An extended Hubbard model with large short and long-ranged Coulomb repulsions and distant transfer is numerically investigated by use of the Lanczos exact diagonalization (ED) method to study the charge order and unconditional dimerization of a chain at density rho (ρ)= 0.4. From the analysis of the spin and charge correlation functions, a picture consistent with the formation of a dimer insulating state, which is of Wigner lattice-type (WL) charge order (CO), is obtained. The next-nearest neighbour (NNN) hopping t2 enhances the intradimer correlations and weakens the interdimer correlations. Implications for the CuO2 chains in Sr14Cu24O41 are discussed.We have also introduced a Heisenberg model which parametrically depends on hole positions. If the electrostatic hole-hole repulsion is included such a model allows to evaluate all energy eigenvalues and eigenstates (for small system size) and thus enables us to evaluate thermodynamic properties as function of temperature,magnetic field, and doping. Assuming certain exchange constants we can investigate the influence of the electrostatic hole-hole repulsion on ground state properties as well as on thermal averages like the magnetization which include contributions of low-lying spin-hole configurations.

Processes at the air-water/ice interface are known to play a very important role in the release of reactive halogen species with atmospheric aerosols serving as catalysts. The ability to make different types of ice with various morphologies, hence, different adsorption and surface properties in vacuum, provide a useful way to probe the catalytic effect of ice in atmospheric reactions. Also, the use of the liquid jet technique provides the rare opportunity to probe liquid samples at the interface; hitherto impossible to investigate with traditional surface science techniques. Studies of reactions on both ice and liquid surfaces at ambient conditions are usually complicated by the rapid desorption and adsorption processes due to the high evaporation rates at the surface. To gain a better understanding and improve modeling of several atmospheric relevant reactions, it is therefore important to develop laboratory techniques that provide an opportunity to investigate non-thermal reactions on both ice and liquid surfaces. Detailed investigation of the interactions of atmospheric relevant molecules (methyl iodide and hydrogen chloride) on water ice at low temperature in UHV conditions has been carried out. These interactions were studied using different techniques such as temperature programmed desorption (TPD), electron stimulated desorption (ESD) and resonance enhanced multiphoton ionization (REMPI). Unlike probing reactions on ice surfaces, investigating air/liquid interfaces present several challenges. This is because traditional surface science techniques require an ultra high vacuum environment to prevent distortion of information due to interference from equilibrium vapor above the liquid surface during data acquisition. The liquid jet technique facilitates the direct study of continually renewed liquid surfaces in high vacuum, thereby preventing the constant changing of the properties and composition of the liquid surface due to the aging process (diffusion of impurities or liquid constituent). A linear time-of-flight mass spectrometer has been used to monitor ion ejection during laser irradiation of liquid jet containing aqueous solutions and pure water. Since these ions are ejected exclusively from the surface of the liquid and the cluster distributions observed are influenced by the local structure, these experiments provide a sensitive probe of the liquid vacuum interface of these solutions. Though the research is fundamental, the results obtained from these investigations indicate how the discontinuity of bulk properties on the surface of both ice and aqueous solutions affects interfacial reactions.