Calculations strain energy

The calculations described here have been called strain calculations, molecular mechanics, or force field calculations. We prefer the latter term. For a discussion of historical developments and a literature survey of earlier work, which are not given here, the reader is referred to a number of other reviews (1-3). The present paper deals with the description of force field types, techniques of energy minimisation, and procedures for the determination of force field parameters, and with some applications, preferentially taken from our own field of interest. In accordance with the experiences of the author, the work of Lifson and coworkers is given special attention other authors are nevertheless well represented in the context of critical comparisons. We hope that this selection, although inevitably biased, will help to improve the consistency of the presentation of the subject. 

At one time it was believed that cyclooctane occurs in the extended crown form and the saddle conformation as shown below but on the basis of calculations of minimum energy strain, Hendrickson (1964) and Wiberg (1965) suggested that neither of the above two forms is the correct picture. R. Srinivasav and T. Srikrishnan (Tetrahedron 27, 5, 1009-1012, 1971) showed that the molecule exists as the boat-chair form in a number of crystalline derivatives. 

According to a newer theory83), see also84), the fracture energy 7 calculated from Eq. (43) or a similar relation has no connection with true surface energy. Energy is needed not to create a new surface but to deform the solid to its maximum strain. This rule is unquestionably correct for liquids. As was proved by Plateau (1869), a liquid cylinder can be extended by an external force until its length exceeds its circumference then it spontaneously splits into two spherical drops, and the combined area of the drops is smaller than that of the stretched cylinder. Thus, external work is required to stretch the cylinder, not to break it. 

A (average) for the ds-a-isomer. Potential energy minimization calculations have been carried out for the three isomers and the strain energy was found to decrease in the sequence cis-a > trans > ds-[3. The electronic... 

The strain energy is calculated as the energy of the residue in the vasopressin molecule minus the energy of the isolat residue. 

The boat-boat (417) and the twist-boat-boat (418) have low torsional strains but severe non-bonded repulsions, which, as usual, are transferred to internal angle strains. However, heteroatoms can modify these repulsions and certain transannular interactions can drastically reduce them. Even so, the boat-boat family is relatively unimportant as its energy is calculated to be quite high (12 kj mol-1) in cyclooctane. It probably serves as an intermediate for certain conformational interconversions of the boat-chair, especially when the twist-boat-chair pseudorotation itinerary is of high energy. In cyclooctane the boat-boat and its twisted partner have nearly the same energies and are not separated by a significant barrier. 

The strain energies are calculated as the difference in heats of formation in the preceding column and the heats of formation of an imaginary strainless compound with the same number of... 

The strain energy as calculated for 66b (24.4 kcal mol-1) compares well with the previously predicted value of 24.5 kcal mol-1 by Engel <1976JA1972>. The successful prediction of both the AH( and the strain energy for tetramethyl diazetine 66b suggested that the computational approach to obtain the strain energy for diazetines is practical. Thus, both the AHf and the strain energy of diazetines could be predicted with reasonable accuracy. 

TABLE 1. Strain energies (kcalmol ) calculated using homodesmotic reactions"... 

Stacking faults are characterised by a fault plane and a fault displacement vector. On one side of the fault plane, the atoms that are located fer from the fault are displaced by a vector R in relation to the positions they would occupy in the absence of the fault. Strain fields emanating from any reconstructive bonding that is present near the fault plane will lead to additional displacements for atoms near the fault plane. Thus, the specification of R determines the positions of the atoms that are sufficiently distant so that the strain field generated by the fault is below some specified tolerance. For a planar fault, R may be determined experimentally by analysis of the diffraction contrast obtained with different diffraction vectors g. The positions of atoms near the fault may be determined theoretically by total energy minimisation calculations. Knowledge of these positions is essential to determine the electronic structure of the fault. 

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