Locally updated planes method

This is an identical equation for the minimum energy path [9,10] or the so-called steepest descent path. The first implementation of an algorithm to compute minimum energy paths based on the above formula was the LUP (Locally Updated Planes) method [9] that did not include the constraint on the displacement size. This is formally correct since different parameterizations of the path are possible, but may lead to numerical problems in which the distances between the intermediates grow without control. This was adjusted to produce more stable algorithms by the Nudge Elastic Band approach [11] and later by the String method [10]. 

The Locally Updated Plane.s- (LUP) minimization is related to the chain method, but the relaxation is here done in the hyperplane perpendieular to the reaction coordinate, rather than along a line defined by the gradient. Furthermore, all the points are moved in each iteration, rather than one at a time. 

N C The Locally Updated Planes (LUP) minimization " is related to the chain method, but... 

Multi-structure interpolation methods chain, locally updated planes, self-penalty walk, conjugate peak refinement and nudged elastic band... 

The locally updated planes (LUP) method also optimizes a chain of points simultaneously. For each point x, along the pathway, a hyperplane orthogonal to the path is defined. The points are then energy minimized with the constraint that each has to remain in its initial plane. The planes are periodically updated to account for the changing shape of the path. The LUP algorithm is ideally suited for refining a chain that is already near the adiabatic path. 

Linear dependence of basis functions, 164 Linear response function, 261 Linear scaling techniques, 80 Linear Synchronous Transit (LST) optimization method, 328 Local Density Approximation (LDA), Local Spin Density Approximation (LSDA) functionals, 182 Local minimum, 339 Localized Molecular Orbitals (LMO), 227 Localized orbital methods, 227 Localized Orbital/local oRiGin (LORG), for calculating magnetic properties, 252 Locally Updated Planes (LUP) optimization method, 330... 

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