Combined Density Functional Theory and Interatomic Potential Study of the Bulk and Surface Structures and Properties of the Iron Sulfide Mackinawite (FeS) A. J. Devey,* R. Grau-Crespo, and N. H. de Leeuw Department of Chemistry, UniVersity College, UniVersity of London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom ReceiVed: January 9, 2008; ReVised Manuscript ReceiVed: April 10, 2008 The iron sulfide mackinawite (FeS) is modeled by density functional theory calculations, the results of which are used to derive a set of interatomic potentials for this material. We have investigated the effect of adding a Hubbard U eff term to the gradient-corrected (GGA) functional, but whereas good agreement is shown with experimental data when pure GGA (U eff ) 0) is employed, for values of U eff greater than zero the solution becomes unphysical, an indication that the Fe valence electrons within mackinawite are delocalized. This property is further evidenced by the density of states, which confirms a metallic nature from delocalization of the Fe d orbital at all U eff values. Mackinawite is calculated to be a nonmagnetic material, in accord with experiment. We have also derived a set of interatomic potentials by fitting to observables including geometry, phonon frequencies, and elastic constants, which were calculated for isolated mackinawite layers using DFT. The derived potential model is used to calculate the unrelaxed and relaxed structures and energies for the {100}, {010}, {001}, {110}, {101}, {011}, and {111} surfaces of mackinawite. The {001} surface, terminating at S atoms, with a calculated surface energy of 0.07 J m -2 , is found to be the most stable surface with very little surface relaxation compared to the bulk material. 1. Introduction Mackinawite, often referred to as tetrahedral FeS, is composed of FeS layers with Fe sandwiched between S sheets, which are held together by weak van der Waals interactions. 1 It is the first iron sulfide to form in most ambient environments 2 and is also produced by certain types of bacteria. 3 Mackinawite has been implicated in many important processes, particularly in its ability to capture heavy metal atoms within vacancy sites between layers 4 and in the development of prebiotic metabolism. 5 Naturally occurring mackinawite is often reported as nonsto- ichiometric, 6 resulting from a sulfur deficiency, and as such its formula is conventionally written as FeS 1-x (typically 0 < x < 0.07). However, synthetic mackinawite is close to the stoichio- metric material. 7 The structure of mackinawite is now well-known (Figure 1) with space group P4nmm (no. 129) 8 and a tetragonal unit cell with parameters a ) b ) 3.674 Å and c ) 5.033 Å. 9 Sulfur atoms are tetrahedrally coordinated in relation to a basal plane of iron atoms. A number of experimental studies have reported the properties of mackinawite, including its phase transition to greigite 10,11 and also pyrrhotite, 9 its surface chemistry, 2 and its thermodynamic stability. 12 Mo ¨ssbauer effect spectroscopy mea- surements have confirmed the absence of any magnetic mo- ment. 6 There has been some confusion concerning the conduc- tive nature of mackinawite, with Bertaut et al. 1 claiming nonmetallic behavior. However, the absence of any magnetic moment and the close Fe-Fe distance (2.65 Å) within each layer indicate that there is likely to be extensive Fe d orbital delocalization and associated metallic behavior in the basal plane. 6,9 The high reactivity of mackinawite toward oxygen has resulted in little being known about the physical characteristics of this material, in particular its elastic behavior. Computational studies of the iron sulfides have tended to focus upon pyrite, e.g., refs 13 and 14. The approximate linear muffin tin orbital method used by Welz and Rosenberg 15 is the only instance of a computational study into the electronic structure of FeS tetrahedra. However, this study dealt exclusively with isolated FeS 4 tetrahedra with corner-sharing units, whereas mackinawite is actually composed of edge-sharing, slightly distorted tetrahedra. 16 A study of mackinawite using modern quantum mechanical techniques is clearly desirable. In this paper, density functional theory (DFT) calculations of the mackinawite structure are performed in order to investigate the electronic structure and magnetic behavior of this material. We also calculate the elastic constants and phonon frequencies of isolated mackinawite layers, and we use this information to derive a set of classical interatomic potential parameters for mackinawite. A successful interatomic potential model for * Corresponding author. E-mail: a.devey@ucl.ac.uk. Figure 1. Structure of mackinawite, viewed along the a-axis. (Fe is shown in black, S in white with shading.) J. Phys. Chem. C 2008, 112, 10960–10967 10960 10.1021/jp8001959 CCC: $40.75  2008 American Chemical Society Published on Web 06/25/2008