ARTICLE pubs.acs.org/JPCC
Optical Excitations in Hematite (α-Fe2O3) via Embedded Cluster Models: A CASPT2 Study Peilin Liao† and Emily A. Carter*,‡ †
Department of Chemistry and ‡Department of Mechanical and Aerospace Engineering, Program in Applied and Computational Mathematics, and Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544-5263, United States ABSTRACT: Hematite is a candidate for use as a photoanode in watersplitting reactions. Part of the efficiency depends on the capability of hematite to absorb sunlight and convert solar energy to electron energy. While there have been optical spectroscopy measurements as well as molecular orbital studies on the optical spectra of hematite, accurate characterizations of excited states from theory are missing. To fill this gap, we study excited states of electrostatically embedded hematite clusters using complete active space self-consistent field theory and complete active space with second-order perturbation theory. Overall, we found that the lowest lying excitations within hematite are Fe dd ligand field transitions (starting at ∼2.5 eV), which are highly localized around Fe centers. The O 2p to Fe 3d ligand to metal charge transfer excitations are higher lying excited states (∼6 eV). These excitation energies are used to verify some of the earlier peak assignments for the optical spectra of hematite. In addition, we demonstrate that density functional theory energy differences between different spin states of Fe in the embedded FeO69 cluster are significantly biased by the choice of exchange-correlation functional. Therefore, any conclusions derived from those types of calculations should be viewed with caution.
I. INTRODUCTION Harvesting solar energy has been proposed as a promising way to satisfy the ever-increasing global energy demand.1 For wide industrial application, it is desirable to use materials that are stable, nontoxic, cheap, and abundant. Hematite (α-Fe2O3, “α-” is omitted henceforth) is one promising candidate that fulfills all these requirements.2 It has an optical band gap of 2.02.2 eV, capable of absorbing ∼40% of the solar spectrum.3 Its band edges are aligned such that it can oxidize water to oxygen but requires an external potential to reduce water to hydrogen.4 There have been active research efforts on hematite to improve its efficiency by nanostructuring,58 surface modifications,9 or doping.6,10 The main drawbacks of hematite are that it has low conductivity, a low optical absorption coefficient, and high electronhole recombination rates.6,11,12 Both p-type or n-type dopants can be introduced to increase carrier concentrations and conductivity.1317 With regard to high electronhole recombination rates, a deeper understanding of the optical spectrum of hematite is needed. In addition, optical excitations are of great importance to the performance of photoanodes, because they are the key events in converting sunlight into electron energy and determine on which atoms the resulting holes and excited electrons reside. Experimentally, there have been several optical absorption studies on hematite.11,1822 A small absorption peak is observed at ∼1.5 eV. Starting at ∼2 eV, the absorption coefficient increases by at least 1 order of magnitude. Some of the subsequent absorption peaks are at 2.0, 2.4, 3.2, 4.0, and 4.8 eV. The initial peaks have been assigned to Fe dd ligand field transitions, while the higher energy absorptions are thought to be due to O 2p to Fe 3d ligand to metal charge transfer (LMCT). However, the onset r 2011 American Chemical Society
of LMCT is not clear from these optical experiments. On the basis of peak locations and absorption intensities, several authors11,1820 suggested that LMCT starts at ∼3.2 eV, while Sherman and Waite21 suggested that LMCT begins at ∼4.6 eV. In the 1970s and 1980s, hematite clusters were studied theoretically using the semiempirical atom superposition and electron delocalization (ASED) theory23 or the SCF Xα scattered wave method24,25 to generate molecular orbital energy levels. The energy differences among Fe 3d and O 2p orbitals were used to derive Fe dd ligand field transitions or LMCT energies. While the orbital energy differences match some of the peaks in the optical spectra, these interpretations are problematic. First of all, it is a severe approximation to compare actual excitation energies with orbital energy differences, since the latter neglects many-body wave function relaxation effects. Second, these methods represent the wave function as a single determinant, which remains unchanged after any unitary transformation. Consequently, the orbitals are not uniquely defined, calling into question the validity of identifying specific Fe 3d or O 2p orbitals. Besides these drawbacks, the lowest LMCT energies predicted by these two methods differ widely, from 3.1 to 4.7 eV. Along with increasing computational power, electronic structure theory has advanced to include more accurate treatments of the physical interactions producing higher fidelity predictions for excited states. Although the number of atoms that can be treated is still limited by available computing power, post-HartreeFock Received: July 21, 2011 Revised: September 13, 2011 Published: September 14, 2011 20795
dx.doi.org/10.1021/jp206991v | J. Phys. Chem. C 2011, 115, 20795–20805
The Journal of Physical Chemistry C
Figure 1. Illustrations for the three clusters used: (a) FeO69, (b) Fe2O912, and (c) Fe2O1014. The capping ECPs and point charge arrays are not shown. Fe ions are in gray. O ions are in red. This color scheme is followed throughout.
(HF) correlated wave function (CW) methods2629 are available to explicitly solve for excited state wave functions and excitation energies. For metal oxides with localized electrons, embedding techniques are commonly used, in which the cluster region is treated with accurate yet computationally demanding CW methods, while the extended crystalline surroundings are modeled by classical electrostatics.30 Early investigations of the excitation energies of Ni2+ and Cr3+ in the fluoride or oxide lattices used limited configuration interaction (CI) calculations for the cluster region and point charges that were fitted to reproduce the Madelung field of the crystal for the extended region.3134 Later, effective core potentials (ECPs)35 or ab initio model potentials36,37 were placed at the boundary between the terminating anions of the cluster and the point charges to simulate the electrostatic and Pauli repulsions between the cluster and the environment, thereby avoiding artificial drift of electron density from the anions onto their nearby positive point charges. Additional polarization interactions between the cluster and the environment can be accounted for by applying the shell model in the boundary region.38,39 In this paper, we adopt an electrostatically embedded cluster scheme, using CW methods for the cluster and surrounding the cluster with ECPs and point charges. In the specific case of hematite, the excited states consist of nearly degenerate electronic configurations, necessitating a multireference starting point for the wave function to attain the desired level of accuracy. We begin with unrestricted HF (UHF) wave functions and then use complete active space self-consistent field (CASSCF) theory40 and complete active space with secondorder perturbation (CASPT2) theory4143 to account for static and dynamic correlations. In the following sections, we first provide details of our calculations, then present predicted excitation energies, and finally use these values to guide interpretation of the optical spectrum of hematite.
II. COMPUTATIONAL DETAILS Three clusters (Figure 1) are built from the experimental crystal structure of hematite (a = 5.035 Å, c = 13.747 Å).44 The geometries are held fixed in all calculations. Experimentally, below the Neel temperature (TN = 963 K), hematite is antiferromagnetic with weak ferromagnetism.45 Along the [0001] direction of the hematite hexagonal unit cell, the high-spin d5 Fe cations within one Fe bilayer are ferromagnetically coupled but are antiferromagnetically coupled to the adjacent Fe bilayers.46 The FeO69 cluster in Figure 1a consists of only one Fe(III) cation and its six coordinated O dianions. The Fe2O912 and Fe2O1014 clusters in panels b and c of Figure 1 are extensions of the FeO69 cluster with one more face-sharing or edge-sharing FeO6 octahedron added. According to the antiferromagnetic
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ordering of hematite crystal, the two Fe(III) cations have opposite spins in Fe2O912 but have parallel spins in Fe2O1014. These two clusters are used to test how cluster size and geometry, as well as spin ordering, affect excitation energies. These clusters are then subjected to an electrostatic embedding that aims to mimic the rest of the extended crystal via a large point charge array. However, first the Fe cations that would have been bonded to the terminating O anions in the bulk but are not included in the cluster are replaced by Al ECPs,47 which have a charge of +3 and similar ionic radii to Fe3+. The clusters along with their capping ECPs are then embedded into point charge arrays. Within the point charge array, the Fe and O ions in the bulk are replaced by point charges of +3 and 2, respectively, and the ions on the edges or surfaces are replaced by point charges determined through Evjen’s method48 to ensure that the whole system is charge neutral. Except for the Fe2O1014 cluster, a 5 5 3 type hexagonal point charge array is used (∼6800 point charges, see ref 49 for details on how the point charge array is constructed). For Fe2O1014, a point charge array built from a 5 5 3 hematite hexagonal primitive unit cell is used (∼2500 point charges). Different point charge arrays are used to ensure that symmetric point charge arrays are used around each of the clusters. The distance between the cluster and edges of the point charge array is >10 Å. With these choices of point charge arrays, the excitation energies are converged to
