Single Points on a Potential Energy Surface

An N-atom molecular system may be described by 3N Cartesian coordinates. Six independent coordinates (five for linear molecules, three for a single atom) describe translation and rotation of the system as a whole. The remaining coordinates describe the molecular configuration and the internal structure. Whether you use molecular mechanics, quantum mechanics, or a specific computational method (AMBER, CNDO, etc.), you can ask for the energy of the system at a specified configuration. This is called a single point calculation. 

For a diatomic molecule, for example, there is only one internal coordinate and the energy as a function of configuration (inter-nuclear distance) will look something like the following  

A single point calculation at the points b, c, d, or e will give a higher energy, E, than a single point calculation near the minimum at a. 

For multi-dimensional potential energy surfaces a convenient measure of the gradient vector is the root-mean-square (RMS) gradient described by 

For a molecular mechanics calculation the energy and the gradient are essentially the only quantities available from a single point calculation. An analysis of the components of this molecular mechanics energy is placed in the log file for further detail. In the case of MM-h a much more complete description of the individual 

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