Supporting Information
Electronic Structures and Nonlinear Optical Properties of Highly
Deformed Halofullerenes C3v C60F18 and D3d C60Cl30
Shu-Wei Tang, Jing-Dong Feng, Yong-Qing Qiu, Hao Sun, Feng-Di Wang, Ying-Fei
Chang,* Rong-Shun Wang*
Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal
University, Changchun, Jilin 130024, People’ Republic of China
Correspondence to:
Y. F. Chang; e-mail: changyf299@nenu.edu.cn;
R. S. Wang; e-mail: wangrs@nenu.edu.cn
Fax/Tel: +86-431-85099511
S1
Contents
1. Figure S1. Schlegel diagram and B3LYP/6-31G(d) optimized structures of C60X18
(X=H, F, and Cl) molecules…………………………………………………..Page S3
2. Table S1. Computationally predicted C-C and C-X bond lengths [Å] for C60X18
(X=H, F, and Cl) on the B3LYP/6-31G(d) optimized geometries…………...Page S4
3. Table S2. The HOMO-LUMO energy gaps (Egap, eV) and NICS values (ppm) of
C60X18 (X=H, F, and Cl) calculated at B3LYP/6-31G(d) level……................Page S6
4. Table
S3.
Static
linear
polarizability

(in
Å3),
and
second-order
hyperpolarizability   (in 10-36 esu) for C60, and C60X18 (X=H, F, and
Cl)…………………………………………………………………………… Page S8
References………………………………………………………………………..Page S9
S2
Section 1:
Figure S1. Schlegel diagram and B3LYP/6-31G(d) optimized structures of C60X18
(X=H, F, and Cl) molecules.
S3
We have calculated all the C-C and C-X bond lengths of C60X18 (X=H, F, and Cl)
molecules on the geometries optimized at B3LYP/6-31G(d) level, as listed in Table S1.
The corresponding Schlegel diagram which illustrates the different types of carbon
atoms and C-C bonds is shown in Figure S1. As can be seen in Table S1, changing the
X atom species of C60X18 molecules from H to Cl have significantly elongated the
C(sp3)-C(sp3) bond lengths, whereas the other C-C bonds are almost unaffected. As a
consequence, the frameworks of fullerene moieties in C60X18 (X=H, F, and Cl)
molecules show nearly the same structures. The largest deviations of C(sp2)-C(sp2),
C(sp2)-C(sp3) and C(sp3)-C(sp3) bonds are 0.008 Å, 0.009 Å and 0.099 Å, respectively.
Moreover, the C(sp2)-C(sp3) bonds (b, f, i, l and n) in C60X18 are longer than the sp2-sp2
C-C bonds (a’ and a’’, h, j, k, m, o, p, q, r and s), but substantially shorter than those of
sp3-sp3 type (c, d, e and g). The lengths four symmetrically independent C-X (α, β, γ and
δ) bonds are elongated with the order of C60H18, C60F18, and C60Cl18, with average
lengths of 1.097Å, 1.375Å, and 1.817Å, respectively.
Table S1. Computationally predicted C-C and C-X bond lengths [Å] for C60X18 (X=H,
F, and Cl) on the B3LYP/6-31G(d) optimized geometries.
Bond type
C60H18
C60F18
C60Cl18
a’, sp2-sp2, 6/6
1.378
1.377
1.386
a’’, sp2-sp2, 5/6
1.383
1.379
1.381
b, sp2-sp3, 5/6
1.489
1.483
1.487
c, sp3-sp3, 6/6
1.574
1.568
1.582
C-C
S4
d, sp3-sp3, 5/6
1.614
1.630
1.679
e, sp3-sp3, 5/6
1.644
1.674
1.743
f, sp2-sp3, 5/6
1.513
1.509
1.504
g, sp3-sp3, 6/6
1.563
1.573
1.599
h, sp2-sp2, 6/6
1.369
1.369
1.366
i, sp2-sp3, 5/6
1.530
1.529
1.523
j, sp2-sp2, 5/6
1.440
1.439
1.438
k, sp2-sp2, 5/6
1.433
1.432
1.430
l, sp2-sp3, 6/6
1.398
1.396
1.396
m, sp2-sp2, 5/6
1.437
1.437
1.436
n, sp2-sp3, 6/6
1.396
1.394
1.391
o, sp2-sp2, 5/6
1.453
1.453
1.454
p, sp2-sp2, 5/6
1.440
1.443
1.437
q, sp2-sp2, 5/6
1.448
1.447
1.446
r, sp2-sp2, 6/6
1.400
1.399
1.400
α
1.100
1.389
1.864
β
1.092
1.359
1.782
γ
1.099
1.378
1.818
δ
1.096
1.373
1.806
C (sp3)-X
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Section 2:
As previous works reported, the HOMO-LUMO gap of fullerene and their
derivatives is often correlated with the kinetic stability.1-3 Hence, Table S2 presents the
HOMO-LUMO energy gaps (Egap, eV) of C60X18 obtained at B3LYP/6-31G(d) level. It
can be seen from the Table S2 that all the C60X18 molecules possess large Egaps, ranging
from 3.49 to 3.62 eV, much larger than that of C60 (2.76 eV). Therefore, C60X18 should
be kinetically stable, especially for the case of C60F18.
The NICS values (ppm) for depicting the aromaticity of C60X18 molecules are
calculated using GIAO-B3LYP/6-31G(d) method and also listed in Table S2. The
C60H18 and C60Cl18 also possess larger aromatic stabilization energies, just like the case
of C60F18, which are as evidenced by the negative NICS values. This phenomenon can
be explained by the strong delocalization effects of the remaining π system in these
molecules. However, the values decrease generally with the order of C60H18 > C60F18 >
C60Cl18.
Table S2. The HOMO-LUMO energy gaps (Egap, eV) and NICS values (ppm) of C60X18
(X=H, F, and Cl) calculated at B3LYP/6-31G(d) level.
C60H18
C60F18
C60Cl18
Egap
3.49
3.62
3.50
NICS
-13.50
-15.09
-15.40
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Section 3:
Table S3 displays the values of  and  tensor components of C60X18 (X=H, F,
and Cl) molecules obtained by PBEPBE/6-31G(d)//B3LYP/6-31G(d) method, as well as
the corresponding values of C60 for comparison. As can be seen from Table S3, owing
to the highly molecular symmetry (Ih) of electron distribution in C60, the values of
diagonal components of  are essentially equivalent, which indicate the strong isotropy
character. While in the cases of C60X18, the distributions of π electron density are
destroyed in consequence of the structure changes deriving from the X atom
attachments. However, as different types of X (X=H, F, and Cl) atoms attached to C60,
the structural changes and distribution of π electron density in C60X18 are appreciably
different, although they have the same C3v point group. The tensor components of
 xx and  yy in C60X18 are approximate to each other and larger than those of  zz . The
  values increase with the order of C60H18 < C60F18 < C60Cl18. The tensor components
of  in C60F18 and C60Cl18 (  xxxx =  yyyy >  zzzz ) are very similar to the situation of  ,
especially for the case of C60Cl18. However, the corresponding values in C60H18
completely contradict with those of C60F18 and C60Cl18. The  xxxx =  yyyy are smaller with
respect to  zzzz . The main reason may be that H atom possesses smaller electronegativity
in comparison with C atom, while F and Cl atoms have larger electronegativity than C
atom, and thus lead to sharply reverse electron transfer. Meanwhile, due to the C-Cl
bond lengths in C60Cl18 are much longer than the counterparts in C60H18 and C60F18,
which represents the highly deformed structure change, resulting in the large secondorder hyperpolarizability.
S7
Table S3. Static linear polarizability   (in Å3), and second-order hyperpolarizability
  (in 10-36 esu) for C60, and C60X18 (X=H, F, and Cl).
Polarizability
C60
C60H18
C60F18
C60Cl18
 xx
70.9
78.8
81.4
120.6
 yy
70.9
78.8
81.4
120.6
 zz
70.9
68.2
69.7
97.4
 
70.9
75.3
77.5
112.9
 xxxx
13.8
15.5
30.4
137.2
 yyyy
13.8
15.5
30.4
137.2
 zzzz
13.8
21.5
23.5
64.2
 
13.9
27.9
25.5
108.7
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References
1. Aihara, J. I. Theor Chem Acc 1999, 102, 134.
2. Aihara, J. I. Chem Phys Lett 2001, 343, 465.
3. Tang, C.; Deng, K.; Tan, W.; Yuan, Y.; Liu, Y.; Wu, H.; Huang, D.; Hu, F.; Yang,
J.; Wang, X. Phys Rev A 2007, 76, 013201.
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