### Browsing by Author "Jónsson, Hannes, Prof., University of Iceland, Iceland"

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Item Algorithms for Finding Saddle Points and Minimum Energy Paths Using Gaussian Process Regression(Aalto University, 2019) Koistinen, Olli-Pekka; Tietotekniikan laitos; Department of Computer Science; University of Iceland; Perustieteiden korkeakoulu; School of Science; Vehtari, Aki, Prof., Aalto University, Department of Computer Science, Finland; Jónsson, Hannes, Prof., University of Iceland, IcelandChemical reactions and other transitions involving rearrangements of atoms can be studied theoretically by analyzing a potential energy surface defined in a high-dimensional space of atom coordinates. Local minimum points of the energy surface correspond to stable states of the system, and minimum energy paths connecting these states characterize mechanisms of possible transitions. Of particular interest is often the maximum point of the minimum energy path, which is located at a first-order saddle point of the energy surface and can be used to estimate the activation energy and rate of the particular transition. Minimum energy paths and saddle points between two known states have been traditionally searched with iterative methods where a chain of discrete points of the coordinate space is moved and stretched towards a minimum energy path according to imaginary forces based on gradient vectors of the potential energy surface. The actual saddle point can be found by reversing the component of the gradient vector parallel to the path at one of the points of the chain and letting this point climb along the path towards the saddle point. If the end state of the transition is unknown, the saddle point can be searched correspondingly by rotating a pair of closely spaced points towards the orientation of the lowest curvature, reversing the gradient component corresponding to this direction, and moving the pair towards the saddle point. These methods may, however, require hundreds of iterations, and since accurate evaluation of the gradient vector is often computationally expensive, the information obtained from previous iterations should be utilized as efficiently as possible to decrease the number of iterations. Using statistical models, an approximation to the energy surface can be constructed, and a minimum energy path or a saddle point can be searched on the approximate surface. The accuracy of the solution can be checked with further evaluations, which can be then used to update the model for following iterations. In this dissertation, machine learning algorithms based on Gaussian process regression are developed to enhance searches of minimum energy paths and saddle points. Gaussian process models serve here as flexible prior probability models for potential energy surfaces. Observed values of both energy and its derivatives can be used to update the model, and the posterior predictive distribution obtained as a result of Bayesian inference provides also an uncertainty estimate, which can be utilized when selecting new observation points. Separate methods are presented both for finding a minimum energy path between two known states and a saddle point located in the vicinity of a given start point. Based on simple test examples, the methods utilizing Gaussian processes may reduce the number of evaluations to a fraction of what is required by conventional methods.Item Escape Rates of Externally Confined Polymers(Aalto University, 2016) Mökkönen, Harri; Jónsson, Hannes, Prof., University of Iceland, Iceland; Teknillisen fysiikan laitos; Department of Applied Physics; Multiscale Statistical Physics; Perustieteiden korkeakoulu; School of Science; Ala-Nissilä, Tapio, Prof., Aalto University, Department of Applied Physics, FinlandA polymer escaping from a confining external potential represents a generic description of long macromolecules crossing an energy barrier. This type of barrier crossing problems are typical in nano- and microscale polymeric systems, where the polymers are escaping from entropic traps by thermal fluctuations. These systems have possible bioengineering applications, where they can be for example used in sorting polymers. In this thesis, polymer escape from one- and two-dimensional external potentials was studied theoretically and computationally. In a two-dimensional asymmetric external potential, the escape rate of a polymer was solved using Path Integral Hyperdynamics (PIHD) simulations and Kramers' theory using effective potentials for different lengths of polymers. We found that Kramers' theory predicts the escape rate of PIHD simulations qualitatively but the prediction agrees quantitatively only for shorter chains. We also determined that a one-dimensional reaction coordinate is not sufficient to describe the dynamics of the longer polymer chains. In a one-dimensional symmetric double-well external potential, the escape rate was solved using Langevin dynamics simulations, Brownian dynamics simulations, harmonic transition state theory (HTST) with dynamical corrections (DC), Langer's theory, and Forward flux sampling (FFS). FFS and HTST with DC both predict the rate by Langevin and Brownian dynamics simulations quantitatively within a factor of two. We also introduced a new method for computing dynamical corrections using forward flux sampling type of algorithm and compared computational efficiency of the different methods.