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 (1989) 36) 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. However, it 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 the 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. 285 (1993) L517). 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 solution-phase 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.
Bibliographical noteFunding Information:
The authorsth ankG regS chenteor f the Pacific NorthwesNt ationaLl aboratorfyo r providingh is code that implementtsh e Parry methodf or the benchmarcka lculationsJ..R .R. is gratefutl o the MinnesotaS upercomputIenrs titutefo r hospitality over the courseo f completintgh is work and to Neil C. Sturchioo f ArgonneN ationaLl aboratory for the discussiono f experimenttael chniquefso r surfaces tructurea nalysis.T his work was sup-portedb y the Office of Basic Energy Sciences, Engineeringa nd GeoscienceDs ivision,contract 18328a, ndby LaboratorDy irectedR esearcha nd Developmentf unds from Pacific Northwest NationalL aboratoryP.a cificN orthwesNt ational Laboratoriys operatefdo r the US Departmenotf Energy by Battelle Memorial Instituteu nder ContracDt E-AC06-76RL01 830.
- Computer simulations
- Iron oxide
- Low index single crystal surfaces
- Molecular dynamics
- Single crystal surfaces
- Surface relaxation and reconstruction