Confinement effects on the spin potential of first row transition metal cations

Abstract

By using a spherical confinement method, the behaviour of spin potential and pairing energy is studied and compared to the free ion limit for a representative sample of first row transition metal cations. The study was carried out using three approximations within the Kohn–Sham model; exchange-only, exchange plus correlation contribution and correcting the self-interaction error. For the three approaches, the spin potential shows a close connection with the capability of a system to perform a spin-flip process. Namely, in accordance with Hund’s rule, the spin potential increases from low d occupation up to maximum for the half filled configurations; and it decreases from that point on, as d occupation grows. Such a conclusion is reached for confined and non-confined cations, even under extreme confinement conditions. In addition, two important observations are obtained: (a) In contrast to the neutral atoms situation, in the case of cations no eigenvalue crossings are observed under confinement conditions for the whole sample of ions tested. (b) The self-interaction error found in many exchange–correlation functionals does not affect the pairing energy over confined atoms, even when this error has an important contribution on a single eigenvalue. Therefore, pairing energy predicted by exchange–correlation functionals non-corrected by the self-interaction error can be made safely on transition metal cations under high pressures.

Keywords:

• Confined many-electron atoms
• pairing energy
• spin potential
• Kohn–Sham

Acknowledgements

We thank the Laboratorio de Visualización y Cómputo Paralelo at UAM-Iztapalapa and ML acknowledges CONACYT for a PhD fellowship.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by CONACYT [grant number 155698], [grant number 155070].