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Timothy J. Lee,a Xinchuan Huang,b
Highly Accurate Quartic Force Fields, Vibrational Frequencies, and Spectroscopic Constants for Cyclic and Linear C3H3+ Including 13C and Deuterium Isotopologues Timothy J. Lee,a Xinchuan Huang,b and Peter R. Taylorc aSpace Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA, USA bSETI Institute, 189 Bernardo Ave, Suite 100, Mountain View, CA 94043, USA cVLSCI, University of Melbourne, Vic 3010, Australia
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NASA, ESA & Ground Based IR Astronomy Missions
NASA has several missions focused on infrared astronomy: SOFIA, Spitzer, Herschel (ESA), JWST. Spitzer Space Telescope is in extended operation, but the IR spectra are medium resolution. SOFIA (Stratospheric Observatory for Infrared Astronomy) is an airplane-based observatory, which should allow for updates to instruments periodically – initial science flights ongoing! The Herschel Space Observatory (an ESA endeavor with NASA involvement); Launched in 2009; high-resolution. James Webb Space Telescope (JWST) launch in 2015. Atacama Large Millimeter Array (ALMA) Early science 2011. Beginning of a Golden Age for IR and Far IR Astronomy!
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SOFIA Flying! And…
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Recording scientific data!
False color image of the heart of the Orion star-formation complex taken from the SOFIA (Stratospheric Observatory for Infrared Astronomy) using the FORCAST mid-infrared camera (P.I. Terry Herter, Cornell University). SOFIA is optimized for observations at infrared wavelengths that cannot be accessed by any telescope on the ground or currently in space. This image, a two-filter composite (19.7 microns – green, 37.1 microns – red), reveals detailed structures in the clouds of star construction material, as well as heat radiating from a cluster of luminous newborn stars seen in the upper right.
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Early HIFI Spectra
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c-C3H3+ : Background c-C3H3+ has been of interest in astronomy/astrochemistry for more than 20 years: it is the precursor to formation of cyclopropenylidene which is present in many astrophysical environments 1989: Anharmonic fundamentals predicted; MP2/TZ2P+SCF/DZP 2002: Dopfer, Roth, and Maier observe vibrational spectra of LC3H3+, where L = Ne, Ar, N2, O2, and CO2 2010: Duncan and coworkers observe vibrational spectra of ArC3H3+: 3182 cm-1 is assigned to ν4(e’) (antisymmetric C-H str) Scaled ab initio calculations [CCSD(T)] suggest a fundamental for ν4(e’) near 3138 cm-1 Duncan and coworkers state “The difficulties of theory for these ions require significant further investigation.” 2011: Botschwina and Oswald compute cuts of a PES for ArC3H3+ and find for c-C3H3+ that there is not a preferred minimum
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l-C3H3+ : Background The linear form, l-C3H3+, is 27.9 kcal/mol (0 K) higher in energy than the cyclic form, but both are usually found in experiments Dopfer, Roth, and Maier’s experiments (2002) and later Duncan and coworkers experiments (2010) both observe many vibrational band assigned LC3H3+, where L = Ne, Ar, N2, O2, and CO2 2010: Botschwina and Oswald compute a partial PES (including the totally symmetric modes) and compute anharmonic vibrational spectra – their calculations generally agree with the experiments and confirm assignments, but they question the assignment for the C-C single bond stretch, ν5(a1) 2011: Botschwina and Oswald compute cuts of a PES for ArC3H3+ and find for l-C3H3+ that there is a preferred minimum – our study suggest that this result may explain the discrepancy for ν5(a1)
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Approach for Accurate Quartic Force Fields (QFFs)
Determine “reference” geometry with at least 5Z basis set; include core-correlation Set up grid of points for a QFF about the reference geometry Calculate CCSD(T) energies for the TZ, QZ, and 5Z basis sets Compute ic-ACPF energies (or different higher-order method); TZ or QZ basis Compute core-correlation correction with CCSD(T) and QZ basis set Compute scalar relativity effects at CCSD(T)/TZ level Compute correction for diffuse functions or include explicitly If desired, compute DBOC (MCSCF or Hartee-Fock) Compute all energies to machine precision! Extrapolate CCSD(T) TZ/QZ/5Z energies to basis set limit or use F12 method Include higher-order correlation, core-correlation, scalar relativity, diffuse function corrections (+DBOC) Fit single QFF to high precision and transform to equilibrium geometry X. Huang and T. J. Lee, J. Chem. Phys. 129, (2008); X. Huang, D. W. Schwenke, and T. J. Lee, J. Phys. Chem. A 113, (2009); X. Huang and T. J. Lee, J. Chem. Phys. 131, (2009); X. Huang, E. F. Valeev, and T. J. Lee, J. Chem. Phys. 133, (2010).
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C3H3+ : Structures Our best equilibrium structures, including CCDS(T)/TQ5 basis set extrapolation, core-correlation, and scalar relativity Values in italics are vibrationally averaged quantities (position average) These should be the most accurate geometrical structures available X. Huang, P. R. Taylor, and T. J. Lee, J. Phys. Chem. 115, 5005 (2011)
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c-C3H3+ : Results Agreement between PT and VCI is excellent!
Mode PT VCI Expt1 Expt2 Expt3 ν1(a1’) 3176.6 3175.4 3183 ν2(a1’) 1618.3 1622.1 1626 ν3(a2’) 1040.3 1040.6 (1031) ν4(e’) 3131.7 3134.8 3138 3182 3129 ν5(e’) 1299.6 1296.2 1290 1293 ν6(e’) 924.2 927.0 927 ν7(a2”) 756.6 757.1 758 ν8(e”) 1004.5 1002.0 (990) Agreement between PT and VCI is excellent! Expt1 refers to matrix isolation experiments; agreement is good Expt2 refers to Duncan and coworkers; agreement for ν4(e’) is poor Expt3 is an average of the results from Dopfer, Roth, and Maier; agreement is very good Conclusion: the 3182 cm-1 band is not ν4(e’)
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l-C3H3+ : Results Mode PT VCI Expt ν1(a1) 3228.7 3239.0 3238 ν2(a1) 2997.0 2998.7 3004 ν3(a1) 2084.0 2082.2 2077 ν4(a1) 1429.8 1434.4 1445 ν5(a1) 1128.5 1131.8 1222 ν6(b1) 3061.9 3071.0 3093 ν10(b2) 1054.6 1058.1 1111 Agreement between PT and VCI is very good (not quite as good as for c-C3H3+) Expt is a combination of the recent gas-phase experiments (where they overlap, there is no discrepancy) Agreement with Expt is good in some cases (ν1, ν2, ν3, ν4, and to a lesser extent ν6; only the lower component of resonance doublet is given for ν6) The differences for ν5 and ν10, can be explained by the preferred structure of ArC3H3+ Cheuk Ng recently obtained (about) 1133 cm-1 for ν5
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Isotopologues Since c-C3H3+ has D3h symmetry, it has no permanent dipole moment However, c-13CC2H3+, c-C3H2D+, and similar isotopologues will possess a permanent dipole moment since the center of mass and center of nuclear charge are no longer the same c-13CC2H3+, c-C3H2D+, and c-13CC2H2D+ have dipole moments of D, D, and D, respectively. These are plenty large enough for the molecules to be observed in rotational spectroscopy, provided there is a large enough concentration. Spectroscopic constants for c-13CC2H3+, c-C3H2D+, and c-13CC2H2D+ isotopologues of c-C3H3+ have been predicted as well as the H2CCCD+, HDCCCH+, H213CCCH+, H2C13CCH+, and H2CC13CH+ isotopologues of l-C3H3+ For ALMA, the increased sensitivity should allow for some of these to be identified, with the most likely c-C3H3+ isotopologue being c-C3H2D+ X. Huang and T. J. Lee, Astrophys. J. 73x, 0000 (2011)
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Notes and Conclusions Golden age for IR and Far IR astronomy has begun high-resolution spectroscopic constants of many, many molecules are needed. High-level ab initio theory is well positioned to make a significant contribution to these needs, including minor isotopologues of transient molecules. Best approach for computing accurate purely ab initio QFFs and PESs continues to evolve, but state-of-the art includes many “small” corrections. All the QFFs computed here had full symmetry (D3h for c-C3H3+) and yield degenerate vibrational frequencies for degenerate modes. The QFFs were used in variational calculations after transforming them into a Morse-Cosine coordinate system (Morse-Cosine-Sine for c-C3H3+). 3182 cm-1 band assigned to ν4(e’) for c-C3H3+ by Duncan et al is misassigned. Agreement between theory and experiment for the other bands of c-C3H3+ and l-C3H3+ is reasonable with plausible explanations of perturbations due to the Ar tag for those bands of l-C3H3+ that do not agree as well. Spectroscopic constants for 13C and deuterium isotopologues of cyclic and linear C3H3+ have been predicted (together with dipole moments).
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Acknowledgements Funding from the following programs is gratefully acknowledged: Guest Observer program of Herschel (NASA) Astrophysics Research and Analysis (NASA; APRA) Venus Express Participating Scientists (NASA) Guest Observer program of Spitzer (NASA)
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