Ewald methods for polarizable surfaces with application to hydroxylation and hydrogen bonding on the (012) and (001) surfaces of α-Fe2O3

Abstract

We present a clear and rigorous derivation of the Ewald-like method for calculation of the electrostatic energy of the systems infinitely periodic in two-dimensions and of finite size in the third dimension (slabs). We have generalized this method originally developed by Rhee et al. [Phys. Rev. B 40, 36(1989)] to account for charge-dipole and dipole-dipole interactions and therefore made it suitable for treatment of polarizable systems. This method has the advantage over exact methods of being significantly faster and therefore appropriate for large-scale molecular dynamics simulations. It however involves a Taylor expansion which has to be demonstrated to be of sufficient order. The method was extensively benchmarked against the exact methods by Leckner and Parry. We found it necessary to increase the order of the multipole expansion from 4 (as in original work by Rhee et al.) to 6. In this case the method is adequate for aspect ratios (thickness/shortest side length of the unit cell) ≤ 0.5. Molecular dynamics simulations using the transferable/polarizable model by Rustad et al. were applied to study the surface relaxation of the nonhydroxylated, hydroxylated, and solvated surfaces of α-Fe2O3 (hematite). We find that our nonhydroxylated structures and energies are in good agreement with previous LDA calculations on α-alumina by Manassidis et al. [Surf. Sci. Lett. 285, L517, 1993]. Using the results of molecular dynamics simulations of solvated interfaces, we define end-member hydroxylated-hydrated states for the surfaces which are used in energy minimization calculations. We find that hydration has a small effect on the surface structure, but that hydroxylation has a significant effect. Our calculations, both for gas-phase and solutionphase adsorption, predict a greater amount of hydroxylation for the α-Fe2O3 (012) surface than for the (001) surface. Our simulations also indicate the presence of four-fold coordinated iron ions on the (001) surface.

A Density Functional Theory Study of the Adsorption of Benzene on Hematite (α-Fe2O3) Surfaces

“…The top view shows that the surface cations are five-fold coordinated with oxygen, in agreement with the coordination predicted by Henderson et al [157]. Our geometry optimization calculations show that the clean surface undergoes relaxation within the first five interlayer spacings with percentage relaxation respectively calculated to be +22%, −20%, +6%, +23%, and −7% of the associated bulk layer spacing which is consistent with the results of earlier theoretical results of Wasserman et al [65] and Lo et al [69]. The relaxed surface energy is calculated to be 1.92 J m −2 , which compares well with the results of de Leeuw et al [63] using different methods (see Table 2).…”

“…In Table 1, we summarize the optimized interlayer spacings compared with previous theoretically predicted values and experimentally observed interlayer spacings (Thevuthasan et al) using X-ray photoelectron diffraction [151]. Generally, our calculated inward relaxations of the layer spacings of the single-Fe terminated α-Fe 2 O 3 (0001) surface are consistent with the X-ray photoelectron diffraction results and with earlier theoretical calculations [62,65] but the magnitude of the relaxation differs. The antiferromagnetic ordering of the bulk hematite is retained at the (0001) surface.…”

“…Trainor et al [61] and Wang et al [62] have computed various possible structures of the hematite (0001) surface using spin-density functional theory, whereas, de Leeuw and Cooper have employed classical interatomic potential calculations to simulate the hydrated surface structures of white rust [Fe(OH) 2 ], goethite (FeOOH) and hematite (α-Fe 2 O 3 ) [63]. The structure of the {0001} and {011  2} surfaces of hematite and their interaction with water have also been reported by other theoretical groups [64][65][66][67][68][69][70][71][72]. Some of these calculations have shown that adsorbed water molecules dissociate heterolytically on the (1 × 1)-α-Fe 2 O 3 (01 1  2) surface and that the presence of surface hydroxyls results in large interlayer relaxations [64].…”

“…Theoretical calculations have, however, proven to be an indispensable complementary tool to experiments in elucidating our understanding of the surface structures of metal oxides and they have been used extensively to study the structure of the clean and hydrated hematite surfaces in the literature [63][64][65][66][67][68][69][70][71][72].…”

Iron oxide surfaces

“…The interaction of water with α-Fe 2 O 3 (0001) surfaces has been studied both experimentally [413][414][415][416], and theoretically [416][417][418][419][420]. Kurtz and Heinrich [414] determined that water adsorbed dissociatively on an α-Fe 2 O 3 (0001) surface prepared by sputtering and 1100 K UHV annealing for pressures over 10 -5 torr, while the XPS study of Liu et al [349] suggested a threshold for hydroxylation at 10 -4 torr (both studies conducted at room temperature).…”