Geometrical Properties of PES

Subject of this section are the (local) geometrical features of a PES that are related to the first and second partial derivatives of the energy functional. 

The vector of the first partial derivatives of an energy functional E at a point xeSD is called the gradient of E at x and is denoted by grad E(x) (or VE(x)), 

By assigning to each point xeV the vector grad E(x), a function 

Frequently (two-dimensional) PES are visualized by the level surfaces of E, i.e. the sets 

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