@phdthesis{Grebner2012,
  author    = {Grebner, Christoph},
  title     = {New Tabu-Search Algorithms for the Exploration of Energy Landscapes of Molecular Systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-75591},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {The visualization of energy functions is based on the possibility of separating different degrees of freedom. The most important one is the Born-Oppenheimer-approximation, which separates nucleus and electron movements. This allows the illustration of the potential energy as a function of the nuclei coordinates. Minima of the surface correspond to stable points like isomers or conformers. They are important for predicting the stability or thermodynamical of a system. Stationary points of first order correspond to transition points. They describe phase transitions, chemical reaction, or conformational changes. Furthermore, the partition function connects the potential hypersurface to the free energy of the system. The aim of the present work is the development and application of new approaches for the efficient exploration of multidimensional hypersurfaces. Initially, the Conformational Analysis and Search Tool (CAST) program was developed to create a basis for the new methods and algorithms. The development of CAST in object oriented C++ included, among other things, the implementation of a force field, different interfaces to external programs, analysis tools, and optimization libraries. Descriptions of an energy landscape require knowledge about the most stable minima. The Gradient Only Tabu Search (GOTS) has been shown to be very efficient in the optimization of mathematical test functions. Therefore, GOTS was taken as a starting point. Tabu-Search is based on the steepest descent - modest ascent strategy. The steepest descent is used for finding local minima, while the modest ascent is taken for leaving a minimum quickly. Furthermore, Tabu-Search is combined with an adaptive memory design to avoid cycling or returning. The highly accurate exploration of the phase space by Tabu-Search is often too expensive for complex optimization problems. Therefore, an algorithm for diversification of the search is required. After exploration of the proximity of the search space, the algorithm would guide the search to new and hopefully promising parts of the phase space. First application of GOTS to conformational search revealed weaknesses in the diversification search and the modest ascent part. On the one hand, the original methodology for diversification is insufficiently diverse. The algorithm is considerably improved by combining the more local GOTS with the wider searching Basin Hopping (BH) approach. The second weak point is a too inaccurate and inefficient modest ascent strategy. Analysis of common transition state search algorithms lead to the adaption of the Dimer-method to the Tabu-Search approach. The Dimer-method only requires the first derivatives for locating the closest transition state. For conformational search, dihedral angles are usually the most flexible degrees of freedom. Therefore, only those are used in the Dimer-method for leaving a local minimum. Furthermore, the exact localization of the reaction pathway and the transition state is not necessary as the local minimum position should only be departed as fast as possible. This allows for larger step sizes during the Dimer-search. In the following optimization step, all coordinates are relaxed to remove possible strains in the system. The new Tabu-Search method with Dimer-search delivers more and improved minima. Furthermore, the approach is faster for larger systems. For a system with approximately 1200 atoms, an acceleration of 40 was measured. The new approach was compared to Molecular Dynamics with optimization (MD), Simulated Annealing (SA), and BH with the help of conformational search problems of bio-organic systems. In all cases, a better performance was found. A comparison to the Monte Carlo Multiple Minima/Low Mode Sampling (MCMM/LM) method proved the outstanding performance of the new Tabu-Search approach. The solvation of the chignolin protein further revealed the possibility of uncovering discrepancies between the employed theoretical model and the experimental starting structure. Ligand optimization for improvement of x-ray structures was one further new application field. Besides the global optimization, the search for transition states and reaction pathways is also of paramount importance. These points describe different transitions of stable states. Therefore, a new approach for the exploration of such cases was developed. The new approach is based on a global minimization of a hyperplane being perpendicular to the reaction coordinate. Minima of this reduced phase space belong to traces of transition states between reactant and product states on the unchanged hypersurface. Optimization to the closest transition state using the Dimer-method delivers paths lying between the initial and the final state. An iterative approach finally yields complex reaction pathways with many intermediate local minima. The PathOpt algorithm was tested by means of rearrangements of argon clusters showing very promising results.},
  subject      = {Globale Optimierung},
  language  = {en}
}