Projects per year
Abstract
Finding the mechanisms and estimating the rate of chemical reactions is an essential part of modern research of atomic scale systems. In this thesis, the application of well established methods for reaction rates and paths to important systems for hydrogen storage is considered before developing extensions to further identify the reaction environment for a more accurate rate. Complex borohydrides are materials of high hydrogen storage capacity and high thermodynamic stability (too high for hydrogen storage). In an effort to gain insight into the structural transitions of two such materials, Ca(BH4)2 and Mg(BH4)2, experiments on low temperature rotational dynamics were performed.
The work presented here revolved around assisting in the data analysis by performing density functional theory calculations on the possible dynamical events. For the Mg(BH4)2, in good agreement with the experiments, C2type rotations occur at lower temperature than C3type rotations and approximately 15% of the BH4 units activate at a lower temperature than the rest. For the Ca(BH4)2, in addition to the rotational dynamics, an unidentified event was detected which, according to the calculations was most likely due to H2interstitial defects. In good agreement with the experiments, C3type rotations activate at lower temperature than C2type rotations. In order to investigate the environment of reaction pathways, a method for finding the ridge between first order saddle points on a multidimensional surface was developed. Information about the ridge can be used to test the validity of the harmonic approximation to transition state theory for reaction rates, in particular to verify that second order saddle points  maxima along the ridge  are high enough compared to the first order saddle points. Furthermore, corrections to the harmonic approximation can be estimated by direct evaluation of the configuration integral along the ridge. New minima along the ridge can also be identified during the path optimisation, thereby revealing additional transition mechanisms. The method is based on modifying the gradient of a set of points along a path connecting the saddle points to iteratively converge to the ridge. At each iteration during the optimisation, the gradient is inverted along
an unstable eigenmode perpendicular to the path, locally mapping the ridge to a minimum energy path which can be located using various techniques. The method was applied to Al adatom diffusion on the Al(100) surface to find the ridge between 2, 3 and 4atom concerted displacement and hop mechanisms for diffusion. Significant corrections were offered for the 3 and 4atom concerted
displacements. The method offers a simpletouse way to check the validity of reaction rates but has the potential to offer more accurate rates on its own by representing the transition state with the ridge.
The work presented here revolved around assisting in the data analysis by performing density functional theory calculations on the possible dynamical events. For the Mg(BH4)2, in good agreement with the experiments, C2type rotations occur at lower temperature than C3type rotations and approximately 15% of the BH4 units activate at a lower temperature than the rest. For the Ca(BH4)2, in addition to the rotational dynamics, an unidentified event was detected which, according to the calculations was most likely due to H2interstitial defects. In good agreement with the experiments, C3type rotations activate at lower temperature than C2type rotations. In order to investigate the environment of reaction pathways, a method for finding the ridge between first order saddle points on a multidimensional surface was developed. Information about the ridge can be used to test the validity of the harmonic approximation to transition state theory for reaction rates, in particular to verify that second order saddle points  maxima along the ridge  are high enough compared to the first order saddle points. Furthermore, corrections to the harmonic approximation can be estimated by direct evaluation of the configuration integral along the ridge. New minima along the ridge can also be identified during the path optimisation, thereby revealing additional transition mechanisms. The method is based on modifying the gradient of a set of points along a path connecting the saddle points to iteratively converge to the ridge. At each iteration during the optimisation, the gradient is inverted along
an unstable eigenmode perpendicular to the path, locally mapping the ridge to a minimum energy path which can be located using various techniques. The method was applied to Al adatom diffusion on the Al(100) surface to find the ridge between 2, 3 and 4atom concerted displacement and hop mechanisms for diffusion. Significant corrections were offered for the 3 and 4atom concerted
displacements. The method offers a simpletouse way to check the validity of reaction rates but has the potential to offer more accurate rates on its own by representing the transition state with the ridge.
Original language  English 

Publisher  Department of Energy Conversion and Storage, Technical University of Denmark 

Number of pages  126 
Publication status  Published  2012 
Note re. dissertation
The work was financially supported by DTU and CAMD, as well as the Nordic Center of Excellence on Hydrogen Storage Materials, the European Graduate School for Sustainable Energy Technologies  The Molecular Approach and Catalysis for Sustainable Energy (CASE).Fingerprint Dive into the research topics of 'Identifying Reaction Pathways and their Environments: Methods and Applications'. Together they form a unique fingerprint.
Projects
 1 Finished

Computational methods for describing reaction rates at interfaces of energy materials
Maronsson, J. B., Vegge, T., Jonsson, H., Rossmeisl, J., Henkelman, G. & Wahnström, G.
01/12/2008 → 18/04/2012
Project: PhD