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The compliance matrix (inverse force constant matrix) has been used to estimate metal–metal bond character for the homoleptic transition metal carbonyls Fe 2 (CO)  n   and Co 2 (CO)  n  . The results are often in agreement with other methods, but the compliance matrix provides a unique measure while other methods may be ambiguous. The more unsaturated compounds with fewer carbonyls have stronger metal–metal linkages, indicating a general, if not infallible, correlation between the diagonal compliance matrix element and the formal bond order, given by the 18-electron rule. It is found that the apparent metal–metal bond strength, as judged by the compliance matrix, is significantly enhanced by the bridging (as opposed to terminal) carbonyls. Thus one must only make precise comparisons between systems with the same numbers of bridging carbonyls.

The Characterization of Metal–Metal Bonds in Unsaturated Binuclear Homoleptic Transition Metal Carbonyls. The Compliance Matrix