Stationary point characterizing

Both minima and saddle points are stationary points characterized by a zero gradient. However, unlike a minimum, a first-order saddle point must be a maximum along one (and only one) direction. In general, this direction is not known in advance and must be determined during the course of the optimization. Numerous algorithms have been proposed to deal with the problem of locating transition structures. In this section a few of the more... 

Relate characterization of stationary points via the eigenvalues of the Hessian to the corresponding matrix under the harmonic oscillator problem. 

There are two pieces of information from the output which are critical to characterizing a stationary point ... 

The table on the next page summarizes the most important cases you will encounter when attempting to characterize stationary points. 

Fig. 1.1 (a) In traditional quantum chemical methods the potential energy surface (PES) is characterized in a pointwise fashion. Starting from an initial geometry, optimization routines are applied to localize the nearest stationary point (minimum or transition state). Which point of the PES results from this procedure mainly depends on the choice of the initial configuration. The system can get trapped easily in local minima without ever arriving at the global minimum struc-... 

All stationary point geometries were fully optimized at the HF/6-31G level of theory and characterized by harmonic frequency analysis. Single point energies were evaluated at the MP2/6-31G level to account for the effects of electron correlation. Since experiments were carried out in a relatively low dielectric environment (chlorobenzene solvent), it is likely that the shape of the potential energy surface in the gas phase and solution would be comparable... 

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