Total strain energy

If we assume that there are certain ideal val ues for bond angles bond distances and so on itfol lows that deviations from these ideal values will destabilize a particular structure and increase its po tential energy This increase in potential energy is re ferred to as the strain energy of the structure Other terms for this increase include steric energy and steric strain Arithmetically the total strain energy ( ) of an alkane or cycloalkane can be considered as... 

Problem 3.18 Draw a Newman projection along the C2-C3 bond of the following conformation of 2,3-dimethylbutane, and calculate a total strain energy ... 

For a Hookian material, the concept of minimum strain energy states that a material fails, for example cell wall disruption occurs, when the total strain energy per unit volume attains a critical value. Such an approach has been used in the past to describe a number of experimental observations on the breakage of filamentous micro-organisms [78,79]. Unfortunately, little direct experimental data are available on the Young s modulus of elasticity, E, or shear modulus of elasticity G representing the wall properties of biomaterial. Few (natural) materials behave in an ideal Hookian manner and in the absence of any other information, it is not unreasonable to assume that the mechanical properties of the external walls of biomaterials will be anisotropic and anelastic. 

Maximum strain energy theory, which postulates that failure will occur in a complex stress system when the total strain energy per unit volume reaches the value at which failure occurs in simple tension. 

Equation 32 gives the total strain energy stored in a domain of a fibre with an orientation angle 0 in the unloaded state after the stress has been increased from 0 to o. The first term on the right-hand side is the strain energy of the chain extension, and the second term is the shear strain energy. The continu-... 

Some of the potential energy functions used to calculate the total strain energy of a molecule are similar to the functions used in the analysis of vibrational spectra. Because the parameters used to derive the strain energies from these functions are fitted quantities, which are based on experimental data (for example X-ray structures), molecular mechanics may be referred to as empirical force field calculations (more often the simplification force field calculations is used). The quality of such calculations is strongly dependent on the reliability of potential energy functions and the corresponding parameters (the force field). Thus, the selection of experimental data to fit the force field is one of the most important steps in a molecular mechanics study. An empirical force field calculation is in essence a method where the structure and the strain energy of an unknown molecule are interpolated from a series of similar molecules with known structures and properties. 

It is common practice to represent the total strain energy, Utotab of a molecule by a set of potential energy functions, including bonding (Eb), valence (Eg) and torsional angle (E interactions as well as nonbonded (Enb) and electrostatic interactions (Ec) (see Eq. 2.2). 

From the discussion above it emerges that the total strain energies, which are often equated with enthalpy terms, are dependent on the molecular mechanics model used and its associated parameter set. For this reason strain energies are generally taken to have significance only relative to one another. Even with the same model and force field, strain energies are generally of little value in terms of absolute potential en-... 

Important, though not generally appreciated, problems of the application of molecular mechanics to the prediction of metal ion selectivities are the neglect of solvation and entropic effects. These have been discussed in Chapter 2, Sections 2.7 and 2.8. The sum of all the other terms mentioned above may be related to the difference in total strain energy between the metal-free and the coordinated ligand. 

The estimate of relative stabilities via the comparison of total strain energies is in general limited to a series of conformers and isomers (see for instance Chapter 7 and the relevant chapters in Parts I and III). The determination by molecular mechanics calculations of relative stabilities of a series of complexes with metal ions having differing geometric preferences (electronic effects) and preferences in terms of donor atoms is therefore a questionable approach. A comparative study is only useful if the structural preferences of the different metal ions are similar and/or if the electronic effects may be separated from steric effects. 

We now consider separately each function used to calculate the terms that go to make up the total strain energy. We have restricted our discussion here to the simplest forms of the functions. With the greater approximations involved in modeling metal complexes, refinements of the functions are often an unneccessary elaboration. A full account of possible functions is given in Chapter 2, Section 2.2. When the use of other functions is indicated, these can be parameterized by application of the general philosophies of force field development outlined below. 

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