Validity boundary of orbital-free molecular dynamics method corresponding to thermal ionization of shell structure

With ${}^6\mathrm{Li}\text{D}$ as an example, we show that the applicable region of the orbital-free molecular dynamics (OFMD) method in a large temperature range is determined by the thermal ionization process of bound electrons in shell structures. The validity boundary of the OFMD method is defined roughly by the balance point of the average thermal energy of an electron and the ionization energy of the lowest localized electronic state. This theoretical proposition is based on the observation that the deviation of the OFMD method originates from its less accurate description to the charge density in partially ionized shells, as compared with the results of the extended first-principles molecular dynamics method, which well reproduces the charge density of shell structures.

Figure 1

(a) Principal Hugoniots of ${}^6\mathrm{Li}\text{D}$ calculated by using the OFMD method (Calc. 1) and the ext-FPMD method (Calc. 2), compared with preceding OFMD results [28] and SESAME 7360 [28], SESAME 7245 [28]. Ionization ratio $\alpha$ of the 1s state of the lithium element along the ext-FPMD Hugoniot is also displayed. (b) OFMD Hugoniots calculated with different $E_0$, where the red solid curve is the ext-FPMD result, and the black curve is Calc. 1 in (a).

Figure 2

Relative deviation of pressure (${\delta }_P$) and energy difference (${\delta }_E$) of OFMD calculations with respect to the ext-FPMD results. In the subfigure of ${\delta }_E$, results calculated with $E_0=-254.85$ eV and $E_0=-192.82$ eV are displayed. As a reference, ionization ratios of the corresponding thermal states are displayed together.

Figure 3

Density of electronic states and projected density of states of the $1s$ state of Li for selected ${}^6\mathrm{Li}\text{D}$ thermal states along the Hugoniot curves.

Figure 4

Typical charge density distribution along the line connecting two ions, calculated from the OFMD method and the ext-FPMD method. (a)–(c) Charge density distribution in the thermal state $\eta =3.00$ and $T=2.22$ eV. (d)–(f) Charge density distribution in the thermal state $\eta =4.11$ and $T=300$ eV.