Controlling orbital collapse from inside and outside a transition element

Abstract

We report a study of bimodal behaviour of atomic wavefunctions for a transition element (Cr) and how this behaviour can be controlled and even turned into single-mode character either by (i) varying the effective nuclear charge for nonintegral values, or (ii) placing the atom in a spherical cavity of adjustable radius. Our conclusions have relevance to the emergence of valence instabilities for transition metals in the solid state. Also it is shown that the very existence of the bimodal wavefunctions provides an explanation for the frequently experienced instability of self-consistent field algorithms when a double-valley potential occurs, and suggestions are made on how to improve the numerical procedure for such calculations.

Structure and photoionization of confined atoms

“…Fig. 1 exemplifies modifications in the excited 3d % orbital of the confined excited @Cr % ð3p 5 3d 5 4s 3d % Þ; 7 P atom (Connerade and Dolmatov, 1998). The calculations were performed using the ''spin-polarized'' Hartree-Fock (SPHF) (Slater, 1974) approximation for the confined @Cr % atom modified by adding the spherical box potential (1) to the equations and solving them with the Dirichlet boundary conditions P nl ð0Þ ¼ P nl ðr c Þ ¼ 0; where P nl is the radial function for an atomic orbital of given principal n and orbital l quantum numbers.…”

“…Connerade (1997) employed this model to establish new principles underlying soft chemistry at the atomic level. Connerade and Dolmatov (1998) calculated, within the framework of non-relativistic Hartree-Fock (HF) equations, generalized by adding the V c ðrÞ potential (1) to the HF potential, modifications in both the ground state 4s and 3d 5 and excited state 3d % (due to the 3p-3d % excitation) orbitals in the confined Crð3p 6 3d 5 4s 1 Þ atom. For the Cr % ð3p 5 3d 5 3d % 4s 1 Þ excited configuration, the binding energy of the spectator 4s and 3d valence electrons was found to decrease with the decrease in the confinement radius r c ; whereas the energy of the 3d % excited electron at first increased and then decreased, the phenomenon earlier referred to (Connerade, 1997) as ''atomic swing''.…”

“…For the Cr % ð3p 5 3d 5 3d % 4s 1 Þ excited configuration, the binding energy of the spectator 4s and 3d valence electrons was found to decrease with the decrease in the confinement radius r c ; whereas the energy of the 3d % excited electron at first increased and then decreased, the phenomenon earlier referred to (Connerade, 1997) as ''atomic swing''. Also, Connerade and Dolmatov (1998) witnessed induced orbital collapse of the 3d % orbital when, due to increasing pressure on the atom (i.e., due to decreasing r c ) the 3d % orbital suddenly collapsed into the inner region of the atom, even though the radius r c of the spherical box was much greater (r c X11 a.u.) than the size of the atom.…”

“…Fig. 2 shows 3d % wavefunction for different Z for @Cr % ð3p 5 3d 5 4s3d % Þ (Connerade and Dolmatov, 1998). An important observation is that the modification in 3d % orbitals can equally well be modified by altering the nuclear charge Z of the atom.…”

“…3, we show the SPHF calculated results (Connerade and Dolmatov, 1998) for the binding energies of the ground-state 3d and 4s and excited 3d % electrons and the total energy for the excited @Cr % ð3p 5 3d 5 4s3d % Þ; 7 P atom.…”