Computer Science & Engineering Quantum Chemisrty LabList Of Experiments
Geometry Optimization of Molecules
Optimization is the process of selecting the best from a set of alternatives. Optimization is performed for function that is multivariable, continuous and differentiable, and typical optimization techniques find minima or maxima of the function.
In nature, molecules are most likely to be found in those
conformations which are most stable (energy minimum). The potential
energy surface (PES) of the molecular configuration is first computed
using quantum mechanics. Each local minima on the on this PES
represents a stable conformation, and a "movie" of the molecule will
show that most of the time the molecule spends near these locally
stable conformations with sudden jumps to nearby stable conformations,
with the rate that depends on the energy barrier of such a jump. If one
of the stable conformations is significantly more stable then the
molecule will be trapped in that conformation and geometry. Or if the
stable conformations are separated by large barriers, the molecule will
be trapped in whatever stable conformation that is achieved first.
PES is a hypersurface showing the energy of a particular conformation . This many dimensional hypersurface can be characterized by points where the gradient is zero, which can be classified into following categories:

Local Maxima: a point on the hypersurface that has the highest
function value in its near neighborhood;
all nearby points have lower values. A hypersurface will have very many local maxima, in general. 
Local Minima: a point on the hypersurface that has the lowest
function value in its near neighborhood;
all nearby points have higher values. A hypersurface will have very many local minima, in general. 
Global Maxima: From the set of points which are local maxima,
it is that point that has the highest function value.
A hypersurface can have only one global maxima. 
Global Minima: From the set of points which are local minima,
it is that point that has the lowest function value.
A hypersurface can have only one global minima. 
Saddle point: A point on the hypersurface which has minimum in
at least one direction and maximum other directions;
the conformation at the saddle point represents the transition structure between two stable conformations.
To identify the stable conformations, local minima of the PES need to be computed. This is called Geometry Optimization and is used to:
 Characterize a potential energy surface
 Obtain a structure for a singlepoint quantum mechanical calculation, which provides a large set of structural and electronic properties for the stable conformation.
 Prepare a structure for molecular dynamics simulation (if the
forces on atoms are too large, the integration algorithm
may fail; so starting the simulation at stable conformation is crucial).