Locally Updated Planes optimization

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. 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

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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