N 2 CO 2 Consequences for Global Warming

N 2 -CO 2 Consequences for Global Warming? Daniel Frohman Wesleyan University TH 01 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 667. 5 cm-1 in free CO 2 (1) • Corresponds to bending motions • Earth’s thermal emission spectrum maximizes at the (1) Phys. Rev. 41 (1932) 291 P. Martin & E. Barker mode of CO 2

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 Parameter Value Species 12 C 16 O Pressure 1013. 25 mbar Temperature 298 K Concentration 380 ppm Path length 10 cm 2 http: //www. spectralcalc. com/calc/spectralcalc. php Spectral Calculator GATS, Inc.

N 2 -CO 2’s CO 2 bending (ab initio) 656. 33 cm-1 659. 94 cm-1 CO 2 (G 09) = 658. 98 cm-1 CO 2 (exptl. ) = 667. 5 cm-1 Gaussian 09 MP 2/aug-cc-p. VTZ

14 N 2 CO 2 Spectrum 202 - 101 • Ortho: I=0, 2 Para: I=1 separate constants for each improves fit, suggests N 2 tunneling • No odd Ka 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 MP 2/aug-cc-p. VTZ RCN= 3. 15 Å • Counterpoise (CP) correction adjusts geometry from skewed to (C 2 v) T-shaped & RCN increases • G 09 frequency with APF-D/3 Za 1 P A 0, B 0, C 0 and much faster than MP 2/aug-cc-p. VTZ • CP corrected BDE 0. 93 kcal/mol, uncorrected BDE 1. 18 kcal/mol Method/Basis Set A (MHz) (B+C)/2 (MHz) MP 2/aug-cc-p. VTZ 11538. 252 (Ae) 1917. 791 (Be+Ce)/2 APF-D/3 Za 1 P 11749. 004 (Ae) 1890. 305 (Be+Ce)/2 APF-D/3 Za 1 P 11899. 104 (A 0) 1861. 330 (B 0+C 0)/2 Obs. 11885. 3 (IR)(1) 1903. 370 (para) (1) Dyke, Howard , Walsh, J. Mol. Struct. 189 (1988) p. 111

Observed Structure Parameter Value (para I=1) Θa(N 2) 19. 52° Θa(CO 2) 87. 7°, 92. 3° 3. 727 Å -4. 471 MHz Kisiel, Z. , PMIFST, in PROSPE-Programs for Rotational SPEctroscopy. http: //info. ifpan. edu. pl/~kisiel/prospe. htm. (1) Mol. Phys. 84 (1) (1995) 185 -199 J. Hutson

Constants • 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. 111 14 N CO 2 2 14 N 15 NCO 2 15 N 14 NCO 2 A 11885. 3 11878. 89 11871. 77 B 2062. 75 (7) 2062. 88 (7) 2037. 95 (9) 1999. 76 (12) C 1744. 01 (7) 1743. 86 (7) 1725. 90 (9) 1698. 71 (12) (ortho) (para) ∆ 2. 26 2. 30 2. 29 2. 22 A – (B+C)/2 9981. 93 9996. 96 10022. 53 (B+C)/2 1903. 3789 (4) 1903. 3699 (5) 1881. 9283 (6) 1849. 2347 (8) (B-C)/4 79. 69 (3) 79. 76 (3) 78. 01 (4) 75. 26 (6) ∆J (k. Hz) 10. 6 (3) 10. 0 (3) 9. 4 (3) 9. 6 (4) -4. 4726 (8) -4. 4710 (13) -4. 5189 (16) -4. 4585 (20) 1 st N 2 nd N Kisiel, Z. , PMIFST, in PROSPE-Programs for Rotational SPEctroscopy. http: //info. ifpan. edu. pl/~kisiel/prospe. htm.

• • 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 Keq 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) 17. 02 cm-1 30. 41 cm-1 62. 20 cm-1 76. 30 cm-1 G 09 APF-D/3 Za 1 P Prof. George Petersson (1) JMol. Spec 175 (1996) 85 -98 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, zn is in the nuclear spin direction, r is distance from center of nucleus to the charge (p 137) qj 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: Mc. Graw-Hill Book Company

Supersonic Velocity Derivation For monatomic ideal gas, like Ar Beijerinck, H. Physica, 1983 121 C. P 425 Free Jet Sources, Miller, D. p. 17 -18