Millimeter-wave spectroscopy of FeF ( X 6 D i ): Rotational analysis
and bonding study
M. D. Allen and L. M. Ziurysa)
Department of Chemistry, Arizona State University, P.O. Box 871604, Tempe, Arizona 85287-1604
~Received 29 July 1996; accepted 5 November 1996!
The pure rotational spectrum of the FeF radical in its 6Di ground electronic state has been recorded
using millimeter/submillimeter direct absorption techniques. Transitions arising from all six
spin-orbit components have been observed in the v 50, 1, and 2 vibrational levels of 56FeF, the main
isotopic species, and also in the less abundant 54Fe isotopomer. Hyperfine splittings, arising from the
19
F nuclear spin of I51/2, were resolved in the majority of transitions recorded, and
lambda-doubling interactions were observed in the V53/2, 1/2, and 21/2 spin-orbit ladders. The
complete data set has been analyzed using a 6D Hamiltonian, and rotational, spin-orbit, spin–spin,
lambda-doubling, and hyperfine constants determined. This study has conclusively demonstrated
that the ground electronic state of FeF is 6Di . It also suggests that FeF has more covalent character
to its bonding than alkaline earth or alkali metal counterparts. © 1997 American Institute of
Physics. @S0021-9606~97!01806-0#
I. INTRODUCTION
Iron plays a significant role in chemistry from many aspects. First of all, it is used widely as a catalyst for organic
synthesis, for example, in the reduction of aromatic nitro
compounds.1 Also, it functions as the chelating atom for
many transition metal complexes like iron pentacarbonyl and
sandwich compounds such as ferrocence, and consequently
is crucial for organometallic chemistry.1 Moreover, it is critical in biologically important molecules like heme, the iron
chelate of a substituted porphyrin, which functions as the
prosthetic group of hemoglobin, myglobin, and cytovchrome-b.2
Iron also plays a significant role in astrophysics, particularly in the origin of the elements. In stars, iron is the final
product of silicon burning and hence thermal fusion; production of elements heavier than iron requires explosive
nucleosynthesis.3 Astronomical studies of atomic iron, its
less abundant isotopes, and, more recently, Fe-bearing molecules, have impacted on the understanding of stellar evolution and the chemical composition of the interstellar medium.
Despite the frequent appearance of iron in chemistry,
most studies of this element have occurred in the bulk phase
or in coordination complexes.4 Very little is really known
about the bonding to individual iron atoms. Because this element is a 3d transition metal with 6d electrons, its reactivity is high, and how it forms simple molecules is of interest.
One method of investigating how iron bonds to other
atoms is by studying small Fe-containing species in the gas
phase using high resolution spectroscopy. Unfortunately,
very few small iron-bearing molecules have actually been
studied using this approach. To date, the list of species is
limited to FeO, FeH, FeCl, FeCO, and, very recently, FeC.
FeO has been a subject of many optical spectroscopic invesa!
Current address: Depts. of Chemistry and Astronomy, Steward Observatory, University of Arizona, Tucson, AZ 85721.
3494
J. Chem. Phys. 106 (9), 1 March 1997
tigations by Merer and co-workers,5–8 as well as microwave
~MODR!9,10 and millimeter-wave studies.11,12 Various electronic and rotational transitions of FeH have been recorded
in recent years,13–15 a pure rotational study has been done for
FeCO,16 and both optical,17 and millimeter18,19 measurements have been carried out for FeCl. In the past year, FeC
has been observed optically via its 3D– 3D band by Balfour
et al.20 and the pure rotational spectrum of this elusive radical has been recorded as well by this group.21 These species
all have been found to have high spin electronic ground
states, resulting in complicated spectra sometimes confused
by perturbations from nearby excited states. For example, in
FeC, Balfour et al.20 suggest there is mixing of the V52
spin-orbit component in the X 3 D i state with a 1Di state,
lowering its energy significantly.
In this paper we present a study of the pure rotational
spectrum of the FeF radical, using millimeter/submillimeter
direct absorption techniques. Prior to our measurements, FeF
had been observed only optically by Pouilly et al.,22 who
recorded several electronic systems in the 2000–3500 Å region. In conjunction with theoretical calculations,23 these authors suggested that the ground electronic state of FeF is 6Di ,
and determined effective rotational constants for the V59/2,
7/2, and 21/2 ladders. Ram et al.24 have very recently recorded the g 4 D – a 4 D system of FeF as well. In this work,
11 rotational transitions for each of the six spin-orbit components of FeF have been measured, confirming that the
ground state of this radical is indeed 6Di . We are certain of
this assignment because over 45 GHz in frequency was continuously searched, and the 6Di features were by far the
strongest lines observed. ~We have never observed excited
electronic states in our system, and usually have seen only
two or three quanta of excited vibrational modes.! Ten transitions for the 54Fe isotopomer have also been recorded ~four
include all six V ladders!, as well as four transitions for both
the v 51 and v 52 excited states, respectively, in all six sublevels. Lamba-type doubling was observed in the V521/2,
0021-9606/97/106(9)/3494/10/$10.00
© 1997 American Institute of Physics
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M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
3495
1/2, and 3/2 spin-orbit components, while hyperfine interactions, arising from the fluorine nuclear spin, were resolved in
all spin-orbit sublevels. These data were analyzed successfully with a 6D effective Hamiltonian, and rotational, fine
structure, L-doubling, and hyperfine parameters determined
for both iron isotopomers and the two vibrationally excited
levels. The transition frequencies for 56FeF in the v 50 level
have been published previously in the astronomical literature.25 In this paper, we present an analysis of the complete
data set and discuss its chemical significance.
II. EXPERIMENT
The spectra of FeF were recorded using one of the
millimeter/submillimeter direct absorption spectrometers at
A.S.U., which utilizes offset ellipsoidal mirrors as focusing
elements.26 This instrument consists of a frequency-stable
source of millimeter-wave radiation, a reaction cell which
can accommodate three Broida-type ovens, and a heliumcooled InSb detector. The source consists of phase-locked
Gunn oscillators, which operate in the range 65–140 GHz;
higher frequencies ~120–530 GHz! are obtained by using
Schottky diode multipliers. The radiation from the source is
launched from a scalar feedhorn/teflon lens combination and
is directed through the reaction chamber quasioptically using
two offset ellipsoidal mirrors made of polished aluminum.
The radiation passes into the cell through a foam-backed
mylar window. The reaction cell is a double-pass system
with a rooftop reflector affixed to one end, which returns the
incoming beam through the cell as well as rotates its polarization by 90°. After its second pass through the mirrors, the
beam is reflected by a wire grid through another lens and into
the detector. FM modulation of the radiation source at a rate
of 25 kHz is employed for phase-sensitive detection. The
detected signals are processed by a lock-in amplifier and recorded by a 486 PC computer.
Iron monofluoride was synthesized by mixing iron vapor
with F2 gas. The metal vapor was produced using one hightemperature Broida-type oven that operates near 1400 °C.
Unlike the ones used in our previous experiments,27,28 this
oven does not contain a cooling jacket around the melting
chamber, which is also heavily lined with Zirconia insulation. The iron vapor was entrained in 10–20 mTorr of helium
carrier gas, which was added through the bottom of the oven.
The Fe/He mixture was then reacted with no more than 1
mTorr of fluorine gas. The reaction mixture glowed a bright
blue when F2 was added.
The spectra were recorded by taking scans increasing
and decreasing in frequency and averaging them. Typically,
scans 5 MHz in frequency coverage were used. To determine
center frequencies, the lines were fit with Gaussian profiles.
Linewidths were on the order of 500–800 kHz over the 120–
400 GHz range used in this study and the average experimental accuracy for transition frequencies is estimated to be
6100 kHz. The 56 and 54 iron isotopomers of FeF were
observed in their natural abundances ~56Fe: 54Fe591.7%:
5.8%!.
FIG. 1. Plot showing the progression of L-doubling splitting versus J in the
V521/2, 1/2, and 3/2 ladders.
III. RESULTS
Eleven transitions ~J513/2←11/2 to 33/2←31/2! were
recorded for the main iron isotopomer ~56FeF! in all six spinorbit components in the frequency range 147–374 GHz in
the v 50 level. An additional transition was also measured
near 121–122 GHz for the two lowest sublevels, V59/2 and
7/2. The actual frequencies for the v 50 level are published
elsewhere.25 To summarize, a total of 188 separate lines
were recorded for 56FeF. Hyperfine structure, arising from
the 19F spin of I51/2 and indicated by quantum number F,
was observed in all six components for the majority of the
transitions measured. This interaction, which ranged in magnitude from less than 1 MHz at high quantum number J to as
large as 50 MHz for low J lines, split individual transitions
into doublets. @As in all case ~a! molecules, the rotational
quantum number is J.# The hf components merged together
to a single feature for the V51/2 and 3/2 ladders at sufficiently high J, but not for the other sublevels. The splitting
collapses completely only in these two ladders because its
magnitude is proportional to V3S. Lambda-doubling, on the
other hand, was only observed in the V521/2, 1/2, and 3/2
components. This interaction was found to be largest in the
V51/2 ladder, and smallest for the V53/2 component. A
plot of the lambda-doubling splitting versus J is shown in
Fig. 1 for these three sublevels.
The data for 54FeF are listed in Table I. As the table
illustrates, four transitions were recorded for all six spinorbit components in the range 301–378 GHz, and an additional seven for only the V53/2, 5/2, 7/2, and 9/2 sublevels,
in the region 147–284 GHz. For this isotopomer, a total of
129 separate lines were measured. The pattern of the 54FeF
J. Chem. Phys., Vol. 106, No. 9, 1 March 1997
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3496
M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
TABLE I. Observed transition frequencies of FeF: X 6 D i ~MHz!.
FeF ~v 51!
FeF ~v 52!
56
J 8 ←J
V
F 8 ←F
13/2←11/2
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
1.5
1.5
1.5
1.5
7←6a
6←5a
7←6b
6←5b
7←6
6←5
7←6
6←5
7←6
6←5
8←7b
7←6b
8←7a
7←6a
8←7
7←6
8←7
7←6
8←7
7←6
9←8a
8←7a
9←8b
8←7b
9←8
8←7
9←8
8←7
9←8
8←7
10←9b
9←8b
10←9a
9←8a
10←9
9←8
10←9
9←8
10←9
9←8
11←10a
10←9a
11←10b
10←9b
11←10
10←9
11←10
10←9
11←10
10←9
12←11b
11←10b
12←11a
11←10a
12←11
11←10
12←11
11←10
12←11
11←10
13←12a
12←11a
13←12b
12←11b
15/2←13/2
17/2←15/2
19/2←17/2
21/2←19/2
23/2←21/2
25/2←23/2
nobs
no2c
FeF ~v 50!
56
nobs
no2c
54
nobs
no2c
147 247.917
147 245.823
147 246.654
147 244.610
146 502.425
146 506.045
145 780.205
145 795.673
145 073.602
145 106.722
169 894.906
169 893.327i!
169 893.327i!
169 891.773
169 035.877
169 038.530
168 204.831
168 216.185
167 392.578
167 417.085
192 539.404
192 538.287
192 537.287
192 536.209
191 566.635
191 568.663
190 626.360
190 635.126
189 708.172
189 726.995
215 180.930
215 179.972
215 178.284
215 177.329
214 094.423
214 095.994
213 044.855
213 051.701
212 020.390
212 035.208
237 819.077
237 818.340
237 815.838
237 815.060
236 618.898
236 620.161
235 460.058
235 465.495
234 329.165
234 341.070
260 453.394ii!
260 452.954ii!
260 449.634ii!
260 449.194ii!
259 139.714
259 140.846
257 871.597
257 876.041
256 634.349
256 644.096
283 083.896ii!
283 083.546ii!
283 079.260ii!
283 078.910ii!
0.034
0.019
0.005
0.041
0.019
20.041
20.026
0.007
20.026
0.008
20.006
20.074
0.057
0.016
0.002
20.040
0.038
0.011
20.058
20.025
0.040
0.059
0.030
0.089
20.020
20.036
20.024
0.042
20.031
0.016
0.076
20.008
0.057
20.022
20.029
20.048
20.013
0.001
20.027
20.017
0.067
0.014
0.030
20.063
20.051
20.049
0.035
20.008
20.028
20.056
20.073
0.030
20.002
0.102
20.106
0.011
0.012
20.012
20.002
20.038
0.036
0.120
20.087
20.002
J. Chem. Phys., Vol. 106, No. 9, 1 March 1997
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M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
3497
TABLE I. ~Continued.!
FeF ~v 51!
FeF ~v 52!
56
J 8 ←J
27/2←25/2
29/2←27/2
31/2←29/2
33/2←31/2
V
F 8 ←F
2.5
2.5
3.5
3.5
4.5
4.5
20.5
20.5
20.5
20.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
20.5
20.5
20.5
20.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
20.5
20.5
20.5
20.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
20.5
20.5
20.5
20.5
13←12
12←11
13←12
12←11
13←12
12←11
14←13b
13←12b
14←13a
13←12a
14←13a
13←12a
14←13b
13←12b
14←13b
13←12b
14←13a
13←12a
14←13
13←12
14←13
13←12
14←13
13←12
15←14a
14←13a
15←14b
14←13b
15←14b
14←13b
15←14a
14←13a
15←14a
14←13a
15←14b
14←13b
15←14
14←13
15←14
14←13
15←14
14←13
16←15b
15←14b
16←15a
15←14a
16←15a
15←14a
16←15b
15←14b
16←15b
15←14b
16←15a
15←14a
16←15
15←14
16←15
15←14
16←15
15←14
17←16a
16←15a
17←16b
16←15b
nobs
303 714.883
303 716.507
303 815.102
303 816.715
302 077.085ii!
302 076.925ii!
302 235.497ii!
302 235.337ii!
300 613.141ii!
300 612.941ii!
300 607.906ii!
300 607.706ii!
299 122.926ii!
299 123.441ii!
297 682.894
297 685.949
296 275.324
296 282.125
326 190.562
326 192.196
326 290.152
326 291.786
324 434.898i!
324 434.898i!
324 591.922i!
324 591.922i!
322 857.146i!
322 857.146i!
322 851.110i!
322 851.110i!
321 257.662ii!
321 257.862ii!
319 711.881
319 714.475
318 201.271
318 207.018
348 660.476
348 662.152
348 759.473
348 761.119
346 787.516i!
346 787.516i!
346 943.128i!
346 943.128i!
345 096.267i!
345 096.267i!
345 089.395i!
345 089.395i!
343 387.287ii!
343 387.437ii!
341 736.208
341 738.343
340 122.613
340 127.545
371 124.605
371 126.278
371 222.903
371 224.541
FeF ~v 50!
56
no2c
0.033
20.112
0.021
20.133
0.068
20.099
0.078
20.085
20.016
0.137
20.019
0.136
0.015
20.134
0.030
0.051
20.053
0.014
0.092
0.073
0.066
0.049
0.025
20.050
0.003
20.068
20.133
0.152
20.156
0.131
0.160
20.190
0.009
0.045
20.033
20.006
20.077
0.042
20.039
0.051
0.036
20.094
0.047
20.079
20.092
0.138
20.119
0.113
0.076
20.231
0.059
0.022
20.016
0.019
20.113
0.081
20.078
0.083
nobs
301 415.822
301 417.546
301 520.470
301 522.198
299 803.510ii!
299 803.350ii!
299 967.171ii!
299 967.011ii!
298 366.511ii!
298 366.311ii!
298 361.115ii!
298 360.915ii!
296 898.314ii!
296 898.797ii!
295 477.836
295 480.894
294 086.028
294 092.742
323 721.326
323 723.027
323 825.357
323 827.059
321 993.144i!
321 993.144i!
322 155.465i!
322 155.465i!
320 444.093i!
320 444.093i!
320 437.859i!
320 437.859i!
318 868.311ii!
318 868.511ii!
317 343.528
317 346.068
315 849.773
315 855.522
346 021.358
346 022.972
346 124.723
346 126.329
344 177.624i!
344 177.624i!
344 338.411i!
344 338.411i!
342 516.797i!
342 516.797i!
342 509.721i!
342 509.721i!
340 833.161ii!
340 833.311ii!
339 204.418
339 206.542
337 608.930
337 613.842
368 315.444
368 317.086
368 418.096
368 419.752
54
no2c
nobs
no2c
0.031
20.040
0.024
20.040
0.073
20.101
0.068
20.103
0.012
0.172
0.017
0.178
20.054
20.219
0.016
0.063
20.066
20.056
20.017
0.007
20.016
0.011
0.029
20.054
0.056
20.023
20.124
0.166
20.150
0.142
0.144
20.191
0.061
0.065
20.048
0.009
20.013
0.020
20.012
0.015
0.071
20.067
0.027
20.107
20.098
0.136
20.108
0.128
0.078
20.215
0.040
0.013
20.011
0.031
20.051
0.088
20.056
0.099
281 656.604
281 657.526
280 279.291
280 282.952
278 935.673
278 943.704
308 924.103
308 925.929
309 022.655
309 024.455
307 229.482ii!
307 229.332ii!
307 384.157ii!
307 384.007ii!
305 709.703ii!
305 709.503ii!
305 704.506ii!
305 704.306ii!
304 169.318ii!
304 169.900ii!
302 682.790
302 685.881
301 232.876
301 239.723
331 784.961
331 786.619
331 882.764
331 884.432
329 968.268i!
329 968.268i!
330 121.596i!
330 121.596i!
328 330.978i!
328 330.978i!
328 324.850i!
328 324.850i!
326 677.506ii!
326 677.906ii!
325 081.794
325 084.361
323 525.725
323 531.463
354 639.985
354 641.615
354 737.208
354 738.834
352 701.702i!
352 701.702i!
352 853.667i!
352 853.667i!
350 946.963i!
350 946.963i!
350 940.063i!
350 940.063i!
349 180.371ii!
349 180.621ii!
347 476.065
347 478.178
345 813.812
345 818.831
377 489.140
377 490.792
377 585.547
377 587.228
20.129
20.033
0.026
20.005
0.011
20.090
0.026
0.021
0.109
0.079
0.096
20.081
20.085
20.088
20.125
0.023
20.077
0.073
20.032
20.129
0.028
0.037
0.011
0.020
0.060
0.005
0.013
20.030
0.043
20.053
0.029
20.063
20.035
0.246
20.135
0.147
0.171
0.010
0.032
0.003
0.045
20.021
20.074
20.061
20.039
20.028
0.001
20.151
0.056
20.092
20.091
0.134
20.131
0.096
0.023
20.192
0.116
0.027
20.006
0.048
20.021
0.094
20.101
0.045
J. Chem. Phys., Vol. 106, No. 9, 1 March 1997
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3498
M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
TABLE I. ~Continued.!
FeF ~v 51!
FeF ~v 52!
56
J 8 ←J
V
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
4.5
F 8 ←F
17←16b
16←15b
17←16a
16←15a
17←16a
16←15a
17←16b
16←15b
17←16
16←15
17←16
16←15
17←16
16←15
nobs
no2c
i!
369 134.554
369 134.554i!
369 288.618i!
369 288.618i!
367 329.988i!
367 329.988i!
367 322.304i!
367 322.304i!
365 511.747ii!
365 511.847ii!
363 755.431
363 757.232
362 039.054
362 043.296
FeF ~v 50!
56
0.083
20.092
0.078
20.094
20.057
0.128
20.016
0.171
0.042
20.238
0.051
20.002
20.004
0.018
54
nobs
no2c
i!
366 356.424
366 356.424i!
366 515.719i!
366 515.719i!
364 584.124i!
364 584.124i!
364 576.173i!
364 576.173i!
362 792.810ii!
362 792.910ii!
361 060.292
361 062.097
359 363.169
359 367.395
0.042
20.143
0.056
20.124
20.058
0.130
20.036
0.154
0.030
20.237
0.055
0.026
0.011
0.042
nobs
no2c
i!
375 429.527
375 429.527i!
375 579.881i!
375 579.881i!
373 557.493i!
373 557.493i!
373 549.879i!
373 549.879i!
371 678.043ii!
371 678.243ii!
369 865.045
369 866.918
368 097.024
368 101.276
0.087
20.111
0.049
20.145
20.099
0.080
0.026
0.207
20.005
20.191
0.042
0.038
0.044
0.021
i!
Blended lines, not deconvolved.
Blended lines, partially deconvolved.
ii!
spectra closely resembles that of 56FeF. First of all, the majority of transitions are split into doublets due to fluorine hf
interactions, which collapse to a single line at high J for the
V51/2 and 3/2 ladders. Lambda-doubling is observed for
54
FeF in the V521/2, 1/2, and 3/2 sublevels and has nearly
the same magnitude and behavior as for 56FeF ~see Fig. 1!.
For the v 51 and v 52 vibrational levels, four separate
rotational transitions in all six sublevels were recorded, a
total of 60 separate lines per state, respectively. The details
of these data are also given in Table I. The hyperfine splittings are very similar in magnitude to what was found for the
v 50 level of 56FeF. The lambda-doubling interactions in the
v 51 and v 52 transitions behave like those for the v 50 lines
but are somewhat larger ~a difference of 5–10 MHz!. The
differences in lambda-doubling interactions with quantum
number v suggest that the potential curves of the ground and
perturbing excited state are fairly different.
Spectra which illustrate some of these effects just described are given in Figs. 2–4. In Fig. 2, the J531/2←29/2
transition near 340–346 GHz in the lowest spin-orbit ladder
~V59/2! of 56FeF ~both v 50 and v 51! and 54FeF is shown.
As the figure illustrates, because of the effects of the fluorine
nuclear spin, each transition is split into doublets which are
labeled by quantum number F, where F̂5Ĵ1Î. The hf splitting does not vary much between v 50, v 51, and 54FeF data.
Figures 3 and 4 illustrate the lambda-doubling interactions in various spin-orbit components. Figure 3 presents the
J529/2←27/2 transition of 56FeF near 329 GHz in the V
521/2 sublevel. The larger splitting ~on the order of 100
MHz! results from L-doubling, while the smaller doublet
structure is again due to hyperfine interactions. The lambdadoubling is significantly smaller in the V53/2 level, as displayed in Fig. 4. Here three successive transitions of 56FeF
are shown: J513/2←11/2 ~bottom panel!, J515/2←13/2
~middle!, and J517/2←15/2 ~top panel!. The L-doubling in
the top figure, indicated by parity assignments a and b, separates the two sets of hyperfine doublets. The lambdadoubling interactions decrease, however, in the next lower
transition ~J515/2←13/2! such that two of the four hf components are blended. At J513/2←11/2, the doubling is collapsed further and the hyperfine lines in the two parity levels
are interspersed.
In Fig. 5, an overview of the spectra recorded for an
individual transition of FeF ~in this case J533/2←31/2! is
given in the form of a stick figure. Approximate relative
intensities are illustrated by the heights of the sticks. The
excited vibrational states are lower in frequency relative to
v 50, and the 54FeF lines are higher. The strongest transitions
are for v 50 of 56FeF, as expected. Lambda-doubling is
shown for the V51/2 and 21/2 components. ~The hyperfine
splitting is small so it was neglected.! A regular progression
is apparent in the spin-orbit ladders for all three levels of
56
FeF, as well as for the 54Fe isotopomer. Also, the intensities decrease as a function of V level in a uniform way.
There was no obvious deviation from this pattern in any of
the transitions studied.
IV. DATA ANALYSIS
A nonlinear least-squares analysis of the FeF data was
done using a 6D Hamiltonian of Brown et al.29,30 The v 50,
1, and 2 levels of 56FeF and the 54FeF spectra were fit as
separate data sets. Each of these sets was modeled using the
following effective Hamiltonian:
1!
2!
H eff5H rot1H cd1H ~so1 ! 1H ~socd
1H ~so3 ! 1H ~ss2 ! 1H ~sscd
4!
1H ~ss4 ! 1H ~sscd
1H ld1H hf .
~1!
H rot and H cd describe the rotation of the molecule and its
centrifugal distortion correction, characterized by parameters
~1!
~3!
B and D. The terms H ~1!
so , H socd , and H so represent the first
order spin-orbit interaction, its centrifugal distortion correction, and the third rank contribution, which are described by
the constants A, A D , and h, respectively. The spin–spin part
of the Hamiltonian concerns second and fourth rank terms
~4!
H ~2!
ss and H ss , with associated constants l and u, and their
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M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
3499
H rot1H cd5B @ J ~ J11 ! 2V 2 1S ~ S11 ! 2S 2 #
2D ~ J2L2S! 4 ,
~2!
1!
5AL z S z 1 ~ 1/2! A D @~ J2L2S! 2 L z S z
H ~so1 ! 1H ~socd
1L z S z ~ J2L2S! 2 # ,
H ~so3 ! 5 h L z S z @ S 2z 2 ~ 3S2 21 ! /5# ,
~3!
~4!
2!
H ~ss2 ! 1H ~sscd
1H ~ss4 ! 5 ~ 2/3! l ~ 3S 2z 2S2 ! 1 ~ 1/3! l D @~ J2L
2S! 2 ~ 3S 2z 2S2 ! 1 ~ 3S 2z 2S2 !~ J2L
2S! 2 # 1 ~ 1/12! u ~ 35S 4z 230S2 S 2z
125S 2z 26S2 13S4 ! .
~5!
As Eq. ~4! shows, h describes the coupling between the spinorbit and spin–spin interactions. The H ~4!
sscd term, not shown
above, concerns the fourth rank spin–spin term uD that has
been used only once before to fit the five spin-orbit components of FeO.12 Its matrix elements can be constructed by
matrix multiplication ~where N5J2S!12
4!
H ~sscd
5 ~ u D /2!@ $ H ~ss4 ! / u % , N2 # 1 .
~6!
The expressions for lambda-doubling are more complicated and can be found in Brown et al.30 The important point
to note is that of the five possible constants, only ñ D and p̃ D
appear in the diagonal elements of the L-doubling Hamiltonian matrix, for the V51/2 and 3/2 sublevels, respectively.
For the V521/2 spin-orbit component, all five lambdadoubling parameters appear as off-diagonal terms. Because
m̃ D .ñ D .õ D . p̃ D .q̃ D , and each term scales approximately
by A/B with respect to one another, the lambda-doubling
should be largest in the V51/2 ladder, followed by V
521/2, and then V53/2, as has been found.
The following equation describes the hyperfine Hamiltonian:34
FIG. 2. Spectra of the J531/2←29/2 transition in the V59/2 spin-orbit
component of 56FeF in its v 50 and v 51 levels and 54FeF observed in this
work near 340–346 GHz. Each transition is split into doublets, labeled by
quantum number F, because of fluorine hyperfine interactions. Each spectra
covers 50 MHz in frequency and was taken in one 30 s scan.
centrifugal distortion corrections (l D , u D ). Finally, the last
two terms describe lambda-doubling ~H ld! and magnetic hyperfine ~H hf! interactions. The lambda-doubling constants
used are those described by Brown et al.30 for a case ~a!
basis (m̃ D ,ñ D ,õ D ,p̃ D ,q̃ D ) as opposed to those defined by
Mulliken and Christy.31 The hyperfine interactions are defined by the Frosh and Foley32 constants ~a, b, c, and d!. As
with most case ~a! molecules, the spin-rotation term of the
Hamiltonian, H sr , was not found necessary to model the energy levels.
The H rot , H so , and H ss terms of the Hamiltonian can be
expressed as:30,33
H hf5aL z I z 1bI–S1cI z S z 21/2d D ~ J 21 I 1 S 1 1J 22 S 2 I 2 ! .
~7!
The Frosch and Foley b and c constants are related to the
Fermi contact term b F , which describes the electron density
at the nucleus which has the spin. The d D parameter accounts
for differences in the hyperfine splittings between lambdadoubling pairs for D states.34 Such differences were not observed in the FeF data, so this term was not used.
The 56FeF ~v 50! data were fit by first allowing all the
constants to vary. These include the rotational ~B and D!,
lambda-doubling (m̃ D ,ñ D ,õ D ,p̃ D ), and hf (a,b,c) constants, as well as A, l, lD , uD , and h. ~The term u was found
not to affect the analysis, so it was set to zero. Also, the q̃ D
constant, which is very small, could not be determined because lambda-doubling was not seen in the lower spin-orbit
components.! This fit gave reasonable results, except the error in l was found to be an order of magnitude larger than its
value ~;2 GHz!. The error in hyperfine constant a was also
larger than the predicted number. Hence, in the final iteration, l and a were fixed to the values obtained in the first
step of this sequence, and all other parameters allowed to
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3500
M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
FIG. 3. Spectrum of the J529/2←27/2 transition in the V521/2 spin-orbit component of FeF observed near 329 GHz. The larger splitting in this spectrum
arises from lambda-doubling; the two sets of lambda doublets are labeled by a and b, respectively. The smaller splitting is due to 19F hyperfine interactions.
This scan covers 110 MHz in frequency and was recorded in one 60 s scan.
float. For 54FeF and v 51 and 2 levels of 56FeF, the analysis
was simpler. In all three data sets, l and A were fixed in the
first iteration to that established from 56FeF. All other parameters were allowed to vary. The error on hf constant a again
was very large in these fits, so in the final iteration its value
was fixed as well.
Finally, from the v 50, 1, and 2 data, B e , ae , and ge
were derived from the following equation:
B5B e 2 a e ~ v 11/2! 1 g e ~ v 11/2! 2 .
~8!
The second order ro-vibrational correction term ge was
needed to fit the three vibrational levels.
The spectroscopic parameters determined in this manner
are listed in Table II. Despite the number of constants involved, there are several results which lend some confidence
to the data analysis. The rotational constant and spin-orbit
constant A for 56FeF are in good agreement with those of
Pouilly et al.,22 which are also listed in Table II. Also, the
lambda-doubling parameters, determined freely in the fit,
scale in magnitude with respect to one another, as predicted
from the ratio A/B, and have the expected signs, following
the relation34
q̃ D ;48B 4 / ~ E D 2E P ! 2 ~ E D 2E S ! .
~9!
The constants in Table II also reproduce the observed frequencies with the following residuals ~nobs2ncalc! for unblended lines: FeF ~v 50!: &129 kHz; FeF~v 51!: &133
kHz; FeF ~v 52!: &99 kHz; 54FeF: &130 kHz. Although
some of the residuals are a little larger than the estimated
experimental uncertainty of 6100 kHz, the majority are
clearly within this range. The rms of the data fits are 59 kHz
for FeF ~v 50!, 93 kHz for the v 51 and v 52 data, and 71
kHz for the 54FeF. These rms values include use of the
blended features in the fits, which naturally increases the
error.
V. DISCUSSION
One of the results of this study is that these data confirm
that the ground electronic state of FeF is 6Di . All six spinorbit ladders have been observed in both the iron 56 and 54
isotopomers and two excited vibrational levels and those
sublevels expected to have the largest lambda-doubling ~V
51/2,21/2! exhibit the weakest signals. Hence, they must lie
highest in energy, evidence of an inverted multiplet. The
electron configuration for FeF in its ground state consequently is 8s23p49s4p21d310s, as suggested by Pouilly
et al.23
Another significant aspect of this study is that the complete FeF data set ~over 430 individual data points! could be
analyzed successfully with an effective Hamiltonian. Hence,
the effective parameters have been chosen appropriately.
This is the first time that a molecule with a 6Di electronic
ground state has been investigated at high spectral resolution
in all spin-orbit components simultaneously. A similar rotational analysis has been very recently carried out for all five
sublevels of the X 5 D i state FeO by Allen et al.12 with considerable success, using the same Hamiltonian of Brown
et al.29,30 This study did not involve as large a data set and
did not deal with hyperfine interactions, however.
According to the ab initio SCF-CI calculations of
Pouilly et al.,23 the nearest lying excited states of FeF are 6P
and 6S1 terms. These two states should consequently play a
major role in the lambda-doubling of the ground state.
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M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
3501
FIG. 5. A stick figure showing the spectral features observed and their
approximate intensities in the J533/2←31/2 transition of FeF. The six spinorbit components of the 56FeF ~v 50! lines, labeled by quantum number V,
are the strongest features. The components of the v 51 and v 52 vibrational
levels of 56FeF are also indicated, as well 54FeF lines. The spin-orbit components for 56FeF, its v 51 and 2 levels, and 54FeF follow a regular pattern.
FIG. 4. Spectra of three successive transitions of FeF in the V53/2 ladder:
J513/2←11/2 ~bottom!, 15/2←13/2 ~middle!, and 17/2←15/2 ~top!. These
transitions are split into four lines by lambda-doubling ~labeled by a or b!
and hyperfine interactions. In the top spectrum, the hf components of the
two L-doublets are separated from each other; in the middle spectrum, the
L-doubling splitting has decreased such that two hf components are
blended. In the bottom figure, the L-doubling splitting is even smaller, causing the hf components of each doublet to be interspersed. Each of these
spectra covers 10 MHz in frequency and consists of an average of four 30 s
scans.
Pouilly et al. predict that the two states lie close in energy
with respect to one another, with T e ~6P!;4500 cm21 and
T e ~6S1!;6420 cm21. These energies can be estimated from
the L-doubling interactions using Eq. ~9!, and scaling q̃ D
from the p̃ D parameter determined in the data analysis. It also
must be assumed that E S ;E P , but this appears to be valid
considering the Pouilly et al. work. Calculating q̃ D to be
;20.000 82 kHz, Eq. ~9! implies that E P ;E S ;3244 cm21,
close to those derived by Pouilly et al.
The alkali and alkaline earth monofluoride species are
thought to be highly ionic.35 Pouilly et al.23 predict in their
calculations that FeF will be somewhere intermediate between having ionic and covalent bonding. They suggest that
about 65% of the structure is ionic ~Fe1F2!, and approximately 35% is covalent ~Fe0F0!. Some of the structure and
electronic parameters derived here suggest that Pouilly et al.
are correct.
The equilibrium bond length r e has been calculated for
FeF and is listed in Table III along with r e values for various
alkali and alkaline earth monofluorides. All of these quantities have been derived from high resolution microwave36,37
and/or millimeter-wave spectroscopy38–41 and hence are
highly accurate. As the table suggests, the bond lengths of
the alkaline earth group, sodium, and aluminum fluorides
scale roughly as the atomic radii, which are r Mg51.6 Å,
r Ca51.97 Å, r Sr52.15 Å, r Ba52.22 Å, r Na51.90 Å, and
r Al51.43 Å, respectively.42 For example, the sodium and
calcium radii are very close in value, and so are the NaF and
CaF bond lengths; aluminum has the smallest radius ~1.43 Å!
of the group, and AlF the shortest bond distance. Such a
trend might be expected of ionic compounds of the general
formula M1F2. FeF, on the other hand, does not fit in this
pattern. It has r e 51.7803 Å, slightly larger than that of MgF
~1.7499 Å!, although its atomic radius is 1.26 Å.42 If the
bond distance scaled as the atomic radii for FeF, it is more
likely to have a bond length near ;1.5 Å, the shortest of all
the fluorides. The deviation from the trends of the other, very
ionic metal fluorides suggests that FeF may indeed have
more covalent character.
The 19F hyperfine constants of FeF and other metal
monofluorides are presented in Table IV. In the ionic picture
of these monofluorides, unpaired electrons reside primarily
near the metal as opposed to the fluorine nucleus. Therefore,
for BaF, the most ionic of the alkaline earth series, both
fluorine hf constants b and c are quite small. The b and c
values steadily increase from SrF to CaF, and are largest for
MgF, where b5154.7 MHz and c5178.5 MHz. MgF is the
only species in the alkaline earth series where c, the dipolar
anisotropic term, is larger than b. The hyperfine constant b F ,
the Fermi contact term, is a measure of the electron density
at the nucleus and is equal to b1c/3. The fact that c is larger
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3502
M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
TABLE II. Molecular constants for FeF (X 6 D i ).a
Previous workc!
This work
56
Parameter
FeF
11 239.418 ~12!
83.763 ~20!
0.2098 ~74!
----------------
Be
ae
ge
A
AD
h
l
lD
uD
B
D
p̃ D
õ D
ñ D
m̃ D
a
b
c
56
FeF ~v 50!
---22 342 900 ~8400!
21.759 ~94!
331.1 ~3.0!
2000b!
0.134 83 ~90!
20.002 893 ~53!
11 197.5884 ~16!
0.014 3801 ~40!
0.000 186 ~93!
20.0194 ~22!
2.5307 ~54!
2175.60 ~60!
20.45b!
74.5 ~3.5!
51.7 ~3.5!
FeF ~v 51!
56
---22 342 900b!
21.741 67 ~39!
355.8 ~3.0!
2000b!
0.119 03 ~26!
20.003 14 ~12!
11 114.2447 ~86!
0.014 370 ~18!
0.000 21 ~51!
20.020 ~12!
2.629 ~42!
2181.80 ~27!
21.16b!
76 ~10!
48 ~11!
FeF ~v 52!
56
---22 342 900b!
21.725 14 ~39!
401.0 ~3.1!
2000b!
0.103 15 ~26!
20.003 36 ~12!
11 031.3207 ~87!
0.014 366 ~18!
0.000 28 ~51!
20.020 ~12!
2.666 ~42!
2191.03 ~27!
21.74b!
78 ~10!
47 ~11!
FeF ~v 50!
54
---22 342 900b!
21.790 51 ~26!
330.8 ~1.8!
2000b!
0.13 658 ~15!
20.002 930 ~74!
11 302.3737 ~27!
0.014 651 9 ~62!
0.000 28 ~37!
20.0176 ~87!
2.543 ~31!
2175.80 ~19!
20.88b!
78.6 ~6.5!
48.0 ~6.6!
56
FeF
11 244 ~24!d!
84.6 ~1.2!d!
;22 278 000e!
-----11 172 ~33!f!
0.014 ~3!g!
--------
Errors quoted are 3s and apply to the last quoted digits.
Fixed to this value in the fit.
c
From Ref. 22.
d
Estimated from average of values for V59/2 and 21/2 ladders only.
e
Originally quoted as 7666 cm21.
f
Estimated from average of B values for V59/2, 7/2, and 21/2 ladders ~v 50!.
g
For V59/2 ladder only ~v 50!.
a
b
TABLE III. Bond lengths of metal fluorides.
Molecule
r e ~Å!
Reference
Di
S
1
S
2
S
2
S
2
S
2
S
1.7803
1.9260
1.6544
1.7499
1.9516
2.0744
2.1592
This work
36
37
38
39
40
41
6
FeF
NaF
AlF
MgF
CaF
SrF
BaF
TABLE IV.
Ground State
1
19
F Hyperfine constants for metal fluorides.
Molecule
b ~MHz!
c ~MHz!
Reference
MgF
CaF
SrF
BaF
FeFa!
154.7 ~1.4!
107.7687 ~6!
97.6670 ~30!
60 ~6!
74.5 ~3.5!
178.5 ~3.0!
41.175 ~3!
29.846 ~24!
8
51.7 ~3.5!
38
39
40
41
This work
a
Hyperfine constant a fixed to 20.45 MHz.
TABLE V. Bond lengths in diatomic iron species.
Molecule
FeH
FeC
FeO
FeF
FeCl
Ground state
r 0 ~Å!
Reference
Di
Di
5
Di
6
Di
6
Di
1.787
1.593
1.619
1.784
2.176
15
21
12
This work
19
4
3
than b and comparable to b F ~214.2 MHz for MgF! suggests
that the unpaired electron in MgF has a very anisotropic
distribution at the fluorine nucleus, indicating a hybridized
orbital with p character that participates in covalent bonding.38
For FeF, the hyperfine constants have the values b574.7
MHz and c551.5 MHz. Thus, c is somewhat less than b
~constant a is less than 1 MHz!. Simple extrapolation from
the hf constants of the alkaline earth fluorides would indicate
that FeF lies between MgF and CaF in terms of ionicity. This
interpretation would imply that iron fluoride is highly ionic,
while other factors suggest it is not. FeF has a 6D ground
state, not a 2S state, like all the other fluorides considered.
Hence, it has five unpaired electrons which reside in nonbonding or antibonding molecular orbitals created mostly
from iron 3d and 4s atomic orbitals.23 The alkaline earth
fluorides all have one unpaired electron located in a nonbonding s orbital constructed from an s atomic one. Consequently, the interactions of these different types of electrons
in FeF versus MgF, CaF, etc., with the fluorine nucleus may
not be directly comparable.
The covalent nature of the FeF bond is also illustrated in
Table V, which presents r 0 bond lengths for iron species.
The interesting trend to note is that the bond lengths do not
generally scale by the size of the atom ~H, C, O, F, and Cl!
attached to iron. For example, FeH and FeF have very similar bond lengths ~1.787 Å and 1.784 Å!. The bond length of
FeO is shorter ~1.619 Å!, and the shortest one is for FeC
~1.593 Å!. ~The r 0 value for FeCl is largest, and that is likely
accounted for by atom size.! For FeH and FeF, there is a
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M. D. Allen and L. M. Ziurys: Spectroscopy of FeF
3503
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FIG. 6. A qualitative molecular orbital diagram for FeF. The molecular
orbitals are created from the fluorine 2p and iron 4s3d atomic orbitals. The
energies of the iron nonbonding orbitals ~1d,9s,4p! are very close to that of
the 10s antibonding orbital such that the electrons do not pair until the
antibonding orbital is half-filled.
single bond to iron. This bond occurs through a s molecular
orbital constructed from the 4s atomic orbital of iron and
2 p s orbital of fluorine. For FeF, the orbital is 8s, as shown
in the molecular orbital diagram for this species in Fig. 6. In
FeO, an electron is removed from the s antibonding orbital,
which helps to shorten the bond distance. For FeC, a triple
bond exists between the iron and carbon which further decreases the bond distance. This structure results from one s
and two p bonding orbitals, which utilize all three p atomic
orbitals of carbon and one 4s s and two 3d p of iron.
VI. CONCLUSIONS
A comprehensive high resolution spectroscopic investigation has been carried out for the FeF radical, including
measurements of the excited v 51 and 2 levels and the 54FeF
isotopomer. A very regular 6D pattern was found for FeF,
and the data were analyzed with an effective Hamiltonian,
resulting in a determination of accurate rotational, fine structure, lambda-doubling, and hyperfine constants. A comparison of the structural parameters of FeF with other metal diatomic fluorides suggests that its bonding has a considerable
covalent component, as postulated by theory.
ACKNOWLEDGMENTS
This research was supported by NSF Grants Nos. AST92-53682 and AST-95-03274, and NASA Grant No. NAGW
2989. The authors thank Professor John Brown for his help
and use of his Hamiltonian code, and Professors Peter Bernath and Anthony Merer for useful discussions.
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