Local elevation

Local elevation is a technique used in computational chemistry or physics, mainly in the field of molecular simulation (including molecular dynamics (MD) and Monte Carlo (MC) simulations). It was developed in 1994 by Huber, Torda and van Gunsteren to enhance the searching of conformational space in molecular dynamics simulations and is available in the GROMOS software for molecular dynamics simulation (since GROMOS96). The method was, together with the conformational flooding method, the first to introduce memory dependence into molecular simulations. Many recent methods build on the principles of the local elevation technique, including the Engkvist-Karlström, adaptive biasing force, Wang–Landau, metadynamics, adaptively biased molecular dynamics, adaptive reaction coordinate forces, and local elevation umbrella sampling methods. The basic principle of the method is to add a memory-dependent potential energy term in the simulation so as to prevent the simulation to revisit already sampled configurations, which leads to the increased probability of discovering new configurations. The method can be seen as a continuous variant of the Tabu search method.

Local elevation is a technique used in computational chemistry or physics, mainly in the field of molecular simulation (including molecular dynamics (MD) and Monte Carlo (MC) simulations). It was developed in 1994 by Huber, Torda and van Gunsteren to enhance the searching of conformational space in molecular dynamics simulations and is available in the GROMOS software for molecular dynamics simulation (since GROMOS96). The method was, together with the conformational flooding method, the first to introduce memory dependence into molecular simulations. Many recent methods build on the principles of the local elevation technique, including the Engkvist-Karlström, adaptive biasing force, Wang–Landau, metadynamics, adaptively biased molecular dynamics, adaptive reaction coordinate forces, and local elevation umbrella sampling methods. The basic principle of the method is to add a memory-dependent potential energy term in the simulation so as to prevent the simulation to revisit already sampled configurations, which leads to the increased probability of discovering new configurations. The method can be seen as a continuous variant of the Tabu search method. U_{tot}(\mathbf{r})=U_{phys}(\mathbf{r}) +U_{bias}^{LE}(\mathbf{Q};t) The local elevation bias U_{bias}^{LE}(\mathbf{Q};t) depends on the simulation time t and is set to zero at the start of the simulation ( U_{bias}^{LE}(\mathbf{Q};t=0) = 0 ) and is gradually built as a sum of small, repulsive functions, giving U_{bias}^{LE}(\mathbf{Q};(n+1)\Delta t) = U_{bias}^{LE}(\mathbf{Q};n \Delta t) + k_{LE} F(\mathbf{Q}-\mathbf{Q}_{n+1}) , where k_{LE} is a scaling constant and F(\mathbf{Q}-\mathbf{Q}_{n+1}) is a multidimensional, repulsive function with F(0)=1 . The resulting bias potential will be a sum of all the added functions U_{bias}^{LE}(\mathbf{Q};n\Delta t) = \sum_{i=1}^{n} k_{LE} F(\mathbf{Q}-\mathbf{Q}_i) To reduce the number of added repulsive functions, a common approach is to add the functions to grid points. The original choice of F(\mathbf{Q}-\mathbf{Q}_i) is to use a multidimensional Gaussian function. However, due to the infinite range of the Gaussian as well as the artifacts that can occur with a sum of gridded Gaussians, a better choice is to apply multidimensional truncated polynomial functions .

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