C
Journal of
Carbon Research
Article
DFT Study on the Interaction of the Smallest
Fullerene C20 with Lithium Ions and Atoms
Hiroshi Kawabata * and Hiroto Tachikawa
Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan;
[email protected]
* Correspondence: [email protected]
Academic Editor: Tomoya Takada
Received: 28 March 2017; Accepted: 28 April 2017; Published: 10 May 2017
Abstract: The smallest fullerene C20 with positive electron affinity is considered to be a new organic
nano-electronic material. The binding structures and electronic states of lithium ions and atoms
(Li+ and Li) trapped on the surface of C20 have been investigated by means of density functional
theory (DFT) calculation to elucidate the nature of their interaction. It was found that a Li+ can bind
to only one site of C20 . This is, specifically, on top of the site where Li+ binds to the carbon atom of
C20 . On the other hand, in the case of a Li atom, two structures were obtained besides the on-top
structure. One was pentagonal structure which included a Li atom on a five-membered ring of C20 .
The other was a triangular structure in which the Li atom bind to the the carbon–carbon bond of C20 .
Finally, the nature of the interactions between Li ions or atoms and the C20 cluster was discussed on
the basis of theoretical results.
Keywords: C20 fullerene; alkali metal; organic electronic materials; binding energy; transition state;
diffusion mechanism; density functional theory
1. Introduction
Currently, the diameter of the thinnest carbon nanotube synthesized is 4 Å, and its tip is expected
to have a structure similar to that of a C20 fullerene [1]. It has been reported by photoelectron
spectroscopy that C20 is predicted to be the smallest fullerene that is synthesized from vapor growth,
and that its electron affinity is positive [2,3]. Its structure is very simple and highly symmetrical,
consisting of 12 five-membered rings only. Its diameter is about 4 Å, which is less than half of that of
C60 fullerene. It is also known to form one-dimensional chains, the key to a controlled structure, via
vapor deposition using an arc plasma gun [4]. C20 and its derivatives are considered to be not only new
n-type materials, but also ultimate organic nanomaterials capable of controlling size and orientation.
In order to utilize this organic molecule as an electronic material, knowledge of fundamental
physical properties as to how its electronic state is changed by doping is very important. The interaction
of C60 with alkali metal is investigated by various methods such as spectroscopy and electrochemical
methods [5–10]. In particular, superconductivity is reported to occur in systems doped with K
atoms [10]. It is also well known that alkali metal-doped nanostructures are promising for technical
applications such as gas storage and the mobilization of small organic molecules [11,12]. For these
reasons, it is important to know the exact structure and electronic properties of the systems interacting
with alkali metals. We are particularly interested in chemical stability, reactivity of C20 , and the
change of electronic state by doping. However, basic data on the doping state of C20 is rarely found in
experimental research as well as in theoretical research.
Recently, we studied the structures and electronic states of alkyl and hydroxyl radical
functionalized C20 fullerene [13,14]. We also studied the binding structures and electronic states
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sodium ions and atoms trapped on the surface of C20 [15]. However, the interaction between C20 and
sodium
andas
atoms
on themechanisms
surface of Chave
However,
the interaction
+ ions
20 [15].
Liof
or Liions
atoms,
well trapped
as its reaction
never
been studied
so far. between C20
andTachikawa
Li+ ions or theoretically
Li atoms, as well
as
its
reaction
mechanisms
have
never
been
studied
far. of C60
+
investigated the diffusion dynamics of an Li ion on the so
surface
+
Tachikawa
theoretically
investigated
the diffusion
dynamics
an Li
ion on states
the surface
of Li
C+60
fullerene
by the direct
dynamics
method [16,17].
This study
revealedoftwo
transition
(TSs) of
fullerene
by
the
direct
dynamics
method
[16,17].
This
study
revealed
two
transition
states
(TSs)
+
ion diffusion. It also revealed that a Li ion diffuses along the node faces of the highest occupiedof
Li+ ion diffusion.
It also revealed
that graphene
a Li+ ion diffuses
the node
faces of thebetween
highest occupied
molecular
orbital (HOMO)
of C60 and
[17,18]. along
However,
the interaction
C20 and
molecular
orbital
(HOMO)
of
C
and
graphene
[17,18].
However,
the
interaction
between
C20
and
60
other alkali metals, the transition states of the reaction, and the migration path on the surface
have
other
alkali
metals,
the
transition
states
of
the
reaction,
and
the
migration
path
on
the
surface
have
not
not yet been elucidated.
yet been
elucidated.
In this
study, the interactions of Li+ ions and Li atoms with C20 were investigated by means of
In
this
study,theory
the interactions
of Li+their
ions binding
and Li atoms
with
density functional
(DFT) to clarify
site and
TS.C20 were investigated by means of
density functional theory (DFT) to clarify their binding site and TS.
2. Results and Discussion
2. Results and Discussion
2.1. C20–Li+ +
2.1. C20 –Li
2.1.1.
20–Li+ System
+
2.1.1.Optimized
OptimizedStructure
Structureofofthe
theCC
20 –Li System
The
20–Li+ were
fully optimized at the CAM-B3LYP level. The structure
+
Thestructures
structuresofofCC2020and
andCC
20 –Li were fully optimized at the CAM-B3LYP level. The structure
+ was
obtained
is
illustrated
Figure
1.
The
only
stable
structure
ofof
C20
the on-top structure with a
+
obtained is illustrated Figure 1. The only stable
structure
C–Li
20 –Li was the on-top structure with
+ ion is
Lia+ Li
ion
on C0.
In
the
pentagonal
structure
where
a
Li
on
the
carbon
five-membered
ring, there
+ ion
+
on C0. In the pentagonal structure where a Li ion is on the carbon
five-membered
ring,
was
a
vibration
mode
of
the
imaginary
part.
Thus,
it
was
not
a
stationary
point
in
this
system.
The
there was a vibration mode of the imaginary part. Thus, it was not a stationary point in this system.
distance
R1 between
C0 and
Li ofLithe
on-top
structure
waswas
2.055
Å, Å,
and
thethe
angle
The distance
R1 between
C0 and
of the
on-top
structure
2.055
and
angleθ1θ1ofof<C1–C0–Li
<C1–C0–Li
was
121
degrees
(Table
1).
The
Li–C0
stretching
mode
(ν
C0–Li+) was calculated to be 399 cm−1
was 121 degrees (Table 1). The Li–C0 stretching mode (νC0–Li+ ) was calculated to be 399 cm−.1In
. Inour
our
previous
research,
the
hexagonal
structure
and
pentagonal
structure
were
more
stable
than
the
onprevious research, the hexagonal structure and pentagonal structure were more stable than the on-top
+ [16]. In addition, it is known that the Li+
+
top
structure
60–Li
+ [16].
structure
in in
C60C–Li
In addition, it is known that the Li ion
ion on
on graphene
graphenehas
hasaahexagonal
hexagonal
+
structure.
The
on-top
structure
is
a
structure
unique
to
C
20–Li , +which seems to be related to the
structure. The on-top structure is a structure unique to C20 –Li , which seems to be related to the
curvature
curvatureofofCC20. .
20
Figure
level.
Figure1.
1.Optimized
Optimizedstructure
structureof
ofCC2020–Li
–Li+ +calculated
calculatedatatthe
theCAM-B3LYP/6-311+G(d)
CAM-B3LYP/6-311+G(d)
level.
Table
Table1.1.Optimized
Optimizedstructural
structuralparameters,
parameters,natural
naturalpopulation
populationanalysis
analysis(NPA)
(NPA)atomic
atomiccharge
chargeon
onC0
C0
+,+and binding energies of Li+ +
20 calculated
at
several
levels
of
theory.
Zero
point
energy
and
andLiLi
, and binding energies of Li totoCC
calculated
at
several
levels
of
theory.
Zero
point
energy
20
corrected
correctedvalues
valuesare
areininparentheses.
parentheses.
Method
Method
Structural Parameter
Structural Parameter
NPA Atomic Charge
NPA Atomic Charge Ebind (a)/kcal
−1 −1
molmol
Ebind (a) /kcal
−1
◦
◦
−
1
R1/Å
/cm/cm C0 C0
Li+Li+
θ1/ θ2/°
θ2/ νC0–Li+
νC0–Li+
R1/Å R2/Å
R2/Å θ1/°
CAM-B3LYP/6-311G(d)
2.0548 3.1288 121.0 24.7 399
CAM-B3LYP/6-311G(d)
2.0548
3.1288 121.0 24.7 399
CAM-B3LYP/6-311+G(d) 2.0547 3.1293 121.0 24.7 399
−0.630
−0.630
−0.621
0.957
0.957
0.955
43.24 (41.31)
43.24
(41.31)
42.36 (40.40)
(a) The energy of the Li
+ ion binding
+ ) − [ E(C42.36
+ )]. Here,
CAM-B3LYP/6-311+G(d)
2.0547
3.1293 to C
121.0
24.7
399 by −Ebind
−0.621
0.955
(40.40)
) is defined
= E(C20 –Li
20 (Ebind
20 ) + E(Li
E(C20 –Li+ ) represents the total energy of the Li+ ion added to C20 , E(C20 ) represents that of the free C20 molecule,
+ ) represents that
(a)and
of the
free Li+to
ion,
respectively.
TheE(Li
energy
of the Li+ ion
binding
C20
(Ebind) is defined by −Ebind = E(C20–Li+) − [ E(C20) + E(Li+)].
Here, E(C20–Li+) represents the total energy of the Li+ ion added to C20, E(C20) represents that of the
+ ion, respectively. +
molecule,
and E(Li+) represents
that of the
free Licharges
free
TheC20natural
population
analysis (NPA)
atomic
on the Li ion and C0 were +0.955
and −0.621, respectively. These results imply that the Li+ ion and+ C0 atom have a positive and
The natural population analysis (NPA) atomic charges on the Li ion and C0 were +0.955 and
−0.621, respectively. These results imply that the Li+ ion and C0 atom have a positive and a negative
C 2017, 3, 15
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a charge,
negativerespectively.
charge, respectively.
The bond
C0–Liisbond
is polarized.
The binding
energy
calculated
The C0–Li
polarized.
The binding
energy
waswas
calculated
to to
bebe42
1 . This energy is significantly larger than the binding energy for the C –Li
+ system [16].
−1.−This
+ system
42kcal·mol
kcal·mol
energy is significantly larger than the binding energy for the C60–Li
[16].
The
60
+
−
1
+
−1
The
binding
energy
on-top
structure
was
about
kcal·mol
, and
it was
found
binding
energy
of of
thethe
on-top
structure
ofof
C60C–Li
was
about
30 30
kcal·mol
, and
it was
found
thatthat
C20–
60 –Li
+ produces a stronger bond than C +–Li+ .
+ produces
CLi
–Li
a
stronger
bond
than
C
60
–Li
.
20
60
+
2.1.2.
2020and
2.1.2.Electronic
ElectronicStructures
StructuresofofPure
PureCC
andCC2020–Li
–Li+
Figure
Figure2 2shows
showsthe
thehighest
highestoccupied
occupiedmolecular
molecularorbital
orbital(HOMO)
(HOMO)and
andthe
thelowest
lowestunoccupied
unoccupied
+ . When doping with Li
+ ions, the electronic state of
molecular
orbital
(LUMO)
of
C
and
C
–Li
+
+
molecular orbital (LUMO) of C2020 and C20
20–Li . When doping with Li ions, the electronic state of C20
+
Cchanges
drastically.
Themolecular
molecularorbital
orbitalisisspread
spread between
between C0
C0 and
20 changes
drastically.
The
and Li
Li+ at
at HOMO.
HOMO.The
Theenergy
energy
difference
between
the
HOMO
and
LUMO
orbitals
of
C
is
4.2
eV,
that
is,
C
acts
as
an
insulator.
20
20
difference between the HOMO and LUMO orbitals of C20 is 4.2 eV, that is, C20 acts as an insulator.
+
Using
ofof
C20
–Li
2020
Usingthe
theoptimized
optimizedstructure
structure
C20and
andCC
–Li+, ,the
thevertical
verticalexcitation
excitationenergies
energieswere
werecalculated
calculatedby
by
+
TD-CAMB3LYP/6-311+G(d).
first excitation
excitation energies
energies (S
(S11))of
ofCC2020and
andCC
were
3.01
+ were
20 –Li
TD-CAMB3LYP/6-311+G(d). The
The first
20–Li
3.01
eV eV
andand
1.48
+ at HOMO.
1.48
respectively.
These
results
mean
that
a charge
transfer
occurs
between
and
eV,eV,
respectively.
These
results
mean
that
a charge
transfer
occurs
between
C20C20
and
Li+Liat HOMO.
+ calculated at the CAM-B3LYP/6-311+G(d) level.
Figure
2. Molecular
orbitals
of C
C C–Li
Figure
2. Molecular
orbitals
of20Cand
20 and 20
20–Li+ calculated at the CAM-B3LYP/6-311+G(d) level.
+ ion. Tothe
The
states
of Cof
be changed
by the by
doping
of the Li+ofion.
electronic
Theelectronic
electronic
states
C20 will
be changed
the doping
theTo
Lielucidate
elucidate
the
20 will
+ system.
states
of thestates
binding
site,binding
natural site,
bondnatural
orbitalbond
(NBO)
analysis
wasanalysis
carried out
the Cout
–Li
electronic
of the
orbital
(NBO)
wasfor
carried
for
the
C
20–
20
+
The
NBO
of
the
C0–C1
bond
of
pure
C
was
expressed
by:
Li system. The NBO of the C0–C1 bond
20 of pure C20 was expressed by:
σC0–C1 = 0.701 (sp2.03)C0 + 0.713 (sp2.03)C1
σC0-C1 = 0.701 (sp2.03 )C0 + 0.713 (sp2.03 )C1
where, C0 and C1 indicate the carbon atom in the addition center and the neighbor-positioned carbon
where,
and C1 indicate the carbon atom in the addition center and the neighbor-positioned carbon
atom, C0
respectively.
atom, respectively.
After the Li+ ion doping to C20, the NBO was changed to be:
After the Li+ ion doping to C20 , the NBO was changed to be:
σC0–C1 = 0.690 (sp2.72)C0 + 0.724 (sp2.05)C1
2.72
= 0.690
(spatom
)C0in+the
0.724
(sp2.05site
)C1(C0) takes an electronic state of
C0-C1the
Before the doping of Li+σion,
carbon
doping
2.03
2.72
sp . After the doping, the+state was changed to sp . This result indicates that the carbon atom (C0)
Before the doping of Li ion, the carbon atom in the doping site (C0) takes an electronic state of
is2.03
changed from sp2 to sp3.
sp . After the doping, the state was changed to sp2.72 . This result indicates that the carbon atom (C0)
2 to sp3 .
is2.1.3.
changed
from spState
Transition
of C20–Li+ and the Movement Path of the Li Ion on the Surface of C20
+ and
2.1.3. Transition
State ofthe
C20structure
–Li+ and the
Movement
Path
of the
the its
Surface
of C
Figure 3 shows
of the
transition
state
of Li
C20Ion
–Lion
energy
diagram.
The
20
structure of the transition state was found to be a triangular+ structure with the Li+ ion on the C–C
Figure 3 shows the structure of the transition state of C20 –Li and its energy diagram. The structure
bond (Table 2). Intrinsic reaction coordinate (IRC) analysis was performed,
and it was confirmed that
of the transition state was found to be a triangular structure with the Li+ ion on the C–C bond (Table 2).
+
the Li ion migrated from C0 (RC, reactant) onto the adjacent carbon (C1) (PD, product) via the
triangular structure as the transition state. Its activation energy (Eact) is as high as about 12 kcal·mol-1. The
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Intrinsic reaction coordinate (IRC) analysis was performed, and it was confirmed that the Li+ ion
migrated
C 2017, 3, 15from C0 (RC, reactant) onto the adjacent carbon (C1) (PD, product) via the triangular structure
4 of 8
as the transition state. Its activation energy (Eact ) is as high as about 12 kcal·mol-1 . The structure of
structure
of the
transition
in+which
the Li+onto
ion diffuses
onto
C60 is alsostructure.
a triangular
structure.
the
transition
state
in whichstate
the Li
ion diffuses
C60 is also
a triangular
However,
its
−1 . In
−1. Inthe
However,energy
its activation
energy
is less
4 other
kcal·mol
other
words, the
movement
ofthe
thesurface
Li+ ion
activation
is less than
4 kcal
·molthan
words,
movement
of the
Li+ ion on
+ ionthat
+ ion
onCthe
of C20alternation.
is like a bond
alternation.
It cannot
the Liby
diffuses by heat.
of
like a bond
It cannot
be said
that thebe
Lisaid
diffuses
heat.
20 issurface
+ ion
+ ion
Figure 3.
3. Energy
migration
reaction
on the
of C20ofcalculated
at the at
CAMFigure
Energydiagram
diagramofofLiLi
migration
reaction
on surface
the surface
C20 calculated
the
CAM-B3LYP/6-311+G(d)
B3LYP/6-311+G(d) level. level.
Table2.2. Structural
Structural parameters
parameters of
of the
the transition
transition state
stateand
andactivation
activationenergies
energies(E(E
act in
inkcal
kcal·mol
Table
·mol–1–1))
act
calculatedat
atseveral
severallevels
levelsof
oftheory.
theory.Zero
Zeropoint
pointenergy
energycorrected
correctedvalues
valuesare
areininparentheses.
parentheses.
calculated
SystemSystem
Structural Parameter
Structural Parameter
R1/Å R1/ÅR3/ÅR3/Å
θ1/◦
θ2/◦
θ1/° θ2/°
CAM-B3LYP/6-311G(d)
2.2856
1.4347
71.7
36.6
CAM-B3LYP/6-311G(d)
CAM-B3LYP/6-311+G(d)
2.28842.2856
1.4352
1.4347 71.7
71.7 36.5
36.6
2.2. C20 –Li CAM-B3LYP/6-311+G(d)
2.2884
1.4352
71.7
36.5
–1
–1
act /kcal·mol
/kcal·mol
EactE
/cm–1
νν
/cm
C0–Li+
C0–Li+
–1
399 i
400i i
399
11.94 (11.34)
11.88
(11.31)
11.94
(11.34)
400 i
11.88 (11.31)
2.2.1. Optimized Structure of C20 –Li
2.2. C20–Li
The structures of C20 –Li optimized at the CAM-B3LYP/6-311+G(d) level are illustrated in Figure 4.
Three
foundofinCC20–Li,
an on-top structure where the Li atom is located on the carbon
2.2.1. structures
Optimizedwere
Structure
20–Li
atom, a triangular structure where the Li atom binds to the center of the C–C bond (triangle), and a
The structures of C20–Li optimized at the CAM-B3LYP/6-311+G(d) level are illustrated in Figure
pentagonal structure where the Li atom is located in the center of the five-membered ring (pentagon).
4. Three structures were found in C20–Li, an on-top structure where the Li atom is located on the
There was no vibration mode of the imaginary part. That is, the structures are stationary points,
carbon atom, a triangular structure where the Li atom binds to the center of the C–C bond (triangle),
respectively. Very interestingly, the triangular structure, which was in the transition state of C20 –Li+ ,
and a pentagonal structure where the Li atom is located in the center of the five-membered ring
was the most stable in C20 –Li. This means that the movement path of the Li+ ion and Li atom on the
(pentagon). There was no vibration mode of the imaginary part. That is, the structures are stationary
surface of C20 can be controlled by an electric charge.
points, respectively. Very interestingly, the triangular structure, which was in the transition state of
The C0–Li distance of C20 –Li of the on-top structure is about 0.1 Å shorter than that of C20 –Li+ .
C20–Li+, was the most stable in C20–Li. This means that the movement path of the Li+ ion and
Li atom
In the triangular structure, the C0–Li distance is about 0.3 Å shorter than that of C20 –Li+ . In other
on the surface of C20 can be controlled by an electric charge.
words, C20 –Li formed in the on-top structure and triangular structure is thought to have larger binding
The C0–Li distance of C20–Li of the on-top structure is about 0.1 Å shorter than that of C20–Li+. In
energy and charge transfer than C20 –Li+ .
the triangular structure, the C0–Li distance is about 0.3 Å shorter than that of C20–Li+. In other words,
C20–Li formed in the on-top structure and triangular structure is thought to have larger binding
energy and charge transfer than C20–Li+.
C 2017, 3, 15
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Figure 4.4. Optimized
Optimizedstructures
structuresofofCC2020
–Lisystem;
system;onontop,
top,triangular,
triangular,and
andpentagonal
pentagonalstructures
structures
Figure
–Li
calculated
at
the
CAM-B3LYP/6-311+G(d).
In
parentheses,
values
were
calculated
at
the
CAM-B3LYP/
calculated at the CAM-B3LYP/6-311+G(d). In parentheses, values were calculated at the CAM6-311G(d) level. The
bond
and angles
are in Å
in and
degrees,
respectively.
B3LYP/6-311G(d)
level.
Thedistances
bond distances
and angles
areand
in Å
in degrees,
respectively.
The
and
NPA
atomic
charge
of each
atomatom
of C20of
–LiCcalculated
at the CAMThebinding
bindingenergy
energy
and
NPA
atomic
charge
of each
at the
20 –Li calculated
B3LYP/6-311+G(d)
level
are
provided
in
Table
3.
The
NPA
atomic
charge
of
the
Li
atom
in
the
on-top,
CAM-B3LYP/6-311+G(d) level are provided in Table 3. The NPA atomic charge of the Li atom
the
triangular,
the pentagonal
sites
were +0.934,
+0.869,
and +0.823,
respectively.
in the
on-top, and
the triangular,
and the
pentagonal
sites
were +0.934,
+0.869,
and +0.823, respectively.
Table
Table3.3. Binding
Bindingenergies
energiesof
ofLi
Lito
toCC2020, ,and
andNPA
NPAatomic
atomiccharges
chargesof
ofCC2020, ,C0,
C0,and
andLiLicalculated
calculatedatatthe
the
CAM-B3LYP/6-311+G(d)
level.
Zero
point
energy
corrected
values
are
in
parentheses.
CAM-B3LYP/6-311+G(d) level. Zero point energy corrected values are in parentheses.
System
System
On-top
On-top
Triangle
Pentagonal
(b)
Triangle
(b)/kcal
Ebind(b)
/kcal·mol
Ebind
·mol−−11
49.42 (49.32)
49.42
(49.32)
52.96
(52.85)
46.89 (47.95)
52.96 (52.85)
NPA
Atomic Charge
NPA Atomic Charge
Part
C(0)
Part
ofofCC
2020
C(0)
–0.934
–0.934
–0.869
–0.823
–0.869
–0.662
–0.662
Li Li
+0.934
+0.934
+0.869
+0.823
+0.869
The energy of the Li atom binding to C20 (Ebind ) is defined by −Ebind = E(C20 –Li) − [E(C20 ) + E(Li)]. Here,
E(C20 –Li) represents the total energy of the Li atom added to C20 , E(C20 ) represents that of the free C20 molecule,
Pentagonal 46.89 (47.95)
–0.823
+0.823
and E(Li) represents that of the free Li atom, respectively.
The energy of the Li atom binding to C20 (Ebind) is defined by −Ebind = E(C20–Li) − [E(C20) + E(Li)].
In allE(C
structures,
it can be
seen
the charge
C20 is
changed
negative
due tothat
the of
addition
of
20–Li) represents
the
totalthat
energy
of the Liofatom
added
to C20to
, E(C
20) represents
the
Here,
the Li
atom,
indicating
that
charge
transfer
occurs
from
Li
to
C
.
The
magnitude
of
the
dipole
moment
free C20 molecule, and E(Li) represents that of the free Li atom, respectively.
20
(b)
is 11.3 D, 7.2 D, and 6.7 D in each of the on-top, triangular, and pentagonal structures, which is related
In all structures, it can be seen that the charge of C20 is changed to negative due to the addition
to the charge transfer amount.
of the Li atom, indicating that charge transfer occurs from Li to C20. The magnitude
of the dipole
The binding energy between C20 and the Li atom was 49.42 kcal mol−1 for on-top structure,
moment is 11.3−D,
7.2
D,
and
6.7
D
in
each
of
the
on-top,
triangular,
and
pentagonal
structures,
which
52.96 kcal mol 1 for triangular structure, and 46.89 kcal mol−1 for pentagonal structure. These binding
is related to the charge transfer−1amount.
energies are 4.5–10.6 kcal mol greater than that of C20 –Li+ . This is due −1to the fact C20 –Li produces a
The binding energy between C20 and the Li atom was 49.42 kcal mol for on-top structure, 52.96
strong charge transfer to C20 rather than C20 –Li+ .
kcal mol−1 for triangular structure, and 46.89 kcal mol−1 for pentagonal structure. These binding+
The electronic states of C20 were changed by the doping of Li atoms as well as that of C20 –Li .
energies are 4.5–10.6 kcal mol−1 greater than that of C20–Li+. This is due to the fact C20–Li produces a
To elucidate the electronic states of the interaction
site, natural bond orbital (NBO) analysis was carried
strong charge transfer to C20 rather than C20–Li+.
out for the C20 –Li system. The NBO of the C0–C1 bond of C20 –Li was expressed by:
The electronic states of C20 were changed by the doping of Li atoms as well as that of C20–Li+. To
elucidate the electronic states
of the
site,
analysis was carried
2.72
σC0-C1
(oninteraction
top) = 0.695
(spnatural
)C0 +bond
0.719orbital
(sp2.06 )(NBO)
C1
out for the C20–Li system. The NBO of the C0–C1 bond of C20–Li was expressed by:
C 2017, 3, 15
6 of 8
C 2017, 3, 15
6 of 8
σC0–C1 (on top) = 0.695 (sp2.72)C0 + 0.719 (sp2.06)C1
σC0–C1(triangle)
(triangle)==0.707
0.707(sp
(sp3.13 ))C0 ++0.707
)C1)
σC0-C1
0.707(sp
(sp3.13
C0
C1
2.14
2.15
σC0–C1 (pentagonal) = 0.707 (sp )C0 + 0.708 (sp )C1
σC0-C1 (pentagonal) = 0.707 (sp2.14 )C0 + 0.708 (sp2.15 )C1
where, C0 and C1 are carbon atoms of C20 (see Figure 4). After the doping, the electronic states of the
where, C0 and C1 are carbon atoms of C20 (see Figure 4). After the doping, the electronic states of the
on-top and triangular structures were drastically changed. These results indicate that the electronic
on-top and triangular structures were drastically changed. These results indicate that the electronic
state in the carbon atom (C0) is changed from sp22 to sp33. In contrast, the hybridization of C0 was
state in the carbon atom (C0) is changed from sp to sp . In contrast, the hybridization of C0 was
hardly changed in the pentagonal structure. It seems that, in this case, the interaction of the Li–C
hardly changed in the pentagonal structure. It seems that, in this case, the interaction of the Li–C bond
bond was spread into five carbon atoms.
was spread into five carbon atoms.
3.13
3.13
2.2.2.
–Li and the Movement Path of the Li atom on the Surface of C20
2.2.2. Transition
Transition State
State of
of C
C20
20 –Li and the Movement Path of the Li atom on the Surface of C20
Figure
the transition
transition state
state and
and energy
energy diagram
diagram of
of C
C20–Li.
When the
Figure 55 shows
shows the
the structures
structures of
of the
20 –Li. When the
position
position of
of the
the Li
Li atom
atom changes
changes from
from the
the on-top
on-top site
site and
and pentagonal
pentagonal site
site to
to the
the triangular
triangular site,
site, itit turns
turns
out
that
there
is
one
transition
state
in
each.
The
transition
state
when
changing
from
out that there is one transition state in each. The transition state when changing from the
the on-top
on-top
structure
tothe
thetriangular
triangular
structure
is TS-1,
and
the transition
state
when changing
from the
structure to
structure
is TS-1,
and the
transition
state when
changing
from the pentagonal
pentagonal
to the
triangular
structure
is TS-2.
each hasmode
a vibrational
mode of
structure to structure
the triangular
structure
is TS-2.
TS-1 and
TS-2TS-1
eachand
hasTS-2
a vibrational
of one imaginary
one
imaginary
part.
IRC
confirmed
that
the
on-top
structure
and
the
pentagonal
structure
are
part. IRC confirmed that the on-top structure and the pentagonal structure are triangular structures
triangular
structures
via
TS-1
and
TS-2,
respectively.
via TS-1 and TS-2, respectively.
Figure 5.
5. Energy
Energydiagram
diagramand
andstructures
structures
transition
state
of20–Li
C20 –Li
system
calculated
at
Figure
of of
thethe
transition
state
of C
system
calculated
at the
the
CAM-B3LYP/6-311+G(d)
level.
In
parentheses
are
the
values
calculated
at
the
CAM-B3LYP/
CAM-B3LYP/6-311+G(d) level. In parentheses are the values calculated at the CAM-B3LYP/6-311G(d)
6-311G(d) level.
level.
Table
Table 54 shows the activation energies (Eact
and the
the vibrational
vibrational frequencies
frequencies for
for the
the imaginary
imaginary
act)) and
modes.
mode
of of
thethe
imaginary
part,
respectively.
BothBoth
Eact of
TS-1
and
modes. TS-1
TS-1and
andTS-2
TS-2have
haveone
onevibration
vibration
mode
imaginary
part,
respectively.
Eact
of TS-1
−1 . was
TS-2
werewere
less than
1 kcal·mol
. This
smaller
than than
that of
theofEthe
act of
theofCthe
20–Li
. This
and TS-2
less than
1 kcal·−1mol
Thissignificantly
was significantly
smaller
that
Eact
C+20
–Li+ .
means
that the
structure
andand
the the
pentagonal
structures
areare
easily
This means
thaton-top
the on-top
structure
pentagonal
structures
easilychanged
changedtotothe
thetriangular
triangular
−1
−
1
structure
is 6.1
6.1 kcal
kcal mol
mol more
structure by
by thermal activation. However, the triangular structure is
more stable
stable than
than
the
unlikely
that
thethe
Li Li
atom
willwill
diffuse
thethe
surface
of Cof
20 C
via
the pentagonal
pentagonalstructure.
structure.Therefore,
Therefore,it itis is
unlikely
that
atom
diffuse
surface
20
TS-2.
via TS-2.
Table 5. The activation energies (Eact in kcal mol−1) and imaginary frequencies (νi in cm−1) of TS-1 and
TS-2 in the C20–Li system calculated at the CAM-B3LYP/6-311+G(d) level. In parentheses, values were
calculated at the CAM-B3LYP/6-311G(d) level.
C 2017, 3, 15
7 of 8
Table 4. The activation energies (Eact in kcal mol−1 ) and imaginary frequencies (νi in cm−1 ) of TS-1
and TS-2 in the C20 –Li system calculated at the CAM-B3LYP/6-311+G(d) level. In parentheses, values
were calculated at the CAM-B3LYP/6-311G(d) level.
State
Eact /kcal mol−1
νi /cm−1
TS-1
TS-2
0.65 (0.55)
0.04 (0.12)
252 i (182 i)
110 i (120 i)
On the other hand, the difference in heat of formation between the triangular structure and the
on-top structure is 3.5 kcal mol−1 . The activation energy for Li+ ions to diffuse onto the surface of C60
is ca. 4 kcal mol−1 [16]. Thus, there is a possibility that the Li atom diffuses its surface along the C–C
bond of C20 .
3. Method of Calculation
All hybrid DFT calculations were carried out using the Gaussian 09 program package [19].
Clusters of C20 and Li+ ions or Li atoms were examined. All calculations performed in this study are
only Γ points. The structures and electronic states of C20 , C20 –Li+ (denoted by C20 –Li+ ), and C20 –Li
atom (denoted by C20 –Li) were calculated using the CAM-B3LYP functional, which produces accurate
results for long-range interactions, and these results were combined with several basis sets [20–23].
Calculations on C20 and C20 –Li+ were performed using the RCAM-B3LYP functional. Since C20 –Li
is an open shell, the calculation was made using the UCAM-B3LYP functional. The geometries of all
systems were fully optimized at the CAM-B3LYP/6-311G(d) and CAM-B3LYP/6-311+G(d) levels of
theory. The convergence criterion of SCF (self-consistent field) was set to 10− 7 . These levels of theory
have given reasonable electronic structures of C20 –Li+ and C20 –Li systems [13–15,24,25]. All of the
geometries studied here were characterized as stationary or transition states by analytically vibrational
frequency calculation.
Furthermore, each transition state was checked to be connected to the initial state and the final
state by IRC analysis.
4. Conclusions
In this study, the interaction between C20 and Li+ ions and Li atoms were investigated by density
functional theory. The only stable structure of C20 –Li+ is the on-top structure, where the Li+ ion is on
top of the carbon atom of C20 . The Li+ ion migrates to an adjacent carbon atom through a triangular
structure consisting of C–C and Li+ . Its activation energy is 12 kcal·mol−1 , and the migration of the Li+
ion is due to coupling substitution. On the other hand, C20 –Li has three structures: the on-top structure,
triangular structure, and pentagonal structure. The most stable is the triangular structure, while the
other two are metastable. The activation energy from on-top structure and pentagonal structure to the
triangular structure is smaller than 1 kcal·mol−1 . From the magnitude of the relative energy of each
structure, it was revealed that the Li atom diffuses with heat along the C–C bond of C20 .
Acknowledgments: The author acknowledges partial support from JSPS KAKENHI Grant Number 15K05371
and MEXT KAKENHI Grant Number 25108004.
Author Contributions: Hiroshi Kawabata and Hiroto Tachikawa designed this study and wrote the paper; All of
the computer experiments and analyses were conducted by Hiroshi Kawabata.
Conflicts of Interest: The authors declare no conflict of interest.
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