Geometry Optimization

Introduction
Geometry optimization is used to find minima on the potential energy surface, with these minimum energy structures representing equilibrium structures. Optimization also is used to locate transition structures, which are representedhttp:// by saddle points on the potential energy surface. Optimization to minima is also referred to as energy minimization. During minimization, the energy of molecules is reduced by adjusting atomic coordinates. It is applied to model-built structures as well as to those derived from coordinate data banks. Energy minimization is done when using either molecular mechanics or quantum mechanics methods, and it must precede any computational analyses in which these methods are applied. For example, geometry optimization can be used to

characterize a potential energy surface
obtain a structure for a single-point quantum mechanical calculation, which provides a large set of structural and electronic properties
prepare a structure for molecular dynamics simulation - if the forces on atoms are too large, the integration algorithm may fail.

The energy obtained from the potential energy function at the optimized geometry is sometimes called a steric or conformational energy. These energies can be used to calculate differences between stereoisomers and between isologous molecules (i.e., those differing in connectivity but having the same number of each type of functional group). These energies apply to molecules in a hypothetical motionless state at 0 Kelvin. Additional information is needed to calculate enthalpies (e.g., thermal energies of translation, vibration, and rotation) and free energies (i.e., entropy). Programs such as Gaussian provide the information needed for calculating free energies of small molecules. Free energy simulations for macromolecules also are possible.

On-Line Text
An introduction to geometry optimization is available in the NIH Guide to Molecular Modeling.

Printed References
Burkert, U. and Allinger, N.L. (1982) Molecular Mechanics, ACS Monograph 177, American Chemical Society, Washington, D.C., pp. 64-72.

Hirst, D.M. (1990) A Computational Approach to Chemistry, Blackwell Scientific Publications, Oxford, pp. 108-111; 400-403.