CPL 2014 planar c

Chemical Physics Letters 595-596 (2014) 272–276

Contents lists available at ScienceDirect

Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett

Planar tetracoordinate carbon stabilized by heavier congener
cages: The Si9C and Ge9C clusters
Nguyen Minh Tam a,c, Vu Thi Ngan b,⇑, Minh Tho Nguyen c,⇑
a

Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Viet Nam
Faculty of Chemistry, Quy Nhon University, Quy Nhon, Viet Nam
c
Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium
b

a r t i c l e

i n f o

Article history:
Received 3 December 2013
In final form 7 February 2014
Available online 15 February 2014

a b s t r a c t
Using quantum chemical computations and analysis of electron distribution (MO, DOS, ELF) we showed
that in some carbon-doped silicon and germanium clusters, it is possible to achieve a planar tetracoordinate carbon with enhanced stability. While the driving force for C-planarization in the square dications
CX2þ

4 (with X = Si, Ge) is electron delocalization on X4 frame together with single bonds along C–X bonds,
the larger neutral CSi9 and CGe9 clusters enjoy combined stabilization from both electronic effect and
geometrical constraint of the X9 cages. In CX9, an additional electrostatic interaction reinforces stabilization within the CX4 moiety in maintaining the ptC configuration.
Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction
There has been a persistent fascination of chemists with compounds containing planar tetracoordinate carbon (ptC) [1]. We
would refer to numerous review articles [2–9] for extended accounts of theoretical and experimental efforts performed during
the last four decades aimed at identifying and preparing the systems that involve a ptC center. Although this type of compounds
is nowadays no longer regarded as an exotic and unusual feature
of hydrocarbons [4] or organometallic compounds [3] but becomes
a real structural alternative, only a limited number of ptC compounds have been prepared successfully in laboratory and characterized spectroscopically [2,5,6].
Two main ptC classes have been known so far. The first are
hydrocarbon derivatives (fenestranes [6] and fenestrindanes
[10], spironpentadiene analogues [11], and other cyclic derivatives [12]. . .) that contain unusually strained centrotetracyclic
frameworks bearing a ptC atom at the central position [4]. The
second class includes small binary clusters in which the atomic
carbon acts as a dopant of a cluster of another element [13–21].
The emergence of both classes can be understood as a consequence of two different approaches in stabilizing a ptC center.
In the mechanical approach, a ptC could be achieved by structural
constraints forcing the central carbon atom, for example of a

⇑ Corresponding authors. Fax: +32 16 32 79 92 (M.T. Nguyen).
E-mail addresses: (V.T. Ngan), minh.nguyen@chem.
kuleuven.be (M.T. Nguyen).
/>0009-2614/Ó 2014 Elsevier B.V. All rights reserved.

fenestrane derivative, to be planar. In the electronic approach,
strong effects of electron delocalization within the cluster could
end up favouring a ptC configuration over a more classical tetrahedral 3D shape.

The pentaatomic dianion [CAl4]2À is a well known representative of the second class, which was experimentally identified
having a typical structural unit in salt complexes [22]. This carbon-doped aluminum cluster dianion exhibits a squared planar
shape with a central carbon (D4h). A number of derivatives of
[CAl4]2À in which Al atoms are replaced by isoelectronic or isovalent elements (B, Si+, Ge+, Ga, In, Tl. . .) also feature a ptC
[23–26]. A common view on the stability of these pentaatomic
clusters is that each contains 18 valence electrons completing
the orbital shell formed by the highest occupied orbitals [11]
that arise from four-center peripheral ligand–ligand interactions
[12].
Recently, interest in stable ptC-containing clusters emerges in
a different direction, as they could be potentially used as building
blocks for assemblies forming new nanomaterials. As for an
example, the presence of ptC in metal-terminated graphene nanoribbons was suggested to enhance their third-order nonlinear
optical response [27]. In the course of our continuing theoretical
and experimental studies on silicon clusters [28–37], we realize
that it is possible to design small ptC clusters with enhanced stability by combining both mechanical and electronic stabilizing
factors. In fact we find that the clusters of heavier congeners of
carbon including silicon and germanium could lead us to such
an achievement. As far as we are aware, Si has been up to now


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examined in mixed pentaatomic clusters such as CAl3Si- [19],
CSi2Ga2 [21] etc. . . but the corresponding isoelectronic C-doped
2þ
silicon cluster CSi4 has not been investigated yet. We recently
demonstrated that it is possible to encapsulate a carbon dication

2þ
at the center of a silicon cube [27]. In the resulting CSi8 cube 1,
the carbon element is obviously multi-coordinated. However this
2þ
cube can also be regarded as formed by a diagonal CSi4 unit
which contains a ptC, and is in the mean time stabilized by two
Si2 ligands.

3. Results and discussion
3.1. The (CX4) systems (X = Si, Ge) in different charge states from À2 to
+2
We first consider the structures of the (CSi4) system. Figure 1
summarizes some geometrical characteristics of (CSi4) in different
charged states, ranging from the dianion to the dication. In the first
series of structure (A), the species is constrained in a planar form

(A)

(B)

D4h, 1A1g, 1.79
(4 imag. Freq.)

C2v, 1A1

D2h, 2B1g, 1.52
(3 imag. Freq.)

C2v, 2A1

D2h, 1A1g, 1.68
(2 imag. Freq.)

C3v, 1A1

D2h, 2B2g, 0.26
(3 imag. Freq.)

C2v, 2B1

CSi42-

1 CSi 82+

2 Si 52-

In this context, it also appears possible to stabilize further the dica2þ
tion CSi4 by interacting it with another stable counterion such as
2À
the Si5 dianion 2. As a matter of fact, the latter is well known as
a Zintl ion characterized by high stability in different solid state
salts [38,39]. Interaction of the ion pair [CSi4]2+[Si5]2À leads to a
neutral C-doped silicon CSi9 cluster. In this Letter, we aim to demonstrate that in the CSi9 cluster a ptC center is stabilized further
within a silicon cage. Extending this design we also consider the
derivatives of the heavier germanium congener, namely the
CGe2þ
4 and CGe9 clusters. This finding is meaningful as a series of
small mixed silicon carbide clusters SinCm (n + m = 6) has just been
generated in the gas phase and been characterized by free electron
laser IR technique [40].

The purpose of the present study is twofold. The first is to determine the molecular geometries of the CX2þ
4 and CX9 clusters, with
X = Si and Ge, in order to identify the dopant as having a ptC configuration. The second aim is to rationalize the chemical bonding of
these C-doped clusters.

2. Computational Methods
To tackle the first aim, we use DFT computations with the popular hybrid B3LYP functional which is among the most common
choice to access the geometrical and electronic structures of Si
clusters that do not contain transition metal elements [28,29]. Calculations are carried out using the GAUSSIAN 09 package [41]. Geometries of the small neutral SinC with n = 2–19 have been reported
using an empirical molecular dynamics method [42]. We carry
out additional searches for possible lower-lying isomers of each
of the considered CX9 sizes using a stochastic search algorithm
[43,44]. Geometry optimizations and harmonic vibrational calculations of the structures located are performed using the B3LYP functional in conjunction with the 6-311+G(d) basis set. Relative
energies between some low-energy isomers are further improved
using the composite G4 approach [45] which also uses B3LYP
geometries but with the 6-31+G(2df) basis set. For the analysis of
the electronic distribution and chemical bonding, we make use of
the density of states and the electron localization function (ELF)
approach [46].

CSi4-

CSi4

CSi4+

CSi42+

D4h, 1A1g (ground state)
Figure 1. Shape and identity of (CSi4) structures in different charged states: (A)

constrained planar forms; ‘imag. Freq.’ stands for imaginary frequency; relative
energies given in eV are obtained at the G4 level with respect to the corresponding
global minimum; and (B) the optimized global minimum structures of the
corresponding species.


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N.M. Tam et al. / Chemical Physics Letters 595-596 (2014) 272–276

HOMO-4

HOMO

Figure 2. Plot of the HOMOs of the neutral CSi4 cluster.

with high symmetry point group. In the second series (B), the
shape of the optimized global minimum is given. Their relative
energies are evaluated by using the G4 approach.
The planar neutral CSi4 (D2h) exhibits 2 imaginary frequencies
(Figure 1). While one imaginary vibrational mode shows an outof-plane movement, the other corresponds to an in-plane movement. In the electron shell model, the electron configuration of this
fragment including 20 valence electrons is described as follows:

h
i
CSi4 : 1S2 1P4x;y 2S2 1D2 1P2z 2P2 1D2 2P2 1D2 1D0
where both the HOMO (1D) and HOMO-4 (1Pz) have molecular
plane as their nodal plane (Figure 2). The remaining 16 electrons
distributed on the molecular plane are describing the 8 r bonds
including 4 Si–Si bonds and 4 C–Si bonds. The two p-character orbitals (fully occupied by 4 electrons) are not symmetrically distributed, thus the squared planar CSi4 turns out to be an energy

second-order saddle point. Some other factors thus need to be
introduced to stabilize this squared plane.
Upon removal of the one electron on the HOMO-1D orbital of
þ
the CSi4 (D2h), the resulting radical cation CSi4 remain non-planar
(C2v shape, Figure 1). The planar ion is characterized by 3 imaginary
frequencies. Further removal of one electron from the 1D orbital
2þ
leads to a planar CSi4 dication. Our calculations point out that
the squared planar D4h structure is the true global minimum of
the dication (Figure 1). The Si–Si and C–Si bond distances amount
to 2.67 and 1.89 Å, respectively (B3LYP/6-311+G(d)). Similar features can be found for the analogous CGe4 systems. In its ground
state, the dication CGe2þ
4 exhibits a squared planar shape (D4h) with
the longer Ge–Ge (2.83 Å) and C–Ge (2.01 Å) bond distances.
2þ
Each of the dications CSi4 and CGe2þ
4 has 18hvalence electrons
with the electron shell configuration
1S2 1P4x;y 2S2 1D2
1P2z 2P4x;y 1D2 Š. Occupation of the HOMO orbital in CSi4 (1D character, Figure 2) thus tends to push the carbon atom out of the plane.
It has been found that the Al4CÀ anion, which possesses 17 valence electrons, has a nearly-planar tetracoordinate carbon [47].
The propensity of 17 and 18 valence electron pentaatomic systems
to achieve planarity can be understood by considering of the
HOMO (noted as the 1D orbital in the electron shell model), which

HOMO of C52+

Figure 4. Total and partial densities of states of the ground state of the dication
2þ

CSi4 (B3LYP/6-311+G(d)).

is a bonding orbital with respect to ligand–ligand interactions and
thus plays the key role in maintaining the planarity of the whole
system.
Indeed, our minimum explorations for the CSi4 system in different charge states (Figure 1) point out that the systems having more


2À
À
þ
than 18 electrons CSi4 ; CSi4 ; CSi4 ; CSi4 are not planar. Figure 3
displays a comparison of the HOMOs of the dications CX2þ
with
4
X = C, Si and Ge in the planar shape. It is clear that the HOMOs of
both Si and Ge derivatives are similar to each other, and they basically differ from that of the C2þ
5 dication. In the former, the central
ptC atom interacts with the all four-atomic framework so that the
dications can be stable in a high symmetrical form while that is not
the case for the latter. This confirms the important role of the ligand–ligand interaction for the planarity [42].
However, the factors stabilize the two considered dication in
squared planar form need to be investigated further. Figure 4 displays the total and partial densities of states (DOS) of the ground
2þ
state of CSi4 (B3LYP/6-311+G(d)). This plot shows a clear picture
of electron shells and the large HOMO–LUMO gap which indicates
a stable species.
It also emphasizes the contributions of different atomic orbitals
to the molecular orbitals. We also use the electron localization
function (ELF) [41] which is an effective indicator to evaluate the

electron distribution of molecules, including novel organic molecules and atomic clusters [48,49] to further probe the chemical

HOMO of CSi42+

HOMO of CGe42+

2þ
Figure 3. A comparison of HOMOs of squared planar dications CX2þ
4 with X = C, Si and Ge (B3LYP/6-311+G(d)). The C5 dication (D4h) is a stationary point with two imaginary
frequencies.


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N.M. Tam et al. / Chemical Physics Letters 595-596 (2014) 272–276
2þ

2þ

Figure 5. Plot of the electron localization function of the dication CSi4 at the
bifurcation ELF = 0.82. The values stand for the average integrated numbers of
electrons (e) in the corresponding C–Si and Si lone pair basins (B3LYP/6-311 +G(d)).

localization function (ELF) of the dication CSi4 . The electrons are
2þ
largely delocalized over the entire structure of the dication CSi4
with a high bifurcation value of the ELF isosurface. Note that a
complete separation of basins is only observed at ELFp = 0.90
which is the value of ELFp = 0.91 of benzene.
Integration of the electron densities of different basins points

out that the electrons are localized within the C–Si bonds and
around the Si atoms. While the C–Si basins correspond well to
single bond (1.8 electrons), the Si lone pair regions have a larger
concentration of electrons (2.6 electrons on each Si lone pair, Figure 5). This imply that the stability of the dication as the global
minimum, and thereby the ptC characteristic, is significantly contributed by C-Si bonding. Therefore, besides the ligand–ligand
interaction as found in previous studies [42], the center-ligand
bonds also play important role in maintaining the planarity in
2þ

the CSi4 and CGe2þ
4 dications.
3.2. Some larger C-doped clusters

(a)

(b)

Let us now consider some larger doped clusters. Figure 6 displays the shapes and relative energies of the global minima and
2À

2þ

the ptC structures of the CSi6 and CSi6 systems. In each of the
doubly charged species, a local minimum structure having a ptC
atom has been located but is calculated to lie higher in energy than
the corresponding lowest-lying isomer. We found that the ptC

CSi62-

2À

1

1

A1, 0.0

A1, 1.84

structure of the CSi6 dianion that looks like a part of the cube containing two fragments (Si2–Si4C) lies 1.84 eV higher than the
ground state. In the dication, the ptC-containing structure corresponds rather to an interaction between C2+ with two Si3 moieties
(Figure 6) and is only 0.66 eV higher in energy than its ground
2þ

CSi62+
1

1

A1, 0.0

A1g, 0.66

2À

2þ

Figure 6. Some lower-lying isomers of CSi6 and CSi6 : (a) global minimum and (b)
ptC containing structure. Relative energies given in eV are obtained from the B3LYP/
6-311+G(d) computations.

bonding of these systems. A topological analysis of the ELF shows
that a structure whose ELF isosurface has high bifurcation value
is aromatic, whereas a structure possessing low bifurcation value
is not aromatic. Figure 5 displays the plots of the electron

CSi9 (Cs, 1A’)

state. Note that the CSi8 dication 1 which was analyzed in detail
in a previous study [27], has a centro-cubic form with a multi-coordinate carbon center. A similar picture emerges for the corresponding Ge derivatives.
We are now going to examine even larger cluster, CX9. As mentioned above, this size can formally be generated upon interaction
h
i
2þ
2À
of an ion pair CSi4 þ Si5 . Fusing the squared planar dication
2þ

2À

CSi4 with the dianion Si5 whose shape is shown in 2 (D3h, see
above) on a face leads to the global minimum structure of the neutral CSi9 isomer shown in Figure 7. Extensive geometry search also
leads to a similar shape for the CGe9 cluster. While CGe9 is characterized by a high symmetry (C4v), the Si counterpart is slightly distorted (Cs). Both clusters have the shape of tetragonal antiprism
with the Si atom or Ge atom capping on one tetraatomic face

CGe9 (C4v, 1A1)

Figure 7. Lowest-lying structures of CSi9 and CGe9. Selected bond distances given in Å are obtained from the B3LYP/6-311+G(d) computations.

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N.M. Tam et al. / Chemical Physics Letters 595-596 (2014) 272–276

No. 104.06-2013.06. N.M.T. thanks ICST for a leave of absence
and the Department of Science and Technology of Ho Chi Minh
City, Vietnam, for support. M.T.N. is indebted to the KU Leuven Research Council for continuing support (GOA and IDO programs).
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
Figure 8. Plot of the ELF of the neutral CSi9 at the bifurcation ELF = 0.82 (B3LYP/6311+G(d)).

and the C atom trapped in the center of the other tetraatomic face
(Figure 7).
In order to investigate charge effect, the NBO charges are calculated at the B3LYP/6-311+G(d) level. The carbon dopant has large
negative charges of 1.85 and 1.69 electrons for CSi9 and CGe9,
respectively. On the squared plane, the Si atoms have a positive
charge of 0.5 electrons and the Ge atoms have a positive charge
of 0.46 electrons. Thus, a net charge of +0.15 electrons is computed
for the CX4 moiety in both clusters and À0.15 for the X5 moiety.

2À
Therefore, upon fusing the CX2þ
4 dication and X5 dianion, a large
charge transfer (1.85 electrons) occurs from the dianion to the
dication. A certain electrostatic attraction between the ptC atom
and the heavier congeners is apparently induced within each plane
rather than with the rest of the cage. The electrostatic attraction in
the large clusters is comparable to that in the CX2þ
4 clusters as the
2þ
NBO charges of the ptC center in CSi4 and CGe2þ
4 are 2.52 and 2.39
electrons, respectively. However, the CX9 clusters enjoy further
geometrical constraint stabilization upon fusing.
Figure 8 shows a plot of the electron localization function of
CSi9 at the bifurcation ELF = 0.82. The average integrated electron
population of each of the Si atoms on the ptC-containing face is
2.6 electrons, and 1.6 electrons on each Si–C bond. The values are
2þ
not much different from those of the CSi4 dication shown above
(Figure 5).
4. Concluding remarks
In summary, we have investigated the geometrical and electronic
structure of the CX2þ
4 dications and the CX9 neutrals, with X = Si and
Ge, using quantum chemical computations. In all cases, a planar tetracoordinate carbon atom is found in the lowest-lying isomer of the
cluster. In the small dications, the driving force for the C-planarization includes not only the electron delocalization on the square
frame as found before but also the bonding between dopant and
the frame. In the larger neutral cluster cages, the X5 group tends to
stabilize the cage by large electron transfer in maintaining a ptC configuration. Overall, it appears possible to achieve a stabilized planar

tetracoordinate carbon within a relatively small neutral Si or Ge
cluster thanking both electronic and mechanical effects.
Acknowledgments
V.T.N. work is funded by the Vietnam National Foundation for
Science and Technology Development (NAFOSTED) under Grant

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