Fermi resonance distortion of the Ru–CO stretching mode
of CO adsorbed on Ru„001…
P. Jakob
Physik Department E 20, Technische Universita
¨
tMu
¨
nchen, D-85747 Garching, Germany
͑Received 27 October 1997; accepted 22 December 1997͒
A Fermi resonance of the Ru–CO stretching mode and the combination band of the hindered
rotationϩhindered translation mode of adsorbed CO on Ru͑001͒ has been detected using infrared
absorption spectroscopy. The Fermi resonance has been unambiguously identified through isotopic
substitution experiments at various CO coverages. Clear evidence for a delocalized nature of the
Fermi resonance is found. © 1998 American Institute of Physics. ͓S0021-9606͑98͒02412-X͔
INTRODUCTION
Fermi resonances ͑FR͒ are well-known distortions in vi-
brational spectroscopy. Briefly, they can be classified as
avoided crossing phenomena of sublevels with identical
symmetry properties. As a result of this coupling the charac-
ter of the individual normal modes changes; the extent of this
mixing depends on the relative strength of the interaction as
compared to their spectral separation.
1
Such a FR mixing of
vibrational states has important implications on the dynamics
of vibrational modes and has been treated theoretically in
great detail for polyatomic hydrocarbon molecules.
2
Due to
the enhanced coupling strength between the contributing
modes intramolecular energy transfer and phase relaxation
processes can be substantially accelerated.
There have been a number of reports on Fermi reso-
nances of various molecular adsorbate species in the past.
3–6
Many of them are associated with CH
3
subgroups for which
an overtone of the C–H bending modes approximately
matches in frequency with the C–H stretching modes
C–H
;
3–5
for molecules containing methyl subgroups the oc-
currence of FR coupling is therefore well established from
gas phase studies. Irregularities in the region of
C–H
modes
as compared to the
C–D
bands can thus be accounted for.
Full clarification of mode coupling schemes, however, re-
quires the usage of partially deuterated CHD
n
species.
4,7
Cases with one contributing mode being associated with
the substrate bond have no counterpart in the gas phase and
reported examples are rare.
5,6
For small molecules observa-
tion of FR is particularly difficult because of the stringent
frequency matching condition. In general, the separation
␦
of
the undistorted modes should be of the order of the interac-
tion splitting W
ab
in order to be detectable. The line posi-
tions then are located at
EϭE
¯
Ϯ
1
2
ͱ
4
͉
W
ab
͉
2
ϩ
␦
2
,
where E
¯
denotes the center of the two undistorted bands.
1
W
ab
represents the coupling term between the two modes
͉
⌿
1
͘
and
͉
⌿
2
⌿
3
͘
and in first order perturbation theory is
given by the integral W
ab
ϭ
͐
⌿
1
␣
123
⌿
2
⌿
3
d
3
r with ⌿
i
la-
beling the unperturbed component fundamental wave func-
tions and
␣
123
is the cubic order anharmonic coupling term
in the Hamiltonian. This interaction generally causes an ap-
parent repulsion of the two bands forming the Fermi reso-
nance. Infrared absorption can therefore result from a direct
͑dipole allowed͒ transition of
͉
⌿
1
͘
or through the second
derivative of the dipole moment which leads to excitation of
͉
⌿
2
⌿
3
͘
. Both vibrational states interact through the anhar-
monic coupling constant
␣
123
which causes a mixing of their
respective wave functions.
␣
123
is therefore a measure on the
transfer time of a vibrational excitation oscillating between
͉
⌿
1
͘
and
͉
⌿
2
⌿
3
͘
.
For isolated diatomic molecules with only a single inter-
nal stretching mode Fermi resonances exist only for vibra-
tional levels of different electronic states. For diatomic ad-
sorbates, extra modes corresponding to hindered translations
and rotations are present and FR may exist within the elec-
tronic ground state as well. The question why FR are gener-
ally not observed for diatomic molecules adsorbed on a sur-
face even though, at first thought, they might be expected has
been discussed at length in a recent paper of Burke and
co-workers.
8
This article mainly concentrates on the role of
FR on the dephasing linewidth of the metal–CO stretching
mode (
M–CO
). It has been argued that
M–CO
and the com-
bination band of the hindered translation and rotation modes
CO
(ϭ
CO
ϩ
CO
) should yield approximately the same fre-
quency and might form a FR pair.
9
Extensive studies of vari-
ous linearly bonded CO/metal systems have been performed
so far, however, without any indication of such a FR;
8
the
continued lack of its detection therefore remained mysteri-
ous. One of the central results of Ref. 8 was that consider-
ation of the non-rigidity and the anharmonicity of the inter-
nal C–O bond when
M–CO
is excited strongly reduces the
coupling strength of a hypothetical FR pair which renders the
second mode of the FR, i.e., the weak combination band,
unobservable. Another consequence would be negligible
mixing of the two modes. Only very recently such a Fermi
resonance has been reported
6
͑and questioned
10
͒ for bridge
bonded CO on Pt͑111͒.
In the present paper it is unambiguously shown that,
despite the challenged validity of the CO/Pt͑111͒ interpreta-
tion, such a Fermi resonance of the metal–CO stretching
mode and the
CO
combination band can be observed for
() ϫ))CO/Ru(001). Clear evidence for a delocalized na-
JOURNAL OF CHEMICAL PHYSICS VOLUME 108, NUMBER 12 22 MARCH 1998
50350021-9606/98/108(12)/5035/9/$15.00 © 1998 American Institute of Physics