THE JOURNAL OF CHEMICAL PHYSICS 135, 184303 (2011)
Millimeter-wave rotational spectroscopy of FeCN (X 4 i ) and FeNC (X 6 i ):
Determining the lowest energy isomer
M. A. Flory and L. M. Ziurysa)
Department of Chemistry and Department of Astronomy, Steward Observatory, University of Arizona,
933 N. Cherry Ave., Tucson, Arizona 85721, USA
(Received 15 July 2011; accepted 29 September 2011; published online 10 November 2011)
The pure rotational spectrum of FeCN has been recorded in the frequency range 140-500 GHz using
millimeter/sub-millimeter direct absorption techniques. The species was created in an ac discharge
of Fe(CO)5 and cyanogen. Spectra of the 13 C, 54 Fe, and 57 Fe isotopologues were also measured,
confirming the linear cyanide structure of this free radical. Lines originating from several RennerTeller components in the v2 bending mode were also observed. Based on the observed spin-orbit
pattern, the ground state of FeCN is 4 i , with small lambda-doubling splittings apparent in the = 5/2, 3/2, and 1/2 components. In addition, a much weaker spectrum of the lowest spin-orbit component of FeNC, = 9/2, was recorded; these data are consistent with the rotational parameters of
previous optical studies. The data for FeCN were fit with a Hund’s case (a) Hamiltonian and rotational, spin-orbit, spin-spin, and lambda-doubling parameters were determined. Rotational constants
were also established from a case (c) analysis for the other isotopologues, excited vibronic states, and
for FeNC. The r0 bond lengths of FeCN were determined to be rFe−C = 1.924 Å and rC−N = 1.157 Å,
in agreement with theoretical predictions for the 4 i state. These measurements indicate that FeCN is
the lower energy isomer and is more stable than FeNC by ∼1.9 kcal/mol. © 2011 American Institute
of Physics. [doi:10.1063/1.3653809]
I. INTRODUCTION
The interplay between ionic and covalent bonding in
small, single-ligand metal-bearing molecules is highly influential in structure determination.1 This competition is wellillustrated by the metal monocyanide/isocyanide systems.
Experimental studies have shown that these species exhibit
at least three stable structures, depending on the nature of the
metal–CN bond.2 The highly ionic species NaCN and KCN
have a T-shaped geometry, resulting from the metal cation
orbiting the CN− moiety.3, 4 Other main group metals such as
magnesium and aluminum form the linear isocyanide structure as the lowest energy isomer.5–7 The 3d transition metals,
in contrast, prefer the linear cyanide arrangement, as exemplified by ZnCN, CuCN, CoCN, NiCN, and CrCN.8–12 Theoretical calculations have generally supported the experimental determination of the lowest energy isomers of these species.13–16
One cyanide/isocyanide system that has been particularly
challenging for experimentalists and theoreticians alike is that
involving iron. Calculations have suggested that the linear isocyanides exhibit the highest stabilities for the early 3d metals,
while the later 3d metals favor the linear cyanide form,13 with
typical energy differences of 5–10 kcal/mol.14–16 The picture
is less clear for iron, which lies at the center of the 3d series.
In 2001, FeNC was detected using laser induced fluorescence
(LIF) spectroscopy by Lie and Dagdigian,17 who recorded vibrational bands of a = 7/2 → = 9/2 electronic transition of the main and 13 C isotopologues. FeNC was created in
a supersonic expansion from the reaction of Fe(CO)5 and acetonitrile, and the rotational analysis indicated that the ground
a) Electronic mail: [email protected].
0021-9606/2011/135(18)/184303/11/$30.00
state involved a = 9/2 spin level. In analogy to FeF and
FeCl,18, 19 these authors assumed that the ground electronic
state was 6 i , and that they had observed the most stable isomer. Subsequent calculations predicted that FeNC is lower in
energy than FeCN by 0.6 kcal/mol.20, 21 A later study by Hirano et al. reported the opposite, namely, that FeCN is more
stable by about 0.43 kcal/mol,22 also debated in a more recent
theoretical work by Redondo et al.23 All theoretical studies
did agree, however, that both isomers should have 6 i ground
electronic states.
In order to better characterize the iron cyanide/isocyanide
system, we have recorded the pure rotational spectrum of
both FeCN and FeNC. This study was partly motivated by
the astrophysical interest in these species. Both isomers were
synthesized in an ac discharge of Fe(CO)5 and (CN)2 . The
strongest signals clearly arose from FeCN, where four isotopologues were observed, and a meticulous search revealed
the presence of four spin components, indicative of a 4 i
ground state. This work is the first spectroscopic study of
FeCN. Much weaker spectra were also found for FeNC. Both
data sets have been analyzed with an appropriate Hamiltonian. In this paper we present our data, the spectral analyses,
and the implications of this study for metal cyanide chemistry.
II. EXPERIMENT
Both the FeCN and FeNC radicals were produced in
the velocity modulation spectrometer of the Ziurys group,
which has been described in detail elsewhere.24, 25 Briefly,
the system consists of a Gunn oscillator/Schottky diode
multiplier radiation source that provides nearly continuous
frequency coverage in the range 65-850 GHz. The glass
135, 184303-1
© 2011 American Institute of Physics
184303-2
M. A. Flory and L. M. Ziurys
reaction chamber, which is cooled to −50 ◦ C with chilled
methanol, supports a longitudinal ac discharge by means of
two ring electrodes located at each end of the cell. Radiation
is focused from the source through the cell with two Teflon
lenses, which also serve as vacuum seals, and into the InSb
detector. The radiation source is modulated at 25 kHz and is
detected at 2f using a lock-in amplifier, all under computer
control. The spectrometer in this case was operated in source
modulation mode (see Ref. 25).
Iron cyanide and isocyanide were created in an ac discharge of Fe(CO)5 , (CN)2 , and argon. A mixture of approximately 1–2 mTorr of Fe(CO)5 , less than 0.5 mTorr (CN)2 , and
30 mTorr of argon resulted in the strongest signals. It was also
found that hydrogen cyanide was a reasonable reactant, as
well. The ac discharge was modulated at a rate of 20 kHz with
150 W of power, lower than typically used for creating ions
in this system. The 54 FeCN and 57 FeCN isotopologues were
observed in their natural abundance ratio of 56 Fe:54 Fe:57 Fe
= 91.7:5.9:2.1. In order to measure spectra of Fe13 CN, approximately 0.3 mTorr H13 CN was used as a precursor gas instead of cyanogen; the H13 CN was synthesized from H2 SO4
and Na13 CN. As an additional chemical test, FeCN was also
created in the high temperature spectrometer of the Ziurys
group using Broida oven methods. In this case, iron vapor
from the oven was reacted with (CN)2 . The signals were significantly weaker than those created from iron pentacarbonyl
such that only FeCN was observable.
Transition frequencies were measured by averaging two
scans, one taken in increasing frequency and one in decreasing frequency, each 5 MHz in width. The recorded line shapes
were fit with Gaussian profiles to establish the center frequencies. Line widths ranged from 0.4 to 1.2 MHz over the range
140–500 GHz. The experimental accuracy is estimated to be
± 50 kHz.
III. RESULTS
Searches for FeNC had been attempted by the Ziurys
group using Broida oven synthesis methods, as employed for
species such as FeC and FeN,26 for several years prior to
this work. Use of an ac discharge with Fe(CO)5 proved to
be a major factor in the success of the project. The initial
search was guided by the rotational constant of FeNC for the
= 9/2 ladder determined by Lie and Dagdigian.17 About
8B or 36 GHz were initially scanned. Harmonically related
lines with half-integer rotational quantum numbers and rotational constants between 4.0 and 4.2 GHz were found in the
course of this search, but nothing obvious at the predicted
frequencies for FeNC. The strongest series of lines had a
rotational constant of 4011 MHz and was subsequently assigned to the ground state spin component of an iron cyanide
species. Weaker patterns were also identified and attributed to
the other spin ladders and Renner-Teller components of the
excited bending mode. Based on the observed intensities and
relative frequency shifts, spectra originating from the lowest
spin components of the 54 Fe and 57 Fe isotopologues were also
identified. It was clear from the observed features that a linear
molecule was involved.
In order to establish the identity of the observed species,
the 13 C isotopologue was sought. Rotational constants were
J. Chem. Phys. 135, 184303 (2011)
FIG. 1. Stick spectrum depicting the typical pattern of a given rotational
transition of FeCN (X 4 i ) with approximate relative intensities, in this case
for J = 50.5 → 51.5, near 420 GHz. The four spin components of this
molecule, labeled in bold by quantum number , are visible across a range of
∼15 GHz. The = 5/2, 3/2, and 1/2 sublevels are further split by
-doubling, barely discernable on the given scale. Satellite lines arising from
the excited v2 bending mode, which undergo Renner-Teller interactions, are
also present, as well as those from the 54 FeCN isotopologue. The vibrational
satellite features for the v2 bending mode are labeled by their respective
vibronic state term symbol.
estimated for both FeN13 C and Fe13 CN, scaled from the observed spectra, and 8 GHz (> 2B) were scanned using H13 CN
as a precursor. Spectral lines were observed at the predicted
frequencies for Fe13 CN but not for FeN13 C, confirming the
molecular carrier as FeCN. At this point, it also became clear
that the observed spin pattern arose from a quartet, as opposed
to a sextet, state.
After assigning the spectra as arising from FeCN (X 4 i ),
a weaker harmonic pattern was identified with a rotational
constant that was considerably larger (∼200 MHz) than all
other observed features. This constant agreed very well with
that of FeNC, determined by Lie and Dagdidian,17 and consequently, these lines were assigned to the = 9/2 component
of this molecule.
A stick spectrum of the typical pattern observed for
a single rotational transition of FeCN, in this case for J
= 50.5 → 51.5, is shown in Fig. 1, with approximate relative intensities. As can be seen, the four fine structure components ( = 7/2, 5/2, 3/2, and 1/2) extend over a very large
frequency range, in fact spanning across multiple rotational
transitions, although these intervening lines are not shown for
clarity (see Table I). The = 5/2, 3/2, and 1/2 spin components exhibit small lambda-doubling splittings, barely discernable on the given frequency scale of the figure. Lines from
the less abundant 54 FeCN isotopologue ( = 7/2 and v2 = 1)
are apparent, as well, but not those from 57 FeCN and Fe13 CN,
as they appear at much lower frequencies not included on the
diagram. The v2 vibrational satellite lines are also prominent
features. The v2 bending mode exhibits Renner-Teller effects,
and rotational transitions from several components have been
observed up to v2 = 5. These states are labeled with the appropriate vibronic term symbol.
Figure 2 shows the observed spectrum of the J = 50.5
→ 51.5 transition of FeCN (X 4 i ) near 412–424 GHz.
Four panels are displayed in the figure, one for each fine
184303-3
Millimeter-wave spectroscopy of FeCN and FeNC
J. Chem. Phys. 135, 184303 (2011)
TABLE I. Rotational transition frequencies of FeCN (X 4 i ) and isotopologues.a
J
→
J+1
= 7/2
ν
ν obs-calc
− 0.130
− 0.116
− 0.098
− 0.129
− 0.090
0.078
0.054
0.080
= 5/2
Parity
ν
ν obs-calc
= 3/2
Parity
ν
ν obs-calc
e
f
e
f
e
f
289 192.245
289 195.354
297 318.443
297 321.922
305 442.994
305 446.897
0.021
0.126
− 0.015
0.109
− 0.055
0.111
e
f
e
f
299 158.167
299 206.028
307 334.315
307 384.520
0.069
− 0.250
0.063
− 0.160
e
f
e
f
e
f
e
f
e
f
e
f
378 483.538
378 492.605
386 589.480
386 599.333
394 693.357
394 704.016
402 795.125
402 806.648
410 894.727
410 907.170
418 992.142
419 005.554
− 0.191
0.082
− 0.190
0.093
− 0.174
0.090
− 0.149
0.103
− 0.134
0.108
− 0.114
0.111
e
f
e
f
e
f
e
f
380 843.952
380 914.861
389 002.589
389 075.698
397 159.235
397 234.588
405 313.892
405 391.409
− 0.013
0.068
− 0.007
0.064
− 0.029
0.102
− 0.038
0.105
e
f
421 617.104
421 698.782
− 0.002
0.113
e
f
499 838.080
499 864.016
0.382
− 0.272
e
f
503 000.010
503 098.798
0.013
− 0.136
e
f
374 725.457
374 734.057
0.207
0.251
e
f
e
f
e
f
e
f
390 774.712
390 784.828
398 796.165
398 807.159
406 815.566
406 827.386
414 832.736
414 845.548
− 0.186
− 0.181
− 0.235
− 0.204
− 0.048
− 0.095
0.254
0.241
= 1/2
Parity
ν
ν obs-calc
f
e
f
e
f
e
f
e
f
e
f
e
f
375 033.739
383 146.117
383 241.961
391 351.417
391 448.124
399 554.495
399 652.040
407 755.398
407 853.831
415 954.033
416 053.096
424 150.419
424 250.251
0.778
0.628
0.025
− 0.050
− 0.403
− 0.473
− 0.619
− 0.516
− 0.419
− 0.190
− 0.123
0.608
0.768
56 Fe12 CNb
16.5
17.5
18.5
19.5
20.5
30.5
31.5
33.5
34.5
17.5
18.5
19.5
20.5
21.5
31.5
32.5
34.5
35.5
140 377.362
148 396.971
156 416.251
164 435.128
172 453.702
252 614.297
260 627.370
276 651.681
35.5
36.5
292 673.330
0.125
36.5
37.5
37.5
44.5
45.5
38.5
45.5
46.5
308 692.055
0.116
372 734.235
0.092
46.5
47.5
380 735.393
0.077
47.5
48.5
388 735.542
0.057
48.5
49.5
396 734.682
0.059
49.5
50.5
404 732.738
0.037
50.5
51.5
412 729.729
− 0.115
54.5
55.5
56.5
60.5
55.5
56.5
57.5
61.5
444 706.166
452 697.275
460 687.080
492 633.230
− 0.235
0.033
− 0.290
− 0.190
61.5
62.5
500 616.299
0.399
56 Fe13 CNb
45.5
46.5
46.5
47.5
47.5
48.5
376 974.979
384 896.016
− 0.056
0.007
48.5
49.5
392 816.028
0.056
49.5
50.5
400 734.979
0.082
50.5
51.5
408 652.848
− 0.089
47.5
48.5
49.5
50.5
51.5
52.5
54.5
55.5
384 832.924
392 919.116
401 004.345
409 088.510
417 171.552
425 253.437
441 413.824
449 492.115
0.026
− 0.031
− 0.012
0.012
0.011
− 0.020
0.037
− 0.023
54 Fe12 CNc
46.5
47.5
48.5
49.5
50.5
51.5
53.5
54.5
184303-4
M. A. Flory and L. M. Ziurys
J. Chem. Phys. 135, 184303 (2011)
TABLE I. (Continued.)
J
→
J+1
= 7/2
ν
ν obs-calc
42.5
46.5
47.5
48.5
50.5
338 976.410
370 826.104
378 786.302
386 745.405
402 661.163
− 0.015
0.038
0.052
− 0.098
0.023
= 5/2
Parity
ν
ν obs-calc
= 3/2
Parity
ν
= 1/2
Parity
ν obs-calc
ν
ν obs-calc
57 Fe12 CNc
41.5
45.5
46.5
47.5
49.5
a
In megahertz (MHz).
Case (a) fits.
c
Case (c) fits.
b
structure component, labeled by quantum number . The
upper two panels show data over a 100 MHz range, while
the two lower ones cover 125 MHz and 140 MHz, respectively. The = 5/2, 3/2, and 1/2 lines are further split into
-doublets, indicated by e and f parity assignments. It was
arbitrarily assumed that the f levels lie higher in energy than
the e levels for the = 5/2 ladder; symmetry assignments
for the other two ladders was then established by the signs of
the lambda-doubling constants. The -doubling splitting is
generally small in magnitude (≤100 MHz; see Table I), and
increases from the = 5/2 to the = 12 components as the
signal strength decreases, consistent with a 4 inverted electronic state.
Figure 3 displays the spectrum of the 49.5 → 50.5 rotational transition of Fe13 CN, recorded in this study near 400–
407 GHz. In this case, only the = 7/2 (upper panel) and 5/2
4
FeCN (X Δi): J = 50.5
(lower panel) components are shown because the other two
sub-levels were too weak to be measured. Small -doubling
exists in the = 5/2 component, comparable in magnitude
to that of Fe12 CN, and labeled by e and f. Again, it was assumed that the f levels lie higher in energy than the e levels. A spectrum of the = 9/2 component in the J = 46.5
→ 47.5 transition of FeNC (X 6 i ) near 410 GHz is presented in Fig. 4. These lines are clearly less intense than those
of FeCN; cf. Fig. 2.
Twenty-one rotational transitions of FeCN were recorded
in the frequency range 140–500 GHz. Many of the transitions
include all four spin components and the lambda-doublets
of the = 5/2, 3/2, and 1/2 sublevels. For 54 FeCN, the = 7/2 component and lowest excited vibrational state (v2
= 1) were observed in eight transitions. Only the ground state
= 7/2 sublevel was measured for 57 FeCN in a total of five
51.5
13
Fe CN: J = 49.5
Ω = 7/2
50.5
Ω = 7/2
412700
Ω = 5/2
418960
Ω = 3/2
e
412730
e
418990
412760
f
419020
f
400700
Ω = 5/2
421620
Ω = 1/2
e
424140
421650
421680
424170
424200
424230
Frequency (MHz)
400740
e
400780
f
421710
f
1 scanFrequency
(MHz)
424260
FIG. 2. Spectrum of FeCN (X 4 i ) in the J = 50.5 → 51.5 rotational transition near 412–424 GHz, showing the four spin components. Each spin component, labeled by , is displayed in a separate panel. The spectral features
for the = 5/2, 3/2, and 1/2 sublevels consist of -doublets, labeled by e and
f. The lambda-doubling splitting increases with decreasing . The = 7/2
and 5/2 spectra are 100 MHz wide and are averages of 4 scans, each 60 s in
duration. The = 3/2 data cover 125 MHz and are also an average of four,
60 s scans. The spectrum of = 1/2 is 140 MHz wide and was produced
from an average of two scans, each 90 s in duration.
406780
406820
406860
Frequency (MHz)
FIG. 3. Spectrum of Fe13 CN (X 4 i ) in the J = 49.5 → 50.5 rotational transition near 400–406 GHz, displaying the two lower energy spin components.
In the top panel component, the = 7/2 line is shown, consisting of a single
feature. The = 5/2 line (lower panel) consists of closely spaced -doublets,
labeled by e and f. Both spectra are 100 MHz wide and were recorded in a
single, 60 s scan.
184303-5
Millimeter-wave spectroscopy of FeCN and FeNC
J. Chem. Phys. 135, 184303 (2011)
TABLE II. Rotational transition frequencies of FeCN (X 4 i ), v2 > 0.a
v2 = 1
v2 = 2
4
4
9/2
J
→
4
5/2
J+1
ν
ν obs-calc
Par
35.5
36.5
294 812.807
− 0.079
36.5
37.5
45.5
46.5
375 413.073
0.062
46.5
47.5
383 466.530
0.068
47.5
48.5
391 518.626
0.033
48.5
49.5
399 569.410
0.040
e
f
e
f
e
f
e
f
e
f
e
f
294 772.151
294 772.151
302 838.525
302 838.525
375 396.149
375 397.300
383 453.116
383 454.493
391 509.122
391 510.653
399 564.091
399 565.734
− 0.005
− 0.003
0.037
− 0.044
0.065
0.080
− 0.062
0.023
− 0.078
− 0.003
− 0.030
− 0.016
49.5
50.5
50.5
51.5
407 618.758
415 666.736
− 0.004
0.002
51.5
52.5
e
f
e
f
415 670.549
415 672.531
423 722.060
423 724.165
0.004
− 0.015
0.071
− 0.026
54.5
55.5
56.5
60.5
55.5
56.5
57.5
61.5
447 843.686
455 884.045
463 922.766
496 060.912
− 0.066
− 0.070
− 0.087
0.096
ν
ν obs-calc
v2 = 3
→
J+1
36.5
45.5
46.5
47.5
48.5
49.5
50.5
51.5
61.5
4I
ν
ν obs-calc
ν
ν obs-calc
379 666.386
387 795.409
395 922.311
404 047.241
0.073
− 0.003
− 0.099
− 0.040
380 396.828
388 555.051
396 711.624
404 866.482
− 0.085
0.030
0.079
0.048
420 290.623
501 372.414
0.074
− 0.004
421 171.030
502 578.257
− 0.076
0.004
v2 = 5
J
35.5
44.5
45.5
46.5
47.5
48.5
49.5
50.5
a
→
J+1
36.5
45.5
46.5
47.5
48.5
49.5
50.5
51.5
ν
302 912.120
377 332.681
385 591.381
393 847.887
402 102.135
410 354.032
418 603.522
ν obs-calc
0.004
− 0.018
− 0.019
0.005
0.036
0.026
− 0.035
ν
ν obs-calc
295 883.970
0.005
297 026.212
− 0.006
376 712.463
− 0.028
378 219.174
0.009
384 786.312
− 0.012
386 331.450
0.006
392 858.375
0.029
394 442.311
− 0.006
400 928.499
− 0.014
402 551.780
0.030
408 996.790
417 063.129
0.010
0.026
410 659.695
418 766.142
− 0.015
− 0.021
449 308.012
457 363.985
− 0.035
0.019
499 740.159
0.003
15/2
ν
301 018.314
374 984.435
383 192.954
391 399.359
399 603.570
407 805.529
416 005.221
424 202.590
54 FeCN
4K
17/2
4
3/2
ν obs-calc
11/2
v2 = 4
4H
13/2
4
9/2
J
35.5
44.5
45.5
46.5
47.5
48.5
49.5
50.5
60.5
ν
4
7/2
ν
303 000.484
377 437.038
385 697.427
393 955.526
402 211.372
410 464.941
418 716.078
ν obs-calc
− 0.006
0.038
− 0.004
− 0.010
− 0.013
− 0.022
− 0.007
0.024
v2 = 1
4
9/2
ν obs-calc
0.000
− 0.006
0.019
− 0.011
− 0.016
0.022
− 0.007
ν
395 734.542
403 871.901
412 007.883
420 142.275
ν obs-calc
− 0.048
0.027
0.084
− 0.063
In megahertz (MHz); from case (c) fits.
transitions. Seven transitions of Fe13 CN were measured in
the = 7/2 and 5/2 spin components. A list of ground state
transition frequencies recorded for the different isotopologues
is given in Table I, and frequencies of the excited vibrational
transitions are given in Table II. In addition, ten rotational
transitions of FeNC (X 6 i ) were measured. Because of the
weaker signals, only the = 9/2 state was recorded for this
species. Transition frequencies measured for FeNC are given
in Table III.
IV. ANALYSIS
The data for Fe12 CN were analyzed in a Hund’s case (a)
coupling scheme, assuming a ground state assignment of 4 i .
184303-6
M. A. Flory and L. M. Ziurys
J. Chem. Phys. 135, 184303 (2011)
All four spin components were fit simultaneously with the
following effective Hamiltonian:27
FeNC: Ω = 9/2
J = 46.5 47.5
Heff = Hrot + Hso + H(3)
so + Hss + HLD .
410490
410530
410570
Frequency (MHz)
FIG. 4. Spectrum of = 9/2 sublevel of FeNC (X 6 i ) in the J = 46.5
→ 47.5 rotational transition near 410 GHz. This component was the only ladder observed for FeNC. The lower signal-to-noise ratio for this species is
evidence that FeCN is the more stable isomer. The plot is 110 MHz wide and
is made from an average of 3 scans, each recorded in 60 s.
TABLE III. Transition frequencies of FeNC (6 9/2 ).a
J→J+1
30.5 → 31.5
31.5 → 32.5
32.5 → 33.5
33.5 → 34.5
42.5 → 43.5
43.5 → 44.5
44.5 → 45.5
45.5 → 46.5
46.5 → 47.5
47.5 → 48.5
a
ν
ν obs-calc
272 539.513
281 176.037
289 811.205
298 444.871
376 073.891
384 690.404
393 304.969
401 917.522
410 528.027
419 136.547
0.010
− 0.035
0.005
0.026
− 0.018
0.002
0.018
0.006
− 0.029
0.015
In megahertz (MHz).
(1)
Here the terms account for molecular frame rotation, spinorbit coupling, third order spin-orbit coupling, electron
spin-spin interactions, and -doubling. In addition, higher
order centrifugal distortion terms were incorporated into the
Hrot , Hso , and Hss operators, partly because of the very large
range of J values included in the fit. The spin-orbit parameter,
A, could not be established independently from the analysis
and was fixed to −2400 GHz, a value similar to that for
FeF and FeCl.18, 19 Similarly, the spin-spin parameter, λ,
could not be independently determined. When this constant
was allowed to vary, the fit diverged. An analysis was then
systematically conducted where λ was held fixed at different
values over a specified range. The best fit resulted when
λ ∼ 3 GHz, similar to the spin-spin constant found for
other Fe-containing species.18, 19 Finally, the higher order
spin-orbit parameter η and its centrifugal distortion term ηD
were necessary for a satisfactory analysis. This parameter
occurs for states of quartet or higher multiplicity, and the
operator has the following form:27
√
1
3
H(3)
so = ( 10/5)ηTq=0 (L)Tq=0 (S, S, S).
(2)
The results from the fit to the ground vibrational data of
FeCN are presented in Table IV. In total, 70 lines were included in the analysis with an rms of 249 kHz, about twice
the experimental accuracy.
TABLE IV. Spectroscopic constants for FeCN (X 4 i ) and Fe13 CN (X 4 i ).a
B
D
H (108 )
L (1020 )
q
qD
qH (108 )
A
AD
AH
AL (109 )
λ
λD
λH
λL (108 )
η
ηD
ñ
õ
p̃
p̃D (107 )
q̃
rms
a
b
Fe12 CN
= 7/2
= 5/2
= 3/2
= 1/2
Fe13 CN
= 7/2
= 5/2
4080.079(23)
0.0015069(90)
−1.23(12)
4011.2302(16)
0.0007242(11)
−1.458(23)
0.467(73)
4077.9787(34)
0.0019394(13)
1.208(17)
4103.0693(42)
0.0017643(16)
0.247(20)
4129.0229(82)
0.0020411(39)
1.184(62)
4039.821(29)
0.0014069b
−1.26b
3971.66(10)
0.000735(41)
−1.23(53)
4037.41(11)
0.001897(45)
1.01(62)
0.0216(67)
−0.0000234(27)
−0.129(34)
0.3767(84)
0.0001320(33)
−1.333(40)
1.486(16)
−0.0001399(78)
1.07(12)
−2 400 000b
−20.980(14)
0.0000849(53)
−5.86(71)
3000b
−5.140(11)
0.0001407(42)
1.052(58)
3 614 800(4300)
−13.952(28)
13.8(1.0)
−0.176(64)
0.00793(43)
−2.07(24)
−0.000405(13)
0.249
In megahertz (MHz); errors are 3σ .
Held fixed in final fit.
0.048(14)
−0.0000325(29)
−2 400 000b
−20.98b
0.0000856(29)
3000b
−5.140b
0.0000566(34)
0.029
0.030
0.066
0.038
3 495 600(3200)
−13.952b
13.8b
−0.176b
0.00793b
−2.07b
−0.000388(14)
0.168
0.004
0.016
184303-7
Millimeter-wave spectroscopy of FeCN and FeNC
J. Chem. Phys. 135, 184303 (2011)
TABLE V. Spectroscopic constants for isotopologues and v2 states of FeCN (X 4 i ).a
56 FeCN
(v1 ,v2 ,v3 ) KP
(000) 4 7/2
(010) 4 9/2
(010) 4 5/2
(020) 4 11/2
(020) 4 7/2
(030) 4 H13/2
(030) 4 9/2
(040) 4 I15/2
(050) 4 K17/2
(050) 4 3/2
a
B
D
H
rms
B
D
H
rms
B
D
H
q
qD
rms
B
D
H
rms
B
D
H
rms
B
D
H
rms
B
D
H
rms
B
D
H
rms
B
D
H
rms
B
D
H
rms
4041.3994(69)
0.0010582(25)
−0.000000008 85(31)
0.063
4040.2135(85)
0.0008202(43)
−0.00000001036(70)
0.0196(42)
−0.00000737(91)
0.044
4071.9710(73)
0.0011569(27)
−0.00000000680(32)
0.015
4057.1809(91)
0.0014714(38)
−0.00000001040(51)
0.022
4095.314(28)
0.0010695(95)
−0.0000000285(10)
0.061
4091.595(28)
0.0022294(95)
0.0000000342(10)
0.061
4128.636(15)
0.0019100(73)
−0.0000000016(12)
0.019
4156.239(17)
0.0021001(91)
0.0000000090(15)
0.014
4154.871(17)
0.0020306(91)
0.0000000039(15)
0.024
54 FeCN
57 FeCN
4054.427(57)
0.000745(22)
−0.000000012 6(27)
0.023
4085.119(17)
0.0011437(34)
3990.9052(68)
0.0008158(15)
0.054
0.059
In megahertz (MHz); errors are 3σ .
An attempt to analyze FeCN with a 6 ground state was
also carried out. However, no combination of data or constants
produced a meaningful fit with overall rms less than 2 MHz
(20 times the experimental uncertainty). In particular, it was
not possible to find six sets of harmonically related lines that
could be assigned to the spin components of a 6 state, with
feasible -doubling interactions. Even use of the higher order
terms η and θ did not improve the fitting results.
The data from the Fe13 CN isotopologue were analyzed
with the same case (a) Hamiltonian. However, because only
two of the four components were observed, several of
the fine structure parameters were fixed to the values determined for the main isotopologue. This fit established a global
B0 value for Fe13 CN that was used in the structural analysis. The results of the fit for Fe13 CN are also presented
in Table IV. Fifteen lines were included with an rms of
168 kHz.
The minor isotopologues, the v2 vibrational satellite
lines, and the four individual spin components of the ground
state of FeCN were modeled using a Hund’s case (c)
Hamiltonian, which includes -doubling. The energies in this
coupling scheme have the following form:27
E = BJ(J + 1) − D[J(J + 1)]2 + H [J(J + 1)]3
+ L[J(J + 1)]4 ± 1/2{qJ(J + 1)
+ qD [J(J + 1)]2 + qH [J(J + 1)]3 }.
(3)
The results from the individual fits are presented in
Tables IV and V. The rotational transitions of the = 9/2
184303-8
M. A. Flory and L. M. Ziurys
J. Chem. Phys. 135, 184303 (2011)
TABLE VI. Spectroscopic constants for FeNC (6 9/2 ).a
B
D
H
rms
a
b
Millimeter-wave
Opticalb
4329.735(11)
0.0018788(69)
0.0000000060(14)
0.020
4331(12)
In megahertz (MHz); errors are 3σ .
Reference 17.
component of FeNC were similarly analyzed, and the results
are summarized in Table VI.
V. DISCUSSION
A. FeCN: The lower energy isomer
The spectra recorded here indicate that FeCN is the lower
energy isomer of the cyanide/isocyanide pair, in agreement
with the most recent, high-level calculations of Hirano et al.22
The signals measured for FeCN were consistently stronger
than the equivalent lines for FeNC by factors of 10–15. Moreover, all spin components in FeCN were seen in the observed
spectra, as well as vibrational satellite lines up to v2 = 5.
In contrast, only the lowest energy spin component in FeNC
could be identified.
This experimental result cannot be a result of differing
transition strengths. These two molecules are predicted to
have almost identical dipole moments.20, 22 If anything, that
of FeNC should be larger because it is more ionic, with almost a +1 charge on the iron nucleus.22 The synthesis of both
species was also identical, being simultaneously produced
under the same reaction conditions, roughly at a temperature of ∼400 K. Given their predicted energy difference of
∼150 cm−1 or 200 K,22 both isomers should be present. Furthermore, the same type of millimeter-wave experiments were
conducted on a similar isomer pair, MgNC/MgCN.28, 29 In this
case, MgCN lies about 500 cm−1 or 700 K higher in energy.
Both isomers were created in the same reaction mixture, and
the spectra of MgNC were about a factor of 20 stronger than
those of MgCN28, 29 —roughly what is expected, given the energy difference between the species. Furthermore, all other
millimeter-wave experiments of metal cyanides/isocyanides
conducted in the Ziurys laboratory (AlNC, ZnCN, CuCN,
NiCN, CrCN, and CoCN6, 8–12 ) have identified the lowest energy isomer. It is therefore very likely that the striking differences in intensity between the spectra of FeCN and FeNC
result from their relative energies.
The millimeter spectra of FeNC are consistent with the
results of Lie and Dagdigian. The rotational constant for the = 9/2 component of FeNC in the LIF study was determined to
be B = 4331(12) MHz,17 in excellent agreement with the millimeter value of B9/2 = 4329.735(11) MHz. Moreover, there
can be no confusion with FeCN, because the rotational constant of FeNC is 173 MHz higher than any other observed;
all the FeCN spectra have rotational constants in the range
4011–4156 MHz.
It is puzzling in the LIF measurements of FeNC, no fluorescence was observed from FeCN, the more stable isomer.17
These experiments were conducted in a supersonic jet expansion, and the lower energy isomer should have been
created. Very recent Fourier transform microwave measurements, done with a similar jet expansion coupled with a laser
ablation source, have generated rotational spectra of FeCN in
its X 4 state.30 A possible explanation for the absence of
FeCN in the LIF experiments could be predissociation of the
quartet excited state in FeCN. More pathways likely exist for
a quartet state as opposed to a sextet state, given the S = 0,
±1 predissociation selection rule.
The energy difference between iron cyanide and isocyanide can be estimated from the intensities of the millimeter spectra, assuming that the gas mixture is near equilibrium.
Based on a cell gas temperature of 400 K, the relative intensities of the lines of FeNC ( = 9/2) and of FeCN (
= 7/2) suggest an energy separation of roughly 1.9 kcal/mol.
This difference, obviously a coarse approximation, is in rough
agreement with the 0.43 kcal/mol separation calculated by
Hirano et al.21 The energy separation is notably smaller than
the usual MCN/MNC difference for other transition metal
cyanides: CrCN, E = 4.9 kcal/mol; CoCN, E = 14.7;
NiCN, E = 8.7–12.2; CuCN, E = 10.2–10.7; ZnCN, E
= 5.1.13, 15, 16
According to Hirano et al.,22 FeCN is the more stable
species using higher levels of theory, and relativistic corrections always favor the cyanide. They found that FeCN
has more covalent character than FeNC, because more electron density is shared between iron and the CN moiety in
the cyanide. Enhanced stability of the more covalent, metal
cyanide geometry is found throughout the latter half of the 3d
series, and also in chromium.12 This trend has been explained
as a result of backbonding of the 3dπ electrons into the empty
π * orbital of the CN group.10 This orbital is principally created from carbon, hence the preferred metal-carbon bond. Experimental studies of the manganese system (Mn:d5 ) would
be a revealing test of this simple interpretation, as would investigations of the earlier 3d metals.
B. Electronic ground state and structure of FeCN
The electronic ground state of FeCN has been determined to be 4 i , based on the spectral assignment here and,
in addition, very recent Fourier transform microwave data.30
This ground state is the same as that of FeH,31 but differs from FeF and FeCl, which both have 6 i ground state
terms.18, 19 This result is perhaps not unexpected. The transition metal cyanides that have been characterized experimentally thus far have the same electronic ground states as
the corresponding hydrides, not necessarily the halides. The
outstanding example is NiCN, which has a 2 ground state
term, as does NiH.10, 32 Yet, NiF and NiCl exhibit 2 ground
states.33, 34 The assignment for FeCN differs from the 6 i
term predicted by theory,20, 22 although at the cc-pCVT/augcc-pCVTZ CCSD level of calculation, considering relativistic
effects and core correlation, the 4 energy drops below that of
the 6 state.20 As will be discussed, the bond lengths derived
for FeCN in this study also agree with those predicted for the
184303-9
Millimeter-wave spectroscopy of FeCN and FeNC
4
state, not the 6 state.20 The likely electron configuration
for FeCN is then [core]1δ 3 4π 2 11σ 2 .
The spectra observed for FeCN and Fe13 CN clearly indicate that this species is linear with the cyanide geometry. From the rotational constants of the two isotopologues,
derived with global fits to multiple spin components, an r0
structure has been calculated. In addition, r0 , rs , and rm (1)
bond lengths were determined from the rotational constants
of the = 7/2 component of the four observed FeCN isotopologues. The r0 values were determined from a nonlinear
least squares fit to the moments of inertia, while the rs structure was calculated from Kraitchman’s equations,35 invoking
the center of mass condition. The rm (1) bond lengths were established from a nonlinear least squares fit using the method
of Watson.36 This analysis partly compensates for zero-point
energy differences and is probably closest to the equilibrium
structure.
The resulting bond lengths are listed in Table VII, as well
as those of other known 3d cyanides. As shown in the table,
the r0 value for the Fe−C bond distance in FeCN is rFe−C
= 1.9244 (8) Å, while the C−N bond length is rC−N
= 1.157 (1) Å. The C−N bond length is comparable to the
re bond distance of 1.153 Å for HCN;37 it does not appear to
be unusually short, unlike the case for CoCN (see Table VII),
but large amplitude bending motions could nonetheless be influencing the experimentally derived value.14 The Fe−C bond
distance is longer than that of FeC itself, which has rFe−C
= 1.5931 Å.26 There is triple bond character in FeC, however,
TABLE VII. Bond lengths of transition metal monocyanides.a
Molecule
FeCN
r0 b
r0( = 7/2) c
rs( = 7/2) c
rm (1) ( = 7/2) c,d
CrCN
r0
rs
rm (1)
CoCN
r0 ( = 4)
NiCN
r0
r0 ( = 5/2)
rs ( = 5/2)
rm (1) ( = 5/2)
CuCN
r0
rs
rm (1)
ZnCN
r0
rs
rm (1)
a
rM−C (Å)
rC−N (Å)
1.9244(8)
1.938(27)
1.9355(68)
1.917(12)
1.157(1)
1.171(38)
1.146(23)
1.128(21)
2.02317(83)
2.0216(22)
2.019
1.1529(12)
1.1495(35)
1.148
1.8827(7)
1.1313(10)
1.8281(6)
1.8293(1)
1.8292
1.8263(9)
1.1580(8)
1.1590(2)
1.1534
1.152(1)
1.83231(7)
1.83284(4)
1.8358
1.1576(1)
1.15669(3)
1.1573
1.9545
1.9525
1.9496
1.1464
1.1434
1.1417
See Ref. 12 for molecules other than FeCN.
Based on global fit of two isotopologues.
c
Derived from = 7/2 data of 4 isotopologues. Errors are 3σ .
d
The rm (1) parameter is cb = 0.42(20).
b
J. Chem. Phys. 135, 184303 (2011)
not found in the iron-carbon bond in FeCN. The experimental FeCN bond lengths are in reasonable agreement with the
values predicted for the 4 i state by deYonker et al.: rFe−C
= 1.9796 Å and rC−N = 1.1672 Å.20 In contrast, the experimental Fe–C distance does not agree well with the theoretically predicted bond lengths for the 6 i state, which lie in the
range rFe−C = 2.0484–2.113 Å.13, 20, 22
C. Perturbations in the spectrum of FeCN
As shown in Table IV, higher order centrifugal constants
were needed for both the spin-orbit parameter, A, and the spinspin constant, λ. Note that while D/B ≈ 3.7 × 10−7 , λD /λ
≈ 1.7 × 10−3 . The higher order spin-orbit constant η is unusually large, as well, at 3614.8 (4.3) GHz. The need for these
constants in the spectral analysis and their large magnitudes
indicate the presence of perturbations from nearby excited
states.
According to theory, the nearby-excited states are 4 − ,
4
6
, , and 6 .20 The spin-orbit operator connects states via
the selection rules S = 0, ± 1, = 0, and = −
= 0, ∓1.38 Thus, all the nearby states except 4 − could be
contributing to the ground state perturbations in FeCN. The
stick spectrum in Fig. 1, however, shows that the = 5/2, 3/2,
and 1/2 components are fairly evenly spaced in frequency, but
are considerably shifted from the = 7/2 line. This effect
suggests that the major perturbing state is a 4 state, which
would interact with only the = 5/2, 3/2, and 1/2 levels. If
the quartet manifold lies lower in energy than the sextet one in
FeCN, the 4 would likely be the nearest excited state, with
the electron configuration [core]1δ 2 4π 3 11σ 2 .
The lambda-doubling interactions in FeCN, observed in
three spin components, have been reasonably reproduced with
the terms ñ , õ , p̃ , q̃ , as expected for a 4 state.39 The
centrifugal distortion term p̃D was also needed to model this
interaction, while use of the terms ñD and õD did not appreciably improve the fit. The energy splitting of the e/f states in
a -doublet should be proportional to [J(J+1)] .40 Figure 5
shows a plot of the energy difference between the lambdadoublets in each ladder vs. [J(J+1)] for FeCN. This relationship ideally should be linear for each sublevel, as is generally the case. The = 3/2 component, however, seems to
diverge slightly from the expected pattern. For a 4 state, the
parameter p̃ is in the diagonal block of the Hamiltonian matrix only for = 3/2 sublevel. The need for p̃D in the analysis for FeCN reflects these small deviations in the -doubling
of this component, probably a result of local perturbations.
D. Vibrational structure and Renner-Teller effects
In the v2 vibrational mode for degenerate electronic states
in triatomic molecules, the angular momentum l from the
bending motion couples to the orbital angular momentum:
the Renner-Teller effect. In this case, + l = K, where l
= v2 , v2 – 2, . . . 0, and J = K + S; the projection of J is
P.10 Thus, Renner-Teller coupling significantly complicates
the pattern of the vibrational satellite lines of degenerate electronic states, such as the ground state of FeCN. Many of the
184303-10
M. A. Flory and L. M. Ziurys
J. Chem. Phys. 135, 184303 (2011)
TABLE VIII. Renner-Teller components for FeCN (X 4 7/2 ).a
Omega = 5/2
0.16
(v1 , v2 , v3 )
l
Terms, KP
(0, 0, 0)
(0, 1, 0)
(0, 2, 0)
0
1
2
0
3
1
4
2
0
5
3
1
7/2
5/2 , 9/2
( 3/2 ), 11/2
7/2
(1/2 ), H13/2
(5/2 ), 9/2
(1/2 ), I15/2
( 3/2 ), ( 11/2 )
(7/2 )
3/2 , K17/2
(1/2 ), (H13/2 )
(5/2 ), (9/2 )
Energy: e-f (GHz)
0.14
0.12
0.1
0.08
0.06
(0, 3, 0)
0.04
0.02
(0, 4, 0)
0
0.0E+00
1.0E+08
2.0E+08
3.0E+08
4.0E+08
[J(J+1)]Ω
(0, 5, 0)
Omega = 3/2
3
a
Terms in parentheses not identified in spectrum.
Energy: e-f (GHz)
2.5
2
1.5
1
0.5
0
0
50000
100000
150000
200000
250000
300000
[J(J+1)]Ω
Omega=1/2
4.7
Energy: e-f (GHz)
4.6
4.5
4.4
4.3
4.2
4.1
4
3.9
45
46
47
48
49
50
51
52
53
[J(J+1)]Ω
FIG. 5. Plots showing the lambda-doublet energy splitting for the three ladders of FeCN versus [J(J+1)] . A linear relation is expected and the doublets in all three spin components generally follow this trend. The plot for
the = 3/2 sublevel, however, is not quite linear, suggestive of some local
perturbations.
Renner-Teller components were assigned in the spectrum of
iron cyanide, but only in the = 7/2 ladder (see Fig. 1 and
Table VIII). In the v2 = 1 state, the vibronic terms 2S+1 KP
= 4 5/2 and 4 9/2 were both identified, the former exhibiting
small lambda-doubling. The v2 = 2 level is split into 3/2 ,
11/2 , and 7/2 vibronic states. The latter two states were
found but not the component, which could be widely split
due to spin-rotation interactions and could also be shifted due
to perturbations. The v2 = l, K = l + 2 components were
assigned up to v2 = 5; see Table VIII.
An estimate of the vibration-rotation constant α 2 for
FeCN can be obtained from the progression of the v2 = l, K
= l + 2 satellite lines, which form a fairly regular pattern (see
Fig. 1). Using the expression Bv = Be - α 2 (v2 + 1), where
Be = Be – 12 (α 1 + α 3 ), and the B values for 4 7/2 , 4 9/2 ,
4
11/2 , 4 H13/2 , 4 I15/2 , and 4 K17/2 vibronic states (see Table V),
a least-squares analysis yields α 2 = −28.9(1.5) MHz and Be = 3983.1(5.9) MHz. The value for α 2 is similar to those obtained for the other 3d cyanides. For ZnCN, for example, α 2
= −31.5974(6) MHz,8 while in CoCN, α 2 = −27 MHz.11
This similarity suggests that FeCN is as rigid as other transition metal cyanide species.
The pure rotational spectra measured here indicate that
for FeCN, the spin-orbit interactions are significantly larger
than the Renner-Teller coupling. In the rotational spectra, the frequency splitting between the spin components
is >2 GHz. It varies for the vibronic components: about
∼10 MHz in the v2 = 1 state and about 800 MHz for the v2
= 3 components. There is a much larger frequency difference
between the 11/2 , and 7/2 components in v2 = 2, but this
splitting is likely influenced by Fermi resonance with the v1
= 2 state, which also has 7/2 symmetry. These findings are
in agreement with Hirano et al., who conclude that RennerTeller coupling is negligible for FeCN.22
The energy of the symmetric v1 stretching mode in FeCN
can be estimated using the Kratzer relation,35 treating the CN
moiety as a single point mass
4B 3
ω1 ≈
.
(4)
D
From this expression, the frequency of the v1 mode is
estimated to be ω1 ≈ 448 cm−1 for FeCN; for FeNC, ω1
≈ 438 cm−1 , considering the = 9/2 component only. The
symmetric stretch is theoretically calculated to lie between
410 and 420 cm−1 for FeCN, in reasonable agreement with
the Kratzer-derived value.20, 22 The Kratzer-estimated stretching frequency for FeNC is consistent with that observed by
Lie and Dagdigian for the = 9/2 component, ω1 (FeNC)
= 468 cm−1 .17
VI. CONCLUSIONS
Establishing the properties of small, transition metalbearing molecules remains a challenging area of investigation, as this study illustrates. Contrary to previous work,
184303-11
Millimeter-wave spectroscopy of FeCN and FeNC
measurements of the pure rotational spectra of FeCN and
FeNC indicate that the cyanide is the more stable species of
the isomer pair and that it has a 4 i ground state term. This
stability seems to result from increased covalent character in
the molecule. The spectrum of FeCN, however, appears to
be perturbed, as evident in the fine structure pattern and the
derived spectroscopic constants. Low energy excited states
clearly exist for this species. The structure determined for
FeCN from the rotational constants suggests a single Fe−C
bond and a triple C–N bond. Thus far, all 3d transition metals
with the CN ligand have the linear cyanide geometry, in
contrast to main group metals. Intriguing questions concerning the lowest energy structures of the remaining 3d metals
Sc, Ti, V, and Mn have yet to be answered. Experimental
and theoretical studies of these species would be chemically
enlightening.
ACKNOWLEDGMENTS
This work was funded by NSF Grant Nos. CHE-0718699, CHE-10-57924, and AST 09-06534. The authors acknowledge late J. M. Brown for use of his fitting program,
HUNDA. The authors also wish to thank N. J. DeYonker, P. J.
Dagdigian, and T. Hirano for many informative discussions.
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