Estimation effective cluster interactions

Figure 7.13. Estimated fractional change in the ordering temperature resulting fiem incorporating the effect of ordering on the vibrational spectrum by an additional effective cluster interaction (ElCIvib) (Gaibulsky and Ceder 1996).

From the biological area, iron-sulfur clusters in biomolecules such as rubredoxin mononuclear Fe-S clusters (Rao et at., 1972), plant-type ferredoxin 2Fe-2S clusters (Johnson, 1975) and bacterial-type ferredoxin 4Fe-2S clusters (Thompson et at., 1974) are readily distinguished from one another by their Mossbauer spectra. The temperature dependence of relaxation effects can provide information about the types of internuclear interaction and can even lead to estimates of the distance between paramagnetic sites, for example, the two 4Fe-4S clusters in ferredoxin in Peptococcus aerogenes (Adman etal., 1973). 

The reader may have noted that experi mental spectra of H-bonded species are com monly measured in either the gas phase or in inert gas matrices. Of course, there may be some differences as the molecules of the matrix can interact in various ways with the H-bonded complex. A recent set of measurements provides some estimates as to the perturbations caused by the matrix. Table 3.39 reports in the first row the frequencies of the OH stretches of the free and bridging hydrogens of the proton donor molecule of the water dimer in the gas phase. The next row indicates that a Ne matrix has only a very small effect, perhaps 10 cm . The Ar and Kr matrices produce larger perturbations, reducing the frequencies by about 30 cm . A smaller cluster of Ar atoms, averaging perhaps 50 such atoms yields a result very much like a full Ar matrix. With the single exception of the very small increase for the free OH stretch in the Ne matrix, all matrices and the Ar cluster lower the frequencies of both of the modes studied. 

A powerful impetus in the calculations of the interactions between water molecules in a condensed phase has been provided by quantum mechanical ab initio methods. Indeed, the advent of powerful computers provided the opportunity to use quantum mechanical ab initio methods for large clusters of water (containing up to several dozen water molecules). In addition, quantum mechanical ab initio methods are the only ones which allow one to calculate separately the energy contributions from the interactions between two, three, and more molecules and therefore allow one to make a direct estimate of the cooperative effect. 

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