On the energy dependence of the Zeeman and hyperfine parameters in the ?2σ+ state of OH and OD

Article abstract of DOI:10.1016/S0301-0104(03)00184-8

We report quantum beat studies of the energy dependence of the Zeeman parameters in the ?²Σ⁺ state of OH and OD, and the nuclear hyperfine parameters of OD(?²Σ⁺). In contrast to previous work, we find that the sign and magnitude of the anisotropic g-factor g₁ for v′ = 0 is consistent with that expected from Curl's relationship. However, at higher energies g₁ changes sign, a result we attribute to interaction with the repulsive I⁴II state, which is known to lead to predissociation at higher energies. The magnetic and electric quadrupole hyperfine constants were determined for OD(?²Σ⁺, v′ = 0-3), and the constants for v′ = 2, 3 are reported here for the first time. The derived values are consistent with previous experimental results and available ab initio calculations.

Full text of DOI:10.1016/S0301-0104(03)00184-8

Chemical Physics 291 (2003) 61–72
www.elsevier.com/locate/chemphys
On the energy dependence of the Zeeman and
þ
2
~
hyperfine parameters in the A R state of OH and OD
Ju Xina, Ionela Ionescub, David Kuffelb, Scott A. Reidb,*
a
Department of Physics and Engineering Technologies, Bloomsburg University, Bloomsburg, PA 17815, USA
b
Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881, USA
Received 13 March 2003
Abstract
þ
2
~
We report quantum beat studies of the energy dependence of the Zeeman parameters in the A R state of OH and
þ
2
~
OD, and the nuclear hyperfine parameters of OD(A R ). In contrast to previous work, we find that the sign and
magnitude of the anisotropic g-factor gl for t0 ¼ 0 is consistent with that expected from CurlÕs relationship. However, at
higher energies gl changes sign, a result we attribute to interaction with the repulsive 14P state, which is known to lead
to predisþsociation at higher energies. The magnetic and electric quadrupole hyperfine constants were determined for
2
0
0
~
OD(A R ; t ¼ 0–3Þ, and the constants for t ¼ 2; 3 are reported here for the first time. The derived values are consistent
with previous experimental results and available ab initio calculations.
Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction
O(3P) + H(2S), [41] providing a classic example of
Case I predissociation [2]. Experimental studies
[41,46,50,52,55] show that for low N the onset of
predissociation occurs at t0 ¼ 2 for OH and t0 ¼ 3
for OD, and the trends in lifetime as a function of
excited rotational and vibrational state are well
reproduced by ab initio calculations [67,73,74]. At
higher energies, theoretical studies [68–72] predict
that interferences among direct and indirect path-
ways will lead to asymmetric (Fano) lineshapes and
a pronounced wavelength dependence of the
product yields, which has been observed experi-
mentally in only a few cases [75–80]. Thus, experi-
mental and theoretical interest in this molecule
The hydroxyl radical is an important species
in atmospheric and combustion chemistry and
astrophysics [1,2], and the subject of numerous
experimental [3–56] and theoretical [57–74] inves-
tigations. Much of this work has focused on the
þ
2
2
~
~
ultraviolet A R X P system, which was ob-
served in flames and electric discharges more than
þ
2
~
80 years ago [2]. The A R state correlates with
O(1D) + H(2S) products, and is crossed by several
repulsive states (2RÀ, 4RÀ, 4PÞ correlating with
continues to this day.
* Corresponding author. Tel.: +414-288-7565; fax: +414-288-
7066.
E-mail address: scott.reid@mu.edu (S.A. Reid).
þ
2
2
~
~
Spectroscopic studies of the A R X P sys-
tem have examined the rotational and fine structure
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0301-0104(03)00184-8

62
J. Xin et al. / Chemical Physics 291 (2003) 61–72
[9,27], hyperfine structure [25,26,33,39,40,42,44,
54], and Zeeman [22,25,26,33,38,40,42,53,54] and
Stark [23,26] effects. Metcalf and co-workers [15,22]
used the Hanle effect, level crossing spectroscopy,
there is a need for further studies of the Zeeman
þ
2
~
effect in the A R state and its energy dependence.
Our group has been interested for several years
in the application of high-resolution quantum beat
methods to free radicals [82–85]. The quantum beat
method offers the advantages of other coherent
time-domain spectroscopies [86], with an intrinsic
resolution (ꢀ160 kHz for a radiative lifetime of 1
ls) capable of revealing molecular hyperfine
structure and splittings induced by weak magnetic
or electric fields. As a prelude to the application of
quantum beat methods to polyatomic radicals, and
in view of the unanswered questþions regarding the
ꢀ
and optical double resonance to determine Lande
þ
2
0
~
g-factors for some rotational levels in A R (t ¼ 0).
Zare and co-workers [16,25,26] employed zero- and
high-field level crossing and optical-radio fre-
quency double resonance to determine the OD
ꢀ
hyperfine constants, radiative lifetime and Lande g-
þ
2
0
~
factors in A R (t ¼ 0), and conducted Stark
measurements to determine the excited state dipole
moment [26]. Subsequently, Metcalf and co-work-
ers [38,40,42] applied the quantum beat technique
2
~
Zeeman parameters in the A R state, we under-
took a detailed study of the energy dependence of
the Zeeman parameters for both OH and OD, and
also report the magnetic and electric quadrupole
hyperfine constants for OD (t0 ¼ 0–3).
þ
2
0
~
ꢀ
to measure Lande g-factors for OH A R (t ¼ 0),
and the same method was used by Carter et al. [54]
þ
2
0
~
to probe the A R (t ¼ 0) level of OD and the
OD Á Ar van der Waals complex. The ensuing years
have witnessed increasingly precise measurements
of the hyperfine parameters for the t0 ¼ 0,1 levels in
þ
2
~
the A R state of OH and OD [39,44,54], which are
in reasonable agreement with available ab initio
predictions [59].
2. Experimental procedure
2.1. Experimental apparatus
In light of these studies, it is surprising that
fundamental questions remaþin regarding the Zee-
The apparatus consisted of a cubic, black-an-
odized vacuum chamber evacuated by a 6 in. dif-
fusion pump (Varian VHS-6) and equipped with a
molecular beam source and fluorescence detection
assembly. The chamber was surrounded by a tri-
axial Helmholtz coil system (Walker Scientific)
used to null the earth field and generate fields for
Zeeman experiments. Power to each coil came from
independent power supplies (Kepco), and the field
strength was calibrated using a Hall effect Gauss-
meter. The field vector was oriented along the de-
tection (space fixed X) axis, perpendicular both to
the direction of laser propagation (along the space
fixed Y axis) and to the polarization axis of the
linearly polarized laser beam (oriented along the
space fixed Z axis). In this configuration the selec-
tion rule for Zeeman quantum beats is: DMF ¼ Æ2.
The laser system consisted of a tunable, fre-
quency doubled, etalon narrowed dye laser
(Lambda-Physik Scanmate 2E) pumped by the
second (532 nm) or third (355 nm) harmonic of a
Nd:YAG laser (Continuum Powerlite 7010). The
following dyes or dye combinations were used:
R640/R610 (OH and OD, t0 ¼ 0), R6G (OH and
2
~
man parameters of the A R state. For example,
Coxon conducted a tþwo-state fit of the measured
2
2
~
~
spectrum for the A R X P system of OD [30],
and þfound that the spin–rotation splittings in the
2
~
A R state of OD arose predominantly from a
2
~
second order spin–orbit interaction with X P (a
case of ‘‘pure precession’’). Therefore, CurlÕs re-
lationship [81] for the anisotropic correction to the
electron spin g-factor, gl, should approximately
hold. However, a recent quantum beat study [54]
of OD(A R , t ¼ 0) determined a value of the
correct sign but an order of magnitude larger than
expected from CurlÕs relationship. In addition, the
reported electron spin g-factor was significantly
larger than the free electron value. These results
were attributed to mixing with excited quartet
states [54]. We find this surprising, in that the
A R (t ¼ 0) level of OD lies ꢀ4000 cm below
the opening of the lowest dissociation channel, and
ꢀ24 000 cmÀ1 below the lowest lying quartet state
(4RÀ) in the Franck–Condon region [67]. More-
over, such an effect should also be found for
þ
2
0
~
þ
2
0
À1
~
þ
2
0
~
OH(A R ; t ¼ 0), which is not the case [42]. Thus,

J. Xin et al. / Chemical Physics 291 (2003) 61–72
63
OD, t0 ¼ 1), C540 (OD, t0 ¼ 2), C307 (OD, t0 ¼ 3;
2.2. Data collection and analysis procedures
OH, t0 ¼ 2). The laser output passed through a
linear polarizer (CVI laser, 105:1 extinction) prior
to entering the chamber. Typical pulse energies
were 10–200 lJ, and the unfocused beam was of
ꢀ3 mm diameter. The pulse energy was increased
with increasing t0 to offset the decreasing Franck–
Condon factor.
Pairs of waveforms were collected at a given
magnetic field strength for parallel and perpen-
dicular orientations of the detector polarization
with respect to the polarization axis of the laser,
achieved by rotating a linear ultraviolet (UV) po-
larizer (Meadowlark Optics) placed between the
condenser lens system and PMT. The waveforms
were typically averaged over 2500 laser shots. The
time-dependent degree of polarization [P(t)] was
calculated for each pair according to the equation:
The OH (OD) radicals were generated by a
pulsed electrical discharge through a mixture of
H2O (D2O) in Argon, generated by passing Ar at a
typical backing pressure of 20 psig through a
bubbler containing H2O (D2O) at room tempera-
ture. The mixture was expanded into vacuum via a
commercial pulsed valve (General Valve IOTA-1),
modified by the addition of a ring electrode dis-
charge assembly [87]. The discharge was initiated
by a negative going 800 V pulse of ꢀ20 ls dura-
tion, which passed through a 10 kX ballast resis-
tor, and was set near the falling edge of the gas
pulse to minimize the effects of the transient
magnetic field generated by the (magnetically ac-
tivated) valve. The timing of laser, nozzle, and
discharge firing was controlled via a digital delay
generator (Stanford Research Systems DG535),
which generated the gate pulse for the high voltage
pulser (Directed Energy GRX-1.5K-E). The laser
beam crossed the molecular beam at a distance of
ꢀ15 mm (30 nozzle diameters) downstream. Flu-
orescence was collected at right angles to both the
laser and molecular beam by a two lens f =2:4
condenser assembly, and passed through a UV
polarizer (Meadowlark Optics) prior to striking a
photomultiplier tube detector (Orion) held at
typically )550 V. The PMT output was terminated
into 50 X and digitized by an oscilloscope (HP
54521A) operated at a sampling rate of 1 GHz and
record length of 4096 points.
I ðtÞ À I ðtÞ
k
?
PðtÞ ¼
:
ð1Þ
I ðtÞ þ I ðtÞ
k
?
Fig. 1 displays representative data for the R21(1)
transition in the t0 ¼ 1 t00 ¼ 0 band of OH at a
field strength of 2.72 G. The upper panel displays
the waveforms, and the lower panel the calculated
degree of polarization. Consistent with the theory
of anisotropic quantum beats, the modulations in
Under typical experimental conditions, the OH
(OD) radicals were produced almost exclusively in
2
the J ¼ 3=2 level of the P3=2 state, and we esti-
mate a rotational temperature of ꢁ10 Kfrom a
comparison of intensity ratios for R21(2)/R21(1)
and R11(2)/R11(1) pairs. Zeeman quantum beats
were observed on the S21(1), R21(1), R11(1), and
Q11(1) transitions, which provided access to ex-
cited state levels with N ¼ 1–3 and J ¼ 3=2–5=2.
Transition frequencies were obtained from [9,27].
Fig. 1. Upper panel: Waveforms observed following excitation
of the R21(1) transition in the t0 ¼ 1 t00 ¼ 0 band of OH at a
magnetic field strength of 2.72 G, obtained in parallel (top) and
perpendicular (bottom) orientations of laser and detection po-
larizations. Lower panel: Degree of polarization calculated
following Eq. (1) in the text.

64
J. Xin et al. / Chemical Physics 291 (2003) 61–72
the two waveforms exhibit a phase shift of 180°,
and reduced amplitude for the perpendicular
configuration.
The Fourier transform of P(t) was obtained
using PSIplot software. Fig. 2 displays the trans-
form of the P(t) shown in Fig. 3, which reveals two
strong quantum beats. The center frequencies were
obtained by fitting each peak to a Gaussian func-
tion using the Marquardt–Levenburg method. We
tested both Gaussian and Lorentzian functions,
and obtained similar goodness-of-fit statistics for
isolated peaks. The fits to a Gaussian function
typically gave correlation coefficients P0.999,
with a typical standard deviation of 30 kHz in the
determined peak center frequency. This procedure
was repeated for 8–10 different field strengths in
the range over which linear tuning was observed.
For OH, this range extended to the highest fields
used (ꢀ10 G), while for OD to fields below ꢀ5 G,
consistent with the observations of Zare and co-
workers [16,25,26]. Beats arising from different
hyperfine components (inter-manifold beats) were
not observed for OH, as the hyperfine splittings
are much larger than the coherence width of our
Fig. 3. Upper panel: Magnetic field dependence of the quantum
beat frequencies for the R21(1) transition in the t0 ¼ 1 t00 ¼ 0
band of OH. The lines mark linear fits to the data. Lower panel:
Fit residuals.
ꢀ
laser [44]. Thus, the Lande factor for a given F
component was determined by a linear fit of the
magnetic field dependence of the intra-manifold
beat frequency using the formula:
x ¼ 2lBBgF ;
ð2Þ
where lB ¼ 1.39967 MHz GÀ1. An example for the
R21(1) transition of the t0 ¼ 1 t00 ¼ 0 band of
OH is shown in Fig. 3, which includes the residuals
to the linear fit and a typical error bar describing
the uncertainty in our determination of the peak
position.
For OD, hyperfine (zero-field) quantum beats
were also observed, as initially reported by Huber
and co-workers [53,54]. Fig. 4 displays a typical
OD quantum beat spectrum, obtained for the
R21(1) transition of the t0 ¼ 1 t00 ¼ 0 band at a
field strength of 2.72 G. A global least squares fit
ꢀ
was performed to determine the Lande factors for
each F component and the zero-field hyperfine
splittings, from which the hyperfine coupling
constants were determined as described below. The
inter-manifold beat frequencies were fit using the
formula:
Fig. 2. Fourier transform of the degree of polarization data
shown in bottom panel of Fig. 1. The beats are labeled in terms
of the excited state hyperfine quantum number.
0
0
x ¼ D þ lBB½MF gF À MF gF Š;
ð3Þ

J. Xin et al. / Chemical Physics 291 (2003) 61–72
65
where
Hsr ¼ cN Á S
ð5Þ
is the spin–rotation interaction [25,26]. For OH
the hyperfine Hamiltonian [88]:
Hhfs ¼ bI Á S þ cIzSz
ð6Þ
was used, where b, c are the Frosch and Foley
constants and the Fermi-contact interaction is
given by b þ c=3. For OD, the Hamiltonian
included a quadripolar coupling term: [33,88]
ꢀ
ꢁ
IðI þ 1Þ
Hhfs ¼ bI Á S þ cIzSz þ eqQ 3Iz2 À
:
4Ið2I À 1Þ
ð7Þ
The effective Zeeman Hamiltonian for a dia-
tomic molecule in a R state can be expressed as:
[89,90]
þ
2
X
HZ ¼ gslBB0Tp1¼0ðSÞ þ gllBB0
Dð01qÞðxÞTq1ðSÞ
q¼Æ1
À grlBB0Tp1¼0ðNÞ À gNlNB0Tp1¼0ðIÞ;
ð8Þ
Fig. 4. Zeeman quantum beat spectrum of the R21(1) transition
in the t0 ¼ 1 t00 ¼ 0 band of OD at a field strength of 2.72 G.
The intra- and inter-manifold beats are labeled in terms of the
excited state hyperfine quantum numbers.
where the first term is the isotropic electron spin
interaction, the second term represents anisotropic
corrections to gs, the third term accounts for the
rotational Zeeman effect, and the final term rep-
resents the nuclear Zeeman effect. We included the
nuclear Zeeman term in our analysis for both OH
and OD.
where D is the zero-field splitting of the two com-
ponents F , F 0. This procedure was followed for all
transitions except R11(1), where the inter-manifold
beats were particularly weak and difficult to ob-
serve above the noise. In this case, the zero-field
splittings were obtained from a zero-field spectrum
averaged over 5000 laser shots, and the LandeÕ
factors were determined from the intra-manifold
beats, following Eq. (2).
The Hamiltonian matrix elements were evalu-
ated in the case bbJ basis. The hyperfine matrix
elements were taken from Radford [88], using the
correction noted by German [33], while the Zee-
man matrix elements were taken from [90]. The
Hamiltonian matrix was factored into submatrices
for J ¼ N Æ 1=2 and F ¼ J Æ 1=2 (for I ¼ 1=2) or
F ¼ J þ I; J þ I À 1; . . . ; J À I (for I ¼ 1). The
matrix was of size 4 Â 4 for OH, and for OD either
5 Â 5 or 6 Â 6. We used published spin–rotation
constants for OD(t0 ¼ 0–3) [30], and determined
the hyperfine coupling constants b, c, and eQq by
fitting the zero-field hyperfine splittings to values
calculated by diagonalizing each submatrix with
B0 ¼ 0. The diagonalization used a Jacobian
transformation, and the fitting a least-squares
routine. For OH, we used the hyperfine and spin–
rotation constants for t0 ¼ 0 and 1 determined by
ter Meulen et al. [44] and the parameters for t0 ¼ 2
3. Theory and data modeling procedures
The A2Rþ state of OH conforms to case bbJ
coupling [16,25,26], where J ¼ N þ S and F ¼
J þ I, and I ¼ IHðDÞ. Consistent with previous
treatments [22,25,26,33,38,40,42,53,54], for Zee-
man experiments involving an unperturbed state
with rotational angular momentum N the follow-
ing Hamiltonian was assumed:
H ¼ Hsr þ Hhfs þ HZ;
ð4Þ

66
J. Xin et al. / Chemical Physics 291 (2003) 61–72
were estimated from the energy dependence of the
OD parameters. The rotational dependence of c
was neglected in our analysis, at it varies by only
ꢀ0.2% over the range N ¼ 1–3 [44].
fine structure parameters [25,26,91]. For OD, the
uncertainty in c varies from ꢀ0.1% for t0 ¼ 0 to
ꢀ9% for t0 ¼ 3 [30]. We conducted a series of fits
of the data for OD(t0 ¼ 3) to assess the sensitivity
of the fitted values to uncertainties in c and the
hyperfine constants b, c, and eQq. Only the former
produced a noticeable change, with the 9% un-
certainty in c leading to a 30% change in the fit
value of gl and 11% change in the fit value of gr.
These are significantly smaller than the experi-
mental uncertainties.
We first diagonalized each submatrix at a single
value of the field strength (B0) in the range em-
ployed. Changing the value of B0 in this range did
not alter the calculated values, consistent with our
observation of linear Zeeman tuning. The calcu-
lated Zeeman energies were averaged over all pairs
of Zeeman sublevels of a given hyperfine compo-
nent differing in MF by 2, and divided by lBB0 to
give the theoretical gF factor. The calculated gF
factors were fit to the experimental values using a
least-squares algorithm. In practice, we found that
the data set did not allow simultaneous determi-
nation of the three g-factors: gs, gl, and gr, a fact
also noted by Carter et al. [54] in QBS studies of
4. Results and discussion
4.1. Zeeman parameters
Tables 1 and 2 list the experimental low field
gF -factors determined for various hyperfine levels in
þ
2
~
OD(A R ; t ¼ 0). In that work, the value of gr was
constrained to be zero, since the predicted mag-
nitude (ꢀ0.002) is around three times smaller than
the value of gl predicted from CurlÕs relationship.
However, the matrix elements for this term are
typically 4–5 times larger than those for gl, and the
relative contributions of these terms may thus be
similar. We fixed gs at the free electron value
(2.002), and used gl, and gr as fit parameters, a
procedure similar to that uþsed by Raab et al. [42]
þ
0
2
~
the t ¼ 0, 1, and 2 levels of OH(A R ) and the
þ
0
2
~
t ¼ 0, 1, 2, and 3 levels of OD(A R ). For
OH(t0 ¼ 0) (Table 1) the previous (and more pre-
cise) results of[42] are included for comparison. Due
to the short lifetime of OH(t0 ¼ 2), it was not pos-
sible to obtain data for the weak S21(1) transition,
however, the data obtained for other rotational
levels in this band is similar in precision to those
for t0 ¼ 0 and 1, which demonstrates that QBS
can be applied to the study of predissociating states.
Tables 3 and 4 list the fit values of gl and gr for
OH(t0 ¼ 0–2) and OD(t0 ¼ 0–3), respectively. In a
2
0
~
in QBS studies of OH(A R ; t ¼ 0).
It is well known that fitted g-factors are sensi-
tive to uncertainties in rotational constants and
Table 1
Experimental gF -factors for the A2Rþ state of OH
N
J
F
Experimental gF factors
t0 ¼ 0a
)0.2412(2)
)0.3336(6)
t0 ¼ 0b
)0.2397(9)
t0 ¼ 1b
)0.2417(8)
t0 ¼ 2b
c
3
2
2
1
2.5
2.5
1.5
1.5
3
2
c
)0.3338(26)
)0.3387(17)
3
2
0.3308(2)
0.4701(6)
0.3282(20)
0.4747(30)
0.3290(12)
0.4754(22)
0.3265(12)
0.4743(33)
2
1
)0.3078(3)
)0.4991(6)
)0.3087(17)
)0.5015(37)
)0.3070(7)
)0.5011(24)
)0.3103(34)
)0.5144(27)
2
1
0.4973(8)
0.8649(14)
0.4969(29)
0.8633(49)
0.5002(37)
0.8807(90)
0.4962(48)
0.8819(75)
a Ref. [42].
b This work.
c Not determined.

J. Xin et al. / Chemical Physics 291 (2003) 61–72
67
Table 2
Experimental gF -factors for the A2Rþ state of OD
N
J
F
Experimental gF factors
t0 ¼ 0
t0 ¼ 1
t0 ¼ 2
t0 ¼ 3
3
2.5
3.5
2.5
1.5
)0.2022(16)
)0.2582(23)
)0.4061(28)
)0.2020(10)
)0.2631(25)
)0.4020(30)
)0.2036(18)
)0.2594(20)
)0.4097(35)
)0.2052(28)
)0.2662(34)
)0.4176(55)
2
2
1
2.5
1.5
1.5
3.5
2.5
1.5
0.2786(11)
0.3603(20)
0.5659(40)
0.2799(15)
0.3600(34)
0.5681(35)
0.2841(21)
0.3663(29)
0.5735(43)
0.2815(18)
0.3658(39)
0.5696(41)
2.5
1.5
0.5
)0.2434(14)
)0.2994(29)
)0.666(18)
)0.2407(10)
)0.2996(49)
)0.665(16)
)0.2459(12)
)0.2936(96)
)0.685(30)
)0.2459(17)
)0.303(11)
)0.675(34)
2.5
1.5
0.5
0.3982(17)
0.5020(94)
1.141(30)
0.3988(19)
0.5064(64)
1.141(24)
0.4059(30)
0.510(17)
1.140(55)
0.4015(24)
0.510(11)
1.139(36)
Table 3
Zeeman parameters for the A2Rþ state of OH
derived from this fit, gl ¼ À0:007ð7Þ (Table 5), is in
good agreement with that calculated from Eq. (9).
Our fit value of gl for OD(t0 ¼ 0) is much
smaller than that of Carter et al. [54] who report
gl ¼ À0:095ð41Þ. This discrepancy does not arise
from the analysis procedure, as when fitting our
results with gr set to 0.0 we derive gl and gs values
of 0.004(36) and 1.997(35), respectively. Although
Carter et al. [54] did not include the nuclear Zee-
man effect in their analysis, we find that the mag-
nitude of this effect for OD is at the precision of
our measurements, and thus cannot account for
the discrepancy. We have also not identified any
systematic error (field calibration, etc.) that could
reasonably explain this result, and thus at present
the origin of this discrepancy remains unexplained.
If gl was determined solely via coupling with
t0
gs
gl
gr
rb
a
0
1
2
2.002
2.002
2.002
)0.020(10)
)0.002(8)
0.007(13)
0.0035(22)
0.0013(18)
0.0056(33)
0.0035
0.0028
0.0041
a Fixed.
b Standard deviation of the fit.
Table 4
Zeeman parameters for the A2Rþ state of OD
t0
gs
gl
gr
rb
a
0
1
2
3
2.002
2.002
2.002
2.002
)0.001(8)
0.000(8)
0.001(2)
0.000(2)
0.002(2)
0.004(2)
0.0041
0.0040
0.0053
0.0049
0.016(11)
0.010(10)
a Fixed.
b Standard deviation of the fit.
2
0
~
X P, its value should not depend on t , since the
second-order contribution that gives rise to c is
two-state model, gl can be predicted from the
perturbation treatment of Curl [81]
~
proportional to B. Indeed, the observed decrease in
þ
0
2
~
c with increasing t in OD(A R ), from 0.12010(12)
c
~
cmÀ1 for t0 ¼ 0 to 0.106(9) cmÀ1 for t0 ¼ 3, closely
gl ffi À
:
ð9Þ
2B
Using the reported constants [9,27,44], the calcu-
Table 5
Zeeman parameter values for the combined fits
þ
2
0
~
lated value for (A R , t ¼ 0) is ꢀ)0.007. Our
experimental results for OH fgl ¼ À0:020ð10Þg
and OD{gl ¼ À0:001ð8Þ} bracket this value. To
increase the precision, we conducted a global fit of
the OH and OD values, using the appropriate
dependence on reduced mass for gr. The value
a
t0 (OH/OD) gs
gl
gr
rb
0/0
2/3
2.002
2.002
)0.007(7) 0.0028(25)
0.011(9) 0.0056(38)
0.0045
0.0055
a Fixed.
b Standard deviation of the fit.

68
J. Xin et al. / Chemical Physics 291 (2003) 61–72
À1
~
mirrors the decrease in B, from 9.04351(12) cm
for t0 ¼ 0 to 8.0746(5) for t0 ¼ 3 [30]. Our results, in
contrast, show that with increasing t0, gl changes
sign (Tables 3 and 4), although the effect is near the
limit of our experimental precision. The upper pa-
nel of Fig. 5 displays a combined plot of the vi-
brational energy dependence of gl for OH and OD
lower panel of Fig. 5 shows the vibrational energþy
2
~
dependence of gr for OH and OD in the A R
state. It appears that gr increases at higher energies
(Tables 3–5), but the trend is not outside our ex-
perimental uncertainty.
We considered several explanations for the ob-
served energy dependence of gl, which are sum-
marized below.
þ
2
~
in the A R state. To better resolve this trend, as
noted above we conducted a simultaneous fit of the
g-factors for OH and OD levels lying close in energy
ft0 ¼ 0 (OH) with t0 ¼ 0 (OD), and t0 ¼ 2 (OH)
with t0 ¼ 3 (OD)}, and the derived parameters are
listed in Table 5.
Turning to the rotational g-factor (gr), the val-
ues determined for OH(t0 ¼ 0) and from a simul-
taneous fit of the t0 ¼ 0 data for OH and OD are
consistent with the (more precise) value of
0.00248(6) determined by Raab et al. [42] and with
4.1.1. Interactions with higher lying P states
A change in sign of gl could arise from inter-
actions with higher lying P states, leading to a
change in sign of the energy denominator in the
second-order contribution: [89–92]
þ
þ
X
hPjAL jRihRjL jPi
ER À EP
gle ffi
:
ð10Þ
P
Candidates include 22P, which correlates to
O(1D) + H(2S) and is calculated to lie ꢀ48,000
2
~
calculations based on coupling to X P [42]. The
þ
cmÀ1 above A R [61], and the repulsive 1 P state,
which correlates to O(3P) + H(2S) and lies slightly
higher than 22P in the Franck–Condon region
[61,67]. The 14P state should be more important,
as the configuration of this state differs from that
2
4
~
þ
2
~
of A R by one spin–orbital [93]. Using the ab
initio potential curves and spin–orbit matrix ele-
ment at R ¼ 2:0 bohr [67,73], from which a value
for hPjALþjRi of ꢀ200 cmÀ1 is derived [9þ3], we
2
4
~
estimate a contribution to gl from the A R –1 P
interaction of ꢀ0.007 for the highest t0.
4.1.2. Interactions with higher lying R stÀate(s)
Interactions with the higher lying 14R state can
influence gl via the third-order term: [92]
2
2
4
X
h RjHSOj Ri
ð3Þ
gle ffi À
:
ð11Þ
2
½E2R À E
Š
4R
4R
However, as the sign of this term is negative, it
would lead to a decrease in gl. Moreover, given the
calculated spin–orbitÀ matrix element (HSO) be-
þ
2
tween A R and 14R in the Franck–Condon re-
~
gion ()2.2 cmÀ1 at R ¼ 2:00 bohr) [67,73],
the contribution from this term is negligibly small.
4.1.3. Modification of gs via interactions with higher
lying states
Fig. 5. Upper panel: Fit values of gl for OH, OD, and thþe
2
~
In our analysis, we fixed gs at the free electron
value. This might not be a good assumption, as
combined fits plotted against vibrational energy in the A R
state. Lower panel: Similar plot for gr.

J. Xin et al. / Chemical Physics 291 (2003) 61–72
69
interactions with 22P and 14P can modify gs via
the third order term [92,94]:
0–3Þ, and compared with the results of Carter et al.
[54] for t0 ¼ 0. Table 7 compares the determined
hyperfine parameters (b, c, eQq and the Fermi-
contact constant b þ c=3) with previous measure-
ments and theoretical predictions for t0 ¼ 0 and 1.
Our results are generally in good agreement with
the QBS measurements of Carter et al. [54] and
previous experimental studies [25,26,33].
2
X
jhPjHSOjRij
gsð3Þ ffi À
:
ð12Þ
2
½ER À EPŠ
P
However, as the sign of this term is negative, ne-
glecting it should produce a decrease in the fit
value of gl. Moreover, based upon the ab initio
matrix elements [67,73], these terms are negligibly
small in the Franck–Condon region.
The Fermi-contact hyperfine constant (b þ c=3)
is proportional to the spin density of the unpaired
2
electron, jwð0Þj , at the deuterium nucleus. As the
On the basis of these considerations, we sug-
gest thatþthe energy dependence of gl may reflect
O–D bond is stretched, this term should approach
the value for the 2S state of atomic deuterium,
which is 218.256 MHz [95]. Thus, an increase in
2
4
~
the A R À 1 P interaction, which is known to
lead to predissociation at higher energies. The
estimated contribution to gl is of the correct sign
and order of magnitude; however, it is curious
Table 7
Hyperfine parameters (in MHz) for the A2Rþ state of OD
þ
2
~
that this effect should not be manifest in the A R
spin–rotation constants [30], and at present we
have no explanation for this. Further analysis
would benefit from additional calculations, par-
ticularly of the radial dependence of the Lþ
matrix element, and additional experiments en-
compassing a larger range of N, which would al-
low a more precise determination of the energy
dependence of gr [42].
t0
b
c
b + c=3
eqQ
0a
0b
0c
0d
1b
1c
1d
2c
3c
110.182(20)
109.73(5)
110.18(3)
112.7
24.72(11)
25.73(20)
24.85(17)
25.4
118.42
0.238(30)
0.22(5)
0.29(5)
0.262
118.31(14)
118.46(7)
121.2
111.15(5)
111.29(5)
115.7
24.40(20)
23.81(24)
24.3
119.28(14)
119.23(10)
123.8
0.05(4)
0.20(10)
0.258
112.63(8)
114.49(8)
22.78(40)
21.40(39)
120.22(14)
121.62(15)
0.30(13)
0.31(13)
4.2. Hyperfine parameters
a Experiment [54].
b Experiment [33].
c Experiment, this work.
d Theory [59].
Table 6 lists the experimental hyperfineþsplit-
2
0
~
tings determined in this work for ODðA R ; t ¼
Table 6
Experimental hyperfine level splittings (in MHz) for the A2Rþ state of OD
N
J
F 0
F 00
Experimental hyperfine level splittings in MHz
t0 ¼ 0a
52.90
t0 ¼ 0b
52.84(3)
37.91(2)
t0 ¼ 1
53.50(4)
38.49(3)
t0 ¼ 2
54.37(4)
38.94(3)
t0 ¼ 3
55.44(4)
39.72(4)
3
2
2
1
2.5
2.5
1.5
3.5
2.5
2.5
1.5
37.86
3.5
2.5
2.5
1.5
78.55
57.18
78.58(2)
57.31(3)
79.25(3)
57.72(2)
80.02(4)
58.34(4)
81.13(4)
59.17(4)
2.5
1.5
1.5
0.5
51.40
31.03
51.35(2)
31.10(3)
52.02(2)
31.57(2)
52.85(2)
32.10(2)
54.04(3)
32.76(2)
1.5
2.5
1.5
1.5
0.5
94.37
58.50
94.29(3)
58.71(2)
95.04(3)
59.16(3)
96.00(4)
59.76(4)
97.32(4)
60.56(3)
Not determined.
a Ref. [54].
b This work.

70
J. Xin et al. / Chemical Physics 291 (2003) 61–72
this term with increasing t0 is expected, and clearly
observed (Table 7). The calculations [59] repro-
duce this trend but overestimate its magnitude,
predicting a ꢀ2% increase in going from t0 ¼ 0–1,
while the experiment shows an increase of only
ꢀ0.7%. Ter Meulen et al. [44] observed a similar
trend for OH, with b þ c=3 increasing by ꢀ0.2% in
going from t0 ¼ 0–1.
The parameter c represents the dipole–dipole
interaction, given by: [88]
ꢂ
ꢃ
P2ðcos hÞ
c ¼ 3gegIlBlN
;
ð13Þ
r3
where ge and gI are the electron and nuclear g-
factors, lB and lN are the Bohr and nuclear
magneton, the argument of the Legendre polyno-
mial P2ðxÞ ¼ ð3x2 À 1Þ=2 is the cosine of the angle
of the electron coordinate with respect to the in-
ternuclear axis, and r is the distance between the
electron and the nucleus of spin I. For OH, ter
Meulen et al. [44] observed a significant (ꢀ10%)
decrease in c in going from t0 ¼ 0–1. We find a
decrease of ꢀ4% for OD, in reasonable agreement
with the results of German [33] and theoretical
predictions [59]. This trend continues to higher
energy, with a total decrease of ꢀ14% in going
from t0 ¼ 0–3.
Fig. 6. Fit values for the dipole–dipole hyperfine constant c of
þ
2
0
~
OD(A R ; t ¼ 0–3) plotted against the inverse cube of the
average internuclear separation approximated from the data of
[30]. The solid line marks a linear fit.
do not support the sharp (ꢀ4 fold) drop in eQq
from t0 ¼ 0–1 reported by German [33]. For fur-
ther analysis, it is highly desirable to have ab initio
predictions of the trend in hyperfine parameters
for t0 > 1.
5. Conclusions
The magnitude of c is usually interpreted in
terms of a p orbital on the nucleus in question;
however, for protons the p orbital lies too high in
energy to contribute, and the dominant contribu-
tion comes from interaction of the deuterium nu-
cleus with the oxygen atom unpaired spin-density
[96]. Indeed, the ground state c constants in a se-
ries of XH radicals approximately scale with the
inverse cube of the equilibrium internuclear sepa-
ration (re) [96]. As a simple test of this hypothesis,
we plot in Fig. 6 the experimental values for c
versus the inverse cube of the average value of the
internuclear separation r approximated from the
data of Coxon [30]. The graph is linear to within
our experimental precision, and a fit using linear
regression is shown as the solid line in Fig. 6.
In contrast to b and c, the small quadrupolar
coupling constant eQq is not well determined, and
no obvious dependence on energy is found to
within our experimental precision. Our findings
are consistent with theoretical predictions [59], and
We have examined the energy dependence of
þ
2
~
the Zeeman parameters in the A R state of OH
and OD, and the nuclear hyperfine parameters for
OD, using the technique of quantum beat spec-
troscopy. We find that the sign and magnitude of
the anisotropic g-factor gl for t0 ¼ 0 is consistent
with that expected from CurlÕs relationship, but at
higher energies this factor appears to change sign.
The rotational g-factor gr is not well determined
and its energy dependence is not well character-
ized; however, its magnitude is consistent with
previous results and theoretical expectations. We
examined several explanations for the observed
energy dependence of gl, and concludþe that the
2
~
most likely involves interaction of A R with the
4
higher lying P state, which is known to lead to
predissociation at higher energies. We also deter-
mined the magnetic and electric quadrupole hy-
þ
2
0
~
perfine constants for OD(A R , t ¼ 0–3), the
constants for t0 ¼ 2, 3 being reported here for the

J. Xin et al. / Chemical Physics 291 (2003) 61–72
71
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with previous experimental results and available
ab initio calculations.
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