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Germanium Dicarbide: Evidence for a T-Shaped Ground State Structure Oliver Zingsheim, Marie-Aline Martin-Drumel, Sven Thorwirth, Stephan Schlemmer, Carl A. Gottlieb, Jürgen Gauss, and Michael C. McCarthy J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01544 • Publication Date (Web): 25 Jul 2017 Downloaded from http://pubs.acs.org on July 26, 2017

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The Journal of Physical Chemistry Letters

Germanium Dicarbide: Evidence for a T−Shaped Ground State Structure Oliver Zingsheim,† Marie-Aline Martin-Drumel,‡,§ Sven Thorwirth,† Stephan Schlemmer,† Carl A. Gottlieb,‡ Jürgen Gauss,¶ and Michael C. McCarthy∗,‡ †I. Physikalisches Institut, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 77, 50937 K¨ oln, Germany ‡Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, and School of Engineering & Applied Sciences, Harvard University, Cambridge, MA 02138, United States ¶Institut f¨ ur Physikalische Chemie, Universit¨ at Mainz, 55099 Mainz, Germany §Permanent address: Institut des Sciences Moléculaires d’Orsay, CNRS, Univ. Paris-Sud, université Paris Saclay, Orsay, France E-mail: [email protected]

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The structure and spectroscopy of metal dicarbides MC2 has a long and fascinating history. Because these species are closely related to tricarbon C3 but are highly polar, both first- (C2 O 1 and C2 N 2 ) and second-row (SiC2 , 3 C2 S, 4 and C2 P 5 ) dicarbides have been detected in astronomical sources. One of the most prominent of these is SiC2 , the carrier of the Merrill-Sanford bands, 6,7 which has long been known to dominate photospheric absorption between 400 and 500 nm in cooler N and J-type carbon stars. 8 Its structure however was widely thought to be linear 9 before elegant laser experiments by Smalley and co-workers in 1984, 10 in combination with new quantum chemcial calculations, 11 established it was a three-membered ring with C2v symmetry instead. On the basis of the approximate rotational constants derived from the experimental work, Thaddeus et al. 3 soon afterward identified nine rotational lines of SiC2 toward the carbon star IRC+10216. Carbon-rich Group 14 materials have received considerable attention because of their potential application in nanoelectronics and material science. 12–16 This interest is fundamentally linked to the diversity in chemical behavior of Group 14 elements, and the unusual structures and properties of compounds with the same stoichiometry. Numerous quantum chemical calculations on binary Ge-C clusters 16–21 indicate a plethora of stable structures may exist even when these clusters consist of a small number of atoms. Like SiC2 , the ground state structure of GeC2 has been a subject of debate. It too was initially assumed to be a linear chain with the atom connectivity Ge–C–C, 22,23 but subsequent calculations predicted a T-shaped geometry. 16,21 The most recent high-level calculations, both with and without relativistic corrections, favor an L-shaped structure, 24–28 while the linear structure, lying 10 to 20 kJ/mol higher in energy, is found to be a second-order saddle point connecting the two L-shaped geometries. 24,25 Because the potential surface is quite flat along the bending coordinate, the T- and L-shaped structures are very close in energy, but with the former usually predicted less stable by up to 8 kJ/mol. 24,25 For this reason, and because imaginary vibrational frequencies have occasionally been derived for the T-shaped form depending of the level of theory and basis set, Sari et al. 24 concluded the L-shaped

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form is likely to be the global minimum of the potential energy surface, a prediction shared by more recent calculations. 25–28 In this paper, we report the first experimental study of GeC2 from which — in contrast to previous theoretical predictions — a T-shaped structure has been found for its ground state; this finding is supported by new high-level quantum chemical calculations. By measuring the pure rotational spectra of 14 isotopic variants, a precise experimental (r0 ) structure is derived: the Ge–C bond length is 1.952(1) ˚ A and the apex angle is 38.7(2) °. GeC2 was produced by laser ablation of a germanium carbide rod with a molar ratio Ge:C of 2:1 using 532 nm radiation from a Nd-YAG laser operating at 5 Hz, in which the average energy was ∼ 20 mJ/pulse. Ablation products were entrained in an inert gas (Ar) by synchronously opening a pulsed valve nozzle, and then expanded adiabatically into a large vacuum chamber where the rotational temperatures drop to as low as a few K. Details of the laser ablation apparatus can be found elsewhere. 29,30 Because there are many collisions in the throat of the nozzle, new molecules can be formed in high abundance, as our earlier laboratory work on TiO2 , made from ablation of Ti metal in the presence of O2 , demonstrates. 30 As the jet passes through the center of the chamber, the products can be probed either with a chirped-pulse (CP) Fourier-transform microwave (FTMW) spectrometer, operating between 7.5 and 18 GHz, or a cavity-enhanced one, in the range 5 to 40 GHz, because both spectrometers are positioned along perpendicular axes in the vacuum chamber. To optimize the experimental conditions prior to the germanium carbide study, the intensity of the fundamental rotational line of SiC2 near 23 GHz was optimized with the cavity spectrometer using a rod of the same stoichiometry but where Ge powder was replaced with Si powder. Under these conditions, the SiC2 line was observed with a signal-to-noise ratio (SNR) in excess of 100 in 30 s of integration. Following optimization, the Si:C rod was replaced with the Ge:C rod, and a CP spectrum was immediately measured between 7.5 and 18 GHz. Within a few minutes of integration, a prominent set of features clustered around 15.3 GHz was observed but to achieve still higher SNR, a deep integration of approximately 17 h was

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ultimately performed, as illustrated in Fig. 1. While the potential energy surface of GeC2 and the relative stability of the various minima have proven challenging to calculate, equilibrium structural parameters of the three different conformers can be predicted with high degree of confidence even at relatively modest level of theory, and these structures have rotational spectra that are markedly different from each other. Most significant for the present work is the predicted frequency of their fundamental rotational transitions (either J = 1 → 0 or 10,1 → 00,0 ): the L-shaped structure is near 13.9 GHz, the T-shaped structure is near 15.6 GHz, and that of the linear form is near 8.8 GHz (with its 2-1 line at twice this frequency, 17.6 GHz). For this reason, CP-FTMW spectroscopy is an ideal tool to explore GeC2 . As illustrated in Fig. 1, its instantaneous bandwidth of more than 10 GHz covers all three possible J = 1 − 0 transitions. It is apparent from this Figure that a Ge-bearing molecule is responsible for the strongest features: Ge has five isotopes with significant fractional abundance (70 Ge: 21% natural abundance, 72

Ge: 28%,

73

Ge: 8%,

74

Ge: 36%, and

76

Ge: 8%, see Figure S2), and as a result, each

rotational transition should give rise to multiple lines of comparable intensity. Furthermore, subsequent analysis indicates that the frequency spacing between these strong lines is almost perfectly reproduced if the carrier is GeC2 with a T-shaped geometry. As Fig. 2 indicates, this tentative assignment is also consistent with detection of weak lines at the expected frequencies for 74 Ge13 C12 C and 72 Ge13 C12 C with roughly the expected intensity (i.e. ∼ 1/50, or twice the natural abundance of 13 C, if the molecule possesses C2v symmetry with two equivalent bosons). When these features were subsequently observed at higher spectral resolution with the cavity spectrometer [Fig. 2 (inserts)], they are found to possess very closely-spaced (∼ 10 kHz) structure characteristic of nuclear spin-rotation hyperfine splitting. This structure has previously been observed in isotopic lines of small silicon carbides such as and

29

29

SiCSi

SiC3 , and arises in the present case from the interaction of the I = 1/2 spin of

13

C

with the very small magnetic field induced by rotation. 31 Crucial confirmation of the identification is provided by measurements of higher-J tran-

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74Ge13CC

13C

10

72Ge13CC

spin-rotation ~10 kHz

8

6

0

0.2

-0.2

0

0.2

x10

-3

-0.2

0.0044

Intensity

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2

0.00 14.70 14700

14.75

14.80 14800

14.85 3

14.90 14900

14.95

15.00 15000

15.05

x10 Frequency (MHz)

Figure 2: A portion of the spectrum shown in Fig. 1, in which the vertical scale has been expanded by a factor of 100, showing two, weak unidentified features close in frequency to those expected for 74 Ge13 C12 C and 72 Ge13 C12 C, on the assumption that GeC2 has a Tshaped structure. The inserts are spectra of each line after approximately 10 min using a cavity microwave spectrometer; the frequency axis is given as an offset (in MHz) from the rest frequencies listed in Table S2. At high spectral resolution, closely-spaced 13 C spinrotation splitting is partially resolved. The line shape is instrumental in origin: because the supersonic jet expands through a small hole in one of the mirrors, along the axis of the Fabry-Pérot cavity, each hyperfine transition is split into two Doppler components. The rest frequency is simply the arithmetic average of these two frequencies, while the frequency separation between the doublets is proportional to the velocity of the jet.

With it, a total of 9 additional isotopic variants of GeC2 , i.e. all possible isotopologues with the exception of characterizing the 13

13

73

Ge13 C2 , were ultimately detected. An important motivation for

C isotopologues is to determine their A0 rotational constants. Since

C is a fermion as opposed to

12

C, which is a boson, transitions involving the Ka = 1

levels are allowed by spin statistics in both the singly or doubly-substituted species; these measurements break the correlation between the three rotational constants, allowing each

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Table 1: Experimental rotational constants of isotopic GeC2 (in MHz). 12 13 13 12 C C C2 Constant∗ C2 A0 [53431.4] 51397.0(201) 49297.4(221) 70 7745.5872(50) 7512.07635(120) 7294.79366(198) Ge (B0 + C0 )/2 (B0 − C0 )/4 317.74(39) 306.80032(85) 301.07628(85) A0 [53431.4] 51381.8(207) 49309.0(228) 72 7694.1462(52) 7460.67187(120) 7243.44571(198) Ge (B0 + C0 )/2 (B0 − C0 )/4 313.80(40) 302.63221(85) 296.87040(85) A0 [53431.4] 51377.9(109) − 73 7669.41276(58) 7435.95145(144) − Ge (B0 + C0 )/2 (B0 − C0 )/4 311.744(60) 300.6374(48) − A0 [53431.4] 51382.3(213) 49308.4(235) 74 Ge (B0 + C0 )/2 7645.4226(53) 7411.97649(120) 7194.80702(198) (B0 − C0 )/4 309.72(42) 298.70926(85) 292.91178(85) A0 [53431.4] 51343.6(90) [49308.6] 76 Ge (B0 + C0 )/2 7599.2042(55) 7365.78453(95) 7148.66602(112) (B0 − C0 )/4 305.93(44) 295.01088(88) 289.18212(88) ∗ Note: 1σ uncertainties (in parentheses) are in the units of the last significant digits. Best-fit constants derived from the transition frequencies in Tables S2 and S3; numbers in square brackets were kept fixed in the fit; for details see Supplementary Material.

74GeC 2 72GeC 2

U 70GeC 2

76GeC 2

90

91

90

92

91

92

3

93x10

93

Frequency (GHz)

Figure 3: A portion of the W-band spectrum of a supersonic jet containing products formed in the laser ablation of a Ge:C rod. The total integration time was approximately 1 h. The feature indicated by ‘U’ is unidentified.

to be determined independently. Tables S2 and S3 summarize the measured lines of all the singly- and doubly-substituted

13

C species. As with the normal species, the best-fit

spectroscopic constants (Table 1) were obtained from a least-squares fit; a complete list of spectroscopic parameters is provided in Table S1. The structure of GeC2 in its vibrational ground state was calculated by least-squares 8


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optimizing 33 the two unique structural parameters, the Ge–C bond length and the apex angle, ∡CGeC, to reproduce all the experimentally-derived rotational constants (36 in total). All experimentally derived constants were equally weighted in the optimization rather than using a smaller subset because no correction was made for zero-point vibrational effects, nor was it clear if one constant (e.g., A) was more sensitive to this correction. This procedure yields 1.952(1) ˚ A for the bond length and 38.7(2)° for the apex angle, where the numbers in parentheses are estimated 1σ uncertainties in the last digit. The derived structure reproduces the A rotational constants to better than 6%, but is roughly an order of magnitude more precise (0.5%) for B and C. Structural fits using only two constants (e.g., B and C) yield a nearly identical bond length (1.955 ˚ A), but the apex angle differs by roughly 1° (39.9°). Although the inertial defect of isotopic GeC2 is large (e.g., 1.228 amu ˚ A2 for

74

Ge13 C12 C)

even compared to SiC2 (0.363 amu ˚ A2 ) 34 and Si2 C (0.335 amu ˚ A2 ), 35 this level of agreement is not surprising in the absence of zero-point correction. To support the experimental investigations, quantum chemical calculations were performed to improve upon the results reported in the literature. The calculations were performed at the coupled-cluster singles and doubles level augmented by a perturbative treatment of triple excitations, CCSD(T), 36 using a core-polarized basis set of quadruple-zeta quality (cc-pwCVQZ) 37 and with all electrons included in the correlation treatment. The equilibrium geometries and harmonic vibrational frequencies were determined for the linear, T- and L-shaped geometries using analytic derivative techniques. 38,39 All computations were carried out with the CFOUR program package 40 and the results are summarized in Table 2. The new calculations predict, unlike those reported in Ref. 24, the T-shaped form to be the lowest in energy, although the energy difference of about 0.02 kJ/mol with respect to the L-shaped form is vanishingly small. The linear form in contrast is found to be significantly less stable, with an energy difference relative to either the T- and L-shaped form of about 15 kJ/mol. The present results can be taken as a strong indication that the T-shaped form is indeed the global minimum for GeC2 . While the energy differences obtained in our calcu-

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Table 2: Energies (in Hartree), relative energies (in kJ/mol), geometries (distances in ˚ A, angles in degrees), and dipole moments (in D) for the three different forms of GeC2 as obtained experimentally and in CCSD(T)/cc-pwCVQZ computations. experimental∗ E ∆E rGe−C rC−C apex angle

1.952(1) [1.294] 38.7(2)

T-shaped −2152.710648 0 1.9296 1.2750 38.58

L-shaped −2152.710639 0.02 1.8184 1.2810 86.29

linear −2152.705033 14.74 1.7717 1.2836

µa 3.11 3.57 4.92 0.60 µb ∗ Note: 1σ uncertainties (in parentheses) are in the units of the last significant digits. Experimental geometries are derived from the rotational constants in Table 1 using STRFIT; 33 number in square brackets was derived from the others.

lations are too small to draw a definitive conclusion (see also Ref. 24), the trend seen in the calculations suggests that a further increase in the basis set size will most likely favor the T-shaped form even more. Such calculations, 41 however, are currently not feasible for GeC2 . Even though we cannot rule out – in an absolute sense – that the ground state structure is a vibrationally-average of the L-shaped form facilely tunneling between two equivalent minima, this explanation appears highly unlikely given that: (1) the experimental rotational constants of the normal species are in very good agreement with those predicted for the T-shaped form, and those of its isotopic species are extremely well predicted (to better than 1%) by simply scaling of the equilibrium geometry, regardless of the location or mass of the substituted atom; (2) the derived structural parameters compare very well with those predicted for the T-shaped form. Significant vibrationally averaging of the L-shaped form might be expected to yield a shorter effective Ge–C bond length compared to theory (1.8184 ˚ A); in contrast the length derived from experiment is actually slightly longer than that predicted even for the T-shaped structure [1.952(1) vs. 1.9296 ˚ A]; and (3) no evidence is found for additional lines or line structure in the spectra of the double-substituted

13

C species, which

should be observed if the two equivalent fermions undergo tunneling in a potential well with 10


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a significant barrier. Because calculations predict GeC2 to be extremely floppy, with large amplitude motion involving the bending vibration, it was not possible to derive a semi-experimental equilibrium structure (reSE , e.g. Ref. 35). Although second-order perturbation theory (VPT2) is inadequate to properly describe large-amplitude, low-frequency motion in this dicarbide, a more sophisticated variational calculation 42 may be worth pursuing to properly account for zero-point vibrational effects; this approach was recently used with good success for Si2 C. 35 Nevertheless, the present work should serve as a valuable benchmark for future ab initio quantum chemical investigations, both because it establishes the symmetry of the ground isomer, and it provides an exhaustive study of how the rotational spectrum, and therefore the structure, is affected by isotopic substitution. In light of the high abundance of GeC2 produced by laser ablation, gas-phase studies of larger germanium-carbon species are worth pursuing. Further analysis of the spectrum shown in Fig. 1 reveals evidence for rotational lines of linear GeC4 and GeC5 , and GeC6 was found during subsequent cavity searches. 43 Detection of other germanium-carbon clusters, particularly bent or cyclic forms, would be a starting point to systematically explore the structural diversity of group 14 elemental clusters. By analogy to the bent Si2 C cluster detected recently, 35 isovalent Ge2 C is a promising target as is GeC3 for which calculations 25 predict a rhombic ground state structure similar to what is observed for SiC3 (see, e.g., Ref. 44 and references therein). No carbon-rich group 14 clusters containing heavy elements beyond germanium have been studied at high spectral resolution to date. Quantum chemical calculations suggest both linear (C∞v ) and cyclic (C2v ) forms are minima on the SnC2 potential energy surface 45 and hence are intriguing targets for future microwave studies. For PbC2 , calculations predict a bent form of Cs symmetry as the minimum. 46

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Acknowledgement The experimental work is supported by NSF Grant AST-1615847. O.Z gratefully acknowledges support from the Bonn-Cologne-Graduate School of Physics and Astronomy (BCGS) and his student exchange was carried out within the Sonderforschungsbereich (SFB) 956, sub-project B3, funded by the Deutsche Forschungsgemeinschaft (DFG). S.T. gratefully acknowledges funding by the DFG through grants TH 1301/3-2, SCHL 341/15-1 and SFB 956. J.G. gratefully acknowledges support by the DFG through grant GA 370/6-1 and 370/6-2. We thank Brightspec, Inc. for the loan of a W-band spectrometer, and Justin Neill and Matt Muckle for technical assistance on its use and operation. The assistance of P. Antonucci in maintaining the laser ablation source is also acknowledged. Supporting Information Available: A detailed description of the experimental conditions, the spectroscopy of GeC2 , and the analysis of the experimental spectrum is included together with lists of all determined spectroscopic constants and assigned transitions.

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Scalar Relativity, and Core-Valence Correlation. J. Chem. Phys. 2002, 117, 10008– 10018. (25) Wielgus, P.; Roszak, S.; Majumdar, D.; Leszczynski, J. Thermodynamic Properties of Germanium/Carbon Microclusters. J. Chem. Phys. 2005, 123, 234309. (26) Rayón, V. M.; Redondo, P.; Barrientos, C.; Largo, A. Structure and Bonding in Thirdrow Main Group Dicarbides C2 X (X=K−Br). J. Chem. Phys. 2010, 133, 124306. (27) Goswami, S.; Saha, S.; Yadav, R. K. Structural, Electronic and Vibrational Properties of Gex Cy (x + y = 2 − 5) Nanoclusters: A B3LYP-DFT Study. Physica E-lowdimensional Systems & Nanostructures 2015, 74, 175–192. (28) Parida, S. K.; Sahu, S.; Sharma, S. Regioselectivity of Third-Row Maingroup Dicarbides, C2 X (X = K−Br) for CO Interaction: Fukui Function and Topological Analyses. Chem. Phys. Lett. 2016, 659, 216–220. (29) Br¨ unken, S.; McCarthy, M. C.; Thaddeus, P.; Godfrey, P. D.; Brown, R. D. Improved Line Frequencies for the Nucleic Acid Base Uracil for a Radioastronomical Search. Astronom. Astrophys. 2006, 459, 317–320. (30) Br¨ unken, S.; M¨ uller, H. S. P.; Menten, K. M.; McCarthy, M. C.; Thaddeus, P. The Rotational Spectrum of TiO2 . Astrophys. J. 2008, 676, 1367–1371. (31) McCarthy, M. C.; Apponi, A. J.; Thaddeus, P. Rhomboidal SiC3 . The Journal of Chemical Physics 1999, 110, 10645–10648. (32) Pickett, H. M. The Fitting and Prediction of Vibration-Rotation Spectra with Spin Interactions. J. Mol. Spectrosc. 1991, 148, 371–377. (33) Kisiel, Z. Least-Squares Mass-Dependence Molecular Structures for Selected Weakly Bound Intermolecular Clusters. J. Mol. Spectrosc. 2003, 218, 58–67.

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(34) Gottlieb, C. A.; Vrtilek, J. M.; Thaddeus, P. Laboratory Measurement of the Rotational Spectrum of SiCC. Astrophys. J. 1989, 343, L29–L32. (35) McCarthy, M. C.; Baraban, J. H.; Changala, P. B.; Stanton, J. F.; MartinDrumel, M. A.; Thorwirth, S.; Gottlieb, C. A.; Reilly, N. J. Discovery of a Missing Link: Detection and Structure of the Elusive Disilicon Carbide Cluster. J. Phys. Chem. Lett. 2015, 6, 2107–2111. (36) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A 5th-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479–483. (37) Balabanov, N. B.; Peterson, K. A. Systematically Convergent Basis Sets for Transition Metals. I. All-Electron Correlation Consistent Basis Sets for the 3d Elements Sc–Zn. J. Chem. Phys. 2005, 123, 064107. (38) Watts, J. D.; Gauss, J.; Bartlett, R. J. Open-Shell Analytical Energy Gradients for Triple Excitation Many-Body, Coupled-Cluster Methods - MBPT(4), CCSD+T(CCSD), CCSD(T), and QCISD(T). Chem. Phys. Lett. 1992, 200, 1–7. (39) Gauss, J.; Stanton, J. F. Analytic CCSD(T) Second Derivatives. Chem. Phys. Lett. 1997, 276, 70–77. (40) CFOUR, a quantum chemical program package written by J. F. Stanton, J. Gauss, M. E. Harding, P. G. Szalay with contributions from A. A. Auer, R. J. Bartlett, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, L. Cheng, O. Christiansen, F. Engel, R. Faber, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W. J. Lauderdale, F. Lipparini, D. A. Matthews, T. Metzroth, L. A. M¨ uck, D. P. O’Neill, D. R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J. D. Watts and the integral packages MOLECULE (J. Almlöf and P. R. Taylor), PROPS (P. R. Taylor), 16


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ABACUS (T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van W¨ ullen. For the current version, see http://www.cfour.de. (41) Heckert, M.; Kállay, M.; Tew, D. P.; Klopper, W.; Gauss, J. Basis-Set Extrapolation Techniques for the Accurate Calculation of Molecular Equilibrium Geometries Using Coupled-Cluster Theory. J. Chem. Phys. 2006, 125, 044108. (42) Changala, P. B.; Baraban, J. H. Ab Initio Effective Rotational and Rovibrational Hamiltonians for Non-Rigid Systems via Curvilinear Second Order Vibrational Møller–Plesset Perturbation Theory. J. Chem. Phys. 2016, 145, 174106. (43) Lee, K. L. K.; Martin-Drumel, M.-A.; Thorwirth, S.; McCarthy, M. C. Talk TC09 entitled “Generation and Structural Characterization of the Ge Carbides GeC4 , GeC5 , and GeC6 by Laser Ablation, Broadband Rotational Spectroscopy, and Quantum Chemistry,” 72nd International Symposium on Molecular Spectroscopy, June 2017, Urbana, IL. (44) McCarthy, M. C.; Gottlieb, C. A.; Thaddeus, P. Silicon Molecules in Space and in the Laboratory. Mol. Phys. 2003, 101, 697–704. (45) Li, G.; Wang, C. Structures and Properties of the Tin-Doped Carbon Clusters. J. Mol. Struct.: THEOCHEM 2007, 824, 48–57. (46) Li, G.; Xing, X.; Tang, Z. Structures and Properties the Lead-Doped Carbon Clusters − PbCn /PbC+ n /PbCn (n = 1 − 10). J. Chem. Phys. 2003, 118, 6884–6897.

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Germanium Dicarbide: Evidence for a T-Shaped ... - ACS Publications

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