Energy Factored Force Fields

I ) These modes all correlate to some extent with each other and with modes of all three symmetry types in M CO)6. 

There is no lack of well-analysed model systems with which to compare a proposed assignment (7). Laser Raman instruments are commercially available. 

There remain the carbonyls of the second class. This includes all complexes containing carbonyls in chemically different environments for which, as shown above, A is necessarily repeated, as well as a few polymeric carbonyls, such as [Mn(CO)3SR]4 13) and [Ir(CO)3]4, in which the representation Tz of Ta is repeated 21, 22). 

Faced with an underdetermined problem, one can impose enough constraints on the solution to render it formally determined one can decide to settle for less than a complete solution or one can seek additional information. The only useful source of additional information is isotopic substitution, given the difficulties associated with intensity studies both isotopic substitution and intensity studies are discussed below. 

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The energy factored force field for carbonyls contains interaction parameters as well as stretching parameters. Such parameters are invariably required to be positive, for CO groups attached to the same metal, by the experimental finding that symmetric combinations of the individual CO vibrations occur at higher frequencies than similar antisymmetric combinations. 

Correlation with higher frequency component of precursor spectra, based on form of energy factored force fields. 

The approximate solutions to the energy factored force field offered by the approximations of Cotton and Kraihanzel (7, 8) and by van der Kelen and his colleagues 31, 32) are compared in Table (5) with the results of isotopic substitution studies. For purposes of comparabihty, all results are based on the same data i.e. the approximate parameters have been re-calculated for this work from the all —12C160 data of the more exact studies. 

The equations were solved analytically after substitution of the assumed relationships of interest into the exact energy factored force field. For the Cotton-Kraihanzel treatment of species M(CO)5X, v B2) was not used. In the corresponding treatment of species cw-M(CO)4X2, the expressions for K(Bi), K Bz), and K A ) - -K A were used this procedure means that all the available data are used, as well as obviating the need to solve a quadratic. 

This approach was first described in detail by Cotton and Kraihanzel in 1962. The Cotton-Kraihanzel Force Field (CKFF) was very quickly taken up by workers in the field and extensively used as a tool for analyzing v(CO) frequencies to produce force constants that made chemical sense and were readily accessible. Now, with its application in metal nitrosyl and dinitrogen spectroscopy the CKFF often appears under the more general name of the Energy Factored Force Field (EFFF) or Frequency Factored Force Field (F ). An equally important paper, by Haas and Sheline, followed Cotton s pioneering work and investigated the mathematics rather more fully, and facilitated work on isotopic species. 

Table 7 Energy factored force fields of mononuclear carbonyl complexes...

Pentacarbonyliron(O) is the best known example of a pentacarbonyl complex. Others in this category include [Mn(CO)5] , [Cr(CO)5] , Ru(CO)s, and Os(CO)5. As they have D h symmetry (see Table 17), the energy factored force field requires five force constants bnt there are only four v(CO) frequencies (only two of which appear in the infrared) so the force field is underdetermined. Two of the v(CO) modes are fully symmetrical (a[) and are IR-inactive. The asymmetric stretches are labeled a 2 (due to the stretching of the axial CO groups) and e (due to stretching of the equatorial CO groups). The e mode is IR and Raman-active the a 2 mode is active in the IR only. 

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