Force from structural data

The question of how accurately a given structural parameter need be known is difficult to answer in a general way. Most would agree that a measurement of the interatomic distance in the HC1 molecule to the nearest 0.00001 A is mainly a tour de force that has limited bearing on the correlation of this distance with other properties. On the other hand, it is easy to find examples in the literature where very shaky conclusions have been drawn from structural data that were not as reliable as implied by the original investigator. In particular, when one tries to interpret differences in a certain structural parameter—variations from one molecule to another-the question of accuracy becomes critical. The one point that cannot be disputed is that a realistic assessment of the accuracy of a structural parameter is just as important as the value of that parameter itself. 

The I3 example thus illustrates how signs of force constants and their ordering by magnitude can be obtained from structural scatter plots. Under certain conditions, it may even be possible to deduce ratios of force constants from structural data. Again, this is best illustrated by a simple example. Suppose that the relevant part of V for a structural fragment takes the form... 

The ratio of force constants estimated in this way from structural data, or rather the dependence of this ratio on double-bond character, is matched by corresponding ratios from vibrational spectroscopy [12 a]. 

Restraints due to artifacts may, by chance, be completely consistent with the correct structure of the molecule. However, the majority of incorrect restraints will be inconsistent with the correct structural data (i.e., the correct restraints and information from the force field). Inconsistencies in the data produce distortions in the structure and violations in some restraints. Structural consistency is often taken as the final criterion to identify problematic restraints. It is, for example, the central idea in the bound-smoothing part of distance geometry algorithms, and it is intimately related to the way distance data are usually specified The error bounds are set wide enough that all data are geometrically consistent. 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

Chemical reactivity differences may be calculated if for the transition state of a rate-determining step of a reaction a structural model can be given which is describable by a force field with known constants. We give only two examples. Schleyer and coworkers were able to interpret quantitatively a multitude of carbonium-ion reactivities (63, 111) in this way. Adams and Kovacic studied the pyrolysis of 3-homoadamantylacetate (I) at 550 °C and considered as transition state models the two bridgehead olefins II and III (112). From kinetic data they estimated II to be about 2 kcal mole-1 more favourable than III. 

Examples of the application of correlation analysis to diene and polyene data sets are considered below. Both data sets in which the diene or polyene is directly substituted and those in which a phenylene lies between the substituent and diene or polyene group have been considered. In that best of all possible worlds known only to Voltaire s Dr. Pangloss, all data sets have a sufficient number of substituents and cover a wide enough range of substituent electronic demand, steric effect and intermolecular forces to provide a clear, reliable description of structural effects on the property of interest. In the real world this is not often the case. We will therefore try to demonstrate how the maximum amount of information can be extracted from small data sets. 

The task in using these simple expressions (7) and (8) lies in finding the number of ligands n, the force constants Xt./o> and values for the bond length difference Ar. The values of n and Arare obtained from X-ray crystallographic or extended X-ray absorption fine structure data. The force constants /, and fs are obtained from available vibrational spectroscopic data using the equation. 

One of the most valuable outcomes of the Marcus theory is that it provides a quantitative, albeit simple, description of how the activation barrier varies with the driving force of the reaction. The factors constituting the intrinsic barrier are clearly identified and can be approximately estimated from available data characterizing the structure of the reactants of the products and of the reaction medium. 

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