N 2 -CO 2 Consequences for Global Warming? Daniel Frohman Wesleyan University TH01 June 22, 2010

Motivation for study N 2 is the most abundant atmospheric species ~ 78% CO 2 is of importance as a greenhouse gas Complexation is expected to influence CO 2 ’s role as a greenhouse gas Study of the N 2 -CO 2 suggested by Prof. Klemperer (Harvard) and built upon previous work in a Wesleyan senior thesis by Edwin Contreras ’00

mode of CO 2 Occurs at cm -1 in free CO 2 (1) Corresponds to bending motions Earth’s thermal emission spectrum maximizes at the mode of CO 2 (1) Phys. Rev. 41 (1932) 291 P. Martin & E. Barker

Influence on of complexation Q-branch narrow relative to P & R branches CO 2 Q-branch (∆J=0) is saturated by rot. transitions Complexation may alter Q-branch rot. transition saturation  CO 2 absorption changes Spectral Calculator GATS, Inc. ParameterValue Species 12 C 16 O 2 Pressure mbar Temperature298 K Concentration380 ppm Path length10 cm

N 2 -CO 2 ’s CO 2 bending (ab initio) Gaussian 09 MP2/aug-cc-pVTZ cm cm-1 CO 2 (exptl.) = cm -1 CO 2 (G09) = cm -1

14 N 2 CO 2 Spectrum Ortho: I=0,2 Para: I=1  separate constants for each improves fit, suggests N 2 tunneling No odd K a transitions FTMW++

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Isotopomer spectrum Only 14 N(I=1), not 15 N(I=1/2) causes quadrupole splitting Isotopomer spectra less complicated Obtained in natural abundance 14 N 15 NCO 2

Ab initio & Counterpoise Gaussian 09 MP2/aug-cc-pVTZ Counterpoise (CP) correction adjusts geometry from skewed to (C2v) T-shaped & R CN increases G09 frequency with APF-D/3Za1P  A 0, B 0, C 0 and much faster than MP2/aug-cc-pVTZ CP corrected BDE 0.93 kcal/mol, uncorrected BDE 1.18 kcal/mol Method/Basis SetA (MHz)(B+C)/2 (MHz) MP2/aug-cc-pVTZ (A e ) (B e +C e )/2 APF-D/3Za1P (A e ) (B e +C e )/2 APF-D/3Za1P (A 0 ) (B 0 +C 0 )/2 Obs (IR) (1) (para) R CN = 3.15 Å (1) Dyke, Howard, Walsh, J.Mol.Struct. 189 (1988) p. 111

Observed Structure ParameterValue (para I=1) Θ a (N 2 )19.52° Θ a (CO 2 )87.7°, 92.3° Å MHz (1) Mol.Phys. 84 (1) (1995) J. Hutson Kisiel, Z., PMIFST, in PROSPE-Programs for Rotational SPEctroscopy.

Constants Kisiel, Z., PMIFST, in PROSPE-Programs for Rotational SPEctroscopy N 2 CO 2 (ortho) 14 N 2 CO 2 (para) 14 N 15 NCO 2 15 N 14 NCO 2 A B (7) (7) (9) (12) C (7) (7) (9) (12) ∆ A – (B+C)/ (B+C)/ (4) (5) (6) (8) (B-C)/ (3)79.76 (3)78.01 (4)75.26 (6) ∆ J (kHz)10.6 (3)10.0 (3)9.4 (3)9.6 (4) (8) (13) (16) (20) All values given in MHz unless otherwise specified A & A - (B+C)/2 were fixed with A from Dyke, Howard, Walsh, J.Mol.Struct. 189 (1988) p st N   2 nd N

Cross and Parallel Structures Represent transition states for N 2 tunneling Parallel structure N 2 rotates in the complex’s ab plane Cross structure N 2 rotates in the ac plane Barrier height of ~ 155 cm -1 (cross), 203 cm -1 (parallel), making the cross somewhat favored Gaussian 09

N 2 tunneling w.r.t. N, N interchange

Atmospheric [CO 2 ] Favorability of complex formation and [CO 2 ] vary with location in atmosphere Atmosphere is complicated system making K eq difficult to get Simplified model of temperature and pressure as a function of altitude Estimates suggest influence by N 2 CO 2 in CO 2 ’s overall role as a greenhouse gas likely negligible

Results Experimental and ab initio data indicate the N 2 -CO 2 complex is T-shaped Separate constants for ortho and para states indirectly suggest that N 2 tunneling occurs in a non-rigid N 2 -CO 2 complex similarly to that in N 2 OCS (1) cm cm cm cm -1 G09 APF-D/3Za1P Prof. George Petersson (1) JMolSpec 175 (1996) J. Connelly, S. Duxon, S. Kennedy, B.Howard, J. Muenter

Acknowledgements Prof. Novick & Pringle Ross Firestone * Prof. Petersson * Wesleyan University ‘12

QUADRUPOLE SPLITTING Q is the nuclear quadrupole moment dyadic, E is the electric field gradient e is the charge of a proton, z n is in the nuclear spin direction, r is distance from center of nucleus to the charge (p137) q j is the molecular field gradient in the z direction, theta is angle between z axis in space and r (or I and J)pg 136, rho-jj is electron charge density for mj=J Kroto, H.W., Molecular Rotation Spectra. 1992, Mineola: Dover Publications, Inc. Townes, C.H. and A.L. Schawlow, Microwave Spectroscopy. 1955, New York: McGraw-Hill Book Company

Supersonic Velocity Derivation For monatomic ideal gas, like Ar Beijerinck, H. Physica, C. P 425 Free Jet Sources, Miller, D. p