1. 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

2. 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

3. 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].

4. 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

5. 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.

6. ? Formation of HO2+ from O2 and H3+ NIST WebBook values:
PA(O2) = kcal/mol
NIST WebBook values:
PA(H2 ) = kcal/mol
endothermic by 0.31 kcal/mol?
However, Ruscic et al. [JPCA 2006, 110, 6592] recommended:
PA(O2) =  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)

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

8. Equilbrium Structure HO2 HO2+ Treatment rOO (Å) rOH (Å) q (°)
RCCSD(T) Valence CBS
+CVDZ
Robbe et al
HO2+
Treatment rOO (Å) rOH (Å) q (°)
RCCSD(T) Valence CBS
+CVDZ
Robbe et al

9. 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:

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

11. 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)

12. 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)

13. 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, ] and Neese [JCP 2007, 127, ] 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.

14. 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

15. <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

16. 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

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

18. 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 DEAC02-06CH BJM: UIUC Critical Research Initiative program, NSF CAREER award (NSF CHE ).
Kirk A. Peterson (Washington State University)
Frank Neese (Universität Bonn)
Thom H. Dunning, Jr. (University of Illinois)

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