Mathematical Chalenges from Theoretical/Computational Chemistry


BOX 2.2 Molecular Mechanics/Molecular Dynamics

Molecular mechanics and molecular dynamics refer to methods for computing certain molecular properties, particularly molecular structure and relative energy. They both typically use fairly simple potential energy functions that are derived from classica l mechanics (e.g., a parabolic function to calculate the energy required to stretch or to compress a chemical bond). In addition, they both rely on parameters that are derived either from experiment (e.g., infrared spectroscopy and X-ray crystallography) or from quantum mechanics-based calculations (e.g., high-level ab initio molecular orbital calculations). A collection of potential energy functions and the associated parameters that are employed for molecular mechanics/molecular dynamics calculations is frequently referred to as a "force field"; thus, calculations that utilize the molecular mechanics or molecular dynamics approach are often referred to as empirical force field calculations.

The molecular mechanics method is generally employed to compute the relative energies of different geometries (conformations) of the same molecule that arise from rotations about chemical bonds as well as relative energies of intermolecular complexes. Often, energy minima are sought; thus, the molecular mechanics method is frequently coupled with optimization procedures. On the other hand, in the molecular dynamics method, Newton's equations of motion are solved by using the gradient of the above-ment ioned potential energy function (force field) to compute the dynamic trajectory of a molecule or of an ensemble of molecules. Both the molecular mechanics and the molecular dynamics methods have found widespread use in the modeling of biomolecular system s, for which quantum mechanical calculations are simply not practical due to the overwhelming number of particles involved. Nonetheless, these methods are quite accurate for the estimation of certain molecular properties (i.e., those for which classical mechanics is appropriate), and they have been successfully employed to compute conformational energies (as described above), to estimate the binding affinity of small molecules bound to a macromolecular receptor, and as an adjunct for the refinement of st ructures derived from protein X-ray crystallography and protein nuclear magnetic resonance spectroscopy.


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