In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

ABSTRACT:Total ground-state energies of free and confined many-electron atoms are studied through use of the Thomas-Fermi-Dirac-Weizsäcker energy density functional using known properties of the orbital electron densities. The concept of complete neglect of differential overlap put forward by Pople and Segal is combined with the original ideas of Wang and Parr on the development of statistical atomic models. For free atoms, it is found that total energies within 0.1% difference relative to Hartree-Fock values can be obtained using a prefactor ϭ 1/8 in the Weizsäcker inhomogeneity correction. The corresponding description of total radial densities and shell structure is found to be overall moderate when compared with Hartree-Fock calculations. It is also shown, for the first time, that this approach properly accounts for the ground-state energy evolution of many-electron atoms confined by hard spherical walls.

A generalization of previous theoretical studies of molecular confinement based on the molecule-in-a-box model for the H + 2 and H 2 systems whereby the confining cavity is assumed to be prolate spheroidal in shape is presented. A finite height for the confining barrier potential is introduced and the independent variation of the nuclear positions from the cavity size and shape is allowed. Within this scheme, the non-separable Schrödinger problem for the confined H + 2 and H 2 molecules in their ground states is treated variationally. In both cases, an important dependence of the equilibrium bond length and total energy on the confining barrier height is observed for fixed cavity sizes and shapes. It is also shown that-given a barrier height-as the cavity size is reduced, the limit of stability of the confined molecule is attained for a critical size. The results of this work suggest the adequacy of the proposed method for more realistic studies of electronic and vibrational properties of confined one-and two-electron diatomics for proper comparison with experiment.

A confinement model for many-electron atoms enclosed by a spherical boundary with finite-barrier potential height is presented. The model is based on the Thomas-Fermi-Dirac-Weizsäcker (TFDW) functional formalism using known properties of the orbital electron densities and constitutes a natural extension of a previously published report for the case of infinitely hard walls [Cruz et al., Int J Quantum Chem, 2005, 102, 897]. The confining barrier potential is considered as a step-like function of finite height V 0 . This assumption demands of the appropriate description of the TFDW energy functional for both the interior and exterior regions together with corresponding ansatz orbital density representations, subject to continuity boundary conditions at the wall. For a given cage radius R and confining barrier height V 0 , the total ground-state energy is variationally optimized with respect to the characteristic parameters defining the interior and exterior orbital densities. The total ground-state energy and corresponding electronic density are obtained as function of barrier height and cage radius for many-electron atoms and ions. The model is explicitly applied to He, Li, C, and Ne and various ionic species for barrier heights (atomic units) V 0 ϭ 0, 5, and ϱ. Given a barrier height V 0 , the results are presented for the critical cage size to produce one or more unbound electrons-yet, confined by the box-until reaching threshold size values for which electron escape from the confinement region take place.

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