Detection and Structure of the Elusive Disilicon Carbide Cluster

Letter pubs.acs.org/JPCL

Discovery of a Missing Link: Detection and Structure of the Elusive Disilicon Carbide Cluster Michael C. McCarthy,*,† Joshua H. Baraban,‡ P. Bryan Changala,¶ John F. Stanton,§ Marie-Aline Martin-Drumel,† Sven Thorwirth,∥ Carl A. Gottlieb,† and Neil J. Reilly†,⊥ †

Harvard-Smithsonian Center for Astrophysics and School of Engineering & Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States ‡ Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309, United States ¶ JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, United States § Institute for Theoretical Chemistry, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States ∥ I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany ABSTRACT: The rotational spectrum of the elusive but fundamentally important silicon carbide SiCSi has been detected using sensitive microwave techniques aided by high-level ab initio methods. Its equilibrium structure has been determined to very high precision using isotopic substitution and vibrational corrections calculated quantumchemically: it is an isosceles triangle with a Si−C bond length of 1.693(1) Å, and an apex angle of 114.87(5)°. Now that all four SimCn clusters with m + n = 3 have been observed experimentally, their structure and chemical bonding can be rigorously compared. Because Si2C is so closely linked to other Si-bearing molecules that have been detected in the evolved carbon star IRC+10216, it is an extremely promising candidate for detection with radio telescopes.

S

mall silicon carbides are of considerable fundamental and applied interest because of the role they are thought to play in low-pressure chemical vapor deposition of solid silicon carbide,1 as well as in the chemistry of evolved carbon-rich stars such as IRC+10216. Among these, disilicon carbide, SiCSi, is perhaps the most important. Mass spectrometric studies conclude that Si2C is the most common gas-phase molecular fragment in the evaporation of bulk silicon carbide at high temperature,2,3 implying that it is unusually stable. In IRC +10216, thermodynamic equilibrium calculations4 suggest that after SiO and SiS, Si2C together with SiC2 are the most abundant Si-bearing species in the photosphere. A plethora of quantum chemical calculations have focused on the structure and properties of Si2C.5−12 Although early calculations suggested this cluster might adopt a linear geometry or have a triplet electronic ground state, the consensus now favors a closed-shell C2v structure (Figure 1) with a low bending frequency and barrier to linearity. In vivid contrast with its isovalent counterparts C3, SiC2, and Si3, the rotational and low-lying vibrational structure of Si2C are essentially unknown, although several infrared bands were observed some time ago in inert cryogenic matrices.13,14 Very recently, its ground state rovibrational structure has been investigated by several of us using fluorescence spectroscopy and variational calculations.15 In the present paper, we report detection of intense pure rotational lines of Si2C, and © XXXX American Chemical Society

Figure 1. Structures of Si2C (bottom left, this work) and the three other silicon carbides SimCn with m + n = 3. Structural parameters were determined from a least-squares fit (see Table 2), with estimated uncertainties in units of the last significant digit given in parentheses (see text).

determination of a precise semiexperimental equilibrium structure for this elusive silicon carbide, using a combination Received: April 13, 2015 Accepted: May 5, 2015

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Figure 2. (Left panel) Lower rotational levels of Si2C, showing the 12 transitions measured in the laboratory; solid arrows indicate those measured by FT microwave spectroscopy, whereas dashed arrows indicate those measured by double resonance. The red colored solid arrow indicates the transition of the two sample spectra shown in the right panel. Owing to the Bose−Einstein statistics of the equivalent Si nuclei, transitions involving energy levels with KaKc = oe or eo (dashed horizontal lines) are forbidden for the normal isotopic species and Si213C but are allowed for 29SiCSi and 30 SiCSi. (Right panel) Sample spectra of Si13CSi and 29Si13CSi, showing well-resolved Doppler splitting, which arises because the molecular beam propagates along the axis of the Fabry−Perot cavity, and closely spaced hyperfine structure (hfs), owing to the interaction of the 29Si nuclear spin with molecular rotation (see text) . The integration time for the Si13CSi spectrum was 10 s, while that of 29Si13CSi was approximately 15 min.

two electrodes. Sufficient collisions occur on the time scale of expansion to efficiently produce many new molecules, but by the time the fast moving beam reaches the center of a large Fabry−Perot cavity, the kinetic and rotational temperature are as low as 1 K. Rotational transitions are excited by a short (1 μs) pulse of resonant microwave radiation, and the resulting free induction decay is detected with the sensitive receiver; the FT of the time domain signal yields the power spectrum. Frequency agility is accomplished by synchronously stepping the mirror position and changing the applied frequency under computer control. The search for Si2C was based on new quantum chemical calculations in which the equilibrium rotational constants were corrected for the effects of zero-point vibrational motion as obtained by a variational calculation. The strongest predicted rotational transition in the range of our spectrometer (20,2 → 11,1) is calculated to lie very close to the frequency ceiling (42.1 vs 43 GHz). For this reason, a search was first undertaken for 13 CH4 in place of its carbon-13 isotopic species Si13 2 C (using 12 CH4), because replacing C with the heavier 13C shifts this transition down in frequency by 4 GHz to 38.1 GHz. Owing to the large uncertainty in frequency, a wide search, covering ±1 GHz about this prediction, was performed. The 10,1 → 00,0 line of Si13C2 (at 22552.1 MHz) was periodically monitored during this search. Only about a dozen lines requiring both silane (SiH4) and 13CH4 were observed in this frequency range, and

of sensitive microwave techniques and high-level coupled cluster calculations. Si2C is a very challenging molecule to detect in the radio band. Because it is relatively light, with a shallow bending potential and C2v symmetry, its rotational spectrum at low frequency is extremely sparse, with half of the levels absent owing to nuclear spin statistics (Figure 2). Furthermore, because the only nonzero component of the dipole moment is along the intermediate (b) inertial axis, the rotational spectrum is extremely sensitive to the bending angle. Even small changes in the calculated value of this angle result in large frequency shifts of its lowest few rotational lines (e.g., a change of 1° shifts the 31,3 → 40,4 transition by roughly 10%, or 2.2 at 22 GHz). The theoretical dipole moment of 0.9−1.0 D is less sensitive to the level of theory and basis set. The rotational spectrum of Si2C was detected with a Fourier transform (FT) microwave spectrometer which has previously been used to characterize the silicon trimer Si3,16 silicon carbide chains (SiCn, n = 3,5−8)17 and rhomboidal rings (c-SiC3),18,19 as well as many other highly reactive molecules. It operates between 5 and 43 GHz, and is equipped with a sensitive microwave receiver possessing parts per billion detection sensitivity. Si2C and other species are produced by passing a dilute mixture of silane and hydrocarbon gas (either HCCH or CH4) in Ne through the throat of a small supersonic nozzle source in which a low-current dc discharge is applied between 2108

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The Journal of Physical Chemistry Letters Table 1. Experimental and Vibrationally-Corrected Rotational Constants of Isotopic Si2Ca Constantb

SiCSi

A0 B0 C0 Δ0c

64066.645(6) 4395.5218(6) 4102.1269(17) 0.3350

ASE e BSE e CSE e ΔSE,b e

61627.30 4438.01 4139.70 0.0053

Si13CSi

SiC29Si

SiC30Si

59948.041(6) 63858.698(8) 4396.6510(7) 4319.6047(14) 4084.7048(17) 4035.1220(16) 0.3481 0.3344 Semiexperimental Equilibrium Rotational Constantsd 57711.98 61439.64 4438.04 4361.23 4120.95 4072.01 0.0054 0.0049

63665.366(9) 4248.4565(14) 3972.2187(16) 0.3344 61265.27 4289.27 4008.45 0.0052

a

In megahertz. bNote: 1σ uncertainties (in parentheses) are in the units of the last significant digits. cInertial defect is in units of amu Å2. Vibrational corrections have been calculated variationally for the J = 1 energies at the FC−CCSD(T) /PVQZ level of theory and have been applied to the experimentally derived rotational constants using the expression BSE e = B0 + ΔB0 to yield semiexperimental equilibrium rotational constants. d

Table 2. Experimental and Theoretical Structures of Si2C this worka

ref 6

ref 10

parameter

r0b

rSE e

theoryc

CISD/(DZ + 2P)

MP2/TZ2P

CI

ref 12 CCSD

CSi (Å) apex angle (degrees)

1.693(1) 115.8(2)

1.69272(2) 114.871(3)

1.6939 114.91

1.686 120.4

1.706 120.6

1.704 116.6

1.693 115.9

a

Statistical uncertainties in units of the last significant digit are given in parentheses. bStructure that best reproduces the observed rotational transitions of the four isotopic species. cCCSD(T) /cc-pwCV5Z+ΔQ/PVTZ best estimate structure, that is, calculated at the all-electron CCSD(T)/ cc-pwCV5Z level of theory and complemented by a higher-order correction calculated at the CCSDT(Q)/cc-pVTZ basis level in the frozen core approximation.

as those of normal Si2C (see Table 1). 29Si or 30Si substitution at one of the two equivalent silicon atoms breaks the C2v symmetry, allowing several otherwise symmetry-forbidden transitions to be observed. Because so few low-J lines of 29 SiCSi can be directly measured with our spectrometer and only one or two of these have fine structure, it is not possible to determine the individual components of the spin-rotation tensor for this species, but where comparison is possible, the experimental and predicted splittings agree well. The experimentally derived inertial defect of Si2C (Δ = Ic − Ib − Ia = 0.335 amu Å2) is close in magnitude to that of both Si3 (0.379 amu Å2)16 and SiC2 (0.363 amu Å2),21 indicating that the bending potential surface is also shallow. For a triatomic molecule, the major contribution to Δ comes from the lowest frequency vibration, Δ ≈ h/2π2v, where v is the vibrational frequency in cm−1.22 Our value from Table 1 yields 195 ± 20 cm−1,23 which is somewhat larger than either that computed (∼150 cm−1)12 or derived from the optical data (∼145 cm−1).15 As a point of comparison, SiC2 has a 5.8 kcal/mol barrier to linearity,24 a slightly larger inertial defect, and a low frequency (196 cm−1)25 bending vibration. Because of symmetry, only two geometrical parameters are needed to describe the structure of Si2C: the CSi bond length and the apex angle, ∠SiCSi. Using a now standard fitting procedure, the experimental rotational constants of each isotopic species have been corrected theoretically for zeropoint vibrational motion,26 and the two structural parameters have then been least-squares optimized27 to simultaneously reproduce all 12 rotational constants (three for each of the four isotopic species). The resulting semiexperimental (reSE) structure is summarized in Table 2, along with predictions from several levels of theory. We note that the rSE e structure is remarkably precise, yielding extremely small statistical uncertainties for both parameters. From experience, however, we believe that these may be too optimistic and that uncertainties of order 1 mÅ for the bond length and 0.05° for the bond angle

only one, near 38.6 GHz, was intense (see Figure 2). On the assumption that the carrier of this line is SiCSi, two additional lines were subsequently detected at exactly the predicted frequencies for the 29Si and 30Si isotopic shifts from the theoretical structure, in spite of the low fractional abundances of these Si isotopes (4.7% and 3.1%, respectively). In addition, the putative line of 29Si13CSi also displays partially resolved structure (see Figure 2) characteristic of the nuclear spinrotation hyperfine splitting,16 owing to the interaction of the magnetic moment of the 29Si nucleus (I = 1/2) with the rotationally induced magnetic field. Taken together, these observations provide compelling evidence that the assigned lines are produced by Si213C and no other molecule. A total of 10 b-type transitions of this isotopic species were then measured up to J = 10 between 7 and 85 GHz, 4 in the frequency range of the FT microwave spectrometer, and the remaining 6 by microwave/millimeter-wave double resonance. By scaling the calculated rotational constants to the measured ones for Si213C, a refined set of predictions was made for the normal isotopic species. A few lines of this species were then detected within 20 MHz of these predictions, allowing additional lines to be predicted to better than 1 MHz after the first three were found. Ultimately, 12 lines were measured over the same range of frequency and J as that for Si213C (Figure 2). Spectroscopic constants for both species were determined by fitting a theoretical spectrum calculated from a standard asymmetric top Hamiltonian with centrifugal distortion20 to the observed frequencies. With three rotational constants (Table 1) and three quartic centrifugal distortion terms, the rms of the two fits is less than 20 kHz, in very good agreement with the experimental uncertainties. Although the data set is limited, Si2C appears to behave as a fairly rigid asymmetric top in its ground vibrational state in the range of J and Ka studied here. Eight lines of both rare Si isotopic species (29SiCSi and 30 SiCSi) have also been detected and analyzed in the same way 2109

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with size and thus provide clues as to the stoichiometry of the most stable clusters.

are more realistic (Figure 1). The equilibrium structure that represents a best theoretical estimate agrees well with the results of the rSE e structure. We estimate that in excess of 1012 Si2C molecules are produced per gas pulse, by comparing line intensities to those of a stable molecule with a known fractional abundance, accounting for differences in the dipole moment and rotational partition function. This abundance estimate is probably conservative because the amount of rotational excitation in the Si2C produced in our experiment is not known precisely. For example, a transition originating from a rotational level lying nearly 15 K above ground is readily observed in our molecular beam, and it can be made more intense by increasing the discharge voltage. This finding suggests that the degree of rotational excitation of this near-prolate asymmetric top (κ = −0.9902) is not efficiently quenched by collisions, and therefore its temperature in our beam may be warmer than the canonical 1−3 K. At the abundance level of 1012 molecules/ pulse, the infrared spectrum of Si2C should be detectable. A systematic comparison of the structures of the four triatomics SimCn, where m + n = 3, is now possible (see Figure 1). When Si is the central atom, the molecule adopts a strongly bent or cyclic geometry with an apex angle of well less than 90°.16,28 When carbon is at the same position, however, the geometry is much closer to linear, with C3 exhibiting quasilinear behavior, and SiCSi having an obtuse bending angle and a low barrier to a linear configuration. The structural simplicity of these small isovalent molecules illustrates the propensity of Si to prefer single bonding via p orbitals, while C prefers sp or sp2 hybridization when multiply bonded to either Si or another C atom. Because the rotational spectrum of Si2C in its ground state is now well characterized, searches for vibrational satellites from the bending and symmetric modes should be pursued. The lowlying bending mode is of particular interest because this motion represents the large amplitude coordinate. Recent optical experiments15 find that, like C3, the bending mode of this cluster is efficiently populated in a discharge source similar to that used here, implying that vibrational satellites of Si2C may be intense. Vibrational corrections calculated variationally should provide good estimates for the rotational spectra of both modes. Now that precise laboratory frequencies are available, an astronomical search for this fundamental silicon carbide is obligatory. The best astronomical source would appear to be IRC+10216 because both smaller and larger silicon carbides have been detected there,29 and because chemical models predict this species may be abundant in its photosphere.4 Despite the limited data set, the principal low-K radio lines can still be predicted to better than 1 km sec−1 in equivalent radial velocity up to 150 GHz, more than sufficient for a search in the 3 mm band. Detection of Si2C would be significant because it may be a progenitor to silicon carbide dust, which is frequently observed in emission at 11.3 μm.30 Laboratory detection of larger SimCn (with m > n) clusters may be feasible. Although Si3C would appear to be an obvious candidate, its dipole moment is calculated to be quite small (of order 0.1 D).31 Because Si3 is also abundantly produced under the same expansion conditions, clusters such as Si3C2, which is predicted to adopt a nonlinear structure,32,33 are attractive targets for detection. Structural information derived from such high-resolution studies should be helpful in understanding how the chemical and physical properties of silicon carbides evolve

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ⊥

(N.J.R.) Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53233, United States.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work in Cambridge is supported by NASA Grant NNX13AE59G. P.B.C. is supported by an NSF Graduate Research Fellowship (Award No. DGE1144083). J.F.S. would like to thank the Welch Foundation of Houston, Texas (Grant F-1283), and the U.S. National Science Foundation (Grant CHE-1361031). S.T. gratefully acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) through grants TH 1301/3-1 and TH 1301/3-2. We thank E.S. Palmer and P. Antonucci for technical assistance, and D.L. Kokkin for assistance with early laboratory searches.

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REFERENCES

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The Journal of Physical Chemistry Letters (15) Reilly, N. J.; Changala, P. B.; Baraban, J. H.; Kokkin, D. L.; Stanton, J. F.; McCarthy, M. C. J. Chem. Phys. 2015, submitted. (16) McCarthy, M. C.; Thaddeus, P. Rotational Spectrum and Structure of Si3. Phys. Rev. Lett. 2003, 90, 213003. (17) McCarthy, M. C.; Apponi, A. J.; Gottlieb, C. A.; Thaddeus, P. Laboratory Detection of Five New Linear Silicon Carbides: SiC3, SiC5, SiC6, SiC7, and SiC8. Astrophys. J. 2000, 538, 766−772. (18) McCarthy, M. C.; Apponi, A. J.; Thaddeus, P. Rhomboidal SiC3. J. Chem. Phys. 1999, 110, 0645−10648. (19) McCarthy, M. C.; Apponi, A. J.; Thaddeus, P. A Second Rhomboidal Isomer of SiC3. J. Chem. Phys. 1999, 111, 7175−7178. (20) Pickett, H. M. The Fittting and Prediction of Vibration-Rotation Spectra with Spin Interactions. J. Mol. Spectrosc. 1991, 148, 371−377. (21) Gottlieb, C. A.; Vrtilek, J. M.; Thaddeus, P. Laboratory Measurement of the Rotational Spectrum of SiCC. Astrophys. J. Lett. 1989, 343, L29−L32. (22) Gordy, W., Cook, R. L. Microwave Molecular Spectra; Wiley: New York, 1984. (23) The uncertainty has been estimated from other three and four atom molecules, where this approximation is generally accurate to about 10%. See, e.g., Watson, J. K. G. Approximations for the Inertial Defects of Planar Molecules. J. Chem. Phys. 1993, 98, 5302−5309. (24) Nielsen, I. M. B.; Allen, W. D.; Császár, A. G.; Schaefer, H. F. Toward Resolution of the Silicon Dicarbide (SiC2) Saga: Ab Initio Excursions in the Web of Polytopism. J. Chem. Phys. 1997, 107, 1195− 1211. (25) Ross, S. C.; Butenhoff, T. J.; Rohlfing, E. A.; Rohlfing, C. M. SiC2: A Molecular Pinwheel. J. Chem. Phys. 1994, 100, 4110−4126. (26) Bak, K. L.; Gauss, J.; Jørgensen, P.; Olsen, J.; Helgaker, T.; Stanton, J. F. The Accurate Determination of Molecular Equilibrium Structures. J. Chem. Phys. 2001, 114, 6548−6556. (27) Kisiel, Z. Least-Squares Mass-Dependence Molecular Structures for Selected Weakly Bound Intermolecular Clusters. J. Mol. Spectrosc. 2003, 218, 58−67. (28) Thaddeus, P.; Cummins, S. E.; Linke, R. A. Identification of the SiCC Radical Toward IRC+10216: The 1st Molecular Ring in an Astronomical Source. Astrophys. J. Lett. 1984, 283, L45−L48. (29) McCarthy, M. C.; Gottlieb, C. A.; Thaddeus, P. Silicon Molecules in Space and in the Laboratory. Mol. Phys. 2003, 101, 697− 704. (30) Sloan, G. C.; Kraemer, K. E.; Matsuura, M.; Wood, P. R.; Price, S. D.; Egan, M. P. Mid-Infrared Spectroscopy of Carbon Stars in the Small Magellanic Cloud. Astrophys. J. 2006, 645, 1118−1130. (31) Stanton, J. F.; Dudek, J.; Theulé, P.; Gupta, H.; McCarthy, M. C.; Thaddeus, P. Laser Spectroscopy of Si3C. J. Chem. Phys. 2005, 122, 124314. (32) Presilla-Marquez, J. D.; Rittby, C. M. L.; Graham, W. R. M. Vibrational Spectra of Penta-Atomic Silicon-Carbon Clusters. III. Pentagonal Si3C2. J. Chem. Phys. 1996, 104, 2818−2824. (33) Hunsicker, S.; Jones, R. O. Structure and Bonding in Mixed Silicon-Carbon Clusters and Their Anions. J. Chem. Phys. 1996, 105, 5048−5060.

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NOTE ADDED IN PROOF Rotational lines of Si2C have now been detected in IRC+10216 by J. Cernicharo et al.

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