Table 3.

Comparison of hydration structures of Ba²⁺ and Ra²⁺. ${\overline{\mathit{r}}}_{M–O}$, CN, tilt angle ($\mathit{\Psi }$), Debye–Waller factor (${\mathit{\sigma }}^2$), and $\mathrm{\epsilon }$ for Ra²⁺ and Ba²⁺

M		Method	${\overline{\mathit{r}}}_{M–O}$ (Å)	CN	$\mathit{\Psi }(°)$	${\mathit{\sigma }}^2$ (Å2)	$\mathrm{\epsilon }$ (Å)	Ref.
Ra2+	Exp.	EXAFS	2.87 ± 0.06	9.2 ± 1.9	–	0.027	–	This study
Ra2+	Sim.	AIMD SCAN	2.88	8.4	132	0.041	0.31	This study
Ra2+	Sim.	FMO-MD	2.85	8.1	–	–	–	Previous study (Matsuda and Mori, 2014b)
Ra2+	Sim.	MCP	2.80–2.95	7–9	–	–	–	Previous study (Matsuda and Mori, 2014a)
Ra2+	Sim.	MD	2.93	9.8	135	0.034	0.24	Previous study (Pappalardo et al., 2021)
Ba2+	Exp.	EXAFS	2.79 ± 0.02	8.0 ± 1.9	–	0.020	–	Previous study (Yamaguchi et al., 2021)
Ba2+	Exp.	EXAFS	2.81 ± 0.03	8.1 ± 0.3	–	–	–	Previous study (Persson et al., 1995)
Ba2+	Exp.	EXAFS	2.85 ± 0.02	8.0 ± 0.2	–	–	–	Previous study (Migliorati, Caruso and D’Angelo, 2019)
Ba2+	Sim.	AIMD SCAN	2.78	7.8	138	0.031	0.26	This study and previous study (Yamaguchi et al., 2021)
Ba2+	Sim.	AIMD PW91	2.80	8.0	–	–	–	Previous study (Chaudhari et al., 2015)
Ba2+	Sim.	MD	2.81	9.4	138	0.034	0.22	Previous study (Pappalardo et al., 2021)
Ba2+	Sim.	MD	2.85	8.1	–	–	–	Previous study (Migliorati, Caruso and D’Angelo, 2019)
Ba2+	Sim.	QM/MM	2.86	9.3	–	–	–	Previous study (Hofer et al., 2005)