Vibrational spectra and structures of Si n C clusters ( n = 3 – 8 ) †

The effects of doping bare silicon clusters with carbon on their physical properties are of fundamental interest for the chemistry of the interstellar medium and the development of novel nanostructures in materials science. Carbon-doped silicon clusters (SinC, n = 3–8) are characterized in the gas phase with infrared-ultraviolet two-color ionization (IR-UV2CI) spectroscopy, mass spectrometry, and quantum chemical calculations. Structural identification is achieved by comparing the measured and calculated vibrational absorption spectra of the low-energy SinC isomers identified by global optimization algorithms. Except for planar Si3C, the most stable SinC clusters have three-dimensional configurations. While the Si3C and Si6C structures are uniquely assigned, several stable isomers of Si4C, Si5C, Si7C, and Si8C may co-exist under the present experimental conditions. Interestingly, some of the structures observed here are different from the ground state structures predicted previously. For the small neutral clusters (n r 5), structures similar to those reported previously for the anions are observed. The highly stable Si3C unit with a nearly linear Si–C–Si motif is identified as characteristic building block in several of the most stable SinC structures. In all identified structures, a large negative charge of almost 2e is located on the C atom, indicating its role as electron donor in the Sin host moiety. The B3LYP/cc-pVTZ level proves reliable in finding the experimentally observed isomers.


I. Introduction
Silicon-carbon based nanotubes, nanowires, and clusters are of great interest as promising building blocks for the synthesis of novel materials at the nanoscale. 13][4][5][6][7] Hence understanding the nature of Si-C bonding might, on the one hand, open a way toward engineering of such nanostructures at the atomic level.][10][11] Although located in the same main group of the periodic table, silicon and carbon exhibit very different physical and chemical properties.Silicon prefers multidirectional single bonds, while carbon can easily form single, double, and triple bonds.Generally, substituting a single Si atom with a C atom in a pure Si n cluster induces strong distortions, but the geometric topology maintains. 12,13When doped into silicon clusters, the C atom favors locations with more than threefold coordinated bonding in the ground state structures, making most Si n C m clusters more stable than their pure silicon counterparts. 13here have been numerous theoretical studies on siliconcarbon clusters.  For all-sized clusters, for example, the ground state structures and vibrational spectra of Si 3 C and Si 2 C 3 were determined using Hartree-Fock (HF) and second-order many body perturbation (MP2) theories. 14,15A clear trend of favorable geometries in the transition from pure carbon to pure silicon clusters was observed, i.e., the chain-like carbon-rich and three-dimensional silicon-rich clusters.This has also been observed for Si n C m (n + m r 8) cluster anions in both theory 32 and experiments. 12Most close to our work, two lowest-energy Si 4 C structures were found at the CCSD(T) level, i.e., the minimum trigonal C 3v pyramid and a distorted edge capped C 2v pyramid (about 21 kJ mol À1 higher). 33At the HF level, however, the latter structure lies about 8 kJ mol À1 lower than the former.Additional calculations of infrared (IR) spectra, isotopic shifts, and dipole moments indeed hinted at their coexistence. 33n contrast to theory, spectroscopic characterization of silicon-carbon clusters is largely lacking.Most previous studies have concentrated on charged clusters isolated in the gas phase or neutrals in an inert matrix.For instance, photoelectron (PE) spectra of Si n C m À (1 r n r 7, 1 r m r 5) cluster anions found a Institut fu ¨r Optik und Atomare Physik, Technische Universita ¨t Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany.E-mail: dopfer@physik.tu-berlin.deb Institut fu ¨r Physikalische Chemie, Georg-August-Universita ¨t Go ¨ttingen, that Si n C À (3 r n r 7) and their Si n+1 À counterparts have a similar topology. 12The PE spectrum of SiC 3 À shows electronic transitions, corresponding to both linear and cyclic forms. 34owever, no conclusion about the true global minimum on the SiC 3 potential energy surface could be drawn.With Fouriertransform infrared spectroscopy in Ar matrices combined with quantum chemical calculations, the molecular structures of small Si n C m (n + m r 5) clusters were determined, e.g., a linear centrosymmetric geometry for Si 2 C 3 and a rhomboidal C 2v structure for Si 3 C. [35][36][37][38] Furthermore, Si 3 C 2 is a pentagon, and Si 2 C 4 has a linear symmetric geometry in the ground state. 391][42][43] For small Si n C m clusters with n + m r 4, the electronic structure has been studied by resonant photoionization. 11,44,45In general, little spectroscopic information is available for somewhat larger Si-rich Si n C m clusters, which is the topic of the present work.Through recent advances in the generation of intense IR laser radiation, novel spectroscopic methods for neutral clusters in the gas phase have been developed, such as IRMPD (infrared multiple photon dissociation), 46,47 IR-REMPI (infrared resonance enhanced multiple photon ionization), 48 and IR-UV2CI (infraredultraviolet two-color ionization). 49While IR-REMPI spectra are often broadened due to the absorption of several hundred IR photons, the IR-UV2CI spectra can be better resolved and more closely related to the linear IR absorption spectra.Employing the IR-UV2CI technique for neutral Si n C m clusters, we recently observed the evolution from 3D to 1D chain-like configurations in Si n C 6Àn clusters by sequentially substituting Si with C atoms in pure Si 6 . 50In addition, the influence of first-row dopant atoms on the properties of bare silicon clusters (Si 6 X with X = Be, B, C, N, O) has been determined. 51As expected, the geometric and electronic properties of silicon containing clusters can substantially be modified by changing the dopant atom.
Here we identify the geometric and electronic structures of Si n C clusters with n = 3-8 via their IR-UV2CI spectra.Combining quantum chemical calculations with global optimization, 52,53 the low-energy Si n C isomers are determined.Structural identification is achieved through comparison of the measured IR-UV2CI spectra with the IR spectra predicted for the corresponding low-energy isomers.Results for Si 5 C and Si 6 C have been reported elsewhere, 50,51 but are included here with additional insights for completeness.Electronic properties and charge distributions of selected low-energy isomers will also be discussed.

II. Experimental and computational methods
The IR-UV2CI setup has been described elsewhere. 47,49,50Briefly, carbon-doped silicon clusters are produced by laser ablation of a pure silicon rod within a pulsed flow of He gas containing 1% CH 4 and thermalized to about 100 K in a liquid-nitrogen cooled expansion channel.After passing through a skimmer, the neutral Si n C m clusters are overlapped with counter-propagating IR radiation from the 'Free Electron Laser for Infrared eXperiments' (FELIX) 54 and then post-ionized by an unfocused F 2 laser (E F 2 = 7.87 eV) in the extraction zone of a reflectron time-of-flight mass spectrometer.For clusters of specific sizes, with an ionization energy (IE) close to E F 2 , prior resonant excitation with IR photons from a FELIX pulse raises the internal energy and thereby enhances the efficiency for ionization by the UV laser pulse that is about 30 ms delayed.Resonant excitation of a vibrational mode is followed by rapid internal vibrational energy redistribution, leading to complete thermalization on this experimental timescale.The ionization efficiency usually follows a S-curve behavior as a function of excitation energy, with a slope depending on the Franck-Condon factor for ionization.An increase of the internal energy of the cluster upon IR absorption therefore results in an enhancement of the ionization yield and its IR wavelength dependence closely reflects the linear vibrational absorption spectrum of the neutral cluster.The IR-UV2CI spectra in Fig. 1 are obtained from the relative ionization enhancement normalized by the IR photon flux. 55The observed widths of the bands of 15-45 cm À1 arise from a combination of unresolved rotational structure, sequence hot band transitions involving low-frequency modes, the FELIX bandwidth (ca.0.5-1% full width at half maximum (FWHM) of the central wavelength), and possibly the multiple photon absorption process.
Quantum chemical calculations are performed for both singlet and triplet states of each cluster.In an effort to thoroughly explore the complex potential energy surface of the cluster, we employ global optimization (GO) techniques such as the genetic (GA) and basin hopping (BH) algorithms. 56,57Details of our BH implementation have been given elsewhere. 51,52Basically, there are two major steps.First, up to five thousand candidate structures are evaluated in terms of the total energy by the GO coupled with DFT calculations at the RI-BP86/def-SVP level as implemented in TURBOMOLE V6.3.1. 58Second, the first twenty nonequivalent lowest-energy isomers are tightly re-optimized at the B3LYP/cc-pVTZ level including the Grimme dispersion correction (D3) 59 with the resolution-of-the-identity approximation as implemented in GAUSSIAN09. 60At this level, the linear IR absorption spectra, ionization and binding energies, and natural bond orbital (NBO) populations are obtained.To facilitate convenient comparison with the experimental spectra, the theoretical IR absorption stick spectra are convoluted with a 20 cm À1 FWHM Gaussian profile.The reported vibrational frequencies are unscaled.Similar calculations for selected clusters have been performed at the TPSS/cc-pVTZ and MP2/cc-pVTZ levels, which have also proven reliable for doped Si clusters. 47,49,50The vertical electronic transitions of selected Si n C clusters are calculated at the second-order approximate coupled cluster RI-CC2/def2-TZVP and TD-DFT/cc-pVTZ levels using TURBOMOLE V6.3.1. 58As the excited-state calculation for high-symmetry structures (e.g., C 3v , C 4v , and C 5v ) is not supported at the CC2 level, the C 1 point group is used for these clusters.

III. Results and discussion
The IR-UV2CI spectra measured for Si n C (n = 3-8), the linear IR absorption spectra and the geometries of the respective lowest-energy isomers calculated at the B3LYP/cc-pTVZ level are shown in Fig. 1-7.The computational spectra are all drawn to the same linear intensity scale for direct comparison.The relative energies, ionization and binding energies are listed in Tables 1 and 2, respectively.Vertical excitations (Table 3) of selected Si n C isomers are also provided.Natural bond orbital charges, vibrational and geometric data of all structures considered are available in Tables 1-3 in the ESI.† In the following discussion, the optimized structures obtained at the B3LYP level are used if not stated otherwise.
A. Vibrational spectra and geometries Si 3 C.The experimental IR-UV2CI spectrum of Si 3 C is compared in Fig. 2 with the linear absorption spectra calculated for the first three lowest-energy isomers 3a-3c.Three bands are observed at 509 (A), 651 (B), and 1080 cm À1 (C), which can readily be explained with structure 3a.In the investigated spectral range (350-1250 cm À1 ), 3a exhibits significant absorptions at 509 (a 1 ), 652 (a 1 ), and 1109 cm À1 (b 2 ), arising from the Si-C-Si symmetric stretching mode, the symmetric breathing mode, and the Si-C-Si asymmetric stretching mode, respectively.Our results are consistent with previous work based on Ar-matrix Fourier-transform IR spectroscopy combined with ab initio calculations 37 and excited-state measurements. 44,45In the former, five of the six vibrational fundamental frequencies (in cm À1 ) were determined as 309.5 (a 1 ), 357.6 (b 2 ), 511.8 (a 1 ), 658.2 (a 1 ), and 1101.4 (b 2 ).The shifts from the IR-UC2CI data are rather small and may be related to matrix effects and/or the multiphotonic IR excitation in the gas-phase experiments.
Structure 3a has been predicted as the ground state of Si 3 C. 13,14,22,61,62 While the ground state of neutral Si 4 has a D 2h ( 1 A g ) rhomboidal geometry, [63][64][65] 3a is a distorted rhombus (C 2v , 1 A 1 ) with shorter and stronger C-Si bonds and a nearly linear Si-C-Si bridge (+4Si-1C-2Si = 164.91).The calculated C-Si bond lengths of 1.764 and 1.944 Å are close to the previous results. 44The anion counterpart Si 3 C À has been concluded to be a distorted planar rhombus (C 2v , 2 A 2 ), due to the similarity between the PE spectra of Si 3 C À and Si 4 À . 11,12,61The good agreement observed between the measured and predicted frequencies of Si 3 C in Fig. 2 supports the use of the B3LYP/ cc-pVTZ level for the structural and vibrational assignment of the larger carbon-doped silicon clusters described below.The next two stable isomers 3b (C 2v , 3 B 1 ) and 3c (C s , 3 A 00 ) are triplet states with relative energies well above 100 kJ mol À1 (Fig. 2).Isomer 3b exhibits a planar Y-shaped geometry, while 3c is a distorted triangular pyramid.At the MP2 level, isomer 3c relaxes to a C 3v ( 3 A 1 ) distorted tetrahedron.Si 4 C. Fig. 3 compares the measured IR-UV2CI spectrum of Si 4 C with linear IR spectra predicted for the four lowest-energy isomers 4a-4d.Six distinct bands are observed at 388 (D), 499 (E), 571 (F), 659 (G), 710 (H), and 1037 cm À1 (I).Except for band F, all features can be explained with the fundamental modes of the two most stable isomers 4a and 4b.Specifically, bands D and E are assigned to Si-C-Si bending modes of 4a predicted at 378 (a) and 490 cm À1 (a), while band I is attributed to the asymmetric stretching of the nearly linear 4Si-1C-5Si moiety (176.81) at 1047 cm À1 (b).Bands G and H with similar peak intensities are assigned to the breathing mode at 660 cm À1 (a 1 ) and the asymmetric Si-C stretching mode at 721 cm À1 (e) of isomer 4b.In addition, the breathing mode at 395 cm À1 (a 1 ) of 4b fits well to band D with a small redshift of about 10 cm À1 .
Interestingly, isomer 4b (C 3v , 1 A 1 ) is often predicted as the ground state structure of Si 4 C, 12,13,61,64 as also obtained here with the TPSS and MP2 methods (Table 1).This structure is formed by replacing the Si atom at one of the apexes of the trigonal bipyramidal Si 5 (D 3h , 1 A 1 0 ) cluster. 66However, the energy difference between 4a and 4b is known to be strongly dependent on the theoretical level. 33For example, the present B3LYP calculations predict a lower-symmetry ground state structure 4a (C 2 , 1 A), and the next stable structures are 1.1 (4b), 18.7 (4c, C s , 1 A 0 ), and 27.9 kJ mol À1 (4d, C s , 1 A 0 ) higher in energy.Structure 4a with an estimated IE of about 7.9 eV (Table 2) is expected to yield a somewhat different IR-UVC2I enhancement than 4b with a slightly higher IE (8.15 eV).Nonetheless, the observed relative band intensities in Fig. 3 suggest that the population of both isomers are of similar order of magnitude.The ground state structure of Si 4 C (4a) is similar to the most stable structure of its anion counterpart Si 4 C À (C 2v , 2 A 1 ) predicted at the MP2/6-31G* level. 12,61A significant contribution of  4c and 4d to the IR-UV2CI spectrum is ruled out, because of their substantially higher energies and the mismatch of their predicted IR spectrum with the measured one.Finally, we note that the Si 4 C structures assigned from the IR-UV2CI spectrum are different from those postulated from the analysis of the photodetachment experiments of the corresponding anions. 61his example illustrates the importance of the direct spectroscopic study of the neutral clusters for the reliable experimental determination of the true ground state.Si 5 C. The experimental IR-UV2CI spectrum of Si 5 C 50 is compared in Fig. 4 to the linear IR spectra of the four lowest-energy isomers (5a-5d).Four bands are observed at 427 (J), 573 (K), 785 (L), and 868 cm À1 (M), which are mostly related to structures 5a/b.6][67] This scenario is also supported by our TPSS and MP2 calculations (Table 1), and the IR-UV2CI spectrum has indeed been assigned to 5b in our previous study by the comparison with the calculated TPSS spectrum. 50The bands J, K, and L, agree well with the predicted fundamentals, while band M has been explained with the overtone of J, 50 although its intensity is surprisingly high for an overtone.
The B3LYP/cc-pVTZ level suggests an alternative scenario.In contrast to the MP2 and TPSS levels, B3LYP yields a ground state structure 5a (C 2v , 1 A 1 ) resulting from a distortion of the C 4v cage 5b, along with an energy lowering of only 0.1 kJ mol À1 , while 5b is a low-lying transition state, leading to a fluxional structure.Similar to 5a, the low frequency bands J and K can again be assigned to deformation and breathing modes at 424 (a 1 ) and 565 cm À1 (a 1 ).While in the higher frequency range, the 5b spectrum shows a single intense degenerate peak at 785 cm À1 (e) in excellent agreement with band L, 5a exhibits two split vibrational modes at 726 cm À1 (b 1 , asymmetric Si-C stretching of 4Si-1C-6Si) and 847 cm À1 (b 2 , asymmetric Si-C stretching of 3Si-1C-5Si).These may be assigned to bands L and M, however with unusually large redshifts of up to 50 cm À1 from experiment, which possibly arise from unusual anharmonicity along the distortion coordinate.
Similar findings were noted for isovalent Si 6 . 47,49Two possible ground state structures have also been proposed for Si 6 showing  the best agreement with the measured IR-UV2CI spectra, i.e., a C 2v ( 1 A 1 ) structure found by DFT and a D 4h ( 1 A 1g ) structure predicted with MP2.This difference has been reasoned as distortions in Si 6 induced by a pseudo Jahn-Teller effect. 67,68t was impossible to draw a firm conclusion on the true ground state structure of Si 6 , as a potential band splitting for the C 2v structure was unresolved experimentally.For Si 5 C, the splitting is larger (B120 cm À1 ) and hence observable.More theoretical efforts need to be devoted to the pseudo Jahn-Teller effects in Si 6 and Si 5 C to fully understand the measured IR spectra.Such efforts are, however, beyond the scope of the present work.
For comparison, quantum chemical calculations for Si 5 C À have indicated a C 2v ( 2 A 1 ) ground state for the anion, but the PE spectrum has been interpreted to mainly originate from a C s ( 2 A 0 ) anion into a C s ( 1 A 0 ) neutral state (corresponding to 5c). 12,61Similar to Si 4 C, the structures of the neutral Si 5 C clusters derived from the IR and PE spectra are different, due to the vertical transitions favored by the Franck-Condon principle.
Si 6 C. The results for Si 6 C published recently 51 are included here for completeness.Fig. 5 compares the IR-UV2CI spectrum of Si 6 C with linear IR spectra of the four lowest-energy isomers (6a-6d).Five bands are detected at 438 (N), 566 (O), 664 (P), 842 (Q) and 1137 cm À1 (R).All these features can readily be explained by structure 6a (C 5v , 1 A 1 ) with the C atom at the apex of a pentagonal bipyramid, which has widely been accepted as the ground state structure of Si 6 C. 13,22,32,51 Its shape is similar to the D 5h ( 1 A 1 0 ) ground state of Si 7 determined in experiments 49,66,69 and theory. 63,66,70Band N is assigned to the breathing mode at 425 cm À1 (a 1 ), while band O is assigned to the asymmetric and Fig. 4 Comparison of the experimental IR-UV2CI spectrum of Si 5 C (bottom) 50 with linear vibrational spectra of the four lowest-energy isomers (5a-5d) calculated at the B3LYP/cc-pVTZ level.Molecular symmetries and electronic states are given in parentheses, while vertical ionization energies are given in eV.Relative energies are given in kJ mol À1 .The red line is the three-point adjacent average of the original data (circles).The experimental peak positions (in cm À1 ) are 430 (J), 574 (K), 786 (L), and 863 (M).symmetric Si-C stretching modes at 544 cm À1 (e 1 ) and 550 cm À1 (a 1 ), respectively.A fundamental mode near 660 cm À1 (P) is not predicted for any of the low-energy isomers.Therefore, we tentatively assign it to a combination band of the a 1 mode predicted at 425 cm À1 with the low frequency modes at 226 (e 1 ) or 257 cm À1 (a 1 ).Similarly, the weaker band Q might be an overtone of the mode at 425 cm À1 (a 1 ), and band R may be related to an overtone and/or combination of the modes at 544 cm À1 (e 1 ) and 550 cm À1 (a 1 ).Si 7 C.The IR-UV2CI spectrum of Si 7 C and the linear absorption spectra and geometries of the four lowest-energy isomers (7a-7d) are displayed in Fig. 6.Three bands are observed at 464 (S), 1075 (T), and 1163 cm À1 (U).The two intense bands S and U can be explained with structure 7b (C 1 , 1 A), which at the B3LYP level is slightly higher in energy (0.2 kJ mol À1 ) than the most stable one, 7a (C 1 , 1 A).Band S is assigned to the Si-C-Si bending mode at 461 cm À1 (a), while band U is attributed to the asymmetric Si-C-Si stretching mode at 1195 cm À1 (a).Although structures 7a and 7c (C 3v , 1 A 1 ) also exhibit IR active modes close to band S, neither of their intense bands at 680 (7a) and 768 cm À1 (7c) is observed in the experiment.We therefore exclude their substantial contribution to the observed spectrum.Actually, closer inspection of Fig. 6 reveals that the small signal at 678 cm À1 marked by an arrow may be attributed to 7a.Indeed, band T fits well to the asymmetric Si-C-Si stretching mode of 7a calculated at 1103 cm À1 (a).Similar to 3a and 4a, the Si-C stretching modes at high frequency are characterized by the nearly linear Si-C-Si motifs present in 7a (+5Si-1C-3Si = 175.81)and 7b (+4Si-1C-3Si = 168.41).Interestingly, while 7d (C s , 1 A 0 ) has been predicted as the ground state structure of Si 7 C (see ref. 22 and 32 and our TPSS and MP2 calculations), no signal of its most intense stretching mode at 526 cm À1 (a 00 ) is observed in the IR-UV2CI spectrum.This structure is obtained by substituting a Si atom by a C atom in a deformed bicapped Si 8 octahedron (C 2h , 1 A g ). 47,70,71We note that the relative energies of the four considered isomers 7a-7d are quite small (o15 kJ mol À1 at the B3LYP and TPSS levels, Table 1).Their calculated IE values (7.5-7.8 eV, Table 2) are relatively low compared to the photon energy of the F 2 laser.This may strongly affect the possibilities of detecting substantial enhancements in the ionization yield upon resonant IR absorption. 47i 8 C. The experimental IR-UV2CI spectrum of Si 8 C and the calculated linear IR spectra of the five lowest-energy isomers 8a-8e are compared in Fig. 7.The present B3LYP and TPSS calculations predict 8a (C s , 1 A 0 ) as the most stable structure, which is in agreement with previous work.13 Structure 8a is analogous to its Si 9 counterpart (C s , 1 A 0 ).47,70 Other stable isomers (8b-8e) higher in energy have similar topological geometries.The IR-UV2CI spectrum of Si 8 C shows three major bands at 449 (V), 574 (W), and 922 cm À1 (X).These features can readily be explained with isomer 8b, which is only 1.3 kJ mol À1 above the putative global minimum 8a.Specifically, band V and W are assigned to Si-C-Si bending modes at 452 cm À1 (a) and 563 cm À1 (a), respectively.Band X is attributed to the asymmetric Si-C-Si stretching mode at 962 cm À1 (a) of the almost linear Si-C-Si unit (+7Si-1C-6Si = 1601).
The main feature in the IR spectrum of isomer 8a at 446 (a 0 ) coincides with band V. Interestingly, structure 8a also contains the linear Si-C-Si block with +4Si-1C-2Si = 179.51.The corresponding asymmetric Si-C-Si stretching mode at 1051.7 cm À1 (a 0 ) is, however, weak.Therefore, a contribution of this isomer to the measured spectrum cannot be ruled out from the calculated IR spectrum.However, its calculated IE value is rather low (7.52 eV), so that the IR-UV2CI enhancement using 7.87 eV photons is probably weak.Similar conclusions apply to all higher energy isomers (7.41-7.47eV for 8c-8e) with the notable exception of the identified isomer 8b (7.75 eV).Hence, our favored assignment of the measured spectrum is mainly to isomer 8b, while the presence of further isomers in the beam cannot be excluded.No other experimental information about Si 8 C is available for comparison.
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B. Structural and electronic properties
The evolution of structures with increasing size for Si n C (n = 3-8) is summarized in the left part of Fig. 8 showing the isomers that explain the major features of the experimental spectra.Most of these structures contain a Si 3 C substructure with a (nearly) linear Si-C-Si unit, except Si 5 C and Si 6 C. Interestingly, the Si 3 C cluster (along with Si 2 C) has been identified as a particular stable size in fragmentation experiments. 72,73his stability, thermodynamically and as structural element, may be explained in terms of its valence structure as shown in Fig. 8 (right).Boys localization of the eight valence orbitals reveals the presence of three lone pairs, each at one of the Si atoms, two Si-C s-bonds in the Si-C-Si unit, as well as three delocalized bonds, one of them being a p-bond delocalized over the entire cluster.The resulting formal bond orders range from 0.53 between neighboring Si atoms to 1.53 within the linear Si-C-Si unit.The high bond order in the Si-C-Si unit goes along with relatively short Si-C bond lengths of 176 pm as compared to the third Si-C bond, which is 194 pm long and has formal bond order of only 0.87.The larger clusters also have similar bond lengths within the Si-C-Si bridge unit.The average of the corresponding Si-C distances in this unit is a measure of its strength and can be directly related with the frequency of the asymmetric Si-C-Si stretching mode observed experimentally.For the structures in which we identify this element (3a, 4a, 7b, 8b) this particular mode is found at 1080, 1037, 1163 and 922 cm À1 , respectively, and the average Si-C distances are 176, 178, 174 and 183 pm, i.e. there is a clear anti-correlation between bond length and stretching frequency.
The NBO charge analysis is increasingly used for a view of local charge instead of the unreliable Mulliken population analysis.As expected for Si n C clusters, a large negative charge is located at the C atom (almost À2e, Table S1 in ESI †), which is more electronegative than Si.The positive part is mainly shared by the Si atoms directly bound to the C atom.This result suggests that these Si atoms are very good electron donors, as observed previously for the first-row element doped silicon clusters. 51ertical excitations of selected stable clusters calculated with the second-order approximate coupled cluster and TD-DFT methods are listed in Table 3 for the first three transitions.The first electronic transition energies for the considered clusters are relatively high (41.65 eV).

IV. Conclusions
Carbon-doped silicon clusters are characterized with IR-UV2CI spectroscopy combined with quantum chemical simulations.The structures of the Si n C (n = 3-8) clusters are determined by comparison of the measured IR-UV2CI spectra with linear IR absorption spectra of the low-energy isomers calculated at the B3LYP/cc-pVTZ level.Optimized stable structures are found employing global optimization algorithms coupled with electronic structure (DFT) methods.This technique is robust and reliable in searching for the ground state structures of such type of clusters, in which electronic effects might play an important role.For Si 3 C and Si 6 C, only the lowest-energy isomers are present in the prepared cluster sample, while for Si 4 C, Si 5 C, Si 7 C, and Si 8 C multiple stable structures may co-exist.The nearly linear motif (Si-C-Si) is identified as characteristic building block in several of the most stable Si n C structures (n = 3-5, 7, 8).The NBO analysis shows that most charge is located on the C atom and its nearest-neighbor Si atoms.Although the theoretical approaches used in this work agree well on predicting low-energy isomers, the B3LYP method proves to be the most reliable one in finding the ground state structures.

Fig. 1
Fig. 1 Measured IR-UV2CI spectra of Si n C (with n = 3-8).All spectra are drawn to the same scale, according to the relative IR enhancement normalized by laser fluence.

Fig. 2
Fig. 2 Comparison of the experimental IR-UV2CI spectrum of Si 3 C (bottom) with linear IR spectra of the three lowest-energy isomers (3a-3c) calculated at the B3LYP/cc-pVTZ level.Molecular symmetries and electronic states are given in parentheses, while vertical ionization energies are given in eV.Relative energies are given in kJ mol À1 .The red line is the three-point adjacent average of the original data (circles).The experimental peak positions (in cm À1 ) are 509 (A), 651 (B) and 1080 (C).

Fig. 3
Fig. 3 Comparison of the experimental IR-UV2CI spectrum of Si 4 C (bottom) with linear vibrational spectra of the four lowest-energy isomers (4a-4d) calculated at the B3LYP/cc-pVTZ level.Molecular symmetries and electronic states are given in parentheses.Relative energies are given in kJ mol À1 , while vertical ionization energies are given in eV.The red line is the three-point adjacent average of the original data (circles).The experimental peak positions (in cm À1 ) are 388 (D), 499 (E), 571 (F), 659 (G), 710 (H), and 1037 (I).

Fig. 5
Fig.5Comparison of the experimental IR-UV2CI spectrum of Si 6 C (bottom) with linear vibrational spectra of the four lowest-energy isomers (6a-6d) calculated at the B3LYP/cc-pVTZ level.Molecular symmetries and electronic states are given in parentheses.Relative energies are given in kJ mol À1 , while vertical ionization energies are given in eV.The red line is the three-point adjacent average of the original data (circles).The experimental peak positions (in cm À1 ) are 438 (N), 566 (O), 664 (P), 842 (Q), and 1137 (R).

Fig. 7
Fig.7Comparison the experimental IR-UV2CI spectrum of Si 8 C (bottom) with linear vibrational spectra of the five lowest-energy isomers (8a-8e) calculated at the B3LYP/cc-pVTZ level.Molecular symmetries and electronic states are given in parentheses.Relative energies are given in kJ mol À1 , while vertical ionization energies are given in eV.The red line is the three-point adjacent average of the original data (circles).The experimental peak positions (in cm À1 ) are 449 (V), 574 (W), and 922 (X).

Fig. 8 (
Fig. 8 (left) Overview of the structures observed for Si n C (n = 3-8).Most of these structures contain a Si 3 C substructure with a (nearly) linear Si-C-Si unit, except Si 5 C and Si 6 C. (right) Valence structure and localized molecular orbitals for Si 3 C as obtained from a Boys localization.Formal bond orders (bold) are compared to the bond lengths in pm (italics).

Table 1
Relative energies (in kJ mol À1 ) of the most stable Si n C (n = 3-8) isomers calculated at the B3LYP, TPSS, and MP2 levels using the cc-pVTZ basis set a Relaxing to a (C 3v ,3A 1 ) structure.b C 2v ( 1 A 1 ).