Interpolated optimized energies

The interpolated optimized energies (lOE) scheme " is like the IOC scheme except that the frequencies are not corrected at the higher level. Although the lOE method only uses high-level data at the stationary points. 

The interpolated optimized corrections (IOC) method " uses HE energies, gradients, and Hessians at the high-level stationary points to improve the quality of a Vmep and of frequency and moment of inertia profiles originally calculated at EE. 

In simple relaxation (the fixed approximate Hessian method), the step does not depend on the iteration history. More sophisticated optimization teclmiques use infonnation gathered during previous steps to improve the estimate of the minunizer, usually by invoking a quadratic model of the energy surface. These methods can be divided into two classes variable metric methods and interpolation methods. 

As an example of why linear interpolation is not always a useful way to initialize an NEB calculation, consider the molecule HCN in the gas phase. This molecule can rearrange to form CNH. Optimize the structures of HCN and CNH, then use these states to examine the bond lengths in the structures that are defined by linear interpolation between these two structures. Why are the intermediate structures defined by this procedure not chemically reasonable Construct a series of initial images that are chemically reasonable and use them in an NEB calculation to estimate the activation energy for this molecular isomerization reaction. 

Figure 4.45. Pareto plot of interpolated catalysts predicted to be good compromises with respect to cost and activity for methanation. The positions of the interpolated catalysts are determined by the cost of their constituent elements vs. their distance from the optimal dissociative chemisorption energy for CO with respect to the experimentally observed optimum (see Figure 4.44 right-bottom). Adapted from Ref. [55].

Molecular mechanics is an interpolative method. It thus follows that the strain energy and the structure of a very strained species may not be reliably computed on the basis of a parameterization scheme fitted with a set of experimental data obtained from unstrained molecules, since this amounts to extrapolation. Therefore, to obtain a generally reliable force field, extreme cases have to be included in the fitting procedure of the force field. The speed with which structure optimizations are produced (minutes of CPU time on a simple personal computer for molecules with around 100 atoms) does not place any restriction on the size of a data base for the parameterization of a class of compounds - the limit is usually given by the amount of experimental data available. The major appeal of molecular mechanics is the fact that unknown compounds may be modeled in much the same way as model kits are used, with the important difference that quantitative information becomes available, enabling an effective design of new compounds. 

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