Strain energy difference

A further complication associated with the application of molecular mechanics calculations to relative stabilities is that strain energy differences correspond to A(AH) between conformers with similar chromophores (electronic effects) and an innocent environment (counter ions and solvent molecules), whereas relative stabilities are based on A(AG). The entropy term, TAS, may be calculated by partition functions,... 

The redox potentials and the strain energies at the cobalt(III) and cobalt(II) oxidation states of die most stable conformers of a number of hexaaminecobalt(III/II) complexes are listed in Table 10.1. The strain energy difference between the two oxidation states was found to correlate with the experimentally determined reduction potential11331. Fig. 10.2 shows a plot of the redox potentials of the hexaaminecobalt(III/II) complexes from Table 10.1 as a function of die strain energy differences between the oxidized and reduced forms. The experimentally determined redox potentials are given as solid points while the line corresponds to the calculated potentials. Based on Eq. 10.1,... 

Fig. 10.2. Experimentally determined redox potentials of the hexaaminecobalt(III/II) complexes from Table 10.1 as a function of the strain energy difference between the oxidized and reduced forms11321.

The three isomers of [Co(dien)2]3+/2+ have, as predicted by molecular mechanics calculations (see also Table 7.1 in Chapter 7, Section 7.1 for calculated and observed isomer ratios of [Co(dien)2]3+), measurably different redox potentials1415. However, the strain energy differences between various conformers of each isomer were calculated to be too small for a measurable difference of the redox potentials, and the order of stability in both oxidation states was the same[44]. A similar problem occurred with [Co(sep)]3+/2+t44]. For [Co (S)-pn 3]3+/2+ the four redox potentials between isostructu-ral pairs lie within the predicted range of 20 mV However due to lack of resolution, a quantitative analysis was not possible. An unambiguous proof of the model is, therefore, still lacking. 

Breton also calculated the strain energy difference (AEstrain) which is localized within the diazetine ring itself. 

With most metal ions the complex stability decreases as the size of the chelate rings formed by open-chained polyamine ligands increases from five to six mem-bered. Examples of this effect are presented in Table 9.1, where experimental data are compared with predictions based on strain energy differences between metal-free and coordinated ligands (Eq. 9.1). 

Once the corrected strain energy differences have been calculated they can be used to determine the isomer proportions using Eq. 17.4.1. For example, the difference between the statistically corrected energies of the lel3 and lel2ob conformers is -1.65 kJ mol1. Thus, Eq. 17.4.1 becomes ... 

The electronic contribution to A(AG ) (metal-donor bonding) for a set of similar compounds (identical metal center, same type of donor, similar coordination polyhedra, e.g., hexaaminecobalt(III/II) couples with variable amines) is only dependent on the metal-donor distance, i.e., A(AGc) is correlated with the strain energy difference between the oxidized and the reduced forms of the couples. 

If these assumptions are valid, then the major contribution to AG° for redox couples with identical metal centers and similar ligands is the strain energy difference between the oxidized and the reduced forms of the complex (AC/strajn), and the neglected terms vary roughly linearly with A 7strai . 

Theoretically, each pair of conformers of a redox couple will lead to a specific and different reduction potential (see Fig. 17.18.1). However, if the variation in strain energy difference A /Strain is small the difference in reduction potentials will generally not be resolved experimentally. On the other hand, large strain energy differences AC/strain will usually lead to situations where the less stable conformer is not abundant enough to be observed. Thus, there has only been one report so far, where more than one reduction potential has been resolved experimentally (see Section ll.l)[310l... 

We now need to set up and refine the corresponding files for the reduced forms. Save the refined coordinates (. out files) of each of the structures with a new name (e. g. co2 a6.hin). This can be done in Edit/View/HyperChem File with the usual Save as command. Open Tools/Set Metal Type for each of the new files and change the Oxidation state from III to II. Refine the structures, calculate the strain energy differences between the oxidized and the reduced forms for the most stable conformers, calculate the reduction potentials using Eq. 17.18.5 and compare the results with those in Table 17.18.1. 

Fig. 47. Plot of the strain energy differences versus the observed redox potential for hexamine Co- 2+ couples [237].

The strain energy values that SpartanBuild calculates have another use besides structure refinement. They also can be used to compare the energies of models that share the same molecular formula—that is, stereoisomers or conformational isomers. Allowed comparisons are shown below. Strain energy differences between these pairs of molecules correspond closely to differences in heat of formation and to differences in free energy. SpartanBuild reports strain energies in kcal/mol (1 kcal/mol = 4.184 kj/mol) in the lower left-hand corner of the SpartanBuild window. 

For systems where hydrogen-bonding interactions are not of great importance as far as the CD is concerned, but dipolar interactions are important, it is theoretically possible to determine the strain-energy difference and the dipolar-interaction... 

AGS is the strain-energy difference, AV is the dipolar-interaction energy difference, and D is the dielectric constant. If both R j and Rjj are known, AGS and AV can be determined by plotting the left-hand side of equation 2 against l/D. This should be a straight line with slope AV and intercept AGS. If only R is known, the above plot is repeated for various values of R-j-j. The value that gives the best straight line relationship is chosen for R.jj. 

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