Reexamination of the interaction of atoms with a LiF(001) surface

Pairwise additive potentials for multielectronic atoms interacting with a LiF(001) surface are revisited by including an improved description of the electron density associated with the different lattice sites, as well as nonlocal electron density contributions. Within this model, the electron distribution around each ionic site of the crystal is described by means of a so-called “onion” approach that accounts for the influence of the Madelung potential. From such densities, binary interatomic potentials are then derived by using well-known nonlocal functionals. Rumpling and long-range contributions due to projectile polarization and van der Waals forces are also included. We apply this pairwise additive approximation to evaluate the interaction potential between closed-shell (He, Ne, Ar, Kr, and Xe) and open-shell (N, S, and Cl) atoms and the LiF surface, analyzing the relative importance of the different contributions. The performance of the proposed potentials is assessed by contrasting angular positions of rainbow and supernumerary rainbow maxima produced by fast grazing incidence with available experimental data. One important result of our model is that both van der Waals contributions and thermal lattice vibrations play a negligible role for normal energies in the eV range.

Figure 1

Crystal potential, as a function of the radial distance $r$ to an ${\mathrm{F}}^{-}$ site of the crystal lattice. Red thick solid line, Madelung potential, $V_M^{+}$, as given by Eq. (2); black thin solid line, radial grid potential, $V_G^{+}$, as given by Eq. (5) of Ref. [19]; blue dashed line, asymptotic limit $-1/r$ of the crystal potential.

Figure 2

Binary interatomic potential, as a function of the internuclear distance $R$, for different closed-shell atoms. (a) Absolute value of ${\text{F}}_{AO}^{\left(\mathrm{short}\right)}\left(R\right)$, given by Eq. (12), for the interaction of different closed-shell atoms with ${\text{F}}_{@}^{-}$ anions. (b) Analogous to panel (a) for the interaction with ${\text{Li}}_{@}^{+}$ cations. In both panels, LLPB3LYP results for different atom-onion pairs are plotted with different colors. Projectile dipole polarizabilities, ${\alpha }_A$, and van der Walls contributions, $C_{AO}^{\left(6\right)}2R^{-2}$, are displayed in the ranges 8 a.u.$\le R\le 10$ a.u. and 10 a.u.$\le R\le 12$ a.u., respectively, as explained in the text.

Figure 3

Analogous to Fig. 2 for the binary interaction of open-shell atoms—N(${}^{4}S$), S(${}^{3}P$), and Cl(${}^{2}P$)—with (a) ${\text{F}}_{@}^{-}$ anions and (b) ${\text{Li}}_{@}^{+}$ cations.

Figure 4

(a) Interonion reduced potential (absolute value), as a function of the internuclear distance $R$, for the following onion pairs: ${\text{F}}_{@}^{-}-{\text{F}}_{@}^{-},{\text{F}}_{@}^{-}{\text{-Li}}_{@}^{+},{\text{Li}}_{@}^{+}{\text{-Li}}_{@}^{+}$. Such reduced potentials were derived within the proposed potential model by multiplying by $R(1+2R^3)$ [analogous to Eq. (12)], after extracting the asymptotic Coulomb interaction. (b) Energy per onion pair at the bulk, as a function of the nearest-neighbor internuclear distance $s_o$. The vertical arrow indicates the equilibrium position.

Figure 5

Absolute value of the short-range atom-surface potential $W^{\left(\mathrm{short}\right)}\left(z_A\widehat{\mathbf{z}}\right)$, as defined by Eq. (18), as a function of the atom-surface distance $z_A$ measured on top of an ${\mathrm{F}}^{-}$ site. Interactions with different (a) closed-shell and (b) open-shell atoms are displayed with different colors.

Figure 6

Rainbow deflection angle ${\mathrm{\Theta }}_{\text{rb}}$, as a function of the normal energy $E_{\perp }$, for closed-shell atoms (Ne and Kr) in the left column and for open-shell atoms (S and Cl) in the right column. Panels in the upper and lower rows correspond to the incidence directions $\langle 110\rangle$ and $\langle 100\rangle$, respectively. Red solid line, results obtained from the proposed LLPB3LYP model; blue dashed line, values derived from the LLPB model (neglecting the correlation term); solid symbols, experimental data for different impact energies extracted from Refs. [13, 17]. Inset: Depiction of the FAD processes.

Figure 7

Deflection angles $\mathrm{\Theta }$ corresponding to maxima of FAD distributions, as a function of the normal energy $E_{\perp }$, for (a) Ne (closed-shell) and (b) N (open-shell) atoms scattered along the $\langle 110\rangle$ direction. In both panels, red solid (blue dashed) line, SIVR rainbow, and supernumerary rainbow angles derived from the LLPB3LYP (LLPB) models, including (without including) the correlation term. Symbols: experimental data for rainbow (circles) and first (diamonds), second (up triangles), and third (down triangles) supernumerary rainbow angles, extracted from Refs. [13, 53].

Figure 8

Angular FAD distribution, as a function of the deflection angle $\mathrm{\Theta }$, for Ne projectiles impinging along the $\langle 110\rangle$ channel with $E_{\perp }=0.3$ eV. Blue dashed (red solid) line, SIVR probability derived from the LLPB3LYP model including (without including) thermal vibrations.

Figure 9

Effective corrugation $\mathrm{\Delta }z$ of the He-LiF(001) potential across the $\langle 110\rangle$ channel, as a function of the normal energy $E_{\perp }$. Blue dashed (red solid) line, $\mathrm{\Delta }z$ values derived from the LLPB3LYP model including (without including) thermal vibrations, as explained in the text; green dot-dashed line, effective DFT corrugation from Ref. [20]; symbols, experimentally derived data extracted from Ref. [20].