Cotton-Kraihanzel method

When there is only me CO-stretching vibration belonging to a particular symmetry species, a constant K is obtained from the expression Xg= K using the Cotton-Kraihanzel method. This can be related to the correction terms a, j8, and y discussed above by the equation ... 

These approximations discussed above are important in attempting an assessment of the validity of the Cotton-Kraihanzel method. Thus, force constants calculated by this simplified approach for the compounds M(C0)e (M = Cr, Mo, or W) were compared with the values obtained using the complete secular equations and a more rigorous force field (195). Considerable discrepancies in the CO stretch-stretch interaction constants were noted. Furthermore, 8 values have been calculated (d ) and were found to be of the same order of magnitude as the CO stretch-stretch interaction constants. Thus, the possibility that 8 values are significant must be considered in discussing the applications of the Cotton-Kraihanzel force field. 

The Cotton-Kraihanzel method has been applied extensively to systems for which two of the CO-stretching fundamentals belong to the same symmetry species. A mathematical treatment of the secular equations governing such systems has been developed which facilitates force constant calculations (15, 52, 128, 185). This is now described and its usefulness will be demonstrated later. 

Using a simpler approach which elaborated upon earlier proposals 42), Cotton and Kraihanzel 39, 41, 95) assumed that the carbonyl oscillators could be factored out both electronically and mechanically from all other molecular vibrations, and that only electronic coupling among the individual carbonyl bonds need be considered. In addition, they introduced relationships, similar in origin to those proposed by Jones 80, 82), in order to reduce the number of carbonyl bond stretching force constants. Because of its simplicity and qualitative success, the Cotton-Kraihanzel method (CKM) has been applied widely, but it has also been the subject of some controversy 22, 24, 40, 43-45, 78, 79, 83). What is beyond dispute, however, is that its use has brought to the attention of the chemist the variations in, and possible... 

Carborane-metal complexes, 8, 87-113 Catalysis by organometallics carbonylation, 6, 158-163 hydroformylation, 6, 128-136 olefin reactions, 7, 199-202 organic syntheses by nickel compounds, 8, 48-83 reviews, 10, 331-336 Cationic metal carbonyls, 8, 117-159 Chromium carbonyls, 8, 133-159, see also Benchrotrenes Cobaloximes, 7, 161, 203 Cobalt carbonyl, 6, 119-163 8, 152-155 Cotton-Kraihanzel method, 10, 213-214 Coupling reactions, on nickel, 8, 30-39, 82-83... 

The period under review has seen a small, but apparently real, decrease in the annual number of publications in the field of the vibrational spectroscopy of transition metal carbonyls. Perhaps more important, and not unrelated, has been the change in perspective of the subject over the last few years. Although it continues to be widely used, the emphasis has moved from the simple method of v(CO) vibrational analysis first proposed by Cotton and Kraihanzel2 which itself is derived from an earlier model4 to more accurate analyses. One of the attractions of the Cotton-Kraihanzel model is its economy of parameters, making it appropriate if under-determination is to be avoided. Two developments have changed this situation. Firstly, the widespread availability of Raman facilities has made observable frequencies which previously were either only indirectly or uncertainly available. Not unfrequently, however, these additional Raman data have been obtained from studies on crystalline samples, a procedure which, in view of the additional spectral features which can occur with crystalline solids (vide infra), must be regarded as questionable. The second source of new information has been studies on isotopically-labelled species. 

Following the discovery in 1972 by Turner and co-workers 18) that Cr(CO)5 could form complexes with CH4, Poliakoff and Turner used matrix isolation and infrared spectroscopy 19) to study the photolysis of Fe(CO)5. Photolysis of Fe(CO)5 in a neon or argon matrix produced Fe(CO)4, which was found to have a relatively unusual structure with C2v symmetry. The energy-factored (or Cotton-Kraihanzel) force field (EFFF) is a powerful method used in the analysis of the... 

The effort required to obtain results of the kind just discussed is so great that there have been many attempts to devise some simple method of calculating useful force constants from limited data and by simple means. The most widely used of these simple methods is that commonly called the Cotton-Kraihanzel (CK) method,19 although very similar approximations have been suggested by others.20 The most important approximation is that CO force constants can be calculated from the CO stretching frequencies alone because these are at very much higher frequencies (> 1850 cm 2) than all other vibrations (< 700 cm-1) in simple metal carbonyls as well as most substituted carbonyls. The main effect of this approximation is that the force constants so obtained are not absolute but in a series of related molecules the shift from absolute values will probably be essentially constant. Hence, relative values, and, thus the differences between force constants for different but similar molecules should be rather reliably given. 

Understandably, the force constants obtained by the GVFF method differ from those calculated with the help of the Cotton and Kraihanzel approximation (1962, 1963, 1964). However, the latter form a reasonable basis on which to compare similar molecules. 

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