Vibrational spectroscopy and theory of Fe+(CH4) n (n = 1-4)

Article abstract of DOI:10.1021/jp104602k

Vibrational spectra are measured for Fe⁺(CH₄) _n (n = 1-4) in the C-H stretching region (2500-3200 cm^-1) using photofragment spectroscopy. Spectra are obtained by monitoring CH ₄ fragment loss following absorption of one photon (for n = 3, 4) or sequential absorption of multiple photons (for n = 1, 2). The spectra have a band near the position of the antisymmetric C-H stretch in isolated methane (3019 cm^-1), along with bands extending >250 cm^-1 to the red of the symmetric C-H stretch in methane (2917 cm^-1). The spectra are sensitive to the ligand configuration (η² vs η³) and to the Fe-C distance. Hybrid density functional theory calculations are used to identify possible structures and predict their vibrational spectra. The IR photodissociation spectrum shows that the Fe ⁺(CH₄) complex is a quartet, with an η³ configuration. There is also a small contribution to the spectrum from the metastable sextet η³ complex. The Fe⁺(CH ₄)₂ complex is also a quartet with both CH₄ in an η³ configuration. For the larger clusters, the configuration switches from η³ to η². In Fe⁺(CH ₄)₃, the methane ligands are not equivalent. Rather, there is one short and two long Fe-C bonds, and each methane is bound to the metal in an η² configuration. For Fe⁺(CH₄) ₄, the calculations predict three low-lying structures, all with η² binding of methane and very similar Fe-C bond lengths. No single structure reproduces the observed spectrum. The approximately tetrahedral C₁ (⁴A) structure contributes to the spectrum; the nearly square-planar D_2d (⁴B₂) and the approximately tetrahedral C₂ (⁴A) structure may contribute as well.

Full text of DOI:10.1021/jp104602k

1
1322
J. Phys. Chem. A 2010, 114, 11322–11329
+
†
Vibrational Spectroscopy and Theory of Fe (CH ) (n ) 1-4)
4
n
Murat Citir, Gokhan Altinay, Geoff Austein-Miller, and Ricardo B. Metz*
Department of Chemistry, UniVersity of Massachusetts Amherst, Amherst, Massachusetts 01003
ReceiVed: May 19, 2010; ReVised Manuscript ReceiVed: July 15, 2010
+
(n ) 1-4) in the C-H stretching region (2500-3200 cm-1)
fragment loss following absorption
of one photon (for n ) 3, 4) or sequential absorption of multiple photons (for n ) 1, 2). The spectra have a
Vibrational spectra are measured for Fe (CH
4
)
n
using photofragment spectroscopy. Spectra are obtained by monitoring CH
4
-
1
band near the position of the antisymmetric C-H stretch in isolated methane (3019 cm ), along with bands
-
1
-1
extending >250 cm to the red of the symmetric C-H stretch in methane (2917 cm ). The spectra are
2
3
sensitive to the ligand configuration (η vs η ) and to the Fe-C distance. Hybrid density functional theory
calculations are used to identify possible structures and predict their vibrational spectra. The IR photodissociation
+
3
spectrum shows that the Fe (CH
4
) complex is a quartet, with an η configuration. There is also a small
contribution to the spectrum from the metastable sextet η complex. The Fe (CH
in an η configuration. For the larger clusters, the configuration switches from η to η . In
Fe (CH ) , the methane ligands are not equivalent. Rather, there is one short and two long Fe-C bonds, and
each methane is bound to the metal in an η configuration. For Fe (CH
low-lying structures, all with η binding of methane and very similar Fe-C bond lengths. No single structure
1
reproduces the observed spectrum. The approximately tetrahedral C ( A) structure contributes to the spectrum;
2 2
the nearly square-planar D2d ( B ) and the approximately tetrahedral C ( A) structure may contribute as well.
3
+
4 2
) complex is also a quartet
3
3
2
with both CH
4
+
4 3
2
+
4 4
) , the calculations predict three
2
4
4
4
I. Introduction
cluster size. This corresponds to the symmetric C-H stretching
vibration in the complex. The symmetric stretch in isolated CH
4
Catalytic activation of methane poses a particular challenge
due to the strength of the C-H bond. The observation that
several of the third-row transition metal cations activate meth-
-1
is at ν
1
) 2917 cm and is IR inactive. Interaction with the
metal red-shifts the frequency and lends it substantial IR
+
intensity (∼100 km/mol). The Al (CH
4 6
) clusters also show a
1
+
ane under thermal conditions, producing MCH
2
2
+ H , has
weak band in the vicinity of the antisymmetric stretch (ν
3
)
spurred many studies of the energetics, intermediates and
products of these reactions. The gas-phase studies can elucidate
the mechanism of the reaction and how the reactivity depends
on the metal, its electronic state and spin, and the available
-1
3
019 cm in CH
candidate structures show that the observed spectrum definitively
establishes that the structure consists of intact CH units bound
to the metal in an η configuration. Dryza and Bieske recently
4
). Comparison with calculated spectra of
4
3
2
–9
energy.
Two key intermediates in the reaction are the
+
19
4 n
extended these studies to Mn (CH ) (n ) 1-6). Again, the
symmetric C-H stretch dominates the spectrum. It shifts from
+
+
M (CH
4
3
) entrance channel complex and the [H-M-CH ]
insertion intermediate. The corresponding reactions of first and
-1
+
2
836 (n ) 1) to 2880 cm (n ) 6). The CH
4
bind to Mn in
second-row M+ are endothermic. Adding additional CH
10
4
5
1
7
3
its ground electronic state (3d 4s , S) in an η configuration.
ligands can reduce the barrier to insertion, resulting in H
elimination, as observed by van Koppen et al. for Ti . Even
2
+
4 n
Here, we report vibrational spectroscopy of Fe (CH ) (n )
-4). The reaction
1
1
+
1
for metals which do not activate methane, the bonding in
+
M (CH
4
)
n
(n g 1) is not merely electrostatic, but includes
+
+
significant covalency due to donation from C-H bonding
orbitals into empty or partially empty 4s and 3d orbitals on the
metal, along with back-donation into C-H antibonding orbitals.
The strength of these interactions, and the structure of the
complexes, depends on the electronic configuration of the metal
Fe + CH f FeCH + H2
4 2
2
0–22
is 123 kJ/mol endothermic,
to C-H insertion
and there is a substantial barrier
23,24
so, at the conditions in our ion source,
we expect to produce only Fe (CH ) entrance channel com-
plexes. Sequential binding energies of methane to Fe have been
+
4 n
and on the size of the cluster. Vibrational spectroscopy is an
+
ideal tool to investigate these noncovalent interactions,1
2–17
as
measured by Schultz and Armentrout via collision-induced
binding to the metal leads to a substantial red-shift in the
proximate C-H stretching frequencies, and increases their
intensity.
dissociation (CID) using a guided ion beam2
1,25
and, more
recently, by Zhang, Kemper, and Bowers by cluster equilibri-
um.26 According to the CID measurements, the first methane
binds by 57 kJ/mol and the second by 97 kJ/mol. The
equilibrium measurements give similar values: 77 and 108 kJ/
mol, respectively. Stronger binding of the second ligand is often
Poad, Thompson and Bieske measured infrared spectra of
+
Al (CH
4
)
n
(n ) 1-6) in the C-H stretching region using
18
photofragment spectroscopy. They observe one strong absorp-
tion, which shifts from 2850 to 2885 cm- with increasing
1
+
observed in electrostatic Fe complexes. The first excited state
+
7 4
of Fe (3d , F) interacts more strongly with ligands than the
†
Part of the “Klaus M u¨ ller-Dethlefs Festschrift”.
6
6
D (3d 4s) ground state, as the 4s orbital is empty, reducing
repulsive interactions. Calculations predict that the ground state
*
To whom correspondence should be addressed. E-mail: rbmetz@
chem.umass.edu.
1
0.1021/jp104602k  2010 American Chemical Society
Published on Web 07/29/2010

+
Vibrational Spectroscopy of Fe (CH4)n
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11323
+
26,27
of Fe (CH
4
) is a quartet,
so its measured binding energy
Wachters, and SDD) for iron. We also carried out MP2(full)
calculations with the 6-311+G(d,p) basis. Some structures that
are local, but not global, minima with some basis sets are not
stable with other basis sets, relaxing to a lower-energy structure.
However, for a particular structure, these four basis sets (and
two levels of theory) predict nearly the same spectra. Here, we
present calculations at the B3LYP/6-311+G(d,p) level. The
calculated vibrational frequencies are harmonic, whereas the
measured vibrational fundamentals include anharmonicity. To
include this effect, the calculated frequencies are scaled by
0.948. All reported energies include zero-point energy and are
corrected for basis set superposition error using the counterpoise
method.
+
6
4
includes the 24 kJ/mol Fe D- F promotion energy. Larger
clusters (at least up to n ) 6) are calculated to remain quartets,
so this promotion energy is no longer an issue. Binding energies
for the third and fourth methane are much smaller, 23 and 20
kJ/mol, respectively.26 Binding energies for additional CH
are
very small, around 2 kJ/mol. The equilibrium measurements
4
+
support a maximum coordination number of four for Fe (CH
with additional CH in the second solvation shell. The large
4 n
) ,
4
change in binding energy with cluster size suggests that the
binding in these complexes is not simply electrostatic. Competi-
tion between covalent and electrostatic interactions leads to
cluster-size dependent binding configurations which are reflected
in the richly structured vibrational spectra.
III. Results and Discussion
II. Experimental and Computational Methods
+
A. Vibrational Spectra of Fe (CH
4
)
n
(n ) 1-4). Vibra-
+
Iron ion-methane complexes are produced in a laser ablation
source and studied in a dual time-of-flight mass spectrometer,
which has been described in detail previously.2 Iron cations
4 n
tional spectra of Fe (CH ) (n ) 1-4) were measured using
photofragment spectroscopy. The larger clusters (n ) 3, 4) are
sufficiently weakly bound that absorption of one photon in the
C-H stretching region leads to vibrational predissociation and
8,29
are produced by laser ablation of an iron rod (Sigma-Aldrich,
+
9
9.8% pure). Fe (CH
4
)
n
clusters are generated in an expansion
loss of CH4.
Methane binding energies are substantially higher
-
1
for the small clusters: 6400 and 9000 cm
for n ) 1 and 2,
gas mixture of methane in helium at 50 psi backing pressure.
respectively.26 Our initial studies used an optical configuration
in which the IR beam makes only one or two passes through
Dilute mixes containing 0.1-1% methane are used to produce
+
+
4 4 2
Fe (CH ) and Fe (CH ) , and more concentrated mixes with
5
% methane are used for larger clusters. Ions produced in the
the ion beam. Under these conditions, we observe no photo-
+
(
4 n
CH ) (n ) 1, 2). An alternate approach to
source expand supersonically into vacuum and cool to a
dissociation of Fe
30
rotational temperature of ∼10 K. Ions are accelerated to 1800
V kinetic energy, then rereferenced to ground potential before
entering the field-free flight tube. Mass-selected ions are
photodissociated at the turning point of the reflectron using an
IR laser system. The light source is a Nd:YAG pumped optical
parametric oscillator/optical parametric amplifier that is tunable
measuring the spectrum is to add a weakly bound spectator atom
such as Ar to the cluster. Rare gas atoms are more weakly bound
than most other ligands so that single-photon excitation, even
in the IR, is typically enough to cause dissociation. Unfortu-
+
nately, Ar-tagging does not work well for Fe
(
CH
4
). Our
), by
500 cm , and significantly perturbs the vibrations, red-shifting
+
calculations predict that argon binds strongly to Fe (CH
2
4
-
1
-1
from 2 to 4.5 µm, producing ∼10 mJ/pulse near 3200 cm .
+
-1
The larger clusters Fe (CH
4
)
n
(n ) 3, 4) are so weakly bound
the lowest-frequency C-H stretches by ∼75 cm
.
that they dissociate after absorbing one photon in the C-H
stretching region. Their spectra were measured in a single-pass
Another possibility is to use vibrationally mediated photo-
34
dissociation (VMP) to measure the vibrational spectrum of
+
+
setup. On energetic grounds, photodissociation of Fe (CH
4
)
n
4
Fe (CH ). This technique combines vibrational excitation with
(
n ) 1, 2) requires 2-4 photons in the C-H stretching region.
selective electronic photodissociation of vibrationally excited
molecules. It has the potential to measure spectra of unperturbed
ions, with laser-limited resolution and good sensitivity. However,
measuring vibrational spectra using VMP requires that the
electronic photodissociation spectra of vibrationally excited
So, vibrational spectra are obtained using infrared multiple
photon dissociation (IRMPD). No photodissociation signal is
observed in the single-pass configuration. Instead, the photo-
dissociation spectrum is measured using a multipass mirror
arrangement3
1,32
in which the laser makes 21 passes through
molecules differ from that of vibrationally cold molecules. The
+
the ion beam. The laser wavelength is calibrated using CH
4
electronic spectra of a few M (CH
4
) have been measured.
absorptions. Fragment ions and undissociated parent ions are
detected by a dual microchannel plate detector.
Kleiber and co-workers have recorded electronic photodisso-
+
35
36
37
ciation spectra of M (CH
4
), M ) Mg, Ca, and Zn, in the
+
+
The ion signal is amplified, collected on a digital oscil-
loscope or gated integrator, and averaged with a LabView
based program. The photodissociation products are identified
using a difference spectrum, which is generated by subtracting
time-of-flight spectra collected at a specific wavelength with
the dissociation laser blocked from when it is unblocked.
The photodissociation spectrum is obtained by monitoring
the yield of the fragment ion of interest as a function of
wavelength and normalizing to parent ion signal and laser
fluence. The photodissociation spectrum is the product of the
absorption spectrum and the photodissociation quantum
yield.
ultraviolet near the M 4p r 4s transition. The Mg (CH
4
) and
) spectrum is
4
stretch and bend.
+
+
Zn (CH
4
) spectra are broad, but the Ca (CH
4
+
structured, with progressions in the Ca -CH
+
For most transition metal M , the first allowed electronic
transition lies deep in the UV. Excited states corresponding to
d-d and s-d transitions are at much lower energies, but are
+
optically forbidden for isolated M . Interaction with a ligand
can make these transitions weakly allowed. Hayes et al.
+
measured the electronic photodissociation spectrum of V (CH
4
)
38
in the visible. The spectrum is sharp, with progressions in the
+
4
V -CH stretch and rock. Their structured spectra make
+
+
Ca (CH
4 4
) and V (CH ) good candidates for VMP studies of
Computations are carried out using the Gaussian 2003
program package.33 Optimized geometries of the reactants,
intermediates, transition states and products are calculated using
the Becke Lee-Yang-Parr hybrid HF/DFT method (B3LYP).
We use the 6-311+G(d,p) basis for carbon and hydrogen and
tried four different basis sets (6-31G(d,p), 6-311+G(d,p),
their vibrational spectra. To evaluate the feasibility of VMP
studies for Fe (CH ), its electronic photodissociation was
4
monitored from 620 to 730 nm. Methane loss is the only
dissociation channel observed. Unfortunately, the dissociation
yield is small, and the photodissociation spectrum is unstruc-
tured, which precludes the use of VMP to measure the
+

1
1324 J. Phys. Chem. A, Vol. 114, No. 42, 2010
Citir et al.
+
Figure 1. Infrared photodissociation spectra of Fe (CH
4
)
n
(n ) 1-4)
in the C-H stretching region. The vertical lines indicate the positions
of the symmetric stretch (ν ) 2917 cm ) and antisymmetric stretch
-
1
1
-
1
(
ν
3
4
) 3019 cm ) in CH .
+
Figure 2. Calculated structures of Fe (CH
4
) at the B3LYP/6-
TABLE 1: Experimental Band Positions and Their Relative
Intensitiesa
311+G(d,p) level. Relative energies, in kJ/mol, are in bold. The Fe-C
bond lengths, in Å, are in black; Fe-H bond lengths are in red.
band position (cm-1)
+
Fe (CH
4
4
4
4
)
)
)
)
2646 (w), 2813 (m), 3000 (s)
2624 (sh), 2670 (m), 3017 (s)
2648 (w), 2703 (s), 2803 (m), 2895 (w), 3015 (m)
2711 (s), 2737 (s), 2838 (s), 2869 (w), 2998 (m)
+
methane distances. To determine the structure and characterize
Fe (CH
2
3
4
+
+
Fe (CH
the vibrations of each Fe (CH
)
4 n
cluster, we carry out geometry
+
Fe (CH
optimization and vibrational frequency calculations for several
potential isomers. By comparing the measured and predicted
vibrational spectra, we determine which isomer(s) are present,
and hence energetically favored.
a
s ) strong; m ) medium; w ) weak; sh ) shoulder.
vibrational spectrum. In addition, at 266 nm we observe very
B. Analysis of the Structure and Vibrational Spectra of
+
+
+
+
4
7
+
interesting dissociation channels for Fe (CH
4
)
n
. Fe (CH
4
)
Fe (CH
4
)
n
(n ) 1-4). i. Fe (CH
4
). The F (3d ) state of Fe
6
6
dissociates via loss of methane. In addition to methane loss,
lies 24 kJ/mol above the D (3d 4s) ground state. However,
metals with a d s configuration interact more strongly with
ligands than those with a d s configuration, as the 4s orbital
is empty, reducing repulsive interactions. A key question is
whether the enhanced interaction of the quartet state with
methane is sufficient to overcome this energy difference.
+
n
0
we also observe Fe (H
2
) as a minor channel in photodissociation
+
+
n-1 1
of Fe (CH
4
)
2
and Fe (CH
4
)
3
.
3
1,32
After implementing a multipass mirror setup,
we were
(n ) 1, 2)
using IR multiple photon dissociation (IRMPD). Figure 1 shows
+
4 n
able to measure vibrational spectra of Fe (CH )
+
the vibrational photodissociation spectra of Fe (CH
-4). Band positions and intensities are listed in Table 1. All
of the clusters have a peak near the antisymmetric stretch (ν
4
)
n
(n )
Calculations indicate that it is. Early MP2 calculations by Ricca
+
1
et al. predict that Fe (CH
4
) has a quartet ground state, with an
3
27
3
η
configuration. To complement their ligand exchange
-1
)
3019 cm ) in isolated CH
4
, indicated by a vertical line in
equilibrium measurements, Zhang et al. calculated structures
+
the figure. The remaining peaks exhibit a pronounced red shift
relative to the symmetric stretch in isolated CH (ν ) 2917
4 n
of low-lying isomers of Fe (CH ) (n ) 1-6) and their binding
energies.26 They used the B3LYP method with the 6-31G(d,p)
basis on carbon and hydrogen. For iron, they tried two basis
sets: the double-ꢀ valence polarization (DZVP) and an aug-
mented Wachters basis set. For several of the clusters they
identify multiple isomers with similar calculated energies, with
the energy difference depending on the basis set. They also
4
1
-
1
cm ), with larger red shifts generally observed for the smaller
clusters. These peaks are due to vibrations of C-H bound to
the metal, resulting in the large red shift. The red shifts are
+
+
much larger than those observed for Al (CH
)
4 n
and Mn (CH
4 n
) ,
+
consistent with the much larger Fe -methane binding energies.
Spectra of the n ) 1, 2 clusters show broader features than
those of the smaller clusters. A laser ablation/molecular beam
source cools rotations very well, but is much less efficient at
cooling vibrations. These hot ions preferentially contribute to
the photodissociation spectrum, as IRMPD is more efficient for
the hot ions, which need to absorb fewer IR photons to
dissociate. In addition, the small binding energies of larger
clusters limit their internal energy.
predict a quartet ground state, with the CH
4
ligand binding to
+
3
2
Fe in an η configuration. Two quartet η configurations lie at
+
4
slightly higher energy. Sextet Fe (CH ) is calculated to be 21
3
kJ/mol above the quartet ground state. It also adopts an η
configuration, with much longer Fe-C bond length.
+
3
For Fe (CH
4
) we also find a quartet ground state with an η
4
configuration with C
s
( A′′) symmetry, slightly distorted from
C
3V with 2.10 Å Fe-C bond length (Figure 2). We also find a
2
4
The vibrational spectra show large differences with cluster
low-lying quartet state with an η configuration with C
1
( A)
2
3
size, reflecting varying configurations (η vs η ) and metal-
symmetry, slightly distorted from C2V. For the sextet state, we

+
Vibrational Spectroscopy of Fe (CH4)n
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11325
by the C-H stretch of the hydrogen pointing away from the
+
2 4
Fe . For the η ( A) structure, four intense peaks are predicted
-
1
at 2596, 2686, 2925, and 2982 cm . Symmetric and antisym-
metric C-H vibrations of the bound hydrogens give the peaks
-
1
at 2596 and 2686 cm , respectively. The corresponding
+
vibrations of the hydrogens pointing away from the Fe give
-
1
3
the peaks at 2925 and 2982 cm . For the sextet state, η C3V
(
6
-1
1
A ), the very intense peak at 2790 cm is due to the symmetric
C-H stretch, which involves all the hydrogens. The small peak
at 2892 is the doubly degenerate antisymmetric combination
-
1
of bound C-H stretches. The 2908 cm peak is primarily due
to the C-H stretch vibration of the free hydrogen. The spectral
signatures persist in the larger clusters and allow us to identify
the methane configuration. At this level of theory, the C-H
bond length in isolated CH
4
is 1.091 Å. The bound C-H bond
2
4
3
lengths are 1.120 Å for the η ( A) state, 1.112 Å for the η C
s
4
3
(
A′′) state, and 1.099 Å for the η sextet state. Binding in an
2
η configuration results in the largest extension of the C-H
bond length, and most red-shifted spectrum. The free C-H bond
lengths are almost unchanged from isolated CH : 1.090-1.092
Å for the quartet states and 1.096 for the sextet state.
4
+
4
Figure 3. Experimental IR photodissociation spectrum of Fe (CH ),
3
2
3
along with calculated spectra of quartet η and η and sextet η
The experimental photodissociation spectrum has an intense
complexes. The maximum calculated IR intensities are 38, 27, and 100
-
1
-1
4
4
6
km/mol for the A′′, A, and A
1
complexes, respectively.
peak at ∼3000 cm , a smaller peak at 2813 cm , and a weak
-
1
3
4
peak at 2646 cm . The calculated spectrum of the η C
s
( A′′)
-
1
complex reproduces the 3000 and 2646 cm peaks. However,
the calculated intensity of the peaks near 2800 cm is far too
low. It appears that the 2813 cm peak is due to the sextet
1
state, η C3V ( A ). Although this state is calculated to lie at
calculate an η configuration with C3V (6A
3
) symmetry and 2.52
1
-
1
Å Fe-C bond length. Our calculations show that the sextet
structure has a significantly longer Fe-C bond than the quartet
-
1
3
6
6
1
structures, as would be expected from the 3d 4s configuration
higher energy than the quartet states, it would be produced by
+
6
of Fe ( D).
+
+
binding of methane to ground state Fe with conservation of
Calculations on bare Fe at the B3LYP/6-311+G(d,p) level
incorrectly predict a quartet ground state, 19.8 kJ/mol below
the sextet state. This is a well-known failure of the B3LYP
method with this type of basis set.
energies of sextet and quartet Fe (CH
+
spin. Relaxation of sextet Fe (CH
4
) to the quartet state by the
helium carrier gas in the molecular beam is likely to be
-
1
3
9,40
inefficient. The 2790 cm vibration for the sextet state has a
calculated absorption intensity of 100 km/mol, compared to only
To find the relative
+
4
), we calculate the energy
-
1
3
8 km/mol for the 2946 cm vibration for the quartet state. In
of each cluster relative to spin-allowed products, then correct
+
addition, we calculate absorption spectra and measure IRMPD
by the experimental Fe sextet-quartet energy. Conserving spin,
+
+
4
spectra, so the intensities may differ. IRMPD of sextet Fe (CH )
the binding energy of sextet Fe (CH
kJ/mol; that of quartet Fe (CH
4
) is calculated to be 40
+
is likely to be more efficient than for the quartet state, as it is
more weakly bound. Thus, the relative amount of sextet
4
) is more than twice as large:
3 kJ/mol. Thus, the dissociation energy of quartet Fe (CH )
+
8
4
+
+
Fe (CH
4
) is likely to be quite small. There is no evidence that
4
relative to ground state, sextet, Fe + CH is 59 kJ/mol. This
2
4
the η ( A) complex contributes to the spectrum.
The interaction of the sextet ground state of Fe (3d 4s )
with methane to produce sextet Fe (CH ) is similar to the
4
interactions of Mn (3d 4s , S) and Al (3s , S) with methane.
is in good agreement with the experimental values of 57 kJ/
+
6
1
mol (CID)2 and 77 kJ/mol (equilibrium). In addition, our
1,25
26
+
+
calculations predict that sextet Fe (CH
4
) lies 19 kJ/mol above
+
5
1
7
+
2 1
the quartet state, in agreement with the previous calculations.
3
+
The complexes adopt an η configuration, with the Fe-C bond
3
We also considered the possibility of an inserted [H-Fe-CH ]
4
1
structure. Calculations by Chiodo et al. at the B3LYP level,
length (2.52 Å) slightly shorter than the Mn-C bond length
(2.64 Å)19 and significantly shorter than the Al-C bond length
using a modified TZVP basis set for iron, predict that the quartet
+
18
+
[
H-Fe-CH
3
]
insertion intermediate lies 18 kJ/mol above
4
(2.90 Å). Accordingly, sextet Fe (CH ) (40 kJ/mol) is more
+
+
+
reactants. It is separated from the Fe (CH
4
) entrance channel
strongly bound than Mn (CH
kJ/mol).
4
) (34 kJ/mol) and Al (CH
4
) (25
+
19,26,42
by only a 4 kJ/mol barrier. In our calculations, [H-Fe-CH
3
]
In the C-H stretching region, the vibrational
+
is not a local minimum; it relaxes to Fe (CH
4
). In summary,
] is not likely to be an observable intermediate.
The predicted spectra of the three most stable structures of
spectra are also similar: each spectrum consists of a single peak
due to the symmetric C-H stretch, with stronger, shorter
metal-methane bonds leading to larger red shifts, from
+
[
H-Fe-CH
3
+
+
-1 18
+
-1 19
Fe (CH
4
) are shown in Figure 3 and the calculated vibrational
Al (CH
4
) (2850 cm ) to Mn (CH
4
) (2836 cm ) to sextet
+
-1
frequencies and their intensities are summarized in Table S1.
Fe (CH
4
) (2813 cm ).
3
2
+
+
As seen in the figure, the η and η configurations for the quartet
ii. Fe (CH
)
4 2
. The photodissociation spectrum of Fe (CH
)
4 2
-
1
state have completely different calculated spectra. The calculated
consists of a band at 2670 cm (with a weak shoulder at 2624
3
4
-1
-1
spectrum of the η C
s
( A′′) structure has two intense peaks at
cm ) and a strong band at 3017 cm . These two peaks are
-
1
+
-1
2
685 and 2946 cm and two weak bands at 2786 and 2799
cm . The symmetric C-H stretch vibration of the “bound”
hydrogens (hydrogens pointing toward the Fe ) gives the most
similar to those observed for Fe (CH
band in Fe (CH
4
). However, the 2813 cm
-1
+
+
4
) is not present in Fe (CH
4
)
2
. The B3LYP
+
calculations of Zhang et al. predict that the ground state for
-1
+
4
3
red-shifted peak, at 2685 cm . The weak bands at 2786 and
4 2 g
Fe (CH ) is a quartet, D3d ( E ), with both ligands in an η
2
799 cm- are due to the antisymmetric stretches of these
1
configuration and 2.12 Å Fe-C bond length. They also find
a higher-energy isomer with D2h ( B1g) symmetry and 2.23 Å
26
-1
4
hydrogens. The most intense peak is at 2946 cm and is caused

1
1326 J. Phys. Chem. A, Vol. 114, No. 42, 2010
Citir et al.
+
Figure 4. Calculated structures of Fe (CH
4
)
2
at the B3LYP/6-
3
11+G(d,p) level. Relative energies, in kJ/mol, are in bold.
2
Fe-C bond length in which both methanes are in an η
+
configuration. Our calculations for Fe (CH
4 2
) at the B3LYP/
+
Figure 5. Experimental IR photodissociation spectrum of Fe (CH
4
)
2
3
6
-311+G(d,p) level predict a very similar ground state structure
3
3
4
(bottom), and calculated spectra of quartet η (middle) and sextet η
complexes (top). The maximum calculated IR intensities are 59 and
92 km/mol for the quartet and sextet complexes, respectively.
g
with both methanes in an η configuration. It has C2h ( B )
2
symmetry and 2.12 Å Fe-C bond distance (Figure 4). The η
1
configuration is not a local minimum with the 6-311+G(d,p)
3
basis setsit relaxes to the η configuration. The lowest-energy
3
sextet structure is also η , with C2h symmetry. The Fe-C bond
distance is 2.78 Å, much longer than for the quartet state.
configuration.18,19 We see a similar effect for Fe (CH
+
4 n
) (n )
1
, 2). This is consistent with vibrations on adjacent ligands being
Our calculations predict that the binding energy of methane
only weakly coupled. The calculated splittings between in-phase
+
to quartet Fe (CH
4
) is 84 kJ/mol. This is slightly lower than
and out-of-phase combinations of C-H stretches on different
2
1,25
-1
the experimental values of 97 kJ/mol (CID)
and 108 kJ/
binds more strongly to
Fe than the first. This effect is mostly due to the 24 kJ/mol
CH are calculated to be e10 cm , also indicating that the
4
26
mol (equilibrium). The second CH
4
vibrations of different methanes are independent. This observa-
tion simplifies the assignment of the spectra of the larger
clusters.
+
6
6
+
required to promote ground state D (3d 4s) Fe to the excited
4
7
+
F (3d ) state. In fact, we calculate essentially the same binding
iii. Fe (CH ) . We observe strong photodissociation signals
4
3
+
+
+
energies for the first and second CH
4
to quartet Fe , in accord
4 3 4 4
for Fe (CH ) and Fe (CH ) without using a multipass con-
with the experiments. For comparison, we also calculated the
figuration. This is consistent with the equilibrium measurements
+
26
+
sequential binding energies of CH
spin. They are 40 and 15 kJ/mol for the first and second CH
respectively. These binding energies are much lower than those
4
to sextet Fe , conserving
of Zhang et al. which predict that the Fe (CH ) -CH binding
4
2
4
-
1
4
,
energy is only 21.8 kJ/mol (1800 cm ). Thus, absorption of
one photon in the C-H stretching region leads to loss of CH4
via vibrational predissociation. The photodissociation spectrum
+
+
to quartet Fe . As a result, sextet Fe (CH
4 2
) is calculated to lie
+
8
8 kJ/mol above the quartet state. The Fe-C and C-H bond
of Fe (CH ) is shown in Figure 1. It has an intense absorption
4
3
+
-1
lengths of quartet Fe (CH
4
)
2
are very similar to those of
at 2703 cm , with smaller peaks at 2648, 2803, 2895, and 3015
cm . The lowest-energy peak is red-shifted 269 cm relative
to the 2917 cm symmetric C-H stretch in bare CH . As with
the smaller clusters, the peaks near 2700 cm are likely due to
+
-1
-1
Fe (CH
energies. The Fe-C bond in sextet Fe (CH
longer than in sextet Fe (CH
4
), consistent with the similar first and second binding
+
-1
4
)
2
is significantly
4
+
-1
4
), also consistent with weaker
binding of the second methane in the high-spin complex.
stretching of C-H bonds proximate to the metal, where binding
Figure 5 compares the experimental photodissociation spec-
to the metal weakens the C-H bonds. The broad peaks at 2895
+
-1
trum of Fe (CH
4
)
2
to the calculated spectra for the low-spin
and 3015 cm are near the positions of the C-H stretches in
3
and high-spin η isomers. The calculated vibrational frequencies
bare CH and are likely due to vibrations of the C-H bonds
4
+
and their intensities are given in Table S1. The calculated
pointing away from the metal. As Fe (CH ) has 12 C-H bonds,
4
3
+
spectrum of quartet Fe (CH
4
)
2
consists of two peaks, at 2695
it will have 12 C-H stretches. Depending on the symmetry of
the complex, some of these may be degenerate (or nearly
degenerate) or have very low intensity. To understand the
-1
-1
and 2964 cm . The 2695 cm vibration is due to the out-of-
phase combination of symmetric C-H stretches of the hydro-
+
+
gens pointing toward the Fe . The most intense peak is at 2964
vibrations of Fe (CH ) and determine its structure, we carried
4
3
-1
cm and is due to the out-of-phase C-H stretches of the outside
out geometry optimization and vibrational frequency calculations
for several potential isomers. By comparing the measured and
predicted vibrational spectra, which should be able to determine
+
4 2
hydrogens. The calculated spectrum of sextet Fe (CH ) consists
-1
of a single, intense peak at 2814 cm , which is due to the out-
of-phase combination of symmetric C-H stretches of all the
which isomer(s) are present, and hence energetically favored.
3
+
hydrogens. The simulated spectrum of the quartet η complex
Our calculations for the Fe (CH
)
4 3
complex predict three low-
matches the experimental photodissociation spectrum of
lying isomeric structures at the B3LYP/6-311+G(d,p) level,
+
+
Fe (CH
4 2
) . There is no evidence that the sextet state contributes
shown in figure 6. While the smaller clusters Fe (CH
1
4
)
n
(n )
3
2
to the spectrum. This is not surprising, as the calculations predict
that the sextet complex is much less stable than the quartet
, 2) favor η coordination, η structures dominate for the larger
clusters. We find that the lowest-energy state has C2V ( B )
2
4
complex.
symmetry with two short (2.29 Å) and one long (2.47 Å) Fe-C
+
Bieske and co-workers observe that the spectra of Mn (CH
)
4 n
bonds. This structure is very similar to the ground state found
+
26
and Al (CH
4
)
n
(n ) 1-6) change very little with the number3
by Zhang et al. The other two low-lying structures have C2V
4
4
of ligands, as the complexes are all high spin and adopt an η
1 1
( A ) and C ( A) symmetry with two long and one short Fe-C

+
Vibrational Spectroscopy of Fe (CH4)n
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11327
+
Figure 7. Experimental IR photodissociation spectrum of Fe (CH
4
)
3
(
bottom), and calculated spectra of low-lying isomers. The maximum
4
4
2
calculated IR intensities are 73, 69, and 72 km/mol for the B , A and
4
1
A complexes, respectively.
+
+
Figure 6. Calculated structures of Fe (CH
3
4
)
3
at the B3LYP/6-
result, the calculated spectra of Fe (CH
4 3
) reflect the Fe-C
2
11+G(d,p) level. All the methanes are in an η configuration, except
distance for each methane ligand. This is illustrated by the C2v
A ) structure, which has one short (2.31 Å) and two long (2.39
1
4
3
for the C
1
( A) structure, in which one methane is η . Relative energies,
4
(
in kJ/mol, are in bold.
Å) Fe-C bonds. The most red-shifted peak in the calculated
-1
spectrum (at 2648 cm ) is due to the symmetrical bound C-H
bonds. In the C2V (4B
4
stretches of the methane closest to the iron. The doublet at 2695/
2
1
and A ) structures, all of the ligands
have an η configuration. However, for the C
one methane is η . The lowest energy sextet structure is
calculated to lie much higher in energy, 135 kJ/mol above the
2
4
-1
1
( A) structure,
2706 cm is due to the symmetrical bound C-H stretches of
the other two methanes. They are further from the metal and
thus exhibit a smaller red shift. The smaller peaks at 2732 and
2793 cm are due to the antisymmetric bound C-H stretches
4
of the nearer and more distant CH , respectively. The symmetric
and antisymmetric free C-H stretches give rise to the weak
peaks at 2946 and 3005 cm . The vibrational spectrum,
particularly in the bound C-H stretching region, is very
sensitive to the geometry of the cluster. The peak intensities
appear to reflect the number of short versus long Fe-C bonds,
3
4
3
-1
B
2
state. As expected, it has all three CH
Our calculations predict that there are eight infrared active
C-H vibration bands with intensities of at least 1.0 km/mol
4
in an η configuration.
4
4
-1
for the C2V ( B
2
), C
1
, and C2V ( A
1
) structures, but many of them
-1
overlap at 10 cm resolution. The calculated vibrational
frequencies and their intensities are summarized in Table S1 of
the Supporting Information. In Figure 7, the experimental
spectrum is compared to the predicted spectra of the three
isomers. The simulated spectrum of C2V ( A
coordination and one short and two long Fe-C bonds, is in
excellent agreement with experiment for both band positions
( A) structure may also contribute to
the spectrum, as it shares many peaks with the A
and the spacing reflects the Fe-C bond length. This can be
seen by comparing the vibrational spectra of the B
that of the A . The B structure has two short and one long
1 2
4
4
1
), which has η
2
2
state to
4
4
-1
Fe-C distance. The 2656 cm peak, which is due to the bound
4
and intensities. The C
1
symmetric C-H stretches of the methanes at rFe-C ) 2.29 Å,
4
-1
1
state, but
is more intense than the 2732 cm peak due to the analogous
-1
does not reproduce the 2648 cm peak. On the other hand,
vibration of the methane at rFe-C ) 2.47 Å. In addition, the
splitting between these two peaks is much larger for the B
4
4
although the C2V ( B
2
) is (barely) calculated to be the lowest
energy structure, its predicted peak spacings and intensities are
in much poorer agreement with experiment.
2
4
1
state than for the A . As expected, the C-H red shifts reflect
4
1
changes in the C-H bond lengths. In the A state, the methane
+
2
+
In Fe (CH
4
)
3
each methane is bound to the metal in an η
close to the Fe has bound C-H bond lengths of 1.114 Å,
4
configuration, except in the C
1
( A) structure, and two methane
whereas they are 1.110 Å in the more distant methanes. The
ligands are symmetrical to each other. As was discussed for
free C-H bond lengths are 1.089 Å.
+
2
+
4
Fe (CH ), the vibrational spectrum of an η complex will consist
iW. Fe (CH
4
)
4
. Figure 1 shows the photodissociation spec-
+
of two pairs of peaks. For C-H bonds pointing away from the
metal, the symmetric and antisymmetric “free” C-H stretches
trum of Fe (CH ) in the C-H stretching region. The spectrum
has strong bands at 2711, 2737, 2838, and 2998 cm and a
weak band at 2869 cm . The most intense peak(s) in the
4 4
-
1
-1
-1
lie near 3000 cm . Interaction with the metal causes the
+
-1
symmetric and antisymmetric “bound” C-H stretches to be
Fe (CH
)
4 4
spectrum is the doublet at 2711/2737 cm . This has
-1
+
strongly red-shifted, down to ∼2700 cm . The extent of this
red shift depends on the Fe-C distance. For larger clusters,
the C-H stretches on different methanes are not strongly
a smaller red shift than the corresponding peaks for Fe (CH
4
)
3
,
-
1
which are at 2648 and 2703 cm . This is not surprising as the
methane in the smaller cluster should be more strongly bound
and closer to the metal, leading to weaker C-H bonds.
-1
coupled (e.g., the calculations predict <12 cm splitting between
vibrations consisting of in-phase and out-of-phase combinations
Our calculations identify three low-lying isomeric structures
+
of equivalent C-H motions on different CH
4
ligands). As a
for Fe (CH
4
)
4
. In each case, all of the methanes are bound in

1
1328 J. Phys. Chem. A, Vol. 114, No. 42, 2010
Citir et al.
+
Figure 9. Experimental IR photodissociation spectrum of Fe (CH
4
)
4
(
bottom), and calculated spectra of low-lying isomers. The maximum
4
2
calculated IR intensities are 203, 199, and 166 km/mol for the C A,
4
4
B
2
, and C
1
A complexes, respectively.
-
1
-1
cm ) and ν
2
4 4
+ ν (2845 cm ) bands in bare CH . The positions
of these peaks are nearly independent of cluster size, but their
intensity varies dramatically, depending on their proximity to
C-H stretch peaks, whose position depends strongly on cluster
size.
+
The calculated spectra of Fe (CH
4
)
4
are surprisingly simple,
considering the molecule has sixteen C-H stretches. This
simplicity is due to the fact that all the CH share the same
configuration, with nearly identical Fe-C bond lengths. Also,
vibrations on adjacent CH are very weakly coupled. As a result,
the calculated spectra of Fe (CH
+
Figure 8. Calculated structures of Fe (CH
4
)
4
at the B3LYP/6-
4
2
3
(
11+G(d,p) level. All the methanes are in an η configuration. The C
2
4
4
4
A) and C
1
( A) structures are approximately tetrahedral; the D2d ( B
2
)
4
structure is square planar. Relative energies, in kJ/mol, are in bold.
+
2
4 4
) are analogous to that of η
+
-1
4
Fe (CH ). The band near 2700 cm is due to the symmetric
2
(4A) and C
(4A),
an η configuration. Two of the structures, C
are very close to tetrahedral (Figure 8). The third structure, D2d
), is approximately square-planar. These three isomers have
very similar energies, differing by only 0.5 kJ/mol. Zhang et
al. find a square-planar ground state for Fe (CH ) . Their
4 4
second low-energy calculated structure is tetrahedral, with a
2
1
+
C-H stretch of hydrogens bound to Fe . There are four of these
-1
vibrations, which all lie within 15 cm . The band near 2840
4
(
B
2
-1
cm is due to the antisymmetric C-H stretch of bound
-1
hydrogens. The weak band near 2950 cm is due to the
2
6
+
symmetric C-H stretch of free hydrogens. The corresponding
-1
antisymmetric stretch is at 3002 cm and is extremely weak.
4
4
similar geometry to our C
2
( A) and C
1
( A) structures.
+
In Figure 9, the experimental spectrum of Fe (CH
4
)
4
is
IV. Summary and Conclusions
compared to the predicted spectra for the three low-energy
structures. The three structures have very similar calculated
spectra. The spectrum in the C-H stretching region is sensitive
to the local environment of the methane, and all three structures
+
In this work, we present vibrational spectra of Fe (CH
4
)
n
(n
4
) 1-4) obtained by monitoring loss of CH following IR
photoexcitation. Calculations predict that the positions and
2
have an η configuration, with very similar Fe-C bond lengths.
intensities of bands in the C-H stretching region depend
2
3
However, in this case, the vibrational spectrum is not sensitive
to the configuration around the metal (square-planar vs tetra-
hedral). In fact, the calculations predict that the entire IR spectra
4
strongly on the configuration of the CH (η vs η ) and on the
Fe-C bond length. Thus, we determine the structures of the
complexes by comparing the observed IR photodissociation
spectra to calculated vibrational spectra of low-lying candidate
4
4
of the tetrahedral C
2 2
( A) and square-planar D2d ( B ) complexes
are nearly identical. No single structure reproduces the doublet
observed at 2711/2737 cm . It is likely that the 2711 cm
1
( A) structure. Either one or
both of the other two structures may be responsible for the 2737
cm peak. Another possible cause of the 2711/2737 cm
+
6
structures. Although the ground state of Fe is high-spin D
-1
-1
6
4
7
(3d 4s), the low-spin F (3d ) state, which lies 24 kJ/mol above
the ground state, has a more favorable electron configuration
for noncovalent binding. The vibrational spectra show that all
of the complexes are quartets, in accord with theoretical
the methanes are in an
configuration. In the larger clusters, Fe (CH
Fe (CH ) , the methanes adopt an η configuration. The
vibrational spectrum of Fe (CH ) is consistent with a structure
4 3
4
peak is due to the tetrahedral C
-1
-1
+
+
doublet is Fermi resonance between the C-H stretch and an
overtone or combination band of the C-H bend. The vibrational
predictions. In Fe (CH
4
) and Fe (CH
4
)
2
3
+
η
4
)
3
and
-
43
+
2
spectra of F (CH
4
)
n
(n ) 1-8) provide a textbook example.
(2612
4 4
+
All of the clusters show peaks near the position of the 2ν
4

+
Vibrational Spectroscopy of Fe (CH4)n
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11329
+
with one short and two long Fe-C bonds. In Fe (CH
4
)
4
the
(24) Hendrickx, M.; Gong, K.; Vanquickenborne, L. J. Chem. Phys.
997, 107, 6299.
1
calculations predict, and the photodissociation spectrum is
consistent with, structures in which all of the Fe-C bond lengths
are very similar.
(
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9
Acknowledgment. Financial support from the National
Science Foundation under award CHE-0911225 is gratefully
acknowledged.
(
28) Metz, R. B. Int. ReV. Phys. Chem. 2004, 23, 79.
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29) Husband, J.; Aguirre, F.; Ferguson, P.; Metz, R. B. J. Chem. Phys.
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(
Supporting Information Available: Calculated harmonic
(
+
vibrational frequencies and intensities for Fe (CH
4
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n
(n ) 1-4)
L.; Perry, D. S. Appl. Opt. 1990, 29, 119.
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