A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Soil organic carbon management for sustainable land use in Sudano-Sahelian West Africa

Judged by their negative nutrient balances, low soil cover and low productivity, the predominant agro-pastoral farming systems in the Sudano-Sahelian zone of West Africa are highly unsustainable for crop production intensification. With kaolinite as the main clay type, the cation exchange capacity of the soils in this region, often less than 1 cmol_c kg^-1 soil, depends heavily on the organic carbon (Corg) content. However, due to low carbon sequestration and to the microbe, termite and temperature-induced rapid turnover rates of organic material in the present land-use systems, Corg contents of the topsoil are very low, ranging between 1 and 8 g kg^-1 in most soils. For sustainable food production, the availability of phosphorus (P) and nitrogen (N) has to be increased considerably in combination with an improvement in soil physical properties. Therefore, the adoption of innovative management options that help to stop or even reverse the decline in Corg typically observed after cultivating bush or rangeland is of utmost importance. To maintain food production for a rapidly growing population, targeted applications of mineral fertilisers and the effective recycling of organic amendments as crop residues and manure are essential. Any increase in soil cover has large effects in reducing topsoil erosion by wind and water and favours the accumulation of wind-blown dust high in bases which in turn improves P availability. In the future decision support systems, based on GIS, modelling and simulation should be used to combine (i) available fertiliser response data from on-station and on-farm research, (ii) results on soil productivity restoration with the application of mineral and organic amendments and (iii) our present understanding of the cause-effect relationships governing the prevailing soil degradation processes. This will help to predict the effectiveness of regionally differentiated soil fertility management approaches to maintain or even increase soil Corg levels.

Influence of the buffer environment on the Relative Biological Effectiveness of carbon ion radiation, investigated by Scanning Force Microscopy and gel electrophoresis

This work focuses on the analysis of the influence of environment on the relative biological effectiveness (RBE) of carbon ions on molecular level. Due to the high relevance of RBE for medical applications, such as tumor therapy, and radiation protection in space, DNA damages have been investigated in order to understand the biological efficiency of heavy ion radiation. The contribution of this study to the radiobiology research consists in the analysis of plasmid DNA damages induced by carbon ion radiation in biochemical buffer environments, as well as in the calculation of the RBE of carbon ions on DNA level by mean of scanning force microscopy (SFM). In order to study the DNA damages, besides the common electrophoresis method, a new approach has been developed by using SFM. The latter method allows direct visualisation and measurement of individual DNA fragments with an accuracy of several nanometres. In addition, comparison of the results obtained by SFM and agarose gel electrophoresis methods has been performed in the present study. Sparsely ionising radiation, such as X-rays, and densely ionising radiation, such as carbon ions, have been used to irradiate plasmid DNA in trishydroxymethylaminomethane (Tris buffer) and 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES buffer) environments. These buffer environments exhibit different scavenging capacities for hydroxyl radical (HO0), which is produced by ionisation of water and plays the major role in the indirect DNA damage processes. Fragment distributions have been measured by SFM over a large length range, and as expected, a significantly higher degree of DNA damages was observed for increasing dose. Also a higher amount of double-strand breaks (DSBs) was observed after irradiation with carbon ions compared to X-ray irradiation. The results obtained from SFM measurements show that both types of radiation induce multiple fragmentation of the plasmid DNA in the dose range from D = 250 Gy to D = 1500 Gy. Using Tris environments at two different concentrations, a decrease of the relative biological effectiveness with the rise of Tris concentration was observed. This demonstrates the radioprotective behavior of the Tris buffer solution. In contrast, a lower scavenging capacity for all other free radicals and ions, produced by the ionisation of water, was registered in the case of HEPES buffer compared to Tris solution. This is reflected in the higher RBE values deduced from SFM and gel electrophoresis measurements after irradiation of the plasmid DNA in 20 mM HEPES environment compared to 92 mM Tris solution. These results show that HEPES and Tris environments play a major role on preventing the indirect DNA damages induced by ionising radiation and on the relative biological effectiveness of heavy ion radiation. In general, the RBE calculated from the SFM measurements presents higher values compared to gel electrophoresis data, for plasmids irradiated in all environments. Using a large set of data, obtained from the SFM measurements, it was possible to calculate the survive rate over a larger range, from 88% to 98%, while for gel electrophoresis measurements the survive rates have been calculated only for values between 96% and 99%. While the gel electrophoresis measurements provide information only about the percentage of plasmids DNA that suffered a single DSB, SFM can count the small plasmid fragments produced by multiple DSBs induced in a single plasmid. Consequently, SFM generates more detailed information regarding the amount of the induced DSBs compared to gel electrophoresis, and therefore, RBE can be calculated with more accuracy. Thus, SFM has been proven to be a more precise method to characterize on molecular level the DNA damage induced by ionizing radiations.

Delocalization of a hole in van der Waals clusters: Ionization potential of rare-gas and small Hg_n clusters

The size dependence of the ionization potential I_p(n) of van der Waals (vdW) bound clusters has been calculated by using a model Hamiltonian, which includes electron hopping, vdW interactions, and charge-dipole interactions. The charge-density and dipole-density distributions for both neutral and ionized n-atom clusters are determined self-consistently. The competition between the polarization energy of the neutral atoms surrounding a partially localized hole and the tendency toward hole delocalization in the ionized clusters is found to dominate the size dependence of I_p(n). To test our theory, we culculate I_p(Xe_n) and I_p(Kr_n) for n \le 300. Good quantitative agreement with experiment is obtained. The theory is also applied to calculate I_p(Hg_n). Comparison with experiments suggests that in Hg_n^+ clusters with n \le 20 the positive charge is mainly distributed within a trimer which is situated at the center of the cluster and which polarizes the n - 3 surrounding neutral atoms.

Theory for Optical Absorption in Small Clusters: Dependence on Atomic Structure and Cluster Size

We present a theory which permits for the first time a detailed analysis of the dependence of the absorption spectrum on atomic structure and cluster size. Thus, we determine the development of the collective excitations in small clusters and show that their broadening depends sensitively on the tomic structure, in particular at the surface. Results for Hg_n^+ clusters show that the plasmon energy is close to its jellium value in the case of spherical-like structures, but is in general between w_p/ \wurzel{3} and w_p/ \wurzel{2} for compact clusters. A particular success of our theory is the identification of the excitations contributing to the absorption peaks.

Unrestricted hartree-fock calculation of the ionization potential of small Hg_n clusters

The ionization potential of small Hg_n clusters has been calculated. For the first time good agreement with experimental results has been obtained. It is shown that interatomic Coulomb interactions are important. The energy of Hg_n^+ is calculated using the unrestricted inhomogeneous Hartree-Fock approximation. As a consequence of a change in the charge distribution in Hg_n^+ , we obtain an abrupt change in the slope of the ionization potential at the critical cluster size n_cr ~ 14. The presented results are expected to be valid for covalent clusters in between ionized van der Waals clusters and metallic clusters.

Calculation of the electronic properties of neutral and ionized divalent-metal clusters

The electronic properties of neutral and ionized divalent-metal clusters have been studied using a microscopic theory, which takes into account the interplay between van der Waals (vdW) and covalent bonding in the neutral clusters, and the competition between hole delocalization and polarization energy in the ionized clusters. By calculating the ground-state energies of neutral and ionized. Hg_n clusters, we determine the size dependence of the bond character and the ionization potential I_p(n). For neutral Hg_n clusters we obtain a transition from van del Waals to covalent behaviour at the critical size n_c ~ 10-20 atoms. Results for I_p(Hg_n) with n \le 20 are in good agreement with experiments, and suggest that small Hg_n^+ clusters can be viewed as consisting of a positive trimer core Hg_3^+ surrounded by n - 3 polarized neutral atoms.

On the localization of electrons and holes in Hg_n and rare-gas clusters

We have used a microscopic theory to study the size dependence of the degree of localization of the valence electrons and holes in neutral an ionized rare-gas and Hg_n clusters. We discuss under which circumstances localization of the electrons and holes is favoured. We have calculated the ionization potential of Xe_n, Kr_n and small Hg_n clusters. Good agreement with experiments is obtained. We have also determined the dependence of the ionization potential on cluster structure.

On the transition from localized to delocalized electronic states in divalent-metal clusters

The transition from van der Waals to covalent bonding, which is expected to occur in divalent-metal clusters with increasing cluster size, is discussed. We propose a model which takes into account, within the same electronic theory, the three main competing contributions, namely the kinetic energy of the electrons, the Coulomb interactions between electrons, and the s \gdw p intraatomic transitions responsible for van der Waals like bonding. The model is solved by taking into account electron correlations using a generalized Gutzwiller approximation (slave boson method). The occurrence of electron localization is studied as a function of the interaction parameters and cluster size.

Theory for the optical properties of small Hg_n clusters

The static and dynamical polarizabilities of the Hg-dimer are calculated by using a Hubbard Hamiltonian to describe the electronic structure. The Hamiltonian is diagonalized exactly within a subspace of second-quantized electronic states from which only multiply ionized atomic configurations have been excluded. With this approximation we can describe the most important electronic transitions including the effect of charge fluctuations. We analyze the polarizability as a function of the intraatomic Coulomb interaction which represents the repulsion between electrons. We obtain that this interaction results in strong electronic correlations in the excited states and increases the first excitation energy of the dimer by 0.8 eV in comparison to a calculation which neglects correlations, resulting in a better agreement with the experiment.

Theory for the change of bond character in divalent-metal clusters

To determine the size dependence of the bonding in divalent-metal clusters we use a many-electron Hamiltonian describing the interplay between van der Waals (vdW) and covalent interactions. Using a saddle-point slave-boson method and taking into account the size-dependent screening of charge fluctuations, we obtain for Hg_n a sharp transition from vdW to covalent bonding for increasing n. We show also, by solving the model Hamiltonian exactly, that for divalent metals vdW and covalent bonding coexist already in the dimers.

Slave-boson approach to the size-dependent transition from van der Waals to covalent bonding in Hg_n clusters

We use a microscopic theory to describe the dynamics of the valence electrons in divalent-metal clusters. The theory is based on a many-body model Harniltonian H which takes into account, on the same electronic level, the van der Waals and the covalent bonding. In order to study the ground-state properties of H we have developed an extended slave-boson method. We have studied the bonding character and the degree of electronic delocalization in Hg_n clusters as a function of cluster size. Results show that, for increasing cluster size, an abrupt change occurs in the bond character from van der Waals to covalent bonding at a critical cluster size n_c ~ 10-20. This change also involves a transition from localized to delocalized valence electrons, as a consequence of the competition between both bonding mechanisms.

Electronic structure calculations of small AI_n (n = 2 - 8) clusters

The electronic states of small AI_n (n = 2 - 8) clusters have been calculated with a relativistic ab-initio MOLCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photoelectron spectra.

Nuclear charge radii from X-ray transitions in muonic atoms of carbon, nitrogen and oxygen

Energies of muonic X-rays of the K-series of carbon, nitrogen and oxygen have been measured with an accuracy of about 15 eV. Root mean square radii of the nuclear charge distributions were deduced. The results 2.49±0.05 fm for carbon, 2.55 ±0.03 fm for nitrogen and 2.71 ±0.02 fm for oxygen are in good agreement at comparable accuracy with recent electron scattering data.

Time-resolved studies of neutral and ionized Na_n clusters with femtosecond light pulses

The real-time dynamics of Na_n (n=3-21) cluster multiphoton ionization and fragmentation has been studied in beam experiments applying femtosecond pump-probe techniques in combination with ion and electron spectroscopy. Three dimensional wave packet motions in the trimer Na_3 ground state X and excited state B have been observed. We report the first study of cluster properties (energy, bandwidth and lifetime of intermediate resonances Na_n^*) with femtosecond laser pulses. The observation of four absorption resonances for the cluster Na_8 with different energy widths and different decay patterns is more difficult to interpret by surface plasmon like resonances than by molecular structure and dynamics. Timeresolved fragmentation of cluster ions Na_n^+ indicates that direct photo-induced fragmentation processes are more important at short times than the statistical unimolecular decay.