The Astrophysical Journal, 687:731–736, 2008 November 1
# 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
DIRECT MEASUREMENTS OF THE FUNDAMENTAL ROTATIONAL
TRANSITIONS OF CD AND 13CH (X 2 r)
D. T. Halfen,1 L. M. Ziurys
Departments of Chemistry and Astronomy, Arizona Radio Observatory, and Steward Observatory,
University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721
and
J. C. Pearson and B. J. Drouin
Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive, Pasadena, CA 91109-8099
Received 2008 May 8; accepted 2008 June 29
ABSTRACT
The lowest energy rotational transitions of CD and 13CH in their 2r ground electronic states have been directly
measured using submillimeter direct absorption spectroscopy. These two radicals were produced in an electrical dis1/2, N ¼ 1 1 transition at 439 GHz and the
charge of either CD4 (or CH4 and D2) or 13CH4. The J ¼ 3/2
J ¼ 3/2
3/2 and 5/2
3/2 fine structure lines of the N ¼ 2 1 rotational transition near 885 GHz and 916 GHz
were recorded for CD (Hund’s case b notation), each of which consist of lambda doublets. In addition, hyperfine splittings due to the deuterium nuclear spin of I ¼ 1 were measured in several doublets, although some hyperfine components were blended together at higher frequency. For 13CH, the lambda doublets of the fundamental N ¼ 1 1 line
near 532–536 GHz were recorded; in this case, hyperfine interactions arising from both 13C and H nuclei were resolved. These data were fit with a case b effective Hamiltonian, and spectroscopic parameters were derived. In particular, the deuterium hyperfine constants for CD were improved by about an order of magnitude, while for 13CH the
hydrogen Fermi contact and dipolar terms were established for the first time. These measurements will enable definitive searches for CD and 13CH in interstellar gas, in particular with the upcoming Herschel Space Observatory.
Subject headingg
s: astrochemistry — ISM: molecules — methods: laboratory — molecular data —
submillimeter — techniques: spectroscopic
spectra of the v ¼ 1 0 and 2–1 vibrational transitions in the 2r
ground state of this molecule have also been recorded (Morino
et al. 1995). High-resolution measurements have been obtained
for the ground and excited vibrational states, as well. For example, the far-infrared spectrum of this radical has been investigated
by Brown & Evenson (1989) using laser magnetic resonance
( LMR). Rotational transitions up to N ¼ 6
5 in the v ¼ 0
state were recorded in a magnetic field, including the lowest
frequency transition, N ¼ 1
1, with a zero-field 1 accuracy
of 3 MHz. Rotational, fine-structure, lambda-doubling, and
deuterium hyperfine constants were determined from these data.
More recently, far-infrared rotational transitions within excited
vibrational states (v ¼ 1 and 2), and the v ¼ 1 0, 2–1, and 3–2
rotation-vibration transitions of CD in the mid-infrared were recorded by Wienkoop et al. (2003). These measurements enabled
a refinement of the ground-state spectroscopic parameters from a
global fit of all mid- and far-infrared data.
In the case of 13CH, the electronic spectra of the A 2r –X 2r
and C 2+ –X 2r transitions have been measured ( Zachwieja
1997; Bembenek et al. 1997), as well as the lambda-doubling
transitions using microwave optical double resonance (MODR:
Steimle et al. 1985, 1986). Recently, the far-infrared spectrum
of 13CH (X 2r) was recorded using LMR by Davidson et al.
(2004), who measured the lowest energy transitions N ¼ 1
1,
2
1, and 3
2 to an accuracy of several MHz. In addition,
McCarthy et al. (2006) re-examined several of the lambdadoubling transitions of this radical using Fourier transform microwave spectroscopy (FTMW). A combined fit of the LMR, MODR,
and FTMW data was performed in this work for 13CH, and the
most accurate spectroscopic constants to date were determined,
1. INTRODUCTION
The CH radical (X 2r) has been used as a tracer of the diffuse
interstellar medium for decades. Toward diffuse gas, this species
has been observed in the ultraviolet, far-infrared, and microwave
regions of the spectrum (Herzberg 1950; Stacey et al. 1987;
Goicoechea et al. 2004; Rydbeck et al. 1974; Ziurys & Turner
1985). It has also been found to exhibit maser emission in its
ground-state lambda-doubling transition at 9 cm toward H i and
H ii regions ( Rydbeck et al. 1974). Higher-lying rotational transitions of CH have been detected in high-density sources as well
(Ziurys & Turner 1985).
CH has been studied intensely in the laboratory for the past 65 yr
via its electronic, vibrational, rotational, and lambda-doubling
transitions (e.g., Huber & Herzberg 1979; Brown & Evenson
1983; McCarthy et al. 2006). Recently, the lowest favorable rotational transition, N ¼ 1 1 (case b notation) near 535 GHz
was directly measured by Amano (2000) using submillimeter
absorption methods. This transition, however, is not observable from the ground because it is obscured by a strong atmospheric absorption line of water near 557 GHz (JKa; Kc ¼ 110 101 ;
De Lucia et al. 1974). Observations of the N ¼ 1 ! 1 line will
undoubtedly be conducted by the Herschel Space Observatory
and other future space missions.
The isotopologues of CH, in contrast, have not been studied as
extensively. Various electronic transitions of CD have been measured, including the A 2r –X 2r , B 2 –X 2r, C 2+ –X 2r ,
D 2i –X 2r , F 2+ –X 2r bands (e.g., Herzberg & Johns 1969);
1
NSF Astronomy and Astrophysics Postdoctoral Fellow.
731
732
HALFEN ET AL.
Vol. 687
including the 13C hyperfine parameters; however, the proton hyperfine constants bF and c could not be independently established
( McCarthy et al. 2006).
In this paper, we report direct measurements of the lowest
energy rotational transitions of CD (N ¼ 1
1 and 2
1) and
13
CH (N ¼ 1
1). These species were measured in the velocity
modulation spectrometer of the Ziurys group (CD and 13CH: N ¼
1 1), and the millimeter-wave system at JPL (CD: N ¼ 2 1).
Rest frequencies were recorded with a precision of 100–500 kHz,
included resolution of the D, 13C, and H hyperfine structure. Spectroscopic constants have been determined that are typically more
accurate by an order of magnitude. The results of this work are described in this paper.
2. EXPERIMENTAL
The measurements below 800 GHz were conducted with the
velocity modulation spectrometer of the Ziurys group (Savage
& Ziurys 2005). The instrument uses a Gunn oscillator /Schottky
diode multiplier combination for the radiation source, which operates from 65 to 720 GHz. The gas cell is a glass cylinder approximately 80 cm long with two ring discharge electrodes that
is cooled to 65 C with a methanol chiller. The detector is a
helium-cooled InSb hot electron bolometer. The system is computer controlled, and can be run in source modulation or velocity
modulation mode (see Halfen & Ziurys 2005).
CD and 13CH were both created in a 200 W AC discharge of
argon carrier gas and D- or 13C-substituted methane (Cambridge
Isotope Laboratories). CD was produced using 40 mTorr of Ar
and 5 mtorr of CD4. 13CH was generated using 40 mtorr of Ar
and 1 mtorr of 13CH4. A mu-metal shield was employed to reduce
Zeeman splittings caused by the Earth’s magnetic field. The discharge plasma exhibited a purple color during the course of the
measurements.
The spectrum of CD above 800 GHz was measured using a
millimeter-wave spectrometer at the Jet Propulsion Laboratory
( Drouin et al. 2005). The system consists of a radiation source,
a gas cell, and a detector. Radiation in the 840–950 GHz range
in this instrument is produced by cascaded amplification of a 70–
83 GHz source, followed by a series of two frequency doublers
and a tripler. The sample cell is a glass system with 5 cm open
end flanges and three sidearms, enclosed in a glass jacket and
aerogel insulation. The cell is cooled to liquid nitrogen temperatures, and the ends of the cell are capped by polypropylene windows. Gases are flowed through the tube from sideports toward
a liquid nitrogen trap and a rotary vane vacuum pump with pump
speed of 4 L s1. At these frequencies, the detector used is a
composite Si bolometer. In this case, CD was created in a DC
discharge of 135 mtorr He, 5 mtorr CH4, and 20 mtorr D2. The
discharge uses a hollow anode and cathode placed at opposite
ends of the 1 m tube.
The spectrum of CD near 439 GHz was initially searched for
using the predictions of Brown & Evenson (1989), which did not
include the deuterium hyperfine effects. Signals due to CD were
found within 10 MHz of these predictions. The hyperfine splittings were identified based on the improved spectroscopic constants of Wienkoop et al. (2003). The transitions near 900 GHz
were also found using the predictions of Brown & Evenson
(1989), but for these lines the hyperfine splittings are generally
collapsed.
The 13CH spectrum was searched for near 532 and 536 GHz
based on the predictions given in Davidson et al. (2004). The hyperfine pattern was estimated using the constants of these authors.
Features arising from 13CH were found over a range of several
hundred MHz, within a few MHz of the predictions.
Fig. 1.—Energy level diagram of CD (X 2r) showing the lowest rotational
levels, N ¼ 1 and 2. The measured transitions are marked on the figure by dashed
arrows; the rest frequencies are also given. The levels are labeled in Hund’s case b
notation, and total parity (+ or ) of the lambda doublets is indicated.
Rest frequencies at 400–500 GHz were determined by recording 5 MHz wide scans in pairs of increasing and decreasing frequency; at 900 GHz, scans 20 MHz wide were used. Typically,
2–4 scan pairs were needed for both isotopologues to achieve an
adequate signal-to-noise ratio. The line profiles of the absorption
features were fit with a Gaussian profile to determine the center
frequency. Line widths ranged from 1.5 to 1.8 MHz in the range
439–536 GHz, and 4 MHz for the 900 GHz data. The experimental accuracy is estimated to be 100 kHz for the lower frequency
data and 500 kHz for the higher frequency lines.
3. RESULTS
13
CD and CH each have a 2r ground state that conforms best
to a Hund’s case (b) coupling scheme because of the small ratio of A to B (4:1 for CD and 2:1 for 13CH ). Therefore, N
is more appropriate as a rotational quantum number (see Fig. 1).
Each rotational J level is split into plus and minus parity states
by lambda-type doubling. In addition, for CD, the deuterium
nuclear spin of I(D) ¼ 1 couples with J to produce F, where
F ¼ J þ I. For 13CH, both nuclei have spin angular momentum,
and thus J couples with I1 (13 C) ¼ 1/2 to first generate F1, where
F1 ¼ J þ I 1 , then F1 couples with I2 ( H ) ¼ 1/2 to yield F, i.e.,
F ¼ F1 þ I 2 . The measured rest frequencies of the hyperfine components of CD and 13CH are listed in Tables 1 and 2, respectively.
For CD, the eight strongest hyperfine components out of the possible 10 were recorded for the N ¼ 1
1, J ¼ 3/2
1/2 transition near 439 GHz. In addition, several hyperfine components
from the N ¼ 2
1, J ¼ 3/2
3/2, and J ¼ 5/2
3/2 transitions were measured in the range 884–916 GHz. Many hyperfine components at high frequency were not resolved, due to the
No. 1, 2008
ROTATIONAL TRANSITIONS OF CD AND
13
CH (X 2r)
733
TABLE 1
Observed Transition Frequencies of CD (X 2r)
N0
N 00
J0
1
1 ...........
1.5
1
1 ...........
1.5
2
1...........
1.5
2
2
1...........
1...........
1.5
2.5
2
1...........
2.5
J 00
F0
F 00
0.5 1.5
2.5
0.5
1.5
0.5 2.5
1.5
1.5
0.5
1.5 0.5
0.5
1.5
1.5
1.5
2.5
2.5
1.5 2.5
1.5 3.5
2.5
1.5 3.5
2.5
1.5
1.5
0.5
0.5
1.5
1.5
0.5
0.5
1.5
0.5
2.5
1.5
0.5
1.5
2.5
2.5
2.5
1.5
2.5
1.5
Parity
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
obs
( MHz)
obs calc
( MHz)
439255.608a
439257.449a
439271.905a
439272.694a
439794.923
439800.005
439803.008
439806.093
884764.787a
884764.787a
884770.707a
884770.707a
884772.903a
884781.449a
884781.449a
887230.840
915851.970a
915854.900a
916954.496a
916954.496a
0.076
0.101
0.093
0.117
0.027
0.003
0.015
0.039
0.093
0.906
0.984
0.680
0.517
1.095
0.570
0.000
0.196
0.196
0.617
0.617
Note.—Coupling scheme: J = N + S; F = J + I; where I is the D nuclear spin.
a
Blended lines.
intrinsically broader line widths (see Table 1). For 13CH, 17 hyperfine components of the N ¼ 1
1, J ¼ 3/2
1/2 transition
were measured out of 20 possible transitions (see Table 2).
Figure 2 shows the laboratory spectrum of the lambda doublets
of N ¼ 1
1, J ¼ 3/2
1/2 transition of CD near 439 GHz
measured in this study. For the þ
parity lambda doublet,
the four hyperfine components are collapsed into two observable
features (top panel ). In contrast, the hyperfine lines are completely
resolved in the þ parity component (bottom panel ). The
two spectra are displayed on the same frequency and intensity
scales, and the positions and relative intensities of the hyperfine
components, labeled by F, are indicated underneath the data. An
unknown feature in the bottom panel is marked with an asterisk.
Fig. 2.—Laboratory spectrum of the J ¼ 3/2
1/2 component of the N ¼
1
1 rotational transition of CD (X 2r) near 439 GHz, which consists of lambda
doublets. The top panel shows the þ
lambda doublet, while the bottom
panel presents the þ parity component. Each of the two doublets are split
into four hyperfine components, labeled by F, and their positions and relative intensities are shown below the data. Both spectra are plotted on the same frequency
and intensity scales. An unknown feature in the lower spectrum is marked with
an asterisk. Each spectrum was created from an average of four scans, each 70 s
in duration, 50 MHz wide, and cropped to display a 40 MHz range.
TABLE 2
Observed Transition Frequencies of
N0
N 00
J0
J 00
1
1 ............
1.5
0.5
1
1 ............
1.5
0.5
F1 0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
F1 00
F0
F 00
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0.5
1.5
0.5
1.5
1.5
2.5
1.5
0.5
1.5
1.5
0.5
1.5
0.5
0.5
2.5
1.5
1.5
1.5
1.5
0.5
0.5
1.5
1.5
0.5
0.5
0.5
0.5
0.5
1.5
1.5
0.5
1.5
1.5
0.5
13
CH (X 2r)
Parity
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
obs ( MHz)
obs calc ( MHz)
531859.975
531862.711
531910.901
531913.471
532083.360
532086.251
532134.740
532224.939
532227.528
536005.094
536024.969
536026.643
536046.477
536057.826
536101.144
536121.035
536132.344
0.565
0.182
0.142
0.076
0.238
0.316
0.640
0.479
0.242
0.173
0.567
0.144
0.497
0.133
0.373
0.030
0.374
Note.—Coupling scheme: J ¼ N þ S; F1 ¼ J þ I1 ; F ¼ F1 þ I 2 ; where I1 and I2 are the
respectively.
13
C and 1H nuclear spins,
734
HALFEN ET AL.
Vol. 687
lambda doubling, deuterium or 13C and hydrogen magnetic hyperfine interactions, and deuterium quadrupole coupling:
ĤeA ¼ Ĥrot þ Ĥso þ Ĥld þ Ĥmhf ( H ) þ Ĥmhf ( D)
þ Ĥmhf ( 13 C) þ ĤeQq( D) :
Fig. 3.—Spectrum of the J ¼ 5/2
3/2 component of the N ¼ 2
1 rotational transition of CD (X 2r), consisting of lambda doublets. The top panel displays the þ doublet at 915.8 GHz, and the bottom panel shows the þ
transition near 916.9 GHz. The hyperfine structure in this case, shown underneath
the spectra, is largely unresolved given the line widths of ~4 MHz. The top spectrum was created from a 30 MHz wide scan, while the bottom spectrum represents
a 20 MHz wide scan displayed over the same frequency range.
In Figure 3, the two lambda doublets of the N ¼ 2
1 transition near 916 GHz are displayed. Here the hyperfine components
are not resolved, and each doublet appears as a single feature.
Figure 4 displays the spectrum of the lambda doublets of the
N ¼1
1, J ¼ 3/2
1/2 transition of 13CH. The top panel
presents the þ
parity lambda doublet near 532 GHz, and
the bottom panel shows the þ parity doublet near 536 GHz.
The positions and relative intensities of the hyperfine components
are given below the data. As shown, nine hyperfine components
were recorded for the þ
parity transition, and eight components were measured for the other doublet. The hyperfine components are labeled by F1 and F. The two spectra are shown on the
same frequency and intensity scales, and an unknown feature in
the bottom spectrum is marked with an asterisk.
4. ANALYSIS AND DISCUSSION
The spectra of CD and 13CH were modeled with a Hund’s
case b effective Hamiltonian, which includes rotation, spin orbit,
ð1Þ
The least squares nonlinear fitting routine SPFIT developed by
Pickett (1991) was used to analyze the data.
The spectroscopic constants determined for CD are listed in
Table 3, along with the best previous constants (Wienkoop et al.
2003). Due to the limited number of rotational transitions recorded,
the parameters H, A, and pD had to be fixed in our fit to values
from previous studies of Wienkoop et al. (2003). Note that H was
also been held fixed by these authors. The constants are in good
agreement between this study and that of Wienkoop et al. (2003),
except for our rotational constant B, which is larger by about
1 MHz, outside of the statistical errors. This discrepancy reflects
the small number of rotational transitions in our fit, along with
the broad line widths (4 MHz) and blended hyperfine components
of the N ¼ 2
1 transition. (The two transitions in each blended
line were equally weighted in the fit.) The accuracy of the hyperfine
constants for CD have been improved by about an order of magnitude in this work, however, as well as , p, and q. The electric
quadrupole constant eQq was also determined for the first time.
The rms of the fit is 192 kHz.
The spectroscopic parameters for 13CH are listed in Table 4
along with the previous values (Davidson et al. 2004; McCarthy
et al. 2006). For this fit, the FTMW data of McCarthy et al. (2006)
were used in the analysis, which consists of 14 hyperfine components of the N ¼ 2, J ¼ 3/2 lambda-doubling transition and
two lines of the N ¼ 3, J ¼ 5/2 doublet. Again due to the limited amount of data, many fine-structure constants (, A ) and numerous centrifugal distortion parameters (D, D, pD, qD, etc.) had
to be set to the previous quantities of McCarthy et al. (2006). Besides the hyperfine terms, the only constants that could be determined independently were B, p, and q. This work is unique in
that it provides the first determination of bF (H) and c(H) for 13CH;
the hydrogen hyperfine constants of Davidson et al. (2004) and
McCarthy et al. (2006) were only scaled from the values of 12CH,
not established from the measurements. Furthermore, the precision of the 13C hyperfine and lambda-doubling parameters have
all been improved by about an order of magnitude. While the
lambda-doubling constants agree within the quoted errors, the rotational constant B found here is smaller by about 4 MHz than in
the previous work. Because our analysis includes the FTMW data
of McCarthy et al. (2006), this small discrepancy is most likely
due to the LMR measurements, which were carried out in a magnetic field and had frequency errors as large as 10 MHz. The
rms of the fit carried out here is 3 kHz for the microwave data and
355 kHz for the submillimeter measurements, with residuals no
larger than 5 kHz for the microwave transitions.
The 13C, hydrogen, and deuterium hyperfine constants can
be used to examine the bonding characteristics of 13CH and
CD. The electron configuration of these species is (core) 3 21 1,
where the 3 orbital forms the bond between the C and H atoms,
and the 1 orbital is nonbonding and mostly C 2p in character.
The hyperfine parameters are defined by the following equations
(Townes & Schawlow 1975):
X 1 ;
ð2Þ
a ¼ 2B gN N
ri3 o
i
No. 1, 2008
ROTATIONAL TRANSITIONS OF CD AND
13
CH (X 2r)
735
Fig. 4.—Spectrum of the J ¼ 3/2
1/2 lambda doublets of the N ¼ 1
1 transition of 13CH (X 2r), plotted on the same intensity scale. The top spectrum shows
the þ
parity component near 532 GHz, while the lower panel displays the þ transition near 536 GHz. Each doublet consists of hyperfine components; their
positions and relative intensities are indicated underneath the data, and are labeled by F1 and F. An unidentified feature is marked by an asterisk in the bottom panel. The
data displayed each cover 400 MHz and were created from four successive 110 MHz wide spectra, consisting of two averaged scans, each acquired in 70 s.
XD
E
8
ð0Þ 2 ;
gs B gN N
i
s
3
i
X 3 cos2 i 1
3
c ¼ gs B gN N
;
2
ri3
s
i
X sin2 i 3
d ¼ gs B gN N
:
2
ri3
s
i
bF ¼
TABLE 3
Spectroscopic Constants for CD (X 2r)
Parameter
This Work
Previous Worka
B ...........................
D...........................
H...........................
A ...........................
...........................
p............................
pD .........................
q............................
qD .........................
a ( D) ....................
bF ( D) ..................
c ( D) ....................
d ( D) ....................
eQq ( D)................
rms........................
230895.03(80)
12.698(90)
0.0004751b
842308.59b
424.049(91)
544.89(53)
0.047b
339.424(97)
0.082(34)
8.74(27)
8.797(72)
9.26(81)
7.054(87)
0.69(40)
0.192
230896.08(13)
12.8216(36)
0.0004751b
842308.59(90)
423.80(23)
544.41(57)
0.047(39)
339.45(18)
0.0761(69)
8.05(99)
8.99(87)
8.9(1.6)
7.06(90)
...
...
Note.—In MHz; errors are 3 in the last quoted decimal places.
Wienkoop et al. (2003).
b
Held fixed.
a
ð3Þ
ð4Þ
ð5Þ
13
13
From the value
of
the orbital hyperfine constant for C, a( C ),
3
the value of 1/r o can be calculated, where ri is the distance between the interacting nucleus and the unpaired
electron with orbital angular momentum. We find that 1/r 3 o ¼ 1:1 ; 1031 m3,
or 1.63 in units of a3
0 , where a0 is the Bohr radius of 0.529 8.
13
13
From this value, the constants
3 of
c( 3 C ) and d( C ) can be estimated,2assuming
that 1/r s 1/r o . Using angular factors of
3 cos 1 ¼ 2/5 and hsin2 i ¼ 4/5 (Varberg et al. 1991),
respectively, the spin dipolar and parity-dependent hyperfine parameters are calculated to be c(13 C) ¼ 131:2 MHz and d(13 C) ¼
262:4 MHz. These predictions are in excellent agreement with
the experimentally determined values of c(13 C) ¼ 127:1 MHz
and d(13 C) ¼ 272:75 MHz. Hence, there is consistency among
the fitted hyperfine parameters, which lends confidence to the fit.
To first order, the values of bF (13C ) and bF (H ) should be zero
because 13CH has no unpaired electrons in orbitals with s character. The nonzero magnitudes of bF (13C ) and bF ( H ) must arise
from spin polarization of the respective C 3s and H 1s orbitals by the C 1p orbital (Carrington & McLachlan 1967). The
736
HALFEN ET AL.
TABLE 4
Spectroscopic Constants for
13
CH (X 2r)
Parameter
This Work
Previous Worka
Previous Workb
B ....................
D....................
H....................
A ....................
....................
D ..................
p.....................
pD ..................
pH ..................
q.....................
qD ..................
qH ..................
a (13C) ...........
bF (13C) .........
c (13C) ...........
d (13C) ...........
dD (13C) .........
a ( H ).............
bF ( H ) ...........
c ( H ) .............
d ( H ).............
dD ( H )...........
MW rms ........
MMW rms.....
422962.01(18)
43.3319c
0.00308c
843799.80c
765.26c
0.156c
997.674(53)
0.298c
0.0000334c
1146.056(10)
0.4476c
0.00009412c
217.752(85)
41.989(91)
129.83(19)
276.67(16)
0.393(24)
54.410(88)
57.60(10)
57.19(23)
42.841(41)
0.0836(50)
0.003
0.355
422966.125(270)
43.3319(150)
0.00308c
843799.80(1.14)
765.26(33)
0.156c
998.12(48)
0.298(54)
0.0000334c
1145.971(81)
0.4476(78)
0.00009412c
218.20(57)
41.83(90)
131.02(1.17)
275.14(1.20)
0.166(177)
54.2169(39)
57.855c
57.266c
42.836(54)
0.0826(78)
...
...
422966.021(285)
43.3291(144)
0.00308c
843799.44(1.23)
765.10(36)
0.156c
998.39(72)
0.305(69)
0.0000334c
1146.073(132)
0.4554(117)
0.00009412c
218.10(1.26)
41.99(84)
131.0(3.6)
275.54(78)
...
54.006c
57.777c
56.52c
43.513c
...
...
...
Note.—In MHz; errors are 3 in the last quoted decimal places.
a
McCarthy et al. (2006).
b
Davidson et al. (2004).
c
Held fixed.
opposite signs of bF (13C ) and bF ( H ) can be rationalized by the
spin polarization model. The electrons in the carbon 1p and 3s
orbitals are polarized parallel to each other due to their favorable
exchange interactions (Carrington & McLachlan 1967). The electron in the H 1s orbital must therefore be antiparallel to the C 3s
and thus 1p electrons, yielding a negative sign for bF ( H ).
From the magnitude of the 13C Fermi contact term, the spin
density at the carbon nucleus can be estimated for 13CH relative
to the free carbon atom. The value of bF for 13CH indicates a spin
density of 2 ð0Þ ¼ 0:037a3
0 , as opposed to that of the free atom
13
value of 2 ð0Þ ¼ 0:017a3
0 , based on bF ( C 2p) ¼ 19:46 MHz
(Wolber et al. 1970). Consequently, there is a higher spin density
at the 13C nucleus in the CH molecule than for the free atom. The
electron distribution of the C-H bond must be polarized toward
the C atom. The same comparison can be made for the hydrogen
spin density determined from bF (H). The value for the free H atom
13
is 2 ð0Þ ¼ 0:31818a3
0 (Morton & Preston 1978), while for CH
2
3
it is ð0Þ ¼ 0:01320a0 . These values indicate that the majority of the hydrogen electron spin density is pushed away from the
H atom, consistent with the calculations from the 13C Fermi contact parameter. These comparisons suggest that there is some ionic
character in the C-H bond.
With the first direct measurements of the fundamental transitions of CD and 13CH, submillimeter observations can now be
conducted. Unfortunately, atmospheric absorption limits the range
of ground-based telescopes. The N ¼ 1 ! 1, J ¼ 3/2 ! 1/2 transition of 13CH is obstructed by the same telluric water line near
557 GHz that hinders submillimeter observations of CH. However, the N ¼ 1 ! 1, J ¼ 3/2 ! 1/2 transition of CD is sufficiently lower in frequency (439 GHz) such that there is significant
transmission through the atmosphere. Awindow also exists around
800–900 GHz; hence, the N ¼ 2 ! 1, J ¼ 1:5 ! 1:5 lambda
doublets near 884 and 887 GHz could be observed from the ground.
Therefore, searches for CD could be conducted with ground-based
telescopes, while submillimeter observations of CH and 13CH will
have to wait for the launch of Herschel.
This research is supported by NASA grant NNX06AB64G.
D. T. H. is supported by an NSF Astronomy and Astrophysics
Postdoctoral Fellowship under award AST-0602282. This paper
presents research carried out at the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National Aeronautics and Space Administration. Any opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect
the views of NASA.
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