The Interaction of Iron-Sulfur Clusters with N 2 : Biomimetic Systems in the Gas Phase

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1 Supporting Information to The Interaction of Iron-Sulfur Clusters with N 2 : Biomimetic Systems in the Gas Phase Heiko C. Heim, a Thorsten M. Bernhardt, a Sandra M. Lang, a* Robert N. Barnett, b Uzi Landman b* a Institute of Surface Chemistry and Catalysis, University of Ulm, Albert-Einstein-Allee 47, Ulm, Germany b School of Physics, Georgia Institute of Technology, Atlanta, Georgia , United States S.1 Theoretical methods The theoretical explorations of the atomic arrangements and electronic structures of the iron-sulfur clusters and their complexes with di-nitrogen were performed with the use of the Born-Oppenheimer spin densityfunctional theory molecular dynamics (BO-SDFT-MD) method 1 with norm-conserving soft (scalar relativistic for Fe) pseudopotentials 2 and the generalized gradient approximation (GGA) 3 for electronic exchange and correlations. In these calculations we have used a plane-wave basis with a kinetic energy cutoff E c = 96 Ry, which yields convergence. This corresponds to a real-space grid spacing of 0.32 a 0 (Bohr radius); the real-space grid spacing for the density (and potential) was a 0 corresponding to E c = 867 Ry. In the construction of the Fe ([Ar] 3d 6 4s 2 ) pseudopotentials the valence electrons, 3d 6 and 4s 2, were characterized by core radii r c (s) = r c (d) = 2.2 a 0 while r c (p) = 2.4 a 0 with the s orbital treated as local. Additionally, we employ a non-linear core correction in which the partial core charge density includes 10% of the real core and matches at 1.66 a 0. For the sulfur atom ([Ne] 3s 2 3p 4 ) pseudopotential the valence 3s 2 and 3p 4 electrons were treated with r c (s) = 1.8 a 0 and r c (p) = 2.3 a 0 with the p orbital treated as local. Finally, for nitrogen ([He] 2s 2 2p 3 ) the pseudopotential core radii are r c (s) = r c (p) = 1.1 a 0 with s taken as local and there is a non-linear core correction in which the partial core charge density includes 10% of the real core and matches at 0.64 a 0. The BO-SDFT-MD method 1 is particularly suitable for investigations of charged systems since it does not employ a supercell (i.e., no periodic replication of the ionic system is used). In all the calculations the S1

2 dependence on spin multiplicity has been checked, and the results that we report correspond to the spin multiplicities with the lowest energies (global minimum for the ground-state configuration, and local minim for the isomeric structures); both spin and geometrical isomers are explored. At each step of the calculation the energy levels of the SDFT up-spin and down-spin manifolds in the vicinity of the Fermi level are examined, and the occupation is adjusted such that the spin- Kohn-Sham level with the lower energy eigenvalue gets occupied. The energy minimization to find the optimal cluster geometry was done with a steepest-descent method. The convergence criteria was that the maximum force magnitude on any particle is less than Hartree/Bohr and that the average over all particles is less than Hartree/Bohr. In some cases BO- SDF-MD simulations of typically a few picosecond duration at 300 K (that is, canonical, constant temperature, simulations, with stochastic thermalization) were used to insure that the resulting optimal configurations were stable; a time-step of 1.0 fs was used in these simulations. Such ab-initio Born- Oppenheimer MD simulations were also performed at elevated temperatures, in order to select candidate structural configurations (particularly those found to have lowest potential energies following lowtemperature quenches) for the aforementioned steepest-descent optimization. The configurations obtained in these dynamical simulations, together with those constructed by starting from structural configurations of 3D cuboidal or 2D ring motifs, form a rich structural pool for (steepest descent) searching for the optimal ground state, and isomeric structures. S.2 Definitions and case studies Definitions of several quantities given in Figures S1-S8: (1) atomization energy E A E A = E{Fe x S x (N 2 ) q y } xe{fe} xe{s} ye{n 2 }, q = 0 (neutral), 1; x = 2,3,4; y = 0,1 (2) energy difference between the isomeric geometry and the ground state δe δe = E{isomer} E{ground state} S2

3 (3) adiabatic ionization potential aip aip = E{cation gs} E{neutral gs} (4) N 2 binding energy E A E A = {Fe x S x (N 2 ) q } E{Fe x S q x } E{N 2 }, q = 0, 1, x = 2,3,4 (5) : the difference between the number of majority (spin up) and minority (spin down) electrons; spin related quantities are expressed as 0.5 μ. In the following we give values for the elementary units of our system. These serve to illustrate the level of accuracy achieved in our calculations. Fe ([Ar] 3d 6 4s 2 ) Fe: = 4 Fe : = 5, aip = 7.7 ev (experimental: 7.9 ev) 4 FeS: = 4 E A = 3.06 ev (various experimental: 3.37 ± 0.15 ev, 3.34 ev) 5,7 d Fe-S = 2.1 Å (various experimental: Å) 8,9 N 2 : = 0 E A = E{N 2 }-2E{N} = 9.96 ev (experimental: 9.81 ± 0.01 ev) 10 d N-N = 1.11 Å (experimental: 1.10 Å) 5 N-N = 2324 cm -1 (experimental: 2358 cm -1 ) 5 Figure S1: Results from DFT calculations for Fe, Fe, FeS and N 2. S3

4 S.3 Optimized isomeric structures In the structure figures displayed in this section lines drawn between neighbouring atoms indicate bonds, except those between neighbouring Fe atoms; Fe-Fe indicates interaction between the Fe atoms but not necessarily formation of a real chemical bond. Figure S2: Isomeric structures for neutral Fe 2 S 2 (N 2 ) and Fe 2 S 2. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 2 S 2 (N 2 ) complex to the corresponding bare Fe 2 S 2 cluster with the same and the same geometry. The thin arrow depicts the transition from the ground state Fe 2 S 2 (N 2 ) complex to the ground state of the bare Fe 2 S 2 cluster. S4

5 Figure S3: Isomeric structures for neutral Fe 3 S 3 (N 2 ) and Fe 3 S 3. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 3 S 3 (N 2 ) complex to the corresponding bare Fe 3 S 3 cluster with the same and the same geometry. The thin arrow depicts the transition from the ground state Fe 3 S 3 (N 2 ) complex to the ground state of the bare Fe 3 S 3 cluster. S5

6 Figure S4: Isomeric structures for neutral Fe 4 S 4 (N 2 ) and Fe 4 S 4. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 4 S 4 (N 2 ) complex to the corresponding bare Fe 4 S 4 cluster with the same and the same geometry. The thin arrow depicts the transition from the ground state Fe 4 S 4 (N 2 ) complex to the ground state of the bare Fe 4 S 4 cluster. Figure S5: Isomeric structures for cationic Fe 2 S 2 (N 2 ) and Fe 2 S 2. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 2 S 2 (N 2 ) complex to the corresponding bare Fe 2 S 2 cluster with the same (number of unpaired electrons) and the same geometry. S6

7 Figure S6: Isomeric structures for cationic Fe 3 S 3 (N 2 ) and Fe 3 S 3. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 3 S 3 (N 2 ) complex to the corresponding bare Fe 3 S 3 cluster with the same and the same geometry. The thin arrows depict the transitions from the ground state Fe 3 S 3 (N 2 ) complex to the ground state of the bare Fe 3 S 3 cluster as well as its first higher energy isomer. Figure S7: Further higher energy isomeric structures for cationic Fe 3 S 3 (N 2 ) and Fe 3 S 3. S7

8 Figure S8: Transition from the ground-state Fe 3 S 3 (N 2 ) to the ground-state Fe 3 S 3. The brown/orange arrows show the spin state of the neighboring Fe ions (brown/orange balls). Sulfur atoms are depicted by the yellow balls, and nitrogen atoms are represented by the blue balls. S8

9 Figure S9: Isomeric structures for cationic Fe 4 S 4 (N 2 ) and Fe 4 S 4. Ground state isomers are indicated in bold. The heavy arrow depicts the transitions from the ground state Fe 4 S 4 (N 2 ) complex to the corresponding bare Fe 4 S 4 cluster with the same and the same geometry. S9

10 Figure S10. Multiple N 2 adsorption: (a) Fe 2 S 2 (N 2 ) y (y = 1-4), (b) Fe 4 S 4 (N 2 ) y (y = 1-4). The N-N bond remains essentially unchanged for all these adsorption configurations (1.11 Ǻ). For the ground state configurations with y = 1, see Fig. 4 of the main text, Fig. S5 (for Fe 2 S 2 (N 2 ) ), and Fig. S9 (for Fe 4 S 4 (N 2 ) ). For the calculated adsorption energies see Table S1. neutral cation cluster Fe 1 S ev 1.48 ev Fe 2 S ev 0.83 ev 0.74 ev 0.60 ev 0.45 ev Fe 3 S ev 0.53 ev (0.81) Fe 4 S ev 0.54 ev 0.46 ev 0.48 ev 0.46 ev Table S1. DFT-calculated binding energy (BE(y) in ev) of N 2 molecules to Fe x S x neutral and cationic clusters (x = 1-4). The columns labeled 1, 2, 3, 4 give the binding energy per molecule for y = 1, 2, 3, and 4 adsorbed N 2 on the cation clusters, Fe x S x (N 2 ) y. The number in parenthesis for Fe 3 S 3 is the energy to remove the N 2 molecule from the cationic cluster leaving the bare cluster with the same spin state and structure (see Fig. S8). All other numbers are for groundstate to ground-state transitions. From the values given in the Table one can obtain the energy, δ(y), for adding an extra N 2 molecule to a cluster having already y-1 adsorbed molecules, from: δ(y) = ybe(y)-(y-1)be(y-1), for y = 1, 2, 3, 4. S10

11 S4. Experimental determination of rate constants The normalized kinetic data are evaluated by fitting integrated rate equations of potential reaction mechanisms to the experimental data by using the software Detmech. 10 This program generates rate equations from the proposed reaction mechanism and integrates them. The best set of rate constants k is subsequently found by minimizing the sum of the squares of the deviations from the measured to the fitted concentrations. This leads to the determination of the simplest reaction mechanism that best fits the experimental data as well as to the corresponding rate constants k. Since the experiment is operated under multi-collision conditions in the kinetic low pressure regime 11,12, each association reaction Fe x S x N 2 Fe x S x (N 2 ) k (1) can be described by the Lindemann energy transfer model for association reactions: Fe x S x N 2 (Fe x S x (N 2 ) ) * k a, k d (2a) (Fe x S x (N 2 ) ) * He Fe x S x (N 2 ) He * k s (2b) including the association rate constant k a, the unimolecular dissociation rate constant k d, and the stabilization rate constant k s. As a result, the rate constant k depends on the concentration of nitrogen [N 2 ] and helium [He]. Since these concentrations are typically orders of magnitude larger than the cluster ion concentration and a steady flow of the reactants is ensured, the rate constants k are of pseudo-first-order with the termolecular rate constant k (3) : k = k (1) = k (3) [He][N 2 ] (3) In the kinetic low pressure limit this termolecular rate constant can also be expressed by k (3) = (k a k s )/k d (4) The association and stabilization rate constants k a and k s are usually well presented by ion-molecule collision rate coefficients as specified by Langevin theory. 15 According to Langevin theory, ion-molecule reactions are basically interactions between a charge and an induced dipole and thus exhibit no activation barrier and hence no temperature dependence. Therefore, any observed temperature dependence must be contained in the unimolecular decomposition rate constant k d. The activation barrier for this unimolecular decomposition results in a negative temperature dependence of the overall reaction (1) and thus an enhanced reactivity with decreasing temperature. This also means that products Fe x S x (N 2 ) y observed at room temperature must contain strongly bound N 2 whereas products with weakly bound N 2 are only observed at lower temperatures. Furthermore, Eq. (4) allows for the determination of experimental dissociation rate constants k d. S11

12 S5. Reaction mechanism To determine the termolecular rate constant for the adsorption of N 2 on Fe 2 S 2 and the corresponding unimolecular decomposition rate constant k d, the normalized kinetic data were evaluated by fitting integrated rate equations of potential reaction mechanisms to the experimental data. The simplest reaction mechanism that best fits the experimental kinetic data at room temperature is: Fe 2 S 2 N 2 Fe 2 S 2 (N 2 ) (1a) Fe 2 S 2 (N 2 ) H 2 O Fe 2 S 2 (N 2 )(H 2 O) (1b) Fe 2 S 2 (N 2 )(H 2 O) Fe 2 S 2 (H 2 O) N 2 (1c) Fe 2 S 2 (H 2 O) H 2 O Fe 2 S 2 (H 2 O) 2 (1d) At this temperature an alternative reaction mechanism fits the data slightly worse, however, cannot be ruled out completely: Fe 2 S 2 N 2 Fe 2 S 2 (N 2 ) (2a) Fe 2 S 2 H 2 O Fe 2 S 2 (H 2 O) (2b) Fe 2 S 2 (N 2 ) H 2 O Fe 2 S 2 (N 2 )(H 2 O) (2c) Fe 2 S 2 (N 2 )(H 2 O) H 2 O Fe 2 S 2 (H 2 O) 2 N 2 (2d) Fe 2 S 2 (H 2 O) H 2 O Fe 2 S 2 (H 2 O) 2 (2e) The resulting rate constant for the adsorption of the first N 2 molecule amounts to (2.2 ± 0.4) cm 6 s -1 for the first mechanism and (3.7±0.7) cm 6 s -1 for the second mechanism. For the determination of the N 2 binding energy to the cluster both values have been considered. The simplest reaction mechanism that best fits the experimental kinetic data at 250 K is: Fe 2 S 2 N 2 Fe 2 S 2 (N 2 ) (3a) Fe 2 S 2 (N 2 ) N 2 Fe 2 S 2 (N 2 ) 2 (3b) Fe 2 S 2 (N 2 ) H 2 O Fe 2 S 2 (N 2 )(H 2 O) (3c) Fe 2 S 2 (N 2 )(H 2 O) 2 H 2 O Fe 2 S 2 (H 2 O) 3 N 2 (3d) This results in a termolecular rate constant for the adsorption of the first N 2 molecule of (12 ± 3) cm 6 s -1. S12

13 All rate constants for Fe 2 S 2, Fe 3 S 3, and Fe 4 S 4 as well as the corresponding experimental conditions are given in Table S2. T / K p(he) / Pa p(n 2 ) / Pa k / s -1 k (3) / cm 6 s -1 k a / cm 3 s -1 k s / cm 3 s -1 k d / 10 8 s -1 Fe 2 S ± ± ± ± ± ± ±3 9.0± ± ± ±1.3 12± ±0.6 Fe 3 S ± ± ± ± ± ± ±5 6.1±1.2 Fe 4 S ± ± ± ± ±44 Table S2: Measured pseudo-first-order (k), termolecular (k (3) ) and decomposition (k d ) rate constants for the investigated reactions of iron-sulfur clusters with N 2 at various temperatures T and experimental pressure conditions as well as approximated (via Langevin theory) association (k a ) and stabilization (k s ) rate constants. S6. Determination of experimental Fe x S x -N 2 binding energies The unimolecular dissociation rate constant k d is well represented by statistical unimolecular reaction rate theory in the framework of the RRKM (Rice-Ramsperger-Kassel-Marcus) model. 16 This theory is usually applied to determine k d from the known binding energy between the adsorbed ligand and the cluster ion under assumption of the dissociation to proceed via a transition state (TS) (Fe x S x (N 2 ) ). In our experimental approach, however, k d is the measured quantity which consequently allows for the determination of the binding energies between a first adsorbed N 2 molecule and the clusters. To obtain such binding energies the experimental decomposition rate constants k d are simulated using the software package MassKinetics. 17 Details of the procedure as well as the error analysis have been described elsewhere. 12 For these simulations, the vibrational frequencies of the stabilized complex Fe x S x (N 2 ) as well as the transitions state (Fe x S x (N 2 ) ) are required. Since neither vibrational frequencies of iron-sulfur clusters nor of their nitrogen complexes have been reported so far, the vibrational frequencies have been estimated (see Table S3). S13

14 From experimental infrared spectroscopic data for iron-sulfur proteins 18 and iron-sulfur model compounds 19 as well as preliminary data for small iron-sulfur clusters 20 it is known that the energies of the metal-metal and metal-sulfur vibrations typically range between 200 cm -1 and 450 cm -1. Thus, the distributions of the Fe x S x vibrations are estimated by applying the Debye model of phonon frequency dispersion as described by Jarrold et al. 21 with a cut-off at 450 cm -1. Employing different sets of vibrational frequencies obtained by reducing the cut-off to 355 cm -1 changes the binding energies at maximum by 0.05 ev. This is in accordance with previous studies on gold-oxygen complexes which showed that not the exact frequencies but rather their distribution is important for the determination of the binding energy. 12 The stretch frequency of the free N 2 molecule 22 amounts to 2359 cm -1 and the Fe x S x -N 2 stretch frequency is estimated to amount to 300 cm -1 which can be considered as a typical metal-n 2 stretch frequency. 23,24 Furthermore, variation of this frequency in the range between 200 and 400 cm -1 resulted in a variation of the binding energy by only 0.02 ev, which is well inside the error bars of the resulting binding energies. The additional unknown bending vibrations are chosen to be 50 cm -1 which has been proven to be a realistic estimate in previous studies. 12,25 Furthermore, a loose transitions state model is employed which has previously been shown to represent a suitable model for cluster-molecule bond cleavage reactions. 26 According to this model the transition state is described by the same vibrational modes as the energized molecule minus the Fe x S x -N 2 stretch vibration that is treated as internal translation along the reaction coordinate. In addition, the low frequency bending modes are scaled by a factor of ,25 Furthermore, adiabatic rotations are taken into account by considering a rotational barrier of 0.1 ev for all clusters. The unimolecular dissociation rate constant used for the determination of experimental binding energies is deduced based on the assumption that k a and k s can be described by Langevin theory and are temperature independent. This assumption is valid for Fe 2 S 2 and Fe 4 S 4 for which both the geometry and the spin state are retained upon adsorption of N 2. In marked contrast, N 2 adsorption on Fe 3 S 3 results in a change of the geometry and spin state (from planar S- bridged triangle, = 13 B for Fe 3 S 3 to an incomplete hexagon, = 5 B for Fe 3 S 3 (N 2 ) ; see Figures 1 and 4 of the manuscript as well as Figure S6). In case the structural rearrangement is associated with an energy barrier (see Figure S8), the association rate constant k a cannot be described by Langevin theory anymore but becomes temperature dependent. Consequently, the temperature dependence of the overall reaction (1) might become a complex function of the temperature dependence of k a (T) and k d (T). In this case, the Fe 3 S 3 -N 2 binding energy determined under assumption of Langevin theory is not reliable anymore. This might (in addition to contributions from higher energy isomers; see discussion in the manuscript) explain the discrepancy between the experimental and theoretical binding energy for Fe 3 S 3 -N 2. S14

15 (Fe x S x (N 2 ) ) * (Fe x S x (N 2 ) ) vibrational frequencies / cm -1 vibrational frequencies / cm -1 Fe 2 S 2 Fe 3 S 3 Fe 4 S 4 197, 283, 336, 376, 409, 437, 300, 2359, 50, 50, 50, , 225, 267, 298, 325, 347, 367, 385, 401, 416, 430, 444, 300, 2359, 50, 50, 50, , 197, 233, 261, 283, 303, 320, 336, 350, 364, 376, 388, 399, 409, 419, 428, 437, 446, 300, 2359, 50, 50, 50, , 283, 336, 376, 409, 437, 2359, 25, 25, 25, , 225, 267, 298, 325, 347, 367, 385, 401, 416, 430, 444,, 2359, 25, 25, 25, , 197, 233, 261, 283, 303, 320, 336, 350, 364, 376, 388, 399, 409, 419, 428, 437, 446, 2359, 25, 25, 25, 25 Table S3: Approximated frequencies for the energized complexes (Fe x S x (N 2 ) ) * and the loose transition state (Fe x S x (N 2 ) ). References: (1) Barnett, R. N.; Landman, U. Phys. Rev. B 1993, 48, (2) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, (3) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, (4) American Institute of Physics (AIP) Handbook; 3rd ed.; Gray, D. E., Ed. McGraw-Hill, (5) Handbook of Chemistry and Physics; 76th ed.; Lide, D. R., Ed.; CRC Press, Inc.: Boca Raton, (6) Lin, S.-S.-.; Kant, A. J.Phys.Chem. 1969, (7) Koszinowski, K.; Schröder, D.; Schwarz, H.; Liyanage, R.; Armentrout, P. B. J. Chem. Phys. 2002, 117, (8) Petz, R.; Lüchow, A. ChemPhysChem 2011, 12, 2031 (9) Batsanov, A. S. Introduction to Structural Chemistry; Springer, Berlin, (10) Schuhmacher, E.; University of Bern, Chemistry Department: Bern, (11) Bernhardt, T. M. Int. J. Mass Spectrom. 2005, 243, 1. (12) Bernhardt, T. M.; Hagen, J.; Lang, S. M.; Popolan, D. M.; Socaciu-Siebert, L. D.; Wöste, L. J. Phys. Chem. A 2009, 113, (13) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; 2nd ed. Prentice Hall, Upper Saddle River, (14) Laidler, K. J. Chemical Kinetics; HarperCollins: New York, (15) Langevin, P. M. Ann. Chim. Phys. 1905, 5, 245. (16) Marcus, R. A. J. Chem. Phys. 1952, 20, 359. (17) Drahos, L.; Vékey, K. J. Mass Spectrom 2001, 36, 237. (18) Khoury, Y. E.; Hellwig, P. ChemPhysChem 2011, 12, (19) Oshio, H.; Ama, T.; Watanabe, T.; Nakamoto, K. Inorg. Chim. Acta 1985, 96, 61. (20) Lang, S. M. unpublished work (21) Jarrold, M. F.; Bower, J. E. J. Chem. Phys. 1987, 87, (22) NIST Chemistry WebBook, NIST Standard Reference Database Number 69; National Institute of Standards and Technology: Gaithersburg MD; Vol. (23) Ding, X.; Yang, J.; Hou, J. G.; Zhu, Q. J. Mol. Struct.: THEOCHEM 2005, 755, 9. (24) Pillai, E. D.; Jaeger, T. D.; Duncan, M. A. J. Am. Chem. Soc. 2007, 129, (25) Lang, S. M.; Bernhardt, T. M.; Barnett, R. N.; Landman, U. Chem. Phys. Chem. 2010, 11, 1570 (26) Baer, T.; Mayer, P. M. J. Am. Soc. Mass Spectrom. 1997, 8, 103. S15