Investigation of the spin-density functional method for calculating spin-magnetic-moment densities

The spin-density functional formalism is investigated with the objective of producing practical methods for calculating the spin (magnetic moment) density, $m\left(\overrightarrow{\mathrm{r}}\right)$, of atoms, molecules, and metals. Calculations are performed for the atoms Li, Na, K, N, P, Mn, and As in their spherically symmetric ground states using two approximations for the exchange-correlation functional: (i) the exact treatment of exchange with a local approximation for correlation (referred to as "SUHF-C"), (ii) the local spin-density (LSD) approximation for both exchange and correlation. The "SUHF-C" values of $m\left(0\right)\mathrm{}$ for Li, Na, K, N, P, Mn, and As are 108, 99, 91, 200, -30, 108, and 93% of experiment, respectively. For Li, Na, and K the LSD approximation yields 98, 109, and 106%, respectively. Away from the nucleus, in all the cases studied, the LSD and "SUHF-C" results for $m\left(\overrightarrow{\mathrm{r}}\right)$ are in close agreement. We conclude that for systems where there is a large direct contribution the LSD approximation should give better than 90% accuracy, even at the origin. The results using "SUHF-C" suggest that it has the capability of yielding accurate values of $m\left(\overrightarrow{\mathrm{r}}\right)$ for atoms and molecules.