ARTICLE pubs.acs.org/JPCA
Assignment of the Photoelectron Spectra of FeS3 by Density Functional Theory, CASPT2, and RCCSD(T) Calculations Van Tan Tran and Marc F. A. Hendrickx* Afdeling Kwantumchemie en Fysicochemie, Departement Chemie, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee-Leuven, Belgium
bS Supporting Information ABSTRACT: The geometric structures of FeS3 and FeS3 with spin multiplicities ranging from singlet to octet were optimized at the B3LYP level, allowing two low-lying conformations for these clusters to be identified. The planar D3h conformation contains three S2 atomic ligands (S3Fe0/), whereas the C2v structure contains, in addition to an atomic S2 ligand, also a S22 ligand that is side-on-bound to the iron cation: an η2-S2FeS conformation. Subsequently, energy differences between the various states of these conformations were estimated by carrying out geometry optimizations at the multireference CASPT2 level. Several competing structures for the ground state of the anionic cluster were recognized at this level. Relative stabilities were also estimated by performing single-point RCSSD(T) calculations on the B3LYP geometries. The ground state of the neutral complex was unambiguously found to be 5B2. The ground state of the anion is considerably less certain. The 14B2, 24B2, 4B1, and 6A1 states were all found as low-lying η2-S2FeS states. Also, 4B2 of S3Fe has a comparable CASPT2 energy. In contrast, B3LYP and RCCSD(T) mutually agree that the S3Fe state is at a much higher energy. Energetically, the bands of the photoelectron spectra of FeS3 are reproduced at the CASPT2 level as ionizations from either the 4B2 or 6A1 state of η2-S2FeS. However, the FranckCondon factors obtained from a harmonic vibrational analysis at the B3LYP level show that only the 4B2-to-5B2 ionization, which preserves the η2-S2FeS conformation, provides the best vibrational progression match with the X band of the experimental photoelectron spectra.
’ INTRODUCTION A variety of types of ironsulfur clusters are known to be versatile active sites in proteins that enable numerous biological processes such as electron transfer and catalysis.1,2 The physical properties and electronic structures of this type of cluster have been studied with a wide range of methods, from spectroscopic measurements to various computational approaches.38 The electronic structure and reactivity of FenSm (n = 18, m = 26) clusters were first investigated by Nakajima et al. by photoelectron spectroscopy (PES) with different photon energies.9,10 For the FeS3 cluster, three vibrationally unresolved bands below 4 eV were reported. Several years later, Zhai and coworkers investigated the photoelectron spectroscopy of the anionic FeSn (n = 16) clusters in more detail.11 For the first time, the vibrational progression of the lowest-binding-energy band was resolved. In the same study, preliminary pure density functional theory (DFT) calculations with generalized-gradient PerdewWang exchange-correlation functional calculations and triple-ζ plus polarization functions (TZP) Slater-type-orbital (STO) basis sets were carried out to optimize the low-lying structures of the anionic cluster. Previously, theoretical investigations at different quantum chemical levels were performed with the purpose of assigning the photoelectron spectra of small transition-metal-containing clusters.1218 The tiny energy differences among the low-lying states of these clusters make it difficult to identify their ground states, and therefore, highly accurate ab initio wave function r 2011 American Chemical Society
methods are needed to make reliable predictions. Furthermore, particularly for the high-energy part of the spectra, low-spin excited states of the neutral clusters can be involved. In these cases, multireference wave function methods such as CASPT2 (complete active-space second-order perturbation theory) or MRCI (multireference configuration interaction) offer the best prospects for exploring the full nature of the experimental electron-detachment processes. The success of these methods in explaining the anion photoelectron spectroscopy of several clusters strongly confirms this conclusion.1319 However, because of their high computational cost, these methods have not yet been applied to the larger ironsulfur clusters. With the specific purpose of recovering a larger portion of the dynamical correlation, RCCSD(T) calculations were also performed, which we found to be particularly useful for determining the relative stabilities of the various conformations considered and, consequently, identifying the initial state of the photoelectron spectrum. This article demonstrates in detail that only by combining the rapid B3LYP method for exploring the complex potential energy surface of the clusters, the CASPT2 methods for completely characterizing the low-lying electronic states, and RCCSD(T) for assessing the stabilities of the ground states of the various conformations is it possible to reach an elaborate and trustworthy Received: September 13, 2011 Revised: October 28, 2011 Published: October 28, 2011 13956
dx.doi.org/10.1021/jp208824b | J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
Figure 1. Choice of coordinate systems for the CASPT2 and RCCSD(T) calculations and qualitative orbital energy schemes for the valence 3d orbitals as derived from the CASPT2 results for (a) S3Fe0/ and (b) η2-S2FeS0/.
assignment of the experimental anion photoelectron spectroscopy. The interplay between theory and experiment in this work leads to a substantiated insight into the electronic structure. This study mainly focuses on the lowest band below 3 eV in the photoelectron spectra of the FeS3 anion by calculating the adiabatic detachment energy (ADE). Vertical detachment energies (VDE) were used to identify the higher-energy ionization processes that were observed in the spectra. Vibrational progression simulations were performed by calculating multidimensional FranckCondon factors. The geometric parameters and harmonic vibrational frequencies of B3LYP calculations for the lowest FeS3 and FeS3 states were used for this purpose.
’ COMPUTATIONAL DETAILS DFT calculations employing the hybrid B3LYP functional,2022 which combines the Becke exchange functional (B) with the Lee, Yang, and Parr (LYP) correlation functional, are known to perform reasonably well for geometry optimizations and harmonic vibrational frequency analyses of small iron-containing complexes.23 Our calculations therefore used this functional with the QZVP basis set24 to obtain the equilibrium structures of all lowlying spin multiplicities of these clusters. Geometries of FeS30/ were optimized within the spin-unrestricted self-consistent field (SCF) scheme by applying no spatial symmetry constraints. Harmonic vibrational frequency analyses were systematically carried out to ensure that the found stationary points were true minima on the potential energy surfaces. All of these hybrid DFT calculations were performed with the TURBOMOLE 6.0 set of programs.25 These optimized structures for the various relevant spin multiplicities of the FeS30/ clusters were subsequently used as starting points for CASPT2 geometry optimizations and harmonic vibrational analyses employing the MOLCAS 7.4 suites of programs.26 Because only Abelain point groups are implemented in MOLCAS, these calculations were done with the C2v point group, even though the actual symmetry of the cluster can be D3h. As presented in Figure 1, the molecule was placed in the yz plane with one sulfur atom on the z axis. The basis sets utilized were of the ANO-RCC type with a contraction scheme [7s,6p,4d,3f,2g] for iron27 and [6s,5p,3d,2f] for sulfur.28 Scalar relativistic effects
ARTICLE
were included by the DouglasKroll formalism.29 Within the CASPT2 computational scheme, the molecular orbitals and zeroth-order wave functions were obtained by the complete active space self-consistent field (CASSCF) method. The active space for these CASSCF calculations included the 3p orbitals of all sulfur atoms and the 3d and 4s orbitals of iron. In total, the active space consisted of 20 (neutral cluster) or 21 (anionic cluster) electrons distributed among 15 orbitals. This active space is of a similar quality as the one used in our previous FeO30/ study.38 Because of the pronounced near-degeneracy properties of the complex studied, namely, a larger number of states close to each other, single-point state-average CASSCF and multistate CASPT2 (MS-CASPT2) calculations were also preformed. During the CASPT2 calculations, the 3p, 3d, and 4s electrons of iron and the 3s and 3p electrons of the three constituent sulfur atoms were correlated. The assessment of the relative energetic positions of the two lowest conformations of an anionic cluster is of paramount importance for determining the initial state that is at the origin of its photoelectron spectroscopy. From past experience, which also proved to be useful here, RCCSD(T) appears to be an efficient method in this respect. As a single-reference computational method, it turns out to quite robust in mild multireference circumstances, while at the same time being able to account for adequate amounts of dynamical correlation energies. Because of restrictions on the extent of the active space and its nature as a second-order perturbation theory technique, CASPT2 appears to be less efficient in this respect. Within a specific conformation, on the other hand, the near-degeneracy effects seem to be of more importance, and consequently, this method is generally able to provide better ionization energies. Correlation-consistent basis sets were used to perform the RCCSD(T) calculations. Results for three basis sets were used to obtain the relative energies of the various low-lying states, for which the vital electronic configurations were determined by CASPT2. From data available on the EMSL basis set exchange Web site,30,31 the aug-cc-pVTZ-DK, aug-cc-pwCVTZ-DK, and aug-cc-pwCVQZDK basis sets for iron32 and sulfur33 were assembled. Scalarrelativistic effects up to second order were included in the oneelectron integrals. For the first basis set mentioned, only the valence orbitals of iron (4s and 3d) and sulfur (3s and 3p) were correlated, whereas for the two largest basis sets the outer core of iron, namely, the 3s and 3p electrons, was also involved in the expansion of the coupled-cluster wave function. The calculated RCCSD(T) electron affinities can be compared to the CASPT2 values. The relative vibrational transition intensities of the lowest bands of the FeS3 photoelectron spectra were assessed by calculating the multidimensional FranckCondon integrals. Their evaluation was based on the coherent state model of Doktorov et al.,34 as implemented in the FC-LabII package.35,36 The structures, harmonic normal vibrational modes, and frequencies that were obtained at the B3LYP/QZVP level were used for this vibrational simulation. In this fashion, the FranckCondon factors were derived for a progression of up to 20 quanta in any vibration mode.
’ RESULTS AND DISCUSSION A previous DFT study using the generalized gradient Perdew Wang exchange-correlation functional in combination with the TZP STO basis sets11 indicated that the FeS3 anionic cluster 13957
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
ARTICLE
Figure 2. Calculated structures for the relevant low-energy spin multiplicities of FeS3 and FeS3 at the B3LYP/QZVP level and their relative energies in electronvolts.
has two stable low-lying conformations. The first one of D3h symmetry does not have any SS bond and is denoted as S3Fe0/. Other stable anionic conformations exhibit C2v symmetry, containing one SS bond. Because the resulting S22 ligand was found to bind most favorably in a side-on fashion to the iron, we refer to it as η2-S2FeS. The 4E00 state of D3h symmetry was predicted to be the ground state of S3Fe, with estimated ironsulfur bond lengths of 2.04 Å. On the other hand, the lowest state of η2-S2FeS was calculated to be a 4A1 state of C2v symmetry with FeS bond distances of 2.06 and 2.22 Å and a SS bond length of 2.11 Å. As the 4A1 conformation is positioned just 0.32 eV higher than the 4E00 conformation, we feel that a conclusive determination of the true ground state of FeS3 that lies at the origin of the photoelectron spectrum cannot be made with great certainty at the computational level used in ref 11. Clearly, a more profound wave function computational approach is required to explore in greater detail the potential energy surfaces of both the neutral and anionic clusters for all low-lying states and conformations. Because of the complexity of the potential energy surfaces of the systems, in this work, we performed complete unrestricted geometry optimizations for the lowest spin multiplicities and conformations of FeS30/, by utilizing the B3LYP hybrid DFT method in combination with the higher-quality QZVP basis sets. The optimized geometries together with the structural parameters are presented in Figure 2. The corresponding relative energies and harmonic frequencies are collected in Table 1. For the neutral species, we found a quintet state of the η2-S2FeS conformation with C2v symmetry as the global minimum of all possible neutral clusters corresponding to the FeS3 stoichiometry. The equilibrium bond distances for both types of FeS bonds were calculated to be 2.073 and 2.260 Å, whereas for the S22 moiety, the SS bond distance was 2.026 Å. At this
Table 1. Relative Energies and Harmonic Vibrational Frequencies for the Considered Spin Multiplicities of FeS3 and FeS3 as Calculated at the B3LYP/QZVP Level cluster S3Fe S3Fe
η2-(S2)FeS
η2-(S2)FeS
spin relative energy multiplicity (eV)
frequency (cm1)
2
1.12
80 153 202 351 524 597
4
0.62
104 158 159 397 531 531
1
4.49
114 164 165 373 485 485
3
4.12
73 116 117 367 478 479
5
4.24
97
2 4
0.83 0.00
55 66 246 282 485 533 66 102 265 297 439 519
6
0.03
70
76 256 284 441 512
8
1.65
28
52 140 267 333 490
1
4.53
91 107 326 377 557 605
3
3.02
65
77 240 245 430 594
5
2.87
63
78 226 325 435 579
7
3.19
30
56 233 267 485 572
98
98 472 481 482
computational level, the first excited state of different spin multiplicity was predicted to be a triplet lying only 0.15 eV higher than the quintet ground state. The lowest state of the S3Fe conformation had a triplet spin multiplicity and was located at 1.25 eV, which is much higher than the low-energy states of the η2-S2FeS conformation. For the anion, the B3LYP description of the low-lying states is more complicated. The global minimum corresponds to a quartet state with C2v symmetry in an η2-S2FeS conformation. The two unique FeS bond lengths are 2.091 and 2.262 Å, and this structure also has a SS bond of 2.101 Å. Just marginally higher at 0.03 eV, we located a sextet conformation of C2v symmetry. 13958
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A This nearly degenerate state had a similar geometry with the following equilibrium distances: FeS bond lengths of 2.100 and 2.278 Å and a SS bond length of 2.142 Å. Considering the extremely small energy difference with the quartet state and the fact that the computational level employed most certainly had a larger error bar, we considered this sextet together with the quartet as a candidate ground state. The lowest state of D3h symmetry (S3Fe conformation) was a quartet situated at 0.62 eV. At this computational level, it therefore represents a much higherlying local minimum, exhibiting three equal FeS bond lengths of 2.045 Å. Our B3LYP prediction for the ground state of the anionic cluster sharply contradicts the previous pure DFT results of Zhai et al.11 Indeed, they proposed a 4E00 ground state of D3h symmetry, whereas the lowest electronic state for the η2-S2FeS conformation appears to be a 4A1 state of C2v symmetry at 0.32 eV. This manifest contradiction in the characterization of the ground state for the anionic cluster makes it absolutely necessary to study both conformations more carefully at a higher level of computation. Before doing so, we can use the energies from our B3LYP/ QZVP calculations to obtain a first estimate of the adiabatic detachment energies (ADEs) for the lowest band in the photoelectron spectra of FeS3. The vibrational progession starting at 2.90 eV can be ascribed to a one-electron-detachment process from the quartet or the sextet η2-S2FeS conformation to a quintet state of the same conformation. Our B3LYP computational model predicts ADEs for these ionization processes of 2.87 and 2.84 eV, respectively, which represent a good match between theory and experiment. The electron detachment from the quartet of S3Fe to the triplet of the same conformation has an ADE value of 3.50 eV, which is more than a 0.5 eV larger than the experimental position of the lowest peak of the X-band progression in the experimental spectrum. These results point to one of the two lowest η2-S2FeS states as the initial state for the photoelectron spectra. The very large difference between the relative stabilities of the two conformations at the pure DFT level of ref 11 and our B3LYP calculations, however, prevents us from reaching a definite conclusion about the true global minimum of FeS3 and, therefore, about the initial state of the experimentally observed ionizations. Clearly, we need to utilize higher-level computational techniques to reach a more well-founded conclusion. However, the first task was to fully identify the symmetry of all low-lying states of the two conformations of both the anionic and neutral clusters. This was done by performing CASPT2 single-point calculations at the B3LYP-optimized geometries of the specific spin multiplicities. In all cases, the C2v point group was used to determine the electronic structures of the lowest states. The CASSCF/CASPT2 combination is particularly well-suited to carry out this task in an effective manner. Once the lowest states were identified, a geometry optimization at the CASPT2 level was performed. The resulting structural parameters and relative CASPT2 energies for the different low-lying states can be found in the Supporting Information, whereas their CASSCF leading configurations and totally symmetrical vibrational mode frequencies are collected in Table 2. The global minimum for the neutral cluster was found to be a 5B2 state of η2-S2FeS conformation, with the 1A1 (1A10 ) state of S3Fe 0.81 eV higher. This finding confirms the B3LYP/QZVP result. Again, the electronic structure of the anionic cluster is more complicated because the 14B2, 24B2, 4B1, and 6A1 states of η2-S2FeS and the 4B2 state of S3Fe are situated quite close in energy. The calculated differences
ARTICLE
Table 2. Relative Energies (REs) and Harmonic Frequencies for the Totally Symmetric Vibrational Modes of the LowLying States of FeS30/ as Obtained by CASPT2 Geometry Optimizations cluster
state
S3Fe
RE (eV)
18a1119a106b127b1111b223a21
0.00
147, 372, 486
2
18a1219a106b127b1011b223a21
0.40
163, 416, 563
2
18a1219a106b127b1111b223a20
0.39
154, 409, 545
1
18a1219a106b127b1011b223a20
3.43
170, 436, 603
3
18a1119a106b127b1011b223a21
3.70
165, 447, 587
B1 18a1119a106b127b1111b223a20 14B2 18a1219a116b127b1111b203a21
3.68 0.03
152, 445, 558 284, 490, 594
24B2 18a1119a126b127b1111b203a21
0.23
290, 563, 597
4
18a1119a116b127b1111b203a22
0.18
279, 581, 621
6
18a1119a116b127b1111b213a21
0.10
271, 426, 525
5
18a1119a116b127b1111b203a21
2.62
402, 520, 641
A2 B1 A1 A2
3
η2-(S2)FeS
B1 A1
η2-(S2)FeS
frequency (cm1)
4
B2
S3Fe
leading configuration
B2
Table 3. RCCSD(T) Relative Energies (eV) with Respect to the 4B2 State of η2-(S2)FeS for Relevant Low-Lying States of FeS30/a cluster
state
S3Fe
0.61
0.74
0.68
0.76
0.83
1
3.83
3.51
b
3
B1
4.00
4.08
4.22
14B2
0.00
0.00
0.00
24B2
0.05
0.07
0.07
4
0.16
0.13
6
0.21 3.13
0.05 3.21
A1
η -(S2)FeS
B1
η2-(S2)FeS
aug-cc-pwCVQZ
2
B1
2
aug-cc-pwCVTZ
4
B2
S3Fe
aug-cc-pVTZ
A1 5 B2
0.80
0.13 0.03 3.22
a
For the smallest basis set (aug-cc-pVTZ) only the valence electrons of iron (3d and 4s) and sulfur (3s and 3p) are correlated, whereas for the two larger basis sets, aug-cc-pwCVTZ and aug-cc-pwCVQZ, the outer core of iron (3s and 3p) is also correlated. b Calculation did not converge because of persistent oscillations.
among them are smaller than 0.33 eV. In contrast, the B3LYP/ QZVP calculations characterized the quartet state of S3Fe as a higher-lying local minimum, lying as much as 0.62 eV higher than the lowest η2-S2FeS state. However, at the CASPT2 level, the two conformations had comparable energies, with a difference between them of just 0.10 eV, so that neither of them should be ruled out as a candidate for the global minimum of the anion. Concerning the nature of the ground state of S3Fe, CASPT2 predicts 4B2 (4A20 ) as its ground state, as opposed to the pure DFT approach, which predicts 4E00 . CASPT2 places this spatially degenerate state much higher, which, because of a small Jahn Teller effect, is split into 2A2 and 2B1 states at 0.40 and 0.39 eV, respectively, in Table 2. The comparatively large differences between the pure DFT,11 hybrid DFT, and CASPT2 results was the motivation to study the relative positions of the mentioned states by the RCCSD(T) technique. The results for these single-point calculations at the B3LYP structures are collected in Table 3. Already with the smallest basis set used, the η2-S2FeS conformations were found to be more stable by around 0.8 eV than the high-symmetry 13959
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
ARTICLE
Table 4. Vertical Relative Energies (VREs) for the Lowest One-Electron Ionizations As Calculated for the 4B2 State (Upper Part) and 2B1 State (Lower Part) of the S3Fe Conformation by Multistate (Two-Root) CASPT2 cluster
state
S3Fe
4
S3Fe
3
B2 B1
3
A2
Figure 3. Photoelectron spectrum of FeS3 taken from ref 11 as recorded using laser detachment photons of 193 nm. Arrows indicate the calculated CASPT2 vertical detachment energies expressed in electronvolts.
S3Fe structures. Apparently, the hybrid DFT method B3LYP and RCCSD(T) favor the more compact η2-S2FeS. The pure DFT method that was used in ref 11 and CASPT2, on the other hand, predict the more delocalized S3Fe structures as either the most stable identity or as very low-lying. Similar observations were made for the relative stabilities of the related η2-O2FeO2 (with one peroxide ligand) and the nearly tetrahedral O4Fe complexes.37 As a possible explanation for these pronounced differences, the self-interaction error of the pure DFT methods, the insufficient recovery of the dynamical electron correlation energy by CASPT2 as a second-order perturbation theory technique, and the use of a limited active space were tentatively invoked in our previous theoretical study on FeO40/.37 Indeed, these deficiencies are expected to destabilize the less delocalized structures witht respect to the more delocalized structures, so that this leads to the acceptance of an η2-S2FeS conformation as the global minimum of the potential energy surface of the FeS3. Regarding the nature of the specific electronic state that corresponds to this minimum, the B3LYP and RCCSD(T) results deviate. Indeed, the DFT method positions the quartet η2-S2FeS just 0.03 eV lower than the sextet state. RCCSD(T) calculations conducted with the smallest basis set point to a 6A1 ground state that is 0.21 eV more stable than the 4B2 state. Inclusion of the 3s and 3p outer core of iron in the correlation treatment appears to be of crucial importance in these circumstances. Both the extended triple-ζ and quadruple-ζ basis sets reduce the energy gap between the sextet and quartet states to as little as 0.03 eV, but still in favor of the sextet state. In view of the well-known fact that high-spin states exhibit less correlation energy because of the Fermi hole for parallel spins, it does not come as a surprise that the quartet state is calculated too high in comparison with the sextet. A more elaborate treatment of the correlation energy would most likely invert the two states and consequently confirm the B3LYP finding that the 4B2 state corresponds to the global minimum of FeS3 and, therefore, to the initial state of the photoelectron spectrum of FeS3. The photoelectron spectrum of FeS3 as recorded with 193-nm detachment photons is shown in Figure 3.11 By using a lower photon energy (355 nm), the highest resolution was obtained, which showed an X band commencing at 2.90 eV that exhibited a simple vibrational progression of 500 ((20) cm1. This ADE corresponds to the electron affinity (EA) for FeS3, which is actually smaller than the value of 3.22 eV for FeS2. As the underlying ionizations are thought of as one-electron removal processes of iron 3d valence electrons, these experimental data indicate that the oxidation state of iron remains unaltered between FeS2 and FeS3. Additionally, the ADEs were measured
S3Fe
2
B1
2
A2
S3Fe
1
A1
3
B1 3 A2
leading configuration 18a1 6b127b1111b223a21 18a116b127b1111b223a20 18a116b127b1011b223a21 18a126b127b1111b223a20 18a126b127b1011b223a21 18a126b127b1011b223a20 18a116b127b1111b223a20 18a116b127b1011b223a21
orbitala
1
VRE (eV) 0.00
3a2
3.80
7b1
3.82 0.00 0.04
7b1
3.22
18a1 18a1
3.54 3.48b
a Denotes the molecular orbital that is ionized for the specific electrondetachment process. b Relative energy with respect to 2A2 at the geometry of 2B1.
to increase linearly for FeSn with n = 02. All of these experimental findings and assumptions imply that FeS3 has, in addition to one S2 atomic ligand, a S22 molecular ligand. The photoelectron spectra of FeS3, as recorded with higher-energy detachment photons, show A, B, C and D bands at 3.35, 4.16, 4.40, and 4.95.5 eV, respectively. It is the intention of the present contribution to assign these bands to ionizations from the low-lying states of the anion by calculating the vertical detachment energies at the MS-CASPT2 level. Based on previous experience from wave function studies of small iron oxide clusters,37,38 CASPT2 is the method of choice for estimating the relative energies of various electronic states of a specific conformation and, therefore, for deriving an assignment for the photoelectron spectrum. The CASSCF orbitals used in this analysis are thus best suited to conduct a study into the electronic structure of the involved states and, in this way, to identify the nature of the ionization processes underlying the experimentally observed bands. For this purpose, average state CASSCF and MS-CASPT2 calculations were carried out on all relevant states of FeS3. Obviously, the 4A20 state as the global CASPT2 minimum of the S3Fe conformation must be considered as an initial state. Because it was concluded for the related FeO3 cluster, also using CASPT2, that the photoelectron spectrum has the 2E00 state as its initial state,38 we also need to include this S3Fe state in our investigation. The 5B2 state of the η2-S2FeS conformation is the global minimum of the neutral molecule. By applying the one-electron-detachment selection rule, one can easily deduce that it can be formed from the 4B2 and 6 A1 low-lying states of the same conformation. In short, we will try to assign the spectra with the 4A20 and 2E00 states of S3Fe and the 4B2 or 6A1 states of η2-S2FeS, as possible candidates for the initial state of the anionic cluster. From past experience,37 CASPT2 is the preferred method for obtaining the most reliable VDEs, and we therefore utilized this method in the present study. In the first part of Table 4, we collected these vertical detachment energies for the anionic 4B2 (4A20 in D3h) state of the S3Fe conformation. Figure 4 presents the CASSCF molecular orbitals, together with their natural occupation numbers for this state. All of the orbitals with predominant sulfur 3p character are doubly occupied in the leading configuration, implying an oxidation state of 5+ for iron in this anion. Under the trigonal ligand field of the three sulfur anions, the five 3d orbitals of iron are split into three levels as depicted in Figure 1a. The lowest a10 level corresponds 13960
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
Figure 4. CASSCF natural orbitals for the 4B2 state of the S3Fe conformation classified according to their symmetry and natural occupation numbers in parentheses. The type of predominant iron 3d orbitals is also indicated.
to the 3dx2 orbital, the intermediate e00 level comprises the 3dxz and 3dxy orbitals, and the highest e0 level is made up of the 3dyz and 3dy2z2 orbitals. The 4B2 state has a CASSCF leading configuration with the three unpaired electrons occupying the 18a1 (3dx2), 7b1 (3dxz), and 3a2 (3dxy) orbitals. From this configuration, we denote the 4B2 state as 4A20 (D3h symmetry). Removing one electron from the e00 level of 4A20 creates the 3E00 state of the neutral cluster. The optimized structure of the corresponding triplet state of C2v symmetry that was found at the B3LYP/QZVP level is the result of a JahnTeller distortion that splits this state into 3A2 and 3B1 components. The VDEs for these two lowest calculated ionization processes starting from the 4B2 state amounts to 3.82 and 3.80 eV at the CASPT2 level, which is much too high to correspond to the X band at 2.90 eV. This pronounced discrepancy clearly leads to the conclusion that the 4A20 state of S3Fe conformation is not responsible for the photoelectron spectroscopy of the FeS3 cluster. In view of the very recently made assignment of the photoelectron spectrum of FeO3, we should take into account also
ARTICLE
the 2A20 as an initial state. The orbitally allowed transition to the closed-shell 1A10 state of the neutral cluster is predicted in Table 4 to occur at a binding energy of 3.22 eV, which compares relatively well with the position of the X band at 2.90 eV. Because this ionization implies the removal of an electron from a predominatly π-antibonding 3d orbital on iron, a vibrational progression that possibly resembles the experimental silhouette of the X band can be expected. Indeed, Figure 2 shows that the bond distance decreases from 2.0222.029 Å in the doublet state to 1.986 Å in the singlet state of the neutral cluster. However, quantitatively, the frequency of the totally symmetric stretch of the singlet D3h state amounts to only 373 cm1 (Table 1), which is more than 100 cm1 short of the experimental intervals of about 500 ((20) cm1 between the peaks of the X band. This B3LYP frequency was confirmed at the CASPT2 and RCCSD(T) levels by constructing the totally symmetric stretching mode potential energy curves. In these cases, harmonic frequency analyses yielded a slightly higher frequency of around 420 cm1. This result, when combined with its higher CASPT2 energy with respect to the 4 0 A2 state in Table 2, allows the 2A20 state to be disregarded with almost certainty as the initial state for the photoelectron spectroscopy of the FeS3 stoichiometric species in the gas phase. Thus, all together, the S3Fe0/ conformations are most likely not responsible for the photoelectron spectra that are currently under investigation, and we turned our attention to the η2-S2FeS0/ conformations for their assignment. The 4B2 ground state of the η2-S2FeS conformation has an electronic structure that is quite dissimilar to that of the 4B2 state of the S3Fe conformation. The CASSCF molecular orbitals of the active space and their natural occupation numbers are shown in Figure 5. These plots show that there are four predominantly d orbitals that are occupied by five electrons. The 18a1 (dx2y2) orbital is doubly occupied, whereas the 19a1 (dz2), 7b1 (dxz), and 3a2 (dxy) orbitals are all singly occupied. For the S2 moiety of the cluster, the molecular orbitals derived from the valence sulfur 3s orbitals are situated in the inactive space as intended and are not depicted in Figure 5. The 3p orbitals, on the other hand, give rise to the following doubly occupied orbitals: two π orbitals (15a1, 5b1), two π* orbitals (9b2, 2a2), and a σ orbital (17a1). Clearly, the analogous σ* orbital (12b2) is not occupied, allowing us to deduce that the S2 ligand of the η2-S2FeS conformation is formally double negatively charged. The remaining doubly occupied active space orbitals 16a1, 6b1, and 10b2 have unmistakably predominantly 3p character of the S2 ligand. On the whole, the formal charge distribution in the η2-S2FeS cluster corresponds to a lower 3+ oxidation state of iron and the following scheme: η2-(S22)Fe3+(S2). The VDE values obtained by the CASPT2 calculations based on the geometry of this 4B2 state are collected in the lower part of Table 5. The lowest ionization process occurs by detaching one electron from 18a1 (3dx2y2) orbital to reach the final 5B2 state with a VDE value 2.51 eV. Although this transition corresponds formally to the removal of a d electron from the iron cation, a Mulliken population analysis of the CASSCF wave function shows that the charge of the iron cation is just slightly increased from +1.11 e for the anion to +1.33 e in the neutral cluster. The relaxation effects in the lower-lying predominantly sulfur molecular orbitals, which become more covalent after ionization, oppose the originally electronic charge decrease on iron as a result of the removal of an electron from the mainly 3d molecular orbital. The calculated VDE value corresponds to the X future of the photoelectron spectrum at 2.90 eV. Further, according to the lower part 13961
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
ARTICLE
Figure 5. CASSCF natural orbitals for the 4B2 initial state of the η2-(S2)FeS conformation classified according to their symmetry and natural occupation numbers in parentheses. The type of predominant iron 3d orbitals is also indicated.
Table 5. Vertical Detachment Energies (VDEs) for the Lowest One-Electron Ionizations As Calculated for the 6A1 State (Upper Part) and the 4B2 State (Lower Part) of the η2-(S2)FeS Conformation by Multistate (Four-State) CASPT2 cluster
η -(S2)FeS 2
η2-(S2)FeS η2-(S2)FeS η2-(S2)FeS
orbitala
state
leading configuration
A1b 5 b B2 4 b B2 5 B2 3 A2 3 B1 3 B2 5 B1 3 c B2 5 A1 5 A2 5 d A1
18a1119a116b127b1110b2211b212a223a21 18a1119a116b127b1110b2211b202a223a21 18a1219a116b127b119b2210b222a223a21 18a1119a116b127b119b2210b222a223a21 18a1219a116b127b109b2210b222a223a21 18a1219a116b127b119b2210b222a223a20 18a1119a116b127b119b2210b222a223a21 18a1219a116b127b119b2210b222a213a21 18a1219a106b127b119b2210b222a223a21 18a1219a116b127b119b2210b212a223a21 18a1219a116b117b119b2210b222a223a21 18a1219a116b117b119b2210b222a223a21
6
VDE (eV)
expt
0.00 11b2
2.98 0.00
18a1 (dx2y2) 7b1 (dxz)
2.51 3.17
3a2 (dxy)
3.21
18a1 (dx2y2)
3.32
2a2 (π* S22)
3.39
2.90 3.35
19a1 (dz2)
3.82
4.16
10b2 (pπ S2)
4.09
4.40
6b1 (pπ S2)
4.20
9b2 (π* S22)
5.02
5.09
a
Denotes the molecular orbital that is ionized for the specific electron-detachment process with its predominant character in parentheses. b Calculated as an average of two states. c Calculated as an average of six states. d Calculated as an average of eight states.
of Table 5, the A band at 3.35 eV can be ascribed to no less than three triplet states and one quintet. The 3A2, 3B1, and 3B2 states
with VDE values of 3.17, 3.21, and 3.32 eV correspond to oneelectron detachments from the singly occupied 7b1 (3dxz), 3a2 13962
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A
Figure 6. Calculated FranckCondon factors at the B3LYP level for the η2-S2FeS conformation. Relative transition probabilities (in arbitrary units) for the (a) 4B2-to-5B2 and (b) 6A1-to-5B2 ionizations. The inset in panel a depicts the experimental vibrational progression of the X band as obtained with 355-nm detachment photons in ref 11.
(3dxy), and 18a1 (3dx2y2) orbitals of 4B2, respectively. Quite curiously, the 5B1 state at 3.39 eV is the result of the ionization of the 2a2 with a predominant S22 character. Its antibonding π* nature makes it the highest occupied molecular orbital of the free ligand, which, in turn, explains its low VDE, just slightly higher than those of the 3d obritals. At a somewhat greater energy, the ionization from the remaining 3d orbital, i.e., 19a1, can be found. The associated CASPT2 VDE of 3.82 eV allows the B band observed at 4.16 eV to be assigned to this ionization. The C band at 4.40 eV is then to be associated with the 5A1 or 5A2 final states. Both occur as one-electron detachments from the doubly occupied 10b2 and 6b1 orbitals, which are both mainly pπ of S2. The calculated VDE values of 4.09 and 4.20 eV deviate no more from the experimental result than is the case for the X band. Because the D band of the photoelectron spectrum lies in a very high-energy region, its assignment by CASPT2 is much more complicated. It took an MS-CASPT2 calculation with no less than eight roots to obtain the 5A1 state that results from ionization out of the 9b2 orbital. The σ metalligand bonding between 3dyz and π*(S22) stabilizes this orbital substantially more than the related 2a2. In this way, all of the bands in the experimental photoelectron spectra of FeS3 are explained. Comparing the experimental with the theoretical VDEs as depicted in Figure 3, reveals that the latter are a few tenths of an electronvolt too small. This can be ascribed to the larger electronic dynamical correlation of the anion, which shifts the theoretical VDEs downward. However, as additional assurance, the 6A1 state of η2-S2FeS should also be investigated as the initial state of the photoelectron spectra of FeS3. The leading configuration of this state can be obtained from the 4B2 state by transfer of one electron from the doubly occupied 18a1 (3dx2y2) orbital to the 11b2 (dyz)
ARTICLE
orbital. Consequently, all of the 3d orbitals of iron represent open-shell orbitals in this high-spin sextet state. The upper part of Table 5 shows that the CASPT2 VDE value for the ionization to the 5B2 ground state of the neutral cluster amounts to 2.98 eV, which compares very well to the position of the X band. We must conclude that solely on the basis of the assignment of the X band, the photoelectron spectrum can be explained from both the 4B2 and 6A1 states of η2-S2FeS. Attempts to assign the higherenergy part of the spectrum by a single computational technique failed. However, by combining the B3LYP, CASPT2, and RCCSD(T) results, the A band can be attributed to either ionizations from the 3a2 (dxy), 7b1 (dxz), or 2a2 orbitals, the B band as electron detachments from the 6b1 or the 10b2 oribitals, and the C band as the removal of an electron from the 19a1 (dz2) orbital. CASPT2 calculations place these ionizations at 3.39 eV (5A2), 3.44 eV (5B1), 3.38 eV (7A2), 4.04 eV (7B1), 3.92 eV (7B2), and 4.27 eV (5A1). In view of these results, the 6A1 state cannot definitely be ruled out as being responsible for the experimentally observed photoelectron spectra of FeS3. Clearly, additional theoretical data are needed to resolve the problem. Consequently, a FranckCondon simulation was carried out to examine the shape of the X band in the PES and to gain additional information concerning the initial state responsible for the PES. The X band as observed using 355-nm detachment photons has a vibronic progression of three peaks of decreasing intensity with increasing binding energy. In Figure 6a,b, the calculated FranckCondon factors of the 4B2-to-5B2 and 6A1to-5B2 ionization processes are presented. For the first ionization process, we found that only two of the three a1 vibrational modes, with frequencies of 435 and 579 cm1, are of importance in relation to the photoelectron spectrum. Interestingly, the average of these two vibrational frequencies is in good agreement with the experimental determined frequency of 500 ( 20 cm1 for the X band. Moreover, the calculated FranckCondon factors for the 4B2-to-5B2 ionizations show three peaks, which therefore resemble in an excellent way the vibrational progression of the X band of the experimental spectrum as depicted in the inset of Figure 6a. The analogous FranckCondon factors for the 6A1to-5B2 ionization in Figure 6b should give rise to at least four vibrational progression peaks in the experiment. Thus, according to this simulation the 6A1 is likely not responsible for the X band and by extension for the entire photoelectron spectrum.
’ CONCLUSIONS The electronic structures of FeS3 and FeS3 have been investigated at the B3LYP, CASPT2, and RCCSD(T) levels of computation. The ground state of the neutral cluster was firmly identified as the 5B2 state of the η2-S2FeS conformation. The electronic structure of this state can be described formally as (S22)Fe4+(S2). The two π* orbitals of the S22 ligand are doubly occupied, and the S2 ligand also has a closed-shell structure. In the resulting Fe4+ cation, the four valence electrons occupy the lowest 3d orbitals and are therefore responsible for the quintet spin multiplicity of the cluster. Both B3LYP and RCCSD(T) agree on a much more stable planar η2-S2FeS (C2v) ground state for the anion, as opposed to the CASPT2 method, which ascribes almost equal stability to the quartet S3Fe (D3h) conformation. The lack of sufficient recovery of dynamical correlation energy by CASPT2 is most likely at the origin of its failure to predict the correct energy positions of the two lowest FeS3 conformations. Because B3LYP and RCCSD(T) 13963
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
The Journal of Physical Chemistry A predict a much more stable η2-S2FeS by 0.62 or 0.80 eV, respectively, it is concluded that this conformation is at the origin of the observed anion photoelectron spectra. Small energy differences among the lowest states of η2-S2FeS, as calculated by all three computational techniques, make it extremely complicated to characterize unambiguously the true initial state for the spectra. CASPT2 and RCCSD(T) predict 6A1 as the lowest state, which appears to be only scarcely more stable than the 4B2 state. However, we believe that the extrapolation of the RCCSD(T) results to the complete-basis-set limit would point to the latter state as the global minimum for the FeS3 stoichiometry in the gas phase and consequently as the initial state for the photoelectron spectra. A statement supported by B3LYP. Additionally, the calculated FranckCondon factors obtained by a harmonic vibrational analysis at the B3LYP level confirm the vibrational progression of the X band as a 4B2-to-5B2 ionization process. Further evidence for the proposed assignment was found by reproducing the entire photoelectron spectrum of FeS3 on the basis of the MS-CASPT2 energies of various triplet and quintet η2-S2FeS states. Indeed, all observed bands could be ascribed to one-electron-detachment processes from the 4B2 state.
’ ASSOCIATED CONTENT
bS
Supporting Information. CASPT2-optimized structures and relative energies of the low-lying states of FeS30/. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ REFERENCES (1) Beinert, H. FASEB J. 1990, 4, 2483. (2) Beinert, H.; Holm, R. H.; M€unck, E. Science 1997, 277, 653. (3) Ogino, H.; Inomata, S.; Tobita, H. Chem. Rev. 1998, 98, 2093. (4) Ullmann, G. M.; Noodleman, L.; Case, D. A. J. Inorg. Biochem. 2001, 86, 464. (5) Noodleman, L.; Lovell, T.; Liu, T. Q.; Himo, F.; Torres, R. A. Curr. Opin. Chem. Biol. 2002, 6, 259. (6) Li, J.; Nelson, M. R.; Peng, C. Y.; Bashford, D.; Noodleman, L. J. Phys. Chem. A 1998, 102, 6311. (7) Mouesca, J. M.; Noodleman, L.; Case, D. A. Int. J. Quantum Chem. 1995, 22 (Suppl.), 95. (8) Noodleman, L.; Peng, C. Y.; Case, D. A.; Mouesca, J. M. Coord. Chem. Rev. 1995, 144, 199. (9) Zhang, N.; Hayase, T.; Kawamata, H.; Nakao, K.; Nakajima, A.; Kaya, K. J. Chem. Phys. 1996, 104, 3413. (10) Nakajima, A.; Hayase, T.; Hayakawa, F.; Kaya, K. Chem. Phys. Lett. 1997, 280, 381. (11) Zhai, H. J.; Kiran, B.; Wang, L. S. J. Phys. Chem. A 2003, 107, 2821. (12) Bauschlicher, C. W.; Maitre, P. Theor. Chim. Acta 1995, 90, 189. (13) Clima, S.; Hendrickx, M. F. A. Chem. Phys. Lett. 2007, 436, 341. (14) Clima, S.; Hendrickx, M. F. A. J. Phys. Chem. A 2007, 111, 10988. (15) Hendrickx, M. F. A.; Clima, S. Chem. Phys. Lett. 2004, 388, 290. (16) Hendrickx, M. F. A.; Clima, S. Chem. Phys. Lett. 2004, 388, 284. (17) H€ubner, O.; Termath, V.; Berning, A.; Sauer, J. Chem. Phys. Lett. 1998, 294, 37. (18) Schr€oder, D.; Kretzschmar, N.; Schwarz, H.; Rue, C.; Armentrout, P. B. Inorg. Chem. 1999, 38, 3474.
ARTICLE
(19) Hendrickx, M. F. A.; Anam, K. R. J. Phys. Chem. A 2009, 113, 8746. (20) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (21) Lee, C.; Yang, W.; Parr, P. G. Phys. Rev. B 1988, 37, 785. (22) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (23) Glukhovtsev, M. N.; Bach, R. D.; Nagel, C. J. J. Phys. Chem. A 1997, 101, 316. (24) Weigend, F.; Furche, F.; Ahlrichs, R. J. Chem. Phys. 2003, 119, 12753. (25) TURBOMOLE - Program Package for ab initio Electronic Structure Calculations, version 6.2 2010; TURBOMOLE GmbH: Karlsruhe, Germany, 2007. (26) Karlstr€om, G.; Lindh, R.; Malmqvist, P.-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P.-O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. Comput. Mater. Sci. 2003, 28, 222. (27) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. J. Phys. Chem. A 2005, 109, 6575. (28) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. J. Phys. Chem. A 2005, 108, 2851. (29) Douglas, N.; Kroll, N. M. Ann. Phys. 1974, 82, 89. Aquilante, F.; Malmqvist, P.-Å.; Pedersen, T. B.; Ghosh, A.; Roos, B. O. J. Chem. Theory Comput. 2008, 4, 694. (30) Feller, D. J. Comput. Chem. 1996, 17, 1571. (31) Schuchardt, K. L.; Didier, B. T.; Elsethagen, T.; Sun, L.; Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T. L. J. Chem. Inf. Model. 2007, 47, 1045. (32) Balabonov, N. B.; Peterson, K. A. J. Chem. Phys. 2005, 123, 64107. (33) Peterson, K. A.; Dunning, T. H., Jr. J. Chem. Phys. 2002, 117, 10548. (34) Doktorov, E. V.; Malkin, I. A.; Manko, V. I. J. Mol. Spectrosc. 1977, 64, 302. (35) Pugliesi, I.; M€uller-Dethlefs, K. J. Phys. Chem. A 2006, 110, 4657. (36) Schriever, C.; Cockett, M. C. R.; Pugliesi, I. FC-LabII, version 2009a; Ludwig-Maximilians-Universit€at M€unchen: M€unchen, Germany, 2009. More information available at http://www.fclab2.net/. (37) Tran, V. T.; Hendrickx, M. F. A. J. Chem. Phys. 2011, 135, 094505. (38) Tran, V. T.; Hendrickx, M. F. A. J. Chem. Theory Comput. 2011, 7, 310.
13964
dx.doi.org/10.1021/jp208824b |J. Phys. Chem. A 2011, 115, 13956–13964
