1 Diffusion

^[1]The fundamental kinetic equation for surface diffusion is given in eq 2. $D={\nu}a^2(\frac{-E_{diff}}{k_BT})$ where $D$ = diffusion coefficient, $\nu$ = jump frequency = $k_BT/h$ = $\sim6\times10^{12}$ s⁻¹ at 300 K, $a$ = jump distance ($\sim2\times10^{−8}$ cm for the activation step), and $E_{diff}$ = diffusion activation energy.

^[2]The kinetic equation for surface diffusion is given by Ref.^[1], $D=D_0exp(\frac{-E_m}{k_BT})={\nu}d^2exp(\frac{-E_m}{k_BT})$ where $D$ is the diffusion coefficient, $D_0$ is the diffusion prefactor, $n$ is the attempt frequency, $d$ is the jump distance, and $E_m$ is diffusion barrier. Assume that the motion of Ca atom around its equilibrium position is harmonic, the attempt frequency n can be estimated by a parabolic fit the curve of total energy as a function of Ca near the equilibrium position along the diffusion path using Eq. (2). with $k$ is the force constant and $m$ the mass of Ca. $E=\frac{1}{2}kr^2$ $\nu=\frac{1}{2\pi}\sqrt{k/m}$ The calculated attempt frequency and the diffusion prefactor are 1.64 THz and $1.37\times10 ^{-3}$ cm²/s, respectively. The estimated diffusioncoefficient for Ca on the novel boron sheet at 300 K is $1.2\times10^{-10}$ cm²/s.

2 Stability

^[2]The stability of the hydrogen adsorbed structures is judged by the relative energy, which are defined by formula (5) and (6) for CaB₈(H₂)_n and Ca₂B₈(H₂)₁₂, respectively, of the adsorbed system with respected to the separated species: $E_r=E_{CaB_8(H_2)_n}-E_{CaB_8}-n(E_{H_2}+\mu_{H_2}(T,P))$ Where $E_{CaB_8(H_2)_n}$, $E_{CaB_8}$ and $(E_{H_2}$ are still the DFT energy for $CaB_8(H_2)_n$ , $CaB_8$ and $H_2$ molecule, respectively. $\mu_{H_2}(T,P)$ is chemical potential of hydrogen molecule at given pressure and temperature. The $\mu_{H_2}(T,P)$ can be calculated by the formula $\mu_{H_2}(T,P)=\Delta{H}-T\Delta{S}+k_BTln(\frac{P}{P^0})$ where $P^0 = 1$ bar=0.1 mPa, $k_B$ is Boltzmann constant, ($\Delta{H}-T\Delta{S}$) is the changing of chemical potential due to changing the temper- ature from $T=0$ K to target temperature T at constant pres- sure $P^0$ . $\Delta{H }$is the changing in the enthalpy and $T\Delta{S}$ is entropy factor. For calculation values of ($\Delta{H}-T\Delta{S}$) the thermochemical tables[50] were used.