Computational investigations of the electronic structure of molecular actinide compounds

In this PhD thesis the electronic structure of a range of actinide compounds has been investigated using density functional theory. The reason for using DFT instead of other methods is mainly due to the size of the compounds which makes multireference calculations prohibitively expensive, but also to make comparisons with previously calculated DFT results. The first chapter presents the basic concepts of electronic structure theory and the chemical properties of the actinides and lanthanides. The theoretical foundation of DFT and the consequences of relativity are also introduced. In the second chapter the bonding in mixed MUCl6, MUCl8 2-, NpReCl8 2- and PuOsC NpReCl8 2- (M = Mo, W) systems is investigated and compared with previous work on the M2Cl6, M2C NpReCl8 2- U2Cl6 and U2C NpReCl8 2- systems. The study shows that the total bonding energy in the mixed compounds is the average of the two “pure” compounds. The third chapter deals with systems of plenary or lacunary Keggin phosphomolybdate coordination to actinide (Th), lanthanide (Ce, La, Lu) and transition metal (Hf, Zr) cations: [PMo12O40]3-, [PMo11O39]2 14-, [PMo12O40]2 6- and [PMo11O39][PMo12O40]10-. These large, highly anionic systems proved to be very challenging computationally. The main result of the study confirms that the bonding is ionic and that there are few differences in the behaviour of the transition metals. In the fourth chapter the electronic spectrum of NpO2 2+, NpO2Cl4 2- and NpO2(OH)4 2- is calculated using time dependent DFT. TDDFT has proved adequate for the uranium analogues of these systems and this extends previous work on f0 systems to f1 systems. The results show that TDDFT is in poor agreement with both experimental results and multireference calculations for these compounds. In chapter five, group 15 and 16 uranyl analogues have been investigated. For the UE2 (E = O, S, Se, Te) analogues the geometry bends for all chalcogens heavier than O. The UE2 2+ analogues remain linear all the way down group 16. In U(NCH3)2 2+ the formation of a {pi} “back bone” along the axis of the molecule was noted. The {sigma}-bonding valence MOs stabilize while the {pi} MOs are destabilized down group 15 and 16. Chapter six is a summary of the results in this thesis and an outlook on potential future work

Correlated time-dependent transport through a 2D quantum structure

We use a generalized master equation (GME) to describe the nonequilibrium magnetotransport of interacting electrons through a broad finite quantum wire with an embedded ring structure. The finite quantum wire is weakly coupled to two broad leads acting as reservoirs of electrons. The mutual Coulomb interaction of the electrons is described using a configuration interaction method for the many-electron states of the central system. We report some non-trivial interaction effects both at the level of time-dependent filling of states and on the time-dependent transport. We find that the Coulomb interaction in this non-trivial geometry can enhance the correlation of electronic states in the system and facilitate it's charging in certain circumstances in the weak coupling limit appropriate for the GME. In addition, we find oscillations in the current in the leads due to the correlations oscillations caused by the switched-on lead- system coupling. The oscillations are influenced and can be enhanced by the external magnetic field and the Coulomb interaction.Comment: RevTeX (pdf-LaTeX), 10 pages with 15 included jpg figure

The key aspects of innovation-oriented regional industrial and economic policy

Integration processes taking place in the economy, the new requirements to enhance the effectiveness of production during international competition as well as the need to ensure the social conditions lead to the development and implementation of innovation-oriented regional industrial and economic policy, which in its turn, requires adopting substantial organizational and economic recommendations

Reconstruction of Random Colourings

Reconstruction problems have been studied in a number of contexts including biology, information theory and and statistical physics. We consider the reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for large $k$. Bhatnagar et. al. showed non-reconstruction when $\Delta \leq \frac12 k\log k - o(k\log k)$ and reconstruction when $\Delta \geq k\log k + o(k\log k)$. We tighten this result and show non-reconstruction when $\Delta \leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$ and reconstruction when $\Delta \geq k[\log k + \log \log k + 1+o(1)]$.Comment: Added references, updated notatio

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components