The pure rotational spectrum of TiF (X4Φr): 3 d transition metal fluorides revisited

Article abstract of DOI:10.1063/1.1615753

The first measurement of the pure rotational spectrum of the TiF radical using millimeter/sub-mm direct absorption methods is presented. The given data is modeled using a Hund's case (a) effective Hamiltonian, leading to the determination of rotational, fine structure, and hyperfine parameters. This paper presents the results, interpret the constants and discuss their implications for bonding in 3d transition metal fluorides.

Full text of DOI:10.1063/1.1615753

The pure rotational spectrum of TiF ( X 4 r ):3d transition metal fluorides revisited
P. M. Sheridan, S. K. McLamarrah, and L. M. Ziurys
Citation: The Journal of Chemical Physics 119, 9496 (2003); doi: 10.1063/1.1615753
View online: http://dx.doi.org/10.1063/1.1615753
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/119/18?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Fine structure and hyperfine perturbations in the pure rotational spectrum of the VCl radical in its X 5 r state
J. Chem. Phys. 130, 164301 (2009); 10.1063/1.3108538
The rotational spectrum of the CCP ( X r 2 ) radical and its C 13 isotopologues at microwave, millimeter, and
submillimeter wavelengths
J. Chem. Phys. 130, 014305 (2009); 10.1063/1.3043367
Completing the 3 d metal fluoride series: The pure rotational spectrum of ZnF ( X + 2 )
J. Chem. Phys. 125, 194304 (2006); 10.1063/1.2355495
Perturbations in the pure rotational spectrum of CoCl (X 3 i ): A submillimeter study
J. Chem. Phys. 121, 8385 (2004); 10.1063/1.1795691
High resolution spectroscopy of BaCH 3 (X 2 A 1 ): Fine and hyperfine structure analysis
J. Chem. Phys. 108, 2703 (1998); 10.1063/1.475662
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 18
8 NOVEMBER 2003
The pure rotational spectrum of TiF„X4⌽r…: 3d transition metal
fluorides revisited
P. M. Sheridan, S. K. McLamarrah, and L. M. Ziurysa)
Department of Chemistry, Department of Astronomy, and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
͑Received 29 April 2003; accepted 13 August 2003͒
The pure rotational spectrum of TiF in its X 4⌽ ( ϭ0) ground state has been measured using
v
r
millimeter/sub-millimeter wave direct absorption techniques in the range 140–530 GHz. In ten out
of the twelve rotational transitions recorded, all four spin–orbit components were observed,
confirming the 4⌽r ground state assignment. Additional small splittings were resolved in several of
the spin components in lower J transitions, which appear to arise from magnetic hyperfine
interactions of the 19F nucleus. In contrast, no evidence for ⌳-doubling was seen in the data. The
rotational transitions of TiF were analyzed using a case ͑a͒ Hamiltonian, resulting in the
determination of rotational and fine structure constants, as well as hyperfine parameters for the
fluorine nucleus. The data were readily fit in a case ͑a͒ basis, indicating strong first order spin–orbit
coupling and minimal second-order effects, as also evidenced by the small value of ␭, the spin–spin
parameter. Moreover, only one higher order term, ␩, the spin–orbit/spin–spin interaction term, was
needed in the analysis, again suggesting limited perturbations in the ground state. The relative
values of the a, b, and c hyperfine constants indicate that the three unpaired electrons in this radical
lie in orbitals primarily located on the titanium atom and support the molecular orbital picture of TiF
1
with a ␴1␦1␲ single electron configuration. The bond length of TiF ͑1.8342 Å͒ is significantly
longer than that of TiO, suggesting that there are differences in the bonding between 3d transition
metal fluorides and oxides. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1615753͔
I. INTRODUCTION
Furthermore, high values of electron orbital and spin angular
momenta often occur in such species. Despite these com-
plexities, several titanium radicals have been studied to date
via near-infrared and optical spectroscopy. For example, the
b 1⌸–X 3⌬ transition of TiS, the 4⌫–X 4⌽ band of TiH, and
Titanium is encountered in a wide variety of research
areas. For example, because of its low density and excep-
tional corrosion resistance, the metal and its alloys are used
in the construction of aircraft and marine vehicle equipment.1
Metal oxides containing titanium have shown high dielectric
and ferroelectric properties and thus appear to be useful in
the design of microelectronic devices.2,3 Titanium com-
pounds are also employed as Ziegler–Natta type catalysts;
cyclopentadienyl titanium species, for example, are used to
polymerize olefins such as styrene and ethylene,4 while
bis͑phenoxyimine͒-titanium based molecules are currently
being investigated for their unique regioselectivity in poly-
merization insertion reactions.5 From an astronomical aspect,
gas-phase titanium bearing species such as TiO and TiH have
been identified in the spectra of cool M-type stars,6,7 while
titanium carbide crystals have been found in meteorites8 and
perhaps even in circumstellar gas.9
Small titanium containing molecules are additionally of
interest for gas phase spectroscopy. From their spectra, elec-
tronic and geometric properties of these species can be elu-
cidated, leading to a better understanding of the macroscopic
characteristics of larger Ti-bearing compounds. Titanium has
a 4s23d2 valence electron configuration, however, such that
Ti-bearing molecules usually have an extensive manifold of
closely spaced electronic states which can perturb each other.
the ⌬–X 3⌽ system of TiFϩ have been investigated;10–12
3
TiF (G 4⌽–X 4⌽) and TiCH (2⌸–X 2⌺) have been studied
as well.13,14 Millimeter-wave and PPMODR work have also
been conducted, but thus far have been limited to
TiO (X 3⌬), TiN (X 2⌺), and TiCl (X 4⌽).15,16 Hyperfine
structure was observed in TiN, giving some insight into the
bonding in titanium compounds.
One titanium radical of interest is TiF, partly because
high resolution data on the 3d transition metal fluorides, in
general, are limited. While electronic spectra of these species
have been recorded,17–19 they are certainly not as well char-
acterized as their oxide counterparts.20 For example, pure
rotational spectra exist only for ScF, CrF, FeF, NiF, and
CuF;21–25 in fact, only in the past year has the first high-
resolution optical study of VF been conducted.17 While these
molecules are expected to exhibit highly ionic bonds, some,
such as FeF,23 show signs of covalent character.
TiF has been the subject of relatively few spectroscopic
investigations. It was first observed in absorption using flash
heating techniques by Diebner and Kay in 1969, who as-
26
4
signed the ground state as ⌺Ϫ. Additional studies con-
ducted by Chantalic, Deschamps, and Pannetier27 again indi-
cated a 4⌺Ϫ ground state. Shenyavskaya and Dubov in 1985
conducted further optical work, resulting in the reas-
a͒
Telephone: 1-520-621-6525; Fax: 1-520-621-1532; Electronic mail:
lziurys@as.arizona.edu
0021-9606/2003/119(18)/9496/8/$20.00
9496
© 2003 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Pure rotational spectrum of TiF
9497
signment of the electronic ground term as 2⌬.28 Very re-
cently, Ram et al. have observed the spectrum of TiF in
emission by Fourier transform techniques and by laser exci-
tation spectroscopy, performing the first rotational analysis.13
In their work, the ground state of TiF was once again reas-
adequate signal-to-noise ratios. In order to obtain the center
frequency of each transition, Gaussian curves were fit to the
line profiles. Typical linewidths ranged from 360 kHz at 142
GHz to 1230 kHz at 523 GHz.
4
signed, this time as ⌽. Their assignment was partly based
on theoretical work by Harrison,29 and in analogy to
III. RESULTS
TiH (X 4⌽).11 Subsequent calculations by Boldyrev and
4
The ground state of TiF was initially assumed to be ⌽r
Simons30 for TiF again suggested a ⌽ ground state. Con-
4
for the purpose of our initial spectroscopic search. In this
state, spin–orbit coupling results in four fine structure levels
per rotational transition, labeled by quantum number ⍀. Fur-
thermore, these levels may be split again due to ⌳-doubling.
Although this interaction is thought to be negligible for mol-
ecules with high orbital angular momentum, lambda-
doubling has been observed in pure rotational spectra of
CoH (X 3⌽i) and in the ground state of CoF, as deduced
clusive experimental evidence for this assignment, however,
has not been obtained to date.
Here we present the first measurement of the pure rota-
tional spectrum of the TiF radical using millimeter/sub-mm
direct absorption methods. Multiple rotational transitions
were recorded for the main titanium isotopomer, 48TiF, each
consisting of four fine structure components, which defini-
tively establish the ground state of the molecule as X 4⌽r . In
addition, magnetic hyperfine splittings, resulting from the 19F
nucleus, have been observed. These data have been modeled
using a Hund’s case ͑a͒ effective Hamiltonian, leading to the
determination of rotational, fine structure, and hyperfine pa-
rameters. In this paper we present these results, interpret the
constants and discuss their implications for bonding in 3d
transition metal flourides.
from studies of the ⌽–X 3⌽ transition.32,33 Also, magnetic
3
hyperfine coupling due to the 19F nucleus (Iϭ1/2) may be
present, as observed in FeF in its X 6⌬i state.23
Searches for the rotational spectrum of TiF were aided
by the optical work of Ram et al.,13 in which effective rota-
tional constants of each fine structure component had been
determined. Individual spin components were therefore
readily located by scanning only a few hundred MHz, con-
firming the ground state assignment. Initially, the higher J
transitions were studied. Here the two higher ⍀ ladders ͑⍀
ϭ7/2 and 9/2͒ were found to consist of closely-spaced dou-
blets; their separation varied from approximately 2 MHz in
the ⍀ϭ7/2 ladder to 3 MHz in the ⍀ϭ9/2 component. Fur-
thermore, this splitting decreased in magnitude with increas-
ing J, ruling out lambda-doubling interactions as their origin.
In addition, transitions in the ⍀ϭ5/2 sub-level appeared
somewhat broader than expected, although the ⍀ϭ3/2 sig-
nals had typical line widths. The closely-spaced doublets
were attributed to hyperfine interactions of the 19F nucleus,
which would be expected to decrease with increasing J.
The pure rotational data recorded for TiF are presented
in Table I. As the table shows, twelve rotational transitions
were measured in the frequency range 140–530 GHz. For
ten of these transitions, all four fine structure components
were observed with the relative intensities decreasing as the
⍀ value increased, definitively establishing the ground state
II. EXPERIMENT
The pure rotational spectrum of TiF was measured using
one of the quasi-optical millimeter/sub-millimeter wave di-
rect absorption spectrometers of the Ziurys group. The major
features of this instrument are outlined in Ziurys et al.,31
except that offset ellipsoidal mirrors are used as the focusing
elements in this case, resulting in a different optics path.
Also, a pathlength modulator is employed to improve base-
line stability. The reaction chamber has a robust doubled-
walled construction, which enables the melting of transition
metals in a Broida-type oven attached to the cell.
The synthesis of TiF was particularly difficult because of
the high melting point and reactivity of titanium. Several
modifications to the oven were necessary in order to success-
fully vaporize this metal: First of all, crucibles constructed of
boron nitride had to be used instead of the usual alumina
type; liquid titanium was found to react destructively with
alumina. Second, the oven electrodes, normally made of steel
or a steel alloy, had to be constructed out of molybdenum in
order to withstand the oven temperatures. Also, zirconia felt
had to be placed around the top of the crucible in order to
prevent liquid titanium from boiling over and onto the heat-
ing element. To create TiF, titanium vapor was first produced
by the oven from heating a solid metal rod. It was then
reacted with 3–5 mTorr of SF6 , which was introduced into
the reaction chamber from underneath the oven. Neither a
carrier gas nor a dc discharge was necessary for molecular
synthesis. Although titanium has several isotopes, only data
for the main isotope, 48Ti, were recorded.
4
of TiF as ⌽r . The spin components also appeared to be
regularly spaced as well, suggesting that spin–orbit coupling
dominates the fine structure. In the higher J transitions, the
fluorine hyperfine splittings were only observable in the
⍀ϭ9/2 and 7/2 ladders, although the ⍀ϭ5/2 lines were un-
usually broad. As J decreased, the splitting increased such
that it was eventually resolved in the ⍀ϭ5/2 ladder at the
Jϭ18.5 17.5 transition and in the ⍀ϭ3/2 ladder at the J
ϭ13.5 12.5 transition.
Representative spectra of TiF are shown in Figs. 1 and 2.
In Fig. 1, a spectrum of the ⍀ϭ3/2 spin component of the
Jϭ21.5 20.5 transition near 469.7 GHz is presented. The
spectrum consists of a single feature, as the hf structure is
collapsed in this ladder at this high J value. In Fig. 2, the
⍀ϭ9/2 spin–orbit component of the Jϭ20.5 19.5 transi-
tion near 456.5 GHz is shown. Here the hf doublet is clearly
visible, indicated by the respective F quantum numbers. In
Final measurements of the rotational transitions were
made from an average of one scan in increasing frequency,
and the other in decreasing frequency, covering the same 5
MHz range. For the lowest frequency measurements, an av-
erage of two such scan pairs was found necessary to achieve
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

9498
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Sheridan, McLamarrah, and Ziurys
TABLE I. Measured rotational transitions for TiF ͑X 4⌽r͒: ͑vϭ0).a
Jϩ1
J
Fϩ1
F
⍀
␯
Jϩ1
J
Fϩ1
F
⍀
␯
obs
␯
␯
obs–calc
obs
obs–calc
18 17
1.5
382 422.304
384 829.420
384 827.632
389 852.043
389 848.279
404 241.985
404 241.985
406 783.622
406 782.206
409 388.332
409 385.767
412 087.036
412 083.552
447 864.621
447 864.621
450 673.700b
450 673.700b
453 553.392
453 551.256
456 535.547
456 532.474
469 666.659
469 666.659
472 609.283b
472 609.283b
475 625.367
475 623.369
478 748.469
478 745.702
491 462.521
491 462.521
494 537.916b
494 537.916b
497 689.716
497 687.828
500 953.309
500 950.642
513 251.593
513 251.593
516 459.256b
516 459.256b
519 746.260
519 744.630
523 149.537
523 147.015
0.161
0.222
Ϫ0.206
Ϫ0.164
0.123
Ϫ0.077
0.114
0.070
Ϫ0.149
0.035
Ϫ0.176
Ϫ0.070
0.127
0.099
0.157
Ϫ0.381
0.559
0.183
Ϫ0.005
Ϫ0.088
Ϫ0.064
Ϫ0.075
Ϫ0.070
Ϫ0.321
0.517
6.5 5.5
9.5 8.5
6
7
6
7
9
10
9
10
9
10
9
10
10
11 10
10
11 10
10
11 10
10
11 10
12 11
13 12
12 11
13 12
12 11
13 12
12 11
13 12
13 12
14 13
13 12
14 13
13 12
14 13
13 12
14 13
16 15
17 16
16 15
17 16
16 15
17 16
16 15
17 16
17 16
5
1.5
1.5
2.5
2.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
142 130.638
142 125.283
143 034.798
143 023.571
207 703.507
207 701.270
209 019.847
209 014.655
210 369.579
210 361.072
211 769.550
211 757.027
229 556.230
229 554.452
231 009.810
231 005.651
232 500.158
232 493.213
234 045.720
234 035.453
273 252.290
273 251.054
274 979.759
274 976.791
276 750.771
276 745.647
278 586.761
278 579.477
295 094.922
295 093.981
296 958.889
296 956.403
298 869.789
298 865.325
300 850.750
300 844.138
360 597.403
360 597.403
362 869.367
362 867.599
365 197.688
365 194.829
367 610.742
367 606.330
382 422.304
Ϫ0.101
0.093
Ϫ0.101
Ϫ0.039
Ϫ0.025
0.003
17 16
18 17
17 16
18 17
18 17
19 18
18 17
19 18
18 17
19 18
18 17
19 18
20 19
21 20
20 19
21 20
20 19
21 20
20 19
21 20
21 20
22 21
21 20
22 21
21 20
22 21
21 20
22 21
22 21
23 22
22 21
23 22
22 21
23 22
22 21
23 22
23 22
24 23
23 22
24 23
23 22
24 23
23 22
24 23
2.5
2.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
6
5
6
8
9
8
9
8
9
8
9
9
18.5 17.5
20.5 19.5
21.5 20.5
22.5 21.5
23.5 22.5
0.007
Ϫ0.074
Ϫ0.082
Ϫ0.082
0.073
0.065
10.5 9.5
12.5 11.5
13.5 12.5
16.5 15.5
17.5 16.5
Ϫ0.012
Ϫ0.041
0.004
Ϫ0.015
Ϫ0.095
Ϫ0.058
Ϫ0.014
0.045
0.074
Ϫ0.094
0.095
Ϫ0.017
0.058
Ϫ0.101
Ϫ0.043
0.104
0.080
Ϫ0.025
0.054
Ϫ0.013
0.024
Ϫ0.162
0.060
Ϫ0.107
Ϫ0.171
0.208
0.146
Ϫ0.068
0.010
9
9
9
0.221
0.009
Ϫ0.036
0.061
Ϫ0.009
Ϫ0.050
Ϫ0.282
0.468
0.114
Ϫ0.129
0.032
0.026
Ϫ0.014
Ϫ0.095
Ϫ0.281
0.391
0.030
0.068
0.014
0.093
Ϫ0.116
Ϫ0.078
Ϫ0.038
Ϫ0.078
aIn MHz.
bBlended lines, not included in the fit.
IV. ANALYSIS
both figures there are a few unidentified features marked by
asterisks.
The pure rotational data for TiF were analyzed using a
The regularity of the spacing of the fine structure lines in
TiF is illustrated in Fig. 3, which shows a stick figure of
three widely separated transitions: Jϭ9.5 8.5, Jϭ16.5
15.5, and Jϭ23.5 22.5. Approximate experimental in-
tensities are displayed. Hyperfine structure is too small to be
visible on this scale and thus is not shown. In all three spec-
tra, the spin–orbit components are fairly evenly spaced, in-
dicating that TiF closely follows a case ͑a͒ coupling scheme.
The overall splitting of the fine structure components in-
creases with J, as expected. The relative intensities of the
spin components are consistent with the regular designation
of the ground state.
Hund’s case ͑a͒ effective Hamiltonian of the form23,34,35
͑3͒
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
HeffϭHrotϩHsoϩHssϩHso ϩHhf .
͑1͒
The first three terms describe molecular rotation, first order
spin–orbit coupling, and spin–spin coupling, respectively.
The fourth expression in Eq. ͑1͒ contains the interaction
characterized by the parameter ␩. This constant concerns the
coupling of the spin–orbit and spin–spin interactions:35
3S2Ϫ1
Hso ϭ␩L S S2Ϫ
.
͑2͒
͑3͒
ˆ
ͩ
ͪ
z
z
z
5
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Pure rotational spectrum of TiF
9499
FIG. 1. Spectrum of the Jϭ21.5 20.5 rotational transition of TiF (X 4⌽r)
in its lowest spin component, ⍀ϭ3/2, observed near 469.7 GHz. The weaker
lines marked by an asterisk are unidentified. Hyperfine splittings, which
arise from interactions with the 19F nuclear spin, are not apparent in these
data and only appear at much lower J transitions. This spectrum is a single,
100 MHz scan obtained in approximately one minute.
ˆ
The fifth term, Hhf , includes the Frosch and Foley hyperfine
ˆ ˆ
constants a, b and c, which take into account both I"L and
ˆ ˆ
I"S interactions.
The TiF data were fit using this Hamiltonian in a least
squares analysis in two stages. Initially, the centroids of each
hyperfine doublet in all four spin–orbit components of the
higher frequency transitions were analyzed to establish pre-
liminary values of the rotational, spin–orbit, and spin–spin
constants. In the process, it was found necessary to fix the
spin–orbit constant, A, in order to achieve a satisfactory fit.
͑The value found by Ram et al.13 for the spacing between the
⍀ϭ3/2 and 5/2 components was used.͒ The inability to fit A
is not surprising since TiF closely follows a case ͑a͒ coupling
scheme. Once these constants were established, hyperfine in-
teractions were then included in the analysis. Large residuals
were obtained for rotational transitions higher than Jϭ19.5
18.5 in the ⍀ϭ5/2 spin–orbit component, because these
lines had unresolved hyperfine splittings. In the final fit,
these data were not included, as indicated in Table I.
FIG. 3. A stick diagram illustrating the progression of the four spin compo-
nents in TiF, over a wide range of frequency. The approximate relative
intensities are shown, and each plot covers ϳ11 GHz. The separation of spin
components increases with increasing J—almost a factor of two from the
Jϭ9.5 8.5 to the Jϭ23.5 22.5 transitions. However, all four spin com-
ponents are evenly spaced, even at high J, indicating strong spin–orbit cou-
pling in TiF.
equately by the Hamiltonian in Eq. ͑1͒. In the process of the
analysis, various higher order terms such as ␥s , the third
order spin–rotation term,36 and bs , the third order Fermi
contact hyperfine constant,37 were included, but found not to
improve the fit. Centrifugal distortion corrections to ␭, ␩,
and b were also not required. Hence, a limited number of
spectroscopic parameters were needed for the final fit, in
particular for the fine structure, where A, AD , AH , ␭ and ␩
were only used.
The spectroscopic parameters determined for TiF are
presented in Table II. The value of the rms of the millimeter-
wave fit is 102 kHz, indicating the data were modeled ad-
Also presented in Table II are the constants derived from
the optical study of TiF.13 The two sets of constants are in
fairly good agreement, although the values of AD differ by
TABLE II. Spectroscopic parameters for TiF (X 4⌽ ): ϭ0.a
v
r
Parameter
Millimeter-wave
Opticalb
B
D
A
AD
AH
␥
␭
␩
11 040.0976͑29͒
0.014 032 2͑38͒
1 018 000c
Ϫ3.456 63͑84͒
3.22(10)ϫ10Ϫ5
¯
11 037.5͑2.4͒
0.0121͑20͒
1 018 000
22.9
¯
10 400͑1200͒
3681.2͑7.0͒
Ϫ240.0͑4.0͒
67.4͑1.1͒
a
b
bϩc
rms
50͑13͒
21.7͑5.0͒
0.102
FIG. 2. Spectrum of the Jϭ20.5 19.5 rotational transition of TiF (X 4⌽r)
in the ⍀ϭ9/2 spin component recorded near 456 GHz. Here the 19F hf
interactions are clearly visible, splitting the transition into closely-spaced
doublets, which are labeled by quantum number F. The weak feature marked
by an asterisk is unidentified. This spectra is a single 100 MHz scan, lasting
one minute in duration.
aIn MHz; errors are 3␴ and apply to the last quoted decimal places.
bFrom Ref. 13. Values originally quoted in cmϪ1
.
cHeld fixed ͑see the text͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

9500
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Sheridan, McLamarrah, and Ziurys
assumed to be the C 4⌬ state, which lies 3300 cmϪ1 in en-
about an order of magnitude. This discrepancy is expected
because the optical study utilized AD and the spin–rotation
constant, ␥, whereas AD , ␭ and ␩ were used in the millime-
ter wave fit with no spin–rotation parameter. AD and ␥ are
usually highly correlated parameters;39 thus the value of AD
will vary with that of ␥.
4
ergy above the X 4⌽ state. ͑The A and B states are ⌺ and
4⌸.) It has the electron configuration 9␴11␦110␴1. It is
4
likely that a ⌬ state also exists in the manifold of TiF. The
4
energy of the ⌬ state in titanium flouride in fact can be
estimated from the spin–spin constant, under the assumption
that ␭Ϸ␭so, using perturbation theory.39 If the 4⌬ state is the
dominant perturber, then
V. DISCUSSION
A. A 4⌽ ground state for TiF
2
͉
4␲
͉
alϩ
͉10␴ ͉
͘
͗
␭soϭ
,
͑3͒
The measurement of the millimeter-wave spectrum of
72 E ϪE ͒
͑
⌬
⌽
4
TiF has confirmed the ⌽r ground electronic state, as sug-
gested by Ram et al.13 and Boldyrev and Simons.30 No ad-
ditional features beyond the four identified were observed in
this study, supporting the quartet spin multiplicity. Addition-
ally, the half-integer values of the rotational quantum number
where a is the one electron spin–orbit constant for the anti-
bonding 4␲ orbital. An evaluation of the matrix element
10␴ ϭͱ6␨(Ti), assuming that the 4␲ or-
leads to 4␲͉alϩ͉
bital is chiefly 3d in character and the 10␴ orbital is prima-
͗
͘
␲
4
eliminate the possibility of a ⌺ ground state, which is the
rily 3d , centered on the titanium atom ͑see Ref. 20͒. Alter-
␴
next lowest lying term, according to theory.30 ͑All attempts at
fitting the data to a 4⌺ Hamiltonian were unsuccessful.͒
The lack of ⌳-doubling interactions in the rotational
spectrum also suggests a high value of ⌳. The primary
electron configuration for TiF is consequently ͑core͒
8␴23␲49␴11␦14␲1.
natively, the Tiϩ spin–orbit constant may be a more
appropriate choice, as suggested by recent calculations.40
The value in Tiϩ is ␨ϭ117 cmϪ1, which hardly varies from
that of neutral titanium, which is 123 cmϪ1. Using Eq. ͑3͒,
␨(Tiϩ) and the ␭ value from Table II, the energy separation
between the X 4⌽ ground state and the ⌬ state in TiF is
4
This study is only the second measurement of the pure
rotational spectrum of a molecule in a ⌽ ground state ͑and
estimated to be ⌬EϷ9300 cmϪ1. This value is considerably
larger than the C 4⌬–X 4⌽ separation in TiCl, which is 3300
4
the third in any ⌽ state͒. The first such species investigated,
TiCl (X 4⌽r), was also observed by millimeter-wave
spectroscopy.16 Interestingly, both these radicals were fit with
relatively few ͑and identical͒ parameters, excluding hyper-
fine terms, despite the high values of angular momenta con-
cerned. The only higher order constant needed in both cases
was ␩, the spin–orbit/spin–spin interaction, which has a
similar value for both TiCl ͑Ϫ332 MHz͒ and TiF ͑Ϫ240
MHz͒. The relatively simple analysis in both cases results
from the presence of strong first order spin–orbit coupling
and the lack of second-order spin–orbit effects. Second-
order interactions, isoconfigurational or otherwise, result
cmϪ1 16 Because TiF is a lighter molecule, the C 4⌬–X 4⌽
.
separation will be larger than that in TiCl, but probably not
by a factor of three. Other excited electronic states are per-
haps contributing to ␭so to decrease its value. One such state
2
is the isoconfigurational ⌽ level, for which
3A2
␭soϭ
.
͑4͒
16 E2 ϪE4 ͒
͑
⌽
⌽
Using the A value for the X 4⌽ state, this equation suggests
that the 2⌽ state lies ϳ1760 cmϪ1 higher in energy above the
2
2
2
4
4
2
from the perturbations of nearby ⌽, ⌫, ⌬, ⌫, ⌽, and
ground state. Hence, the ⌽ state is probably a major per-
4⌬ excited states. According to Boldyrev and Simons,30 the
turber as well.
lowest lying excited state in both TiF ͑and TiCl͒ is ⌺Ϫ,
Although lambda-doubling is thought to be negligible
for ⌽ states, this interaction has in fact been observed in
CoH (3⌽i) and CoF (3⌽i).32,33 In CoH, lambda-doubling
splittings on the order of Ͼ70 MHz were observed in LMR
rotational spectra for the ⍀ϭ3 spin–orbit component. This
effect was unexpected, because the lambda-doubling matrix
4
which would not participate in these types of perturbations.
The only other state in the energy manifold calculated for
Ϫ1
2
TiF is ⌬, which is predicted to be Ͼ2000 cm above the
ground 4⌽ state,30 and hence may be sufficiently far away in
energy to have little effect.
˜
Additional evidence for minimal second-order spin–
orbit effects is the relatively small value of the spin–spin
parameter in TiF ͑␭ϭ3681 MHz͒. This constant has been
shown to consist of two contributions: pure spin–spin inter-
actions and second-order spin–orbit coupling, namely ␭
ϭ␭ssϩ␭so. The second-order term is thought to dominate in
elements for ⍀ϭ3 are diagonal only in q⌽ , which is usually
a small number.32,41 ͑The o⌽ constant is largest in magnitude
˜
of the doubling parameters for triplet states.͒ The presence of
significant lambda-doubling in the ⍀ϭ3 ladder suggests the
presence of a nearby ⌺ state in CoH. The q⌽ parameter
3
˜
˜
derived from the analysis of the CoH spectra is q⌽
heavier molecules.38 Contributions to ␭ in TiF can occur
ϭ0.01667(24) MHz.32 Because q⌽ scales approximately as
so
˜
via perturbations from doublet and quartet ⌫, ⌽, and ⌬
states, as mentioned. With the exception of the high lying
G 4⌽ state, there is little definitive spectroscopic data pro-
viding the energies of these other states, except for the
B6,41 diatomic hydrides may be the extreme case.
The effects of ⌳-doubling have also been reported for
CoF, from Fourier transform spectroscopy of the
͓10.3͔3⌽i –X 3⌽i transition.19 Splittings attributable to this
interaction were found in the ⍀ϭ2 and 3 sub-bands for both
electronic states. They were analyzed with a case ͑c͒ Hamil-
tonian, involving the effective ⌳-doubling constant q. In the
30
2
theoretically-predicted ⌬ term. Therefore, it is difficult to
establish which terms actually contribute to ␭so.
The primary second-order spin–orbit perturber in TiCl is
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
TABLE III. Hyperfine parameters for TiF and related species.a
Pure rotational spectrum of TiF
9501
1/r3
͘
n
b
bF
␺2(0)b
Molecule
a
b
c
͚
͗
n
TiF (X 4⌽r)
67.4͑1.1͒
50͑13͒
18.535͑14͒
74.5͑3.5͒
Ϫ28͑14͒
0.166͑21͒
51.7͑3.5͒
41 ͑14͒
18.480͑9͒
91.7͑3.7͒
0.0101
0.057261
0.0218
0.134
0.00090
2
ϩ
c
TiN (X
⌺
)
FeF (X 6⌬i)d
Ϫ0.45e
aIn MHz.
dReference 23.
eFixed value.
bIn units of aϪ0 3
.
cReference 42.
final fit, interestingly, only centrifugal distortion corrections
to this parameter were used for the ground state, namely qD
and qH .
In contrast to these cobalt radicals, there was no evi-
dence of lambda-doubling in any spin component in TiF, at
least up to Jϭ23.5. In analogy to ⌬ states,41 the sub-level
that should exhibit the largest effect is the ⍀ϭ3/2 ladder,
The hf constant a is proportional to the inverse, cubed,
of the distance r between the orbiting electrons and the
nucleus possessing the spin I. Hence, this constant can be
used to determine the expectation value of ͚ 1/r3 . For the
͗
͘
n
n
fluorine atom, 1/r3 ϭ5.9ϫ1031 mϪ3 or 8.77 in units of
͗
͘
aϪ0 3 44 which primarily represents the electron–nuclear sepa-
,
ration for a 2p electron. The value for TiF is 9.07ϫ1029
mϪ3 or 0.134aϪ0 3—over an order of magnitude smaller ͑see
Table III͒, indicating that the unpaired electrons contributing
to a in this radical are located, on average, much further from
the F atom than a simple 2p orbital. The two contributing
electrons are thought to reside in ␲ and ␦ molecular orbitals,
located primarily on the titanium atom. The small value de-
rived for ͚ 1/r3 supports this assumption.
˜
where n⌽ would be the major contributing term. Unfortu-
nately, the theory of ⌳-doubling for ⌽ states has not been
examined in any detail. However, using a Van Vleck
transformation,41 the n⌽ parameter can be approximated as
˜
B3A3
˜
n⌽ϰ
,
͑5͒
5
⌬E͒
͑
͗
͘
n
n
Another comparison of interest are the respective Fermi
contact terms. This parameter is directly proportional to the
electron density at the nucleus with the spin, i.e., bF
ϰ ␺2(0) ; thus, ␴ molecular orbitals are thought to make
where B and A are the rotational and spin–orbit constants,
and (⌬E)5 are the energy differences between the X 4⌽ state
and excited 4⌬, 4⌸, and 4⌺ states. The obviously small
͓
͔
˜
value of n⌽ must arise from significant energy differences
the principal contribution to this parameter. For TiF, bF
Ϸ41 MHz, while the value for FeF is 91.7 MHz ͑see Table
III͒. This factor of two increase occurs because FeF has two
unpaired ␴ electrons, while TiF has one. TiN also has a
single ␴ electron, but the smaller value for the nitride com-
pound (bFϭ18.5 MHz) versus the fluoride in this case arises
from the smaller magnetic moment of nitrogen relative to
fluorine ͑0.404 versus 2.63 Bohr magnetons44͒. In fact, nor-
malizing the Fermi contact terms by these moments, the
␺2(0) value in TiN is actually larger than in TiF ͑see Table
III͒. This result can be attributed to the shorter bond length in
TiN relative to TiF. Consequently, the single ␴ electron, lo-
cated in the nonbonding 9␴ orbital in both cases, can pen-
etrate the nitrogen nucleus more effectively than that of fluo-
rine.
Because of configuration interaction, elemental fluorine
has an atomic Fermi contact term, Aiso ͑F)ϭ52 870 MHz.45
In contrast, bF in TiF is substantially smaller. The percent of
fluorine character retained on the formation of TiF is
Ϸ0.08%. This result is not surprising; the ␴ electron in TiF is
located in a nonbonding orbital primarily composed of the
titanium 4s orbital, in analogy to TiN.45 The electron density
at the fluorine nucleus must be minimal.
4
4
between the ground and ⌸ and ⌬ states. ͑Theory predicts
the ⌺ state to be relatively close in energy. ͒
30
4
B. Interpretation of hyperfine parameters
In this study, the 19F hyperfine splitting was modeled
with a, b, and (bϩc) Frosh and Foley parameters. From
these constants, the Fermi contact term bF and spin dipolar
constant c were calculated. These values are given in Table
III. For comparison, hyperfine parameters for similar radicals
are also listed; the sample is unfortunately limited to FeF23
and TiN.42 FeF and TiN have X 6⌬ and X 2⌺ϩ ground states,
respectively.
The nuclear spin orbital constant, a, exhibits the greatest
variations between these molecules. For example, a is Ϸ67
MHz for TiF but virtually zero for FeF. FeF has a
1
9␴11␦34␲210␴ electron configuration as opposed to
1
9␴11␦14␲ for TiF, and thus has one additional electron in
an orbital with angular momentum. ͑The ␴ orbitals do not
contribute to a.͒ At first glance, one might expect the a pa-
rameter to be larger in FeF than TiF. However, the two ␲
electrons in FeF have their spins aligned and there-
ˆ ˆ
fore must have equal but opposite I"L matrix elements so
ϩ
ϩ
as to not violate the Pauli principle:
␭
͉
aiIzliz
͉
␭
͗
͘
The final parameter of interest is c, the dipolar constant,
i
i
Ϫ
i
Ϫ
i
which is an anisotropic term. It is defined as46
ˆ ˆ
ϭϪ ␭
͉
aiIzliz
͉
␭
. Their I"L contributions therefore effec-
͗
͘
tively cancel, in analogy to MnH.43 The single electron in the
␲ orbital in TiF, in contrast, can contribute fully to the
nuclear spin–orbital interaction. ͑The single unpaired elec-
tron in the nonbonding ␦ orbital in both radicals is far
enough away from the fluorine nucleus such that it has a
negligible effect.͒
3␮ ␮
3 cos2 ␪nϪ1
O
I
cϭ
.
͑6͒
͚
ͳ
ʹ
rn3
I
n
For TiF, the value of c is small and negative (c
ϭϪ28 MHz), while the constant is positive and larger for
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

9502
J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Sheridan, McLamarrah, and Ziurys
FeF (cϭ51.7 MHz), and virtually zero for TiN, as shown in
Table III. Because TiN has only one unpaired ␴ electron,
there is little to contribute to the anisotropy of the electron
distribution around the nitrogen nucleus. Hence, the c param-
eter for TiN is very small. The differences in the magnitude
of c for TiF and FeF can be interpreted in terms of their
proposed electron configurations. For TiF the configuration
is 9␴11␦14␲1; the 9␴ orbital must be nonbonding and com-
posed principally of the titanium 4s atomic orbital, in anal-
ogy with TiN.45 The only contributors to c in TiF are the 1␦
orbital (3d␦ orbital from the titanium atom͒ and the 4␲ an-
tibonding orbital, composed principally of Ti 3d and F 2p
␲
␲
atomic orbitals. In the case of FeF, where the principal con-
figuration is 9␴11␦34␲210␴1, there is an additional 4␲
electron as well as one in the 10␴ antibonding orbital ͑a
combination of the F 2p and Ti 3d ). These two electrons
should increase the value of c relative to that in TiF. Indeed,
c in FeF is a factor of two larger in absolute magnitude.
Single electron configurations consequently can explain the
relative hf parameters for TiF, FeF and TiN, and lend some
credence to the molecular orbital picture of these species.
FIG. 4. A graph showing the periodic trends in bond lengths for the 3d
transition metal oxides vs the fluorides. The oxides exhibit the characteristic
‘‘double hump’’ structure in this plot, i.e., the bond lengths increase from V
to Mn and from Fe to Cu, indicating the competition between the addition of
antibonding electrons vs core contraction. The fluorides show a similar
trend, but with variations at titanium and copper. The increase in bond
length at TiF likely results from the addition of an electron to the 4␲ anti-
bonding orbital, which does not start to fill in the oxides until chromium.
␴
␴
increase in bond length at titanium and the lack of an in-
crease at copper. These trends diverge because the fluorides
have an extra electron relative to the oxides; at the same
time, with increasing atomic number, the 3d orbitals drop
rapidly in energy relative to the 4s, while the energies of the
2p orbitals ͑O or F͒ rise.20 From ScO to TiO, the electron
configuration changes from ␴ to ␴␦, i.e., the additional elec-
tron fills a nonbonding orbital; the increase in nuclear charge
causes the orbitals to contract and the bond length decreases.
C. Trends in 3d fluoride species
The bonding in alkali and alkaline-earth fluorides, in
general, is thought to be largely ionic.47 Transition metal
fluorides might be expected to behave similarly. Theoretical
calculations of TiF predict a ϩ0.82e charge on the titanium
atom and a dipole moment of 3 Debye.30 A large amount of
ionic bonding character, however, may not apply to all of the
3d transition metals. As one moves to the right of titanium in
the periodic table, the covalent character of the metal fluo-
ride bond may be expected to increase, using simple elec-
tronegativity arguments. In fact, this increased covalency is
predicted for FeF, where only 65% of the structure is pre-
dicted to be ionic.23 A general comparison of the bonding in
3d transition metal fluorides would therefore be of great in-
terest. Unfortunately, no comprehensive review on the tran-
sition metal fluorides exists, although 3d oxides and sulfides
have been studied extensively.20,48,49
One metric by which 3d oxides ͑and sulfides͒ have been
compared is via their experimentally-measured bond lengths
as a function of the metal atom.49 A so-called ‘‘double
hump’’ structure is apparent in such a plot for the oxides, as
shown in Fig. 4. There is an increase in bond length from V
to Mn, and then another increase from Fe to Cu. This behav-
ior is thought to occur because the 4␲ antibonding orbital
does not start to fill until chromium and manganese. The
M–O bond thus lengthens despite the orbital contraction that
comes with increased nuclear charge.49 This trend is repeated
in the second half of the 3d row.
2
From ScF to TiF, the configuration changes from ␴ to
␴1␦1␲1, and the ␲ antibonding orbital acquires an electron,
1
which subsequently increases the bond length. The ␴1␦1␲
configuration in TiF is generated because the 3d orbitals
have dropped sufficiently in energy at titanium such that the
4␲ orbital is accessible. In addition, the 2p orbitals in fluo-
rine are lower in energy relative to oxygen, which in turn
decreases the 4␲ energy faster in the fluorides. In the oxides
this orbital does not become occupied until CrO (␴1␦2␲1);
VO, unlike TiF, exhibits a ␴␦2 configuration.
The difference in the trend at copper, on the other hand,
is more problematic. Presumably the increase in bond dis-
tance for CuO results from the addition of another electron
into the antibonding 4␲ orbital; core contraction apparently
cannot overcome this effect. The creation of CuF also adds
another electron to this antibonding orbital, but in this case
1
the shell is completed to create a ⌺ state. The filling of the
4␲ shell, perhaps coupled with stronger orbital contraction in
the more electronegative fluorides, results only in a slight
increase in bond distance.
A plot of the bond lengths for the 3d fluorides, also
presented in Fig. 4, does not quite show the same trends. The
most notable difference occurs in the bond lengths, which are
0.2 Å larger in the fluorides relative to the corresponding
oxides, with the exception of copper. This behavior suggests
that the oxides have a more multiple bond character than the
fluorides, which routinely shortens the bond distances. Other
deviations from the oxide trend for the fluorides include the
VI. CONCLUSION
Studies of radicals in high spin states serve as tests of
theory and angular momentum coupling. This investigation
of TiF by pure rotational spectroscopy and subsequent spec-
tral analysis has demonstrated that this 3d transition metal
radical can readily be modeled with a simple case ͑a͒ Hamil-
tonian with very few higher order terms. The regularity of
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01

J. Chem. Phys., Vol. 119, No. 18, 8 November 2003
Pure rotational spectrum of TiF
9503
the splittings of the spin–orbit components indicates that
second-order effects are minimal. It is also notable that there
is no evidence of lambda-doubling in the spectra, unlike
other species in ⌽ states. An analysis of the 19F hyperfine
interactions results in parameters that are consistent with a
15 K. Namiki, S. Saito, J. S. Robinson, and T. C. Steimle, J. Mol. Spectrosc.
191, 176 ͑1998͒.
16 A. Maeda, T. Hirao, P. F. Bernath, and T. Amano, J. Mol. Spectrosc. 210,
250 ͑2001͒.
17 R. S. Ram, P. F. Bernath, and S. P. Davis, J. Chem. Phys. 116, 7035
͑2002͒.
1
␴1␦1␲ configuration, where the ␴ and ␦ orbitals have pri-
18 B. Simard and O. Launila, J. Mol. Spectrosc. 168, 567 ͑1994͒.
19 A. G. Adam and W. D. Hamilton, J. Mol. Spectrosc. 206, 139 ͑2001͒.
20 A. J. Merer, Annu. Rev. Phys. Chem. 40, 407 ͑1989͒.
21 W. Lin, S. A. Beaton, C. J. Evans, and M. C. L. Gerry, J. Mol. Spectrosc.
199, 275 ͑2000͒.
marily nonbonding 3d metal character, and the ␲ orbital is
antibonding, formed from a linear combination of 3d and
␲
2p atomic orbitals. Hence, to a first approximation, the mo-
␲
22 T. Okabayashi and M. Tanimoto, J. Chem. Phys. 105, 7421 ͑1996͒.
23 M. D. Allen and L. M. Ziurys, J. Chem. Phys. 106, 3494 ͑1997͒.
24 M. Tanimoto, T. Sakamaki, and T. Okabayashi, J. Mol. Spectrosc. 207, 66
͑2001͒.
lecular orbital picture can explain the bonding in TiF, which
suggests some degree of covalent behavior. Titanium fluoride
was found to have a bond length 0.2 Å longer than that in
TiO, as is found for virtually all 3d fluorides relative to their
oxide counterparts. The bond distance in TiF lengthens be-
cause of the addition of an electron to the 4␲ antibonding
orbital, which does not begin to fill in the oxides until chro-
mium. Although the 3d fluorides have similar periodic trends
to the corresponding oxides, there are subtle differences
which have yet to be fully investigated.
25 T. Okabayashi, E. Yamazaki, T. Honda, and M. Tanimoto, J. Mol. Spec-
trosc. 209, 66 ͑2001͒.
26 R. L. Diebner and J. G. Kay, J. Chem. Phys. 51, 3547 ͑1969͒.
27 A. Chatalic, P. Deschamps, and G. Pannetier, C. R. Acad. Sci. 270, 146
͑1970͒.
28 E. A. Shenyavskaya and V. M. Dubov, J. Mol. Spectrosc. 113, 85 ͑1985͒.
29 J. F. Harrison ͑unpublished͒.
30 A. I. Boldyrev and J. Simons, J. Mol. Spectrosc. 188, 138 ͑1998͒.
31 L. M. Ziurys, W. L. Barclay, Jr., M. A. Anderson, D. A. Fletcher, and J. W.
Lamb, Rev. Sci. Instrum. 65, 1517 ͑1994͒.
ACKNOWLEDGMENTS
32 S. P. Beaton, K. M. Evenson, and J. M. Brown, J. Mol. Spectrosc. 164,
395 ͑1994͒.
This research was supported by National Science Foun-
dation ͑NSF͒ Grant Nos. CHE-98-17707 and AST-02-04913.
The authors would like to thank Dr. J. M. Brown for use of
his Hamiltonian code. This work was also supported in part
by a fellowship from Merck Research Laboratories.
33 R. S. Ram, P. F. Bernath, and S. P. Davis, J. Chem. Phys. 104, 6949
͑1996͒.
34 J. M. Brown, M. Kaise, C. M. L. Kerr, and D. J. Milton, Mol. Phys. 36,
553 ͑1978͒.
35 J. M. Brown, D. J. Milton, J. K. G. Watson, R. N. Zare, D. L. Albritton, M.
Horani, and J. Rostas, J. Mol. Spectrosc. 90, 139 ͑1981͒.
36 T. Nelis, J. M. Brown, and K. M. Evenson, J. Chem. Phys. 92, 4067
͑1990͒.
1 F. A. Cotton, G. Wilkinson, C. A. Murillo, and M. Bochmann, Advanced
Inorganic Chemistry, 6th ed. ͑Wiley, New York, 1999͒.
2 K. Woo, W. I. Lee, J. S. Lee, and S. O. Kang, Inorg. Chem. 42, 2378
͑2003͒.
37 A. S.-C. Cheung and A. J. Merer, Mol. Phys. 46, 111 ͑1982͒.
38 H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectra of Di-
atomic Molecules ͑Academic, Orlando, 1986͒.
3 R. F. Cava, W. F. Peck, and J. J. Krajewski, Jr., Nature ͑London͒ 377, 215
͑1995͒.
39 J. M. Brown, E. A. Colbourn, J. K. G. Watson, and F. D. Wayne, J. Mol.
Spectrosc. 74, 294 ͑1979͒.
4 R. J. Maldanis, J. C. W. Chien, and M. D. Rausch, J. Organomet. Chem.
599, 107 ͑2000͒.
40 C. Fosca, M. Bencheikh, and L. G. M. Pettersson, J. Phys. B 31, 2857
͑1998͒.
5 P. D. Hustad, J. Tian, and G. W. Coates, J. Am. Chem. Soc. 124, 3614
͑2002͒.
41 J. M. Brown, A. S.-C. Cheung, and A. J. Merer, J. Mol. Spectrosc. 124,
464 ͑1987͒.
6 R. E. S. Clegg, D. L. Lambert, and R. A. Bell, Astrophys. J. 234, 188
͑1979͒.
42 D. A. Fletcher, C. T. Scurlock, K. Y. Jung, and T. C. Steimle, J. Chem.
Phys. 99, 4288 ͑1993͒.
7 R. Yerle, Astron. Astrophys. 73, 346 ͑1979͒.
8 T. J. Bernatowicz, S. Amari, E. K. Zinner, and R. S. Lewis, Astrophys. J.
Lett. 373, L73 ͑1991͒.
43 T. D. Varberg, R. W. Field, and A. J. Merer, J. Chem. Phys. 95, 1563
͑1991͒.
9 G. Von Helden, A. G. G. M. Tielens, D. Van Heijnsbergen, M. A. Duncan,
S. Hony, L. Waters, and G. Meijer, Science 288, 313 ͑2000͒.
10 A. S.-C. Cheung, Q. Ran, W. S. Tam, D. K.-W. Mok, and P. M. Yeung, J.
Mol. Spectrosc. 203, 96 ͑2000͒.
44 W. Weltner, Jr., Magnetic Atoms and Molecules ͑Dover, New York, 1983͒.
45 C. W. Bauschlicher, Jr., Chem. Phys. Lett. 100, 515 ͑1983͒.
46 C. H. Townes and A. L. Schawlow, Microwave Spectroscopy ͑Dover, New
York, 1975͒.
11 O. Launila and B. Lindgren, J. Chem. Phys. 104, 6418 ͑1996͒.
12 C. Fosca, B. Pinchemel, D. Collet, and T. R. Huet, J. Mol. Spectrosc. 189,
254 ͑1998͒.
47 L. B. Knight, Jr., W. C. Easley, W. Weltner, Jr., and M. Wilson, J. Chem.
Phys. 54, 322 ͑1971͒.
I. Kretzschmar, D. Schroder, H. Schwarz, and P. B. Armentrout, in Ad-
48
13 R. S. Ram, J. R. D. Peers, Y. Teng, A. G. Adam, A. Muntianu, P. F.
Bernath, and S. P. Davis, J. Mol. Spectrosc. 184, 186 ͑1997͒.
14 M. Barnes, A. J. Merer, and G. F. Metha, J. Mol. Spectrosc. 181, 168
͑1997͒.
¨
vances in Metal and Semiconductor Clusters ͑Elsevier, New York, 2001͒,
Vol. 5, p. 347.
49 A. J. Bridgeman and J. Rothery, J. Chem. Soc. Dalton Trans. 2000, 211.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
31.51.57.175 On: Fri, 16 May 2014 10:30:01