N. Aquino

Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

The compressed helium atom variationally treated via a correlated Hylleraas wave function

Abstract We calculate ground state energy, critical cage and ionization radius for the confined helium atom centered in a spherical impenetrable box. Total and ionization energies, pressure on the confining boundary and the expectation value 〈 r 12 〉 are obtained as a function of the box radii. Three nonlinear parameters and N (=1,5 and 10) linear coefficients are variationally optimized within wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r 12 , both, via a Slater type exponent and through polynomial terms entering the expansion. The wave function includes a cut-off factor to ensure correct fulfillment of the boundary condition (vanishing wave function at the box edge). With the 10-term basis set we obtain energy values very close (within millihartrees) to the nearly exact results of Joslin and Goldman [J. Phys. B 25 (1992) 1965] obtained by means of a Quantum Monte Carlo method which, computationally, is a great deal more demanding than our variational approach.

DFT reactivity indices in confined many-electron atoms

The density functional descriptors of chemical reactivity given by electronegativity, global hardness and softness are reported for a representative set of spherically confined atoms of IA, IIA, VA and VIIIA series in the periodic table. The atomic electrons are confined within the impenetrable spherical cavity defined by a given radius of confinement satisfying the Dirichlet boundary condition such that the electron density vanishes at the radius of confinement. With this boundary condition the non-relativistic spin-polarized Kohn-Sham equations were solved. The electronegativity in a confined atom is found to decrease as the radius of confinement is reduced suggesting that relative to the free state the atom loses its capacity to attract electrons under confined conditions. While the global hardness of a confined atom increases as the radius of confinement decreases, due to the accompanying orbital energy level crossing, it does not increase infinitely. At a certain confinement radius, the atomic global hardness is even reduced due to such crossover. General trends of the atomic softness parameter under spherically confined conditions are reported and discussed.

Static dipole polarizability of shell-confined hydrogen atom

Using the Sternheimer perturbation-numerical procedure, calculations of static dipole polarizability are reported for the shell-confined hydrogen atom as defined by two impenetrable concentric spherical walls. Unusually high polarizability states are predicted for the hydrogen atom as the inner sphere radius is increased to larger values inside the outer sphere of a constant radius. Implications of this model in mimicking internal compression leading to the metallic behaviour of the shell-confined hydrogen atoms are discussed.

The inversion potential for NH3 using a DFT approach

Abstract Using a density functional theory approach, we generate a potential energy surface (PES) and, by a least-squares method, we obtain a polynomial function which represents the unidimensional potential along the inversion coordinate, with a very high precision. The inversion spectrum of NH3 is then determined by solving the Schrodinger equation for this potential, using a better approximated reduced mass which is a function of the inversion coordinate. The calculated inversion frequencies obtained through this method are compared against those generated by Hartree–Fock theory and also with the experimental values. We find that our theoretical results are by far the most accurate.