Ab initio predictions for HO2+: Theoretical Guidance for an Astronomical Detectability Study David E. Woon, Susanna L. Widicus Weaver, Branko Ruscic, and Benjamin J. McCall FD09

HO2+: Another Approach to the O2 Problem? Molecular oxygen (O2) is a difficult species to observe. The only observation to date – the Odin study of r Oph A [Larsson A&A 2007, 466, 999] – found a limited abundance, just 5 x 10-8 relative to [H2]. This is much less than predicted by models, ~5-10 x 10-6 [Goldsmith, ApJ 2000, 539, 123]. It has been recognized for at least three decades [Herbst, ApJ 1977, 215, 503] that protonated forms of species that are diffi-cult to detect can be useful tracers of the parent molecules. A good example is N2H+, which was observed well before N2 was finally detected. [Turner, ApJ 1974, 193, L83; Green, ApJ 1974, 193, L89; Knauth, Nature 2004, 429, 636]. no m, microwave inactive large m, good spectrum

HO2+: Another Approach to the O2 Problem? While O2 does have observable weak dipole-allowed magnetic transitions, atmospheric spectral interference seriously impedes ground-based observations. Can HO2+ be used as a tracer for O2? 1.934 D 1.518 D MRCI/aug-cc-pV5Z 3A” No rotational spectrum has yet been reported for HO2+, which currently precludes astronomical searches. A wide range of data is available for HO2 and can be used to benchmark theoretical calculations for HO2+. The best prior theory study is the work of Robbe et al. [Chem Phys 2000, 252, 9].

HO2+: Ab initio Predictions Quantum chemical calculations were performed to evaluate the most likely pathway to the formation of HO2+ and to provide guidance for the laboratory study of its rotational spectrum. reaction energetics anharmonic frequencies zero-field splitting tensor dipole moment spin-rotation constants rotational constants Treatment: MRCI and RCCSD(T) calculations with basis sets as large as aug-cc-pV5Z. Programs used included: MOLPRO optimizations and potential energy surfaces SURFIT fitting and analysis of surfaces ORCA prediction of zero-field splitting tensor components

Formation of HO2+ from O2 and H3+ H3+ + O2  H2 + HO2+ (1) Most likely formation pathway: H3+ + O2 H2 + HO2+ H3O2+ The reaction energy for this can be derived from the proton affinities of H2 and O2: H2 + H+  H3+ (2) PA(H2) = –DrH0(2) O2 + H+  HO2+ (3) PA(O2) = –DrH0(3) The reaction enthalpy of (1) is: DrH°(1) = PA(H2) - PA(O2) Parallel expressions exist for DG’s: gas phase basicities replace PA’s.

? Formation of HO2+ from O2 and H3+ NIST WebBook values: PA(O2) = 100.62 kcal/mol NIST WebBook values: PA(H2 ) = 100.93 kcal/mol endothermic by 0.31 kcal/mol? However, Ruscic et al. [JPCA 2006, 110, 6592] recommended: PA(O2) = 100.98  0.14 kcal/mol exothermic by 0.05 kcal/mol? ? … which led to the collaboration with Branko Ruscic of ANL. Active Thermochemical Tables (ATcT) analysis of available data (will be described in FD10)

VERY slightly endothermic Calculations for H3+ + O2  HO2+ + H2 DEe valence complete basis set (CBS) limit: +222.1 cm-1 DEe core-valence contribution +28.3 harmonic vibrational ZPE correction -199.5 anharmonic vibrational ZPE correction +76.4 rotational ZPE correction -63.0 H3+ [Lindsay, JMS 2001, 210, 60]: 64.121 cm-1 O2 [Cosby, JCP 1992, 97, 6108]: -1.0857 cm-1 DE0 NET, Theory +64.3 cm-1 DrE00 from ATcT analysis +50±9 cm-1 VERY slightly endothermic

Equilbrium Structure HO2 HO2+ Treatment rOO (Å) rOH (Å) q (°) RCCSD(T) Valence CBS 1.3270 0.9709 104.458 +CVDZ 1.3247 0.9701 104.549 Robbe et al. 1.337 0.968 103.90 HO2+ Treatment rOO (Å) rOH (Å) q (°) RCCSD(T) Valence CBS 1.2295 1.0110 112.529 +CVDZ 1.2272 1.0102 112.743 Robbe et al. 1.237 1.007 111.8

Anharmonic Properties Potential energy surfaces were fit with SURFIT to 84 energy calculations distributed around the equilibrium structure for a given level of theory and basis set. The potential function include 69 terms consisting of the full quintic potential and selected sextic terms. All RMS fitting errors were <0.8 cm-1. ni = wi + S ( xii, xij ) - anharmonicities B0 = Be – ½ S aiB - rotation-vibration interaction constants (similar for A and C) Perturbation theory was used for anharmonic shifts:

rotational constant (error) (GHz) rotational constant (GHz) Rotational Constants aChance, JMS 1997, 183, 518. A0 610.273 Experimenta B0 C0 33.518 31.668 This work 615.997 33.604 31.643 (+5.724) (+0.086) (-0.025) HO2 rotational constant (error) (GHz) Robbe et al. 612.205 33.247 31.448 A0 659.301 This work B0 C0 38.344 35.885 HO2+ rotational constant (GHz)

frequency (error) (cm-1) Vibrational Frequencies aYamada, JCP 1983, 78, 4379; Burkholder, JMS 1992, 151, 493. n1 3436 Experimenta n2 n3 1392 1098 This work 3457 1406 1128 (+21) (+14) (+30) HO2 frequency (error) (cm-1) Robbe et al. 3449 1396 1106 3028 This work 1440 1068 HO2+ n1 n2 n3 frequency (cm-1)

dipole moment (error) (D) Dipole Moment Components aSaito, JMS 1980, 80, 34. ma 1.412 Experimenta mb 1.541 This work 1.405 1.572 (-0.007) (+0.031) HO2 dipole moment (error) (D) ma mb This work 1.518 1.934 HO2+ dipole moment (D)

Zero-Field Splitting Magnetic interactions between the unpaired electrons in triplet states give rise to line splitting even in the absence of an applied field. ORCA [Neese et al., Universität Bonn] was used to compute the spin-spin (SS) and spin-orbit coupling (SOC) contributions to the D and E tensors. Molecular oxygen O2 (3Sg-) was used for benchmarking. See Ganyushin & Neese [JCP 2006, 125, 024103] and Neese [JCP 2007, 127, 164112] for more extensive comparisons. DSS (ESS) was computed at the CASSCF/AVQZ level, while DSOC (ESOC) was computed at the MRCI/VQZ level and involved summing over four states each of singlet and triplet symmetry.

Zero-Field Splitting O2 HO2+ DSS 1.555 this work 2.220 ZFS (cm-1) DSOC aTinkham, Phys Rev 1955, 97, 937. DSS 1.555 this work 2.220 O2 ZFS (cm-1) HO2+ DSOC 1.810 5.060 D EXPTa 6.870 3.96 ESS ESOC 0.013 0.020 E 0.033 3.775

<0|La|n><n|zbLb|0> Spin-Rotation Coupling Constants eab = –4Ba S n0 <0|La|n><n|zbLb|0> ( E0 – En ) ; z = 151 cm-1 [Barnes, JMS 1978, 72, 86] Angular momentum matrix elements: CASSCF Energies: MRCI Basis set convergence was tested with AVDZ and AVTZ sets HO2: sum over 4 states of 2A” and 2A’ symmetry HO2+: sum over 4 or 6 states of 3A” and 3A’ symmetry

Spin-Rotation Coupling Constants -46730 this work HO2 HO2+ EXPTa -49572 eaa -1094 -432 -422.9 ebb -467 -159 8.748 ecc -429 aFink, JMS 1997, 185, 304. -1182 -481 -476 4 sts 6 sts

Part II: Astronomical Detectability of HO2+ Hang around for Susanna’s talk...

Acknowledgments DEW: NASA Exobiology Program, grant NNX07AN33G. SLWW: UIUC Critical Research Initiative program. BR: Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, US Department of Energy, contract number DEAC02-06CH11357. BJM: UIUC Critical Research Initiative program, NSF CAREER award (NSF CHE-0449592). Kirk A. Peterson (Washington State University) Frank Neese (Universität Bonn) Thom H. Dunning, Jr. (University of Illinois)

Configuration Diagrams for HO2+ 3A’’, 1A’’ 1A’ 3A’ +