Endohedral metal–metal-bonding fullerenes, in which encapsulated metals form covalent metal–metal bonds inside, are an emerging class of endohedral metallofullerenes. Herein, we reported quantum-chemical studies on the electronic structures, chemical bonding, and dynamic fluxionality behavior of endohedral metal–metal-bonding fullerenes Lu2@C2n (2n = 76–88). Multiple bonding analysis approaches, including molecular orbital analysis, the natural bond orbital analysis, electron localization function, adaptive natural density partitioning analysis, and quantum theory of atoms in molecules, have unambiguously revealed one two-center two-electron σ covalent bond between two Lu ions in fullerenes. Energy decomposition analysis with the natural orbitals for chemical valence method on the bonding nature between the encapsulated metal dimer and the fullerene cage suggested the existence of two covalent bonds between the metal dimer and fullerenes, giving rise to a covalent bonding nature between the metal dimer and fullerene cage and a formal charge model of [Lu2]2+@[C2n]2−. For Lu2@C76, the dynamic fluxionality behavior of the metal dimer Lu2 inside fullerene C76 has been revealed via locating the transition state with an energy barrier of 5 kcal/mol. Further energy decomposition analysis calculations indicate that the energy barrier is controlled by a series of terms, including the geometric deformation energy, electrostatic interaction, and orbital interactions.
REFERENCES
1.
X.
Lu
, T.
Akasaka
, and S.
Nagase
, “Carbide cluster metallofullerenes: Structure, properties, and possible origin
,” Acc. Chem. Res.
46
, 1627
–1635
(2013
).2.
P. M.
Felker
and Z.
Bačić
, “Electric-dipole-coupled H2O@C60 dimer: Translation-rotation eigenstates from twelve-dimensional quantum calculations
,” J. Chem. Phys.
146
, 084303
(2017
).3.
A. A.
Popov
, S.
Yang
, and L.
Dunsch
, “Endohedral fullerenes
,” Chem. Rev.
113
, 5989
(2013
).4.
W.
Cai
, C.-H.
Chen
, N.
Chen
, and L.
Echegoyen
, “Fullerenes as nanocontainers that stabilize unique actinide species inside: Structures, formation, and reactivity
,” Acc. Chem. Res.
52
, 1824
–1833
(2019
).5.
T.
Wang
and C.
Wang
, “Functional metallofullerene materials and their applications in nanomedicine, magnetics, and electronics
,” Small
15
, 1901522
(2019
).6.
T.
Halverson
, D.
Iouchtchenko
, and P.-N.
Roy
, “Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods
,” J. Chem. Phys.
148
, 074112
(2018
).7.
K.
Zhang
, C.
Wang
, M.
Zhang
, Z.
Bai
, F.-F.
Xie
, Y.-Z.
Tan
, Y.
Guo
, K.-J.
Hu
, L.
Cao
, S.
Zhang
, X.
Tu
, D.
Pan
, L.
Kang
, J.
Chen
, P.
Wu
, X.
Wang
, J.
Wang
, J.
Liu
, Y.
Song
, G.
Wang
, F.
Song
, W.
Ji
, S.-Y.
Xie
, S.-F.
Shi
, M. A.
Reed
, and B.
Wang
, “A Gd@C82 single-molecule electret
,” Nat. Nanotechnol.
15
, 1019
–1024
(2020
).8.
W.
Shen
, L.
Bao
, Y.
Wu
, C.
Pan
, S.
Zhao
, H.
Fang
, Y.
Xie
, P.
Jin
, P.
Peng
, F.-F.
Li
, and X.
Lu
, “Lu2@C2n (2n = 82, 84, 86): Crystallographic evidence of direct Lu–Lu bonding between two divalent lutetium ions inside fullerene cages
,” J. Am. Chem. Soc.
139
, 9979
(2017
).9.
W.
Shen
, L.
Bao
, S.
Hu
, L.
Yang
, P.
Jin
, Y.
Xie
, T.
Akasaka
, and X.
Lu
, “Crystallographic characterization of Lu2C2n (2n = 76–90): Cluster selection by cage size
,” Chem. Sci.
10
, 829
–836
(2019
).10.
C.
Pan
, W.
Shen
, L.
Yang
, L.
Bao
, Z.
Wei
, P.
Jin
, H.
Fang
, Y.
Xie
, T.
Akasaka
, and X.
Lu
, “Crystallographic characterization of Y2C2n (2n = 82, 88–94): Direct Y–Y bonding and cage-dependent cluster evolution
,” Chem. Sci.
10
, 4707
(2019
).11.
H.
Kurihara
, X.
Lu
, Y.
Iiduka
, N.
Mizorogi
, Z.
Slanina
, T.
Tsuchiya
, S.
Nagase
, and T.
Akasaka
, “Sc2@C3v(8)-C82vs.Sc2C2@C3v(8)-C82: Drastic effect of C2 capture on the redox properties of scandium metallofullerenes
,” Chem. Commun.
48
, 1290
–1292
(2012
).12.
M.
Nie
, L.
Yang
, C.
Zhao
, H.
Meng
, L.
Feng
, P.
Jin
, C.
Wang
, and T.
Wang
, “A luminescent single-molecule magnet of dimetallofullerene with cage-dependent properties
,” Nanoscale
11
, 18612
–18618
(2019
).13.
X.
Zhang
, Y.
Wang
, R.
Morales-Martínez
, J.
Zhong
, C.
de Graaf
, A.
Rodríguez-Fortea
, J. M.
Poblet
, L.
Echegoyen
, L.
Feng
, and N.
Chen
, “U2@Ih(7)-C80: Crystallographic characterization of a long-sought dimetallic actinide endohedral fullerene
,” J. Am. Chem. Soc.
140
, 3907
(2018
).14.
J.
Zhuang
, R.
Morales-Martínez
, J.
Zhang
, Y.
Wang
, Y.-R.
Yao
,C.
Pei
,A.
Rodríguez-Fortea
,S.
Wang
,L.
Echegoyen
,C.
de Graaf
,J. M.
Poblet
,and N.
Chen
, “Characterization of a strong covalent Th3+–Th3+ bond inside an Ih(7)-C80 fullerene cage
,” Nat. Commun.
12
, 2372
(2021
).15.
T.
Zuo
, L.
Xu
, C. M.
Beavers
, M. M.
Olmstead
, W.
Fu
, T. D.
Crawford
, A. L.
Balch
, and H. C.
Dorn
, “M2@C79N (M = Y, Tb): Isolation and characterization of stable endohedral metallofullerenes exhibiting M–M bonding interactions inside Aza[80]fullerene cages
,” J. Am. Chem. Soc.
130
, 12992
–12997
(2008
).16.
W.
Fu
, J.
Zhang
, T.
Fuhrer
, H.
Champion
, K.
Furukawa
, T.
Kato
, J. E.
Mahaney
, B. G.
Burke
, K. A.
Williams
, K.
Walker
, C.
Dixon
, J.
Ge
, C.
Shu
, K.
Harich
, and H. C.
Dorn
, “Gd2@C79N: Isolation, characterization, and monoadduct formation of a very stable heterofullerene with a magnetic spin state of S = 15/2
,” J. Am. Chem. Soc.
133
, 9741
–9750
(2011
).17.
Y.
Wang
, J.
Xiong
, J.
Su
, Z.
Hu
, F.
Ma
, R.
Sun
, X.
Tan
, H.-L.
Sun
, B.-W.
Wang
, Z.
Shi
, and S.
Gao
, “Dy2@C79N: A new member of dimetalloazafullerenes with strong single molecular magnetism
,” Nanoscale
12
, 11130
–11135
(2020
).18.
M.
Yamada
, H.
Kurihara
, M.
Suzuki
, M.
Saito
, Z.
Slanina
, F.
Uhlik
, T.
Aizawa
, T.
Kato
, M. M.
Olmstead
, A. L.
Balch
, Y.
Maeda
, S.
Nagase
, X.
Lu
, and T.
Akasaka
, “Hiding and recovering electrons in a dimetallic endohedral fullerene: Air-stable products from radical addition
,” J. Am. Chem. Soc.
137
, 232
(2015
).19.
L.
Bao
, M.
Chen
, C.
Pan
, T.
Yamaguchi
, T.
Kato
, M. M.
Olmstead
, A. L.
Balch
, T.
Akasaka
, and X.
Lu
, “Crystallographic evidence for direct metal–metal bonding in a stable open-shell La2@Ih-C80 derivative
,” Angew. Chem., Int. Ed.
55
, 4242
(2016
).20.
F.
Liu
, D. S.
Krylov
, L.
Spree
, S. M.
Avdoshenko
, N. A.
Samoylova
, M.
Rosenkranz
, A.
Kostanyan
, T.
Greber
, A. U. B.
Wolter
, B.
Büchner
, and A. A.
Popov
, “Single molecule magnet with an unpaired electron trapped between two lanthanide ions inside a fullerene
,” Nat. Commun.
8
, 16098
(2017
).21.
A.
Jaroš
, C. F.
Nejad
, and M.
Straka
, “From π bonds without σ bonds to the longest metal–metal bond ever: A survey on actinide–actinide bonding in fullerenes
,” Inorg. Chem.
59
, 12608
(2020
).22.
S.
Stevenson
, M. A.
Mackey
, M. A.
Stuart
, J. P.
Phillips
, M. L.
Easterling
, C. J.
Chancellor
, M. M.
Olmstead
, and A. L.
Balch
, “A distorted tetrahedral metal oxide cluster inside an icosahedral carbon cage. Synthesis, isolation, and structural characterization of Sc4(μ3-O)2@Ih-C80
,” J. Am. Chem. Soc.
130
, 11844
(2008
).23.
T.
Xu
, H.
Yin
, P.
Yu
, Z.
He
, N.
Chen
, W.
Shen
, M.
Zhu
, T.
Akasaka
, and X.
Lu
, “Ultraviolet photodetectors based on dimetallofullerene Lu2@Cs(6)-C82 nanorods
,” ACS Appl. Nano Mater.
5
, 1683
–1689
(2022
).24.
F.
Weinhold
and C. R.
Landis
, Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective
(Cambridge University Press
, 2005
).25.
A. D.
Becke
and K. E.
Edgecombe
, “A simple measure of electron localization in atomic and molecular systems
,” J. Chem. Phys.
92
, 5397
–5403
(1990
).26.
D. Y.
Zubarev
and A. I.
Boldyrev
, “Developing paradigms of chemical bonding: Adaptive natural density partitioning
,” Phys. Chem. Chem. Phys.
10
, 5207
(2008
).27.
N. V.
Tkachenko
and A. I.
Boldyrev
, “Chemical bonding analysis of excited states using the adaptive natural density partitioning method
,” Phys. Chem. Chem. Phys.
21
, 9590
(2019
).28.
R. F. W.
Bader
, “Atoms in molecules
,” Acc. Chem. Res.
18
, 9
–15
(1985
).29.
M.
Mitoraj
and A.
Michalak
, “Donor–acceptor properties of ligands from the natural orbitals for chemical valence
,” Organometallics
26
, 6576
–6580
(2007
).30.
M.
Mitoraj
and A.
Michalak
, “Applications of natural orbitals for chemical valence in a description of bonding in conjugated molecules
,” J. Mol. Model.
14
, 681
–687
(2008
).31.
M.
Mitoraj
and A.
Michalak
, “Natural orbitals for chemical valence as descriptors of chemical bonding in transition metal complexes
,” J. Mol. Model.
13
, 347
–355
(2007
).32.
F. M.
Bickelhaupt
, C. F.
Guerra
, M.
Mitoraj
, F.
Sagan
, A.
Michalak
, S.
Pan
, and G.
Frenking
, “Clarifying notes on the bonding analysis adopted by the energy decomposition analysis
,” Phys. Chem. Chem. Phys.
24
, 15726
(2022
).33.
L.
Zhao
, S.
Pan
, N.
Holzmann
, P.
Schwerdtfeger
, and G.
Frenking
, “Chemical bonding and bonding models of main-group compounds
,” Chem. Rev.
119
, 8781
(2019
).34.
J. P.
Perdew
, “Density-functional approximation for the correlation energy of the inhomogeneous electron gas
,” Phys. Rev. B
33
, 8822
–8824
(1986
).35.
A. D.
Becke
, “Density-functional exchange-energy approximation with correct asymptotic behavior
,” Phys. Rev. A
38
, 3098
(1988
).36.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
, 3865
(1996
).37.
J.
Tao
, J. P.
Perdew
, V. N.
Staroverov
, and G. E.
Scuseria
, “Climbing the density functional ladder: Nonempirical meta–generalized gradient approximation designed for molecules and solids
,” Phys. Rev. Lett.
91
, 146401
(2003
).38.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem.Phys.
110
, 6158
–6170
(1999
).39.
A. D.
Becke
, “Density-functional thermochemistry. III. The role of exact exchange
,” J. Chem. Phys.
98
, 5648
(1993
).40.
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
).41.
Y.
Zhao
and D. G.
Truhlar
, “The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other function
,” Theor. Chem. Acc.
120
, 215
–241
(2008
).42.
J.-D.
Chai
and M.
Head-Gordon
, “Systematic optimization of long-range corrected hybrid density functionals
,” J. Chem. Phys.
128
, 084106
(2008
).43.
S.
Grimme
, S.
Ehrlich
, and L.
Goerigk
, “Effect of the damping function in dispersion corrected density functional theory
,” J. Comput. Chem.
32
, 1456
–1465
(2011
).44.
R.
Gulde
, P.
Pollak
, and F.
Weigend
, “Error-balanced segmented contracted basis sets of double-ζ to quadruple-ζ valence quality for the lanthanides
,” J. Chem. Theory Comput.
8
(11
), 4062
–4068
(2012
).45.
Y.
Wang
, G.
Velkos
, N. J.
Israel
, M.
Rosenkranz
, B.
Büchner
, F.
Liu
, and A. A.
Popov
, “Electrophilic trifluoromethylation of dimetallofullerene anions en route to air-stable single-molecule magnets with high blocking temperature of magnetization
,” J. Am. Chem. Soc.
143
, 18139
–18149
(2021
).46.
N. A.
Samoylova
, S. M.
Avdoshenko
, D. S.
Krylov
, H. R.
Thompson
, A. C.
Kirkhorn
, M.
Rosenkranz
, S.
Schiemenz
, F.
Ziegs
, A. U. B.
Wolter
, S.
Yang
, S.
Stevenson
, and A. A.
Popov
, “Confining the spin between two metal atoms within the carbon cage: Redox-active metal–metal bonds in dimetallofullerenes and their stable cation radicals
,” Nanoscale
9
, 7977
–7990
(2017
).47.
F.
Weigend
and R.
Ahlrichs
, “Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
,” Phys. Chem. Chem. Phys.
7
, 3297
–3305
(2005
).48.
M.
Douglas
and N. M.
Kroll
, “Quantum electrodynamical corrections to the fine structure of helium
,” Ann. Phys.
82
, 89
–155
(1974
).49.
B. A.
Hess
, “Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations
,” Phys. Rev. A
32
, 756
–763
(1985
).50.
W. A.
de Jong
, R. J.
Harrison
and D. A.
Dixon
, “Parallel Douglas–Kroll energy and gradients in NWChem: Estimating scalar relativistic effects using Douglas–Kroll contracted basis sets
,” J. Chem. Phys.
114
, 48
–53
(2001
).51.
Q.
Lu
and K. A.
Peterson
, “Correlation consistent basis sets for lanthanides: The atoms La–Lu
,” J. Chem. Phys.
145
, 054111
(2016
).52.
M. J. T.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
, G. E.
Scuseria
, M. A.
Robb
, J. R.
Cheeseman
, G.
Scalmani
, V.
Barone
, B.
Mennucci
, G. A.
Petersson
, H.
Nakatsuji
, M.
Caricato
, X.
Li
, H. P.
Hratchian
, A. F.
Izmaylov
, J.
Bloino
, G.
Zheng
, J. L.
Sonnenberg
, M.
Hada
, M.
Ehara
, K.
Toyota
, R.
Fukuda
, J.
Hasegawa
, M.
Ishida
, T.
Nakajima
, Y.
Honda
, O.
Kitao
, H.
Nakai
, T.
Vreven
, J. A.
Montgomery
, Jr., J. E.
Peralta
, F.
Ogliaro
, M.
Bearpark
, J. J.
Heyd
, E.
Brothers
, K. N.
Kudin
, V. N.
Staroverov
, T.
Keith
, R.
Kobayashi
, J.
Normand
, K.
Raghavachari
, A.
Rendell
, J. C.
Burant
, S. S.
Iyengar
, J.
Tomasi
, M.
Cossi
, N.
Rega
, J. M.
Millam
, M.
Klene
, J. E.
Knox
, J. B.
Cross
, V.
Bakken
, C.
Adamo
, J.
Jaramillo
, R.
Gomperts
, R. E.
Stratmann
, O.
Yazyev
, A. J.
Austin
, R.
Cammi
, C.
Pomelli
, J. W.
Ochterski
, R. L.
Martin
, K.
Morokuma
, V. G.
Zakrzewski
, G. A.
Voth
, P.
Salvador
, J. J.
Dannenberg
, S.
Dapprich
, A. D.
Daniels
, O.
Farkas
, J. B.
Foresman
, J. V.
Ortiz
, J.
Cioslowski
, and D. J.
Fox
, Gaussian 09, Revision E.01, Gaussian, Inc.
, Wallingford, CT
, 2013
.53.
T.
Lu
and F.
Chen
, “Multiwfn: A multifunctional wavefunction analyzer
,” J. Comput. Chem.
33
, 580
(2012
).54.
T.
Ziegler
and A.
Rauk
, “Carbon monoxide, carbon monosulfide, molecular nitrogen, phosphorus trifluoride, and methyl isocyanide as σ donors and π acceptors. A theoretical study by the Hartree-Fock-Slater transition-state method
,” Inorg. Chem.
18
, 1755
(1979
).55.
F. M.
Bickelhaupt
and E. J.
Baerends
, “Kohn-Sham density functional theory: Predicting and understanding chemistry
,” Rev. Comput. Chem.
15
, 1
(2000
).56.
G.
te Velde
, F. M.
Bickelhaupt
, E. J.
Baerends
, C.
Fonseca Guerra
, S. J. A.
van Gisbergen
, J. G.
Snijders
, and T.
Ziegler
, “Chemistry with ADF
,” J. Comput. Chem.
22
, 931
(2001
).57.
M. v.
Hopffgarten
and G.
Frenking
, “Energy decomposition analysis
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
2
, 43
(2012
).58.
P.
Jerabek
, H. W.
Roesky
, G.
Bertrand
, and G.
Frenking
, “Coinage metals binding as main group elements: Structure and bonding of the carbene complexes [TM(cAAC)2] and [TM(cAAC)2]+ (TM = Cu, Ag, Au)
,” J. Am. Chem. Soc.
136
, 17123
(2014
).59.
E. J.
Baerends
, T.
Ziegler
, J.
Autschbach
, D.
Bashford
, A.
Bérces
, F.
Bickelhaupt
, C.
Bo
, P.
Boerrigter
, L.
Cavallo
, and D.
Chong
, ADF 2019, SCM, Theoretical Chemistry, Vrije Universiteit
, Amsterdam, The Netherlands
, 2019
.60.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
,” J. Chem. Phys.
132
, 154104
–154119
(2010
).61.
E.
van Lenthe
, E. J.
Baerends
, and J. G.
Snijders
, “Relativistic regular two‐component Hamiltonians
,” J. Chem. Phys.
99
, 4597
(1993
).62.
P.
Pyykkö
and M.
Atsumi
, “Molecular single-bond covalent radii for elements 1–118
,” Chem. - Eur. J.
15
, 186
–197
(2009a
).63.
P.
Pyykkö
and M.
Atsumi
, “Molecular double-bond covalent radii for elements Li–E112
,” Chem. - Eur. J.
15
, 12770
–12779
(2009b
).64.
P.
Pyykkö
, S.
Riedel
, and M.
Patzschke
, “Triple-bond covalent radii
,” Chem. - Eur. J.
11
, 3511
–3520
(2005
).65.
T.
Yang
, X.
Zhao
, and E.
Osawa
, “Can a metal–metal bond hop in the fullerene cage?
,” Chem. - Eur. J.
17
, 10230
(2011
).66.
H.
Zheng
, H.
Dang
, Y.
Zhao
, Y.-X.
Gu
, M.
Li
, Q.-Z.
Li
, and X.
Zhao
, “Theoretical investigations of Lu2C84: Unexpected impact of metal electronic configuration toward the metal–metal σ-bond in fullerene
,” Inorg. Chem.
59
, 10113
–10122
(2020
).67.
K.
Zhang
, H.
Zheng
, M.
Li
, Q.-z.
Li
, Y.
Zhao
, and X.
Zhao
, “Significant roles of a particularly stable two-center two-electron Lu–Lu σ bond in Lu2@C86: Electronic structure of Lu and radius of Lu2+
,” Inorg. Chem.
60
, 2425
–2436
(2021
).68.
K. B.
Wiberg
, “Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane
,” Tetrahedron
24
, 1083
–1096
(1968
).69.
A. A.
Popov
, S. M.
Avdoshenko
, A. M.
Pendás
, and L.
Dunsch
, “Bonding between strongly repulsive metal atoms: An oxymoron made real in a confined space of endohedral metallofullerenes
,” Chem. Commun.
48
, 8031
–8050
(2012
).70.
K.
Kobayashi
and S.
Nagase
, “Bonding features in endohedral metallofullerenes. Topological analysis of the electron density distribution
,” Chem. Phys. Lett.
302
, 312
–316
(1999
).71.
A. A.
Popov
and L.
Dunsch
, “Bonding in endohedral metallofullerenes as studied by quantum theory of atoms in molecules
,” Chem. - Eur. J.
15
, 9707
–9729
(2009
).72.
P.
Macchi
and A.
Sironi
, “Chemical bonding in transition metal carbonyl clusters: Complementary analysis of theoretical and experimental electron densities
,” Coord. Chem. Rev.
238–239
, 383
–412
(2003
).73.
E.
Espinosa
, I.
Alkorta
, J.
Elguero
, and E.
Molins
, “From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H⋯F–Y systems
,” J. Chem. Phys.
117
, 5529
–5542
(2002
).74.
Q.
Wang
, S.
Pan
, Y. B.
Wu
, G.
Deng
, J. H.
Bian
, G.
Wang
, L.
Zhao
, M.
Zhou
, and G.
Frenking
, “Transition-metal chemistry of alkaline-earth elements: The trisbenzene complexes M(Bz)3 (M = Sr, Ba)
,” Angew. Chem., Int. Ed.
58
, 17365
(2019
).75.
X.
Wu
, L.
Zhao
, J.
Jin
, S.
Pan
, W.
Li
, X.
Jin
, G.
Wang
, M.
Zhou
, and G.
Frenking
, “Observation of alkaline earth complexes M(CO)8 (M = Ca, Sr, or Ba) that mimic transition metals
,” Science
361
, 912
–916
(2018
).76.
L.
Zhao
, S.
Pan
, M.
Zhou
, and G.
Frenking
, “Response to Comment on “Observation of alkaline earth complexes M(CO)8 (M = Ca, Sr, or Ba) that mimic transition metals”
,” Science
365
, 5021
(2019
).77.
T.
Yang
, D. M.
Andrada
, and G.
Frenking
, “Dative versus electron-sharing bonding in N-oxides and phosphane oxides R3EO and relative energies of the R2EOR isomers (E = N, P; R = H, F, Cl, Me, Ph). A theoretical study
,” Phys. Chem. Chem. Phys.
20
, 11856
–11866
(2018
).78.
H.
Umemoto
, K.
Ohashi
, T.
Inoue
, N.
Fukui
, T.
Sugai
, and H.
Shinohara
, “Synthesis and UHV-STM observation of the Td-symmetric Lu metallofullerene: Lu2@C76(Td)
,” Chem. Commun.
46
, 5653
(2010
).79.
Y.
Yang
, D.
Jia
, Y.-J.
Wang
, H.-J.
Zhai
, Y.
Man
, and S.-D.
Li
, “A universal mechanism of the planar boron rotors B11−, B13+, B15+, and B19−: Inner wheels rotating in pseudo-rotating outer bearings
,” Nanoscale
9
, 1443
–1448
(2017
).80.
S.
Pan
, M.
Ghara
, S.
Kar
, X.
Zarate
, G.
Merino
, and P. K.
Chattaraj
, “Noble gas encapsulated B40 cage
,” Phys. Chem. Chem. Phys.
20
, 1953
–1963
(2018
).81.
S.
Jalife
, L.
Liu
, S.
Pan
, J. L.
Cabellos
, E.
Osorio
, C.
Lu
, T.
Heine
, K. J.
Donald
, and G.
Merino
, “Dynamical behavior of boron clusters
,” Nanoscale
8
, 17639
–17644
(2016
).82.
J.
Zhang
, A. P.
Sergeeva
, M.
Sparta
, and A. N.
Alexandrova
, “B13+: A photodriven molecular Wankel engine
,” Angew. Chem., Int. Ed.
51
, 8512
–8515
(2012
).83.
M.
Khatua
, S.
Pan
, and P. K.
Chattaraj
, “Movement of Ng2 molecules confined in a C60 cage: An ab initio molecular dynamics study
,” Chem. Phys. Lett.
610–611
, 351
–356
(2014
).84.
M.
Khatua
, S.
Pan
, and P. K.
Chattaraj
, “Confinement of (HF)2 in Cn (n = 60, 70, 80, 90) cages
,” Chem. Phys. Lett.
616–617
, 49
–54
(2014
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.