The Astrophysical Journal, 637:1143–1147, 2006 February 1
# 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.
IMPROVED FREQUENCIES OF ROTATIONAL TRANSITIONS OF
52
CrH IN THE 6+ GROUND STATE
Jeremy J. Harrison and John M. Brown
Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, UK;
[email protected], [email protected]
and
DeWayne T. Halfen and Lucy M. Ziurys
Department of Chemistry, Department of Astronomy, Arizona Radio Observatory, and Steward Observatory, University of Arizona,
933 North Cherry Avenue, Tucson, AZ 85721; [email protected], [email protected]
Received 2005 August 16; accepted 2005 September 21
ABSTRACT
Previous mid-infrared, far-infrared, and new submillimeter data relating solely to 52 CrH in its X 6 þ state have been
reanalyzed by a least-squares fit using a Hund’s case (b) Hamiltonian to determine the best obtainable set of parameters
for the molecule. In particular, the fine structure and hyperfine constants have been improved. From these parameters,
transition frequencies are determined that are more reliable than those published previously; the latter show systematic
errors of up to 15 MHz. Such frequencies will facilitate the identification of CrH in the interstellar medium.
Subject headinggs: astrochemistry — ISM: lines and bands — ISM: molecules — line: identification —
molecular data — stars: AGB and post-AGB — stars: low-mass, brown dwarfs
Fourier transform emission spectroscopy provided further information on the X 6 þ state. In this work molecular parameters
were determined by fitting their data together with hyperfine-free
pure-rotation and vibration-rotation line positions (i.e., at zero magnetic field) calculated from the parameters of Corkery et al. (1991)
and Lipus et al. (1991). This has the disadvantage of not using the
raw data. The calculated spin-components were all included with
equal weight in the fit, a characteristic that is not reflected in the
experimental data. More accurate and reliable parameters would
have been obtained if the experimental data had been fit directly.
More recently, Halfen & Ziurys (2004) measured the fine and
hyperfine components of the N ¼ 1
0 rotational transition
within the v ¼ 0 level of the X 6 þ state of CrH using submillimeter direct absorption spectroscopy. Surprisingly, they
observed only five of the six hyperfine components. Their data
were analyzed using a least-squares fitting program. In their fit,
B0 was fixed to a value determined by an initial fit, and D0 was
held at the value determined by Corkery et al. (1991). The four
parameters determined in their fit were the spin-rotation and spinspin constants and k, and the hyperfine parameters bF and c.
For a weighted least-squares fit, i.e., when estimates of the
experimental uncertainties are included, one would expect the
overall standard deviation of the fit to be close to unity. Using
the experimental uncertainties provided by Halfen & Ziurys
(2004), one obtains a standard deviation of 0.14. This difference
indicates that the data have been ‘‘over-fit.’’ It is not appropriate
to fit only five data points to such high precision. Furthermore,
the frequency of the N ¼ 1
0 transition depends explicitly
on B0 , which should be varied in the fit if the parameters are
to be believed. As a result, the predictions of Halfen & Ziurys
(2004) for the transitions N ¼ 2
1, 3
2, and 4
3 are not
completely reliable. However, the Ziurys group has recently
remeasured the N ¼ 1
0 transition using an alternating current (AC) discharge to generate CrH, which has resulted in
an improvement in signal-to-noise ratio by a factor of 75. The
missing sixth hyperfine component of this transition was observed
in these new measurements. We have refitted these data along with
other past measurements (Corkery et al. 1991; Lipus et al. 1991)
to determine the best obtainable set of parameters. From these,
1. INTRODUCTION
The CrH molecule is astronomically important. Lines of
the A 6 þ –X 6 þ system have been observed in the spectra of
sunspots (Engvold et al. 1980), and there is evidence for this
transition occurring in the spectra of S-type stars (Lindgren &
Olofsson 1980). CrH has also been identified in brown dwarfs,
and its presence is a primary indicator for the new L-class dwarf
stars (Kirkpatrick et al. 1999).
Direct observation of rotational transitions of CrH in the X 6 þ
ground state requires measurements in the submillimeter and
far-infrared regions of the spectrum. Unfortunately, ground-based
telescopes are limited in their usefulness due to atmospheric obscuration. In the near future such measurements should be more
feasible thanks to missions such as the Stratospheric Observatory
for Infrared Astronomy (SOFIA) and the Herschel Space Observatory (Halfen & Ziurys 2004). The dipole moment of CrH has
been calculated as 3.864 D by Dai & Balasubramanian (1993);
consequently, these transitions should have significant intensities.
Accurate spectroscopic data (better than 1 MHz) are required
for astronomers to identify CrH in the interstellar medium. CrH
is one of the best characterized of all the transition metal hydrides and has been extensively studied in the laboratory for
almost 70 years. A complex band system in the ultraviolet attributed to CrH (368 nm) was first obtained in emission by
Gaydon & Pearse (1937). Kleman & Liljeqvist (1955) later
extended observations to near-infrared wavelengths. The first
detailed rotational analysis of the emission spectra in this region
(A 6 þ –X 6 þ ) was performed by Kleman & Uhler (1959),
whose work was later extended by O’Connor (1967).
The most accurate investigation of CrH in the X 6 þ state to
date was performed by Corkery et al. (1991), in which they measured rotational transitions within the v ¼ 0 level (N ¼ 1
0 up
to 5
4 inclusive) by far-infrared laser magnetic resonance
(LMR). Lipus et al. (1991) later extended these measurements
to the infrared region, observing the v ¼ 1
0 and 2
1 bands
using CO-Faraday magnetic resonance; their results were subject to greater experimental uncertainty. A recent study by
Bauschlicher et al. (2001) of the A 6 þ –X 6 þ transition using
1143
1144
HARRISON ET AL.
kinetic energy, H sr
where H rot
v represents the rotational
v is the
ss
spin-rotation interaction, H v the spin-spin coupling term, H hfs
v
the nuclear spin hyperfine interaction, and H Zeeman
the Zeeman
v
interaction in the applied magnetic field. The detailed forms are
TABLE 1
New Data for the N ¼ 1
0 Rotational Transition
of CrH in its X 6 þ State (v ¼ 0)
N0
1
N 00
0..............
J0
J 00
1.5
1.5
3.5
3.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
F0
2
1
4
3
2
3
F 00
obs
( MHz)
obs calc
( kHz)
3
2
3
2
2
3
337259.080(55)
337266.025(55)
362617.902(60)
362627.691(60)
396541.683(65)
396590.720(65)
28
8
28
25
55
72
2
4
6
H rot
v ¼ Bv N Dv N þ Hv N ;
H srv ¼ v N = S þ Dv N 2 ðN = SÞ
10
Sv
E T 3 L2; N T 3 ðS; S; SÞ;
þ pffiffiffi D 6 T 2 L2 ð2Þ
ð3Þ
q¼0
1
2 2
k v 3Sz S 2 þ kDv 3Sz2 S2 ; N 2 þ
3
3
v 2
2 2
35Sz 30S Sz þ 25Sz2 6S 2 þ 3S 4 ;
þ
12
pffiffiffi
6
hfs
2
H v ¼ bFv I = S þ
ðI; SÞ;
cv Tq¼0
3
HvZeeman ¼ gsv B S = B grv B N = B þ glv B Bx Sx þ By Sy :
H ss
v ¼
Note.—The numbers in parentheses indicate the estimated experimental
uncertainties in the last digits.
transition frequencies can be determined that are much more reliable than those published previously. It has also been possible to
estimate the uncertainties (1 estimates) of these predicted frequencies in the process. For the present work, this uncertainty for
the N ¼ 2
1, 3
2, and 4
3 transitions is never more than
1.1 MHz. The discrepancy with the previous values, however,
ranges from 1 to 15 MHz.
The present paper also corrects some minor errors contained
in previous publications. The earlier version of the program used
in Corkery’s work (1991; HUNDB) identified eigenstates in the
LMR spectrum at a fixed field of 2500 G. It was not realized at
the time that this resulted in some of the rotational transitions being misassigned. In particular, it was suggested that several of the
observed transitions were nuclear-spin forbidden, MI ¼ 1.
The latest version of HUNDB identifies eigenstates at the measured field for each transition frequency, and all observed transitions are now assigned as MI ¼ 0. In addition, the signs for the
parameters kD and D in both Corkery’s and Lipus’ work (1991)
were not chosen according to accepted convention (Brown &
Carrington 2003). These have been changed where necessary.
ð4Þ
ð5Þ
ð6Þ
Each rotational level of the X 6 þ state of CrH, denoted by
the quantum number N, is split by spin-spin and spin-rotation
interactions. From simple angular-momentum coupling rules,
it is readily seen that each rotational level splits into six spin
components, labelled by the quantum number J, except the
N ¼ 0, 1, and 2 levels, which have 1, 3, and 5 components,
respectively. Proton hyperfine interactions (I ¼ 1/2) result in
further splitting of these spin components into levels denoted by
the quantum number F. The overall coupling scheme is
J ¼ N þ S;
F ¼ J þ I:
ð7Þ
ð8Þ
CrH conforms to a Hund’s case (b) coupling scheme in its
X 6 þ state. All the data were analyzed using an effective
Hamiltonian, which for a given vibrational level v, is expressed as
However, in a magnetic field I and J are readily decoupled and
the energy levels are best represented by the quantum numbers
MJ and MI .
The vibrational dependencies of the parameters are described
by the equation
rot
sr
ss
hfs
Zeeman
;
H eA
v ¼ Hv þ Hv þ Hv þ Hv þ Hv
Pv ¼ Pe þ P ðv þ 1=2Þ þ P ðv þ 1=2Þ2 þ : : : :
2. RESULTS AND DISCUSSION
ð1Þ
TABLE 2
Newly Determined Parameters (in cm1) for the Lower Vibrational Levels of the X 6 þ State of
52
CrH
Parameters
v=0
v=1
v=2
eqm Values (Pe)
Tv ................................
Bv ................................
Dv ...............................
0.0
6.13174562(32)
3.49387(16) ; 104
1595.06870(10)
5.950824(27)
3.4700(71) ; 104
3129.15264(24)
5.770093(41)
3.446(10) ; 104
1656.05346(22)
6.222278(17)
3.5058(50) ; 104
0.042735(74)
2.3(17) ; 106
0.215206(47)
2.33(42) ; 105
...
...
...
...
...
...
...
0.052297(32)
4.69(83) ; 106
0.237250(24)
5.9(21) ; 106
...
...
...
...
...
...
...
1.2471(27) ; 108 ( FIXED)
Hv ...............................
v ................................
Dv ..............................
kv ................................
kDv ..............................
v ................................
Sv ...............................
bFv...............................
cv.................................
gsv ...............................
grv ...............................
glv ................................
0.05033354(30)
3.296(54) ; 106
0.23284107(42)
9.41(18) ; 106
8.013(88) ; 105
2.95(20) ; 106
1.1610(39) ; 103
1.4099(23) ; 103
2.001623(31)
1.247(18) ; 103
4.118(41) ; 103
0.046483(50)
5.1(120) ; 107
0.224023(33)
1.64(30) ; 105
...
...
...
...
...
...
...
Notes.—The numbers in parentheses indicate the standard deviation in the last digits. The g-factors are dimensionless.
ð9Þ
TABLE 3
Newly Determined Parameters (in GHz) for the Lower Vibrational Levels of the X 6 þ State of
Parameters
v=0
Tv ................................
Bv ................................
Dv ...............................
v=1
0.0
183.8251090(96)
0.01047434(49)
CrH
eqm Values (Pe)
v=2
47818.9566(31)
178.40120(82)
0.010403(21)
52
93809.6360(73)
172.9830(12)
0.010332(30)
49647.2338(66)
186.53921(51)
0.010510(15)
3.7387(81) ; 107 ( FIXED)
Hv ...............................
v ................................
Dv ..............................
kv ................................
kDv ..............................
v ................................
Sv ...............................
bFv...............................
cv.................................
1.5089617(90)
9.88(16) ; 105
6.980400(12)
2.820(55) ; 104
2.402(26) ; 103
8.84(60) ; 105
3.48067(12) ; 102
4.2267(69) ; 102
1.3935(15)
1.5(35) ; 105
6.7161(10)
4.91(89) ; 104
...
...
...
...
1.2812(22)
6.8(50) ; 105
6.4517(14)
7.0(13) ; 104
...
...
...
...
1.56783(95)
1.41(25) ; 104
7.11257(70)
1.78(63) ; 104
...
...
...
...
Note.—The numbers in parentheses indicate the standard deviation in the last digits.
TABLE 4
Previously Determined Parameters (in cm 1) for the Lower Vibrational Levels of the X 6 þ State of
v=0
v=0
Parametersa
Corkery et al. (1991)
Tv .................................
Bv .................................
Dv ................................
Hv ................................
v .................................
Dv ...............................
k v .................................
k Dv ...............................
v .................................
Sv ................................
bFv................................
cv..................................
gsv ................................
grv ................................
glv .................................
...
6.1317456(11)
3.4951(34) ; 104
1.59 ; 108
0.0503323(18)
3.451(81) ; 106
0.2328341(17)
9.831(21) ; 106
7.73(10) ; 105
...
1.1607(67) ; 103
1.395(21) ; 103
2.001663(39)
1.280(21) ; 103
4.201(50) ; 103
v=1
52
CrH
v=2
Bauschlicher et al. (2001)
0.0
6.1317374(18)
3.48922(24) ; 104
1.2471(27) ; 108
0.0503629(64)
2.903(62) ; 106
0.2328206(56)
9.66(54) ; 106
7.85(30) ; 103
5.27(89) ; 106
...
...
...
...
...
1595.06870(14)
5.9507593(96)
3.44073(88) ; 104
...
0.046454(14)
2.05 ; 106b
0.224003(49)
1.61(31) ; 105
...
...
...
...
...
...
...
3129.15495(48)
5.769783(84)
3.385(24) ; 104
...
0.042577(29)
7.55 ; 106b
0.215132(98)
2.68(60) ; 105
...
...
...
...
...
...
...
Notes.—The numbers in parentheses indicate the standard deviation in the last digits. The g-factors are dimensionless.
a
Signs of kDv and Dv have been corrected where appropriate to be consistent with eqs. (3) and (4).
Fixed to the values determined by Lipus et al. (1991). Note that Bauschlicher et al. (2001) neglected to alter the signs in their
analysis.
b
TABLE 5
Vibrational Parameters for 52 CrH in its X 6 þ State
Parameters
GHz
we xe ...............................
B ..................................
B ..................................
D ..................................
..................................
...................................
D ................................
k...................................
kD ................................
914.1386(41)
5.42964(69)
2.86(31) ; 103
7.1(21) ; 105
0.1185(13)
1.53(52) ; 103
8.3(35) ; 105
0.2643(10)
2.09(89) ; 104
1
cm
30.49238(14)
0.181113(23)
9.6(10) ; 105
2.38(71) ; 106
3.953(43) ; 103
5.1(17) ; 105
2.8(12) ; 106
8.818(33) ; 103
7.0(30) ; 106
Lipus et al.a
(cm1)
30.4914(1)
0.18099(3)
...
5.8(8) ; 106
3.88(4) ; 103
...
5.5(15) ; 106
8.86(4) ; 103
8.9(41) ; 106
Note.—The numbers in parentheses indicate the standard deviation in the last digits.
a
Signs have been corrected where appropriate to be consistent with eq. (9) of the present work.
1146
HARRISON ET AL.
Vol. 637
TABLE 6
Predicted Rest Frequencies (in GHz) for the X 6 þ State
of 52 CrH (v ¼ 0)
TABLE 6—Continued
N0
N0
N 00
J0
J 00
1
0............
2
1............
1.5
1.5
3.5
3.5
2.5
2.5
0.5
0.5
1.5
1.5
2.5
2.5
4.5
4.5
2.5
2.5
3.5
3.5
1.5
1.5
2.5
2.5
3.5
3.5
0.5
1.5
1.5
0.5
0.5
1.5
1.5
2.5
2.5
5.5
5.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
6.5
6.5
4.5
4.5
5.5
5.5
1.5
2.5
2.5
2.5
2.5
2.5
2.5
1.5
1.5
1.5
1.5
1.5
1.5
3.5
3.5
3.5
3.5
3.5
3.5
2.5
2.5
2.5
2.5
2.5
2.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
1.5
1.5
4.5
4.5
4.5
4.5
4.5
4.5
2.5
2.5
2.5
2.5
2.5
2.5
3.5
3.5
3.5
3.5
3.5
3.5
0.5
0.5
1.5
1.5
1.5
1.5
5.5
5.5
5.5
5.5
5.5
5.5
2.5
3
2............
4
3............
F0
2
1
4
3
2
3
0
1
1
2
2
3
5
4
2
3
3
4
1
2
2
3
4
3
1
1
2
0
1
1
2
2
3
6
5
3
4
4
5
1
2
2
3
3
4
2
3
3
4
5
4
1
2
1
2
2
3
7
6
4
5
5
6
1
F 00
(GHz)
Line Strengtha
3
2
3
2
2
3
1
2
1
2
1
2
4
3
3
4
3
4
2
3
2
3
3
2
1
0
1
1
2
1
2
1
2
5
4
4
5
4
5
2
3
2
3
2
3
3
4
3
4
4
3
0
1
1
2
1
2
6
5
5
6
5
6
2
337.259052(34)
337.266033(34)
362.617930(34)
362.627666(35)
396.541628(46)
396.590648(46)
718.60490(42)
718.61834(42)
744.76282(34)
744.83557(33)
776.03263(22)
776.10758(22)
734.948056(64)
734.951147(63)
750.67100(22)
750.74870(22)
764.02299(12)
764.07257(12)
685.48722(34)
685.50398(33)
716.75704(22)
716.77599(22)
730.09985(11)
730.10902(11)
1097.35654(33)
1116.36608(52)
1116.49235(49)
1071.00311(88)
1071.13930(88)
1090.20816(31)
1090.27512(29)
1115.94968(23)
1115.98844(23)
1103.47114(13)
1103.47247(13)
1123.05089(30)
1123.13862(29)
1129.22609(24)
1129.27514(23)
1058.93835(47)
1059.00311(45)
1084.67986(35)
1084.71643(34)
1107.33104(11)
1107.33797(11)
1071.32787(36)
1071.39257(35)
1093.97905(32)
1094.01411(32)
1100.15063(10)
1100.15425(10)
1468.20871(38)
1468.22322(33)
1449.00366(75)
1449.08740(73)
1472.90849(21)
1472.93189(21)
1470.33453(23)
1470.33519(23)
1489.50790(47)
1489.59901(46)
1493.44004(39)
1493.48865(38)
1423.2621(11)
1.63
1.05
3.05
2.26
1.47
2.10
0.40
1.01
0.69
1.24
0.52
0.81
4.42
3.51
0.14
0.19
0.93
1.21
0.38
0.59
1.19
1.70
2.33
1.73
0.67
0.26
0.65
0.10
0.24
0.62
1.11
0.91
1.41
5.58
4.64
0.05
0.06
0.68
0.84
0.16
0.25
0.94
1.35
1.83
2.46
0.12
0.16
0.99
1.29
3.85
3.07
0.57
1.42
0.36
0.65
1.28
1.99
6.67
5.71
0.02
0.03
0.54
0.64
0.05
N 00
J0
J 00
1.5
2.5
2.5
3.5
3.5
2.5
2.5
3.5
3.5
4.5
4.5
3.5
3.5
4.5
4.5
5.5
5.5
2.5
2.5
2.5
2.5
2.5
3.5
3.5
3.5
3.5
3.5
3.5
4.5
4.5
4.5
4.5
4.5
4.5
F0
2
2
3
3
4
2
3
3
4
4
5
3
4
4
5
6
5
F 00
(GHz)
Line Strengtha
3
2
3
2
3
3
4
3
4
3
4
4
5
4
5
5
4
1423.3741(11)
1447.16698(38)
1447.21857(37)
1472.86553(18)
1472.87658(18)
1424.51580(61)
1424.59703(60)
1450.21435(36)
1450.25504(36)
1469.92948(15)
1469.93153(15)
1444.03916(51)
1444.11852(51)
1463.75428(40)
1463.79501(40)
1467.68466(15)
1467.68642(15)
0.08
0.69
0.98
2.07
2.79
0.07
0.09
0.85
1.11
3.05
3.83
0.05
0.07
0.81
1.01
5.13
4.27
Notes.—The numbers in parentheses indicate the estimated standard errors
in the last digits, as determined from a statistical analysis of the least-squares fit
(Albritton et al. 1976).
a
As defined by Brown & Evenson (1983).
Note that this is a different convention from that used by Lipus
et al. (1991).
Molecular parameters were determined using the HUNDB
least-squares fitting program, which is based on the Hamiltonian
in equation (1). The basis set was truncated at N ¼ 4 without
loss of accuracy. The sextic distortion parameter Hv was fixed at
1:2471 ; 108 cm1, as determined by Bauschlicher et al. (2001),
since their data extend to higher values of N within the X 6 þ
state than any of the LMR studies. The data were assigned
the following uncertainties: 0.000055–0.000065 GHz for the
submillimeter data, 0.002 GHz for the far-IR LMR data, and
0.03 GHz for the IR LMR data. The most recent CrH data from
the Ziurys lab are given in Table 1. These measurements are to
be preferred to those reported earlier (Halfen & Ziurys 2004).
The overall standard deviation of the fit relative to experimental uncertainty was 0.754. The new submillimeter frequencies for
the N ¼ 1
0 transitions are extremely well fitted, consistent
with their estimated experimental uncertainties (see Table 1).
The quality of the fit of the far-infrared and mid-infrared LMR
data is essentially the same as in the original papers (Corkery
et al. 1991; Lipus et al. 1991) and so is not reproduced here. The
revised parameters determined in the present work are given in
Table 2 (in cm1) and Table 3 (in GHz). For comparison purposes, the previously determined parameters of Corkery et al.
(1991) and Bauschlicher et al. (2001) are given in Table 4. Vibrational dependence parameters of the type and are given
in Table 5, including a comparison with corresponding parameters determined by Lipus et al. (1991).
A comparison of Corkery’s and Baushlicher’s parameters for
the v ¼ 0 level with the revised ones in this work reveals that all
but kD are now better determined. In particular, the values for
the parameters B0 , k0 , bF , and c are much better determined; for
example, the uncertainty of c has improved by 1 order of magnitude. The improvement in these parameters is a direct result of
the inclusion of the accurate N ¼ 1 0 submillimeter data. In
addition, it can be seen that the parameter is better determined
and has a significantly different value from that obtained in earlier fits. This is because the higher order fine structure parameter
S was not included in the fit reported by Corkery et al. (1991).
No. 2, 2006
ROTATIONAL FREQUENCIES OF GROUND-STATE
As can be seen in Tables 2 and 3, this parameter is well determined by the far-infrared LMR data and leads to a significant
improvement in the fit. The data set used by Bauschlicher et al.
(2001) depends in part on the analysis of Corkery et al. (1991);
to this extent, their parameter set is also somewhat flawed. Although some of these improvements seem small, their effect
on predicted frequencies can be significant. An uncertainty of
0.5 MHz in a given parameter can result in errors of extrapolated rest frequencies of 10–20 MHz—certainly not suitable for
astronomical searches.
The Zeeman parameters obtained in the fit of the LMR data
are similar to those obtained earlier (Corkery et al. 1991; Lipus
et al. 1991) but are somewhat better determined. These parameters are potentially very useful to astronomers because they
provide a means to estimate local magnetic fields on the surfaces of brown dwarfs through observation of the broadening of
lines in the A 6 þ –X 6 þ system. The value for the parameter
gl that describes the anisotropic correction to the electron spin
g-factor agrees spectacularly well with the predictions of Curl’s
relationship (Curl 1965),
gl ¼ =2B;
ð10Þ
which gives gl ¼ 0:00414. This agreement suggests that the
ground 6 þ state of CrH is uncontaminated by states of different multiplicity.
Not all the revised parameters for the v ¼ 1 and 2 levels
are better determined than the values reported by Bauschlicher
et al. (2001). However, there are several points in their analysis
that we briefly touch on. In their fit, they fixed D v¼1 and D v¼2
52
CrH
1147
to the values determined by Lipus et al. (1991) without correcting the signs. (The centrifugal distortion correction to is
additive, unlike D0 .) Second, our analysis shows that the parameter kD should decrease with increasing v, not increase, as
their paper suggests. It appears that they have used an incorrect
sign for kD .
The parameters that describe the vibrational dependence (, )
are now much better determined than those of Lipus et al. (1991)
(Table 5). In addition B and are reported for the first time.
To guide searches for CrH in the interstellar medium, we
have calculated and tabulated the rest frequencies of the first
few rotational transitions within the v ¼ 0 level of the X 6 þ
state, using the revised parameters determined in this work.
These predictions (Table 6) differ by as much as 15 MHz for
given hyperfine transitions from those published previously
(Corkery et al. 1991; Halfen & Ziurys 2004) and are much more
reliable. We have also estimated the standard error of each
frequency, as determined from a statistical analysis of the leastsquares fit (Albritton et al. 1976).
The improved accuracy of these predicted frequencies arises
from the inclusion of six high-precision submillimeter data
points and the reanalysis of all LMR experimental data with
appropriate experimental weightings. This differs from the
study of Bauschlicher et al. (2001), in which equal weightings
were given to calculated hyperfine-free line positions. Such an
equal weighting is not reflected in the experimental LMR data.
We thank the Leverhulme Trust for support of J.J.H.
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