Chemical Physics Letters 496 (2010) 8–13
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Millimeter/submillimeter velocity modulation spectroscopy of FeO+ (X 6R+):
Characterizing metal oxide cations
D.T. Halfen *, L.M. Ziurys
Department of Chemistry and Department of Astronomy, Arizona Radio Observatory and Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson,
AZ 85721, USA
a r t i c l e
i n f o
Article history:
Received 5 June 2010
In final form 13 July 2010
Available online 16 July 2010
a b s t r a c t
The pure rotational spectrum of FeO+ (X 6R+) has been recorded using millimeter/submillimeter velocity
modulation techniques, the first high-resolution measurement of a metal oxide cation. FeO+ was created
in an AC discharge from Fe(CO)5 and N2O. Nine rotational transitions were recorded in the range 299–
544 GHz, each consisting of six fine-structure components. The data were analyzed with a case (b) Hamiltonian, and rotational and spin parameters determined. The spin–spin constant suggests a low-lying
4 R excited state. The bond length established for FeO+, r0 = 1.641 Å, is slightly longer than that of FeO,
consistent with a covalent bonding scheme.
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
Transition-metal oxide cations have been observed to be efficient catalysts in the gas phase [1]. These species were found to
oxidize molecular hydrogen, methane, and larger hydrocarbons,
including alkanes, alkenes, arenes, and benzene [2]. Many of these
processes have potential industrial applications, such as oxidation
of methane into methanol, alkene epoxidation, and arene hydroxylation [3]. However, depending on the transition metal present,
these species vary in their chemical behavior. For example, NiO+
reacts efficiently with methane to form methanol as the sole product, while MnO+ only forms MnOH+ + CH3. The early 3d transitionmetal oxide cations, ScO+, TiO+, and VO+, as well as CoO+, have no or
little reactivity to methane [2]. Investigating the properties of
these metal cations is therefore of interest to gain insight into their
individual chemistries.
One of the most powerful and well-characterized catalysts is
the metal oxide cation FeO+. This species was initially discovered
to oxidize CO to CO2, and is formed when Fe+ reduces N2O to N2
[4]. FeO+ was the first transition-metal oxide cation found to activate methane in the gas phase, leading to methanol as one of the
major products [5]. This process is thought to proceed through a
CH3–Fe–OH+ intermediate, which produces both CH3OH + Fe+ and
FeOH+ + CH3 as the final products in an almost equal ratio [6].
FeO+ has additionally been found to oxidize H2, creating H2O via
the reduction of N2O [7], as well as ammonia, ethane, and acetylene [1]. These catalytic reactions appear to proceed through a
* Corresponding author. Fax: +1 520 621 5554.
E-mail addresses: [email protected] (D.T. Halfen), [email protected]
(L.M. Ziurys).
0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2010.07.044
curve crossing on the reaction potential energy surface, mediated
by spin–orbit coupling [8,9]. FeO+ has also been used as a model
for the active site of methane monooxygenase, an enzyme found
in methanotropic bacteria, and cytochrome P450, a metabolic
enzyme present in animals, plants, bacteria, and fungi [10].
FeO+ is also a species of possible astrophysical interest, because
of the high cosmic abundance of iron (Fe/H = 3 105) [11]. Certain iron-bearing molecules have been detected in astronomical
sources. FeH, for example, has been observed via its electronic
spectra in sunspots, and in the photospheres of M, L, and T dwarf
stars [12–14]. FeO has been tentatively identified in absorption towards the molecular cloud Sgr B2(M) [15]. In addition, FeO+ has
been detected via mass spectrometry in the Earth’s mesosphere,
thought to be a product of the reaction of meteoritic Fe+ and ozone
[16,17].
Because of its catalytic properties, FeO+ has been the subject of
numerous theoretical and experimental investigations. Several
computational studies have been performed for this ion at various
levels of theory [8,18–21]. Bond lengths, dissociation energies, and
spectroscopic constants have been calculated for the ground and
excited electronic states. All of these methods consistently predict
a 6R+ ground state for FeO+. Experimentally, this cation has usually
been studied by mass spectrometry or ion cyclotron resonance
(ICR) to examine its catalytic activity [4,5,7]. The Metz group, however, has made significant progress in the spectroscopic characterization of FeO+. In 1999, Husband et al. used vibrationally-resolved
photofragment spectroscopy to measure the v = 1
0, 0
0, and
1
1 bands of the 6R+
X 6R+ transition, confirming the ground
state assignment [22]. These authors obtained vibrational frequencies for the two states, the ground state dissociation energy, and
upper state rotational constants. More recently, Aguirre et al.
investigated the v = 8
0 and 9
0 bands of the 6P7/2
X 6R+
transition via resonance-enhanced photodissociation (RE-PD) techniques [21]. Estimates of the rotational, spin-rotation, and spin–
spin parameters for the ground state were derived in this work.
These data also refined the spectroscopic constants of the excited
6 +
R state of Husband et al. [22].
Here we present the first measurement of the pure rotational
spectrum of FeO+ in its X 6R+ ground state. This study was carried
out using velocity modulation techniques at millimeter/submillimeter wavelengths. All six fine-structure components were resolved in nine transitions across a 145 GHz frequency range,
allowing for an accurate determination of the spin parameters, as
well as rotational constants. Here we describe our results and analysis, and their implications for bonding and chemistry in 3d metal
oxide cations.
2. Experimental
The pure rotational spectrum of FeO+ was measured using the
millimeter/submillimeter velocity modulation spectrometer of
the Ziurys group [23]. Briefly, the machine consists of a Gunn oscillator/varacter multiplier frequency source, a glass reaction chamber, and a InSb hot electron bolometer detector. The radiation
source, which operates from 65 to 850 GHz, is phase-locked to a
rubidium standard. The glass cell, which is cooled to 65 °C with
methanol, contains two ring electrodes that create a longitudinal
AC discharge. Phase sensitive detection is employed in two modes:
source modulation, where the Gunn frequency is dithered at a rate
of 25 kHz with 2f detection, or velocity modulation, where the
polarity of the AC discharge is switched at a 20 kHz rate with 1f
detection [24]. Source modulation is typically used for sensitive
spectral searches, while velocity modulation is employed to confirm the presence of ions. For more detail, see Halfen and Ziurys
[24].
FeO+ was created in an AC discharge from a mixture of iron
pentacarbonyl and nitrous oxide in argon carrier gas. The best signals were observed for this ion with partial pressures of 1–2 mtorr
of Fe(CO)5, 1–2 mtorr of N2O, and 35 mtorr of Ar. The AC discharge
was run at 200 W with a 600 X impedance. The discharge plasma
glowed light pink as FeO+ was produced, likely due to a dissociation of iron pentacarbonyl, which produces a purple-white color,
and N2O, which exhibits a reddish glow.
Transition frequencies were determined from averaging pairs of
scans in increasing and decreasing frequency, each 5 MHz in scan
width. Typically between 2 and 10 such scan pairs were needed
to acquire a sufficient signal-to-noise ratio for the FeO+ spectra.
Gaussian line profiles were fit to the spectral features to determine
the center frequency, as well as the line width, which ranged from
800–1700 kHz over the region 299–544 GHz. The experimental error is estimated to be ±100 kHz.
by about 36 MHz. Chemical tests showed that these lines were
due to both Fe(CO)5 and N2O, and they were only produced in
the AC discharge. The same spectral features were also detected
in velocity modulation mode, confirming that they arose from an
ion. Strong lines of FeO from the X = 4, 3, and 2 spin–orbit ladders
up to v = 4 were also observed in the search region. Such evidence
clearly pointed to the presence of FeO+.
The progression of the six spin components can be seen in Fig. 1.
Here a stick spectrum of FeO+ is displayed for five transitions
(N = 10
9, N = 12
11, N = 14
13, N = 16
15, and N =
18
17). The splitting between the fine-structure components (labeled by F1, F2, . . . , where F1 is N = J + 5/2, F2 is N = J + 3/2, etc.) is not
regular at low N with the two inner components only about
240 MHz apart. The uneven spacing is caused by the increased
influence of the spin–spin constant k at low N. At higher frequency,
the six components assume more regular spacing. This pattern is
typical for a molecule with a 6R+ state. The overall splitting of the
sextet ranged from 3.9 to 4.1 GHz from N = 10
9 to 18
17.
Representative spectra of the N = 17
16 transition of FeO+ are
displayed in Fig. 2. There are five frequency breaks in the spectra to
display all six spin components. The upper panel shows the data
recorded in source modulation mode with 2f detection; the lower
panel presents the same transition taken in velocity modulation
(VM) mode with 1f detection. The velocity modulation data clearly
demonstrate that the spectral features arise from a molecular ion.
The nearly equal intensity of all six features observed is indicative
of a molecule in a 6R state. Note that the signal-to-noise ratio
Stick Spectrum of FeO+ (X 6Σ+)
N = 18
F1
F2
541
17
F3
F4
542
543
N = 16
481
420
482
421
F5
F6
544
545
15
483
422
484
423
485
424
3. Results
360
Based on frequencies predicted from the constants of Aguirre
et al. [21], a search for FeO+ was conducted in the range 445–
544 GHz. Measurements were made in four separate regions covering a total of 52 GHz. During this search, a series of harmonicallyrelated lines with a widely-spaced sextet pattern were found with
a rotational constant about 40 MHz greater than that reported by
Aguirre et al. [21]. The fine-structure constants of Aguirre et al.
suggested that the splitting between the individual spin components ranged from 840 to 1080 MHz over the observed frequency
range, but the actual pattern had spacings of 560–1010 MHz. As
a result, the sextet pattern was not as easily discernible as in CrCN
[25], for example, where the spin components are only separated
361
362
N = 10
300
301
363
364
9
302
Frequency (GHz)
303
304
10
D.T. Halfen, L.M. Ziurys / Chemical Physics Letters 496 (2010) 8–13
FeO+ (X6Σ+): N = 17 16
F1
F2
+
F3
6 +
510.655
511.648
FeO
(X Σ ):
N = 17 512.415
16
F1
510.655
F2
511.648
F3
512.415
Source Modulation
F4
513.030
F4
513.030
F5
Table 1
Observed rotational transitions of FeO+ (X 6R+).a
F6
N0
N00
J0
10
9
11
mobs
mobs mcalc
12.5
11.5
11.5
10.5
10.5
9.5
9.5
8.5
8.5
7.5
7.5
6.5
299815.073
300932.520
301477.780
301717.387
302521.535
303683.858
0.643
0.003
0.103
0.358
0.238
0.516
10
13.5
12.5
12.5
11.5
11.5
10.5
10.5
9.5
9.5
8.5
8.5
7.5
329944.227
331027.048
331634.396
331973.158
332764.915
333868.852
0.361
0.166
0.182
0.163
0.108
0.266
12
11
14.5
13.5
13.5
12.5
12.5
11.5
11.5
10.5
10.5
9.5
9.5
8.5
360072.603
361129.440
361782.925
362196.854
362981.934
364036.948
0.264
0.094
0.184
0.010
0.006
0.642
13
12
15.5
14.5
13.5
12.5
11.5
10.5
14.5
13.5
12.5
11.5
10.5
9.5
390198.984
391236.081
391923.691
392396.710
393178.240
394196.530
0.150
0.019
0.092
0.086
0.111
0.483
14
13
16.5
15.5
14.5
13.5
12.5
11.5
15.5
14.5
13.5
12.5
11.5
10.5
420321.629
421343.263
422057.585
422577.532
423357.267
424345.929
0.014
0.036
0.117
0.149
0.124
0.001
15
14
17.5
16.5
15.5
14.5
13.5
12.5
16.5
15.5
14.5
13.5
12.5
11.5
450439.349
451448.720
452184.278
452742.225
453521.266
454486.042
0.078
0.162
0.056
0.278
0.091
0.158
16
15
18.5
17.5
16.5
15.5
14.5
13.5
17.5
16.5
15.5
14.5
13.5
12.5
480551.041
481550.822
482303.603
482892.759
483671.711
484616.654
0.044
0.148
0.096
0.323
0.118
0.229
17
16
19.5
18.5
17.5
16.5
15.5
14.5
18.5
17.5
16.5
15.5
14.5
13.5
510655.622
511647.928
512414.998
513030.227
513809.416
514737.736
0.050
0.144
0.144
0.277
0.197
0.107
18
17
20.5
19.5
18.5
17.5
16.5
15.5
19.5
18.5
17.5
16.5
15.5
14.5
540752.442
541738.886
542518.283
543155.048
543934.683
0.094
0.059
0.550
0.329
0.184
Velocity
513.809 Modulation
514.737
F5
513.809
F6
514.737
Frequency (GHz)
Fig. 2. Spectrum of the N = 17
16 transition of FeO+ (X 6R+) near 513 GHz taken
in source modulation mode with 2f detection (upper panel), and in velocity
modulation (VM) mode with 1f modulation (lower panel), plotted on the same
intensity scale. The fine-structure components are shown labeled by F1, F1, etc.
There are five frequency breaks in the spectrum to display all spin components. The
spectral pattern is duplicated exactly in VM mode, indicating that the signals arise
from a molecular ion. The spectrum for each spin component is an average of four
110 MHz wide scans, acquired in about 70 s, then cropped to display a 20 MHz wide
frequency range.
degrades in the VM data by about a factor of four, a result of undermodulation, see Halfen and Ziurys [24].
Nine rotational transitions of FeO+ were measured from 299 to
544 GHz, as shown in Table 1. The six fine-structure components
were recorded in almost every transition, except for the
N = 18
17, J = 15.5
14.5 line, which was just beyond the range
of the frequency source. Altogether, 53 individual lines were
measured.
a
4. Analysis
b
The spectrum were analyzed with a Hund’s case (b) effective
Hamiltonian that includes rotation, spin-rotation, spin–spin,
third-order spin-rotation, and fourth-order spin–spin interactions,
along with their respective centrifugal distortion parameters:
^ eff ¼ H
^ rot þ H
^ sr þ H
^ ss þ H
^ ð3Þ þ H
^ ð4Þ :
H
sr
ss
ð1Þ
The data were fit with a non-linear least squares routine HUNDB [26].
Initially the same parameters used by Aguirre et al. (B, D, c, and k),
along with cD and kD, were employed in the analysis; however, it
become immediately obvious that higher-order centrifugal distortion and fine-structure parameters were needed to obtain a reasonable fit. Therefore, cs and h were added along with their distortion
J00
b
In MHz.
Not recorded.
constants, as well as H and kH. All parameters were typically floated
in the analysis. In the final fit, H, csD, and hH were fixed because their
3r errors were slightly larger than the parameters themselves. The
final rms of the fit was 238 kHz. Without the H, kH, csD, and hH constants, the rms becomes slightly larger: 307 kHz.
The derived constants for FeO+ are listed in Table 2, along with
those determined by Aguirre et al. [21]. The B, D, and k parameters
are in excellent agreement with the past data (e.g. k = 3768 MHz
from our data vs. 3777 MHz from Aguirre et al. [21]), while c is
smaller but within the margin of error of the optical work. The
fourth-order spin–spin parameter h is quite large compared to k
D.T. Halfen, L.M. Ziurys / Chemical Physics Letters 496 (2010) 8–13
Table 2
Spectroscopic constants for FeO+ (X 6R+).a
Parameter
MMW
RE-PDb
B
D
H
15092.812(19)
0.021467(35)
2.5 107c
829.43(55)
0.00553(55)
3768(11)
0.2973(59)
0.000019(12)
1.595(32)
0.000090c
487.4(1.9)
0.00660(98)
5.6 106c
0.238
1.641(1)
844(1)
15 050(36)
0.0210c
c
cD
k
kD
kH
cs
csD
h
hD
hH
rms
r0 (Å)
xe (cm1)
a
b
c
x2e ¼
989(180)
3777(540)
In MHz; errors are 3r in the last quoted decimal places.
From Ref. [21]. Values originally quoted in cm1.
Held fixed (see text).
(h = 487.4(1.9) MHz vs. k = 3768(12) MHz), thus h/k = 13%. For
other molecules with 6R+ ground states, such as CrCN and MnO, this
parameter ranges from 2.7 to 14.7 MHz, while k is 640 and
17 198 MHz, respectively, such that h/k = 0.42% and 0.085%
[25,27]. The magnitude of h in FeO+ probably indicates the presence
of nearby excited states. A large value of h has been previously observed in the (0440) and (0550) vibrational states of CrCN, where
this constant suddenly increases from a few MHz in the (0330) state
to 500–600 MHz [25]. A low-lying 4R state is thought to account
for the abrupt increase in the value of this parameter in CrCN.
5. Discussion
5.1. Bond length and electron configuration
The bond length of FeO+ was established from the rotational
constant to be 1.641 Å, which agrees well with the value determined by Aguirre et al. of 1.643 Å [21]. In comparison, the bond
length in neutral FeO is 1.619 Å [28], a decrease of 0.021 Å. In the
ionic picture, a shorter bond length would be expected for FeO+,
not FeO. For example, the bond lengths in TiCl+ and VCl+ decrease
by 0.08–0.10 Å relative to the neutral species TiCl and VCl [24,29].
This contraction is attributed to the increased electrostatic attraction between Ti2+ or V2+ and Cl.
Covalent bonding offers an explanation for the relative bond
lengths in FeO+ and FeO. In the covalent scheme, the electron configurations of FeO and FeO+ are proposed to be (core)1d39r14p2
and (core)1d29r14p2, respectively [20]. Hence, when FeO is ionized
to produce FeO+, a non-bonding 1d electron is removed which is 3d
in character [30]. The loss of this non-bonding electron should not
significantly affect the bond length, as has been observed, good evidence for the validity of the proposed electron configurations.
A similar situation has been observed in FeCO+ as well. Assuming a CO bond length of 1.13–1.16 Å, the Fe–C bond distance is
1.85–1.87 Å in FeCO+ [31], while FeCO has rFe–C = 1.727 Å [32].
The Fe–C bond in the ion is therefore longer by 0.12–0.14 Å. A r
bonding electron is thought to be removed in the formation of
FeCO+ from the neutral, thus lengthening the Fe–C bond with
decreasing bond order.
The experimental r0 bond length of FeO+ also agrees with the
theoretical re value calculated by Gutsev et al. using DFT at the
B3LYP level (1.641 Å) [20], as well as the MRCI value (1.646 Å)
[19]. Another comparison is the vibrational frequency, xe, which
can be estimated from the experimental data using the Kratzer
relation [33]:
4B3e
:
De
11
ð2Þ
Assuming B0 ffi Be and D0 ffi De for FeO+, the xe 844 cm1. This frequency compares favorably with that determined experimentally
from a vibrational hot band (838 ± 4 cm1) and the DFT and MRCI
values of 819 cm1 and 845 cm1 [19,20,22].
It is interesting to note that while MnO and FeO+ have the same
ground state and almost identical bond lengths (1.641 Å for FeO+
and 1.648 Å for MnO) [27], the fine-structure parameters are very
different. Relative to those of FeO+, the c and h constants of MnO
are smaller by an order of magnitude, while k is about a factor of
five larger and opposite in sign [27]. Hence, even with similar
ground electronic states, the excited state manifolds are likely to
be very different in these two species.
5.2. Interpretation of the fine-structure parameters
The spin–spin constant k produces the irregular fine-structure
pattern of FeO+ observed at low frequency, as mentioned. Compared to other species with 6R+ ground states, k has a rather average value of 3768 MHz. For example, CrCN and MnO have spin–
spin constants of 640 and 17 198 MHz, respectively [25,27],
although the (0440) and (0550) excited vibrational states of chromium cyanide have values k = 3780–4070 MHz [25].
The spin–spin parameter is defined as a sum of the pure microscopic electron spin–spin interactions and second-order spin–orbit
coupling, resulting from perturbations with nearby excited states,
i.e. k = kss + kso [34]. For heavier molecules, the second-order
spin–orbit contribution is dominant [35], and can be estimated
based on the following equation [36]:
kso ¼
30ð2S 2Þ! X X
ð2S þ 3Þ!
R n0 ;K0 ;R0
D
E2
^ ½3R2 SðS þ 1Þ n0 ; K0 ; R0 H
so n; K; R :
En0 En
ð3Þ
The quantum numbers n0 , K0 , and R0 sum over nearby perturbing
states. The selection rules for spin–orbit coupling are DS = 0, ±1,
DX = 0, DR = DK = 0, 1, and R $ R [34]. Therefore, the excited states of FeO+ that can interact with the ground 6R+ state
are 4R, 4P, 6R, 6P, 8R, and 8P. The octet states and the 6R
states involve transitions from core orbitals, and should, therefore, be quite high in energy, and can be neglected to first order.
Theoretical calculations have suggested the presence of low-lying
4
P and 6P states at energies near 4300 cm1 and 9000 cm1;
there were no predicted low-lying 4R states [19,21]. The 4P
state, with a proposed electron configuration of (core)1d39r14p1,
is predicted to the lowest-lying of these two states [19]; therefore, assuming that this state is the primary perturber, Eq. (3)
becomes:
kso ¼
30ð2S 2Þ! X X
ð2S þ 3Þ!
R
R0
D E
^ 6 þ 2
½3R2 SðS þ 1Þ 4 PH
so X R
:
Eð4 PÞ EðX 6 Rþ Þ
ð4Þ
The summation over R generates several matrix elements. However, the Wigner–Eckart theorem
can
be used to
D
E relate the matrix
^ 6 þ
elements such that only one, 4 P5=2 H
so X R5=2 , needs to be evaluated, i.e. [37]:
12
D.T. Halfen, L.M. Ziurys / Chemical Physics Letters 496 (2010) 8–13
rffiffiffi
D
E
E
3D4
^ 6 þ
^ 6 þ
4
P3=2 Hso X R3=2 ¼
P5=2 H
so X R5=2 ;
5
rffiffiffiffiffiffi
D
E
E
3 D4
^ 6 þ
4
^ so X 6 Rþ
P1=2 H
P5=2 H
so X R5=2 ;
1=2 ¼
10
D
E
E
1 D
^ 6 þ
^ 6 þ
4
P1=2 Hso X R1=2 ¼ pffiffiffiffiffiffi 4 P5=2 H
so X R5=2 :
10
The Slater determinants of the X R
E
6 þ
X R5=2 ¼ jdþ ad apþ ap araj
þ
5=2
5.3. Properties of 3d metal oxide cations
4
and P5=2 states are
ð5Þ
and
4
P5=2 ¼ jdþ ad adþ bp araj:
ð6Þ
The matrix element therefore reduces to
D
4
E
þ
þ
^ so X 6 Rþ
^ þ þ P5=2 H
5=2 ¼ d ad ad bp ara H so d ad ap ap ara
¼
1
þ þ
d b a3d l s p a ¼ a3d :
2
þ
ð7Þ
+
Because FeO is an ion, a3d is assumed to be the atomic spin–orbit
constant of Fe+, 416 cm1 [34]. The above expression then becomes:
kso ¼ a23d
1
4
20 Eð PÞ EðX 6 Rþ Þ
ð8Þ
Using the value of k of 3768 MHz, the energy of the 4P state is
estimated to be 68 850 cm1. This value is quite far from the predicted energy of 4337 cm1 [19]. This result suggests that the 6P
and/or 4R states are also contributing to k, lowering its value. Both
of these states will give a positive contribution to k, while that from
the 4P state is negative. If the 4P state is assumed to be at the energy of 4337 cm1, as suggested by theory, the contribution of the
other states can be estimated. Both experiment and theory indicate
that E(6P) is P10 000 cm1, and thus it can be neglected to a first
approximation. Assuming that the lowest-lying 4R state arises
from the 1d29r1(4p+a4pb) configuration, its contribution to the
spin–spin constant is kso 56 044 MHz, placing it at an energy
above the ground state of E 4629 cm1. Based on photoionization
spectroscopy, Metz et al. found at least one quartet state lying at
E > 2900 cm1 (0.36 eV) in energy above the ground state [38].
The exact terms of these states, however, could not be determined.
The spin-rotation parameter c is also a sum of the first-order
spin-rotation and the second-order spin–orbit couplings, i.e.
c = csr + cso [34]. The selection rules for the latter interaction are
DS ¼ 0 and DR ¼ DK ¼ 1; therefore, cso arises from perturbations by nearby 6P states, and in principle can be used to estimate
their energies. The lowest-lying 6P state has the proposed electron
configuration of (core)3p31d34p29r1 [21]. Second-order spin-rotation coupling, however, arises from a cross term between Hso and
Hrot, where Hrot ¼ BPR J L . Evaluation of the corresponding maP trix elements require the rather poor approximation of L± = i li
[39]. Furthermore, estimation of BPR, the average value of the P
and R states, requires information about the rotational constant
of the 6P state, an unknown quantity. The energy of the 6P state
is perhaps better estimated using the fourth-order spin–spin
parameter h, which depends solely on Hso. Matrix elements involving Hso yield better approximations because the unpaired electrons
in FeO+ are generally centered on the iron nucleus [34]. The 6P energy can be estimated by the following equation [40]:
sffiffiffiffiffiffiffi
4
3 a
3d
DE :
jhj
ð9Þ
Using the spin–orbit constant of Fe+ and the value of h = 487.3
MHz measured for FeO+, the energy of the 6P state is approximately
Outside of FeO+, there is virtually no experimental spectroscopic
work on 3d metal oxide cations. Several theory papers exist concerning these species, however. A recent article by Gutsev et al.
[20] predicts their electron configurations, ground electronic
states, and bond lengths. A summary of these properties is given
in Fig. 3. As discussed by these authors, the bonding is 3d metal
oxide species and their cations is a mixture of covalent, ionic,
and dative contributions. Simplistically, the cation results from
the direct loss of an electron from the neutral molecule, but there
are various electrons available. Gutsev et al. [20] predict that from
ScO to VO, the removal of the unpaired 9r electron results in the
cation and the ground electronic states shown in Fig. 3. For CrO
and MnO, however, loss of the 4p electron is predicted, while eliminating a 1d electron creates FeO+ in its 6R+ state.
It might be expected that the cation would have the same electron configuration and ground state as the neutral species proceeding it in the 3d series. Experimentally, this situation has been found
for FeO+, which has the same electronic ground state as MnO. Theory predicts a similar situation for ZnO+, CuO+, CoO+, and MnO+,
which have the same states as CuO, NiO, FeO, and CrO. There are
several exceptions, however, notably TiO+ (X 2Dr), VO+ (X 3R),
and NiO+ (X 4R). These species are predicted to have different
electronic states than their isoelectronic neutral analogs, ScO
(X 2R+), TiO (X 3Dr), and CoO (X 4Di).
Fig. 3 also illustrates some other differences between the cations and the neutral oxides. In the early 3d series, the cations have
shorter bond lengths than the neutrals. The ions likely result from
loss of an electron from a non-bonding r orbital, as described by
Gutsev et al. [20]. Hence, the shortening of the bond lengths relative to the neutrals may be an ionic effect, as found for TiCl+ and
VCl+ [24,29]. The cation bond lengths start to increase relative to
the neutrals at CrO+, and then are consistently longer that their
neutral counterparts from Mn through Zn. Particularly dramatic
1.85
3Σ−
1.80
1.75
Bon
nd Length (Å)
6
12 243 cm1. Aguirre et al. [21] suggest one 6P state has an energy
of 9000 cm1, estimated from their measurements, with another
at E 16 500 cm1, predicted theoretically [21], in qualitative
agreement with our projected value.
1.70
Oxide Neutrals
Experimental
2Σ+
3Δ
1.65
1.60
1.45
r
4Σ−
5Π
1Σ+
2Δ
1.55
1.50
5Π
i
r
6Σ+
6Σ+ 5Δ
i
4Σ−
2Π
i 1Σ+
r
4Σ−
r
2Π
5Δ
i
4Δ
i
3Σ−
Oxide Cations
Experimental
3Σ−
Oxide Cations
Theoretical
1.40
Sc
Ti
V
Cr Mn
Fe
Co
Ni
Cu
Zn
Fig. 3. Graph showing the periodic trends in bond lengths and electronic ground
states for the 3d transition-metal oxide neutrals, determined experimentally, and
corresponding cations, predicted by theory. The one experimental ion value is for
FeO+. The neutral metal oxides are labeled by squares, the cations with diamonds,
and the FeO+ data point is indicated with a triangle. The cations have shorter bond
lengths than the neutrals in the early 3d series, but the bond lengths become longer
after manganese, likely due to competition between ionic and covalent bonding.
D.T. Halfen, L.M. Ziurys / Chemical Physics Letters 496 (2010) 8–13
increases in bond distance occur at MnO+ and CuO+, with the addition of a 4p anti-bonding and 9r non-bonding electron, respectively. The increases in bond length at MnO and CuO are thought
to result from addition of 3d electrons to the 4p anti-bonding orbital, first singly, then doubly [30]. The increase at CuO+ is more difficult to rationalize. Experimental data is clearly needed to test
these theoretical predictions.
5.4. Implications for bond activation in FeO+
The likely existence of low-lying 4R and 4P excited states in
FeO+ may have interesting implications for the catalytic mechanisms of this ion. As described in Böhme and Schwarz [1], H–H
and C–H bond activation for the late 3d metal oxide cations likely
occurs through a transition state on a lower spin surface than that
of the ground state. The curve crossing for the reaction potential
surface is thought to be mediated by spin–orbit coupling.
Theoretical studies of the process of FeO+ + H2, a model system
for reactions of oxide cations with alkanes, suggest that a sextet/
quartet curve crossing on the potential surface leads to the formation of the intermediate (H–Fe–OH+). A second curve crossing results in the products H2O + Fe+(6D). Theoretical work in the past
maintained that the quartet state of FeO+ of importance was either
4
D or 4U [8], but more recent work suggests that other quartet
states may be possibilities [1]. Ab initio calculations performed at
the MR-SDCI level, probably the best to date, predict that the lowest-lying quartet states are 4P and 4U, both at 4300 cm1, while
the 4D state lies higher in energy at 7100 cm1 [19]. If the 4P energy is a reasonable estimate, our data suggest there is also a 4R
state with an energy of 4600 cm1. More experimental data on
the low-lying electronic state manifold of FeO+ is certainly needed
to better evaluate the catalytic processes of this cation.
6. Conclusion
Transition-metal oxide cations play an important role in catalysis and C–H bond activation. Understanding their physical properties is essential in evaluating reaction mechanisms. This work has
clearly verified that FeO+ has a 6R+ ground electronic state, with
nearby 4R and 4P excited states, as suggested in part by theory.
It also has demonstrated that the bond length slightly increases
in FeO+ relative to FeO, evidence for substantial covalent bonding
in the neutral/cation pair. Spectroscopy of other 3d metal oxide
cations such as NiO+, MnO+, and CrO+ would be useful in evaluating
general chemical properties relevant to these intriguing species.
13
Acknowledgment
This research is supported by NSF grant CHE 07-18699.
References
[1] D.K. Böhme, H. Schwarz, Angew. Chem., Int. Ed. 44 (2005) 2336.
[2] D. Schröder, H. Schwarz, Angew. Chem., Int. Ed. 34 (1995) 1973.
[3] K. Weissermel, H.J. Arpe, Industrieile Organische Chemie, VCH, Weinheim,
1988.
[4] M.M. Kappes, R.H. Staley, J. Am. Chem. Soc. 103 (1981) 1286.
[5] D. Schröder, H. Schwarz, Angew. Chem., Int. Ed. 29 (1990) 1433.
[6] D. Schröder, A. Fiedler, J. Hrušák, H. Schwarz, J. Am. Chem. Soc. 114 (1992)
1215.
[7] D. Schröder, H. Schwarz, D.E. Clemmer, Y. Chen, P.B. Armentrout, V.I. Baranov,
D.K. Böhme, Int. J. Mass Spectrom. Ion. Process. 161 (1997) 175.
[8] A. Fiedler, D. Schröder, S. Shaik, H. Schwarz, J. Am. Chem. Soc. 116 (1994)
10734.
[9] Y.-C. Wang, D.-P. Chen, Z.-Y. Geng, J.-H. Zhang, J. Mol. Struct. Theochem. 858
(2008) 26.
[10] K. Yoshizawa, J. Biol. Inorg. Chem. 3 (1998) 319.
[11] N. Grevesse, A.J. Sauval, Space Sci. Rev. 85 (1998) 161.
[12] J.J. Harrison, J.M. Brown, Astrophys. J. 686 (2008) 1426.
[13] M.C. Cushing, J.T. Rayner, S.P. Davis, W.D. Vacca, Astrophys. J. 582 (2003) 1066.
[14] T. Nakajima, T. Tsuji, K. Yanagisawa, Astrophys. J. 607 (2004) 499.
[15] C.M. Walmsley, R. Bachiller, G. Pineau Des Forêts, P. Schilke, Astrophys. J. 566
(2002) L109.
[16] T.J. Kane, C.S. Gardner, J. Geophys. Res. 98 (1993) 16875.
[17] E. Kopp, Eberhardt, U. Herrmann, L.G. Björn, J. Geophys. Res. 90 (1985) 13041.
[18] A. Fiedler, J. Hrušák, W. Koch, H. Schwarz, Chem. Phys. Lett. 211 (1993) 242.
[19] Y. Nakao, K. Hirao, T. Taketsugu, J. Chem. Phys. 114 (2001) 7935.
[20] G.L. Gutsev, L. Andrews, C.W. Bauschlicher Jr., Theor. Chem. Acc. 109 (2003)
298.
[21] F. Aguirre, J. Husband, C.J. Thompson, K.L. Stringer, R.B. Metz, J. Chem. Phys.
119 (2003) 10194.
[22] J. Husband, F. Aguirre, P. Ferguson, R.B. Metz, J. Chem. Phys. 111 (1999) 1433.
[23] C. Savage, L.M. Ziurys, Rev. Sci. Instrum. 76 (2005) 043106.
[24] D.T. Halfen, L.M. Ziurys, J. Mol. Spectrosc. 234 (2005) 34.
[25] M.A. Flory, R.W. Field, L.M. Ziurys, Mol. Phys. 105 (2007) 585.
[26] J.M. Brown, 2006, private communication.
[27] K. Namiki, S. Saito, J. Chem. Phys. 107 (1997) 8848.
[28] M.D. Allen, L.M. Ziurys, J.M. Brown, Chem. Phys. Lett. 257 (1996) 130.
[29] D.T. Halfen, L.M. Ziurys, J. Phys. Chem. A 113 (2009) 13436.
[30] A.J. Bridgeman, J. Rothery, J. Chem. Soc., Dalton Trans. (2000) 221.
[31] D.T. Halfen, L.M. Ziurys, Astrophys. J. 657 (2007) L61.
[32] K. Tanaka, M. Shiraska, T. Tanaka, J. Chem. Phys. 106 (1997) 6820.
[33] W. Gordy, R.L. Cook, Microwave Molecular Spectra, Wiley, New York, 1984.
[34] H. Lefebvre-Brion, R.W. Field, The Spectra and Dynamics of Diatomic
Molecules, Elsevier, Amsterdam, 2004.
[35] J.M. Brown, A. Carrington, Rotational Spectroscopy of Diatomic Molecules,
Cambridge University Press, Cambridge, 2003.
[36] J.M. Brown, E.A. Colbourn, J.K.G. Watson, F.D. Wayne, J. Mol. Spectrosc. 74
(1979) 294.
[37] T.D. Varberg, R.F. Field, A.J. Merer, J. Mol. Spectrosc. 156 (1992) 296.
[38] R.B. Metz, C. Nicolas, M. Ahmed, S.R. Leone, J. Chem. Phys. 123 (2005) 114313.
[39] E.A. Colbourn, F.D. Wayne, Mol. Phys. 37 (1979) 1755.
[40] J.M. Brown, D.J. Milton, Mol. Phys. 31 (1976) 409.