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We discuss some general properties of the wave functions of H-2(+) in two dimensions, when the electron is close to the nucleus, and when it is far away from the nucleus. Based on these properties, some simple, parameter-free wave functions are developed for some of the states. They lead to quite accurate energies and give an insight into the structure of H-2(+) in two dimensions. These wave functions and appropriate correlation functions, are then used to develop reliable wave functions for H-2 in two dimensions. They provide a clear and interesting comparison with the corresponding results in three dimensions. (C) 2003

Some local properties are analysed for (2p)(2) P-3 and (2p)(3p) P-1 states of He and its isoelectronic ions in the domains where one of the electrons is far away, where it is near the nucleus, and where the two electrons are close to each other. Based on these properties, simple wavefunctions with zero free parameters or one free parameter are developed for these states. Apart from giving accurate values for the energies and other properties, these wavefunctions provide a clear insight into the structure of these states.

We have developed a simple model potential with a hard core and the correct larger-tau Coulombic behaviour, to describe the interaction of an electron with a closed shell. One has an exact, analytic ground state wave function for this potential. This potential is used to develop two-electron perturbed and unperturbed wave functions, with the correct asymptotic behaviour and cusp conditions. These wave functions allow us to obtain accurate values for the two-electron energies, polarisabilities, hyperpolarisabilities, and dispersion coefficients of alkaline earth sequences. Many of these results are the only ones available in the literature.