Potential energy surface optimization algorithms

HyperChem provides three types of potential energy surface sampling algorithms. These are found in the HyperChem Compute menu Single Point, Geometry Optimization, and Molecular Dynamics. 

The examples discussed in Section 14.3 show how geometry optimization tools, combined with statistical rate theory, can be employed to access experimental timescales corresponding to folding, conformational changes associated with function, and amyloid formation. Most of the computer time used in such calculations is spent on finding transition states on the potential energy surface. These algorithms have been tested quite extensively, and it does not seem likely that much improvement will be possible beyond the DNEB/hybrid EF approach described in Section 14.2.1, or related schemes. 

Transition state search algorithms rather climb up the potential energy surface, unlike geometry optimization routines where an energy minimum is searched for. The characterization of even a simple reaction potential surface may result in location of more than one transition structure, and is likely to require many more individual calculations than are necessary to obtain equilibrium geometries for either reactant or product. 

The Newton-Raphson block diagonal method is a second order optimizer. It calculates both the first and second derivatives of potential energy with respect to Cartesian coordinates. These derivatives provide information about both the slope and curvature of the potential energy surface. Unlike a full Newton-Raph son method, the block diagonal algorithm calculates the second derivative matrix for one atom at a time, avoiding the second derivatives with respect to two atoms. 

Maxima, minima and saddle points are stationary points on a potential energy surface characterized by a zero gradient. A (first-order) saddle point is a maximum along just one direction and in general this direction is not known in advance. It must therefore be determined during the course of the optimization. Numerous algorithms have been proposed, and I will finish this chapter by describing a few of the more popular ones. 

This illustrates a general principle the optimized structure one obtains is that closest in geometry on the PES to the input structure (Fig. 2.15). To be sure we have found a global minimum we must (except for very simple or very rigid molecules) search a potential energy surface (there are algorithms that will do this and locate the various minima). Of course we may not be interested in the global minimum for example, if we wish to study the cyclic isomer of ozone (Section 2.2) we will use as... 

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