A previous shell-model-style calculation for the ground-state energy of the 'He nucleus, based on coupled cluster techniques, was able to treat exactly the centre-of-mass motion. It is now recast in a precisely equivalent but vastly more computationally efiaent form, directly in terms of coordinate-space correlation functions which are expanded in a Gaussian geminal basis and determined variationally. This reformulation further leads in a straightforward manner to a natural procedure for including higher-order correlations. Its implementation at even the simplest level produces a significant improvement in the already very good upper bounds achieved far the ground-state energy. Further extensions are also discussed.

Abstract. Here we study the singular anharmonic potentials by applying the analytic continuation method of Holubec and Stauffer. In order to do that we have developed several approximations to the problem, because this method cannot be applied when the solution has essential singularities &any point of its domain. All the options here shown have the same precision, giving us the eigenvalues correct to all the decimal places provided by the computer.

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The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both single configuration and multi configuration trial wave functions are implemented. Applications to several atomic systems are presented improving previous works. The results here obtained are very close to those calculated in either the Hartree-Fock and the multi configurational Hartree-Fock framework.

The electronic structure of confined atoms under impenetrable spherical walls is studied by means of the parameterized optimized effective potential method. A cut-off factor is employed to account for Dirichlet boundary conditions. Two atomic basis sets commonly used for describing free atoms have been analyzed within this scheme. The accuracy of the method is similar to that achieved for the free atoms. The ground state electrostatic multiplet of the carbon atom as well as the ground state and both the [Ar] and [Ar] excited states of the iron atom are studied. The behaviour of the energy levels with the confinement has been analyzed in terms of the different contributions to the total energy of the atom. For the iron atom, the effect of confinement on the outermost orbitals is studied.

A study of the first excited states of beryllium atom starting from explicitly correlated wave functions is carried out. Several properties are obtained and discussed focusing on the analysis of the Hund's rules in terms of the single-particle and electron pair intracule and extracule densities. A systematic study of the differences on the electronic distributions of the singlet and triplet states is carried out. The trial wave function used to describe the different bound states consists of a generalized Jastrowtype correlation factor times a configuration interaction model wave function. This model wave function has been fixed by using a generalization of the optimized effective potential method to deal with multiconfiguration wave functions. The optimization of the wave function and the calculation of the different quantities is carried out by means of the Variational Monte Carlo method.

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Abstract. Starting from explicitly correlated wavefunctions, the one-body momentum density, γ ( p), and the expectation values δ( p) and p n , with n = −2 to +3, have been obtained for the atoms helium to neon. All the calculations have been carried out by using the Monte Carlo algorithm. An analysis of the numerical accuracy of the method has been performed within the HartreeFock framework. The effects of the electronic correlations have been systematically studied by comparing the correlated results with the corresponding Hartree-Fock ones.