=Mod:SY3814

Introduction

Potential Energy Surface

A potential energy surface(PES) is a mathematical function that describes molecule as a function of its geometry. It is commonly applied in Chemistry to theoretically explore properties of atomic structures and rates of chemical reactions.

stationary points

There are two stationary points(points with zero gradient) in PES, minimum state point and transition state point. Minimum state is where the molecule in its minimum energy shape(physically stable) and the transition state is the highest energy point along a reaction coordinate.

gradient and the curvature

As the point is evaluated in the PES, the point can be identified by its gradient(first derivatives) and curvature(second derivatives) of the energy related to the position.

Gradient

For a given molecule, r describes the position of molecule and the Function E(r) can be introduced as the energy of the position. The first derivative of the energy corresponds to the position of the molecule is calculated as gradient.

Gradient = ∂E/∂r

Curvature

In the case that the gradient is a zero vector(stationary points), second derivative matrix is used, which describes the PES curvature at r position.