Shi
Yin
and
Elliot R.
Bernstein
*
Department of Chemistry, NSF ERC for Extreme Ultraviolet Science and Technology, Colorado State University, Fort Collins, CO 80523, USA. E-mail: erb@colostate.edu
First published on 21st November 2017
Single hydrogen containing iron hydrosulfide cluster anions (FeS)mH− (m = 2–4) are studied by photoelectron spectroscopy (PES) at 3.492 eV (355 nm) and 4.661 eV (266 nm) photon energies, and by Density Functional Theory (DFT) calculations. The structural properties, relative energies of different spin states and isomers, and the first calculated vertical detachment energies (VDEs) of different spin states for these (FeS)mH− (m = 2–4) cluster anions are investigated at various reasonable theory levels. Two types of structural isomers are found for these (FeS)mH− (m = 2–4) clusters: (1) the single hydrogen atom bonds to a sulfur site (SH-type); and (2) the single hydrogen atom bonds to an iron site (FeH-type). Experimental and theoretical results suggest such available different SH- and FeH-type structural isomers should be considered when evaluating the properties and behavior of these single hydrogen containing iron sulfide clusters in real chemical and biological systems. Compared to their related, respective pure iron sulfur (FeS)m− clusters, the first VDE trend of the diverse type (FeS)mH0,1− (m = 1–4) clusters can be understood through (1) the different electron distribution properties of their highest singly occupied molecular orbital employing natural bond orbital analysis (NBO/HSOMO), and (2) the partial charge distribution on the NBO/HSOMO localized sites of each cluster anion. Generally, the properties of the NBO/HSOMOs play the principal role with regard to the physical and chemical properties of all the anions. The change of cluster VDE from low to high is associated with the change in nature of their NBO/HSOMO from a dipole bound and valence electron mixed character, to a valence p orbital on S, to a valence d orbital on Fe, and to a valence p orbital on Fe or an Fe–Fe delocalized valence bonding orbital. For clusters having the same properties for NBO/HSOMOs, the partial charge distributions at the NBO/HSOMO localized sites additionally affect their VDEs: a more negative or less positive localized charge distribution is correlated with a lower first VDE. The single hydrogen in these (FeS)mH− (m = 2–4) cluster anions is suggested to affect their first VDEs through the different structure types (SH- or FeH-), the nature of the NBO/HSOMOs at the local site, and the value of partial charge number at the local site of the NBO/HSOMO.
Additionally, hydrogen is the most widely distributed element in the world, and it is also the most abundant element in biological systems. Among various aspects of metalloprotein structure, reorganization of metal ligand(s) and/or hydrogen bonding networks around redox-active sites are often utilized in modulating natural redox potentials and functionalities.14–17 Action of sulfhydryl (SH) reagents on enzymes is both varied and complex: most of these reactions produce conformational alterations in the enzyme maintaining the iron–sulfur centers.18 The presence of a hydrogen containing moiety, such as –SH groups, which is essential for catalytic activity in dehydrogenase, has been discovered in recent decades, and has since been widely studied.19–22 Direct evidence for the hydrogen containing groups (–SH) activating enzymes and the important role they play for enzyme function, has been reported recently.23–25
Investigations of iron–sulfur systems, ranging from bare Fe–S clusters to analogous complexes and proteins, are common throughout bioinorganic chemistry.26 Iron sulfur clusters and complexes have been synthesized and characterized, forming a large class of organometallic chemistry.27 Many strategies have been developed to understand the relationship between the remarkable structures of iron sulfur clusters (i.e., Fe2S2, Fe3S4, and Fe4S4) and their associated reactivity in biological systems.28–30 Although a number of studies have been performed on gas phase cationic,31,32 neutral,33,34 and anionic35–42 iron sulfur clusters for investigation of their composition, stability, structure, and reactivity, experimental investigation of single hydrogen containing iron hydrosulfide cluster anions is not been reported to the best of our knowledge.
In this paper, we present a photoelectron spectroscopy (PES) study of a series of single hydrogen containing iron sulfide (FeS)mH− (m = 2–4) cluster anions, employing a magnetic-bottle time-of-flight (MBTOF) PES apparatus. The PES spectra of these cluster anions at 532 nm and 355 nm photon energies are reported, and the structural and bonding properties of these cluster anions not directly detected by the spectroscopic technique employed are investigated at different theoretical levels by Density Functional Theory (DFT). The most probable structures and ground state spin multiplicities of the (FeS)mH− (m = 2–4) anionic cluster series are tentatively assigned by comparing the theoretical VDEs with their experiment values: theory is pursued based on a comparison of the two sets of VDEs (experimental and theoretical) and consequently the appropriate algorithm is employed to determine cluster properties not directly addressed by PES. Values for the electron affinities of their neutral counterparts are presented and analyzed as well. The properties of these single hydrogen containing iron sulfide clusters are compared with their related pure iron sulfur cluster (for example, Fe2S2−/Fe2S2H− and Fe4S4−/Fe4S4H−), which are essential cluster sites in biological systems, to understand the effect of a single hydrogen atom perturbation on the putative (FeS)m− cluster properties.
Generated cluster anions enter the extraction region of the TOFMS/PES spectrometer through a 6 mm skimmer. Anions present in the expansion are extracted perpendicularly from the beam by pulsed voltage applied to the first extraction plate. The voltages on the extraction plates are −250 V (pulsed), 0 V, and +750 V, respectively. A liner for both anion and electron flight tube regions has the same voltage (+750 V) as the last extraction plate. Two sets of ion deflectors and one ion einzel lens are positioned downstream of the extraction plates. The anions are then analyzed by the oaRETOFMS. The photoelectron technique has the following energy conserving relationship: hν = EKE + EBE, in which hν is the photon energy, EKE is the measured electron kinetic energy, EBE is the electron binding energy. In order to obtain a photoelectron spectrum of the anions of interest, a three-grid mass gate is used for cluster and molecule anion mass selection. Following the mass gate, the mass selected ion beam enters a momentum decelerator. Both the pulse width and the pulse amplitude of the momentum decelerator can be optimized to achieve the best deceleration effect.
The mass selected and decelerated anions are exposed to different laser wavelengths (355 nm, 266 nm) at the photo-detachment region. The photo-detached electrons are energy analyzed by MBTOF-PES spectrometer. A cone shape permanent magnet is used for the high magnetic field (∼700 G) generation at the anion beam/photo detachment laser interaction region. The permanent magnet is mounted on a vacuum motor controlled, linear translation stage (Physik Instrumente LPS-24), so that the position of the permanent magnet can be optimized for the best photoelectron spectrometer resolution. The 1 m electron flight tube is surrounded by a solenoid, which is covered with two layers of GIRON magnetic shielding metal. The electric current for the solenoid is about 0.8 A, which produces a magnetic field of ∼10 gauss at the center of the flight tube. The photo-detached electrons pass through the flight tube and are detected by a microchannel plate (MCP) detector. A resolution of ∼4% (i.e., 40 meV/1.00 eV electron kinetic energy) for the overall MBTOF PES apparatus can be achieved. Under the above operating conditions, PES resolution is no longer limited by Doppler broadening associated with the perpendicular motion of the ion beam with respect to the collection and flight path of the photodetached electrons: in other words, momentum deceleration for the ion cluster beam is efficacious. PES spectra are collected and calibrated at this resolution with known spectra of Cu−.45
In this approach, for each spin state of the (FeS)mH− anions, the first vertical detachment energy (VDE = Eneutralatoptimizedaniongeometry − Eoptimizedanion) is calculated as the lowest transition from the spin state (M) of the anion into the final lowest spin state (M + 1 or M − 1, M = 2S + 1) of the neutral (FeS)mH species at the geometry optimized for the anion. The optimized anion geometries are used for the further calculations of the photoelectron spectra using time-dependent density functional theory (TDDFT).55 Vertical excitation energies of the neutral species are added to the first VDE to obtain the second and higher VDEs of these (FeS)mH− anion clusters. The outer valence Green function method (OVGF/TZVP)56 is also used to calculate the second and higher VDEs. Calculated VDEs for each spin state of each (FeS)mH− (m = 2–4) cluster are compared with experimental results to determine the appropriate theoretical algorithm for determination of cluster structures, charge distributions, wave functions, and other anion and neutral cluster properties.
An NBO analysis is an often employed orbital (wave function) localization and population analysis method to help understand the electron distribution in a molecule or cluster around particular sites or moieties of interest. Within this method, natural atomic orbitals (NAOs), determined for the particular species under consideration, are evaluated and employed: NAOs are the effective orbitals of an atom in the particular molecular environment (rather than for isolated atoms). NAOs are also the maximum occupancy orbitals. Information obtained from an NBO analysis, such as partial charges and HOMO–LUMO orbitals, is reported to explain, for example, a number of experimental phenomena of gas phase 1-butyl-3-methylimidazolium chloride ion pairs.57 The NBO calculations in this work are performed using the NBO 3.1 program as implemented in the Gaussian 09 package.
Partial charge distributions of cluster anions studied in this work are calculated using Mulliken population analysis, Breneman's CHELPG algorithm,58 and an NBO analysis as implemented in Gaussian 09. CHELPG employs a grid method to select a point at which the electrostatic potential of the molecule is sampled. Fe is assigned a van der Waals radius of 1.95 Å59 and default atomic radii are used for all other atoms for the CHELPG method.
Fig. 1 Photoelectron spectra of (FeS)2H− cluster anions at 355 nm and 266 nm. X and X′ label the ground state transition peaks of isomer I and II, respectively (presented in Fig. 4). The identifier A in (b) labels the first low-lying excited electronic state transition peak associated with isomer I (X). The downward pointing arrow (↓) in the figure indicates the value of the assigned EA (the slope of the first onset is linearly extrapolated to the base line of signal to assign the experimental EA). |
Fig. 2 Photoelectron spectra of (FeS)3H− cluster anions at 355 nm and 266 nm. X, X′′ and X′ label the ground state transition peaks of isomer I, II and III, respectively, presented in Fig. 4. The downward pointing arrow (↓) in the figure indicates the value of the assigned EA (the slope of the first onset is linearly extrapolated to the base line of signal to assign the experimental EA). |
Fig. 3 Photoelectron spectra of (FeS)4H− cluster anions at 355 nm and 266 nm. X and X′ label the ground state transition peaks of isomer I and II, respectively, presented in Fig. 4 respectively. A and B label the first and second low-lying transition peaks at high VDE. The downward pointing arrow (↓) in the figure indicates the value of the assigned EA (the slope of the first onset is linearly extrapolated to the base line of signal to assign the experimental EA). |
Cluster geometrical structure is an important determination for all cluster, since this cluster property is the basis for the description of all other cluster characteristics (e.g., spin, electronic structure, electron density, charge and spin densities, etc.). Various structural isomers of (FeS)2–4H− are investigated, and different spin multiplicities from low to high are considered for each isomer. ΔE between different structural isomers with different spin multiplicities are calculated and compared to evaluate their relative stability. To evaluate and pursue a good theoretical method to study these (FeS)2–4H− cluster anions, different reasonable functionals (B3LYP and BPW91) coupled with different basis sets (TZVP, 6-311+G(d), and aug-cc-PVQZ) are selected to calculate ΔEs and the first VDE of the (FeS)2H− structural isomers with different spin multiplicities as a test. The two lowest relative energy spin multiplicity states of each isomer are presented in Table 1, and the first VDE for each isomer is calculated. ΔEs for different spin multiplicities are corrected for zero point energies. ΔE = 0.00 eV means that the energy of the given spin multiplicity isomer is the lowest one among all possible spin multiplicities of all possible structural isomers.
Calculational results for (FeS)2H−, obtained employing the BPW91 functional coupled with different basis sets (Table 1) show 1. the spin state M = 9 is the lowest energy state for isomer I, 2. the lowest energy spin state for (FeS)2H− isomer II is also M = 9, and 3. the calculated first VDEs of isomer I (M = 9) and isomer II (M = 9) are within ∼0.2 eV of each other employing BPW91 and any of selected basis sets. This performance suggests that the calculated properties of (FeS)2H− cluster anion are insensitive to the employed basis sets, so the average ΔE and first VDE values for the different basis sets are given in Table 1 for discussion convenience. Calculation results employing B3LYP functional coupled with different basis sets are obtained for comparison with these. The results displayed in Table 1 agree with BPW91 results discussed above: (1) the spin state M = 9 is the lowest energy state for isomer I; (2) the lowest energy spin state for (FeS)2H− isomer II is also M = 9; and (3) the calculated results obtained with the B3LYP DFT functional are insensitive to the employed basis sets. The calculated VDEs for spin state M = 9 of isomers I and II (3.13 eV and 2.35 eV, average values) employing a B3LYP functional are higher than those of M = 9 for isomers I and II (2.84 eV and 1.83 eV, average values) obtained using a BPW91 functional. The BPW91 functional results are in better agreement with the experimental results (2.84 eV and 1.85 eV, see Fig. 1 and Table 1), although reasonable assignments are obtained based on the B3LYP functional results as well.
In summary, comparing calculated VDEs with respect to experimental measurements for (FeS)2H− clusters at a number of different DFT levels, two generalizations can be extracted: (1) calculated properties are insensitive to the basis sets employed; and (2) the BPW91 density functional performs better than the B3LYP density functional for these VDE calculations. Therefore, the BPW91 functional is suggested for the theoretical studies for these single hydrogen containing iron hydrosulfide clusters, and it is thereby selected for calculations employed in the following sections relating with (FeS)3,4H0/−1 cluster anions and neutrals. ΔE between different structural isomers with different spin multiplicities for (FeS)2–4H− cluster anions at BPW91/TZVP level are displayed in Fig. S1 to S3 in the ESI,† respectively.
To estimate the theoretical first VDEs of these open shell (FeS)mH− (m = 2–4) cluster anions (with unpaired electrons), one electron is removed from the highest singly occupied molecular orbital (HSOMO) of the (FeS)mH− cluster with the optimized geometry. Therefore, studies of HSOMOs properties of these (FeS)mH− clusters are helpful to understand their different first VDEs. Furthermore, partial atomic charges are suggested to play a decisive role in determining core electron binding energy in small molecules.60 The partial charge of the HSOMO localized site in these iron hydrosulfide cluster anions may to some extent affect the energy (VDE) required to remove an electron from such clusters through a “charge effect”: a small negative charge number of the site means less electron density distribution on that site, and therefore removal of an electron from that site may require more energy than otherwise estimated based simply on the NBO/HSOMO distribution for that site. Removal of an electron from a site with a positive charge should require still more energy than removal of an electron from a site with a negative charge, and removal of an electron from a site with a large positive charge may require even more energy. With the above ideas, potential effects of the HSOMOs properties and partial atomic charges on HSOMO localized sites to the first VDEs of the iron sulfide/hydrosulfide cluster anions are discussed in following Sections B to E of the Results and discussion.
In Fig. 1–3, the adiabatic electron affinity (EA = Eoptimizedneutral − Eoptimizedanion) for ground state (FeS)2–4H neutral cluster can be estimated. To assign the experimental EA, the slope of the first onset is linearly extrapolated to the base line of signal. The values of EA are indicated by a downward pointing arrow in the figures. EA for ground state of (FeS)2–4H neutral clusters are calculated and summarized in Table 2. Their experimental EAs are also listed there for comparison. Note that the obtained experimental EAs of these iron hydrosulfide clusters are possibly affected by their anion vibrational hot bands due to their high temperature generation conditions (∼3 mJ pulse−1 ablation laser energy) and potential transition state barriers. Thus, experimental EAs might be underestimated in this work.
Cluster | Spin multiplicity | EA (eV) | |
---|---|---|---|
Calculated | Experimental | ||
(FeS)2H | 8 | 1.58 (isomer II) | 1.3 |
(FeS)3H | 12 | 2.27 (isomer III) | 1.5 |
(FeS)4H |
16
8 |
2.35 (isomer II)
2.39 (isomer I) |
1.8 |
The calculated first VDEs of spin state M = 7 of isomer I (2.63 eV, average value) and M = 7 isomer II (2.01 eV, average value) are also close to the experimental VDEs associated with features X (2.84 eV) and X′ (1.85 eV). Their average ΔEs are calculated to be lower than 1 eV, so spin state M = 7 of isomers I and II of (FeS)2H− clusters probably also exist in the experimental system, and should be considered when evaluating the properties and behavior of these iron hydrosulfide clusters in real chemical and biological systems.
The intensity of X′ (isomer II, SH-type) peak is lower than that of X (isomer I, FeH-type) peak, as displayed in Fig. 1 (see structures of isomers in Fig. 4a). This may be due to the higher relative energy of isomer II (M = 9) than that of isomer I (M = 9) (see Table 1): the higher ΔE implies a less stable state and a lower population of the isomer II than isomer I in the experiment cooled molecular beam. Nonetheless, both isomers I and II exist as structural isomers for the (FeS)2H− cluster anion. The single hydrogen of isomer II is bonded to the sulfur site (SH-type), and the single hydrogen of isomer I is bonded to the iron site (FeH-type). Their first VDEs are very different, however. The experimental first VDE of the FeH-type (FeS)2H− (isomer I) is 2.84 eV (X peak in Fig. 1), about 1 eV higher than that of SH-type (FeS)2H− (isomer II), which is 1.85 eV (X′ peak in Fig. 1). From our previous study of the (FeS)m− species,61 the experimental first VDE of the (FeS)2− cluster is observed to be 2.34 eV (see Table S1 in ESI†). Different bonding sites for the single hydrogen in the (FeS)2H− cluster have significantly different effects on its first VDE. The experimental first VDE of FeH-type (FeS)2H− is 0.5 eV higher, and the experimental first VDE of SH-type (FeS)2H− is 0.49 eV lower than that of the (FeS)2− cluster, due to the different bonding types and sites for the single H addition to a pure iron sulfur (FeS)2− cluster.
Mulliken charge distributions are calculated for the FeH-type (isomer I) of (FeS)2H−, and the (FeS)2− cluster anions (whose NBO/HSOMOs are of a similar nature) to explore the “charge effect” (proposed in Section A) for their different first VDEs. The partial charge numbers of the S sites, on which the NBO/HSOMO is localized, are −0.635 for the (FeS)2− cluster and −0.553 for the FeH-type (FeS)2H− (isomer I) cluster (see Fig. 5b). Since the S atom is more electronegative than the iron atom, the negative charge number at the S site in these iron sulfide/hydrosulfide clusters is not unreasonable. The observed higher first VDE for the FeH-type (FeS)2H− is consistent with the smaller negative charge number of the S site, on which the NBO/HSOMO is localized (−0.553), compared to that of the (FeS)2− cluster (−0.635).
Cluster | Observed feature | Experimental VDEs (eV) | Calculated VDEs (eV) | |
---|---|---|---|---|
TDDFT | OVGF | |||
(FeS)2H− | X′ | 1.85 | 1.70 (isomer II, M = 9) | |
X | 2.84 | 2.75 (isomer I, M = 9) | ||
A | 3.59 | 3.26 (isomer I, M = 9) | 4.31 (isomer I, M = 9) | |
(FeS)3H− | X′ | 2.38 | 2.43 (isomer III, M = 11) | |
X,X′′ | 3.33 |
3.14 (isomer II, M = 9)
3.00 (isomer I, M = 5) |
||
(FeS)4H− | X′,X | 2.90 |
2.59 (isomer II, M = 15)
2.62 (isomer I, M = 9) |
|
A | 3.70 |
3.18 (isomer II, M = 15)
3.19 (isomer I, M = 9) |
3.40 (isomer II, M = 15)
3.39 (isomer I, M = 9) |
|
B | 4.17 |
3.38 (isomer II, M = 15)
3.44 (isomer I, M = 9) |
4.28 (isomer II, M = 15)
3.80 (isomer I, M = 9) |
In summary, two types of structural isomers (SH-type, II and FeH-type, I) are found for the (FeS)2H− cluster. Comparing properties of these isomers with the related pure iron sulfur cluster anion, the first VDE of the SH-type (FeS)2H− (I) is found to be ∼0.5 eV lower, and the first VDE of FeH-type (FeS)2H− (II) is found to be ∼0.5 eV higher than that of the (FeS)2− cluster anion (2.34 eV). Such available different SH- and FeH-type structural isomers need to be considered when evaluating the properties and behavior of single hydrogen containing iron hydrosulfide clusters in real chemical and biological systems. Compared with their relatively pure iron sulfur (FeS)2− cluster, the single hydrogen atoms in (FeS)2H− cluster anions probably affect its first VDEs through the different structure types, the changing nature of the NBO/HSOMOs, and differing partial charge numbers of the important sites.
The experimental first VDE of FeH-type (FeS)3H− (isomer II) and Fe3H-type (FeS)3H− (isomer I) is 3.33 eV (not distinguishable, as X,X′′ peak displayed in Fig. 2), about 1 eV higher than that of the SH-type (FeS)3H− (isomer III), which is 2.38 eV (X′ peak in Fig. 2). The experimental first VDE of (FeS)3− cluster is observed to be 3.57 eV in our previous study (see Table S1 in ESI†61). We found the experimental first VDE of SH-type (FeS)3H− is ∼1.2 eV, much lower than that of the (FeS)3− cluster, while the experimental first VDEs of the FeH-type and Fe3H-type (FeS)3H− are close to that of (FeS)3− cluster.
Mulliken charge distributions are considered for these cluster anions (see Fig. 5c), for which the nature of NBO/HSOMOs are the same, to explore the “charge effect” for their first VDEs. The charge number of the mainly NBO/HSOMO localized Fe site is 0.175 for the (FeS)3− cluster, which is close to that for the FeH-type (isomer II) (FeS)3H− cluster (0.180). Their close partial charge number on Fe sites can relate to their close VDEs. These results suggest that the “charge effect” proposed in Section A still make sense.
In sum, the first VDE difference between (FeS)3H− and (FeS)3− noted can be related to the different electron distribution (wave function) properties of NBO/HSOMOs of each cluster anion. Of particular note is the changing nature of their HSOMO from a p orbital on an Fe atom to a p orbital on an S atom, due to the SH-type bonding single hydrogen. Thus, these evolving NBO representations of the HSOMO electronic distribution for (FeS)3H− compared with that of (FeS)3− clusters are quite reasonable, and correlate and explicate the observed different effect to anion cluster first VDEs with various hydrogen bonding types.
Therefore, BPW91/TZVP results is selected for discussions in below. The spin state M = 9 isomer I of (FeS)4H− is suggested to be the ground state for this cluster due to its lowest ΔE: its calculated first VDE is 2.62 eV, which is in good agreement with the experimental value of X′,X labeled feature (2.90 eV) in Fig. 3. For the other spin states and isomers listed in Table 5, ΔEs are lower than 0.37 eV, and calculated first VDEs are in the range 2.43 eV to 2.93 eV. These states can probably exist in the experimental system, and can thereby contribute to the PES spectra of the (FeS)4H− cluster anions. Such a spin/isomer mixture should be considered when evaluating (FeS)4H properties and behavior in real chemical and biological systems.
The calculated first VDEs for the SH-type (FeS)4H− (isomer II) and the FeH-type (FeS)4H− (isomer I) are close, within ∼0.3 eV (see Table 5), so the broad peak observed at ∼2.90 eV (labeled, X′,X for both isomers in Fig. 3) is assigned to the ground state transition of both SH-type and FeH-type (FeS)4H− clusters.
Mulliken charge distributions are also investigated for these (FeS)4H− and (FeS)4− cluster anions (Fig. 5d) to test if the “charge effect” discussed above is still valid or useful for these larger clusters even though their similar first VDEs are already well described and understood to be related to the similar electron distribution properties of their NBO/HSOMOs. The charge numbers of the Fe sites, on which the NBO/HSOMO is localized, are 0.247 for the (FeS)4− cluster, 0.111 for the SH-type (FeS)4H− (isomer II) cluster, and 0.185 for the FeH-type (FeS)4H− (isomer I) cluster. The first VDEs of these three cluster anions are similar (within 0.2 eV) and well understood based on the NBO/HSOMOs discussed above. Thus, the effect of different partial charge values at the respective Fe sites do not appear to be a major contributing factor for the observed first VDE similarity in this instance.
In summary, the first VDEs of SH-type (isomer II) and the FeH-type (isomer I) (FeS)4H− clusters are found to be the same (X′,X peak at ∼2.90 eV in Fig. 3), and close to that of the (FeS)4− cluster. The similar first VDEs of (FeS)4H0,1− clusters are suggested to be mainly related to their indistinguishable NBO/HSOMOs properties (a d orbital on Fe site), and the “charge effect” is found not to be a major contributing factor for the observed close first VDEs of these large iron sulfide/hydrosulfide cluster anions.
Fig. 6 Observed experimental electron binding energies (the first VDEs) of (FeS)mH0,1− (m = 1–4) as a function of number m. The first VDE for (FeS)m− (m = 1–4) and FeSH− are taken from ref. 43 and 61. DB&V: a dipole bound and valence electron mixed character orbital; p on S: a valence p orbital on S; d on Fe: a valence d orbital on Fe; and Fe–Fe BD: an Fe–Fe delocalized valence bonding orbital. |
Group based on HSOMO property | HSOMO plot for cluster | Atomic hybrid orbital composition of HSOMO | Atom localized | Partial charge (BPW91/TZVP) | VDEcal. (eV) | VDEexp. (eV) | |||
---|---|---|---|---|---|---|---|---|---|
Mulliken | CHELPG | NBO | |||||||
a The number in parentheses shows percentage of s-character, p-character, and d-character of each hybrid orbital.2CB: 2-center bond. LP: 1-center valence lone pair. DB&V: a dipole bound and valence electron mixed character orbital. p on S: a valence p orbital on S. d on Fe: a valence d orbital on Fe. p on Fe: a valence p orbital on Fe. Fe–Fe BD: an Fe–Fe delocalized valence bonding orbital. | |||||||||
DB&V | 5FeSH− |
s (72.07%)
p (5.26%) d (22.67%) |
Fe (LP) | −0.503 | −0.509 | −0.503 | 1.13 | 1.63 | |
9(FeS)2H− isomer II |
s (80.76%)
p (6.66%) d (12.58%) |
Fe (LP) | −0.232 | −0.241 | 0.048 | 1.70 | 1.85 | ||
p on S | 4FeS− |
s (0.00%)
p (99.98%) d (0.02%) |
S (LP) | −0.751 | −0.815 | −0.899 | 1.12 | 1.85 | |
8(FeS)2− |
s (0.00%)
p (99.98%) d (0.02%) |
S (LP) | −0.635 | −0.744 | −0.823 | 2.04 | 2.34 | ||
11(FeS)3H− isomer III |
s (0.27%)
p (99.71%) d (0.02%) |
S (LP) | −0.573 | −0.669 | −0.695 | 2.43 | 2.38 | ||
9(FeS)2H− isomer I |
s (0.79%)
p (99.19%) d (0.02%) |
S (LP) | −0.553 | −0.667 | −0.693 | 2.75 | 2.84 | ||
d on Fe | 15(FeS)4H− isomer II |
s (0.00%)
p (0.16%) d (99.84%) |
Fe (LP) | 0.111 | 0.256 | 0.281 | 2.59 | 2.90 | |
9(FeS)4H− isomer I |
s (3.75%)
p (0.63%) d (95.62%) |
Fe (LP) | 0.185 | 0.369 | 0.171 | 2.62 | 2.90 | ||
16(FeS)4− |
s (0.00%)
p (0.11%) d (99.89%) |
Fe (LP) | 0.247 | 0.462 | 0.363 | 2.87 | 2.71 | ||
p on Fe or Fe–Fe BD | 10(FeS)3− |
s (0.00%)
p (93.36%) d (6.64%) |
Fe (LP) | 0.175 | 0.232 | 0.253 | 3.24 | 3.57 | |
9(FeS)3H− isomer II |
s (0.04%)
p (93.41%) d (6.55%) |
Fe (LP) | 0.180 | 0.236 | 0.311 | 3.14 | 3.33 | ||
5(FeS)3H− isomer I |
s (6.01%)
p (48.43%) d (45.55%) |
s (14.73%)
p (14.52%) d (70.75%) |
Fe–Fe (2CB) | 0.131–0.121 | 0.304–0.235 | 0.067–0.089 | 3.00 | 3.33 |
The NBO/HSOMOs of 4FeS−, 8(FeS)2−, 11(FeS)3H− (isomer III, SH-type), and 9(FeS)2H− (isomer I, FeH-type) clusters are localized on S sites with a valence lone pair orbital: their compositions are similar to large p orbital components (>99%) to the NBO/HSOMO wave functions “p on S”. Their sulfur p orbital localized NBO/HSOMOs are probably responsible for their low first VDEs, EAs, and the high reactivity of their respective neutral clusters, associated with a “sulfur radical” electronic nature.34,43 The experimental first VDEs of these four clusters are in the range from 1.85 to 2.84 eV (yellow area in Fig. 6), which are higher than those of 5FeSH− and 9(FeS)2H− (isomer II, SH) clusters (with “DB&V” NBO/HSOMOs).
For 16(FeS)4−, 15(FeS)4H− (isomer II), and 9(FeS)4H− (isomer I, FeH) clusters, their NBO/HSOMOs are localized on Fe sites as a valence lone pair orbital with large d orbital components to the orbital wave functions “d on Fe”, and their experimental first VDEs are 2.71 and 2.90 eV (blue area in Fig. 6). These latter first VDE values are even higher than those for most of the clusters with “p on S” NBO/HSOMOs [4FeS−, 8(FeS)2−, 11(FeS)3H− (isomer III), and except 9(FeS)2H− (isomer I)].
The experimental first VDE of 10(FeS)3− is found to be the highest (3.57 eV, see green area in Fig. 6) among all (FeS)mH0,1− (m = 1–4) clusters. Its NBO/HSOMOs is localized on Fe sites as a valence lone pair orbital with large NAO p orbital components (93.36%) to the NBO wavefunctions “p on Fe”. The calculated first VDEs of 9(FeS)3H− (isomer II, FeH) and 5(FeS)3H− (isomer I, FeHFe) are similar, 3.14 and 3.00 eV, respectively. One broad PES peak is observed at ∼3.33 eV and assigned for their ground state transitions. The NBO/HSOMO nature of 9(FeS)3H− (isomer II) is the same as that for 10(FeS)3−: “p on Fe”, while the NBO/HSOMO nature of 5(FeS)3H− (isomer I) is a two Fe center bonding orbital “Fe–Fe BD”. These results suggest that the first VDEs of clusters with “p on Fe” and “Fe–Fe BD” types NBO/HSOMOs may be close, and are the highest among those of all discussed iron sulfide and single hydrogen containing iron hydrosulfide cluster anions.
In sum, the properties of the NBO/HSOMOs are found to play a key role with regard to the properties of all the anions discussed in this work. The change of cluster first VDE from low to high is related with the changing nature of their NBO/HSOMO from a “DB&V” orbital, to a “p on S” orbital, to a “d on Fe” orbital, and to a “p on Fe” orbital or “Fe–Fe BD” orbital.
For the “p on S” NBO/HSOMO group clusters, the order of Mulliken, CHELPG, and NBO charge numbers on S sites of 4FeS−, 8(FeS)2−, 11(FeS)3H− (isomer III), and 9(FeS)2H− (isomer I) clusters is the same. For example, the CHELPG charge on the S site of the 4FeS− cluster is −0.815, of the 8(FeS)2− cluster is −0.744, and of the 9(FeS)2H− (isomer I) cluster is −0.667. An ∼0.08 systematic difference of partial charge numbers on S sites of these clusters is noted. The experimental first VDE of the 4FeS− cluster is 1.85 eV, of the 8(FeS)2− cluster is 2.34 eV, and of the 9(FeS)2H− (isomer I) cluster is 2.84 eV. Their experimental first VDEs increase about 0.5 eV as their partial charge numbers on an S site increase ∼0.08 positive charge number. These results suggest the proposed “charge effect” still contributes to the experimental first VDEs of these “p on S” NBO/HSOMO clusters. Note that the NBO and Mulliken charges here yield very similar trends, if not absolute values. The 11(FeS)3H− (isomer III) cluster is apparently special in this group, however. Its partial charge number on an S site is close that of the 9(FeS)2H− (isomer I) cluster, but its experimental first VDE is ∼0.4 eV smaller than that of the 9(FeS)2H− (isomer I) cluster. The special behavior of the 11(FeS)3H− (isomer III) cluster may be due to an unexplored cluster size effect on its experimental first VDE.
The Mulliken and CHELPG charge numbers on Fe sites (NBO/HSOMO localized) of 10(FeS)3− and 9(FeS)3H− (isomer II) clusters are barely distinguishable (≤0.005 difference), and their experimental first VDEs are also close (∼7% difference). This behavior is in agreement with the suggested “charge effect”. The NBO charge numbers for these two clusters at the appropriate NBO/HSOMO localized Fe sites, however, differ by almost a factor 10 (∼0.06 difference). These results demonstrate that the relative partial charge trends for large clusters, such as (FeS)3H0,1−, may be different if different calculational methods are employed to obtain the partial charges. For the (FeS)4H0,1− clusters listed in the “d on Fe” NBO/HSOMO group, the proposed “charge effect” is apparently not a dominant factor, and the experimental first VDEs of these clusters are mainly determined by the nature of their “d on Fe” NBO/HSOMOs as discussed in above Section D. Note here too, that the different partial calculational methods do not express the same consistency trends as those discussed above, which may also be an indication that the “charge effect” is not a dominant factor for the first VDEs of these clusters.
In sum, for clusters having the same NBO/HSOMOs composition, the partial charge value of the NBO/HSOMO localized sites are also factors affecting their first VDEs: the less negative or more positive site charge value is correlated with a higher first VDE, especially for small size (FeS)mH0,1− (m = 1, 2) cluster anions. Employing multiple methods to calculate and evaluate partial charge distributions for the (FeS)mH0,1− (m = 1–4) cluster anions is probably reasonable and valuable especially for the grouped cluster anions with the same NBO/HSOMOs composition. If these NBO/HSOMO grouped clusters display consistent partial charge trends for the three different charge calculation methods, a “charge effect” on the first VDE trend of such clusters seems to be a reliable and valuable correlation to note.
Based on above comparisons and analyses, the first VDEs of (FeS)mH0,1− (m = 1–4) cluster anions are found to be principally related to/dependent upon the intrinsic properties of the NBO/HSOMO compositions. Depending on the changing nature of cluster NBO/HSOMO in the order, “DB&V” orbital → “p on S” orbital → “d on Fe” orbital → “p on Fe” or “Fe–Fe BD” orbital, the cluster first VDE predominantly increases from low to high. Additionally, a “charge effect” on the first VDEs of clusters with the same NBO/HSOMO properties can be qualitatively characterized if the partial charge distributions evaluated by multiple calculational methods display similar trends and overall behavior. This hypothesis is probably advantageous for the approximate estimation of the first VDE of the larger, more complex iron sulfide/hydrosulfide cluster anions. More studies are needed on larger and multiple hydrogen containing iron hydrosulfide clusters to explore and support these systematics and trends further.
The first VDE of SH-type (FeS)3H− (isomer III) is found to be ∼1.2 eV lower than that of the (FeS)3− cluster, and the first VDE of FeH-type (FeS)3H− (isomer II) is found to be similar to that of (FeS)3− cluster (within ∼0.2 eV). These distinctly different first VDEs can be related to the different electron distribution (wave function) properties of the NBO/HSOMOs of each cluster anion; in particular, the nature of these NBO/HSOMO wave functions changes from a p orbital on an Fe atom [(FeS)3− and FeH-type (FeS)3H− (isomer II)] to a p orbital on an S atom. For (FeS)4H0,1− clusters, the first VDEs of both SH- and FeH-type (FeS)4H− clusters are close to that of (FeS)4− cluster (within ∼0.2 eV difference), and their NBO/HSOMOs are all found to be localized d orbitals of Fe sites. The theoretical VDEs of SH- and FeH-type isomers of these (FeS)mH− (m = 2–4) clusters are in good agreement with their experimental VDE values. Therefore, these two geometry types of single hydrogen containing iron sulfide (FeS)mH− (m = 2–4) cluster anion likely co-exist under the present experimental conditions. Such available different SH- and FeH-type structural isomers must be considered when evaluating the properties and behavior of these single hydrogen containing iron hydrosulfide clusters in real chemical and biological systems. The single hydrogen in these (FeS)mH− (m = 2–4) cluster anions is suggested to affect their first VDEs through the different structure types (SH- or FeH-), the changing nature of the site localized NBO/HSOMOs, and the changing partial charge number of the localized NBO/HSOMO site.
In order to explore further the relationship between NBO/HSOMO properties, the “charge effect”, and the first VDEs for iron sulfide/hydrosulfide cluster anions, the NBO/HSOMO compositions and properties, partial charge numbers (employing various calculation methods) of the NBO/HSOMO localized site, and the first VDEs of (FeS)mH0,1− (m = 1–4) clusters are compared and contrasted. The first VDEs of diverse type (FeS)mH0,1− (m = 1–4) clusters are found to be rationalized by 1. the different electron distribution properties of NBO/HSOMO, and 2. the partial charge distribution on the NBO/HSOMO localized sites of each cluster anion. Generally, the nature of the NBO/HSOMOs play a key role with regard to the properties of all the anions. The change of cluster VDE from low to high is related to the changing nature of their NBO/HSOMO from a dipole bound and valence electron mixed character orbital, to a valence p orbital on S, to a valence d orbital on Fe, and to a valence p orbital on Fe or an Fe–Fe delocalized valence bonding orbital. For clusters having the same properties of NBO/HSOMOs, the partial charge distributions at the NBO/HSOMO localized sites additionally affect their VDEs: a more negative (less positive) localize charge distribution is correlated with a lower first VDE. In order to test such a NBO/HSOMO localized site partial charge trend for cluster anions with similar NBO/HSOMO properties, multiple atomic partial charge calculational methods must be considered; for example, Mulliken population analysis, Breneman's CHELPG algorithm, and NBO analysis are suggested. If the same trend of partial charges vis a vis first VDEs is obtained by the different calculational methods, a predictive “charge effect” can probably be considered for the first VDE trend of these specifically identified and grouped clusters.
Footnote |
† Electronic supplementary information (ESI) available: The following results are supplied as additional detailed information for these studies: (1) the relative energy of (FeS)2–4H− cluster anions with different spin multiplicities at BPW91/TZVP level in Fig. S1 to S3, respectively; and (2) the first experimental and calculated VDEs (in eV) for (FeS)m− (m = 2–8) cluster anions. See DOI: 10.1039/c7cp07012h |
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