	Embedded Cluster	Isolated Cluster
	Detailed spin orbital population for 3d (Fe), 4d (Rh, Pd), 5p (Rh, Pd) and 4p (As)	Detailed spin orbital population for 3d (Fe), 4d (Rh, Pd), 5p (Rh, Pd) and 4p (As)
Ba₄Fe₅As₈	$S = 5 / 2$	$S = 7 / 2$
Fe	$d_{x y}^{- 0.62} + d_{x z}^{0.12} + d_{y z}^{0.82} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{0.01}$	$d_{x y}^{- 0.01} + d_{x z}^{- 0.01} + d_{y z}^{- 0.01} + d_{x^{2} - y^{2}}^{0.01} + d_{z^{2}}^{- 0.02}$
Fe (n.n.)a	$d_{x y}^{0.1} + d_{x z}^{- 0.07} + d_{y z}^{0.02} + d_{x^{2} - y^{2}}^{0.01} + d_{z^{2}}^{0}$	$d_{x y}^{- 0.01} + d_{x z}^{0.13} + d_{y z}^{- 0.05} + d_{x^{2} - y^{2}}^{- 0.03} + d_{z^{2}}^{0.04}$
Fe (n.n.)b	$d_{x y}^{0.18} + d_{x z}^{0.06} + d_{y z}^{- 0.07} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{- 0.11}$	$d_{x y}^{- 0.03} + d_{x z}^{00.2} + d_{y z}^{0} + d_{x^{2} - y^{2}}^{- 0.01} + d_{z^{2}}^{- 0.01}$
As (n.n.)	$p_{x}^{0.07} + p_{y}^{0} + p_{z}^{0.14}$	$p_{x}^{- 0.04} + p_{y}^{- 0.04} + p_{z}^{0}$
Ba₄Fe₄RhAs₈	$S = 1$	$S = 2$
Rh	$d_{x y}^{- 0.01} + d_{x z}^{0.01} + d_{y z}^{- 0.06} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{0.01}$ $p_{x}^{0} + p_{y}^{0} + p_{z}^{0}$	$d_{x y}^{- 0.01} + d_{x z}^{- 0.36} + d_{y z}^{- 0.46} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{- 0.01}$ $p_{x}^{0.04} + p_{y}^{0.25} + p_{z}^{0}$
Fe (n.n.)a	$d_{x y}^{0} + d_{x z}^{0.01} + d_{y z}^{0.04} + d_{x^{2} - y^{2}}^{- 0.02} + d_{z^{2}}^{- 0.01}$	$d_{x y}^{0.38} + d_{x z}^{- 0.38} + d_{y z}^{0.01} + d_{x^{2} - y^{2}}^{- 0.09} + d_{z^{2}}^{0.05}$
Fe (n.n.)b	$d_{x y}^{- 0.02} + d_{x z}^{0} + d_{y z}^{0.01} + d_{x^{2} - y^{2}}^{0.03} + d_{z^{2}}^{0}$	$d_{x y}^{0.01} + d_{x z}^{0.01} + d_{y z}^{- 0.01} + d_{x^{2} - y^{2}}^{- 0.03} + d_{z^{2}}^{0}$
As (n.n.)	$p_{x}^{0.01} + p_{y}^{0.01} + p_{z}^{0}$	$p_{x}^{0.11} + p_{y}^{- 0.21} + p_{z}^{- 0.21}$
Ba₄Fe₄PdAs₈	$S = 3 / 2$	$S = 5 / 2$
Pd	$d_{x y}^{- 0.01} + d_{x z}^{- 0.04} + d_{y z}^{- 0.02} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{- 0.01}$ $p_{x}^{0.01} + p_{y}^{0} + p_{z}^{0.03}$	$d_{x y}^{- 0.01} + d_{x z}^{0.05} + d_{y z}^{0} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{0}$ $p_{x}^{- 0.05} + p_{y}^{0.08} + p_{z}^{0}$
Fe (n.n.)a	$d_{x y}^{- 0.02} + d_{x z}^{0.01} + d_{y z}^{- 0.03} + d_{x^{2} - y^{2}}^{0.02} + d_{z^{2}}^{0}$	$d_{x y}^{- 0.07} + d_{x z}^{- 0.15} + d_{y z}^{- 0.16} + d_{x^{2} - y^{2}}^{0.03} + d_{z^{2}}^{0.01}$
Fe (n.n.)b	$d_{x y}^{0.47} + d_{x z}^{0.01} + d_{y z}^{0.01} + d_{x^{2} - y^{2}}^{- 0.01} + d_{z^{2}}^{0.15}$	$d_{x y}^{0} + d_{x z}^{0.01} + d_{y z}^{0.01} + d_{x^{2} - y^{2}}^{0} + d_{z^{2}}^{0}$
As (n.n.)	$p_{x}^{0} + p_{y}^{0} + p_{z}^{0}$	$p_{x}^{- 0.01} + p_{y}^{- 0.02} + p_{z}^{- 0.02}$