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 December 2013 In final form 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 (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 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: vuthingan@qnu.edu.vn (V.T Ngan), minh.nguyen@chem kuleuven.be (M.T Nguyen) http://dx.doi.org/10.1016/j.cplett.2014.02.015 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 273 N.M Tam et al / Chemical Physics Letters 595-596 (2014) 272–276 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 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 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- CSi 82+ 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 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 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 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 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 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 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 274 N.M Tam et al / Chemical Physics Letters 595-596 (2014) 272–276 HOMO-4 HOMO Figure 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 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 r bonds including Si–Si bonds and C–Si bonds The two p-character orbitals (fully occupied by 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 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 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 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 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 displays a comparison of the HOMOs of the dications CX2þ 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 basically differ from that of the C2þ 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 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 A comparison of HOMOs of squared planar dications CX2þ with X = C, Si and Ge (B3LYP/6-311+G(d)) The C5 dication (D4h) is a stationary point with two imaginary frequencies 275 N.M Tam et al / Chemical Physics Letters 595-596 (2014) 272–276 2þ 2þ Figure 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 dications 3.2 Some larger C-doped clusters (a) (b) Let us now consider some larger doped clusters Figure 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 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 A1, 0.0 A1g, 0.66 2À 2þ Figure 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 displays the plots of the electron CSi9 (Cs, 1A’) state Note that the CSi8 dication 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 (D3h, see above) on a face leads to the global minimum structure of the neutral CSi9 isomer shown in Figure 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 Lowest-lying structures of CSi9 and CGe9 Selected bond distances given in Å are obtained from the B3LYP/6-311+G(d) computations 276 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 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 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 clusters as the 2þ NBO charges of the ptC center in CSi4 and CGe2þ are 2.52 and 2.39 electrons, respectively However, the CX9 clusters enjoy further geometrical constraint stabilization upon fusing Figure 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) Concluding remarks In summary, we have investigated the geometrical and electronic structure of the CX2þ 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 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