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Morceno Y. Dorensbourg' 
Infrared Determination 
and Donald J. Dorensbourg' 
Vassar College I of Stereochemistry in Metal Complexes 
Poughkeepsie, New York 12601 
I 
An applicafi.on of group theory 
There has been a considerable volume of 
research centered around the syntheses of and bonding 
in substituted metal carbonyl complexes (1-5). Usually 
characterization of these complexes is partially, if not 
wholly, ascertained by studying the CO stretching fre- 
quencies in the infrared region of the spectrum. This 
paper is designed to introduce the reader to the uses 
(and limitations) of group theory in conjunction with 
infrared spectroscopy in assigning stereochemistry to 
transition metal carbonyl complexes. Although the 
CO stretches are employed in this discussion, an identi- 
cal approach can be taken for the metal-carbon 
stretches, as well as other metal-ligand stretching vibra- 
tions. 
It is felt that most chemistry curricula can accom- 
modate an introduction of these concepts to the ad- 
vanced undergraduate student without any difficulty. 
Selection Rules and Group Theory 
The number of vibrational degrees of freedom for a 
non-linear molecule is 3n - 6, where n = number of 
atoms which make up the molecule. This formula 
gives the number of fundamental vibrational fre- 
quencies of the molecule, or, in other words, the number 
of different normal modes of vibration. These originate 
in the transition from v = 0 to v = 1 in the electronic 
ground state. 
The quantum mechanical probability of a vibrational 
transition occurring between states J.,' and J.," is 
given by the following expression 
Here we assume that the interactions between the elec- 
tronic, rotational, and vibrational states are negligibly 
small and may be ignored. This allows us to carry 
out the integration over the vibrational coordinates 
only. The dipole moment M can be broken down into 
its Cartesian components, Atz, M,, and M,. These 
transform under the symmetry operations of the point 
group to which the molecule belongs in the same manner 
as the corresponding translation coordinates, T,, T,, 
and T,. The representations to which these belong are 
given in the character tables. 
General Vibrotional Selection Rule for Infrared 
A vibrational transition between states J.,' and J.," 
is allowed only when there is at least one component of 
the dipole moment M which has the same symmetry 
species as the product J.,' J.,". Since J.," is totally 
1 Present address of both authors, Department of Chemistry, 
State University of New York at Buffalo, Buffalo, New York. 
symmetrical if u = 0, when we're considering a vibration 
from v" = 0 to u' = 1 the product J.,' J.," will always 
have the symmetry of J.,'. J..' must have the sym- 
metry of one of the components M,, At,, or M, in order 
for the vibration to be infrared active. 
Therefore with the aid of the character table for the 
point group to which the molecule belongs, the sym- 
metry selection rules for infrared transitions can be 
readily determined. 
Prediction of lnfrared Active CO Vibrations 
In the substituted metal carbonyl compounds we can 
separate out the CO stretching motions from the M-C 
stretches and M-C-0 bends due to the large energy 
separation in these vibrations. The CO stretches 
generally occur at around 2000 cm-' whereas the M-C 
stretches and M-C-0 bends are observed between 300 
and 700 cm-'. Therefore instead of looking at all 
3n - 6 vibrations only the four CO stretching motions 
will be considered for the i\l~(CO)~h molecules we 
have chosen to use as illustrations. 
Assignment of the molecular symmetry to its proper 
point group is the necessary first step in our analysis 
(4,6). 
The ~is-Mo(C0)~L~ complex is ideally of C2, sym- 
metry, considering L as a point ligand, i.e., neglecting 
the symmetry of L itself. (The inherent limitations of 
this assumption will be discussed later.) 
The CO stretches are drawn as arrows in Figure 1. 
Each of the operations of the Cz. point group are per- 
formed on the arrows and the character (x) contribut- 
ing to the total reducible representation is obtained by 
taking the trace of the transformation matrix in each 
Figure 1. Symmetry elements and numbering scheme for the cis-Mo- 
(COldr ICnJ molecule. 
Volume 47, Number I, January 1970 / 33 
case. Working through this the transformation ma- 
trices are found to be as follows 
X," = 2 x,.' = 2 
Thus we find the reducible representation to be 
Note that the reducible representation could be 
found with less effort by realizing the character for each 
operation is simply the number of unshifted arrows 
for that operation. For example, the E operation 
leaves all 4 arrows unshifted; the a, operation changes 
arrows 2 and 3 into each other but leaves 1 and 4 un- 
shifted; etc2 
The reducible representation is broken down into its 
irreducible components with the aid of the CZ, character 
table (Table 1) and the reduction formula 
Where n.,.,i.. is the number of times the species (A1, 
B1, etc.) in question contributes to the total reducible 
representation; g is the ordcr of the group, or, the 
total number of symmetry operations in the group; 
gt is the number of operations in the symmetry opera- 
Table 1. 4, Character Table 
Ax 1 1 1 1 T, a,,, a,,, a,, 
A2 1 1 -1 -1 R, ~ZY 
B, 1 -1 1 -1 T,R, all 
Be 1 -1 -1 1 T,, Ri %* 
Table 2. Observed CO Stretching Frequencies6 
Compound 
K(CO),DTH 
Frequencies 
(om-') 
Saturated 
hydrocarbon= 
Saturated 
hydrocarbon. 
s, strong; sh, shoulder; w, weak; vs, very strong; vw, 
verv weak 
These are illustrated in Figures 3 through 5. 
bThe CO vibrations suffer a substantial broadening in polm 
8olvents. This can result in severe overlapping of bands and 
may lead to misinterpretation of the number of bands present in 
a. spectrum. Therefore, when at all possible, the spectra, should 
be measured in satorated hydrocarbon solutions. 
'A slight heating is necessary to obtain d~ssolntion. 
Only seen under high resolution conditions. 
tion class i, i.e., the number before each operation in 
the table (all are one for the Cz. character table, however 
for D4h for example gt is 2 for the Cp operation); xmduoibto 
is the total character for each operation found in 
rledUlible; and XX~IP is the character of each symmetry 
operation in each species. Use of the formula is illus- 
trated below. 
And therefore 
ri.rsducibte = 2A1 f BI + Bn 
From the C2&haracter table one finds that each of 
these contributing species are infrared active since they 
all transform as does one of the components of the 
dipole moment ~perator.~ 
Figure 2. Symmetry coordinofer for he CO modes in the cis-Mo(C0kC 
molecule; tr (stretch), -c (contraction). 
These vibrations are depicted in Figure 2. The Al 
vibrations are totally symmetrical and therefore none of 
the arrows change signs when the symmetry operations 
are performed. However, examination of the Cz, 
character table tells us that the stretches for the Bl 
vibration should change signs upon C2 rotation and re- 
flection in the a,' plane. Whereas those for the Bz 
vibration change upon Cz rotation and a, reflection. 
It is easily seen that the CO stretching motions drawn 
in Figure 2 comply with these requirements. 
Since the two A1 modes are of the same symmetry 
and similar in energy, they are strongly coupled. 
Symmetry forbids however any coupling between B, or 
Bz with each other or with the A, vibrations. 
The observed infrared spectrum of Mo(CO)~DTH, 
where DTH is the hidentate ligand dithiahexane,' is 
shown in Figure 3. The spectrum of the complex pre- 
pared from the reaction of MO(CO)~DTH with tri- 
phenylphosphite, ~is-Mo(C0)~ [P(OCBHS)3]2, is shown in 
2 It is worth noting here that if dl 371 - 6 vibrations were con- 
sidered, in order to obtain the reducible representation (F.,auciup) 
it would only be necessary to count the number of unshifted 
(or unperturbed) nuclei when the symmet,ry operations were 
performed. After this the procedures would be the same. 
The Raman sctive modes can be determined by finding which 
of these species transform as does one of the components of 
polarimbility (aij) found in the character table. In this case all 
bands are Raman sctive also. 
34 / Journal of Chemical Education 
Figure 3. CO frequencies of Mo(COItDTH in CHCls. 
Figure 4. Frequency values for these complexes, as 
well as for ~~~~~-MO(CO)~[P(OC~H~)~]~, are listed in 
Table 2. Many similar spectra of cis and trans-Mo- 
(CO)&L2 compounds may be found in the literature (6). 
Although the number, activity, and description of 
the CO stretching motions are readily worked out as 
described above, their assignment to observed bands 
is not always obvious. In many cases formally allowed 
transitions are of low intensity or many are accidentally 
degenerate with other allowed modes, thereby reducing 
the number of bands observed. The reader is referred 
to an often quoted article by Cotton and Kraihanzel(7) 
which outlines rules that are helpful in making these 
assignments. From these it is concluded that the 
frequency of Al") > BI, AI'~' > Bz, and AI"' > A1C2). 
Whether or not the A1@) is greater or less than B1 is not 
easily predicted. In fact, both orders haye often been 
observed. 
Finally the reader is encouraged to carry out the 
described procedure on the trans-Mo(CO)aLz molecule 
which is ideally of Du symmetry. When this is done 
one finds that ri,. = Al, + BI, + E., and the E, mode 
is the only one that is infrared acti~e.~ However, for 
the molecule trans-Mo(C0)r [P(OC6H&]z, perturbation 
by the P(OCsH& groups removes DPh symmetry, and 
the A,, and El, gain slight allowedness and show up as 
weak bands as is seen in Figure 5. The perturbation is 
small so that the E species mode is not noticeably split. 
The fact that for the trans isomer only one active band 
is predicted whereas in the cis strncture four bands are 
expected points out a general rule for infrared activity: 
the more symmetk the molecule, the fewer infrared active 
bands are to be expected. 
The authors are grateful to the Climax Molybdenum 
' DTH = CHsSCH,CHBCHa. 
'The A,, and the B,, are Raman active whereas the E, is 
Raman inactive. This illustrate another symmetry stipulation, 
that is, for molecules having a center of symmetry (an i sym- 
metry element) there can he no bands that are both Rarnan and 
infrared active. Those that are not infrared active will he 
Raman aotive and those that are infrared active will he Raman 
inactive. 
Figwe 4. CO freqvensier of cis-Mo(COI4[P(OCsHs)31~ in *ohrated hydro 
carbon. 
Figure 5. 
CO frequencies of fran*.Mo(CO),[P(OCsHslr]z in muroted 
hydrocarbon. 
Co. for their generous gift of molybdenum hexacarbonyl. 
One of us (M.Y.D.) thanks the Petroleum Research 
Fund administered by the American Chemical Society 
for financial support. 
Bibliography of Selected General References 
COTTON. F. A,. "Chemical Applications of Group Theory:' Intersoienoe 
Publishers, (division of John Wiley & Sons. Ino.). New York. 1963. A 
complete set of character tables included. 
COTTON, F. A,. AND WILYINBON. G.. ''Ad~&nced Inorganic Chemistry:' 
(2nd Ed.), Interscienoe Publishers, (division of John Wiley & Sons, Ino.). 
New York. 1966. 
Dn~ao. R. 8.. "Physioal Methods in Inorganic Chemistry," Reinhold Pub- 
lishing Co., New Yark, 1965. 
NAUMOTO, K., "Infrared Speotra of Inorganic and Coordination Com- 
pounds." John Wilev & So-. Inc.. New York, 1963. 
literature Cited 
(1) Aseb. E. W.. Quart. Rcu. (London) 17, 133 (1963). 
(2) DosaO~. G. R., STOLZ, I. W.. AND SHELINB, R. I<.. Aduan.InoW. Cham. 
Rodiochem.. 8, 1 (1966). 
(3) MANUEL, T. A,, Aduon. in Oroanomlallie Chem.. 3, 181 (1966). 
(4) ZILDIN, M., J. CXEY. EDOL. .. 43, 17 (1966). 
(6) BARROW, G. M., "Physioal Chemistry," (2nd ed). MoGra~Hill, New 
York,1966,Chapter13. 
(6) COTTON. F. A,, I~OTB. Chem.. 3. 702 (1964). 
(7) COTTON, F. A,, AND KRAIHIN~L C. S., .I. Am. Chem. Soe., 84, 4432 
(1962). 
Volume 47, Number I, January 1970 / 35 
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