Thermodynamics of some long-chain biradicals studied by EPR spectroscopy

Abstract: An improved force field for molecular mechanics calculations of the structures and energies of hydrocarbons is presented. The problem of simultaneously obtaining a sufficiently large gauche butane interaction energy while keeping the hydrogens small enough for good structural predictions was solved with the aid of onefold and twofold rotational barriers. The structural results are competitive with the best of currently available force fields, while the energy calculations are superior to any previously reported. For a list of 42 selected diverse types of hydrocarbons, the standard deviation between the calculated and experimental heats of formation is 0.42 kcal/mol, compared with an average reported experimental error for the same group of compounds of 0.40 kcal/mol. I t has been now amply demonstrated that force field calculations offer the method of choice for the determination of the structures and energies of molecules under many circums t a n c e ~ . ~ ~ While many previously published force fields are very good, they do contain errors which are sufficiently large as to be worrisome to those wishing to utilize them to the fullest possible extent. While the organic chemist is primarily interested in compounds which contain functional groups, since the fundamental structure of organic molecules in general is hydrocarbon in character, a high degree of accuracy in the hydrocarbon part of the force field is crucial. “First generation” force fields showed that one could indeed calculate accurate structures and energies, although the fit to experiment was in some cases less good than one would desire. There has been some difficulty in ascertaining exactly where the force fields were in error, and in which cases the experimental data were less accurate than the probable errors indicated. This question is still not fully answerable but, clearly, more and better data have become available in the last several years. The best we can do is to utilize the existing data, and point out where we feel that there may be errors. We will discuss herein three of the earlier force fields. These are our earlier force field M M l ( 1973)3 and the most recent force fields by Schleyer (EAS)5b and Bartell (MUB-2).6 For all of their usefulness and accuracy, these force fields contained various flaws which showed up in different ways. In an effort to minimize the discrepancy between calculations and experiment, the van der Waals characteristics of atoms were important quantities to be evaluated. In Figure 1 is shown a graph taken mainly from a recent paper by Bartel16 in which the force exerted by a pair of atoms as a function of distance is plotted for several different force fields including MUB-2, EAS, and M M I . For present purposes we will define a “hard” atom as one for which the plot of the force vs. distance for the repulsive part of the curve shows a steep slope (as the dashed C/C line in the figure), and a “soft” atom as one where this slope is more gentle (as the solid line). We will also define a “bigger” atom as one where the line is slid farther to the right, and a “smaller” atom as one for which it is slid to the left. With this terminology, it is seen from the graph that in M M I we used a hydrogen atom which was both rather hard and large compared to that used by Bartell (and other workers), while we used a carbon atom which was small. The “hardness” of our curves was determined by the Hill equation, which is known to fit well for interactions between rare gases.’ There is no assurance that such curves are ideal for carbon and hydrogen atoms which are covalently bound. However, they seemed like a reasonable choice in the absence of definite information. Bartell, mainly on the basis of theory, chose a much softer hydrogen.8 Most other workers have been inclined to follow Bartell’s lead. Bartell’s more recent choice (bVIUB-2) is based on theoretical calculations by Kochanski9 on the Hz molecule. His new hydrogen is larger but softer than the old one. In our early worki0 we noticed that we could not fit adequately to the axial-equatorial methylcyclohexane energy difference using Bartell’s hydrogen, and varying the other parameters that it seemed one might reasonably vary. We therefore continued to use the hard Hill-type hydrogens. Bartell was less anxious to fit this energy difference, and felt he could do a better overall job with structure using soft hydrogens. In each case, the C /H interaction was taken to be the mean of the H / H and C/C interactions. White has also pointed out in a recent paper that our hydrogens are too hard to explain certain data .” We too regard the cyclodecane case which he discusses as a key case, because of the data now available, and it will be discussed below. We

Abstract: A general theory of the nonsaturated NMR spectra of chemically exchanging molecules is formulated. As an example the case of a molecule with two nonequivalent protons exchanging with a molecule with one proton is worked out in detail. Connection is made with previous theories by taking limiting expressions of the general results. In the appendix it is shown how the method can be extended to include saturation and hindered rotation.

Abstract: The factors affecting the electron resonance linewidths of a biradical, showing strong spin exchange, tumbling isotropically in solution are considered. For a biradioal with two equivalent magnetic nuclei the hyperfine lines should alternate in width provided the dominant relaxation mechanism is a modulation of the exchange interaction between the unpaired electrons. Certain nitroxide biradicals do indeed exhibit an alternating linewidth effect which we attribute to this mechanism.

Abstract: It is shown that the E.S.R. spectra of long-chain nitroxide biradicals represent the superposition of the spectrum of the non-reacting radical moieties in the elongated conformation and of that of the cage where the radical moieties are close together and can interact with each other. Inside the cage a fast intramolecular motion is observed. Some thermodynamic parameters of the cage as well as thermodynamic parameters of the motion inside the cage are calculated from the experimental E.S.R. spectra of four biradicals.