JOURNAL OF CHEMICAL PHYSICS
VOLUME 108, NUMBER 7
15 FEBRUARY 1998
High resolution spectroscopy of BaCH3„ X̃ 2 A 1 …: Fine and hyperfine
structure analysis
J. Xin, J. S. Robinson,a) A. J. Apponi, and L. M. Ziurys
Department of Chemistry and Department of Astronomy and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
~Received 18 August 1997; accepted 9 October 1997!
The pure rotational spectrum of BaCH3(X̃ 2 A 1 ) in its ground vibrational state has been recorded
using millimeter/submillimeter direct absorption techniques, the first spectroscopic information
obtained for this molecule. The radical was created using Broida-type oven/d.c. discharge methods
by the reaction of barium vapor and Sn~CH3!4. Twenty-eight rotational transitions of the main
isotopomer 138BaCH3 were recorded, as well as five for 136BaCH3 and three for the 137BaCH3
species. Being a prolate symmetric top, K ladder structure was observed in all transitions for
BaCH3, as well as fine structure splittings which arise from the unpaired electron in the molecule.
For the 137Ba isotopomer, hyperfine interactions were also resolved, arising from the spin of the
barium nucleus. The complete data set has been analyzed with a 2 A Hamiltonian, and rotational,
spin-rotational, and magnetic hyperfine/nuclear quadrupole parameters accurately determined. The
fine and hyperfine structure constants established from this study suggest a predominantly ionic
bond for BaCH3, but with a considerable covalent component. Structural parameters for BaCH3
derived in this work are consistent with those of other alkaline earth monomethyl species. © 1998
American Institute of Physics. @S0021-9606~98!02203-X#
I. INTRODUCTION
simple metal-bearing species may be present in interstellar
space.12
Because of their significance for chemical, biological,
and astrophysical sciences, efforts have been made to examine the fundamental structure and bonding properties of
small organometallic species using high resolution gas-phase
spectroscopy. For example, the Bernath group has obtained
LIF measurements of various electronic transitions of calcium and strontium alkyl and aryl species. Among the molecules investigated include CaCH3 and SrCH3. 13,14 This
group has also measured optical spectra of CaCCH and
SrCCH,15,16 as well as several monocyclopentadiene and
monopyrrole radicals such as SrC5H5 and Ca~C4H4N!. 17,18
More recently, Miller and collaborators have done extensive
work on metal monomethyl radicals using laser ablation/
supersonic free jet expansion techniques with laser-induced
fluorescence. This group has obtained rotationally resolved
spectra of ZnCH3, 19 CdCH3, 19 and MgCH3, 20 including a
study of Cd hyperfine interactions in cadmium
monomethyl.21 Fundamental studies have also been done by
this group on calcium and magnesium monocyclopentadiene,
monomethylcyclopentadiene, and monopyrrolates ~see Ref.
22 for a review!. Whitham et al.23,24 have additionally examined various calcium alkyl radicals in an ablation/supersonic
jet source as well, including CaCCH, while Steimle and coworkers have recorded optical/Stark data for CaCH3 and
CaCCH.25,26 Finally, in our group we have obtained the pure
rotational spectra of MgCH3, 27 CaCH3, 28 and SrCH3, 29 using
millimeter-wave direct absorption techniques. These investigations have certainly demonstrated that a variety of small
organometallic species, including many radicals, can be synthesized in the gas-phase; they have also resulted in a better
Although there has been a long history of organometallic
compounds in synthetic applications, only recently has their
structure and bonding been investigated in any detail.1 An
important factor in this recent progress has been the development of various spectroscopic methods such as NMR, xray crystallography, and matrix isolation techniques,1–3 as
well as advancements in computational chemistry ~e.g., Refs.
4–6!. However, despite these improvements, some of the
simplest organometallic compounds such as methyl lithium
(LiCH3) have not been studied in their monomeric form.7
They have often been investigated in the solution phase, as
oligomeric structures in which the degree of aggregation depends strongly on the solvent, or they have been examined in
their crystalline state.7,8 In such environments, establishing
the fundamental properties of a given molecule is difficult if
not impossible.
Alkyl derivatives involving metals are an important class
of molecules from many aspects. First of all, many of them
are thought to be fundamental for catalysis ~e.g., Ref. 9!. As
mentioned, they also function as synthetic reagents, for example, Grignard reagents of the form RMgX, where X is a
halide atom.1 Organolithium compounds are widely used in
preparative organic chemistry as well.8 Moreover, organometallic species involving the later alkaline earth elements
calcium, strontium, and barium have been found to be effective precursors in chemical vapor deposition.10 In addition,
metal alkyl chelates are commonly present in biological systems and play important roles in cellular functions.11 Finally,
a!
Also at: Department of Chemistry, Arizona State University, Tempe, AZ
85287-1604.
0021-9606/98/108(7)/2703/9/$15.00
2703
© 1998 American Institute of Physics
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2704
Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
understanding of metal–carbon interactions ~e.g., Ref. 22!.
However, the extent of chemical interpretation has been limited by the relatively few metals and organic ligand combinations that have been studied.
In this paper we present measurements of the pure rotational spectrum of the BaCH3 radical in its X̃ 2 A 1 ground
electronic state at millimeter/sub-mm wavelengths. This
work is the first study of barium monomethyl by any spectroscopic method, and its first gas-phase detection. The radical was created by the same Broida-type oven methods used
in our studies of MgCH3, CaCH3, and SrCH3. We have recorded rotational transitions of 138BaCH3, the main barium
isotope, in the K50, 1, 2, and 3 components and up to K
56 for selected transitions, as well as the K50, 1, 2 and 3
lines of 136BaCH3. In addition, we have measured several
transitions of 137BaCH3 and have resolved hyperfine splittings for the barium 137 nucleus, which has I53/2. These
three data sets have been analyzed separately using a 2 A
Hamiltonian to produce molecular parameters for all the isotopomers, including the barium 137 hyperfine structure constants. These spectroscopic parameters are then compared
with those of other barium-containing free radicals and metal
monomethyl species and interpreted in terms of the chemical
bonding in BaCH3.
II. EXPERIMENT
The spectra of 138BaCH3 and its 136Ba and 137Ba isotopomers were recorded using one of the millimeter/sub-mm
direct absorption spectrometers of the Ziurys group. This instrument is described in detail elsewhere,30 and will only
briefly be discussed here. The system consists of a phaselocked Gunn oscillator/Schottky diode multiplier source, a
gas cell incorporating a Broida-type oven, and a heliumcooled InSb detector, and is run under computer control. The
optics of the spectrometer were designed using Gaussian
beam methods.31 The radiation is propagated through the reaction chamber, which is a double-pass system, using a scalar feedhorn, a polarizing grid, and a series of Teflon lenses.
The source is modulated at a rate of 25 kHz to achieve
phase-sensitive detection, and all signals are recorded at 2f
such that second derivative spectra are obtained.
The BaCH3 radical was created in a d.c. discharge by the
reaction of barium vapor, produced in the Broida-type oven,
with tetramethyl tin (Sn~CH3!4). The metal vaporized by the
oven was entrained in about 10 mTorr of argon, and flowed
into the interaction region where it was added to 8–10 mTorr
of Sn~CH3!4. This mixture was discharged using a current of
about 450 mA, producing a plasma that was bright green in
color.
Transition frequencies were measured for 236 lines of
138
BaCH3, 40 lines for 136BaCH3, and 96 separate lines for
137
BaCH3 in the frequency range 135–510 GHz. The measurements were typically made from scans 3 MHz wide, obtained from an average of one scan in increasing and one in
decreasing frequency. Typical line widths were 200–1000
kHz over the complete frequency range. Spectra of the three
isotopomers were measured in the natural barium isotope
ratio of 138Ba:137Ba:136Ba571.7:11.3:7.8
III. RESULTS
The data obtained for barium monomethyl are summarized in Tables I and II. Table I lists a subset of the data for
the barium 138 and 136 isotopomers. Because BaCH3 is a
prolate symmetric top molecule with a 2 A ground state, it is
best modeled using a Hund’s case ~b! basis. Hence, the rotational quantum number used in this case is N, while K
describes its projection along the symmetry axis, and J indicates the fine structure ~spin-rotation! splittings, where
J5N1S. Frequencies of the K50, 1, 2, and 3 components
of twenty-eight transitions of 138BaCH3 were measured, as
well as for five transitions of 136BaCH3, some of which are
shown in Table I. In every K component, the spin-rotation
doublets were easily resolved. For the N534→35 and N
535→36 transitions of the main isotopomer, the K54, 5,
and 6 components were additionally recorded. The measurement of higher K components was done in order to determine more accurate spin-rotation parameters. Hyperfine
splittings arising from the three methyl protons, which each
has I51/2, were not observed.
Table II displays the data obtained for 137BaCH3. For
this isotopomer, the frequencies of spin-rotation doublets for
the K50, 1, 2, and 3 components in three separate transitions were measured. As mentioned, barium 137 has a
nuclear spin of I53/2. Therefore, metal hyperfine interactions occur in this isotopomer and were observed. The effect
of barium nuclear spin was to split every spin-rotation energy level into a quartet. Consequently, each K component
consists of eight lines instead of two, which are labeled by
quantum number F, the total angular momentum, where
F5J1I. These transitions, being the strongest and the only
ones observed, follow the selection rule DN5DJ5DF511.
~Some hf components listed in Table II were contaminated
by 138BaCH3 and 136BaCH3 lines and hence were not included in the final fit.!
Representative spectra are shown in Figs. 1, 2, and 3. In
Fig. 1, the K50, 1, 2, and 3 components of the N521
→22 transition of 138BaCH3 near 229 GHz are presented.
Each K component is clearly split into a doublet arising from
the spin-rotation interactions, separated by about 125 MHz
and labeled by quantum number J ~J543/2→45/2 and J
541/2→43/2 in this case!. The spin-rotation splitting is in
fact larger than the K ladder structure. The centroids of the
fine structure doublets for the K50, 1, 2, and 3 components
are separated in frequency with respect to one another approximately by the ratio 1:3:5, as expected. The K53 components are stronger than the others by almost a factor of 2,
which arises from ortho/para statistics of the methyl group
protons. This spectrum is a composite of four separate scans,
each 100 MHz in frequency coverage and about 1 min in
duration.
In Fig. 2, a spectrum of the N545→46 transition of
136
BaCH3 near 478 GHz is displayed. As mentioned, this
isotopomer is observed in the natural barium 136 abundance.
For this transition, only the K50 and 1 components are
shown. Doublets, separated by about 125 MHz, are again
present for each K component, arising from the fine structure
interactions. This spectrum is a composite of two scans, each
about 2 min in duration and covering 100 MHz in frequency.
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Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
TABLE I. Selected observed transition frequencies for
138
BaCH3 and
BaCH3 (X̃ 2 A 1 ). a
136
136
138
BaCH3
BaCH3
N→N 8
K→K 8
J→J 8
n obs
nobs2ncalc
n obs
nobs2ncalc
12→13
0→0
11.5→12.5
12.5→13.5
11.5→12.5
12.5→13.5
11.5→12.5
12.5→13.5
11.5→12.5
12.5→13.5
12.5→13.5
13.5→14.5
12.5→13.5
13.5→14.5
12.5→13.5
13.5→14.5
12.5→13.5
13.5→14.5
24.5→25.5
25.5→26.5
24.5→25.5
25.5→26.5
24.5→25.5
25.5→26.5
24.5→25.5
25.5→26.5
25.5→26.5
26.5→27.5
25.5→26.5
26.5→27.5
25.5→26.5
26.5→27.5
25.5→26.5
26.5→27.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
33.5→34.5
34.5→35.5
44.5→45.5
45.5→46.5
44.5→45.5
45.5→46.5
44.5→45.5
45.5→46.5
44.5→45.5
45.5→46.5
45.5→46.5
46.5→47.5
45.5→46.5
46.5→47.5
45.5→46.5
46.5→47.5
45.5→46.5
46.5→47.5
135 382.563
135 506.749
135 366.753
135 491.516
135 319.511
135 445.842
135 240.898
135 369.825
145 793.562
145 917.862
145 776.620
145 901.463
145 726.028
145 852.069
145 641.725
145 770.037
270 556.833
270 681.827
270 526.473
270 651.548
270 435.387
270 560.779
270 283.765
270 409.726
280 935.961
281 061.031
280 904.520
281 029.662
280 810.168
280 935.572
280 652.957
280 778.987
363 839.282
363 964.994
363 799.311
363 925.039
363 679.487
363 805.389
363 480.110
363 606.279
363 201.571
363 328.129
362 844.574
362 971.553
362 409.712
362 537.355
477 370.060
477 496.921
477 319.391
477 446.279
477 167.531
477 294.471
476 914.803
477 041.870
487 659.696
487 786.666
487 608.126
487 735.118
487 453.538
487 580.585
487 196.274
487 323.439
0.050
20.016
0.002
20.009
0.015
0.004
0.052
0.024
20.009
0.004
20.057
0.050
20.005
20.041
20.016
20.020
20.053
0.013
20.022
0.010
0.002
0.003
0.012
0.004
20.035
0.036
0.010
0.047
0.046
0.028
20.075
0.004
0.017
0.068
0.010
0.022
20.008
0.012
0.001
0.012
20.009
0.005
0.055
20.006
0.001
20.003
0.005
0.017
20.004
0.011
0.002
20.004
0.000
0.002
0.008
0.004
0.007
0.003
0.008
20.007
0.002
20.005
478 042.890
478 169.939
477 992.088
478 119.165
477 839.857
477 966.974
477 586.462
477 713.694
488 346.933
488 474.084
488 295.209
488 422.386
488 140.212
488 267.543
487 882.302
488 009.692
20.022
20.002
20.030
20.008
0.003
20.014
20.012
20.045
20.004
20.003
20.021
20.018
20.019
0.065
0.001
0.023
1→1
2→2
3→3
13→14
0→0
1→1
2→2
3→3
25→26
0→0
1→1
2→2
3→3
26→27
0→0
1→1
2→2
3→3
34→35
0→0
1→1
2→2
3→3
4→4
5→5
6→6
45→46
0→0
1→1
2→2
3→3
46→47
0→0
1→1
2→2
3→3
2705
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2706
Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
TABLE I. ~Continued.!
136
138
BaCH3
BaCH3
N→N 8
K→K 8
J→J 8
n obs
nobs2ncalc
n obs
nobs2ncalc
47→48
0→0
46.5→47.5
47.5→48.5
46.5→47.5
47.5→48.5
46.5→47.5
47.5→48.5
46.5→47.5
47.5→48.5
47.5→48.5
48.5→49.5
47.5→48.5
48.5→49.5
47.5→48.5
48.5→49.5
47.5→48.5
48.5→49.5
497 943.561
498 070.679
497 891.100
498 018.229
497 733.819
497 861.010
497 472.093
497 599.366
508 221.578
508 348.805
508 168.220
508 295.469
508 008.285
508 135.594
507 742.170
507 869.530
20.010
0.007
20.005
0.003
20.006
0.003
0.002
20.009
20.005
20.008
20.010
20.010
20.010
20.006
0.028
20.011
498 645.221
498 772.457
498 592.650
498 719.844
498 434.849
498 562.236
498 172.470
498 299.914
508 937.524
509 064.929
508 884.001
509 011.474
508 723.679
508 851.165
508 456.836
508 584.423
0.037
0.000
0.073
20.029
20.030
20.007
0.011
20.022
20.007
20.001
20.035
0.018
0.003
0.005
0.006
0.005
1→1
2→2
3→3
48→49
0→0
1→1
2→2
3→3
In MHz. Actually a subset of all lines measured. For a complete data set, contact the authors, or see PAPS ~Ref.
32!.
a
Figure 3 shows a typical pattern observed for 137BaCH3.
In this spectrum, only one component of the spin-rotation
doublet (J593/2→95/2) is displayed for the K50 and 1
ladders of the N546→47 transition. Each line is now split
into a quartet, whose total separation is about 16 MHz, due
to 137Ba hf interactions. There are three interloping features
in this spectrum; two arise from the N546→47 transition of
136
BaCH3 ~see Table I! and the third may be due to vibrationally excited 138BaCH3. This spectrum is a single, 100
MHz scan taken in about one minute. A polynomial baseline
has been subtracted from all these data sets.
sured transitions, the centrifugal distortion corrections to
H sr , H srcd , were required to fit the data. Typically the D NS
and D NKS terms of S-reduced form were included in the fit.
Matrix elements for all spin-rotation interactions can be
found in Brown and Sears.34
The magnetic hyperfine Hamiltonian used consists of
three terms: the Fermi contact, the spin dipole–dipole and
the nuclear spin-rotation interactions, i.e.,
H hfs5H F 1H DD 1H NSR5a F ΕŜ1Ŝ•T•Î
11/2
IV. ANALYSIS
An effective Hamiltonian appropriate for a Hund’s case
~b! basis set was used to model the spectra of BaCH3. This
Hamiltonian accounts for molecular frame rotation and its
centrifugal distortion corrections, electron spin-rotation coupling and its centrifugal distortion, and magnetic hyperfine
and nuclear electric quadrupole interactions, and can be written as33–35
H eff5H rot1H cd1H sr1H srcd1H hfs1H Q .
~1!
For a prolate symmetric top, the first two terms of the Hamiltonian can be reduced to a simple rotor equation to produce
the rotational constants A and B, the first-order centrifugal
distortion corrections D N , D NK , D K , and the second order
parameters H N , H NK , H KN , and H K . The third term in the
Hamiltonian, the spin-rotation operator, which gives rise to
fine structure doublets, is defined as
H sr51/2
(
a,b
« ab ~ N a S b 1S b N a ! ,
~2!
where a and b refer to the principal axes. Of the nine possible spin-rotational constants, three are nonzero for a molecule with orthorhombic symmetry, but only two, « aa , and
1/2(« bb 1« cc ), are determinable for a symmetric top. Because high energy rotational levels are involved in the mea-
(
a,b
C ab ~ N a I b 1I b N a ! .
~3!
The nuclear electric quadrupole interaction operator can be
expressed as
H Q 5T 2 ~ Q ! •T 2 ~ “E ! .
~4!
As can be seen, the nuclear spin-rotation interaction operator
is similar in form to that for the electron spin-rotation interaction, with two determinable constants. There are in general
five independent parameters for both the dipole–dipole and
nuclear electric quadrupole hyperfine interaction tensors;
however, for a symmetric top molecule the determinable parameters are reduced to two. The spherical tensor format of
these parameters relate to their Cartesian coordinate
counterparts by the expressions T zz 52(T xx 1T y y )
52g S g N bb N T 20 (C) and T xx 2T y y 5 A24g S g N bb N T 262 (C),
and x zz 52eQT 20 (“E) and x xx 2 x y y 5 A24eQT 262 (“E), respectively, see, for example, Hirota.35 Of the two terms for
the quadrupole coupling interactions, one pertains to the
electric field gradient along the molecular symmetry axis and
the other involves the field transverse to this axis.
The eigenvalues concerning these interactions were determined from diagonalization of the matrix representation of
Eq. ~1! appropriate to a case b b J basis set, C basis
5 u N,K,S,J,I,F & , constructed using spherical tensor algebra.
The expressions for the matrix elements were taken from
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Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
TABLE II. Observed transition frequencies for
BaCH3 (X̃ 2 A 1 ). a
137
2707
TABLE II. ~Continued.!
N→N 8
K→K 8
J→J 8
F→F 8
n obs
nobs2ncalc
N→N 8
K→K 8
J→J 8
F→F 8
n obs
nobs2ncalc
45→46
0→0
44.5→45.5
43→44
46→47
45→46
44→45
44→45
45→46
46→47
47→48
43→44
46→47
45→46
44→45
44→45
45→46
46→47
47→48
43→44
46→47
45→46
44→45
44→45
45→46
46→47
47→48
43→44
46→47
45→46
44→45
44→45
45→46
46→47
47→48
44→45
47→48
46→47
45→46
45→46
46→47
47→48
48→49
44→45
47→48
46→47
45→46
45→46
46→47
47→48
48→49
44→45
47→48
46→47
45→46
45→46
46→47
47→48
48→49
44→45
47→48
46→47
45→46
45→46
46→47
47→48
48→49
477 703.787
477 709.007
477 713.7b
477 719.8b
477 814.834
477 819.836
477 825.351
477 830.686
477 653.073
477 658.377
477 663.779
477 668.793
477 764.201
477 769.178
477 774.590
477 779.935
477 500.973
477 506.289
477 511.901
477 516.798
477 612.1b
477 617.124
477 622.666
477 628.147
477 247.980
477 253.302
477 258.829
477 263.820
477 360.0b
477 364.0b
477 370.050
477 375.1b
488 000.523
488 005.681
488 009.7b
488 015.560
488 112.354
488 116.924
488 122.406
488 127.565
487 948.899
487 954.042
487 959.530
487 963.944
488 060.741
488 065.394
488 070.711
488 075.957
487 794.086
487 799.245
487 804.655
487 809.232
487 906.064
487 910.572
487 916.035
487 921.240
487 536.526
487 541.711
487 547.051
487 551.746
487 649.6b
487 653.1b
487 658.720
487 663.793
0.053
20.071
—
—
20.005
0.041
20.007
0.035
0.059
0.015
20.097
0.002
0.065
0.081
20.075
20.032
20.003
20.048
0.045
0.000
—
0.002
20.042
0.110
20.005
20.065
20.067
20.062
—
—
0.198
—
0.020
20.018
—
20.050
20.030
20.104
0.016
0.027
0.033
20.024
0.147
20.042
20.022
20.017
20.068
0.022
0.006
20.047
0.042
20.009
0.038
20.113
20.034
20.011
0.010
20.038
20.027
20.001
—
—
0.086
20.064
47→48
0→0
46.5→47.5
45→46
48→49
47→48
46→47
46→47
47→48
48→49
49→50
45→46
48→49
47→48
46→47
46→47
47→48
48→49
49→50
45→46
48→49
47→48
46→47
46→47
47→48
48→49
49→50
45→46
48→49
47→48
46→47
46→47
47→48
48→49
49→50
498 291.514
498 295.6b
498 301.689
498 305.971
498 404.159
498 408.473
498 413.679
498 418.713
498 238.942
498 243.950
498 249.125
498 253.473
498 351.633
498 355.890
498 361.131
498 366.201
498 081.528
498 086.546
498 091.660
498 095.987
498 194.130
498 198.511
498 203.724
498 208.741
497 819.458
497 824.554
497 829.666
497 834.0b
497 932.097
497 936.495
497 941.643
497 946.849
0.011
—
0.006
20.017
0.033
20.004
0.030
0.056
20.019
20.069
20.021
0.014
0.033
20.065
0.000
0.054
0.067
0.015
20.002
20.010
20.018
20.002
0.019
20.004
0.073
0.080
0.054
—
20.054
20.038
20.108
0.019
45.5→46.5
1→1
44.5→45.5
45.5→46.5
2→2
44.5→45.5
45.5→46.5
3→3
44.5→45.5
45.5→46.5
46→47
0→0
45.5→46.5
46.5→47.5
1→1
45.5→46.5
46.5→47.5
2→2
45.5→46.5
46.5→47.5
3→3
45.5→46.5
46.5→47.5
47.5→48.5
1→1
46.5→47.5
47.5→48.5
2→2
46.5→47.5
47.5→48.5
3→3
46.5→47.5
47.5→48.5
a
In MHz.
Blended with other lines; not used in fit.
b
Bowater et al.,33 Brown and Sears34 and Hirota.35 Similar
formulations have been carried out for the X̃ 2 A 1 state of
CdCH3 considering the 111Cd and 113Cd nuclear spins of I
5 21 by the Miller group.21 Endo et al. have also derived the
matrix elements for the hyperfine interactions of the three
methyl protons of CH3O36 and CH3S, 37 as well as for the
three fluorine atoms of CF3, 38 which each has a nuclear spin
of 1/2.
The data for the three BaCH3 isotopomers were analyzed
separately. The 136Ba and 138Ba isotopomers were fitted
without use of the hyperfine Hamiltonian because there was
no evidence in any of the spectra of hf splittings from the
methyl protons. The absence of hf interactions is not unexpected, since it is thought that the unpaired electron in the
alkaline earth monomethyl radicals is primarily located on
the metal atom.28,29 Because of the very high N involved and
extended data set of 138BaCH3, a higher order centrifugal
distortion term had to be added to the Hamiltonian to fit the
data to the measurement precision of 6100 kHz. To our
knowledge, such a term has not been used before and we
have tentatively used for it the symbol I NNK , where
H I 5I NNK K 2 N 3 ~ N11 ! 3 .
~5!
138
Also, because of the extensive data set for the Ba isotopomer, the spin-rotation parameter e aa could be fitted satis-
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2708
Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
FIG. 1. Spectrum of the N521→22 rotational transition of 138BaCH3
(X̃ 2 A 1 ) in its ground vibrational state near 229 GHz. Visible in the spectrum are the K50, 1, 2, and 3 components of this transition, which are each
split into doublets due to spin-rotation interactions, indicated by quantum
number J. The K53 lines are the strongest. This spectrum is a composite of
four separate scans, each 1 min in duration with a frequency coverage of
100 MHz.
factorily @e aa 533.0(2.3); see Table III#. However, for the
other two isotopomers, only components up to K53 were
measured; hence, for these species e aa was held fixed, scaled
by the appropriate reduced mass ratio.
For 137BaCH3, the magnetic hyperfine and electric quadrupole coupling Hamiltonian had to be used to account for
the hf interaction of the 137Ba nucleus. Although the dipole–
dipole and nuclear spin-rotation terms were considered in the
initial fit, only the Fermi contact and the electric quadrupole
parameters were needed for a successful analysis.
To fit the data, the fine structure components of the three
isotopomers were modeled by diagonalizing a 232 N-block
matrix of a non-parity coupled basis set, where each block is
FIG. 3. Spectrum of the J593/2→95/2 spin-rotation component of the N
546→47 transition of 137BaCH3 near 488 GHz. Only K50 and K51 lines
are shown, which are split into quartets labeled by quantum number F, due
to the hyperfine interactions of the 137Ba nucleus. Interloping features arise
from 136BaCH3 and 138BaCH3, including vibrationally excited lines. This
spectrum is a single, 50 s, 100 MHz scan.
a 434 matrix consisting of elements associated with the
different K quantum numbers. When modeling the hyperfine
structure, this matrix had to be expanded into a 32332 matrix to incorporate the hyperfine contributions.
The results of this analysis are presented in Table III,
which gives the spectroscopic constants for all three species.
The rms of the fits were 26 kHz, 24 kHz, and 54 kHz for
138
BaCH3, 136BaCH3, and 137BaCH3, respectively. Because
the transitions measured were only within a given K ladder,
any constant dependent solely on K could not be established,
namely, A, D K and H K . The other rotational centrifugal distortion parameters were found necessary for a good fit, as
well as two corrections to the spin-rotation interaction, D NS
and D NKS , as mentioned. All the constants in general are
well determined.
TABLE III. Spectroscopic constants for BaCH3(X̃ 2 A 1 ). a
138
FIG. 2. Spectrum of the N545→46 transition of 136BaCH3(X̃ 2 A 1 ) in its
ground vibrational state near 478 GHz, taken with barium 136 in its natural
abundance. Again shown are the K50 and 1 components, which are split
into fine structure doublets. This spectrum is a composite of two separate
100 MHz scans, each about 2 min in duration.
B
DN
D NK
109 H N
H NK
H KN
109 I NNK
( e bb 1 e cc )/2
e aa
D NS
D NKS
aF
eQT 20 (“E)
rms or fit
BaCH3
5211.140 40~86!
0.005 122 19~70!
0.599 60~16!
2.32~16!
0.000 012 18~13!
0.000 103 9~19!
0.192~29!
124.026~35!
33.0~2.3!
0.000 444 8~81!
20.0192(35)
--0.026
136
BaCH3
5218.4805~48!
0.005 120 8~11!
0.598 14~99!
-0.000 010 89~22!
0.000 107~25!
-124.27~63!
32.0b
0.000 434~95!
20.017(11)
--0.024
137
BaCH3
5214.764~12!
0.005 114 1~27!
0.5959~27!
-0.000 010 54~61!
0.000 110~36!
-124.16~11!
32.0b
0.000 427~17!
20.007(16)
1998.9~8.5!
157.2~1.9!
0.054
In MHz; uncertainties listed in parethesis are 3s deviations, in units of the
last quoted decimal places.
b
Held fixed in data fit.
a
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Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
TABLE IV. Fine and hyperfine constants for barium species.a
Molecule
g /B
( e bb 1 e cc )/2B
BaH
BaCH3
BaOH
BaF
0.057
-0.011
0.012
-0.024
---
bF
b
eqQ
b
--1998.9~8.5! 314.4~3.8!c
2200.2~5.9! 2394.2(1.2)
2326~33!
2117(36)
Reference
42
This work
41
39, 40
a
In MHz.
For 137Ba isotopomer; actually a F for
c
Actually x zz 52eQT 20 (“E).
b
137
BaCH3.
V. DISCUSSION
The alkaline earth monomethyl radicals are thought to be
at least somewhat ionic, with a structure tending towards
13,14,20,28,29
M1CH2
The ionicity of BaCH3 can be evaluated
3.
by comparing it with other barium compounds with differing
ligands. The barium species that have been studied with high
resolution spectroscopy include BaF39,40 and BaOH.41 Optical data for BaH (X 2 S) are also available.42 ~The mm-wave
spectrum of BaCl is also known,40 but will not be considered
because chlorine is in the third row of the Periodic Table.!
One way to examine the bonding character in these various
species is to compare their spin-rotation parameters, normalized by the rotational constant. The major contribution to the
spin-rotation interaction is the second order spin-orbit coupling, i.e.,
be quite covalent. Therefore, the bonding in BaCH3 lies
somewhere between being very ionic and very covalent, with
a larger shift towards ionic character.
Bonding behavior can also be examined through hf constants. Unfortunately, such parameters do not exist for BaH,
but they do for the other species. The Fermi contact term b F
~or a F for BaCH3! indicates the electron density at the
nucleus, in this case for barium, and hence the s character of
the unpaired electron. The more ionic the structure in these
species, the greater the s character for the unpaired electron,
and hence the larger b F value. The Fermi contact constants
are given in Table IV for BaF, BaOH, and BaCH3. BaF has
the largest value of b F 52326(33) MHz, followed by
BaOH (b F 52200.2(5.9) MHz) and finally BaCH3
~1998.9~8.5! MHz!. Hence, the trend again is towards decreasing ionicity for the monomethyl compound relative to
the fluoride or hydroxide.
The percent s character of the unpaired electron in
BaCH3 can also be estimated. The wave function C of the
unpaired electron can be expressed as40
C5a s C 6s 1a p C 6p 1a d C 5d ,
' g /B
^ X u L X u A &^ A u aL X u X & 1 ^ X u aL X u A &^ A u L X u X &
E X 2E A
.
~6!
Here, X refers to the 2 S or 2 A ground state and A refers to
the first excited 2 P or 2 E state. ~More rigorously, the expression should be a summation over all excited states.! The
symbol a is the spin-orbit constant of the excited state. This
matrix element couples the ground state with the nearest excited state that has angular momentum. The degree of this
coupling depends on the percentage of p character of the
unpaired electron in the ground state. If the ground state has
ionic bonding, the unpaired electron will be present mainly
in an s-type orbital, and hence the coupling to the excited
state will be weak. Therefore, second-order spin-orbit contribution to the ground state and subsequently the spin-rotation
constant should be small. On the other hand, if the bonding
in a species is covalent, the unpaired electron will be more
polarized and have significant p and d character. Hence, the
ground state will couple strongly with the excited state, increasing the second-order spin-orbit contribution to the
ground state spin-rotation interaction.
In Table IV, the normalized spin-rotation constants ~g /B
or 1/2( e bb 1 e cc )/B! are given for the barium compounds
mentioned. As is evident from the table, g /B is ;0.012 for
BaF, which is thought to be highly ionic,40 and g /B50.011
for BaOH, also ionic.40,41 The normalized constant is 0.024
for BaCH3, and 0.057 for BaH. Barium hydride is likely to
~7!
a 2s 1a 2p 1a 2d 51,
assuming only the 6p and 5d orbitals
where
mix with the 6s. The amplitude for C 6s can be estimated by
comparing the atomic magnetic hf constant A of the unpaired
electron of the 2 S ground state of 137Ba1 with the Fermi
contact hf constant of the unpaired electron for BaCH3, i.e.,
a 2s 5b F ~ X̃ 2 A ! /A ~ 2 S ! .
1/2~ e bb 1 e cc ! /B
'22
2709
~8!
Using the value of A54014(4) MHz from Ref. 43, a 2s for
BaCH3 is 0.50. Consequently, the unpaired electron in this
radical has 50% s character, as opposed to 58% and 55% for
BaF and BaOH, respectively.
Another parameter to compare are the nuclear quadrupole coupling constants. For a linear molecule, this constant
is eqQ, where q is the electric field gradient along the internuclear axis, which is directly comparable to x zz
52eQT 20 (“E) for a symmetric top. The quadrupole parameters for various barium compounds are also shown in Table
IV. The constants for BaF and BaOH have different signs
from that of BaCH3. This is due to the definition of the
electric quadrupole interaction which can differ by a sign
~see 1994 IUPAC Recommendations!. In magnitude, those
for BaOH and BaCH3 are larger than that for BaF, and are
comparable to one another. The larger values indicate a
greater electric field gradient across the barium nucleus,
which is likely a result of larger p and d character for the
orbital of the unpaired electron, as opposed to the strictly
symmetric s orbital. It should also be noted that the parameter eQT 212 (“E) (51/A24( x xx 2 x y y )) could not be determined in the data fit, which probably indicates a very symmetric field distribution in the transverse direction to the
molecular symmetry axis—not unexpected for a very symmetric top.
From the rotational constants determined for all three
BaCH3 isotopomers, the Ba–C bond length can be estimated,
if the H–C–H bond angle and C–H bond distance are assumed. Using a C–H distance of 1.09 Å44 and a range of
bond angles of 103°–108°, the Ba–C bond length is r Ba–C
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2710
Xin et al.
J. Chem. Phys., Vol. 108, No. 7, 15 February 1998
TABLE V. Metal–carbon bond lengths for alkaline earth monomethyl
species.a
Molecule
r C-M ~Å!
u H-C-H ~deg.!
Reference
MgCH3
CaCH3
SrCH3
BaCH3
2.105a
2.326a
2.478–2.487a
2.557–2.570c
108.2
105.6
103.5–105.9b
103–108b
27
28
29
This work
Assumes r C-H51.1 Å.
Assumed bond angle.
c
Assumes r C-H51.09 Å.
a
b
52.557– 2.570 Å, using the 138Ba isotopomer data. The values chosen for the angle reflect the range in this quantity in
going from MgCH3 to SrCH3; see Refs. 13, 14, 20. Use of
different angles, however, does not appear to change the
metal–carbon bond length significantly. The M–C bond
length derived by using this method follows the pattern of
the other alkaline earth monomethyl species, whose values
are shown in Table V. The bond distances for the metal–
carbon bond appear to increase uniformly with atomic radii,
which are 1.60, 1.97, 2.15, and 2.22 Å for Mg, Ca, Sr, and
Ba, respectively.45
Although there is no information on the excited states of
BaCH3, an estimate of the spin-orbit constant for the à 2 E
state can be obtained from Eq. ~6!, the relationship between
spin-rotation and second-order spin-orbit coupling, if the energy difference between the X̃ 2 A and à 2 E states is assumed. An upper limit to this difference can be approximated from those of MgCH3, CaCH3, and SrCH3, which are
20 030, 14 743, and 13 800 cm21, respectively.20,13,14 Hence,
the value E ˜X – E ˜A for BaCH3 should be less than the value
for SrCH3. If the energy difference for SrCH3 is used as the
upper limit for BaCH3, and assuming u ^ X̃ u L X u à & u 2 51/2, the
case of pure precession for a p electron, then a ~spin-orbit! is
165 cm21 for the à 2 E state of barium monomethyl. This
value is consistent with the increasing trend of spin-orbit
constants for MgCH3 and CaCH3, which are 28.6 and
73.1 cm21; 20 it is also considerably smaller than that for the
A 2 P state of BaH, which is 341 cm21. 42
VI. CONCLUSION
Our measurements of the pure rotational spectra of
BaCH3, including the 138Ba, 137Ba, and 136Ba isotopomers,
complete our studies of the alkaline earth monomethyl series.
The spectroscopic and structural parameters derived for
BaCH3 are consistent with the data obtained for MgCH3,
CaCH3, and SrCH3, and show no unusual trends. The fine
and hyperfine constants determined from our data suggest
that the bonding in BaCH3 is fairly ionic, but shows more
covalent character than BaF or BaOH. Spectroscopic studies
of additional metal alkyl compounds should provide even
more insight into the nature of the carbon–metal bond.
ACKNOWLEDGMENTS
This research was supported by NSF Grant No. CHE-9531244, and NASA Grants No. NAGW 2989 and NAG5-
3785. The authors thank Dr. Mark Anderson for his assistance in the early experimental phases of this project.
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