THE JOURNAL OF CHEMICAL PHYSICS 125, 194304 共2006兲
Completing the 3d metal fluoride series: The pure rotational spectrum
of ZnF „X 2⌺+…
M. A. Flory, S. K. McLamarrah, and L. M. Ziurysa兲
Department of Chemistry, Steward Observatory, University of Arizona, Tucson, Arizona 85721
and Department of Astronomy, Steward Observatory, University of Arizona, Tucson, Arizona 85721
共Received 19 May 2006; accepted 22 August 2006; published online 16 November 2006兲
The pure rotational spectrum of the ZnF radical has been recorded in the range of 176– 527 GHz
using millimeter/submillimeter direct absorption techniques. This study is the first gas-phase
spectroscopic investigation of this species. Between 5 and 11 transitions were measured for each of
five isotopologues of this radical 共64ZnF, 66ZnF, 67ZnF, 68ZnF, and 70ZnF兲 in the ground and several
excited vibrational 共v = 1, 2, and 3兲 states. Each transition consists of spin-rotation doublets with a
splitting of ⬃150 MHz, indicating that the electronic ground state of ZnF is 2⌺+, as predicted by
theory. Fluorine hyperfine splitting was observed in three isotopologues 共64ZnF, 66ZnF, and 67ZnF兲,
and hyperfine structure from the zinc-67 nucleus 共I = 5 / 2兲 was additionally resolved in 67ZnF.
Rotational, fine structure, and 19F and 67Zn hyperfine constants were determined for ZnF, as well
as equilibrium parameters. The bond length of the main isotopologue 64ZnF was calculated to be
re = 1.7677 Å. Evaluation of the hyperfine constants indicates that the ␴ orbital containing the
unpaired electron is ⬃80% 4s共Zn兲 in character with ⬃10% contributions from each of the 2p共F兲
and 4p共Zn兲 orbitals. These results imply that ZnF is somewhat less ionic than CaF, as suggested by
theory. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2355495兴
I. INTRODUCTION
Many difficulties exist in predicting the properties of
transition metal compounds, primarily because of electron
correlation effects and perturbations of close-lying electronic
states.1–3 In recent years, however, a wide range of highresolution spectroscopic studies of simple 3d metal species
have been conducted, many focusing on the monofluoride
and monoxide series.4–13 From such measurements, bonding
characteristics have been better elucidated in these compounds, including the contribution of the 3d orbitals.14 Periodic trends in bond lengths, bond energies, and dipole moments have been examined as well, and the viability of
ligand-field theory in predicting such properties has been
assessed.14,15
In contrast to most 3d-bearing compounds, zinccontaining molecules have in general been neglected by
spectroscopic investigations. Thus far, only gas-phase spectra
of ZnH, ZnCH3, ZnC2H5, and ZnCN have been recorded.
For example, Goto et al. measured the pure rotational spectrum of ZnH,16 which was followed by far IR investigations
by Tezcan et al.17 Cerny et al. investigated the A 2E − X 2A1
electronic transition of ZnCH3,18 and Povey et al. reported
the first measurement of the spectrum of the ZnC2H5
radical,19 both using laser-induced fluorescence 共LIF兲 techniques. The millimeter spectrum of ZnCN was recorded by
Brewster and Ziurys.20 In addition, an ab initio study of compounds with zinc combined with other first- and second-row
main group elements was carried out by Boldyrev and
Simons.21
a兲
Electronic mail: [email protected]
0021-9606/2006/125共19兲/194304/9/$23.00
One species of interest in this context is ZnF. This radical is the only fluoride in the 3d series that has not been
investigated in the gas phase. Zinc fluoride has been detected
in a solid neon matrix using electron spin resonance 共ESR兲
spectroscopy by Knight et al.,22 which established hyperfine
constants for the 19F nucleus. A recent photoelectron spectroscopy study of ZnF has been conducted as well, producing
some vibrational information and evidence for a X 2⌺+
ground state term.23 The calculations of Boldyrev and Simons also predicted a X 2⌺+ ground electronic state and
equilibrium bond length of re = 1.793 Å. Other theoretical
computations for this radical have been conducted, as well,
some of which suggest that ZnF and CaF should have similar
properties.21,24–29
Here we report the first gas-phase study of ZnF. The pure
rotational spectrum of this radical was recorded in its ground
electronic state, which has been identified as 2⌺+, using
millimeter/submillimeter direct absorption methods. Rotational transitions were measured arising from the ground and
several vibrationally excited states 共v = 1 , 2 , 3兲 in each of the
five stable isotopologues of ZnF. Fine structure and hyperfine
interactions were resolved in the spectra. The data have been
analyzed and spectroscopic constants established, including
equilibrium parameters. Here we present these results and
their implications for bonding in ZnF.
II. EXPERIMENT
The pure rotational spectrum of ZnF was measured using
the high-temperature spectrometer of Ziurys et al., which has
been described in detail elsewhere.30 The instrument is a direct absorption, double pass system with a steel-walled,
water-cooled reaction chamber. The radiation sources are
125, 194304-1
© 2006 American Institute of Physics
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194304-2
Flory, McLamarrah, and Ziurys
Gunn oscillator/Schottky diode multiplier combinations that
provide nearly continuous frequency coverage over the range
of 60– 660 GHz. The submillimeter radiation is propagated
through the instrument using Gaussian beam optics, which
include a rooftop reflector and a path length modulator, before being detected with the InSb hot-electron bolometer.
The frequency source is modulated at 25 kHz and detected at
2f.
The ZnF radical was produced by reacting zinc vapor
with a 10% mixture of F2 in He 共Spectra Gases兲. The vapor
was generated by melting metal pieces 共99.9% Aldrich兲 in a
Broida-type oven, over which the F2 : He gas mixture was
introduced. On average, 10 mTorr of the reactant gas mixture produced strong signals, although the line intensity continued to increase with up to 30 mTorr of gas. Additional
carrier gas and a dc discharge were not required for
ZnF synthesis. No chemiluminescence was observed
from the reaction. The ZnF signals were sufficiently
strong that five isotopologues of zinc fluoride were observed
in their natural abundance of 64Zn: 66Zn: 67Zn: 68Zn: 70Zn
= 48.6% : 27.9% : 4.1% : 18.8% : 0.6%.
As no previous spectroscopic studies of this molecule
existed, a fairly extensive search in frequency space was necessary to identify ZnF signals. Initially, the range of
350 to 380 GHz 共approximately 3B兲 was scanned continuously, and series of doublets were found with an approximate
splitting of 150 MHz—near the value of the spin-rotation
constant found for ZnCN.20 The strongest doublets were
found to repeat harmonically and were assigned to the main
isotopologue, 64ZnF. Weaker features could then be identified as arising from excited vibrational states and the less
abundant isotopologues.
Transition frequencies were measured by averaging an
equal number of scans in increasing and in decreasing frequency, which were 5 – 10 MHz in scan width. Two or four
scans were usually needed to obtain an adequate signal-tonoise ratio for most spectral features, except those of 67ZnF.
This species required up to 12 scans because of loss of signal
strength due to additional splitting from hyperfine interactions. Center frequencies were determined by fitting the observed lines with Gaussian profiles. The instrumental accuracy is approximately ±50 kHz, and typical linewidths were
0.5– 1.3 MHz over the range of 176– 527 GHz.
III. RESULTS
An illustration of the spectral pattern observed for the
ZnF species in its 2⌺+ ground state is presented in Fig. 1.
Here a stick figure of the N = 17← 16 transition of ZnF near
370 GHz is shown with approximate relative line intensities.
The hyperfine splitting of 67ZnF is shown to scale. Transitions arising from five ZnF isotopologues are clearly visible,
as are the sequences arising from the excited vibrational state
series 共v = 1, 2, and 3兲.
The transition frequencies recorded in the ground vibrational state of four isotopologues 共64ZnF, 66ZnF, 68ZnF, and
70
ZnF兲 are presented in Table I. As the table shows, each
J. Chem. Phys. 125, 194304 共2006兲
FIG. 1. A stick diagram of the N = 17← 16 transition of ZnF 共X 2⌺+兲 observed near 370 GHz. Line positions and approximate relative intensities of
the five isotopologues and their vibrational sequences are indicated on the
plot 共64ZnF: solid lines; 66ZnF: dashed lines; 68ZnF: dot-dashed lines; 70ZnF:
dots; 67ZnF: smaller dots兲. The doublet fine structure and 67Zn hyperfine
structure are shown to scale.
transition is split into fine structure doublets, and hyperfine
structure arising from the fluorine nuclear spin 共I = 1 / 2兲 was
observed in transitions lower than N = 12← 11. Eleven rotational transitions were measured for the 64ZnF species, spanning the frequency range of 176– 527 GHz, while for 66ZnF,
68
ZnF, and 70ZnF, ten, eight, and eight rotational transitions
were recorded, respectively. Features arising from vibrational
satellite lines were observed for 64ZnF 共v = 1, 2, and 3兲, for
66
ZnF 共v = 1 and 2兲, and for 68ZnF 共v = 1兲. Five rotational
transitions were recorded in each of these states; these vibrational data are available online at EPAPS.31 A total of 88
individual spectral features were measured in the v = 0 state,
and 60 lines were recorded in the excited vibrational states.
Sample transition frequencies measured for 67ZnF are
reported in Table II; the full set is available online.31 Seven
rotational transitions, which each consist of fine structure
doublets, were measured for this isotopologue in its natural
abundance of 4%. Each fine structure component is additionally split in a sextet of doublets by 67Zn and 19F hyperfine
interactions 共I = 5 / 2 and I = 1 / 2兲. Therefore, up to 24 hyperfine components exist per rotational transition. Some of these
lines are blended, as indicated in the online table. In total,
158 individual lines were measured for 67ZnF, of which 146
were included in the final fit.
Figure 2 displays two representative spectra of 64ZnF.
The top panel shows the N = 17← 16 transition and illustrates
the signal-to-noise ratio achieved for this molecule in a
single scan. The fine structure doublet, with a frequency
separation of ⬃150 MHz, is clearly visible, and there is no
evidence of hyperfine interactions. The lower panel shows
the spin-rotation components of the N = 10← 9 transition,
which in this case are additionally split into doublets by the
19
F spin. The spectrum here is a composite of two scans,
each 45 MHz in width with a frequency gap, while the upper
panel is continuous in frequency.
Figure 3 is a sample spectrum of the N = 18← 17 transition of 67ZnF. Each fine structure component is composed of
six hyperfine lines from 67Zn nuclear interactions, labeled by
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194304-3
J. Chem. Phys. 125, 194304 共2006兲
Pure rotational spectrum of ZnF
TABLE I. Transition Frequencies for ZnF 共X 2⌺+兲: v = 0 共in MHz兲.
64
66
ZnF
N⬘
J⬘
F⬘
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
14
14
14
14
17
17
17
17
18
18
18
18
19
19
19
19
21
21
21
21
22
22
22
22
23
23
23
23
24
24
24
24
7.5
7.5
8.5
8.5
8.5
8.5
9.5
9.5
9.5
9.5
10.5
10.5
10.5
10.5
11.5
11.5
13.5
13.5
14.5
14.5
16.5
16.5
17.5
17.5
17.5
17.5
18.5
18.5
18.5
18.5
19.5
19.5
20.5
20.5
21.5
21.5
21.5
21.5
22.5
22.5
22.5
22.5
23.5
23.5
23.5
23.5
24.5
24.5
7
8
8
9
8
9
9
10
9
10
10
11
10
11
11
12
13
14
14
15
16
17
17
18
17
18
18
19
18
19
19
20
20
21
21
22
21
22
22
23
22
23
23
24
23
24
24
25
←
68
ZnF
N⬙
J⬙
F⬙
␯
␯obs−calc
␯
␯obs−calc
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
13
13
13
13
16
16
16
16
17
17
17
17
18
18
18
18
20
20
20
20
21
21
21
21
22
22
22
22
23
23
23
23
6.5
6.5
7.5
7.5
7.5
7.5
8.5
8.5
8.5
8.5
9.5
9.5
9.5
9.5
10.5
10.5
12.5
12.5
13.5
13.5
15.5
15.5
16.5
16.5
16.5
16.5
17.5
17.5
17.5
17.5
18.5
18.5
19.5
19.5
20.5
20.5
20.5
20.5
21.5
21.5
21.5
21.5
22.5
22.5
22.5
22.5
23.5
23.5
6
7
7
8
7
8
8
9
8
9
9
10
9
10
10
11
12
13
13
14
15
16
16
17
16
17
17
18
17
18
18
19
19
20
20
21
20
21
21
22
21
22
22
23
22
23
23
24
175 888.831
175 890.096
176 035.615
176 037.416
197 874.630
197 875.754
198 022.273
198 023.713
219 857.296
219 858.310
220 005.528
220 006.750
241 836.458
241 837.319
241 985.050
241 986.128
0.033
−0.040
0.018
−0.048
−0.017
−0.006
0.005
−0.036
−0.050
0.029
−0.011
0.009
−0.039
0.028
−0.048
0.036
196 504.645
196 505.776
196 651.207
196 652.665
218 335.154
218 336.203
218 482.339
218 483.587
240 162.260
240 163.150
240 309.806
240 310.897
0.025
−0.025
0.022
−0.060
−0.048
0.011
−0.003
−0.006
−0.024
0.026
−0.029
0.027
373 616.076
373 616.076
373 765.625
373 765.625
395 559.947
395 559.947
395 709.524
395 709.524
417 497.329
417 497.329
417 646.916
417 646.916
461 351.144
461 351.144
461 500.703
461 500.703
483 266.874
483 266.874
483 416.391
483 416.391
505 174.642
505 174.642
505 324.114
505 324.114
527 074.112
527 074.112
527 223.525
527 223.525
0.196
−0.164
0.227
−0.186
0.177
−0.146
0.207
−0.161
0.165
−0.127
0.194
−0.136
0.126
−0.116
0.149
−0.120
0.119
−0.101
0.130
−0.115
0.093
−0.109
0.099
−0.125
0.074
−0.112
0.070
−0.136
the upper state quantum number, F1⬘, where F1⬘ = F1⬙ + 1.
Several of these lines are further split by the 19F nuclear spin
and are labeled by the quantum number F. The ordering of
the hyperfine quantum numbers is not straightforward, and
the hyperfine structure of the two spin components overlaps
at the center of the pattern. The hyperfine structure becomes
even more intermixed at lower N.
As a comparison of Figs. 2 and 3 illustrates, the fluorine
371 030.774
371 030.774
371 179.288
371 179.288
392 823.041
392 823.041
392 971.590
392 971.590
414 608.938
414 608.938
414 757.486
414 757.486
458 160.059
458 160.059
458 308.582
458 308.582
479 924.580
479 924.580
480 073.079
480 073.079
501 681.287
501 681.287
501 829.726
501 829.726
523 429.786
523 429.786
523 578.179
523 578.179
70
ZnF
0.207
−0.172
0.241
−0.191
0.168
−0.172
0.206
−0.179
0.165
−0.142
0.188
−0.156
0.131
−0.123
0.147
−0.134
0.111
−0.121
0.130
−0.125
0.109
−0.104
0.107
−0.127
0.090
−0.106
0.088
−0.126
ZnF
␯
␯obs−calc
␯
␯obs−calc
303 612.320
303 612.320
303 759.617
303 759.617
368 595.123
368 595.123
368 742.658
368 742.658
390 244.601
390 244.601
390 392.159
390 392.159
411 887.741
411 887.741
412 035.316
412 035.316
455 153.698
455 153.698
455 301.243
455 301.243
476 775.767
476 775.767
476 923.299
476 923.299
498 390.129
498 390.129
498 537.586
498 537.586
519 996.382
519 996.382
520 143.795
520 143.795
0.094
0.094
−0.098
−0.098
−0.023
−0.023
0.023
0.023
−0.033
−0.033
0.036
0.036
−0.052
−0.052
0.034
0.034
−0.021
−0.021
0.035
0.035
−0.015
−0.015
0.028
0.028
0.019
0.019
−0.013
−0.013
0.030
0.030
−0.046
−0.046
301 718.710
301 718.710
301 865.060
301 865.060
366 296.779
366 296.779
366 443.419
366 443.419
387 811.528
387 811.528
387 958.156
387 958.156
409 319.957
409 319.957
409 466.636
409 466.636
452 316.805
452 316.805
452 463.453
452 463.453
473 804.470
473 804.470
473 951.082
473 951.082
495 284.475
495 284.475
495 431.056
495 431.056
516 756.504
516 756.504
516 903.051
516 903.051
0.105
0.105
−0.130
−0.130
−0.030
−0.030
0.024
0.024
−0.007
−0.007
0.035
0.035
−0.054
−0.054
0.039
0.039
−0.021
−0.021
0.041
0.041
−0.001
−0.001
0.026
0.026
−0.001
−0.001
−0.006
−0.006
0.008
0.008
−0.031
−0.031
hyperfine interactions are not resolved in 64ZnF for the
N = 17← 16 transition, while they are clearly present in the
N = 18← 17 transition of 67ZnF. 共Note the doublets.兲 This
situation arises because the 67Zn nuclear spin creates sufficient splittings in the rotational energy levels that a net shift
results when the fluorine spin is subsequently coupled. The
largest fluorine splittings occur in the lowest F1 transitions,
similar to the case of VCH.32,33
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194304-4
J. Chem. Phys. 125, 194304 共2006兲
Flory, McLamarrah, and Ziurys
TABLE II. Selected transition frequencies for
N⬘
J⬘
F⬘1
F⬘
14
13.5
11
11
12
12
13
13
14
14
15
15
16
16
21
20.5
23
22.5
ZnF 共X 2⌺+兲: v = 0 共in MHz兲.
67
N⬙
J⬙
F⬙1
F⬙
␯
␯obs−calc
J⬘
F⬘1
F⬘
10.5
11.5
11.5
12.5
12.5
13.5
13.5
14.5
14.5
15.5
15.5
16.5
13
12.5
10
10
11
11
12
12
13
13
14
14
15
15
9.5
10.5
10.5
11.5
11.5
12.5
12.5
13.5
13.5
14.5
14.5
15.5
304 598.846
304 599.147
304 659.178
304 663.650
304 657.039
304 653.273
304 637.363
304 634.138
304 622.325
304 619.808
304 609.778
304 608.606
−0.043
0.050
−0.066
−0.153
0.034
0.062
−0.026
0.051
−0.044
−0.025
0.007
−0.043
14.5
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20
21
21
22
22
23
23
17.5
18.5
18.5
19.5
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
20
19.5
17
17
18
18
19
19
20
20
21
21
22
22
16.5
17.5
17.5
18.5
18.5
19.5
19.5
20.5
20.5
21.5
21.5
22.5
456 631.913
456 632.052
456 691.847
456 688.002
456 671.760
456 669.031
456 658.548
456 656.458
456 648.363
456 646.955
456 639.322
456 638.798
−0.005
−0.014
−0.005
0.036
0.015
−0.048
0.069
−0.086
0.248
0.125
¯a
¯a
21.5
20
20
21
21
22
22
23
23
24
24
25
25
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
23.5
24.5
24.5
25.5
22
21.5
19
19
20
20
21
21
22
22
23
23
24
24
18.5
19.5
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
23.5
24.5
500 008.488
500 008.488
500 060.917
500 057.390
500 044.065
500 041.549
500 032.371
500 030.497
500 023.074
500 021.984
500 014.916
500 014.916
0.071
−0.060
−0.071
0.001
0.072
−0.079
0.016
−0.183
¯a
¯a
−0.194
0.245
23.5
←
J⬙
F⬙1
F⬙
␯
␯obs−calc
11.5
12.5
12.5
13.5
13.5
14.5
14.5
15.5
15.5
16.5
16.5
17.5
13.5
11
11
12
12
13
13
14
14
15
15
16
16
10.5
11.5
11.5
12.5
12.5
13.5
13.5
14.5
14.5
15.5
15.5
16.5
304 686.332
304 682.461
304 688.479
304 692.875
304 707.982
304 712.003
304 723.098
304 726.552
304 735.629
304 737.871
304 746.467
304 747.337
−0.011
0.062
0.078
−0.071
−0.046
−0.123
0.008
0.070
0.090
−0.022
0.102
0.145
19
19
20
20
21
21
22
22
23
23
24
24
18.5
19.5
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
23.5
24.5
20.5
18
18
19
19
20
20
21
21
22
22
23
23
17.5
18.5
18.5
19.5
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
456 719.764
456 724.010
456 739.817
456 742.865
456 753.037
456 755.511
456 763.364
456 765.337
456 772.448
456 773.149
456 779.901
456 780.102
0.006
0.003
0.027
−0.005
−0.027
0.080
−0.081
0.149
0.271
−0.116
0.070
−0.070
21
21
22
22
23
23
24
24
25
25
26
26
20.5
21.5
21.5
22.5
22.5
23.5
23.5
24.5
24.5
25.5
25.5
26.5
22.5
20
20
21
21
22
22
23
23
24
24
25
25
19.5
20.5
20.5
21.5
21.5
22.5
22.5
23.5
23.5
24.5
24.5
25.5
500 103.533
500 107.353
500 120.301
500 123.255
500 132.066
500 134.299
500 141.131
500 142.712
500 149.275
500 150.184
500 156.422
500 156.422
0.047
−0.047
−0.119
0.115
0.001
0.189
−0.229
−0.128
¯a
¯a
0.156
−0.123
←
a
Blended line; calculated frequency not included in fit.
IV. ANALYSIS
Molecular constants for ZnF were determined using the
analysis program SPFIT,34 with a case 共b␤J兲 Hamiltonian of
the form
Heff = Hrot + Hsr + Hmhf共F兲 + Hmhf共Zn兲 + HeqQ共Zn兲 .
共1兲
Here the terms account for molecular frame rotation including centrifugal distortion 共Hrot; operator form: N̂2兲, electron
spin-rotation coupling 共Hsr兲, magnetic hyperfine interactions
due to the fluorine nucleus 共Hmhf共F兲兲, and magnetic hyperfine/
quadrupole interactions from the 67Zn nucleus 共Hmhf共Zn兲 and
HeqQ共Zn兲兲, applicable only to 67ZnF. A centrifugal distortion
correction was also used for the spin-rotation term for isotopologues with large data sets, for example, 64ZnF and 66ZnF
共v = 0兲. The 19F hyperfine interactions were modeled with the
Fermi contact term bF and spin-dipolar constant c. Both parameters were initially seeded to the values reported by
Knight et al.,22 but then allowed to vary in the analysis. For
the 67ZnF isotopologue, bF, bFD, c, and eqQ were additionally used to account for the interactions of the zinc-67
nucleus. The centrifugal distortion correction to the Fermi
contact term, bFD, analogous to other distortion constants, is
phenomenological in nature but has been used previously.35
For 67ZnF, the magnetic hyperfine constants calculated by
Malkin et al.29 were used as initial values. The order of the
coupling for the nuclear spins in this case was J + I1共 67Zn兲
= F1 and F1 + I2共 19F兲 = F. The vibrational states of each zinc
isotopologue were individually fitted.
In the 67ZnF spectra, several of the hyperfine lines overlap at low N, and the doublet splitting due to 19F could not
always be resolved. When possible, blended lines were deconvolved into individual features. Otherwise, such blends
were not included in the fit; the calculated positions for those
features are listed in the tables with no corresponding residuals. There are uncharacteristically large residuals for some of
the 19F hyperfine doublets, where the predicted splitting is
smaller than can be resolved. The off-diagonal hyperfine
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194304-5
J. Chem. Phys. 125, 194304 共2006兲
Pure rotational spectrum of ZnF
FIG. 2. Spectra of N = 17← 16 transition of 64ZnF, the main isotopic species,
near 373 GHz 共top panel兲, and the N = 10← 9 transition near 220 GHz
共lower panel兲. The upper spectrum illustrates the distinctive fine structure
doublet of this molecule, indicated by quantum number J. At low N, each
component is then split into an additional, closely spaced doublet by fluorine
hyperfine interactions, as shown in the lower spectrum. The upper spectrum
is a composite of two scans, each 110 MHz wide and acquired in 60 s. The
lower spectrum is a composite of two scans, separated by a frequency gap,
each 45 MHz wide with duration of 30 s.
matrix elements with ⌬J ⫽ 0 are included in the fitting program; therefore, these residuals reflect the inherent uncertainty of the deconvolution process.
The resulting spectroscopic constants for the v = 0 states
are presented in Table III; those for excited vibrational states
are available online at EPAPS.31 As shown in the table, the
rms of the fits for the v = 0 data fall in the range of
22– 49 kHz, with the exception of 67ZnF, where it is 86 kHz.
For the v = 1 – 3 analyses, the rms values are 9 – 21 kHz. One
interesting result is that the hyperfine constants are typically
larger than the spin-rotation parameter 共300– 500 MHz versus ⬃150 MHz兲. The case of 67ZnF is extreme, with
bF共Zn兲 ⬃ 1290 MHz, indicating that a case 共b␤N兲 coupling
scheme might be more appropriate for this species at low
N.36
From the constants in Table III, the vibrational dependences of B, D, and ␥ for 64ZnF, 66ZnF, and 68ZnF were
calculated using the standard equations37 with the following
sign conventions:
Dv = De + ␤e共v + 1/2兲,
共2兲
␥v = ␥e + ␥e⬘共v + 1/2兲.
共3兲
Equilibrium parameters for 64ZnF and 66ZnF were obtained
from a least-squares analysis. Because fewer vibrational
states were observed for 68ZnF, a least-squares fit was not
possible. The resulting equilibrium values Be, ␣e, De, ␤e, ␥e,
and ␥e⬘ for ZnF are listed in Table IV.
FIG. 3. Spectrum of the N = 18← 17 transition of 67ZnF near 391 GHz. For
this isotopologue, hyperfine interactions from both the 67Zn nucleus
共I = 5 / 2兲 and the 19F nucleus 共I = 1 / 2兲 complicate the spectral pattern. The
zinc hyperfine 共hf兲 coupling splits each fine structure component into a
sextet of lines, each labeled by F⬘1, which are then further split into doublets
by the 19F nucleus, labeled by F. This spectrum is a composite of two scans,
each 100 MHz wide and obtained by signal averaging for 3 min.
V. DISCUSSION
A. Ground state
From the rotational spectra measured here, the ground
state term for ZnF appears to be 2⌺+, as predicted by previous experiments and theory. For every transition, a clear doublet feature has been observed with a splitting of about
150 MHz. This splitting is fairly constant, indicative of spinrotation interactions as opposed to ⌳ doubling. A similar
splitting of 104 MHz has been found for the 2⌺+ state of
ZnCN.20 The electron configuration for the ground state is
likely 关core兴8␴23␲49␴21␦44␲410␴1.
B. Equilibrium structural parameters
Using the equilibrium values for Be and De, the harmonic vibrational frequency ␻e, anharmonic correction ␻e␹e,
and dissociation energy DE were estimated from the following approximations:37
␻e ⬇
冑
冉
4B3e
,
De
␻ e␹ e ⬇
DE ⬇
共4兲
冊
2
␣ e␻ e
+
1
Be ,
6B2e
␻2e
.
4 ␻ e␹ e
共5兲
共6兲
The resulting values are listed in Table IV.
The equilibrium bond distance for 64ZnF, established
from four vibrational states, is calculated to be re
= 1.7677共1兲 Å. The degree of accuracy of this value is based
on the agreement of the ratios of the rotational constants
relative to those of the reduced masses. This value is in relatively good agreement with several theoretically predicted
bond lengths, which range from 1.775 to 1.799 Å.21,24–26,28
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194304-6
J. Chem. Phys. 125, 194304 共2006兲
Flory, McLamarrah, and Ziurys
TABLE III. Spectroscopic constants for ZnF 共X 2⌺+兲: v = 0 共in MHz兲. Values in parentheses are 3␴ errors.
64
66
ZnF
B0
D0
␥0
␥D
bF共F兲
c共F兲
bF共Zn兲
bFD共Zn兲
c共Zn兲
eqQ共Zn兲
rms
ZnF
10 999.605 4共23兲
0.015 050 4共27兲
150.93共33兲
−0.000 62共22兲
326.3共7.6兲
524共92兲
10 923.431 8共26兲
0.014 842 7共29兲
149.89共43兲
−0.000 61共27兲
330共10兲
510共140兲
0.026
0.022
The most accurate prediction 共re = 1.775 Å兲 is from Harrison
et al. The experimental bond length of ZnF is longer than
that of CuF by about 0.02 Å 关re = 1.7449 Å 共Ref. 12兲兴, presumably scaling with the atomic radii.
An increase in bond length is predicted for the zinc species relative to copper for the 3d oxides and sulfides.14 In
these cases, the electron is thought to add to the 4␲ antibonding orbital in creating ZnO and ZnS, and therefore the
increase is expected. For the fluorides, the electron in ZnF
adds to the 10␴ orbital, which, as will be discussed, has only
a small amount of bonding character. The bond length
increases also from CuF to ZnF. However, the trends vary
otherwise. The longest bond distances of the fluorides are in
TiF and MnF, which have values of 1.834 and 1.836 Å,
respectively;5,8 in the oxides and sulfides, the scandium, copper, and zinc compounds have the longest bond distances.
Several theoretical values exist for the vibrational frequency ␻e, lying in the range of 593– 633 cm−1, with the
highest value from calculations by Harrison et al.21,24,25,28 In
addition, from photoelectron spectroscopy 共PES兲 data,
Moravec et al. determined ␻e = 620共10兲 cm−1 and ␻e␹e
= 2 cm−1.23 The vibrational and anharmonic constants estimated here are ␻e = 631 cm−1 and ␻e␹e = 4.0 cm−1—in reasonable agreement with these previous values.
The dissociation energy, DE, for ZnF is calculated to be
3.123 eV. This value is higher than predicted by Boldyrev
and Simons21 or Bowmaker and Schwerdtfeger,24 who estimated 2.931 and 2.264 eV, respectively. In contrast, Harrison et al. predicted DE = 3.16 eV, extremely close to the
derived value.28
67
68
ZnF
70
ZnF
10 886.954 4共12兲
0.014 744 5共16兲
149.58共12兲
−0.000 715共99兲
321.4共3.1兲
554共17兲
1291.4共1.6兲
0.00251共57兲
39.1共3.1兲
−60共12兲
0.086
ZnF
10 851.670 2共38兲
0.014 649 8共42兲
147.489共75兲
10 783.953 1共38兲
0.014 466 8共42兲
146.586共75兲
0.045
0.049
From DE, re, and ␻e, a Morse potential curve has been
modeled for 64ZnF and is shown in Fig. 4, indicated by the
solid line. For comparison, potential curves from previous
calculations are also plotted.21,24,28 The curve derived from
Harrison et al.28 using RCCSD共T兲 method 共dot-dashed line兲
lies almost exactly on the experimental data curve. Other
potentials, derived from lower level ab initio techniques
共CISDSC and QCISD兲, deviate considerably from the experimental well, particularly at a larger internuclear distance.
Harrison et al.28 carried out their computations in order
to compare the bonding in CaF and ZnF, which both have 2⌺
ground states and metal atoms with 4s2 valence configurations. Their assumption was that calcium is a pseudotransition metal and, therefore, to a good approximation, the two
species should have similar bonding properties. However,
population analyses and relative potential curves indicate
that ZnF is significantly more covalent than CaF, although
both species are primarily ionic. These authors conclude that
the filled 3d orbitals in ZnF do not effectively shield the
increased nuclear charge in going from calcium to zinc.
Hence, the ionization potential in zinc remains large relative
to calcium, which influences ionic/covalent curve crossings.
C. Interpretation of fine and hyperfine constants
The spin-rotation constant ␥, to first order, scales as the
rotational constant B.38 Therefore, for a series of similar molecules, the ratio ␥ / B 关or 共␧bb + ␧cc兲 / 2B兴 should be approximately the same. In the case of the known zinc-bearing
TABLE IV. Equilibrium parameters for ZnF 共X 2⌺+兲. 共Values in parentheses are 1␴ errors.兲
64
ZnF
Be 共MHz兲
␣e 共MHz兲
De 共MHz兲
␤e 共MHz兲
␥e 共MHz兲a
␥e⬘ 共MHz兲
re 共Å兲
␻e 共cm−1兲
␻e␹e 共cm−1兲
DE 共eV兲
11 043.42共26兲
88.01共12兲
0.015 051 68共36兲
−0.000 002 00共16兲
151.30共17兲
−2.825共78兲
1.767 7
631
4.0
3.123
66
ZnF
10 967.01共15兲
87.28共11兲
0.014 844 20共83兲
−0.000 002 38共59兲
150.30共17兲
−2.86共12兲
1.767 6
629
3.9
3.115
68
ZnF
10 894.973 7共58兲
86.607共10兲
0.014 652共11兲
−0.000 003 7共52兲
148.78共16兲
−2.57共17兲
1.767 6
627
3.9
3.105
From fits not using ␥D.
a
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194304-7
J. Chem. Phys. 125, 194304 共2006兲
Pure rotational spectrum of ZnF
FIG. 4. A Morse potential for 64ZnF constructed from the equilibrium parameters derived in this study, shown by the solid black line in this figure.
The dissociation energy, DE, is indicated. Potential curves derived from
previous theoretical work are shown for comparison by the dotted line 共Ref.
24兲, dashed line 共Ref. 21兲, and dot-dashed line 共Ref. 28兲.
species ZnH, ZnCH3, ZnCN, and ZnF, the ratios are ␥ / B
⬇ 0.038, 0.038, 0.027, and 0.014, respectively.16,18,20 These
ratios deviate considerably, a likely result of second-order
spin-orbit coupling.
The second-order spin-orbit coupling for ZnF in its X
2 +
⌺ state probably primarily arises from interactions with the
A 2⌸ excited state. Based on theoretical calculations,28 the A
state potential well appears to closely resemble that of the
ground state, and, to some extent, it is the main perturber.
⌸
Therefore, ␥共2兲
⬇ p⌸
v , where pv is the lambda-doubling conv
共2兲
stant for the A state and ␥v is the second-order contribution
to ␥. If the pure precession approximation could also be invoked, then an estimate of the A state energy could be derived. However, pure precession implies that the unpaired
electron in the interacting 2⌺ and 2⌸ states resides in p␴ and
p␲ orbitals. The unpaired electron of ZnF is in the 10␴ orbital that is primarily 4s共Zn兲 in character. As will be discussed later, there is ⬃20% p␴ contribution to this orbital,
which gives the pure precession approximation some validity. Assuming pure precession, the second-order contribution
to the spin-rotation constant is given by
␥共2兲
v =
2AvBvleff共leff + 1兲
,
E⌸ − E⌺
共7兲
where Av is the spin-orbit constant of the perturbing ⌸ state,
Bv is the rotational constant for the ground state, and E are
their energies. Using the spin-orbit constant for Zn+
共583 cm−1兲,1 assuming leff = 0.20 for the p␴ contribution to
, the energy of the A 2⌸ state is
the 10␴ orbital and ␥exp ⬇ ␥共2兲
v
−1
approximately 20 400 cm . This value agrees qualitatively
with theoretical computations, which suggest that the A 2⌸
state lies 23 000– 37 000 cm−1 above the ground state.21,28
Previous experimental ESR matrix studies by Knight
et al. found bF共F兲 = 320共4兲 MHz and c共F兲 = 530共4兲 MHz,22 in
excellent agreement with the current work, where bF共F兲
= 321.4共3.1兲 MHz and c共F兲 = 554共17兲 MHz. In fact, the values of Knight et al. are within the experimental uncertainties
of two of the three isotopologues measured here. These results are evidence that the neon matrix used in the ESR study
did not affect the electronic structure of the polar ZnF molecule, contrary to the suggestion of Malkin et al.29
Several theoretical predictions exist for the hyperfine
constants for both the 19F and the 67Zn nuclei. Belanzoni
et al.26 calculated bF共Zn兲 = 1215 MHz and c共Zn兲 = 50 MHz,
while Malkin et al.29 suggested that bF共Zn兲 = 1294 MHz and
c共Zn兲 = 41 MHz. These values are close to the present results
of bF共Zn兲 = 1291.4共1.6兲 MHz and c共Zn兲 = 39.1共3.1兲 MHz.
However, the theoretical values for fluorine hyperfine interaction are less accurate. Belanzoni et al.,26 Quiney and
Belanzoni,27 and Malkin et al.29 all calculated bF共F兲 to be
between 231 and 244 MHz, whereas this term was found to
be 321.4共3.1兲 MHz. The c共F兲 results deviate even more:
636,27 836,26 and 861 MHz 共Ref. 29兲 versus the observed
554共17兲 MHz.
The hyperfine parameters can be used to determine molecular orbital composition and interpret bonding characteristics in ZnF.38,39 Zinc fluoride has a lone unpaired electron
in the 10␴ orbital. This orbital is probably formed from a
combination of 4s共Zn兲 + 4p␴共Zn兲 + 2s共F兲 + 2p␴共F兲 atomic orbitals, in analogy to ZnH.17 关The 3dz2共Zn兲 orbital also has ␴
symmetry but is filled and generally can be neglected as
nonbonding.兴 The amount of fluorine s-orbital character in
this molecular orbital can be determined by taking the ratio
of the molecular and atomic 19F Fermi contact parameters,
bF共molecule兲 / bF共atom兲, where bF共 19F兲 = 47 910 MHz.40 A
similar comparison can be done to determine the p character
in the 10␴ orbital looking at the molecular/atomic ratio of
the 19F dipolar term 关c共 19F兲 = 4545 MHz兴. These ratios indicate that the 10␴ orbital in ZnF is made of 0.7% 2s共F兲 and
12% 2p共F兲. This result is nearly identical with that of Knight
et al.22 and agrees with the calculation of Belanzoni et al., in
which the 10␴ orbital is 15% fluorine in composition.26
Similar calculations in principle can be carried out for
the 67Zn nucleus using hyperfine constants for the Zn+ cation. Such parameters, however, have only been measured in
a calcite matrix and may not be comparable to the gas phase.
If the calcite value of the Fermi contact constant is used
关bF共 67Zn+兲 = 1425.6 MHz兴,41 then the ratio suggests that the
10␴ orbital retains approximately 90% of its original 4s共Zn+兲
character. The value of c共 67Zn+兲 is subject to much more
uncertainty because it is small; in fact, the calcite value is
less than that of ZnF. To examine the contribution of the 4p
orbital, the atomic c constant was calculated using the
method of Goudsmit42,43 and was found to be c共 67Zn+兲
= 3aJ=3/2 ⬇ 500 MHz. This value implies that the 4p共Zn兲 orbital contributes approximately 8% to the 10␴ orbital. Belanzoni et al. calculated that the ZnF 10␴ orbital is 13%
4p共Zn兲.26 Overall, the hyperfine constants of ZnF suggest
that the 10␴ orbital is principally zinc 4s in character, with
about a 10%–20% contribution from other orbitals, primarily
2p共F兲 and 4p共Zn兲. However, estimates of this sort are only
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194304-8
J. Chem. Phys. 125, 194304 共2006兲
Flory, McLamarrah, and Ziurys
qualitative when a molecule is not either wholly ionic or
covalent.43 Harrison et al. have calculated partial charges of
+0.72 and −0.72 for Zn and F, respectively, in ZnF,28 indicating a mixture of ionic and covalent characters.
A further comparison can be made by calculating the
electron density at each nucleus in 67ZnF, where both 19F
and 67Zn Fermi contact terms were established. This parameter is defined as38
bF = 共2gsgN␮N␮B␮0/3h兲⌿2共0兲.
共8兲
Using this expression, the electron density at the Zn nucleus
is ⌿2共0兲 = 3.1⫻ 1031 m−3. In comparison, the density at the
fluorine nucleus is ⌿2共0兲 = 5.1⫻ 1029 m−3—almost two orders of magnitude less than that for zinc. Again, these calculations are consistent with the 10␴ orbital having primarily
4s共Zn兲 character. Therefore, the bond is principally ionic, but
with a partial covalent contribution from the fluorine 2p orbital. In contrast, for CaF, bF共F兲 = 123 MHz and c共F兲
= 33.3 MHz,44 such that only 0.26% of the ␴ orbital has
2s共F兲 character and the contribution from 2p共F兲 is 0.73%.
Hence, there is virtually no orbital overlap between the calcium and fluorine atoms. The hyperfine constants thus are
consistent with the suggestion that ZnF has more covalent
character than CaF, as originally proposed by Harrison
et al.28
The electric quadrupole coupling constant of 67Zn also
provides information about the bonding.45 The value of eqQ
is determined by the electric field gradient in the molecule
and can be broken into two parts: eqQ = 共eqQ兲el + 共eqQ兲pol,
where 共eqQ兲el arises from non-s character of the unpaired
electron and 共eqQ兲pol depends on the polarization of electrons in closed shells on the metal atom. The first term is
related to the magnetic hyperfine dipolar term c, such that
共eqQ兲el = −共ce2Q兲 / 共3gI␮B␮N兲, where e is the charge of an
electron, Q is the nuclear quadrupole moment, gI
is the nuclear g factor for 67Zn, and ␮B and ␮N
are the Bohr and nuclear magnetons.46 From this expression,
共eqQ兲el = −27 MHz, implying that 共eqQ兲pol = −33 MHz. The
polarization term arises from the repulsion by the F− ligand,
which would originate from a Zn+F−, or ionic, structure. The
nonzero 共eqQ兲el component implies some p character in the
␴ orbital, a covalent contribution. Therefore, the quadrupole
term implies a partly ionic, partly covalent bond.
VI. CONCLUSIONS
ZnF is the last 3d fluoride species to be studied by highresolution gas-phase spectroscopy. From this work, rotational, fine structure, and hyperfine constants have been determined for this radical. Evaluation of the hyperfine
parameters indicates that ZnF is an ionic species, but with
some covalent character; in contrast, CaF, which should have
a similar electronic structure, is almost entirely ionic. These
results support the notion that 3d metals have subtle differences in their bonding and electronic properties relative to
other 共nontransition兲 metals.
ACKNOWLEDGMENTS
The authors would like to thank Professor J. M. Brown
for use of his fitting code and M. A. Brewster for helpful
discussions. This work was supported by NSF Grant No.
CHE 04-11551.
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