The Self Penalty Walk Method

In the Self Penalty Walk (SPW) method the whole reaction path is approximated by minimizing the average energy along the path, given as a line integral between the reactant and product geometries (R and P). 

The line element d/(x) belongs to the reaction path, which has a total length of L. In practice the line integral is approximated as a finite sum of M points, where M typically is of the order of 10-20. 

In order to avoid all points aggregating near the minima (reactant and product), constraints are imposed for keeping the distance between two neighbouring points close 

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The Self Penalty Walk Method 330 The Hohenberg-Kohn Theorems 409 ... 

In the self-penalty walk (SPW) method of Czerminski and Fiber [Czerminski and Fiber 1990 Nowak et al. 1991] a polymer is constructed that consists of a series of M -F 2 monomers. Fach monomer is a complete copy of the actual system and so there are (M + 2)N atoms present in the calculation. The two ends of the polymer correspond to the two minima between which we are trying to elucidate the pathway (the reactant and the product ). 

Nowak VV, R Czerminski and R Elber 1991. Reaction Path Study of Ligand Diffusion in Proteins Application of the Self Penalty Walk (SPW) Method to Calculate Reaction Coordinates for the Motion of CO through Leghemoglobin Journal of the American Chemical Society 113 5627-5737. 

Nowak, W., Czerminski, R., 8c Elber, R. (1991). Reaction path study of ligand diffusion in proteins Application of the self penalty walk (SPW) method to calculate reaction coordinates for the motion of CO through leghemoglobin. Journal of the American Chemical Society, 113, 5627. 

In the. self-avoiding walk method the path as a whole is optimized by minimizing a penalty function P. starting from an initial estimate of the path, usually the result of linear interpolation. The path (or chain) consists of... 

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