Please use this identifier to cite or link to this item: http://hdl.handle.net/1946/5346
Calculation of the rate of atomic rearrangements, such as chemical reactions and diffusion events, is an important problem in chemistry and condensed matter physics. When light particles are involved, such as hydrogen, the quantum effect of tunneling can be dominating. Harmonic quantum transition state theory (HQTST), sometimes referred to as ‘instanton theory’, is analogous to the more familiar classical harmonic transition state theory (HTST) except that it includes the effect of quantum delocalization. In this thesis, a new method for finding quantum mechanical saddle points, or instantons, is presented. The method is based on finding the classical periodic orbits on the inverted potential by a path optimization method. A chosen number of the system replicas are distributed along a path to give a convenient numerical representation of the classical orbit, independent of the physical parameters. This is in contrast with the distribution according to equal time segments which places most replicas near the end points. The overall computational cost of estimating rate constants with this method is lower than in previously used formulations of HQTST which is especially important when using directly atomic forces obtained from first principles calculations where each evaluation of the energy and atomic forces usually is computationally demanding. The method was tested on several two dimensional models as well as a multi dimensional problem involving hydrogen molecule adsorption/desorption from a crystal surface, yielding results in excellent agreement with quantum rate constants calculated using full free energy calculations and previously published implementation of HQTST.