Communication: The ground electronic state of Si2C: Rovibrational level structure, quantum monodromy, and astrophysical implications , , Neil J. Reilly , P. Bryan Changala, Joshua H. Baraban, Damian L. Kokkin , John F. Stanton, and Michael C. McCarthy
Citation: The Journal of Chemical Physics 142, 231101 (2015); doi: 10.1063/1.4922651 View online: http://dx.doi.org/10.1063/1.4922651 View Table of Contents: http://aip.scitation.org/toc/jcp/142/23 Published by the American Institute of Physics
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THE JOURNAL OF CHEMICAL PHYSICS 142, 231101 (2015)
Communication: The ground electronic state of Si2C: Rovibrational level structure, quantum monodromy, and astrophysical implications Neil J. Reilly,1,a) P. Bryan Changala,2 Joshua H. Baraban,3 Damian L. Kokkin,1,b) John F. Stanton,4 and Michael C. McCarthy1 1
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, Massachusetts 02138, USA JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA 3 Department of Chemistry, University of Colorado, Boulder, Colorado 80309, USA 4 Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA 2
(Received 9 May 2015; accepted 5 June 2015; published online 18 June 2015) We report the gas-phase optical detection of Si2C near 390 nm and the first experimental investigation of the rovibrational structure of its 1A1 ground electronic state using mass-resolved and fluorescence spectroscopy and variational calculations performed on a high-level ab initio potential. From this joint study, it is possible to assign all observed Ka = 1 vibrational levels up to 3800 cm−1 with confidence, as well as a number of levels in the Ka = 0, 2, and 3 manifolds. Dixon-dip plots for the bending coordinate (ν2) allow an experimental determination of a barrier to linearity of 783(48) cm−1 (2σ), in good agreement with theory (802(9) cm−1). The calculated (Ka , ν2) eigenvalue lattice shows an archetypal example of quantum monodromy (absence of a globally valid set of quantum numbers) that is reflected by the experimentally observed rovibrational levels. The present study provides a solid foundation for infrared and optical surveys of Si2C in astronomical objects, particularly in the photosphere of N- and J-type carbon stars where the isovalent SiC2 molecule is known to be abundant. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4922651]
Triatomic molecules composed solely of silicon and carbon atoms Sin C3−n (n ≤ 3) have a celebrated presence in molecular astronomy. The 4051 Å band of C3 was first observed in the emission spectrum of comet Tebbutt in 1881,1 although many decades passed until it was conclusively assigned to the pure carbon chain on the basis of 13C-substitution measurements.2,3 The carbon trimer has since been detected in the dense interstellar medium in the infrared region,4–6 and it remains the only polyatomic molecule to have been definitively observed optically in the diffuse interstellar gas.7 Similarly, the bluegreen Merrill-Sanford bands of SiC2 were observed in space8,9 long before their carrier was identified in the laboratory.10 Because these bands dominate photospheric absorption in cool N- and J-type carbon stars in the 400–500 nm range,11 they are commonly used in star classification;12–14 additionally, they have been observed in the emission spectrum of the carbon star IRAS 12 311–3509.15 SiC2 has also been identified by radioastronomy in the circumstellar shell IRC+10 21616–18 and is so abundant in that source that some of its rare isotopologues have also been detected.19–22 Small silicon and carbon clusters are also thought to be crucially important intermediates in the generation of thin SiC and diamond films23–26 and have interesting properties that make them compelling targets for both theory and experiment. a)Current address: Department of Chemistry, Marquette University, Milwau-
kee, Wisconsin 53233, USA.
b)Current address: Department of Chemistry and Biochemistry, Arizona State
University, Tempe, Arizona 85287, USA.
For example, C3 is a classic—and very “simple” example— of a quasilinear species, with an extremely low bending frequency (63 cm−1) and a large-amplitude bending potential that depends sensitively on the stretching coordinates.27,28 The SiC2 molecule is an exceedingly complex and highly fluxional species that was not even qualitatively understood until 30 yr after its laboratory identification as the carrier of the MerrillSanford bands. Specifically, SiC2 was long believed to have a linear Si–C–C geometry until analysis of a high-resolution electronic spectrum29 proved it to be significantly bent (∠C-Si-C near 40◦), facilitating its detection in IRC+10 216 by radioastronomy almost immediately thereafter.16 Si3 is perhaps the most complicated of the Sin C3−n series, with a strongly Jahn-Teller-perturbed singlet C2v ground state30,31 (the rotational spectrum of which32 is still not completely understood) that lies only 1 kcal/mol below a D3h triplet state, as well as several low-lying excited states that are coupled by spin-orbit interaction.33 Relatively little is known about the remaining member of this isovalent series, Si2C, although it is thought to be abundant in space,34 it is a postulated intermediate in SiC thin film production,35 and it is also a key species for understanding differences in electronic structure and bonding between silicon and carbon in silicon carbides. Its high stability is evidenced by mass spectrometric investigations of silicon carbide vapor,36,37 in which it has been observed as the primary molecular constituent. Like SiC2, Si2C was initially predicted to be linear,38 although the consensus to emerge from a number of increasingly sophisticated theoretical studies39–45 is that it adopts a bent geometry with an equilibrium bond
© 2015 AIP Publishing LLC
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angle near 115◦, supporting a handful of bending vibrational levels below the barrier to linearity. While knowledge of its spectroscopic properties is, thus, of clear importance in several contexts, the vibronic structure of Si2C remains by far the least explored of the Sin C3−n series, with only limited matrix isolation IR spectra46,47 and a low-resolution gas-phase excitation spectrum48 having been reported. In this letter, we address this glaring deficiency by reporting the first gas-phase work which probes the rovibrational structure of the ground electronic state of Si2C, using dispersed fluorescence (DF) of several laser-excited vibronic levels. The spectra have been assigned with guidance from a theoretically computed spectrum that combines high-level ab initio calculations with an efficient and newly developed code for formally exact rovibrational calculations. The calculated level structure of this molecule, which is confirmed by experiment, reveals a striking case of quantum monodromy,49 with a pronounced lack of rovibrational perturbations allowing the transition from quadratic to linear Ka -dependence at the saddle point to be vividly exhibited. This study should serve as a springboard for a number of future studies on several electronic states of Si2C aimed at understanding its highly complicated excitation spectrum, which may facilitate in situ monitoring in silicon carbide production and provide the crucial data needed for astronomical detection in the infrared and optical bands. II. EXPERIMENTAL
Si2C was produced in a pulsed discharge nozzle (PDN, 1 kV through 5 kΩ ballast resistance, 50 µs duration) through a mixture of silane and acetylene diluted in argon (1% SiH4/0.5% C2H2), in the early stages of a supersonic expansion; the PDN is described elsewhere.50 Experiments using this source were carried out in two separate apparatus: one for resonance-enhanced multiphoton ionization (REMPI), the other for laser-induced fluorescence (LIF) or DF. The REMPI and LIF apparatus have been described previously.51 Briefly, the REMPI setup consists of a source chamber containing the PDN, separated from a differentially pumped chamber by a 2 mm conical skimmer. Jet-cooled Si2C in the skimmed molecular beam was excited by tunable radiation from a dye laser, ionized by the 193 nm output of an ArF excimer laser, extracted into a time-of-flight (ToF) drift tube, and detected with a dual micro-channel plate detector. The Si2C electronic spectrum was recorded by integrating m/z = 68 amu ion signal as a function of dye laser wavelength. Typical pressures in the source and ToF chambers were 3 × 10−5 Torr and 10−7 Torr, respectively. For LIF/DF experiments, jet-cooled Si2C was interrogated approximately 50 mm downstream of the nozzle orifice with tunable dye laser output. Laser-induced fluorescence was collected with an f /1 lens, collimated, and imaged using an f -number-matched lens onto the slit of a 1 m monochromator equipped with a photomultiplier tube at the exit slit. This monochromator was used for collecting both excitation and DF spectra. In excitation scans, it was used as a narrow bandpass filter (ca. 100 cm−1 FWHM) to reject transitions of other species by scanning the grating synchronously with the laser
J. Chem. Phys. 142, 231101 (2015)
wavelength. In DF mode, it was operated with narrow slits (typically 200 µm), resulting in a resolution of 15 cm−1. The monochromator wavelength was calibrated with a mercury arc lamp; uncertainties in reported vibrational frequencies are approximately ±2 cm−1. The laser frequency was calibrated to an accuracy of 0.1 cm−1 using an external wavemeter. All instrument timings were controlled using a delay generator operating at 10 Hz. III. THEORETICAL
Ab initio rovibrational energies were determined from variational calculations on a ground state potential energy surface, performed using code developed by one of the authors of this paper.52 Single point electronic energies were calculated at the frozen core-CCSD(T)/PVQZ level of theory using the CFOUR quantum chemistry package53 over a grid of nuclear geometries and subsequently fit to a power series expansion in the valence bond coordinates. The rovibrational Hamiltonian was calculated in orthogonal Jacobi coordinates, which removes kinetic energy coupling terms between the stretch and bend coordinates.54 The computed wavefunctions were expanded in a product basis of harmonic oscillator discrete variable representation (DVR) functions for the stretch coordinates,55 associated Legendre polynomials for the bending angle, and symmetric-top rotational wavefunctions. Matrix elements of the potential energy operator were calculated by transforming the bending functions to a LegendreDVR quadrature grid, where the potential energy operator is diagonal. Eigenfunctions and eigenvalues of the rovibrational Hamiltonian were calculated with an iterative Lanczos routine that employs a thick-restart method,56 which enables efficient Lanczos vector storage and full reorthogonalization. Assignments of the ab initio energy levels were made by examining the nodal patterns of the computed wavefunctions. IV. RESULTS AND DISCUSSION
The electronic spectrum of a silane-acetylene discharge product recorded at m/z = 68 in the region 25 400–26 260 cm−1 is shown in Fig. 1. The spectrum and the excited state electronic structure of Si2C are extremely complicated: equation of motion-CCSD calculations indicate that vertical excitation from the bent 1A1 ground state is dominated by an orbitally degenerate state with a linear equilibrium geometry, which is subject to the Renner-Teller effect; an additional RennerTeller pair becomes important at higher energy (predicted near 3.9 eV), as does as an extremely bright state ( f = 0.7) near 5 eV, and vibronic interactions between them are possible (in fact, likely, as has been suggested in a theoretical study of the excitation spectrum45). Except to note that the spectrum appears to have multiple overlapping progressions with a spacing of approximately 100 cm−1, it is not our intent to provide a detailed assignment here; vibronic calculations and additional measurements in support of this task are ongoing. Despite the complexity of the spectrum, however, it is possible to obtain a quite detailed picture of the vibrational structure of the ground electronic state, particularly with respect to the bending potential, from DF spectra of only a few excited state
Reilly et al.
J. Chem. Phys. 142, 231101 (2015)
FIG. 1. Upper trace: REMPI spectrum of Si2C produced in a jet-cooled 1% SiH4/0.5% C2H2/Ar discharge, recorded with 193 nm ionizing radiation. Reflected trace: LIF spectrum observed with a tunable narrow bandpass filter using the same discharge source and gas premix. Dispersed fluorescence spectra from bands indicated with asterisks at 25 515 cm−1 and 26 242 cm−1 are shown in Fig. 2.
levels, even though the rovibronic assignments of the emitting states are not known at this stage. Because the spectral region of interest is also replete with strong transitions of Si2 and C3,57,58 fluorescence detection of Si2C is a significant challenge. By simultaneously scanning the monochromator at a constant Stokes-shift from the laser frequency (830 cm−1, corresponding approximately to the Si–C symmetric stretch frequency), however, it was possible to extricate a relatively pristine Si2C fluorescence spectrum (reflected trace in Fig. 1) that displays many correspondences with the mass-resolved spectrum. Several of these common features were further studied by DF. To account for overlapping transitions of unrelated molecules in DF spectra, the fluorescence decay curve was integrated within two temporal gates: one collecting the initial 1 µs (approximately τf ) of the curve, and one collecting the following 2 µs. Integrated
intensities from each gate were scaled to agree for features that could be securely assigned to Si2C; unrelated (i.e., nonSi2C) emission features could then be easily identified because of the relatively short fluorescence lifetimes of their carriers (typically