1. Analysis of the rotational spectrum of HDO in its v2 = 0 and 1 vibrational states up to 2.8 THz
Holger S. P. Müller, J. C. Pearson, S. Brünken, S. Yu,
C. P. Endres, F. Lewen, B. J. Drouin, H. Mäder
I. Physikalisches Institut, Universität zu Köln, Germany
Jet Propulsion Laboratory, Pasadena, CA, USA
Institut für Physikalische Chemie, Univ. Kiel, Germany
66th International Symposium on Molecular Spectroscopy; TC 04

2. Motivation H2O is a very important constituent of Earth's atmosphere
 HDO is also quite important
HDO is abundant in space, particularly in star-forming regions
– deuteration is a probe into star formation
– even HD18O has been seen (next contribution by JCP)
water is a simple, fundamental molecule
 test case for quantum chemical calculations
water (as other light hydrides) exhibits large centrifugal distortion effects
 use of conventional Watson-type Hamiltonian is problematic
 H2O (and isotopologs) as test cases for alternative approaches

3. Basic spectroscopic properties
fundamental vibrations
H2O, C2v
3756 ν3(b2) = νas
3657 ν1(a1) = νs
1595 ν2(a1) = δ
HDO, CS
3707 ν1(a') = ν(OH)
2724 ν2(a') = ν(OD)
1403 ν3(a') = δ ν3 ν1 ν2
common
numbering
numbering according
to symmetry classes
A = GHz
B = GHz
C = GHz
μa = 0.66 D
μb = 1.73 D
κ = –0.6828

4. previous work (selection)
rotational data
M. W. P. Strandberg, J. Chem. Phys. 17 (1949) 901 (3 MW)
F. C. De Lucia et al., J. Chem. Phys. 55 (1971) (< 500 GHz (+))
W. Lafferty et al., Comp. Rend. B 273 (1971) 388 (gs + 6v2 = 1; < 68 GHz)
J. K. Messer et al., J. Mol. Spectrosc. 105 (1984) 139 (gs + 4v2 = 1; < 1010 GHz)
J. W. C. Johns, JOSA B 2 (1985) (FIR)
Paso & Horneman, JOSA B 12 (1995) (FIR)
rovibrational data (ν2 only)
J.-M. Flaud et al., IJIMW 7 (1986) 68
R. A. Toth, J. Mol. Spectrosc. 162 (1993) 20; 195 (1999) 73
K. J. Siemsen et al., J. Mol. Spectrosc. 199 (2000) 144 (52,4 – 51,5 to 2 kHz)
J. Tennyson et al., JQSRT 111 (2010) (hot + rot; cr. ev. compilation)

5. present work wave-guide FTMW (Kiel; 8 – 25 GHz) BWO (Köln, JPL)
laser side band (Köln)
BWO + (superlattice) frequency multiplier (Köln)
multiplier chains (JPL, Köln)
partial analysis in: Sandra Brünken, PhD thesis, 2005, Köln, Germany
80 GHz – 2.8 THz; J  17/13 Ka  9, 5 (v2 = 0, 1)
aim: create as complete set of "MW" connections as possible
 ~230/100 new lines

6. selected spectral recordings

7. the connections
v = 0
v2 = 1

8. the Euler ansatz Ji2 1 + aJa2 + b(J2 – Ja2) Ji*2 = J2 – Ji2
problem: slow convergence of Hamiltonian
& oscillatory behavior; e.g. CH2
A ≈ –DKK2 ≈ HKK4 ≈ – LKK @ K ≈ 5
Ji2
1 + aJa2 + b(J2 – Ja2)
Ji*2 =
a ≈ DK/A
b ≈ 2DJ/(B+C)
J2 – Ji2
1 + aJa2 + b(J2 – Ja2)
J*2 =
H. M. Pickett et al., J. Mol. Spectrosc. 233 (2005) 174.

9. does this ansatz work ? So what ?! however, it does work !
this does not work near dissociation !
problems may occur if convergence changes
however, it does work !
H. M. Pickett et al., J. Mol. Spectrosc. 233 (2005) 174: H2O  4000 cm–1
apparently no advantage for comparatively well behaved H2S !!
S. Brünken et al., PCCP 9 (2007) 2103: D2O, v2  1
S. Brünken et al., J. Chem. Phys. 123 (2005) #164315: CH2

10.   the fitting procedure
start with evaluated IR data set (v2  1) and existing parameter set 
add rotational data with MW accuracy
 the shortest and quickest way to success is to start from scratch !
use reasonable data set, keep everything fixed
start with J  1 (or 2)
release or add as few parameters as possible/reasonable
weight out or omit all lines with large residuals
add 1 or 2 J (or Ka)
release or add ...

11. interactions

12. where are we now ?
J  18, Ka  10: very few lines omitted / corrected / weighted out
J  24/18, Ka  16/11: ~6200 lines; rms error ~0.96; some larger residuals
scrutinize data (higher J rotational & IR)
include remaining data (~1100)
interaction: F2ab ≈ 6 MHz (ΔK = 3 term; maybe more)