Four-Component Relativistic Density Functional Calculations of EPR

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX-XXX

pubs.acs.org/JPCA

Four-Component Relativistic Density Functional Calculations of EPR Parameters for Model Complexes of Tungstoenzymes Sebastian Gohr,† Peter Hrobárik,†,‡ and Martin Kaupp*,† †

Institut für Chemie, Theoretische Chemie/Quantenchemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, 10623 Berlin, Germany ‡ Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Mlynská dolina CH-2, Ilkovičova 6, SK-84215 Bratislava, Slovakia S Supporting Information *

ABSTRACT: For a closer validation of four-component relativistic DFT methods within the matrix Dirac−Kohn−Sham (mDKS) framework with global hybrid functionals for EPR parameter calculations to be applied in the modeling of tungsten enzymes, we refine a previously suggested protocol for computations on 5d systems. This is done for a series of larger, unsymmetrical W(V) complexes thought to closely resemble enzyme active sites in this oxidation state. Particular focus is placed on complexes with thiolate and dithiolene ligands, along with an evaluation of the influence of different amounts of exact-exchange incorporated in hybrid PBE0-xHF functionals, an implicit solvent model, and structural changes on the computed EPR parameters. Compared to previous work, a slightly modified protocol with different optimal exact-exchange admixtures for electronic g- and hyperfine A-tensors is found to provide the best agreement with experimental EPR data. It will provide the basis for our subsequent tungsten enzyme modeling efforts.

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INTRODUCTION Tungsten is the heaviest known element that plays a welldefined role in biology.1,2 In contrast to the more widespread and longer-known molybdoenzymes, tungstoenzymes have only been identified in prokaryots, especially in hyperthermophilic archaea.2−6 While it is known from several prokaryots that they incorporate tungsten instead of molybdenum into their enzymes if provided with a high tungsten:molybdenum ratio in the growing medium, the reverse is usually not observed for archaea and bacteria that use tungstoenzymes. The mechanistic details for this tungsten specificity are still under investigation.7 One assumed reason is the observed higher temperature stability of tungstoenyzmes in contrast to their molybdenum analogues.8 Of the three main families of mononuclear molybdoenzymes, the tungsten analogues resemble the so-called dimethyl sulfoxide reductases (DMSOR), which exhibit two rather than one bispterin cofactors (“molybdopterin”, MPT, shown in Figure 1). Tungsten complexes have in general lower reduction potentials due to the relativistic expansion of the 5d orbitals.9,10 The second dithiolene-type ligand increases this reduction potential:2 in contrast to pure sulfido ligands, the sulfur π orbitals of dithiolenes in general and of MPT in particular are partially delocalized into the unsaturated backbone and are therefore particularly weak π donors,11 which among other things favors nonoctahedral structures of the M(VI) and M(V) states. Additionally, adjustments to the remaining ligands © XXXX American Chemical Society

Figure 1. Structure of molybdopterin (MPT). The name can be seen as a heritage from its discovery in molybdoenzymes since the cofactor itself does not contain molybdenum and is also found in combination with tungsten. MPT coordinates to Mo/W via the dithiolene group.

(oxygen, sulfur, or selenium) are seen to be used in nature to modulate the redox potentials and therefore help to catalyze different reactions.8,12 While the reactions catalyzed by the different tungstoenzymes are known, the reaction mechanisms are still under debate.2,7,8,13−28 One of the most frequently used methods to Received: September 3, 2017 Revised: October 27, 2017 Published: October 27, 2017 A

DOI: 10.1021/acs.jpca.7b08768 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

Figure 2. Investigated tungsten(V) complexes.

investigate the paramagnetic d1 M(V) intermediate states 1 2

(S = )

complexes, none of them had exhibited sulfur ligands. We thus now extend our method screening to a series of 12 W(V) complexes shown in Figure 2. [WOCl5]2− is included to provide comparison against a small nonsulfur containing system. [Tp*WE(XPh)2] (E,X = O, S; Tp* = hydrotris(3,5dimethylpyrazol-1-yl)borate) complexes represent a distorted WEN3X2 octahedral coordination sphere with one terminal oxo or sulfido group, three facially bound nitrogen atoms of the Tp* ligand, and two monodentate phenolate or thiophenolate ligands. [WO(SPh)4]− is a pentacoordinated oxo-W(V) complex with four thiophenol groups and in [WO(SePh)4]− sulfur is replaced by selenium for which an experimental 77Se HFC is available. [WO(bdt)2]− (bdt = benzene-1,2-dithiolate) and [WO(edt)2]− (edt = ethane-1,2-dithiolate) have two dithiolene ligands and thus are most closely related to the enzyme active sites. [W(mdt)3]− (mdt = 1,2-dimethyl-1,2dithiolene), [W(bdt)3]−, and [W(pdt)3]− (pdt = 1,2-diphenyl1,2-dithiolate) provide finally homoleptic tris-dithiolene examples.

during the catalytic cycles is EPR (“electron

paramagnetic resonance”) spectroscopy. The specificity of EPR for the active-site composition is particularly important in the field, since those enzymes also contain iron-sulfur clusters in close proximity (around 10 Å) with relatively strong optical absorptions.29 We have recently demonstrated the efficiency of fourcomponent relativistic DFT (“density functional theory”) calculations of EPR parameters for 4d and 5d systems, using the ReSpect (“relativistic spectroscopy”) program package with the implemented matrix Dirac−Kohn−Sham (mDKS) method and hybrid functionals,30 even for larger complexes of up to 130 atoms.31 The 5d element tungsten requires a proper relativistic treatment incorporating both scalar relativistic effects and spinorbit (SO) effects beyond leading order of perturbation theory. Before embarking on a detailed study of W(V) active sites in tungsten enzymes, here we fine-tune the previously reported computational protocol on larger synthetic model complexes for which reliable experimental data are available. Most notably, while the previous study had included a few simple W(V) B


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The Journal of Physical Chemistry A Table 1. PBE0-D3(BJ)/def2-TZVP Optimized Structural Parameters Compared to Experimenta,b [WOCl5]2− X-ray60c X-ray61d PBE0-D3(BJ) [Tp*WO(OPh)2] X-ray41 PBE0-D3(BJ) +COSMO(DMF) [Tp*WO(SPh)2] X-ray41 PBE0-D3(BJ) [Tp*WS(OPh)2] X-ray62 PBE0-D3(BJ) [WO(SPh)4]− X-ray59 PBE0-D3(BJ) +COSMO(CH3CN) [WO(SePh)4]− PBE0-D3(BJ) [WO(bdt)2]− X-ray63 PBE0-D3(BJ) + COSMO(DMF/CH3CN) [WO(edt)2]− PBE0-D3(BJ) [W(mdt)3]− X-ray40 PBE0-D3(BJ) + COSMO(CH2Cl2/tol) [W(bdt)3]− X-ray64 PBE0-D3(BJ) [W(pdt)3]− X-ray40 PBE0-D3(BJ)

d(WO) 1.724 1.669 1.696 d(WO) 1.705 1.704 1.711 d(WO) 1.698 1.703 d(WO) 2.161 2.149 d(WO) 1.589 1.705 1.708 d(WO) 1.701 d(WO) 1.689 1.700 1.712 d(WO) 1.703 d(W−S) 2.394 2.382 2.380 d(W−S) 2.366 2.387 d(W−S) 2.380 2.375

d(W−Cl)ax 2.565 2.664 2.556 d(W−OPh) 1.941 1.954 1.960 d(W−SPh) 2.385 2.391 d(W−SPh) 1.954 1.946 d(W−S) 2.456 2.403 2.399 d(W−Se) 2.532 d(W−S) 2.366 2.396 2.387 d(W−S) 2.416

d(W−Cl)eq 2.390 2.372 2.432 d(W−N) 2.200 2.229 2.223 d(W−N) 2.218 2.243 d(W−N) 2.197 2.224

RMSD − − 0.0557/0.0725 RMSD − 0.4247e 0.4334e RMSD − 4.4428f RMSD − 4.2938g RMSDf − 2.679h 2.560h RMSD − RMSD − 0.1403 0.1385 RMSD − RMSD − 0.2082 0.2047 RMSD − 0.0972 RMSD − 0.7193I

a All bond-lengths in Å. bIn case of the X-ray structures (especially for [W(mdt)3]− and [W(pdt)3]−), not all bonds of one type are of the exact same length, and only their average values are given. cCambridge structural database (CSD) ID: FORSUA. dCSD-ID: ZAPFUR. eThe high RMSD values are attributed mostly to the phenol rings. Including only the W, B, O, and N atoms, the RMSD values are 0.0518 and 0.0519 Å, respectively. f Including only the W, B, O, S, and N atoms, the RMSD value is 0.0476. gIncluding only the W, B, O, S, and N atoms, the RMSD value is 0.0647. h Including only the W, O, and S atoms, the RMSD values reduce to 0.1575 and 0.1611 Å, respectively. IIncluding only W and S, the RMSD value reduces to 0.3066 Å.

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and toluene (tol) ε = 2.38. An averaged dielectric constant was used to model the CH2Cl2/tol solvent mixture as ε = 5.65 for [W(mdt)3]−, assuming a 1:1 ratio in the absence of more detailed information.40 For [WO(bdt)2]−, a DMF/CH3CN “mixture” with ε = 36.4 is used. A variety of possible solvents (CH2Cl2, DMF, and THF) were mentioned for the EPR measurements of [Tp*WO(XPh)2] (X = O, S), without further specifying the one actually used.41 EPR Parameter Calculations. The four-component relativistic mDKS method with restricted kinetically balanced (RKB)42,43 basis sets is the DFT analogy of the modified Dirac equation44,45 and has been described previously.31,46,47 EPR parameter calculations at this level used the ReSpect program package30 with two different relativistic basis-set combinations: (a) a basis by Hirao48 for tungsten in conjunction with fully uncontracted Huzinaga−Kutzelnigg-type IGLO-II49 basis sets for the ligand atoms or (b) a larger tungsten triple-ζ basis set by Dyall50 with uncontracted IGLO-III49 basis sets for the ligand atoms. Starting from the PBE0 functional33,34 with 25% exact-

COMPUTATIONAL DETAILS 32

Structures. All structures were optimized with Turbomole at the PBE0-D3(BJ)/def2-TZVP level. That is, we used the PBE033,34 hybrid functional, combined with Grimme’s atompairwise D3 dispersion correction35 with Becke−Johnson damping,36 a quasi-relativistic energy-consistent small-core pseudopotential (ECP)37 for tungsten with a (8s7p6d1f)/ [6s4p3d1f] Gaussian-type-orbital valence basis set, and allelectron def2-TZVP38 basis sets for the ligand atoms. The experimental structures are derived from X-ray crystal data. However, since the EPR measurements have been conducted with frozen-solution samples, we use in some cases the conductor-like screening model (COSMO)39 to take bulk solvent effects on the structure into account and to simulate indirect solvent effects in our EPR calculations. The following solvents with the corresponding dielectric constants have been considered: dimethylformamide (DMF) ε = 37.219, acetonitrile (CH3CN) ε = 35.688, dichloromethane (CH2Cl2) ε = 8.93, C


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Table 2. Effect of the Structure on Computed EPR Parameters (PBE0-40HF/Hirao/IGLO-II Level; 183W Hyperfine Couplings in MHz) [WOCl5]2−

[Tp*WO(OPh)2]

[Tp*WO(SPh)2]

[Tp*WS(OPh)2]

[WO(SPh)4]−

[WO(bdt)2]−

[W(mdt)3]−

[W(bdt)3]−

[W(pdt)3]−

a

expt. data/input structure

giso

g11

g22

g33

expt. EPR65 X-ray struct.60 X-ray struct.61 PBE0-D3(BJ) expt. EPR41 X-ray struct.41 PBE0-D3(BJ) +COSMO(DMF) expt. EPR41 X-ray struct.41 PBE0-D3(BJ) expt. EPR62 X-ray struct.62 PBE0-D3(BJ) expt. EPR66 X-ray struct.59 PBE0-D3(BJ) +COSMO(CH3CN) expt. EPR67 X-ray struct.67 PBE0-D3(BJ) +COSMO(DMF/CH3CN) expt. EPR40 X-ray struct.40a PBE0-D3(BJ) +COSMO(CH2Cl2/tol) expt. EPR40 X-ray struct.64 PBE0-D3(BJ) expt. EPR40 X-ray struct.40 PBE0-D3(BJ)

1.773 1.745 1.780 1.748 1.785 1.785 1.784 1.784 1.865 1.871 1.869 1.681 1.700 1.702 1.936 1.928 1.926 1.928 1.962 1.962 1.947 1.948 1.994 2.036 1.990 1.993 1.992 1.986 1.977 1.993 1.982 1.991

1.758 1.726 1.762 1.744 1.707 1.714 1.701 1.702 1.805 1.814 1.809 1.559 1.589 1.590 1.903 1.892 1.888 1.892 1.911 1.907 1.901 1.901 1.988 2.034 1.981 1.982 1.945 1.932 1.925 1.991 1.954 1.987

1.758 1.726 1.767 1.744 1.802 1.795 1.804 1.802 1.843 1.846 1.847 1.693 1.716 1.716 1.903 1.909 1.889 1.892 1.931 1.929 1.923 1.923 2.001 2.037 1.995 1.998 2.007 2.007 2.001 2.002 1.994 1.992

1.804 1.781 1.812 1.758 1.847 1.847 1.847 1.848 1.947 1.954 1.952 1.792 1.795 1.802 2.018 1.982 2.001 2.001 2.044 2.049 2.018 2.020 2.009 2.038 1.995 1.998 2.024 2.020 2.004 2.008 1.998 1.993

Aiso −257 −250 −260 −255 −246 −253 −252 −180 −177 −176 −270 −256 −255 −165 −144 −142 −142 −153 −136 −137 −137 −82 −2 −81 −82 −155 −147 −151 −81 −118 −70

A11

A22

A33

−196 −189 −196

−196 −190 −196

−381 −378 −369 −388

−189 −195 −194

−193 −198 −197

−354 −365 −364

−127 −125

−137 −134

−267 −269

−195 −193 −133 −98 −99 −99 −111 −94 −93 −94 −33 13 −25 −27 −177 −177 −184 −36 −54 −19

−206 −205 −133 −100 −99 −99 −119 −98 −97 −98 −102 −10 −109 −109 −210 −187 −192 −93 −155 −97

−366 −366 −234 −234 −227 −227 −235 −215 −219 −218 −96 −10 −109 −110 −78 −75 −76 −90 −146 −96

The experimental structure is obtained from [W(mdt)3]2−, while the EPR data refer to [W(mdt)3]−.

superposition functionality of Maestro as included in the Schrödinger 2015.3 package.56 Natural population analysis (NPA),57 as implemented in the Turbomole program, was used for the evaluation of spin densities.

exchange (EXX) admixture, two larger EXX admixtures x = 40% and 50% were compared, denoted as PBE0-xHF. Gaussian-type finite nuclear-charge and magnetic-moment models have been used throughout. For comparative purposes, a few calculations at the onecomponent level with Douglas−Kroll−Hess second-order corrections (DKH2) were performed using the ORCA program package (version 3.0.3).51 In some of the four-component calculations, a polarizable continuum solvent model (PCM)52 in the integral equation formalism (IEF)53 using solventaccessible surfaces with van der Waals radii from Allinger’s MM3 model54 has been applied, as introduced in ref 55. g shifts are reported in ppt as deviations from the freeelectron g value (ge = 2.002319): Δg = (g − ge) · 1000. If not stated otherwise, reported hyperfine coupling (HFC) values are in MHz and refer to 183W. Applied nuclear g factors are gN = 0.2356 (183W), 1.0700 (77Se), and 0.7575 (17O). Experimental values in 10−4 cm−1 were converted to MHz by multiplying with a factor 2.99792458 (ν = λc). HFC values in Oe, G, or mT gμ were converted by the factor B , where g is the measured g h factor appropriate for the given HFC component (use of ge instead changes the converted HFCs by 4−5 MHz for [WO(bdt)2]−). Negative signs of all HFC components are based on our computations. RMSD values between computed and experimental structures have been determined using the

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RESULTS AND DISCUSSION Structures. In line with our previous study and with the findings of, e.g., ref 58, the chosen PBE0-D3(BJ)/def2-TZVP level was expected to provide reliable structures for our EPR parameter calculations. This is confirmed in the comparison with available experimental data in Table 1. Except for d(W− Cl)eq/d(W−Cl)ax in the dianionic [WOCl5]2− and d(WO) in [WO(SPh)4]−, all deviations from experiment are below ca. 0.05 Å. The WO distance determined from diffraction data of the (PPh4)[WO(SPh)4] crystal59 is unusually short compared to related systems and is presumably an artifact. Larger RMSD values in five cases are related to the orientation of some ligand planes rather than to the direct metal coordination environment. Effect of the Structure on EPR Parameters. Given the relatively good agreement between optimized and experimental structures (see above), we expect moderate differences between the EPR parameters obtained for these structures. While this is largely the case, we nevertheless explore the structural effects in Table 2 (PBE0-40HF/Hirao/IGLO-II level). This comparison D


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Figure 3. Directions of g-tensor principal components computed for [WO(SPh)4]− (left) and [WO(bdt)2]− (right) at the four-component PBE040HF/Hirao/IGLO-II//PBE0-D3(BJ)/def2-TZVP level.

The homoleptic tris-dithiolene complex [W(mdt)3]− exhibits a different type of structure dependence. Unfortunately, only the dianion has been characterized crystallographically. While this structure has been denoted as “X-ray struct.” in Table 2, its dithiolene fold angles in the mdt ligands are almost nonexistent. Not surprisingly, the computed EPR parameters for this structure, especially the HFC values, do not match the experimental data. Structure optimization of the monoanion introduces a dithiolene fold angle of approximately 15° (cf. Figure S1 in the SI and ref 40) and provides EPR parameters in much better agreement with experiment (but with a somewhat too low g33). Axial symmetry of the tensors can be expected for this almost C3 symmetric structure where small asymmetry in the experimentally observed components are probably attributable to specific solvent−solute interactions, counterion and/or matrix effects, which are absent in our simulations. On the other hand, for the closely related [W(bdt)3]− and [W(pdt)3]− molecules, the experimental structures refer correctly to the monoanions. In contrast to [W(mdt)3]−, [W(pdt)3]− possesses twist angles of roughly 23° and dithiolene fold angles in a range from 6 to 15°.40 Better agreement with the experimental EPR data is nevertheless found for the optimized structure, in particular for the HFC tensor and g11. The [W(bdt)3]− results are in very good agreement with the experimental data with a slight preference for the X-ray structure. Effect of the Functional. Based on the results of our extended previous benchmark studies31 on a more general set of 4d/5d complexes, we restrict our comparison to the PBE0based global hybrid functionals with only three different amounts of EXX admixture (25%, 40%, and 50%). The results for the DFT-optimized structures are collected in Table 3 and Figure 4, while the mean absolute errors for isotropic values and Δg-/A-tensor anisotropies are evaluated in Table 4. It appears that our previously suggested computational protocol (PBE0-40HF/Hirao/IGLO-II) for second- and third-row transition-metal d1 systems works well overall but cannot be considered the best choice for specific subgroups of our test set: g-tensors for systems with small |Δgiso| values below 100 pt (entries from [WO(SPh)4]− to [W(pdt)3]− in Table 3) are best reproduced at the PBE0 level, whereas complexes with |Δgiso| > 100 ppt seem to require larger EXX admixtures. Based on the results for [Tp*WS(OPh)2], one might even be tempted to suggest 50% EXX admixture for systems with |Δgiso| > 300 ppt. Larger EXX admixtures are clearly always required for all metal HFC components in our present test set: best agreement is found either for PBE0-40HF or for PBE0-50HF (Table 3 and

accounts also for the effects of COSMO solvent modeling in the structure optimizations and the subsequent influence on computed EPR parameters (indirect solvent effects). Generally good agreement with experiment is found for [WOCl5]2−. Only for g33 the experimental structures give slightly larger values and thus closer agreement with experiment. Particularly small structural effects are seen for the rigid [Tp*WE(XPh)2] complexes, where excellent agreement with experiment is found both for the g-tensor and Aiso, in fact even somewhat better than one could expect at the DFT level used. The good performance is likely helped by the absence of a net charge on the complex, rendering environmental effects less important. While [WO(SPh)4]− features saturated thiolate ligands rather than dithiolenes, its square pyramidal coordination with four basal sulfur atoms and an apical oxo ligand resembles already a number of structural aspects of molybdo- and tungstoenzymes. The bulk solvent polarity affects the structure only in a minor way, leading to negligible indirect solvent effects on the computed EPR parameters. The overall agreement with experiment is good, albeit g33 is too close to the free-electron value. Here, a test of adjusting specific geometrical parameters shows an appreciable impact of the W− S bond length on g33 but not on the other two g-tensor components (cf. Table S1 in the SI). Visualization of the gtensor (Figure 3) shows that g33 is oriented along the WO bond and roughly perpendicular to the W−S bonds. This has already been found for related 5d transition metal complexes68 and was attributed to contributions of “in-plane” d orbitals. Similar observations are made for the bis-dithiolene oxo complex [WO(bdt)2]−, which is an even closer structural model for tungstoenzyme active sites. Again g33 is particularly sensitive to the W−S bond lengths (Table S2 in the SI and Figure 3), and as a result of its shorter distances, the experimental structure provides better agreement with the experimental EPR parameters than the optimized ones. The structural effect on the HFC values is minor, significantly below the effect of the functional, as will be shown in the next section. Effects of the implicit solvent model on the structure optimization are also small. Unfortunately, we could not find closer experimental details, such as the X-ray structure and solvent used in the EPR characterization, of the close analogue [WO(edt)2]−. However, it can be seen that, compared to [WO(bdt)2]−, the change in d(WO) is negligible, while d(W−S) differs by 0.02 Å, probably due to the missing stabilization by phenyl substituents. E


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Table 3. Dependence of Computed EPR Parameters on the EXX Admixture in the Functional (PBE0 vs PBE0-40HF vs PBE050HF)a [WOCl5]2−

[Tp*WO(OPh)2]

[Tp*WO(SPh)2]

[Tp*WS(OPh)2]

[Tp*WS(SPh)2]

[WO(SPh)4]−

[WO(SePh)4]−

[WO(bdt)2]−

[WO(edt)2]−

[W(mdt)3]−

[W(bdt)3]−

[W(pdt)3]−

a

expt.65 PBE0 PBE0-40HF PBE0-50HF expt.41 PBE0 PBE0-40HF PBE0-50HF expt.41 PBE0 PBE0-40HF PBE0-50HF expt.62 PBE0 PBE0-40HF PBE0-50HF expt.62 PBE0 PBE0-40HF PBE0-50HF expt.66 PBE0 PBE0-40HF PBE0-50HF expt.75 PBE0 PBE0-40HF PBE0-50HF expt.67 PBE0 PBE0-40HF PBE0-50HF expt.76 PBE0 PBE0-40HF PBE0-50HF expt.40 PBE0 PBE0-40HF PBE0-50HF expt.40 PBE0 PBE0-40HF PBE0-50HF expt.40 PBE0 PBE0-40HF PBE0-50HF

Δgiso

Δg11

Δg22

Δg33

−229 −241 −254 −262 −217 −205 −218 −227 −137 −118 −133 −144 −321 −282 −300 −312 −162 −147 −168 −183 −66 −62 −76 −86 −25 −27 −43 −55 −40 −40 −55 −65 −21 −32 −49 −61 −8 −8 −12 −17 −11 −2 −26 −42 −9 −9 −12 −15

−244 −253 −258 −263 −295 −282 −301 −313 −197 −178 −194 −204 −443 −392 −413 −424 −218 −225 −246 −260 −99 −102 −114 −122 −79 −81 −98 −109 −91 −90 −101 −108 −96 −102 −114 −122 −15 −17 −21 −26 −58 −65 −78 −87 −12 −14 −16 −19

−244 −253 −258 −262 −200 −189 −198 −205 −159 −143 −156 −163 −309 −270 −286 −298 −190 −160 −182 −197 −99 −101 −114 −122 −79 −81 −98 −109 −71 −69 −80 −87 −81 −84 −96 −103 −1 −3 −8 −13 5 29 −1 −21 −1 −7 −10 −14

−198 −217 −245 −262 −155 −144 −155 −162 −56 −33 −51 −63 −210 −184 −200 −213 −78 −57 −77 −91 16 16 −1 −14 84 82 65 52 42 38 16 1 114 90 62 43 7 −3 −8 −13 21 31 2 −18 5 −7 −10 −13

Results with Hirao/IGLO-II basis at PBE0-D3(BJ)/def2-TZVP structures.

183

Aiso −226 −260 −283 −255 −218 −253 −276 −180 −146 −176 −196 −270 −220 −255 −279 −216 −154 −187 −210 −165 −116 −142 −159 −160 −99 −124 −142 −153 −109 −137 −155 −153 −111 −140 −159 −82 −60 −81 −100 −155 −124 −151 −168 −81 −52 −70 −87

A11

A22

A33

−163 −196 −219

−163 −196 −219

−381 −353 −388 −412

−160 −195 −218

−163 −198 −221

−329 −365 −389

−95 −125 −144

−106 −134 −153

−237 −269 −290

−158 −193 −218

−171 −205 −229

−331 −366 −390

−103 −136 −160 −133 −75 −99 −115 −130 −61 −84 −100 −111 −66 −93 −112 −119 −65 −93 −112 −33 −11 −25 −39 −177 −155 −184 −202 −36 −8 −19 −30

−120 −151 −172 −133 −75 −99 −115 −130 −61 −84 −100 −119 −72 −97 −115 −122 −74 −101 −118 −102 −85 −109 −131 −210 −164 −192 −211 −93 −75 −97 −116

−240 −275 −298 −234 −198 −227 −247 −222 −175 −205 −224 −235 −188 −219 −240 −217 −193 −225 −246 −96 −85 −109 −131 −78 −52 −76 −92 −90 −74 −96 −116

W hyperfine couplings in MHz, Δg values in ppt.

Given the rather high demands on the accuracy for the application to tungsten enzymes, and since local hybrid functionals, which might allow an improvement on isotropic HFCs without deteriorating g-tensors, currently are not yet available in the four-component code, this may force us to adopt a pragmatic protocol at this point in time: PBE0 may be used for g-tensor calculations but PBE0-40HF or PBE0-50HF are preferred for the metal HFCs (likely also for the ligand

Figure 4). The higher EXX admixture required for the metal HFCs is related to the description of the spin polarization of core-shell s orbitals, which is enhanced (improved) by larger EXX admixture in the core region,31,69−72 as recently confirmed also by preliminary evaluations with local hybrid functionals.73 The HFC anisotropies are less affected by core-shell spin polarization, and here the overall differences between the functionals tend to be small (Table 4). F


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Figure 4. Effect of EXX admixture (PBE0 vs PBE0-40HF vs PBE0-50HF) on deviations from the experimental Δg (ppt) and tensor components. Hirao/IGLO-II based calculations at PBE0-D3(BJ)/def2-TZVP structures.

PBE0 PBE0-40HF PBE0-50HF

Aiso

Δg anisotropyb

A anisotropy

10.3 12.5 20.0

38.5 12.9 10.3

7.4 12.0 16.3

8.9 12.1 14.2

W HFC (MHz)

relative scale for g shifts (with maximum solvent shifts of +14 ppt for g33 in [WOCl5]2− and of -10 to -14 ppt for g11 and g22 in [Tp*WE(XPh)2]) than for metal HFCs (with solvent-induced shifts of about 1−3 MHz for individual A-tensor components) but in general below the influence of varying the EXX admixture (PBE0 vs PBE0-40HF). However, the influence of a PCM in HFC calculations can become sizable for ligand atoms, which are more solvent-accessible as demonstrated, e.g., for the 77 Se HFC tensor in [WO(SePh)4]− (Table 6). The computed A33 value is reduced by 9 MHz (12%). This effect is larger than that of going from 25% to 50% EXX admixture. Furthermore, both effects (solvent model and increasing EXX admixture) act in the same direction, and their simultaneous application is required to achieve reasonable agreement with the experimental value. Direct solvent effects on the 17O HFCs in the same complex are small, however (Table 6). Basis-Set Effects. Given the relatively large size of models required to describe enzyme active sites (typically above 100 atoms), use of moderately sized basis sets might be desirable. In our previous study, the somewhat smaller relativistic Hirao/ IGLO-II basis-set combination gave EPR data in good agreement with those obtained with the larger Dyall(TZ)/ IGLO-III combination and provided partly even better agreement with experiment.31 This performance is confirmed here also for a range of selected complexes (Table S4 in the SI): remarkably, the Hirao/IGLO-II results again agree better with experiment in almost all cases. Given that the Dyall(TZ) basis is clearly larger and optimized within the four-component realm (the Hirao basis was optimized for DKH3 calculations), the excellent performance of the smaller basis may reflect some favorable error compensation.

Table 4. Mean Absolute Deviations (MAD) of Computed vs Experimental EPR Parameters over All Investigated Complexesa Δgiso

183

a

[WOCl5]2− is not included in the HFC MADs, and the Tp* complexes are not included for the HFC anisotropy due to missing experimental data. Values obtained at the mDKS-PBE0-xHF/Hirao/ IGLO-II level. MAD for Δg in ppt and for 183W HFC values in MHz. 1 b Anisotropy defined as Δgzz − 2 (Δgxx + Δgyy) with |Δgzz − Δgiso | ≥

|Δgyy − Δgiso | ≥ |Δgxx − Δgiso | (analogous definition used for the A anisotropy).

HFCs, which tend to also benefit from larger EXX admixtures; cf. Tables 5 and 6). We note in passing that one-component DKH2 calculations, which either neglect SO effects (on the HFCs) or include them only to leading order in perturbation theory (for both HFCs and g-tensors), cannot compete with the four-component relativistic methods with variational treatment of spin-orbit coupling (cf. Table S3 in the SI), consistent with our previous findings.31,74 Direct Solvent Effects. Evaluations of a PCM (cf. Computational Details) in the four-component relativistic calculations on selected complexes are provided in Tables 5 and 6. Since many complexes were characterized experimentally by EPR spectroscopy in frozen solutions of the highly polar CH3CN solvent (ε = 35.688) or its mixtures, we considered this solvent in our calculations. In contrast to indirect solvent effects due to minor structural changes upon solvation of the molecule (cf. Table 1), the direct solvent effects (change of the spin-density distribution in response to the solvent environment) are found to be more important. Here, the effect of the implicit solvent model is somewhat more pronounced on a

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EFFECTS OF SULFIDO VS OXO SUBSTITUTION IN SELECTED COMPLEXES One possible question for tungstoenzyme active sites may be if oxo or sulfido ligands are present.77 It is therefore of interest if such a substitution can be identified by EPR parameters alone G


Article

The Journal of Physical Chemistry A Table 5. Four-Component mDKS EPR-Parameter Results with and without a PCM Solvent Modela expt.65 PBE0

[WOCl5]2−

PBE0-40HF [Tp*WO(OPh)2]

expt.41 PBE0 PBE0-40HF

[WO(SPh)4]−


[WO(SePh)4]−


[WO(bdt)2]−


[W(bdt)3]−


a

gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN) gas phase PCM(CH3CN)

Δgiso

Δg11

Δg22

Δg33

−229 −241 −240 −254 −253 −217 −205 −214 −218 −227 −66 −62 −66 −76 −81 −25 −27 −33 −55 −63 −40 −40 −44 −55 −59 −11 −16 −8 −26 −29

−244 −253 −258 −258 −264 −295 −282 −291 −301 −311 −99 −102 −107 −114 −120 −79 −81 −93 −109 −122 −91 −90 −100 −101 −111 21 31 24 2 −2

−244 −253 −258 −258 −264 −200 −189 −202 −198 −210 −99 −101 −107 −114 −120 −79 −81 −93 −109 −122 −71 −69 −75 −80 −86 5 29 21 −1 −6

−198 −217 −203 −245 −231 −155 −144 −150 −155 −161 16 16 17 −1 −2 84 82 88 52 55 42 38 43 16 21 −58 −65 −68 −78 −80

Results with Hirao/IGLO-II basis at PBE0-D3(BJ)/def2-TZVP structures.

183

Aiso

A11

−226 −223 −260 −256 −255 −217 −219 −253 −254 −165 −116 −117 −142 −143 −160 −99 −97 −142 −139 −153 −109 −110 −136 −137 −155 −124 −127 −151 −154

A22

A33

−163 −161 −196 −193

−163 −161 −196 −193

−381 −353 −348 −388 −382

−160 −160 −195 −196 −133 −75 −76 −99 −100 −130 −61 −59 −100 −97 −111 −66 −67 −93 −93 −177 −155 −159 −184 −188

−163 −164 −198 −199 −133 −75 −76 −99 −100 −130 −61 −59 −100 −97 −119 −72 −73 −97 −98 −210 −164 −168 −192 −196

−329 −332 −365 −368 −234 −198 −200 −227 −230 −222 −175 −173 −224 −221 −235 −188 −189 −219 −220 −78 −52 −54 −76 −78

W hyperfine couplings in MHz, Δg values in ppt.

Table 6. Four-Component mDKS Results for Ligand Hyperfine Couplings of [WO(SePh)4]− with and without a PCM Solvent Modela −

[WO(SePh)4]

expt. PBE0

PBE0-50HF a

ASe iso

ASe 11

ASe 22

ASe 33

AOiso

AO11

AO22

AO33

14 11 13 9

−34 −34 −33 −35

2 1 3 0

55 74 67 69 60

5 5 10 9

8 8 14 13

8 8 14 13

−1 0 1 2

75

gas phase PCM(CH3CN) gas phase PCM(CH3CN)

Results with Hirao/IGLO-II basis at PBE0-D3(BJ)/def2-TZVP structures. 77Se and 17O hyperfine couplings in MHz, Δg values in ppt.

(in the absence of 17O labeling). This seems possible for the [Tp*WE(XPh)2] series which, however, does not closely resemble the active sites of tungstoenzymes. We have thus additionally considered the sulfido analogues [WS(bdt)2]− and [WS(edt)2]− of two of the complexes in our test set to get a broader picture. PBE0-D3(BJ)/def2/TZVP structures (Table 7) reveal the expected longer WS bond (by ca. 0.44 Å) and small further structural changes in the sulfido complexes compared to the oxo analogues, similar to those found within the [Tp*WE(XPh)2] series. Computed g-tensor principal values at the 4c-mDKS PBE0/ Hirao/IGLO-II level along with PBE0-50HF results for metal HFCs are collected in Table 8. A clear distinction between the [Tp*WE(OPh)2] (E = O, S) complexes by EPR spectroscopy is apparent: the thio-substituted complex has larger absolute g shifts (lower principal gii values). Notable differences between

Table 7. Effects of Sulfido vs Oxo Substitution on PBE0D3(BJ)/def2-TZVP-Optimized Structural Parameters [WO(bdt)2]− [WS(bdt)2]− [WO(edt)2]− [WS(edt)2]− [Tp*WO(OPh)2] [Tp*WS(OPh)2] [Tp*WO(SPh)2] [Tp*WS(SPh)2]

d(WS/O)ax (Å)

d(W−S/O)eq (Å)

1.700 2.136 1.703 2.146 1.704 2.149 1.703 2.141

2.396 2.380 2.416 2.384 1.954 1.946 2.391 2.378

the metal hyperfine couplings of these two complexes are also predicted computationally. We note that an exchange of the axial oxygen ligand results in an increase of the absolute Δgiso and Aiso values, whereas the H


Article

The Journal of Physical Chemistry A Table 8. Effects of Oxo vs Sulfido Substitution on Computed EPR Parametersa [WO(bdt)2]− [WS(bdt)2]− [WO(edt)2]− [WS(edt)2]− [Tp*WO(OPh)2] [Tp*WO(SPh)2] [Tp*WS(OPh)2] [Tp*WS(SPh)2]

Δgiso

Δg11

Δg22

Δg33

Aiso

A11

A22

A33

−40 −43 −32 −36 −205 −118 −282 −147

−90 −90 −102 −108 −282 −178 −392 −225

−69 −70 −84 −87 −189 −143 −270 −160

38 31 90 86 −144 −33 −184 −57

−155 −173 −159 −174 −276 −196 −279 −210

−112 −128 −112 −129 −218 −144 −218 −160

−115 −140 −118 −140 −221 −153 −229 −172

−240 −251 −246 −253 −389 −290 −390 −298

a

PBE0 results for the g-tensor, PBE0-50HF data for the HFC tensor, using Hirao/IGLO-II basis sets and PBE0-D3(BJ)/def2-TZVP structures. 183W hyperfine couplings in MHz, Δg values in ppt.

computed EPR data, requiring thus a careful choice of optimized or experimental input structures. The optimum amount of EXX admixture in PBE0-type hybrid functionals for g-tensor data was found to depend on the magnitude of spin-orbit effects, as reflected in the |Δgiso| value: systems with isotropic g shifts below 100 ppt require (only) the 25% exact-exchange admixture included in the PBE0 hybrid functional, whereas larger admixtures of about 40% are recommended for systems with |Δgiso| > 100 ppt (the optimal value might, however, be up to 50% for systems with |Δgiso| > 300 ppt, as shown for [Tp*WS(OPh)2]). On the other hand, the best metal hyperfine tensors are generally provided at an EXX admixture of 40−50%. Notably, these choices are based on the inclusion of higher-order spin-orbit contributions within the four-component relativistic DFT framework. Until better and more sophisticated relativistic electronic-structure methods (such as, e.g., DMRG, coupled-cluster, and configuration interaction approaches) become routinely applicable to large transition-metal complexes, such a combined protocol may currently offer the best compromise. The somewhat more affordable Hirao/IGLO-II basis-set combination was found to perform as well as the larger Dyall(TZ)/IGLO-III combination and is therefore a reasonable choice for applications to larger tungstoenzyme target systems. Differences in the EPR parameters between oxo-W(V) and sulfido-W(V) dithiolene analogues are predicted here to be rather small for those structures that are more closely related to tungsten-enzyme active sites, which may render identification of this substitution by EPR parameters alone difficult.

opposite trend is observed for a substitution in the equatorial position(s). This effect is found to follow certain features of the electronic structure (Table 9): increasing spin densities at the Table 9. Spin Densities from Natural Population Analyses (NPA) and HOMO-LUMO Gaps for Selected Complexesa ΔEHOMO,α−LUMO,α

NPA spin densities [WO(bdt)2]− [WS(bdt)2]− [Tp*WO(OPh)2] [Tp*WO(SPh)2] [Tp*WS(OPh)2] [Tp*WS(SPh)2]

W

Eax

Xeq

[eV]

0.939 0.949 0.880 0.867 0.915 0.903

−0.053 −0.079 −0.060 −0.053 −0.088 −0.080

0.002 0.005 0.047 0.027 0.045 0.023

4.67 3.85 3.89 4.10 3.12 3.24

PBE0-D3(BJ)/def2-TZVP results. “WEax(Xeq)” structural motifs with E, X = O, S. a

tungsten center and decreasing HOMO−LUMO gaps lead to increased absolute Δgiso and Aiso values (this becomes apparent only in a perturbational analysis but is inherent in the polarization of the spinors), and vice versa. While changes in the HOMO−LUMO gaps are of similar magnitude for the axial O → S substitutions, the smaller effect on the giso value of [WS(bdt)2]− compared to [Tp*WS(OPh)2] is due to a smaller change in the metal spin densities. However, in spite of rather large changes in the HOMO− LUMO gap (Table 9), differences in the EPR parameters of [WO(bdt)2]− vs [WS(bdt)2]− and of [WO(edt)2]− vs [WS(edt)2]− are at best moderate (Table 8). Based on the benchmarking reported above, it is currently unclear if these small differences can be distinguished computationally beyond any doubt in models for tungstoenzyme active sites. However, trends may be easier to detect for a series of complexes, or the combination with further spectroscopic techniques (such as, e.g., EXAFS, IR, and pNMR) may help to distinguish such species.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b08768. Cartesian coordinates of optimized structures. (XYZ) Effects of artificial structure modifications, Dyall(TZ)/ IGLO-III data, an overlay of the experimental and optimized structures for [W(mdt)3]2−/[W(mdt)3]−, and an assessment of the importance of (higher-order) spinorbit effects. (PDF)

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CONCLUSIONS As a basis for subsequent applications to EPR spectra of the W(V) state of tungsten enzyme active sites, we have calibrated a four-component relativistic DFT methodology to be applied to both g-tensors and metal hyperfine coupling tensors. Based on our recent benchmarking for a wider set of 4d and 5d complexes, we have now fine-tuned the methodology for a series of synthetic W(V) complexes closer to the tungsten active site targets, including a number of dithiolene and thiolate ligands. W−S bond lengths were found to be important for the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Peter Hrobárik: 0000-0002-6444-8555 Martin Kaupp: 0000-0003-1582-2819 I


Article

The Journal of Physical Chemistry A Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been funded within the Berlin DFG excellence cluster on Unifying Concepts in Catalysis (UniCat). S.G. is indebted to the German National Academic Foundation (Studienstiftung des deutschen Volkes) for financial support and thanks Jan Vı ́cha for stimulating discussions. The authors thank S. Komorovský and M. Repiský for technical assistance with the ReSpect code.

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