Article pubs.acs.org/IC
Revisiting the Electronic Structure of FeS Monomers Using ab Initio Ligand Field Theory and the Angular Overlap Model Vijay Gopal Chilkuri, Serena DeBeer, and Frank Neese* Max Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D45470 Mülheim an der Ruhr, Germany S Supporting Information *
ABSTRACT: Iron−sulfur (FeS) proteins are universally found in nature with actives sites ranging in complexity from simple monomers to multinuclear sites from two up to eight iron atoms. These sites include mononuclear (rubredoxins), dinuclear (ferredoxins and Rieske proteins), trinuclear (e.g., hydrogenases), and tetranuclear (various ferredoxins and high-potential iron−sulfur proteins). The electronic structure of the higher-nuclearity clusters is inherently extremely complex. Hence, it is reasonable to take a bottom-up approach in which clusters of increasing nuclearity are analyzed in terms of the properties of their lower nuclearity constituents. In the present study, the first step is taken by an in-depth analysis of mononuclear FeS systems. Two different FeS molecules with phenylthiolate and methylthiolate as ligands are studied in their oxidized and reduced forms using modern wave function-based ab initio methods. The ab initio electronic spectra and wave function are presented and analyzed in detail. The very intricate electronic structure−geometry relationship in these systems is analyzed using ab initio ligand field theory (AILFT) in conjunction with the angular overlap model (AOM) parametrization scheme. The simple AOM model is used to explain the effect of geometric variations on the electronic structure. Through a comparison of the ab initio computed UV−vis absorption spectra and the available experimental spectra, the lowenergy part of the many-particle spectrum is carefully analyzed. We show ab initio calculated magnetic circular dichroism spectra and present a comparison with the experimental spectrum. Finally, AILFT parameters and the ab initio spectra are compared with those obtained experimentally to understand the effect of the increased covalency of the thiolate ligands on the electronic structure of FeS monomers. rapidly when going from d9 to d5 high-spin metal thiolates.13 These studies indicate that thiolate ligands tend to form strongly covalent metal−ligand bonds despite the presence of a S−αC bond. This S−αC bond has a significant influence on the metal−ligand interaction and hence the electronic structure of the metal.14 This is intimately related to the issue of the orientation of the metal−sulfur σ-bond, which is bent along the S−αC bond, thus influencing the strength of both the sulfur σand π-bonding interactions with the metal d-orbitals. Since such FeS monomers usually occur as high-spin S = 5/2 or S = 2 for the ferric and ferrous molecules, respectively,15 the task of understanding the origin and magnitude of the FeS covalency is rendered even more complex. This results from the presence of a large number of singly occupied molecular orbitals (SOMOs) in the ground-state electronic configuration of the d5−d6 highspin FeS monomers.16 Previous attempts to obtain a detailed understanding of the electronic structure of FeS monomers via single-crystal UV−vis/MCD spectrum of the iron(III) tetrathiolate17 using ligand field theory have proven difficult due to the high covalency of the thiolate ligands. Gebhard et al.
1. INTRODUCTION Iron−sulfur(FeS) clusters are ubiquitous in biological systems. They form the core of many biological proteins, where they perform various functions such as electron transfer,1 hydrogen bond activation,2 biological sensors,3−5 and catalysis.6 They are also the main components that make up the iron−molybdenum cofactor in the nitrogenase enzyme, which performs a complex reaction involving N2 bond cleavage.7 These FeS systems are made up primarily of tetrahedral FeS monomer building blocks. The simplest biological systems that contain such FeS molecules are the rubredoxin (Rb) class of proteins, which are made up of a single FeS monomer. Rb has been extensively studied via absorption and circular dichroism (CD)/magnetic circular dichroism (MCD) spectroscopy, 8,9 resonance Raman,10,11 Mössbauer, and cyclic voltametry.12 Through these studies, the intricate nature of the low-energy spectrum of Rb proteins was revealed, therefore, rendering a detailed analysis of the complex spectrum. To understand the origin of the complexity, X-ray spectroscopic studies have focused on an analysis of the thiolate ligands. It has been shown via ligand Kedge X-ray spectroscopy that thiolate ligands are more covalent than the chlorides by a factor of 2.13 Moreover, a systematic analysis showed that the metal−ligand covalency increases © XXXX American Chemical Society
Received: May 29, 2017
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DOI: 10.1021/acs.inorgchem.7b01371 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry reported an extracted value of the Racah two-electron repulsion parameter18 B of 22 cm−1, which as the authors themselves also elude to, is unphysical when compared to the that of the iron(III) free ion19 B value of 1029 cm−1 or the iron(III) tetrachloride monomer20 (B = 444 cm−1). All these factors considered together render the study of FeS molecules a challenging endeavor. In the present paper, we wish to undertake a thorough analysis of such complex FeS systems. We focus specifically on wave function-based methods to perform an in-depth analysis of the nature of the low-energy spectrum of FeS monomers. A presence of high-spin Fe(III)/Fe(II) centers, along with the highly covalent metal−sulfur bonds, makes wave function-based analysis very challenging, and hence very few studies21,22 have applied such an approach to FeS systems. In the present work, two different monomers, namely, [Fe(SPh)4]1−/2− and [Fe(SCH3)4]1−/2−, were studied to illustrate the relationship between the geometric and electronic structures. The wave functions of the ground and lowest-lying states are analyzed in detail. The connection to the experimental spectrum is made via ab initio ligand field theory (AILFT) and the angular overlap model (AOM),18,19,23−26 which considerably simplifies the connection between the electronic structure and the geometry of the system. The influence of geometric variation on the electronic structure is explained in detail using the AILFT and AOM models. The outline of the paper is as follows; the first section presents the computational details used for the ab initio analysis of the monomers, along with a presentation of their crystal structures. A brief overview of AILFT and AOM is presented in the context of the present work followed by a protocol that was used throughout. In the second part, the ferric and ferrous monomers are studied separately. Each section, in a parallel manner, presents the ab initio results, AILFT/AOM analysis, and a study of effect of geometry variation on the electronic structure. Third, a comparison with experiment is presented via parallel analysis of the ab initio spectra and experimental singlecrystal polarized-absorption/MCD spectrum for both ferric and ferrous monomers. Finally, the main insights resulting from the ab initio study are presented.
Figure 2. Ferric [Fe(SCH3)4]1− monomer based on crystallographic coordinates and the corresponding ferrous [Fe(SCH3)4]2− monomer based on a DFT optimized geometry, with the z-axis is oriented along the S4 symmetry axis.
coordinates for [NEt4] [Fe(SCH3)4] (CSD code: JURHIN), [NEt4] [Fe(SR)4] (CSD Code: BOSTOS, where SR = 2,3,5,6tetramethylphenylthiolate), and [NEt4]2 [Fe(SR′)4] (CSD Code: LAJFUX, where SR′ = 2-phenylbenzenethiolate). To simplify the systems, the additional substituents on the phenyl rings of the ferric and ferrous monomers were substituted by hydrogen atoms. All calculations were performed using the ORCA program package.27 The positions of the hydrogen atoms were then optimized for all monomers using density functional theory (DFT) with the BP86 functional and a def2-TZVP basis set.28,29 The resolution of identity approximation was used for the Coulomb integrals30 with the auxiliary basis generated automatically for the def2-TZVP (def2-TZVP/J) basis set using the AutoAux keyword.31 Since the crystal structure of a ferrous [Fe(SCH3)4]2− monomer is not available, its geometry was obtained by a DFT optimization using the ferric monomer as a starting point. The geometry optimization for the relaxed [Fe(II)(SCH3)4]2− molecule was performed for the high-spin S = 2 state. DFT was used with the BP86 functional and the all-electron scalar relativistic TZVDKH32 basis set; Grimme’s D3 dispersion correction was employed with the Becke−Johnson damping scheme.33,34 The input files for the geometry optimizations are provided in the Supporting Information. The geometry effects on the electronic structure were studied by varying the dihedral angle αC−S−Fe−S. For the ferric case, the dihedral angle ψ was varied from 90° to 180° with increments of 5°; the resulting unrelaxed geometry was used for the single-point CASSCF/NEVPT2 calculations. The ferrous case was studied similarly by varying the dihedral angle αC−S− Fe−S from 45° to 130° by increments of 5°. At each value of αC−S−Fe−S, a single-point CASSCF/NEVPT2 calculation was performed. Each calculation was performed with a def2TZVP basis set along with the resolution of identity approximation and automatic generation of the auxiliary basis. 2.2. Ab Initio Calculations. The state-averaged complete active space self-consistent field (CASSCF)35−37 procedure was used to obtain the orbitals for all systems. For the ferric iron site, the CAS space consists of 5 electrons in 5 orbitals (CAS(5,5)) with 1 sextet state, 24 quartet states, and 75 doublet states; whereas, for the ferrous iron site, the active space is made up of 6 electrons in 5 orbitals (CAS(6,5)), with 5 quintet states, 45 triplet states, and 50 singlet states. Stateaveraged molecular orbitals were used for the calculations. Averaging was done with an equal weight for each spin subblock. The CASSCF calculations were followed by the NElectron Valence state Perturbation Theory (NEVPT2)38−41 correction to recover the bulk of the dynamic correlation energy.
2. COMPUTATIONAL DETAILS Four different monomers were studied, as presented in Figures 1 and 2. These include both the ferric and ferrous form of iron tetramethylthiolate ([Fe(SCH3)4]1−/2−) and iron tetraphenyl thiolate ([Fe(SPh)4]1−/2−). 2.1. Geometry. The tetrahedral FeS monomers consist of a central iron(III) or iron(II) atom surrounded by four bent thiolate ligands in an S4 symmetry (see Figures 1 and 2). The utilized geometries were based on the crystallographic
Figure 1. Ferric and ferrous [Fe(SPh)4]1−,2− monomers in their crystal geometries with the z-axis oriented along the S4 symmetry axis. B
DOI: 10.1021/acs.inorgchem.7b01371 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
parametrizing the 15 independent one-electron parameters of the AILFT Hamiltonian (υLF) in terms of metal−ligand interaction parameters defined as eσ, eπs, and eπc as shown in eq 2, where eσ represents the ligand σ-interaction, whereas the eπs and eπc terms represent the in-plane and out-of-plane π-type metal−ligand interactions, respectively; these will be explained in more detail later. The Fλa functions depend only on the type of d-orbital (a,b) and the three geometric angles θ, ϕ, and ψ illustrated in Figure 3 below; see, for instance, B. N. Figgis.19
It has been shown that the minimal CAS(5,5)/CAS(6,5) calculations underestimate ligand-to-metal electron delocalization.42,43 One can improve the description of ligand−metal delocalization upon including the ligand orbitals in the CAS space.44 Therefore, to have a better description of the lowenergy spectrum, an extended CAS space including four doubly occupied bonding molecular orbitals (MOs, made up primarily of sulfur 3p orbitals) belonging to the a, b, and e irreducible representations in the S4 symmetry group were included in the active space. Note that these ligand-based MOs will have the strongest interaction with the metal-based MOs of the corresponding symmetry. On the one hand, the large active space for the ferric system consists of eight electrons (from the four sulfur-based orbitals) in addition to the five Fe d-electrons, thus leading to a CAS space of (13,9). For the ferrous monomer, on the other hand, since there are six electrons in the five d-orbitals, due to symmetry restrictions there will only be three ligand orbitals that will have strong interaction with the metal d-orbitals. Thurs for the ferrous case, there are three additional ligand orbitals (six electrons) along with the five Fe d-orbitals (six electrons) giving a CAS space of (12,8). Additionally, for the ferric monomer, a larger CAS space was treated, which includes all strongly interacting ligand MOs composed of seven ligand orbitals (1(a), 2(b), and 2(d) symmetry orbitals) given an active space of CAS(19,12). These calculations were performed only for the lowest-lying spin states, that is, the sextet and 24 quartet states for the ferric system and the 5 quintet and 45 triplet states for the ferrous system. State averaging was done to obtain natural orbitals. All CASSCF calculations were followed by the NEVPT2 calculations to obtain the dynamic correlation corrected spectrum. 2.3. Ab Initio Ligand Field. A comparison of the one- and many-particle ab initio energies and spectra with that of experiment requires a common model. For this purpose, the ligand field model Hamiltonian18,23 was adopted, since it is the model of choice in interpreting experimental spectra. The general form of the ligand field Hamiltonian is shown in eq 1. To have an unambiguous one-to-one correspondence between the ab initio spectrum and the ligand field model, ORCA employs the AILFT module. 24,45 First, the ab initio Hamiltonian matrix in the model space (of the five d-orbitals) is constructed from ab initio energies and matrix elements using the effective Hamiltonian theory (EHT) of des Cloizeaux.46 The parameters of the ligand field model Hamiltonian, that is, the 15 one-electron matrix elements (v̂LF) and the Racah twoelectron parameters B and C (Ĝ (i,j)), are then extracted by a least-squares fit to the ab initio effective Hamiltonian matrix elements. The one- and many-particle quantities can then be compared directly with those derived experimentally. In this fashion, the AILFT is a black box method that provides a clearly defined link between the information content of the ab initio wave function and the simple ligand field model. H̑ =
Figure 3. An illustration of the two angles θ and ϕ and the dihedral angle ψ used in the AOM analysis. M represents the metal center, and L1, L2 represent the ligand atoms.
These parameters can then be directly related to experimentally extracted values. Unlike the AILFT methodology, to define the AOM one-electron Hamiltonian, some chemical intuition about the molecule is necessary. Since this requires knowledge of the important interactions in the system, the AOM model helps to significantly simplify the problem. The AOM model also affords a direct relationship between the one-electron spectrum and the geometric parameters (θ, ϕ, and ψ) of the molecule. This relationship will be illustrated and used to explain the variations in electronic structure of the two monomers in terms of their geometry. vLE(a , b) =
L
i
