Transcript Document

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 difficult 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?
3A”
1.934 D
1.518 D
MRCI/aug-cc-pV5Z
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
• dipole moment
• rotational constants
• zero-field splitting tensor
• anharmonic frequencies
• spin-rotation 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
Most likely formation pathway:
H3+ + O2  H2 + HO2+
(1)
H2 + HO2+
H3O2+
The reaction energy for this can
be derived from the proton
affinities of H2 and O2:
H 2 + H +  H 3+
(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(H2 ) = 100.93 kcal/mol
PA(O2) = 100.62 kcal/mol
endothermic by 0.31 kcal/mol?
However, Ruscic et al. [JPCA 2006, 110, 6592] recommended:
exothermic by 0.05 kcal/mol?
PA(O2) = 100.98  0.14 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)
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
H3+ [Lindsay, JMS 2001, 210, 60]:
O2 [Cosby, JCP 1992, 97, 6108]:
-63.0
64.121 cm-1
-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
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.
Perturbation theory was used for anharmonic shifts:
 ni = wi + S ( xii, xij )
 B0 = Be – ½ S aiB
(similar for A and C)
- anharmonicities
- rotation-vibration interaction constants
Rotational Constants
HO2
rotational constant (error) (GHz)
A0
B0
C0
Experimenta
610.273
33.518
31.668
This work
615.997
33.604
31.643
(+5.724)
(+0.086)
(-0.025)
612.205
33.247
31.448
Robbe et al.
aChance,
JMS 1997, 183, 518.
HO2+
rotational constant (GHz)
A0
B0
C0
This work
659.301
38.344
35.885
Vibrational Frequencies
HO2
frequency (error) (cm-1)
n1
n2
n3
Experimenta
3436
1392
1098
This work
3457
1406
1128
(+21)
(+14)
(+30)
3449
1396
1106
Robbe et al.
aYamada,
JCP 1983, 78, 4379; Burkholder, JMS 1992, 151, 493.
HO2+
This work
n1
frequency (cm-1)
n2
n3
3028
1440
1068
Dipole Moment Components
HO2
dipole moment (error) (D)
ma
mb
Experimenta
1.412
1.541
This work
1.405
1.572
(-0.007)
aSaito,
(+0.031)
JMS 1980, 80, 34.
HO2+
dipole moment (D)
ma
mb
This work
1.518
1.934
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+
this
work
this
work
DSS
1.555
1.810
DSOC
2.220
5.060
3.775
6.870
ZFS
(cm-1)
D
EXPTa
3.96
ESS
0.013
ESOC
0.020
E
0.033
aTinkham,
Phys Rev 1955, 97, 937.
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
HO2
HO2+
this work
4 sts
6 sts
EXPTa
this
work
eaa
-49572
-46730
-1094
-1182
ebb
-422.9
-432
-467
-481
ecc
8.748
-159
-429
-476
aFink,
JMS 1997, 185, 304.
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’