DFT Calculations for Mössbauer Properties on Dinuclear Center Models of the Resting Oxidized Cytochrome c Oxidase.

Mössbauer isomer shift and quadrupole splitting properties have been calculated using the OLYP-D3(BJ) density functional method on previously obtained (W.-G. Han Du, et al., Inorg Chem. 2020, 59, 8906-8915) geometry optimized Fea3 3+ -H2 O-CuB 2+ dinuclear center (DNC) clusters of the resting oxidized (O state) "as-isolated" cytochrome c oxidase (CcO). The calculated results are highly consistent with the available experimental observations. The calculations have also shown that the structural heterogeneities of the O state DNCs implicated by the Mössbauer experiments are likely consequences of various factors, particularly the variable positions of the central H2 O molecule between the Fea3 3+ and CuB 2+ sites in different DNCs, whether or not this central H2 O molecule has H-bonding interaction with another H2 O molecule, the different spin states having similar energies for the Fea3 3+ sites, and whether the Fea3 3+ and CuB 2+ sites are ferromagnetically or antiferromagnetically spin-coupled.

Introduction

Cytochrome c oxidases (CcOs) are the terminal electron acceptors in the respiratory chain of mitochondria and many bacteria.[ , , ] These proteins reduce O2 to H2O and use the resulting energy to pump protons across the membrane. This produces the chemiosmotic proton gradient that is subsequently harnessed by ATP synthase to synthesize ATP.[ , , , , ] The catalytic site of CcO that binds and reduces O2 by 4e−/4H+ transfer contains a heme a3 (Fea3) and a Cu (CuB) ion that are in spatial vicinity (∼5 Å distance). This Fea3−CuB active site is usually called the dinuclear (or binuclear) center/complex (DNC or BNC). In all types of CcO enzymes, the iron in the Fea3 site is coordinated to heme and an axial histidine ligand (His384, residue numbers in this paper are by default for ba 3 CcO from Thermus thermophilus (Tt)). The copper in the CuB site is coordinated to three histidine ligands: His233, His282, and His283, where the His233 side chain is also covalently linked to the side chain of Tyr237. This special tyrosine side chain can be alternatively in neutral (Tyr−OH), deprotonated ionic (Tyr−O−), or radical (Tyr−O⋅) states, and plays an important role in electron and proton transfer in the DNC.

The oxidation, spin, and ligation states of the Fea3 and CuB sites change during the catalytic cycle.[ , , , , , , , , , , , ] Although many insights into the intermediate states of the DNC in the catalytic cycle have been obtained (Figure 1) (see review articles[ , , ] and the references therein), the detailed DNC structure of the resting oxidized as‐isolated CcO state (state O) has been under debate for over 20 years despite various spectral and structural analyses that have been made.[ , , , , , , , , ]

Figure 1

Feasible intermediate states of the DNC in the catalytic cycle, in which A, P/P, F, and O were identified by resonance Raman experiments,[ , , ] and their DNC's are likely in the forms presented above. Although the states in the blue frames were not observed experimentally, they may exist for a short time in the catalytic cycle.

The electron density lying directly between Fea3 and CuB in the as‐isolated oxidized aa 3 type CcOs from Paracoccus denitrificans (Pd) and Rhodobacter sphaeroides (Rs) was initially interpreted as a H2O and OH− ligand pair.[ , ] Later, stronger and more compact electron density for a peroxide type dioxygen species (O1−O2) bridging the Fea3 and CuB DNC was observed in higher resolution X‐ray crystal structures of the oxidized CcOs from Pd (PDB code: 3HB3, 2.25 Å resolution), from bovine heart (PDB code: 2ZXW, 1.95 Å resolution), and from ba (3S8G and 3S8F, 1.8 Å resolution). Further, the peroxide type species in the resting oxidized DNC was also observed from analysis of an X‐ray free‐electron laser (XFEL) experiment (1.9 Å resolution), and very recently from analysis of a single‐particle cryo‐electron microscopy (cryo‐EM) experiment at similar resolution. Different groups reported different O1−O2 distances from 1.4∼1.7 Å. Recently, a single hydroxide or alternatively a single water molecule between the Fea3 and CuB sites was reported in a radiation‐damage‐free oxidized ba 3 CcO structure (2.3 Å resolution) at room temperature. However, analysis of very recent low‐dose high‐energy X‐ray data on the oxidized‐resting bovine heart CcO again showed a peroxide‐shaped electron density between the Fea3 and CuB sites. Even at fairly high resolution currently available (1.9 Å), there is considerable uncertainty in the electron density between the metals, and in the correct modeling of the corresponding ligands, which are not clearly known prior to the fits. There is, in practice, both static and dynamic disorder in the ligand positions, typically represented by isotropic B factors. There is further disorder in the Fe and Cu positions as well. (While the variation in the Fe and Cu positions is expected to be geometrically smaller, they have much higher electron densities than di‐oxygen or water species.) These B factors are variables with a potential range of values during the density fitting, and influence the final electron densities found.

In order to examine what species lies between the Fea3 3+ and CuB 2+ sites producing the apparent extended di‐oxygen type electron density in the DNC of the oxidized as‐isolated CcO, previously we have performed DFT calculations[ , , ] on a series of DNC model clusters based on the X‐ray crystal structure 3S8G from Tt ba3 CcO. Our calculations have shown that the observed di‐oxygen species cannot be represented by O2 2−, O2 .−, or H2O2, since the DFT optimized structures with bridging O2 2− or O2 .− have large structural discrepancies compared with the X‐ray crystal structure, and the H2O2 is not stable between the Fea3 2+ and CuB + sites (Fea3 3+ and CuB 2+ metal sites were assumed reduced in the synchrotron X‐ray beam). We initially came to the conclusion that the observed di‐oxygen species was best represented as HO2 −, which could be a product of the photoreaction of the H2O/OH− ligands in Fea3 3+−H2O⋅⋅⋅OH−−CuB 2+/Fea3 3+−OH−⋅⋅⋅H2O−CuB 2+ type DNC structures with associated 2e− transfer to the adjacent oxidized Fea3 3+ and CuB 2+ sites in the X‐ray beam. However, if the resting oxidized DNC structure is originally (before X‐ray irradiation) in the Fea3 3+−H2O⋅⋅⋅OH−−CuB 2+ or Fea3 3+−OH−⋅⋅⋅H2O−CuB 2+ form, the X‐ray crystallographic experiments should still show H2O⋅⋅⋅OH− as the dominant bridging species in the DNC with long O⋅⋅⋅O distance, 2.5 Å or greater. Because the X‐ray crystal structure represents both a spatial and time average over many billions of enzyme molecules, while some effects due to the X‐ray irradiation are probably observable with careful attention to the time course, these effects are not likely to be dominant averaged over billions of structural sites. These arguments are even stronger when applied to XFEL experiments, since the total radiation dose is much smaller than in synchrotron X‐ray experiments, and the relevant time scale for diffraction is far shorter. Further, our very recent calculations have demonstrated that the Fea3 3+−H2O⋅⋅⋅OH−−CuB 2+/Fea3 3+−OH−⋅⋅⋅H2O−CuB 2+ type structures are also unlikely to represent the resting state of the DNC, consistent with the structural evidence and analysis above.

Our most recent calculations have shown that the observed peroxide type electron density between the two metal centers is probably a mistaken analysis due to superposition of the electron density of a water molecule located at alternative positions between Fea3 3+ and CuB 2+ sites in DNC's of different CcO molecules. Our calculations indicate that the H2O molecule in the resting state O[Fea3 3+−H2O−CuB 2+] DNC structures can bind with either the Fea3 3+ or the CuB 2+ site, or can reside at several positions between the Fea3 3+ and CuB 2+ sites that are all energetically similar, depending on the Fea3 3+−CuB 2+ distance and H‐bonding interaction with an additional H2O molecule. (In our modeling, the latter water lies well off the direct line between the Fe and Cu ions.) Figure 2 shows the overlap of the electron density map reconstructed from the X‐ray crystal structure 3S8G of Tt ba 3 and several of our geometry optimized O[Fea3 3+−H2O−CuB 2+] DNC structures with very similar energies and with a H2O molecule (in red) at different positions between the Fea3 3+ and CuB 2+ sites. Because the diffraction pattern and the inferred electron density map represents the effective long‐range order averaged over a large number molecules and unit cells in the X‐ray structure, this averaging can result in an apparent observed superposition of water at different positions between the Fea3 3+ and CuB 2+ metal sites.

Figure 2

The overlap of the electron density map that was reconstructed from the oxidized as‐isolated Tt ba 3 X‐ray crystal structure 3S8G data file with several of our calculated resting O state DNC structures, in which a water molecule (in red color) resides in different locations between the Fea3 3+ and CuB 2+ sites with very similar energies. Reprinted with permission from Figure 7 of Ref. [32], https://pubs.acs.org/doi/10.1021/acs.inorgchem.0c00724, Copyright (2020) American Chemical Society (further permissions for reusing this figure should be directed to the ACS).

Earlier 57Fe Mössbauer experiments also demonstrated extensive structural and electronic heterogeneities in the DNC for the resting O state CcOs.[ , , , ] The major Mössbauer experimental observations on different CcOs are summarized in Table 1. Initial experiments on both Tt c 1 aa 3 and bovine aa 3 show broad 57Fea3 spectra with isomer shift (δ) and quadrupole splitting (ΔE Q) values averaged at (δ=0.41 mm s−1, ΔE Q=1.10 mm s−1) and (δ=0.48±0.06 mm s−1, ΔE Q=1.0±0.1 mm s−1), respectively.[ , ] These particular values show that the Fea3 3+ site is in a high‐spin (HS) state. Later, more complicated Mössbauer spectra were reported for Tt c 1 aa 3 at different pH, which showed that at least three HS−Fea3 3+ species existed at pH=5.7, and at least two HS−Fea3 3+ complexes were observed at pH=6.5, 7.8, and 9.3. However, only one set of the HS parameters was defined at (δ=0.41 mm s−1, ΔE Q=1.3 mm s−1). In addition, a “low‐spin” (LS) Fea3 3+ species was identified at pH=5.7, 7.8, and 9.3 with the parameters (δ=0.29 mm s−1, ΔE Q=2.21 mm s−1). Note that this Fea3 3+ species may be alternatively in an intermediate‐spin (IS) state based on the observed isomer shift and quadrupole splitting values. Further, more complex Fea3 3+ species which were temperature‐dependent in Tt ba 3 were also observed in Mössbauer experiments. Briefly, a HS−Fea3 3+ species with (δ=0.41 mm s−1, ΔE Q=0.71 mm s−1) and a LS−Fea3 3+ (which may be an IS state instead) with (δ=0.29 mm s−1, ΔE Q=2.24 mm s−1) coexisted at 4.2 K. When the temperature was increased above 190 K, the “LS−Fea3 3+ species” began to transform to a different HS species with ΔE Q ≈ 1 mm s−1. The δ value of this HS‐ Fea3 3+ species was not specifically reported. But from the context, we assume that it had the same value of δ=0.41 mm s−1 as the other HS species. (Otherwise, the fit for the new HS species would have required a different isomer shift value from the other HS state.) The LS→HS transformation is finished at 245 K. Therefore, the two different HS−Fea3 3+ species coexisted at 245 K.

Table 1

Experimentally observed[ , , , ] 57Fea3 3+ Mössbauer isomer shifts (δ, mm s−1) and quadrupole splittings (ΔE Q, mm s−1) in different resting oxidized cytochrome oxidases.

Oxidases	Ref.	Fea3 3+‐Spin[a]	T [K]	δ	ΔE Q	Note
Tt c1aa3	[33]	HS	4.2	0.41	1.10	The parameters given are averaged values. The spectrum is broad, suggesting heterogeneities.
bovine aa 3	[34]	HS	4.2	0.48±0.06	1.0±0.1	The a 3 sites also appear to be heterogeneous. The parameters reported are also averaged values.
Tt c 1 aa 3	[35]	HS	4.2	0.41	1.3	Only one set of the HS parameters was defined. However, at least 3 and 2 HS a 3 species were observed at pH=5.7 and pH=(6.5, 7.8, 9.3), respectively. And the LS a 3 species was found at pH=5.7, 7.8, and 9.3.
		LS b	4.2	0.29	2.21
Tt ba 3	[36]	HS	4.2–245	0.41	0.7	The first two HS and LS species coexist at 4.2 K. However, the LS component changes to a different HS species with ΔE Q≈1 mm s−1 when T>190 K, and the transition is complete at 245 K.
		LS [b]	4.2–190	0.29	2.24
		HS	>190	0.41 [c]	∼1

[a] HS stands for high‐spin; IS is for intermediate‐spin; and LS is for low‐spin. [b] Although it was suggested as LS−Fea3 3+, it is not certain whether it is LS or IS Fea3 3+ site. [c] This δ value was not specifically reported in the paper. However, from the context, we assume it is the same as another HS species, 0.41 mm s−1.

Tt c

In our recent publication, we have calculated O state Fea3 3+−H2O−CuB 2+ DNC structures with Fea3 3+ in HS, IS, and LS states. The Fea3 HS,3+−H2O−CuB 2+ results were presented in the main text, while the Fea3 IS,3+−H2O−CuB 2+ and Fea3 LS,3+−H2O−CuB 2+ results have been given in the Supporting Information. Further, our calculations have also shown that the spin coupling between the Fea3 3+ and CuB 2+ sites appears very weak. For a given O state Fea3 3+−H2O−CuB 2+ DNC structure, similar energies are obtained whether Fea3 3+−CuB 2+ are ferromagnetically (F) or anti‐ferromagnetically (AF) coupled. In the current paper, based on the geometries we obtained for the O[Fea3 HS/IS/LS,3+−H2O−CuB 2+] DNC structures, we will calculate their 57Fea3 3+ Mössbauer isomer shift and quadrupole splitting properties and see how the calculated values correlate with the experimental observations. In contrast to the X‐ray structures derived using synchrotron X‐ray beams, or XFEL pulses, Mossbauer gamma rays give far less intense radiation, so the resting O states and their structures will not be sensitive to the gamma irradiation.

The Calculated O State Fea3 HS/IS/LS,3+−H2O−CuB 2+ DNC Structures

Our calculated O[Fea3 HS/IS/LS,3+−H2O−CuB 2+] DNC structures are taken from our recent publication Ref. [32]. The initial geometries of the DNC model clusters were established based on the Cartesian coordinates of the ba 3 CcO X‐ray crystal structure 3S8G. Then geometry optimization calculations were performed using DFT broken‐symmetry[ , , ]/OLYP‐D3(BJ) /Triple‐ξ‐Polarization(TZP) plus COSMO[ , , , , , ] solvation model methodology implemented within the ADF2017 software package.[ , , ] The inclusion of dispersion D3(BJ) force‐field type effects on the geometries distinguishes our current Mossbauer calculations from those we performed previously both for the fit set of Fe structure complexes (see section 57Fea3 3+ Mössbauer Isomer Shift and Quadrupole Splitting Calculations), and for the O state structures. The inner cores of C(1s), N(1s), and O(1s) were treated by frozen core approximation during geometry optimizations. Several Fea3 HS/IS/LS,3+−H2O−CuB 2+ local minima were found with the H2O molecule residing at different positions between Fea3 3+ and CuB 2+. Specifically, one structure for the Fea3 LS,3+−H2O−CuB 2+ state and four structures (noted as a, b, c, and d) for each of the Fea3 HS,3+−H2O−CuB 2+ and Fea3 IS,3+−H2O−CuB 2+ states were presented in our publication Ref. [32], and now are given in Table 2. For each broken‐symmetry optimized geometry, we have also performed an Fea3 3+−CuB 2+ F‐coupled single‐point energy calculation and have presented the relative energies in Table 2.

Table 2

OLYP‐D3‐BJ calculated distances (in Å), relative energies (ΔE, in kcal mol−1), Mössbauer isomer shift (δ, in mm s−1) and quadrupole splitting (ΔE Q, in mm s−1) values of the resting as‐isolated Fea3 3+−H2O−CuB 2+ optimized DNC structures with different Fea3 3+−CuB 2+ spin states.

Fea3 3+‐Spin[a]	Structure	Distances [Å]			Spin‐Coupling	ΔE	δ	ΔE Q
		Distances
		Fe−O	Cu−O	Fe ⋅⋅⋅ Cu
HS	Fea3 HS,3+−H2O−CuB 2+(a)	2.39	2.94	4.98	AF	0.0	0.40	0.80
					F	0.0	0.41	0.80
	Fea3 HS,3+−H2O−CuB 2+(b)	2.47	2.77	4.90	AF	−0.2	0.41	0.92
					F	−0.2	0.41	0.80
	Fea3 HS,3+−H2O−CuB 2+(c)	3.55	2.21	4.73	AF	0.3	0.43	0.78
					F	−0.4	0.45	1.21
	Fea3 HS,3+−H2O−CuB 2+(d)	3.26	2.20	4.73	AF	0.5	0.41	0.77
					F	0.3	0.43	1.24
IS	Fea3 IS,3+−H2O−CuB 2+(a)	2.40	2.90	4.94	AF	−6.2	0.36	2.42
					F	−6.2	0.36	2.42
	Fea3 IS,3+−H2O−CuB 2+(b)	2.46	2.67	4.78	AF	−6.5	0.36	2.50
					F	−6.5	0.36	2.50
	Fea3 IS,3+−H2O−CuB 2+(c)	3.44	2.26	4.71	AF	−4.3	0.34	2.34
					F	−4.1	0.34	2.33
	Fea3 IS,3+−H2O−CuB 2+(d)	3.00	2.24	4.56	AF	−5.5	0.35	2.66
					F	−5.5	0.35	2.65
LS	Fea3 LS,3+−H2O−CuB 2+	2.37	3.10	5.04	AF	−2.7	0.31	2.96
					F	−2.7	0.31	2.96

[a] HS stands for high‐spin; IS is for intermediate‐spin; and LS is for low‐spin.

The four HS−Fea3 3+ structures Fea3 HS,3+−H2O−CuB 2+(a–d) are very similar to the corresponding IS−Fea3 3+ structures Fea3 IS,3+−H2O−CuB 2+(a–d). Further, the optimized Fea3 LS,3+−H2O−CuB 2+ structure is also similar to Fea3 HS/IS,3+−H2O−CuB 2+(a) structures. The full model cluster representing the Fea3 HS,3+−H2O−CuB 2+(a), Fea3 IS,3+−H2O−CuB 2+(a), and the Fea3 LS,3+−H2O−CuB 2+ state is shown in Figure 3, in which the H2O molecule is much closer to the Fea3 3+ site with the distances (see Table 2) r(Fea3 3+−O)=2.39, 2.40, and 2.37 Å and r(CuB 2+−O)=2.94, 2.90, and 3.10 Å for the Fea3 HS,3+−H2O−CuB 2+(a), Fea3 IS,3+−H2O−CuB 2+(a), and Fea3 LS,3+−H2O−CuB 2+ structures, respectively. The H2O molecule is also H‐bonding with another H2O molecule which probably originates from the CuB‐bound H2O ligand in the prior reaction cycle state F (see Figure 1). For a clearer view, the top and the central portions of this structure are also given in Figure 4. The central portions of the Fea3 HS/IS,3+−H2O−CuB 2+(b–c) are also shown in Figure 4.

Figure 3

Our full DNC model cluster representing the Fea3 HS,3+−H2O−CuB 2+(a), Fea3 IS,3+−H2O−CuB 2+(a), and Fea3 LS,3+−H2O−CuB 2+ states, in which the H2O molecule is much closer to the Fea3 3+ site. The top and the central portions of the cluster are also shown in Figure 4. Linking hydrogen atoms were fixed during geometry optimization.

Figure 4

Four optimized O state DNC model clusters (noted as a, b, c, and d) for each of the Fea3 HS,3+−H2O−CuB 2+ and Fea3 IS,3+−H2O−CuB 2+ states and one structure for the Fea3 LS,3+−H2O−CuB 2+ state were presented in our publication Ref. [32]. Here is a closer look at the top and the central portions of these clusters. “a–d” show the central Fea3 HS/IS,3+−H2O−CuB 2+(a–d) structures. “a” also represents the central portion of the Fea3 LS,3+−H2O−CuB 2+ model cluster. The Fe−O, Cu−O and Fe−Cu distances of the optimized Fea3 HS/IS,3+−H2O−CuB 2+(a–d) and Fea3 LS,3+−H2O−CuB 2+ structures are given in Table 2. Relative energies of different states are reported in Tables 2 and 3.

Table 3

OLYP‐D3‐BJ calculated properties (relative energies ΔE in kcal mol−1, Mössbauer isomer shift δ in mm s−1, quadrupole splitting ΔE Q in mm s−1) for the four geometry optimized high‐spin−Fea3 3+ DNC structures starting from Fea3 3+,HS−H2O−CuB 2+(a–d) by deleting the H2O molecule which has H‐bonding interaction with the central H2O molecule.[a]

Starting from Structure	Name in Ref. [32]	Optimized Geometry [Å]			Spin‐Coupling	ΔE	δ	ΔE Q
		Fe−O	Cu−O	Fe ⋅⋅⋅ Cu
Fea3 HS,3+−H2O−CuB 2+(a)	S1	2.61	2.82	5.03	AF	0.0	0.41	0.85
					F	0.0	0.41	0.86
Fea3 HS,3+−H2O−CuB 2+(b)	S2	2.97	2.52	4.98	AF	−1.1	0.41	0.66
					F	−1.2	0.42	0.98
Fea3 HS,3+−H2O−CuB 2+(c)	S3	3.54	2.29	4.76	AF	−1.5	0.42	0.60
					F	−1.9	0.44	1.09
Fea3 HS,3+−H2O−CuB 2+(d)	S4	3.07	2.41	4.87	AF	−0.8	0.41	0.64
					F	−1.1	0.43	1.14

[a]⋅These four geometry optimized structures (S) were given as S1, S2, S3, and S4, respectively, in Table 2 of Ref. [32].

57Fea3 3+ Mössbauer Isomer Shift and Quadrupole Splitting Calculations

In general, the isomer shifts (δ) can be calculated according to the fit equation [Eq. 1]:

where ρ(0) is the calculated electron density at Fe nucleus and A is a predefined constant close to the value of ρ(0). The parameters α and C are normally obtained by linear fitting between the calculated ρ(0) and the experimental (exp) δ values of a set of Fe2+, Fe3+, and Fe4+ complexes. However, we have found that a global fitting of a single equation for all Fe2+,3+,4+ complexes in general underestimates the isomer shifts for the Fe2+ and Fe4+ sites, but overestimates the δ values for the Fe3+ state.[ , , ] In order to reasonably predict the 57Fe isomer shifts in different oxidation states, we have fit the parameters separately for the Fe2+ and for Fe2.5+,3+,4+ complexes with PW91, OLYP, and OPBE functionals,[ , ] and have successfully predicted the isomer shifts for various states of the Fe−Fe, Fe−Mn, and Fe4S4 clusters in methane monooxygenase,[ , , ] ribonucleotide reductases,[ , , , , , ] and APS‐reductase. We have also calculated the isomer shift and quadrupole splitting values with OLYP functional for the Fea3 2+/3+ site of ba 3 CcO based on several X‐ray crystal structures. However, at that time, we did not propose that a single water molecule resides between the Fea3 3+ and CuB 2+ sites in the DNC of oxidized as‐isolated CcO. In the current paper, we have performed the ρ(0) vs. δexp linear fitting for the OLYP‐D3(BJ) potential on the same training set of the Fe2.5+,3+,3.5+,4+ complexes as we have done for the PW91, OLYP, and OPBE potentials.[ , ] The training set contains 19 Fe2.5+,3+,3.5+,4+ sample complexes with total 30 Fe sites. Previously, we used our own program to calculate the electron density ρ(0) at the Fe nuclei. More recently, the ADF computer code package by default also reports the electron density at the nuclei. Based on their description, the electron density is not calculated exactly at the center of the nucleus. Instead, the electron density is calculated at sample points on a small spherical surface surrounding the center of a nucleus. The computed electron density in the output of ADF is the average electron density on these points. We now use that ρ(0) in ADF output to perform the linear fitting and the isomer shift calculations. We note that this procedure bears a close resemblance to the actual physical change in electron density‐nuclear contact interaction (effectively over a thin spherical shell) when the 57Fe nucleus changes its radius and volume upon gamma ray excitation from the ground state (spin I=1/2) to its excited state (with spin I=3/2). This same excitation changes the shape of the 57Fe nucleus from spherical to ellipsoidal. That change produces the quadrupole splitting in the Mossbauer spectrum.

The details of the Fe2.5+,3+,3.5+,4+ complexes in the training set and the ρ(0) vs. δexp linear regression are given in the Supporting Information. Briefly, by taking the constant A=11820.0, our linear fitting for the OLYP‐D3(BJ) potential yields [Eq. 2]:

with correlation coefficient r=−0.946 and a standard deviation SD=0.068 mm s−1. We then performed single‐point energy calculations on each of our optimized O state Fea3 HS/IS/LS,3+−H2O−CuB 2+ DNC model clusters in both broken‐symmetry (representing Fea3 3+−CuB 2+ AF‐coupled state) and F‐coupled states with all electron and all TZP basis set to obtain the ρ(0) values and further predicted the 57Fea3 3+ isomer shift values based on Equation (2). The quadrupole splitting values (ΔE Q) were also obtained from ADF output in these calculations.

Normally the calculated electric field gradient (EFG) tensors V at the Fe nucleus are diagonalized and the eigenvalues are reordered so that |V zz|≥|V yy|≥|V xx|. The asymmetry parameter η is defined as [Eq. 3]:

Then the ΔE Q for 57Fe of the nuclear excited state (I=3/2) can be calculated as [Eq. 4]:

where e is the electrical charge of a positive electron, Q is the nuclear quadrupole moment of Fe. Recently, the ADF software package determines the ΔE Q value using Q=0.16 barn, the current best experimental value.

We have listed our calculated 57Fea3 3+ isomer shift and quadrupole splitting results for our O state Fea3 HS/IS/LS,3+−H2O−CuB 2+ DNC model clusters in Table 2.

Results and Discussion

Calculated Mössbauer Properties for the High‐Spin−Fea3 3+,HS−H2O−CuB 2+(a–d) DNC Model Clusters

First, we compare our calculated Mössbauer properties with experimental data for Fea3 3+ in high‐spin state. In Table 1, the observed isomer shift values for the Fea3 HS,3+ are around 0.41−0.48 mm s−1. Our calculated δ(Fea3 3+,HS) values (see Table 2) for our Fea3 HS,3+−H2O−CuB 2+(a–d) DNC models are 0.40–0.45 mm s−1, which are highly consistent with these experiments. The available observed ΔE Q(Fea3 3+,HS)exp values for different CcOs are reported as 0.7, ∼1, 1.0±0.1, 1.10, and 1.3 mm s−1, while our calculated ΔE Q(Fea3 3+,HS) values are 0.77, 0.78, 0.80, 0.92, 1.21, and 1.24 mm s−1, which also match the experimental values very well.

Note that in our DNC models shown in Figures 3 and 4 and the corresponding calculation results in Table 2, there is another H2O molecule, which likely originates from the CuB‐bound H2O ligand in state F (see Figure 1), and has H‐bonding interaction with the central H2O molecule. In the X‐ray crystal structure 3S8G, a water molecule (HOH608) was seen 3.01 Å above one of the dioxygen atoms that is closer to CuB.. Therefore, the HOH608 may have H‐bonding interaction with the H2O ligand in a position similar to Fea3 3+−H2O−CuB 2+(c) (Figure 4c). No other H2O molecules were identified within the H‐bonding distances around the dioxygen in 3S8G. This probably implies that not all CcO molecules in the crystal have an H‐bonding H2O interacting with the central bridging H2O molecule, and even if there is an H‐bonding H2O molecule in some of the CcO DNCs, the H‐bonding patterns and the positions of the H‐bonding H2O molecules may differ, and therefore, they may not be identified in the X‐ray crystal structure.

Since it is not clear whether there is an H‐bonding H2O molecule in the DNC of the O state, in our previous work in Ref. [32], we also performed broken‐symmetry state geometry optimizations on the four Fea3 HS,3+−H2O−CuB 2+(a)–(d) structures obtained by removing the H‐bonding H2O. The four corresponding optimized structures (S) were labeled as S1, S2, S3, and S4 in Figure 6 of Ref. [32], respectively. Their main bond distances and the calculated energies were given in Table 2 of Ref. [32], and are also given in Table 3 here, together with the single‐point energy Fea3 HS,3+−CuB 2+ F‐coupled state calculations on the broken‐symmetry optimized geometries.

Without the H‐bonding H2O molecule, the binding of the H2O ligand with the two metal sites, especially with the Fea3 HS,3+ site, are weakened. But still the overlap of the S1–S4 structures with the DNC of 3S8G shows the H2O molecules in S1–S4 reside along the apparent dioxygen species direction in 3S8G (see Figure 2). We therefore also calculated the 57Fea3 HS,3+ Mössbauer isomer shift and quadrupole splitting properties of these four structures in both AF‐ (broken‐symmetry) and F‐coupled states, and presented the results in Table 3. The calculated isomer shifts are almost the same as those given in Table 2, and are again highly consistent with the observed values.

Based on the calculated 57Fea3 HS,3+ Mössbauer properties given in Tables 2 and 3, it appears that the 57Fea3 HS,3+ isomer shifts only slightly vary with the position of the H2O molecule, whether or not there is an H‐bonding H2O molecule, and whether Fea3 HS,3+ is F‐ or AF‐coupled with CuB 2+. However, the 57Fea3 HS,3+ quadrupole splitting values are very sensitive to these factors. This explains that the observed Mössbauer spectra are broad, that the parameters are difficult to define precisely, and that many of the reported parameters are averaged values.[ , , ] Our calculated versus the several reported experimentally defined 57Fea3 HS,3+ Mössbauer isomer shift and quadrupole splitting values are compared in Figure 5.

Figure 5

Calculated (black circles, data are given in Tables 2 and 3) versus several experimentally defined (red dots, data are given in Table 1) Mössbauer isomer shift and quadrupole splitting values for the high‐spin (HS) 57Fea3 3+ site in CcOs.

In general, when the H2O molecule is much closer to the Fea3 HS,3+ site (Fea3 HS,3+−H2O−CuB 2+(a)–(b)), the calculated 57Fea3 HS,3+ quadrupole splitting values for the F‐ and AF‐coupled states are similar to each other. On the other hand, when the H2O molecule is much closer to the CuB 2+ site (Fea3 HS,3+−H2O−CuB 2+(c)–(d)), the calculated ΔE Q(Fea3 HS,3+) values for the F‐coupled state are much larger than the corresponding AF‐coupled state. The observed ΔE Q(Fea3 HS,3+)exp values around 1.0 to 1.3 mm s−1 (see Table 1)[ , , , ] likely arise from the DNC structures in which the H2O molecule is much closer to the CuB 2+ site and the Fea3 HS,3+ and CuB 2+ sites are F‐coupled (see Tables 2 and 3). Meanwhile, the observed ΔE Q(Fea3 HS,3+)exp values around 0.7 mm s−1 probably come from the structures where the H2O molecule is close to the Fea3 HS,3+ site (whether the Fea3 HS,3+ and CuB 2+ sites are F‐ or AF‐coupled), or from the structures where the H2O molecule is much closer to CuB 2+ and the two metal sites are AF‐coupled.

Calculated Mössbauer Properties for the Intermediate‐ and Low‐Spin−Fea3 IS/LS,3+−H2O−CuB 2+ DNC Model Clusters

In Tt c 1 aa 3 and ba 3 at certain pH or at low temperature (see Table 1),[ , ] a “low‐spin” Fea3 3+ species was observed with δ=0.29 mm s−1 and ΔE Q=2.21/2.24 mm s−1. Although this was proposed to be a low‐spin Fea3 3+ species, such δ and ΔE Q values could also originate from an intermediate‐spin Fe3+ site. Therefore, we have performed Mössbauer property calculations on our IS and LS Fea3 IS/LS,3+−H2O−CuB 2+ models listed in Table 2.

Unlike the high‐spin−Fea3 HS,3+−H2O−CuB 2+ models, the F‐ and AF‐coupled spin states yield essentially the same isomer shift and quadrupole splitting results for the same Fea3 IS/LS,3+−H2O−CuB 2+ structure. Further, the position of the H2O molecule does not have significant effect on the calculated 57Fea3 IS,3+ isomer shift and quadrupole splitting values on the four Fea3 IS,3+−H2O−CuB 2+(a)–(d) structures. Overall, the calculated δ(Fea3 IS,3+) only varies from 0.34 to 0.36 mm s−1, and ΔE Q(Fea3 IS,3+) from 2.33 to 2.66 mm s−1.

For the low‐spin−Fea3 LS,3+−H2O−CuB 2+ structure, our calculations give δ(Fea3 LS,3+)=0.31 mm s−1 and ΔE Q(Fea3 LS,3+)=2.96 mm s−1.

Compared with experimental δ=0.29 mm s−1 and ΔE Q=2.21/2.24 mm s−1 values, the calculated δ(Fea3 LS,3+)=0.31 mm s−1 is a little closer to experiment than the calculated δ(Fea3 IS,3+) values (0.34 to 0.36 mm s−1). However, the ΔE Q(Fea3 LS,3+)=2.96 mm s−1 deviates more from experiment than the ΔE Q(Fea3 IS,3+) results (2.33 to 2.66) mm s−1. In the Supporting Information, we have used linear regression on the training set of Fe complexes to find the standard deviation (SD) of the fit for the isomer shifts, SD=0.068 mm s −1, and also the standard deviation of the fit for the corresponding quadrupole splittings, SD=0.30 mm s−1. The experimentally observed Mössbauer spectrum with δ=0.29 mm s−1 and ΔE Q=2.21/2.24 mm s−1 spectra has an isomer shift within 1 SD from either the DFT calculated low‐spin or an intermediate‐spin Fea3 3+ species. By contrast, for the predicted versus experimental quadrupole splitting, the calculated low‐spin quadrupole splitting differs by more than 2 SD from experiment, while the calculated intermediate‐spin quadrupole splittings are much closer <1.5 SD.

In addition, the intermediate‐spin Fea3 IS,3+−H2O−CuB 2+(a)–(d) structures have lower energy than the low‐spin Fea3 LS,3+−H2O−CuB 2+ state, and the structure Fea3 IS,3+−H2O−CuB 2+(c) has calculated δ=0.34 mm s−1 and ΔE Q=2.33 mm s−1, which are the closest to the experiment. Therefore, the experimentally observed δ=0.29 mm s−1 and ΔE Q=2.21/2.24 mm s−1 spectra are probably from intermediate‐spin−Fea3 3+ DNCs.

Conclusions

In our previous study, we proposed that a single water molecule is in between the Fea3 3+ and CuB 2+ sites in the resting oxidized as‐isolated O state of CcO. Depending on the Fea3 3+−CuB 2+ distance and presence or absence of H‐bonding to another H2O molecule, this single H2O molecule can coordinate to either the Fea3 3+ or the CuB 2+ site, or can reside at different positions between the Fea3 3+ and CuB 2+ sites that are energetically very close on the potential energy surface. We therefore have also proposed that the extended peroxide type electron density between Fea3 3+ and CuB 2+ observed in several CcO X‐ray crystal structures[ , , ] results are the consequence of the superposition of the electron density of a water molecule at different locations between Fea3 3+ and CuB 2+ in different CcO molecules within the crystals.

The structural heterogeneities of the DNC in the resting oxidized state CcOs (O state) were demonstrated by earlier 57Fe3+ Mössbauer experiments,[ , , , ] in which the spectra were broad, the parameters were difficult to define precisely, and the reported parameters were averaged values.

In this paper, we have calculated the 57Fea3 3+ Mössbauer isomer shift (δ) and quadrupole splitting (ΔE Q) properties of the resting state O[Fea3 3+−H2O−CuB 2+] DNC structures that we obtained in Ref. [32], and have compared the calculated results with the available experimental values (see Table 1). Overall, the span of our calculated δ and ΔE Q results for the high‐spin−Fea3 3+ DNC structures agree very well with the experimental values. Our calculations show that the change of the high‐spin‐57Fea3 3+ isomer shift among different DNC structures is within 0.05 mm s−1. However, the quadrupole splitting values vary with the position of the central H2O molecule, whether or not this H2O molecule has H‐bonding interaction with another H2O molecule, and whether the high‐spin−Fea3 3+ site is F‐ or AF‐coupled with CuB 2+. The observed ΔE Q values around 1.0 to 1.3 mm s−1 (see Table 1)[ , , , ] likely result from the DNC structures in which the central H2O molecule is much closer to the CuB 2+ site and the high‐spin−Fea3 3+ and CuB 2+ sites are F‐coupled. Meanwhile the observed ΔE Q values around 0.7 mm s−1 probably result from the structures where the H2O molecule is close to the high‐spin−Fea3 3+ site with the two metal sites either F‐ or AF‐coupled, or from the structures where the H2O molecule is much closer to CuB 2+ and the two metal sites are AF‐coupled.

Our calculations also show that the observed “low‐spin” Fea3 3+ species with δ=0.29 mm s−1 and ΔE Q=2.21/2.24 mm s−1 more probably arises from an intermediate‐spin−Fea3 3+ state, which exists at low temperature or is more populated at certain pH values.

Overall, our calculations demonstrate that the structural heterogeneities of the resting as‐isolated oxidized state observed in several Mössbauer properties experiments are very consistent with the DFT predicted properties and structures of a single H2O molecule bridging the Fea3 3+ and CuB 2+ sites with variable positions, with further variations explained by the Fea3 3+ spin states, and by the different spin‐couplings between Fea3 3+ and CuB 2+.

Supporting Information

The details of the Mössbauer isomer shift parameters fitting for the OLYP‐D3(BJ) functional, the Fe2.5+,3+,3.5+,4+ complexes in the training set, and the ρ(0) vs. δexp linear regression plots are given in the Supporting Information.

Conflict of interest

The authors declare no conflict of interest.

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Supporting Information

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