Fe L-Edge X-ray Absorption Spectra of Fe(II) Polypyridyl Spin

Article pubs.acs.org/JPCA

Fe L‑Edge X‑ray Absorption Spectra of Fe(II) Polypyridyl Spin Crossover Complexes from Time-Dependent Density Functional Theory Weijie Hua,† Guangjun Tian,† Giovanna Fronzoni,‡ Xin Li,† Mauro Stener,*,‡ and Yi Luo*,†,¶ †

Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden ‡ Dipartimento di Scienze Chimiche e Farmaceutiche, Università di Trieste, Via L. Giorgieri 1, I-34127 Trieste, Italy ¶ National Synchrotron Radiation Laboratory and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China S Supporting Information *

ABSTRACT: L-edge near-edge X-ray fine structure spectroscopy (NEXAFS) has become a powerful tool to study the electronic structure and dynamics of metallo-organic and biological compounds in solution. Here, we present a series of density functional theory calculations of Fe L-edge NEXAFS for spin crossover (SCO) complexes within the timedependent framework. Several key factors that control the L-edge excitations have been carefully examined using an Fe(II) polypyridyl complex [Fe(tren(py)3)]2+ (where tren(py)3 = tris(2-pyridylmethyliminoethyl)amine) as a model system. It is found that the electronic spectra of the low-spin (LS, singlet), intermediate-spin (IS, triplet), and high-spin (HS, quintet) states have distinct profiles. The relative energy positions, but not the spectral profiles, of different spin states are sensitive to the choice of the functionals. The inclusion of the vibronic coupling leads to almost no visible change in the resulting NEXAFS spectra because it is governed only by low-frequency modes of less than 500 cm−1. With the help of the molecular dynamics sampling in acetonitrile at 300 K, our calculations reveal that the thermal motion can lead to a noticeable broadening of the spectra. The main peak position is strongly associated with the length of the Fe−N bond.

1. INTRODUCTION Understanding the ultrafast electron and structural dynamics of photoinitiated chemical reactions in solution is still a fundamental problem in chemistry. In recent decades, special attention has been paid to the light-induced spin crossover (SCO) phenomenon of solvated iron(II) complexes, which carries rich information for the propagation of electronic structure (spin, energy levels, electron density) with molecular structure (symmetry, bond lengths, etc.).1−4 The SCO effect is a typical phenomenon present in transition-metal complexes, and it consists of the change of spin state of the GS according to an external perturbation like light. The growing general interest in this field is also triggered by the peculiar behavior of these magnetic compounds. The dramatic differences in the structure, as well as in the optical and magnetic properties between their low- (LS) and high-spin (HS) configurations have made them potential candidates for a variety of moleculebased devices.5 A good understanding of their electronic structure and charge-transfer dynamics between the metal and the ligands holds the key for the design and the optimization of these fascinating compounds. One of the most powerful tools is the near-edge X-ray fine structure (NEXAFS) spectroscopy with time resolution. Recently, the transient X-ray absorption spectroscopy at the © 2013 American Chemical Society

Fe K-edge of Fe(II) polypyridyl complexes has been extensively investigated (see, e.g., refs 6−13) and has already provided unprecedented details on the structural changes under the excitations. Less work has been done on the Fe L-edge, which is instead potentially more rich of information because it directly probes electronic changes associated with valence orbitals that dominate the chemistry in these systems.14,15 This is because in the L-edge, the 2p → 3d transitions are dipole-allowed, while in the K-edge, the 1s → 3d transitions are dipole-forbidden. The L-edge locates in the soft X-ray region, where ultrahigh vacuum condition are required in detection, which sets the experimental difficulty for liquid samples.16 Huse et al.17−19 reported the first ultrafast soft X-ray spectroscopy measurement of solvated molecules. On the basis of [Fe(tren(py)3)](PF6)2 (Figure 1A) dissolved in acetonitrile, they studied the electronic and structural dynamics from the LS GS (1A1g) to the metastable HS state (5T2g, lifetime of ∼60 ns before decaying back to the LS state), and the spin state conversion mechanism is suggested to go via a 1A1g → 1,3MLCT → 5T2g pathway (MLCT = metalto-ligand charge transfer). However, some basic questions are Received: September 1, 2013 Revised: November 4, 2013 Published: November 27, 2013 14075

dx.doi.org/10.1021/jp408776p | J. Phys. Chem. A 2013, 117, 14075−14085

The Journal of Physical Chemistry A

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well characterized by experiments and calculations,18−20 is a good candidate to test time-dependent density functional theory (TDDFT) methods for the simulation of Fe L-edge spectra. Although this system is rather well understood, in general, many intermediate states may be involved in an ultrafast process, which, in principle, has the possibility to give contributions to the recorded spectra. It would be essential to know from theory what the spectrum of a HS structure really looks like, for instance, its intrinsic energy position and spectral shape that distinguishes it from other states. Another important issue is the role of essential factors, especially the vibrational and solvent effects on the spectra. The special attention on vibration is due to the evident increase of Fe−N bond lengths by ∼0.2 Å after the spin conversion. While intuitively the influence of solvent on the spectra is expected to be weak because the metal center is shielded by the ligands,18 the solvent fluctuations can however effectively change the ligand structure and affect indirectly the spectra. In all respects, a systematic theoretical analysis would be desirable. Many theoretical studies on the structural and energetic analysis of SCO systems have been published so far,21−24 as well as on Fe K-edge absorption.25,26 On the other hand, theoretical modeling of L-edge spectra of general transitionmetal complexes is more challenging than that for the K edge. The single-particle approximation breaks down mainly owing to the multiplet effect brought about by the degeneracy of the 2p core orbitals and the final atomic nd contributions and also to the charge-transfer effect and the spin−orbital (SO) coupling. Particularly for a SCO complex, theory should also predict the relative difference of different spin states. Early theoretical studies on SCO complexes or analogous systems (see, e.g., refs 18 and 27−29) mostly take the semiempirical way by using the crystal field multiplet (CFM) or the charge transfer multiplet (CTM) models developed by de Groot et al.30,31 These theories are based on perturbation of the SO-coupled multiplets of the excited atom, which therefore depend much on the choices of parameters, such as the crystal field splitting and the charge-transfer energy. Other important contributions to this topic have been given from new developments using Russel−Saunders coupling,32 the ab initio CTM method based on DFT-CI,33 and the ab initio multiplet ligand field theory (MLFT) method with Wannier orbitals.34 These methods are usually computationally costly and have been applied for relatively small systems with high symmetry. For instance, in the ab initio CTM method, the difficulty of selecting the CI space has been pointed out in order to include the salient contributions. The restricted active space self-consistent field (RASSCF) method35 in combination with the state-interaction treatment of SO effects36 has been developed for L-edge NEXAFS spectra of SCO complexes and various hydrates of transition-metal ions.20,37−40 Further consideration of the dynamic electron correlation has been accounted for through multiconfigurational second-order perturbation theory (RASPT2) by Odelius et al.20 Very recently, a combined DFT and restricted open-shell configuration interaction with singles (DFT/ROCIS) approach has been proposed by Neese and co-workers.41 This method considers the dynamic correlation in an averaged but efficient way by introducing three global empirical parameters to scale the CI matrix, and excellent agreement with experiment has been yielded in most cases. Alternatively, the TDDFT approach includes the singleelectron configuration mixing in core excitations42 but only for

Figure 1. Fe L3-edge NEXAFS spectra of three Fe(II) polypyridyl complexes (structures shown around with hydrogens omitted for clarity) in the LS, IS, and HS states. (A) Top: Recapture of the latest experimental spectra of [Fe(tren(py)3)](PF6)2 in acetonitrile solution by Huse et al.19 in comparison with their semiempirical multiplet calculations on [Fe(tren(py)3)]2+.18 Middle: Recapture of theoretical spectra of [Fe(tren(py)3)]2+ calculated at RASSCF level by Josefsson et al.20 Bottom: Our calculated results for [Fe(tren(py)3)]2+ at the SAOP-TDDFT level with the nonrelativistic (NR, solid lines) and scalar relativistic (SR, dot, green) methods in the gas phase, as well as the NR result in acetonitrile solution with the COSMO model (dash, gold). (B,C) Calculated gas-phase spectra for [Fe(tren(Me-py)3)]2+ and [Fe(bpy)3]2+ at the NR level in comparison with experiments in acetonitrile by Cho et al.46 and by Aziz et al.14

still not clear to understand the ultrafast spin conversion phenomenon from transient X-ray spectroscopy. One is about the experimental final-state spectrum, obtained by adjusting the pump−probe delay until there is no absorption change at the end of the transient. In this case, Huse et al.19 have been able to follow in time the formation of the HS 5T2g state by “monitoring” the Fe L-edge absorption. For this reason, it would be interesting to calculate the Fe L-edge spectra for different spin states, namely, LS and HS, in order to check if calculations are able to reproduce the most salient observed experimental features. If this were the case, calculations may be used in the future to assign the experimental spectral features in situations where the nature of the involved states is not very well assessed. For this reason, it seems that [Fe(tren(py)3)]2+, 14076



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All Fe 2p NEXAFS spectra are calculated at the TDDFT level by the ADF program.55 Unless otherwise stated, the NR method with the “statistical averaging of orbital potentials” (SAOPs)56 model potential and the TZ2P basis set of Slater orbitals are employed throughout all presented calculations. Discrete spectra are broadened via a Lorentzian line shape with the half-width at half-maximum (hwhm) of 0.3 eV. 2.2. Inclusion of the Vibronic Coupling. The influence of vibronic coupling on the Fe 2p NEXAFS spectra is studied under the Franck−Condon (FC) approximation. We choose [Fe(tren(py)3)]2+ as an example, and because a vibrationally hot HS state is involved during the spin conversion,57 only the HS state is taken for our vibronic study. Briefly, within this framework, each discrete electronic transition is weighted by the so-called FC factors, a square of the nuclear overlap integrals, which leads to a redistribution over a range of sub-1 eV. Summation over all of the distributed spectra leads to the total vibrationally resolved spectra. Let |g⟩ and |e⟩ be the electronic ground and core excited states, |0⟩ = ∏k |0k⟩ and |n⟩ = ∏k |nk⟩, respectively, be the corresponding vibrational states (the product is over all normal modes, and the vibrational GS of each mode assumed in |g⟩); the absorption cross section at photon energy E is given by58

closed-shell systems. In fact, the single-determinant description of the GS assumed in DFT hampers the correct description of electron excitations in open-shell systems. Therefore, at the TDDFT level, open-shell systems can be treated using the unrestricted (spin-polarized) scheme, which misses all of the features necessary to properly describe multiplet effects. However, when the systems are large and therefore many excitations are present in a relatively small energy interval, the calculated excitation spectrum is usually convoluted in order to be more easily compared with the experiment. When multiplet effects are expected to be relatively large, like in the present HS complexes, one expects a deterioration of the TDDFT performances. Therefore, it would be still interesting to test the TDDFT performances in this respect; that is, to assess if for open shell-systems, spin-polarized TDDFT could still be useful, to some extent, to describe at least qualitatively the most salient spectroscopic features. Moreover, also the role of short-range and long-range Hartree−Fock exchange in TDDFT calculations of core electron excitations has been the object of a recent study.26 The NR TDDFT formalism has been also extended to core− hole calculations based on the relativistic two-component zeroth-order regular approximation (ZORA) at both the SR43 and SO coupling44 levels, which is particularly suitable for the L2,3 edges of transition-metal compounds. In principle, the TDDFT theory can also predict the charge-transfer effect only if nonlocal exchange is included in the exchange−correlation kernel.45 Another problem, connected with approximate treatment of exchange, is the self interaction error (SIE), which is quite large for core excitation;26 this problem is usually circumvented by a uniform energy shift to match, for example, an evident experimental feature.42 In the present work, we use the TDDFT method to study the influence of essential factors on the Fe L-edge NEXAFS spectra, including spin, relativistic effects, ligands, DFT functionals, vibronic coupling, and solvent effects.

σabs(E) ∝

∑ fge ∑ ⟨0|n⟩2 Φ(E ; E|e,n⟩ − E|g,0⟩, γ ) e

n

(1)

Here, fge denotes the oscillator strength, ⟨0|n⟩2 is the FC factor, and Φ(E;μ,γ) = (1/π)[γ/(γ2 + (E − μ)2)] is the Lorentzian broadening function with hwhm γ. E|e,n⟩ − E|g,0⟩ stands for the energy difference between the two states |e,n⟩ and |g,0⟩. The FC factors are computed by the linear coupling model (LCM)59 as implemented in our DynaVib code.60 The LCM model is a practical choice for studying the vibronic profile involving lots of excited states, which assumes the same curvature of the ground-state (GS) potential energy surface (PES) and that of the excited state. Within this approach, the FC overlap integral of each mode k is given by58

2. COMPUTATIONAL METHODS 2.1. Models and Spectra Calculations. Three Fe(II) polypyridyl SCO complexes [Fe(tren(py)3)]2+, [Fe(tren(6-Mepy)3)]2+, and [Fe(bpy)3]2+ [Figure 1, Me = methyl, (bpy)3 = trisbipyridine] at their LS (singlet), intermediate-spin (IS, triplet), and HS (quintet) states are chosen for our study. At room temperature, [Fe(tren(py)3)]2+ or [Fe(bpy)3]2+ has a LS GS,8,18 while [Fe(tren(6-Me-py)3)]2+ has a HS GS and is often considered as the HS analogue (HSA) of [Fe(tren(py)3)]2+.6,46 Geometries and vibrational frequencies are computed at the B3LYP47−49 level by using the Gaussian 09 package.50 The modified LanL2DZ basis set with optimized 4p functions51 and the LanL2DZ pseudo potential52 are chosen for iron, and the 631G** basis set is selected for the rest. Optimized structures exhibit strong dependence with the spin. The average Fe−N bond length is 2.0, 2.1, and 2.2−2.3 Å for the LS, IS, and HS states, respectively (detailed geometrical parameters provided in Table S1 in the Supporting Information (SI)). Each spin state also possesses a different symmetry; for instance, the LS state of [Fe(tren(py)3)]2+ has a C3 symmetry, while the IS or HS state has no symmetry. Point tests have also been done to further relax the geometries with the polarizable continuum model (PCM)53,54 for acetonitrile. Only slight structural changes happen; therefore, the gas-phase structures are used for subsequent spectral calculations.

⟨0|nk ⟩ = Sk =

⎛ S ⎞ ( −1)nk exp⎜ − k ⎟Sknk /2 ⎝ 2⎠ nk !

1 ωkdk2 2ℏ

(2)

(3)

where Sk represents the Huang−Ryhs factor, ωk denotes the vibrational frequency, and dk is the displacement of the two sets of normal coordinates. We fit the energies at several points slightly displaced along each normal coordinate to quadratic order, by which we find more numerical stability in our case study. Explicitly, we choose five structures shifted by 0, ±δk, and ±2δk along the GS PES and perform the TDDFT calculations. With the energy of the each core excited state provided, the PES of mode k is fitted to the following quadratic equation U (Q k) = ak (Q k − dk)2 + bk

(4)

where ak, dk, and bk are the parameters to be fitted. The GS PES of each mode is also fitted in the same way, and the obtained tiny displacement (ideally zero) is removed from the dk value of each core excited state for numerical correction. Different δk’s within a range of 0.1−1.0 au·(amu)1/2 are employed for each of the 171 normal modes according to their vibrational frequencies to guarantee an energy change of a few eVs at 14077



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the five positions, which is simply to get a balance between the numerical accuracy (requiring a larger δk) and the harmonicity of the oscillator (requiring a smaller δk). See SI Figure S1 for an illustrative example on fitting the PESs. Other ways for calculating the displacements from numerical gradients of the excited-state PES are given in, for example, refs 58, 61, and 62. 2.3. Spectra of the Iron Complex in Solution. The experimental spectrum18,19 has been recorded in the CH3CN solution, while all of the following calculations are done in the gas phase. To bridge the gap, the solvent effect is examined at two stages. The long-range static effect is first considered with the implicit-solvent model, where acetonitrile is modeled with the conductor-like screening model (COSMO)63 as implemented in ADF. Then, the explicit solvent model is used to study the (short-range) effect of thermal motion caused by solvent fluctuations and temperature. Hybrid quantum mechanical and molecular mechanical molecular dynamics (MD) simulation at 300 K is carried out for [Fe(tren(py)3)]2+ (PF−6 )2 (in its LS and HS states, respectively) and 500 CH3CN molecules within a large sphere of ∼22 Å. Calculations are performed with a locally modified version of the fDynamo code64 interfaced to the Gaussian 09 package;50 the latter forces at each MD step are generated with the ONIOM (our own nlayered integrated molecular orbital (MO) and molecular mechanics) method. The DFT method with the BLYP functional47,49 is used for the cation (high layer), and the OPLS-AA (optimized potential for liquid simulations-all atom) force field65 is used for the rest (low layer). After an equilibrium time of 1 ps, the trajectory is collected for 4 ps. (More details on the MD setup are given in the SI.) For each spin state, Fe 2p NEXAFS spectra of [Fe(tren(py)3)]2+ are then calculated at 100 evenly separated snapshot geometries (removing the coordinates of the solvent and counterions), and their averages lead to the solution-phase spectrum. Early results have shown that a few hundreds snapshots are already enough to represent well the statistical average.66

Table 1. Functional Dependence for the Raw (i.e., uncalibrated) Main Peak Positions in the HS and LS States and Their Difference (Δ) (in eV) in the Theoretical Fe L3Edge NEXAFS Spectra of [Fe(tren(py)3)]2+ Predicted at the NR TDDFT Levela functional

Emain peak (HS)

Emain peak (LS)

Δ

LB94 OLYP RPBE BP86 TPSS M06-L VWN BLYP XLYP SAOP SAOP(SR) exp.

705.89 692.39 691.17 691.34 692.81 698.58 690.15 691.33 691.19 685.95 689.69 707.6

706.40 693.27 692.22 692.44 693.86 699.65 691.38 692.63 692.77 688.19 691.92 709.3

0.5 0.9 1.1 1.1 1.1 1.1 1.2 1.3 1.6 2.2 2.2 1.7

a

Comparison has also been made with the SR result by using the SAOP potential and the experiment19 as well.

value19 (shifted by 21.635 and 17.895 eV, respectively, for the NR and SR levels); and the same shift values are employed for the LS and IS states. As shown in Figure 1A, the spectra are extremely sensitive to the spin state. As expected, the SR effect is rather weak for each state, as illustrated by the almost coincidence of spectra at the NR and SR levels. The calculated spectra agree well with the experiment, with all features reproduced except for two discrepancies. One exists in the HS state; a rather weak but evident postedge structure at ∼711 eV (denoted by arrow) is in fact observed in the experiment, while no corresponding peak appears in the theoretical spectrum. This deterioration can be ascribed to the difficulty of TDDFT to treat multiplet effects in the HS complexes. The other difference is the main peak shift between the LS and HS states (denoted hereafter as Δ), which is overestimated by 0.5 eV (from 1.7 to 2.2 eV). The overestimate of 0.5 eV can be ascribed to the neglect of the SO coupling, whose inclusion would be necessary for a more quantitative description, or to the influence of the model potential. Two more examples in panels B and C confirm that the TDDFT approach can well reproduce the sensitive influence of the spin state and the noticeable influence of the ligands. For L-edge spectroscopy, the SO coupling plays a much more important role than SR effects, and therefore, its contribution must be properly assessed. However, the present TDDFT method is suitable to include SO coupling only for closed shell;44 therefore, we are forced to limit our investigation to the LS state. In Figure 2A, we have reported the Fe L2,3-edge NEXAFS spectra of [Fe(tren(py)3)]2+ calculated at the TDDFT level, including the SO coupling. The results can be compared with a recent experiment46 and RASSCF calculation,20 which cover the energy range encompassing both L3 and L2 edges. The experimental SO splitting between the two edges of the LS compound is 11.6 eV, while our calculation gives 11.7 eV, in excellent agreement with the experiment; RASSCF gives a SO splitting of 10.8 eV. It is worth noting that the experiment gives only a single peak for each of the two edges; present TDDFT results are consistent with this finding because only very weak structures are calculated between the two peaks of the edges. The RASSCF method, instead, gives a double-peak structure for both edges;20 see, in particular, the

3. RESULTS AND DISCUSSION 3.1. Electronic Spectra in the Gas Phase. 3.1.1. Spin, Relativistic, And Ligand Effects. We start our discussion with

Figure 2. (A) (Uncalibrated) Fe L2,3-edge NEXAFS spectra of [Fe(tren(py)3)]2+ calculated at the SAOP-TDDFT level with the inclusion of SO coupling. (B) Comparison of theoretical spectra at the L3-edge at the NR (magneta), SR (green), and SO coupled (black) levels. For better comparison, the SO result is uniformly shifted by 22.522 eV, and the intensity is uniformly scaled.

[Fe(tren(py)3)]2+. To investigate the relativistic effect, spectra of LS, IS, and HS structures are calculated at both the NR and ZORA SR levels. Raw spectra are calibrated by aligning the main peak of the HS state to the corresponding experimental 14078



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Figure 3. Top: Calculated discrete and convoluted Fe L3-edge NEXAFS spectra of [Fe(tren(py)3)]2+ in the (A) LS and (B) HS states at the NRTDDFT level. Major transitions are labeled by the indexes of the excited states. Bottom: MO isosurfaces (contour isovalue = 0.05) involved in the predominant 2p → MO transitions for the labeled excited states. the Fe 3d contribution (or its main character when the Fe 3d contribution is too low) is specified below the MO index. Excited states with large oscillator strengths are included in parentheses for emphasis, and the N 2p contributions in the final-state MOs are also given.

asymptotically corrected potential LB9474 is the one that reproduces better the absolute energies but is the worst with respect to the LS−HS splitting (Δ). The LS−HS main peak difference is sensitive to different functionals, with values ranging from 0.5 to 2.2 eV. Besides such a shift, different functionals predict almost the same spectral shape for each individual spin state. It is well-known that for TDDFT calculations, the correct Coulomb asymptotic behavior of the exchange−correlation potential is very important to get accurate results. In Table 1, only LB94 and SAOP have the correct asymptotic behavior, with SAOP giving a Δ value in much better agreement with the experiment than LB94. We attribute this deterioration of LB94, which performs well in the long-range limit thanks to its correct asymptotic behavior, to its difficulty to describe the intermediate spatial region where chemical bonds are present.75 For this reason, we have chosen the SAOP potential in this work. 3.1.3. Electronic Structure Change from LS to HS. Figure 3 compares the underlying core excitations of the LS and HS states at the NR-TDDFT level. The corresponding energies, oscillator strengths, as well as excited-state compositions are reported in Tables S2 (LS) and S3 (HS) in the SI. In the LS state, three almost degenerate transitions (excited states 31− 33) contribute to the resolved main peak, while in the HS state, they (excites states 28−30) become more separated due to a lowered symmetry in geometry and electronic structure. For this reason, a sharper main peak appears in the LS state. Previous multiplet calculations18 suggested that the spin conversion leads to more ionic Fe−N bonding (i.e., more localized Fe 3d and N 2p orbitals) in the final HS state, which is

Figure 4. Comparison of Fe L-edge NEXAFS spectra of [Fe(tren(py)3)]2+ in the HS state with (red dash) and without (blue solid line) including the vibronic coupling. Spectra are convoluted with a Lorentzian line shape with a hwhm of (A) 0.05 and (B) 0.3 eV.

peak shape of the L3-edge recaptured in the middle of Figure 1A. Figure 2B also provides a comparison of LS spectra at the L3-edge calculated at NR, SR, and SO-coupled levels. Inclusion of the SO coupling introduces visible changes in details, while the global profile keeps its original shape. According to this analysis, the NR level of theory has been employed in all of the following calculations. 3.1.2. Influence of DFT Functionals. To test the functional dependence of spectra, we choose a variety of local density approximation (LDA) (VWN67), gradient-corrected approximation (GGA) (BLYP,47,49 OLYP,49,68 XLYP,49,69 BP86,47,70 and RPBE71), and meta-GGA (TPSS72 and M06-L73) functionals and model potentials (LB9474 and SAOP56) to compute the spectra at the TDDFT level. As shown in Table 1, all functionals underestimate the excitation energies because the approximate treatment of exchange introduces the SIE; the 14079



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Table 2. List of Dominant Normal Modes in Selected CoreExcited States of [Fe(tren(py)3)]2+ in Its HS State, Including the Mode Index (k) and Vibrational Frequency (ωk, in cm−1) and Vibronic Coupling Strength (λk = (Sk)1/2)a λk

a

k

ωk

state 28

state 29

state 30

3 6 7 8 9 10 11 13 14 15 16 18 20 21 22 24 26 27 28 31 39

37.5 63.8 98.2 99.9 102.4 115.6 122.6 135.8 142.1 146.2 184.0 195.9 248.2 251.6 282.0 299.2 319.7 324.4 352.6 410.7 457.9

0.32

0.60

0.38

0.50 0.25 0.34 0.20

0.62 0.31 0.45

0.18 0.22 0.26 0.49

0.20

0.15 0.17 0.26 0.18 0.16

0.25 0.32

0.15 0.19 0.24 0.22 0.28 0.18 0.29

0.25 0.31 0.17 0.34 0.23 0.17 0.16 0.23 0.17 0.21 0.27 0.16 0.17 0.29

A threshold of λk ≥ 0.15 is used.

describes the electronic structure change during the spin conversion. 3.2. Vibronic Coupling Effect. NEXAFS spectra of HS state [Fe(tren(py)3)]2+ with and without the vibronic coupling are compared in Figure 4. To our surprise, we find that inclusion of the FC effect introduces almost no change in the spectra. To understand this, we have plotted the vibrationally resolved spectra of individual electronic states (taking core excited states 28, 29, and 30 as an example) in Figure 5 and presented contributions from 0−0, 0−1, 0−2, 0−3, and 0−4 vibrational transitions. A very small separation (∼12 meV on average) between each neighboring series is found, and each electronic transition is therefore broadened to approximately a Lorentzian-like profile. The small separation is because only low-frequency modes (37.5−457.9 cm−1 or 5−60 meV) make dominant contributions (Table 2). Most of these modes involve Fe−N vibrations (selected modes are visualized in Figure S2, SI). 3.3. Solvent Effect. The inclusion of the implicit solvent introduces almost no change in spectra (Figure 1). It shows that the static influence of the solvent is negligible, consistent with that found previously in the K edge.6 With the explicit solvent model, a histogram analysis over the Fe−N distance for the LS and HS complexes is displayed in Figure 6. It is found that the Fe−N distance in the LS complex covers a range of 1.8−2.2 Å, while in the HS state, it covers a much broader range of 2.0−3.0 Å. Such structural distributions are similar to a recent Car−Parrinello MD study of [Fe(bpy)3]Cl2 in water solution,76 except that our distributions are relatively broader owing to the lower symmetry of the cation. Additionally, here, the distances r2, r4, and r6 (bond lengths between Fe and pyridyl nitrogens) have much broader distributions than r1, r3, and r5 (those between Fe and iminoethyl nitrogens) because

Figure 5. The vibrationally resolved spectra of individual electronic excited states (states 28, 29, and 30, from top to bottom) for [Fe(tren(py)3)]2+ in its HS state. Spectra are decomposed into contributions from 0−0, 0−1, 0−2, 0−3, and 0−4 vibrational transitions. Relative energies with respect to electronic transitions are used. The Lorentzian line shape with hwhm = 0.012 eV is employed (note that such spectral structures are only observable at a very small hwhm value).

interpreted as a consequence of weaker ligand-to-metal σdonation and metal-to-ligand π-back-donation effects. This is more vividly illustrated by the MOs involved in the predominant Fe 2p → MO excitations. For the main peaks, the corresponding MOs in both states represent mostly the σ* antibonding between the Fe 3d and ligand N 2p orbitals. The MOs 129 and 130 involved in the transitions 31−33 of the LS state are, respectively, related to the MOs 126β and 130β in the transitions 28−30 of the HS state, accompanying an increase of the Fe 3d fraction (65 → 72 and 80%) and a decrease of the N 2p fraction (11 → 7% and 9 → 3%). Meanwhile, the HS state also displays a more intense pre-edge structure because a significant Fe 3d participation is involved (34 and 58 versus 7%). Besides, the weak post-edge features in both spin states (∼711 and 709.5 eV, respectively) come from transitions that involve orbitals with mainly ligand character. This finding 14080



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Figure 6. Top: Histogram statistics of the Fe−N bond lengths for the production-phase trajectories of [Fe(tren(py)3)]2+ in acetonitrile solution, (A) LS and (B) HS states. Bottom: A snapshot of [Fe(tren(py)3)]2+(PF−6 )2 solvated in 500 acetonitrile molecules and the definition of the six Fe−N bonds.

the pyridyl terminals are more flexible. Figure 7A compares the simulated radial distribution functions (RDFs) between Fe and the acetonitrile nitrogens for the LS and HS forms of [Fe(tren(py)3)](PF6)2 solutions. A significant difference of the solvation shells of the Fe cluster is found. The underlying reason is the different Fe−N bonding nature in the LS and HS cations. A much looser Fe−N bonding and more opened molecular framework in the HS structure lead to more coordinated acetonitrile molecules. Noticeable difference is also found in the RDFs between Fe and the methyl carbon (panel B). On average, the cyano moiety in the CH3CN molecule tends to be relatively closer to the Fe center than the methyl group. It is worth noting that in an early MD simulation of [Fe(bpy)3]Cl2 in aqueous solution,76 different solvation structures of the LS and HS forms were also found. The solvation structures of the PF−6 counterions remain almost the same (panel C). Figure 8A depicts the spectra of the 100 snapshots as well as the averaged spectra. In each spin state, thermal motion leads to a more broadened profile. The general spectral shape, however, does not change much at different geometries simply because the Fe L-edge spectra capture mainly the features of the ratherlocalized Fe 3d orbitals. The averaged spectra exhibit a main peak position at 710.0 and 707.6 eV for the LS and HS states, respectively, which results in a Δ value of 2.4 eV. In comparison with the gas-phase result (Δ = 2.2 eV), thermal motion only leads to a slight further separation (0.2 eV) for the spectra of the states. Interestingly, we find that the main peak position has

an almost linear relationship with the average Fe−N distance in the LS state (panel B); increase of the Fe−N distance by 0.1 Å (∼1.98 to 2.07 Å) leads to a decrease of the main peak position by 0.5 eV. In the HS state (panel C), although the monotonically decreasing fashion still persists and somewhat more slowly, the linear dependence becomes less evident. This less strict linear relation in the HS state can be ascribed to its more complex electronic structure, that is, the transition energy depends not only on the Fe−N distance but also strongly on the electronic configurations. The statistical study examines the sensitivity of the spectra to the Fe−N distance and adds richer information to the fixed-geometry theoretical result.

4. SUMMARY AND CONCLUSIONS To summarize, we have performed a systematic theoretical study of Fe L3-edge NEXAFS spectra of SCO complexes at the TDDFT level and analyzed the influence of several key factors that control the spectra, by mainly using [Fe(tren(py)3)]2+ as a model system. The spectra are extremely sensitive to different spin states, noticeably sensitive to different ligands, while almost insensitive to the SR effect and the long-range static effect of the acetonitrile solvent. The functionals choice can lead to an evident change in relative energy positions (by ∼1−2 eV) but not in the spectral profiles of different spin states. Vibronic coupling is governed only by low-frequency modes less than 500 cm−1 (0.06 eV), which therefore leads to almost no visible change in the resulting NEXAFS spectra. By MD simulation in acetonitrile at 300 K, our calculations reveal that 14081



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shift between the LS and the HS states is not quantitative, probably due to the neglect of the SO coupling. Further studies are still necessary to better assess the performances of TDDFT to describe L edges of iron compounds, for example, with ligands of different nature.

■

ASSOCIATED CONTENT

S Supporting Information *

MD simulation details, geometrical parameters of all gas-phase optimized structures, tables of MO components of major transitions, an illustrative example for PES fitting, and selective vibrational modes. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (M.S.). *E-mail: [email protected] (Y.L.). Notes

The authors declare no competing financial interest.

■ Figure 7. Comparison of the simulated RDFs of the LS and HS forms of [Fe(tren(py)3)](PF6)2 in CH3CN solutions, (A) Fe−NC, (b) Fe− CT, and (c) P−NC. (NC = acetonitrile nitrogen; CT = methyl carbon.)

ACKNOWLEDGMENTS This work is supported by the Swedish Research Council (VR), the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine, Stiftelsen Lars Hiertas Minne, the National Natural Science Foundation of China (20925311), the Major State Basic Research Development Programs (2010CB923300), and MIUR (PRIN 2010) of Italy. The Swedish National Infrastructure for Computing (SNIC) is acknowledged for computer time.

the thermal motion leads to a noticeable broadening of the spectra. The main peak position is strongly associated with the Fe−N bond length; especially, it has an almost linear relationship with the average Fe−N distance in the LS state. A significant difference of the solvation shells of the LS and HS Fe(II) cluster is also found in the acetonitrile solution. Our results show that the TDDFT method has been proven capable of giving a reasonably good description of the L-edge spectra for the series of iron polypyridyl compounds considered in this work. The method has been proven successful to describe, at least qualitatively, the main spectral differences between the LS and the HS states. More difficult is the description of the weak post-edge structures due to the presence of more pronounced multiplet effects in the HS state. Also, the calculated energy

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Figure 8. (A) Calculated Fe L3-edge NEXAFS of [Fe(tren(py)3)]2+ in the LS (black) and HS (blue) states at 100 MD snapshot geometries (300 K) and their respective averages (yellow dash). (B,C) Plot of main peak positions (relatively to the corresponding gas-phase values) versus the average Fe−N bond lengths for each spin state. Solid lines represent the best linear fit. 14082



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Fe L-Edge X-ray Absorption Spectra of Fe(II) Polypyridyl Spin

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