Live stream: https://livestream.com/hi/doktorsvornvilhjalmurasgeirsson

On June 24 Vilhjálmur Ásgeirsson will defend his doctoral thesis Development and evaluation of computational methods for studies of chemical reactions. The defence takes place in Askja, room 132 and starts at 14:00

**Opponents: **Dr. Gísli Hólmar Jóhannesson,Teacher at Keilir Academy

Dr. Baron Peters, Professor at the University of Illinois at Urbana – Champaign, USA

**Advisor: **Dr. Hannes Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland

**Doctoral committee: **Dr. Egill Skúlason, Professor at the Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland

Dr. Elvar Örn Jónsson, Specialist at the Science Institute, University of Iceland.

**Chair of Ceremony: **Dr. Einar Örn Sveinbjörnsson, Professor and the Head of the Faculty of Physical Sciences, University of Iceland

**Abstract:**

Methods for identifying the mechanism and estimating the rate of chemical reactions are presented and evaluated for a wide range of systems, using both classical and quantum mechanical description of the atomic nuclei. In the classical case, the minimum energy path (MEP) connecting two minima representing states of the system is found. Energy maxima on the path correspond to first order saddle points on the energy surface and give an estimate for the activation energy of the transition. For quantum mechanical description of the atoms, the optimal tunneling path (OTP) is found. This path is equivalent to a first order saddle point on the action surface, referred to as an instanton, and can be used to calculate the rate of thermally assisted tunneling. In order to navigate on these surfaces , the energy and force acting on the atoms needs to be evaluated. Such calculations are typically carried out using computationally intensive electronic structure methods. It is, therefore, important to develop both reliable and efficient algorithms to navigate on these surfaces in an efficient way, with as few evaluations of the energy and atomic forces as possible.

The various methods presented in this work are extensions of the widely used nudged elastic band (NEB) method. In NEB, a trial path represented by a set of points is iteratively displaced towards a target path, an MEP or OTP. The path is displaced downhill on the surface along the directions perpendicular to the path and spring forces are used to keep discretization points evenly distributed along the path. To achieve this, an accurate estimate of the tangent to the path is needed in order to decompose the forces into orthogonal and parallel components. In the first part of this work, the computational efficiency of NEB calculations of MEPs for molecular reactions is addressed. There, excessive computational effort is often needed because the MEPs often include long segments with little or no change in the energy. Computational resources are therefore wasted on resolving irrelevant segments of the path. Moreover, a sparse distribution of points along the path may also yield an inaccurate estimate of the tangent. This can affect the efficiency of an NEB calculation and can even lead to non-convergence. Two NEB variants are presented to automatically focus the computational effort on the most important part of the MEP, i.e. the region around the highest energy maximum. In one of these methods, a loose convergence on the MEP is first obtained and then a new set of points is automatically distributed in the region of the energy barrier to improve the resolution around the energy maximum and hence improve the tangent estimate there. In the second method, an increased density of points is obtained in the critical region of the MEP by adaptively scaling the strength of the spring interaction according to the energy, making the springs stiffer in regions of higher energy. Experience will show which one of these two approaches will turn out to be optimal, or perhaps a combination both. The computational effort when searching for saddle points can be reduced further by using a combination of NEB and an eigenvector-following (EF) method. In this approach, the points along the path are first converged loosely to the MEP. Then, information obtained from the NEB path and the point of maximum energy are used to automatically start an EF search to swiftly target the saddle point. These methods are applied to various chemical reactions and to a database of 121 molecular reactions. Furthermore, they have been implemented in the ORCA quantum chemistry software which is rapidly becoming the most widely used tool for electronic structure calculations in computational chemistry.

In the second part of this work, the focus is on the quantum mechanical description of the atomic nuclei and identification of OTPs. An OTP traces out the same path on the action surface as an instanton and can therefore be used to estimate the tunneling rate. Calculations of OTPs are found to be more optimal than the typical search method used for instanton calculations. The main reason is that the distribution of points along the OTP are controllable while the points tend to accumulate near the endpoints in instanton calculations. Therefore, fewer points can be used to represent the path in OTP calculations compared to instanton calculations.

In the first two parts, the electronic structure computations are carried out using density functional theory (DFT) as is now commonly done in computational chemistry. However, the selection of an appropriate level of theory for calculations of molecules and chemical reactions can be difficult. In this regard, a particularly interesting and challenging diamine cation is studied in the third part of this work. In this case, the existence of both a localized and delocalized electronic state has been inferred from experimental measurements. While, standard electronic structure methods, e.g. commonly used density functionals and the coupled cluster singles-doubles-(triples), method are unable to predict the existence of a localized electronic state. To shed light on this issue, which has turned into a controversy in the literature, and determine whether the localized state truly exists, high-level multireference wavefunction calculations of the energy surface are carried out and found to establish the existence of the localized state.

**About the doctoral candidate**

Vilhjálmur Ásgeirsson was born in 1988. He completed a BS degree in Chemistry from the University of Iceland in 2013 and a Ms degree in Chemistry from the University of Iceland in 2015.

He worked as a Research assistant at the University of Bonn from 2016 - 2017. Vilhjálmur started his Ph.D studies at the University of Iceland in 2017.