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This car-bon-doped aluminum cluster dianion exhibits a squared planar shape with a central carbon D4h.. The CX4 systems X = Si, Ge in different charge states from 2 to +2 We first conside

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Planar tetracoordinate carbon stabilized by heavier congener

cages: The Si 9 C and Ge 9 C clusters

Nguyen Minh Tama,c, Vu Thi Nganb,⇑, Minh Tho Nguyenc,⇑

a

Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Viet Nam

b

Faculty of Chemistry, Quy Nhon University, Quy Nhon, Viet Nam

c

Department of Chemistry, University of Leuven, B-3001 Leuven, Belgium

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 tetracoordi-nate 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 X4frame together with single bonds along C–X bonds, the larger neutral CSi9and CGe9clusters enjoy combined stabilization from both electronic effect and geometrical constraint of the X9cages In CX9, an additional electrostatic interaction reinforces stabiliza-tion within the CX4moiety in maintaining the ptC configuration

Ó 2014 Elsevier B.V All rights reserved

1 Introduction

There has been a persistent fascination of chemists with

com-pounds containing planar tetracoordinate carbon (ptC) [1] We

would refer to numerous review articles[2–9] for extended

ac-counts of theoretical and experimental efforts performed during

the last four decades aimed at identifying and preparing the

sys-tems 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

com-pounds have been prepared successfully in laboratory and

charac-terized 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

deriva-tives [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

conse-quence 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

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 tetra-hedral 3D shape

The pentaatomic dianion [CAl4]2is a well known representa-tive of the second class, which was experimentally identified having a typical structural unit in salt complexes[22] This car-bon-doped aluminum cluster dianion exhibits a squared planar shape with a central carbon (D4h) A number of derivatives of [CAl4]2in which Al atoms are replaced by isoelectronic or iso-valent 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 nano-ribbons 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 sta-bility 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

http://dx.doi.org/10.1016/j.cplett.2014.02.015

0009-2614/Ó 2014 Elsevier B.V All rights reserved.

⇑Corresponding authors Fax: +32 16 32 79 92 (M.T Nguyen).

E-mail addresses: vuthingan@qnu.edu.vn (V.T Ngan), minh.nguyen@chem.

kuleuven.be (M.T Nguyen).

Contents lists available atScienceDirect Chemical Physics Letters

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / c p l e t t

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examined in mixed pentaatomic clusters such as CAl3Si- [19],

CSi2Ga2 [21] etc but the corresponding isoelectronic C-doped

silicon cluster CSi2þ4 has not been investigated yet We recently

demonstrated that it is possible to encapsulate a carbon dication

at the center of a silicon cube[27] In the resulting CSi2þ8 cube 1,

the carbon element is obviously multi-coordinated However this

cube can also be regarded as formed by a diagonal CSi2þ

4 unit which contains a ptC, and is in the mean time stabilized by two

Si2ligands

2-In this context, it also appears possible to stabilize further the

dica-tion CSi2þ4 by interacting it with another stable counterion such as

the Si25 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]2 leads to a

neutral C-doped silicon CSi9cluster In this Letter, we aim to

dem-onstrate that in the CSi9cluster 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 CGe9clusters 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

deter-mine the molecular geometries of the CX2þ4 and CX9clusters, with

X = Si and Ge, in order to identify the dopant as having a ptC

con-figuration 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

pop-ular 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]

Cal-culations are carried out using theGAUSSIAN09 package[41]

Geom-etries 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

calcula-tions of the structures located are performed using the B3LYP

func-tional 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]

3 Results and discussion 3.1 The (CX4) systems (X = Si, Ge) in different charge states from 2 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

CSi4

2-D 4h, 1 A 1g , 1.79

(4 imag Freq.)

C 2v, 1 A 1

CSi4

-D 2h, 2 B 1g , 1.52

(3 imag Freq.)

C 2v, 2 A 1

CSi4

D 2h, 1 A 1g , 1.68

(2 imag Freq.)

C 3v, 1 A 1

CSi4 +

D 2h, 2 B 2g , 0.26

(3 imag Freq.)

C 2v, 2 B 1

CSi4 2+

D 4h, 1 A 1g (ground state)

Figure 1 Shape and identity of (CSi 4 ) 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

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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

out-of-plane movement, the other corresponds to an in-plane

move-ment In the electron shell model, the electron configuration of this

fragment including 20 valence electrons is described as follows:

CSi4: 1S21P4

x;y2S21D21P2

z 2P21D22P21D21D0

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 8rbonds

including 4 Si–Si bonds and 4 C–Si bonds The twop-character

orbi-tals (fully occupied by 4 electrons) are not symmetrically

distrib-uted, 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

the CSi4(D2h), the resulting radical cation CSiþ

4 remain non-planar (C2vshape,Figure 1) The planar ion is characterized by 3 imaginary

frequencies Further removal of one electron from the 1D orbital

leads to a planar CSi2þ4 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

fea-tures can be found for the analogous CGe4systems 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

Each of the dications CSi2þ4 and CGe2þ

4 has 18 valence electrons with the electron shell configuration h1S21P4x;y2S21D2

1P2

z 2P4

x;y1D2

 Occupation of the HOMO orbital in CSi4(1D

charac-ter,Figure 2) thus tends to push the carbon atom out of the plane

It has been found that the Al4Canion, which possesses 17

va-lence 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

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 CSi4system in differ-ent charge states (Figure 1) point out that the systems having more than 18 electrons CSi 24 ;CSi4;CSi4;CSiþ4

are not planar.Figure 3

displays a comparison of the HOMOs of the dications CX2þ4 with

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 basi-cally differ from that of the C2þ5 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 li-gand–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 dis-plays the total and partial densities of states (DOS) of the ground state of CSi2þ4 (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 mole-cules and atomic clusters [48,49] to further probe the chemical

O M O HOMO-4

Figure 2 Plot of the HOMOs of the neutral CSi 4 cluster.

Figure 3 A comparison of HOMOs of squared planar dications CX 2þ

4 with X = C, Si and Ge (B3LYP/6-311+G(d)) The C 2þ

5 dication (D 4h ) is a stationary point with two imaginary

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

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

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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

localization function (ELF) of the dication CSi2þ4 The electrons are largely delocalized over the entire structure of the dication CSi2þ4 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, Fig-ure 5) This imply that the stability of the dication as the global minimum, and thereby the ptC characteristic, is significantly con-tributed 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 the CSi2þ4 and CGe2þ4 dications

3.2 Some larger C-doped clusters Let us now consider some larger doped clusters.Figure 6 dis-plays the shapes and relative energies of the global minima and the ptC structures of the CSi26 and CSi2þ6 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 structure of the CSi2

6 dianion that looks like a part of the cube con-taining two fragments (Si2–Si4C) lies 1.84 eV higher than the ground state In the dication, the ptC-containing structure corre-sponds rather to an interaction between C2+with two Si3moieties (Figure 6) and is only 0.66 eV higher in energy than its ground state Note that the CSi2þ8 dication 1 which was analyzed in detail

in a previous study[27], has a centro-cubic form with a multi-coor-dinate carbon center A similar picture emerges for the correspond-ing Ge derivatives

We are now going to examine even larger cluster, CX9 As men-tioned above, this size can formally be generated upon interaction

of an ion pair CSih 2þ4 þ Si25 i

Fusing the squared planar dication CSi2þ4 with the dianion Si25 whose shape is shown in 2 (D3h, see above) on a face leads to the global minimum structure of the neu-tral CSi9isomer shown inFigure 7 Extensive geometry search also leads to a similar shape for the CGe9cluster While CGe9is charac-terized by a high symmetry (C4v), the Si counterpart is slightly dis-torted (Cs) Both clusters have the shape of tetragonal antiprism with the Si atom or Ge atom capping on one tetraatomic face

Figure 5 Plot of the electron localization function of the dication CSi 2þ

4 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)).

CSi6

2-1A1, 0.0 1A1, 1.84

CSi6 2+

1A1, 0.0 1A1g, 0.66

Figure 6 Some lower-lying isomers of CSi 2

6 and CSi 2þ

6 : (a) global minimum and (b) ptC containing structure Relative energies given in eV are obtained from the B3LYP/

6-311+G(d) computations.

CSi9 (Cs,1A’) CGe9 (C4v,1A1)

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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

calcu-lated 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 CX4moiety in both clusters and 0.15 for the X5moiety

Therefore, upon fusing the CX2þ

4 dication and X2

5 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 CX2þ4 clusters as the

NBO charges of the ptC center in CSi2þ4 and CGe2þ4 are 2.52 and 2.39

electrons, respectively However, the CX9 clusters enjoy further

geometrical constraint stabilization upon fusing

Figure 8shows a plot of the electron localization function of

CSi9at 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

not much different from those of the CSi2þ

4 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 CX9neutrals, with X = Si and

Ge, using quantum chemical computations In all cases, a planar

tet-racoordinate carbon atom is found in the lowest-lying isomer of the

cluster In the small dications, the driving force for the

C-planariza-tion includes not only the electron delocalizaC-planariza-tion on the square

frame as found before but also the bonding between dopant and

the frame In the larger neutral cluster cages, the X5group tends to

stabilize the cage by large electron transfer in maintaining a ptC

con-figuration 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

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 Re-search Council for continuing support (GOA and IDO programs) References

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Figure 8 Plot of the ELF of the neutral CSi 9 at the bifurcation ELF = 0.82

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

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