points is no-longer satisfied, the points can be redistributed, using the spline representation of the path to generate new vectors with the required spacing. Variations on the string method include the growing string method, in which the guess of the pathway is grown in from the end points (that is the reactant and products) as the optimization progresses. Comparison with other techniques Geometry optimization is fundamentally different from a molecular dynamics simulation. The latter simulates the motion of molecules with respect to time, subject to temperature, chemical forces, initial velocities, Brownian motion of a solvent, and so on, via the application of Newton's laws of Motion. This means that the trajectories of the atoms which get computed, have some physical meaning. Geometry optimization, by contrast, does not produce a "trajectory" with any physical meaning – it is concerned with minimization of the forces acting on each atom in a collection of atoms, and the pathway via which it achieves this lacks meaning. Different optimization algorithms could give the same result for the minimum energy structure, but arrive at it via a different pathway. See also Constraint composite graph Graph cuts in computer vision – apparatus for solving computer vision problems that can be formulated in terms of energy minimization Energy principles in structural mechanics References External links Numerical Recipes in Fortran 77 Additional references Payne et al., "Iterative minimization techniques for ab initio total-energy calculations: Molecular dynamics and conjugate gradients", Reviews of Modern Physics 64 (4), pp. 1045–1097. (1992) (abstract) Stich et al., "Conjugate gradient minimization of the energy functional: A new method for electronic structure calculation", Physical Review B 39 (8), pp. 4997–5004, (1989) Chadi, "Energy-minimization approach to the atomic geometry of semiconductor surfaces", Physical Review Letters 41 (15), pp. 1062–1065 (1978) Mathematical optimization Computational chemistry