventional or lower temperatures. It
would be desirable to find the transition state
between the pocket and antipocket minima, but
the size of the system and the multidimensional
character of the problem make this currently too
VOL. 107, NO. 5
DOI 10.1002/qua
laborious. Similar nonrigidity effects (slightly
hindered internal rotation) can also occur in
CH4@C60, due to the high symmetry of the cage
and the very flat potential energy surface (PES)
along rotation coordinates.
The interaction energies for the pocket isomer
are presented in Table V. The supersystem
CH4@C84 is 23.0 kJ/mol higher in energy than the
two components at the BP86 level, a situation that is
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 1167
REHAMAN, GAGLIARDI, AND PYYKKÖ
TABLE VIII ____________________________________________________________________________________________
P86 and MP2 harmonic frequencies (in cmⴚ1) for the pocket and antipocket isomers of CH4@C84 (Td
symmetry), respectively, and for C84 (BP86 only), together with their assignments.*
Pocket/BP86
676 (e)
680 (t1)
685 (t2) (3)
687 (a1)
691 (t1)
699 (t2)
699 (e)
712 (t2)
715 (t1)
720 (t1)
724 (e)
729 (t2) (1)
731 (t1)
735 (e)
736 (t1)
737 (a2)
804 (t1)
811 (a2)
831 (a1)
832 (t1)
860 (t2) (1)
877 (t1)
927 (a2)
1000 (t2)
1002 (a1)
1017 (e)
1031 (t1)
1111 (t2) (1)
1117 (e)
1133 (t2) (2)
1158 (t1)
1187 (t2) (8)
1205 (e)
1209 (a1)
1219 (t1)
1242 (t2)
1246 (t1)
1259 (t2) (1)
Antipocket/BP86
C84
677
709
695 (2)
694
690
700 (1)
706
722 (1)
722
727
728
734 (1)
731
740
736
738
805
812
831
833
861 (1)
878
927
1000
1003
1018
1032
1112 (1)
1118
1134 (2)
1159 (1)
1188 (8)
1206
1210
1220
1242
1247
1260
675
677
686 (10)
687
690
698
699
711 (1)
705
715
718
721 (5)
720
734
735
722
804
812
830
832
859
877
927
999
1002
1017
1031
1111 (5)
1117
1133 (7)
1158
1187 (28)
1205
1209
1218
1241
1246
1259 (5)
Ref. [6]
16
Pocket/MP2
Antipocket/MP2
748
753
774
788
781
792 (8)
798
822
802
818
826
830 (6)
825
841
838
850
895
915
870
940
920 (1)
959
1070
1062
1052
1092
1103
1102
1259
1184 (5)
1294
1271 (12)
1223
1208
1335
1306 (1)
1396
1340 (1)
748
753
774
787
778
792 (8)
798
821
802
818
826
830 (6)
825
840
838
851
894
915
869
940
919 (1)
959
1069
1062
1052
1092
1103
1101 (0)
1259
1184 (5)
1294
1272 (11)
1223
1207
1335
1306 (1)
1396
1340 (1)
* The sizable IR intensities (km/mol) are reported in parentheses.
less endothermic than CH4@C60. The calculated frequencies for CH4 are reported in Table VI.
For comparison, we have also studied the
NH⫹
4 @C 84 system, which is isoelectronic with
CH4@C84, at the BP86 level of theory. The supersystem NH⫹
4 @C 84, unlike CH 4@C 84, is ⫺32.7 kJ/
mol lower in energy than the components NH⫹
4
and C84.
The lowest vibrational frequencies of the two
isomers of CH4@C84, calculated at the BP86 and
MP2 level of theory, are reported in Tables VII and
VIII. Some of the vibrational frequencies are different for the two isomers. It can be seen that the C84
modes vary very little in the presence of CH4. The
CH4 “particle-in-box” and libration modes occur at
different frequencies in the two isomers. In general
1168 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
DOI 10.1002/qua
VOL. 107, NO. 5
POCKET AND ANTIPOCKET CONFORMATIONS FOR CH4@C60 ENDOHEDRAL FULLERENE
the MP2 values for the vibrational frequencies are
⬃20 cm⫺1 higher than the BP86 values.
At the semi-quantitative level, some of the results presented, such as the endothermicity at the
DFT and exothermicity at the MP2 levels of
CH4@C60, the dissociation energy for NH⫹
4 @C84, the
geometric parameters, and frequencies of the libration and translation modes, are similar to the conclusions presented in Refs. [6, 7].
Concerning the translations, the mere localization [18] of the methane in a spherical box of radius
R will lead to the energy levels
2x2
Ek ⫽
.
2mR2
(1)
For the two lowest levels (s-levels with principal
quantum number, n ⫽ 1 and 2), the values of x are
3.142 and 6.283, respectively [18]. Using the methane mass m of 2.917 䡠 104me, the average frequency
of 215 cm⫺1 would correspond to a 1 3 2 frequency
at R ⫽ 38.0 pm.
Concerning the stability of the complex, we expect that the two main interactions in CH4@C60 are
the steric repulsions and a dispersion-type attraction. It should be noted that the derivation for the
London dispersion law has to be rewritten when
one of the partners is inside the other.
Finally, we note that endohedral species with
one or two hydrogen molecules inside a C70
fullerene have been created by a “molecular surgery” approach [19, 20] and separated by highperformance liquid chromatography. Therefore,
compounds of this type may indeed become available for experimental study in the future. The results on the complexes such as CH4 inside C84 seem
particularly promising in this regard, even though
it may be more difficult to synthesize C84 compared
with C60.
VOL. 107, NO. 5
DOI 10.1002/qua
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