Nonoxido VIV Complexes: Prediction of the EPR Spectrum and

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Nonoxido VIV Complexes: Prediction of the EPR Spectrum and Electronic Structure of Simple Coordination Compounds and Amavadin Daniele Sanna,† Giuseppe Sciortino,§ Valeria Ugone,§ Giovanni Micera,§ and Eugenio Garribba*,§ †

Istituto di Chimica Biomolecolare, Consiglio Nazionale delle Ricerche, UOS di Sassari, Trav. La Crucca 3, I-07040 Sassari, Italy Dipartimento di Chimica e Farmacia, Università di Sassari, Via Vienna 2, I-07100 Sassari, Italy

§

S Supporting Information *

ABSTRACT: Density functional theory (DFT) calculations of the 51V hyperfine coupling (HFC) tensor A have been completed for 20 “bare” VIV complexes with different donor sets, electric charges, and coordination geometries. Calculations were performed with ORCA and Gaussian software, using functionals BP86, TPSS0, B1LYP, PBE0, B3LYP, B3P, B3PW, O3LYP, BHandHLYP, BHandH, and B2PLYP. Among the basis sets, 6-311g(d,p), 6-311++g(d,p), VTZ, cc-pVTZ, def2TZVPP, and the “core properties” CP(PPP) were tested. The experimental Aiso and Ai (where i = x or z, depending on the geometry and electronic structure of VIV complex) were compared with the values calculated by DFT methods. The results indicated that, based on the mean absolute percentage deviation (MAPD), the best functional to predict Aiso or Ai is the double hybrid B2PLYP. With this functional and the basis set VTZ, it is possible to predict the Aiso and Az of the EPR spectrum of amavadin with deviations of −1.1% and −2.0% from the experimental values. The results allowed us to divide the spectra of nonoxido VIV compounds in three typescalled “type 1”, “type 2”, and “type 3”, characterized by different composition of the singly occupied molecular orbital (SOMO) and relationship between the values of Ax, Ay, and Az. For “type 1” spectra, Az ≫ Ax ≈ Ay and Az is in the range of (135−155) × 10−4 cm−1; for “type 2” spectra, Ax ≈ Ay ≫ Az and Ax ≈ Ay are in the range of (90−120) × 10−4 cm−1; and for the intermediate spectra of “type 3”, Az > Ay > Ax or Ax > Ay > Az, with Az or Ax values in the range of (120−135) × 10−4 cm−1. The electronic structure of the VIV species was also discussed, and the results showed that the values of Ax or Az are correlated with the percent contribution of V-dxy orbital in the SOMO. Similarly to VIVO species, for amavadin the SOMO is based mainly on the V-dxy orbital, and this accounts for the large experimental value of Az (153 × 10−4 cm−1).

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relatively scarce and is much smaller than that of the “usual” VIVO species. Until now, nonoxido V(IV) structures with VO3S3,13 VO6,14 VS6,15 VO4N2,16 VO4X2 (X = S, Se, P),17 VO4X2 and VS4X2 (X = Cl, Br)18 and, recently, VO2N2S219 coordination have been reported. The formation of these species is significantly favored by the preorganization of the tridentate ligand, as occurs in the case of cis-inositol derivatives.20 However, this rare and unusual family of compounds has a great importance in biology, because V is accumulated in three species of mushrooms of the genus Amanita (A. muscaria, A. regalis, and A. velatipes) as a nonoxido VIV complex called amavadin.1,2 In A. muscaria, the vanadium content exceeds 400 times the value normally detected in other species of the same genus and is independent of the V concentration in the soil. The role of vanadium in the Amanita is still elusive, but the ability of amavadin to act as an electron-transfer mediator in the oxidation of some biological thiols may support a role as a

INTRODUCTION Vanadium is an important trace element for different organisms.1,2 Among others, it is present in vanadiumdependent haloperoxidases,3 in nitrogenases,4 and is accumulated in concentrations up to 0.3 M in the vanadocytes of ascidians and polychaete worms.5 Vanadium has also an important role in the human organism, and it is probably involved in the regulation of phosphate metabolism.6 In humans, V compounds exhibit a wide variety of pharmacological properties, and many complexes have been tested as antiparasitic, spermicidal, antiviral, anti-HIV, antituberculosis, and antitumor agents.7 Particularly, vanadium compounds have therapeutic effects as potential antidiabetic agents,8 whose behavior in the blood9 and cellular environment10,11 was studied by this group and other teams. The chemistry of vanadium(IV) is dominated by the VIVO2+ ion. The formation of nonoxido or “bare” hexa-coordinated VIV complexes is rather difficult because the strong VO bond must be broken and the oxido ligand must leave the complex as a water molecule. The number of “bare” VIV species found within the Cambridge Structural Database12 still remains © XXXX American Chemical Society

Received: February 18, 2016

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DOI: 10.1021/acs.inorgchem.6b00409 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry cofactor in oxidoreductases.2 Amavadin, which was isolated in 1972 by Bayer,21 is a low-molecular-mass, anionic nonoxido VIV compound derived from the ligand N-hydroxyimino-2,2′diisopropionic acid, (S,S)-H3hidpa (Scheme 1a), in its

with Ai (where i = x or z, depending on the geometry and electronic structure of the species), beyond these extremes can result in an incorrect interpretation of an EPR spectrum. Depending on the specific ligand, for a hexa-coordinate nonoxido VIV complex, several types of geometry (octahedral and trigonal prismatic)27 and isomerism (facial or meridional when the ligand is tridentate)16c,17 are possible. The ground state and the EPR spectrum vary accordingly.24b In the literature, EPR spectra of hexa-coordinated VIV complexes were divided on the basis of g and A values: those with gz ≪ gx ≈ gy < 2.0023 and Az ≫ Ax ≈ Ay with a geometry close to an octahedron and those with gx ≈ gy ≪ gz ≈ 2.0023 and Ax ≈ Ay ≫ Az with a geometry that approaches the limit represented by the trigonal prism.28 With bidentate ligands forming fivemembered chelate rings such as o-catechols, o-mercaptophenols, and dithiolenes, the geometry is close to the trigonal prism and there is a change of the ground state from predominant occupation of V-dxy by the unpaired electron, characteristic of VIVO species, to the occupation of other V dorbitals.29 We recently demonstrated that, for tridentate ligands with meridional coordination, the first type of spectrum with gz ≪ gx ≈ gy < 2.0023 and Az ≫ Ax ≈ Ay is observed,30 whereas, for those with facial coordination, an intermediate spectrum is detected.31 For tris-chelated species formed by bidentate ligands, the degree of distortion of the octahedron can be expressed by the twist angle Φ between the triangular faces of the coordination polyhedron (Φ is 60° for a regular octahedron and 0° for a trigonal prism; see Schemes 2a and 2b),15a and for

Scheme 1. Structures of (a) the ligand (S,S)-H3hidpa, (b) the VIV Complex Called Amavadin, and (c) the VIVO Structure Initially Proposed for Amavadin (Adapted from ref 1)

Scheme 2. Definition of (a) the Angle Φ for an Octahedron; (b) the Angle Φ for a Trigonal Prism, and (c) the Angle Ω for the mer and fac Coordination of a Tridentate Ligand

trianionic form hidpa(3−).1,2 Initially, spectroscopic data of amavadin were consistent with an “usual” VIVO2+ species;21 in fact, the solutions containing amavadin are light blue. This interpretation was doubted some years later when a very large value for the overall stability constant (log β2) of the biscomplex formed by VIV with H3hidpa and its analogue Nhydroxyiminodiacetic (H3hida) was measured. Further studies allowed assigning an eight-coordinated structure for amavadin.22 The X-ray structure of the calcium salt of amavadin, [Ca(H2O)5][V((S,S)-hidpa)2]·2H2O, showed that the VIV coordination sphere involves two η2-N,O− groups and four monodentate carboxylate groups (see Scheme 1b).23 The instrumental technique most widely used for the characterization of VIV complexes is EPR spectroscopy.24 It was the EPR spectrum of amavadin that suggested the misleading interpretation of its structure, described as a VIVO species (Scheme 1c). In fact, the 51V hyperfine coupling constant along the z axis (Az) of (152.8−153.0) × 10−4 cm−1 22,25 was compatible, on the basis of the additivity rule,24a,c,26 with a structure with the bidentate coordination of the ligand (S,S)-Hhidpa(2−) through the equatorial binding of N and COO− donors. Generally, a 51V anisotropic hyperfine coupling (HFC) constant in the range of (150−180) × 10−4 cm−1 is detected for VIVO species,24a,c whereas a value significantly smaller, in the range of (90−140) × 10−4 cm−1, is observed for “bare” VIV complexes.24b Therefore, values of the largest HFC constant, indicated in this work generically

bis-chelated complexes of tridentate ligands by the angle Ω formed by the two external donors of the ligand at the V atom (180° for a mer isomer and 90° for a fac isomer, Scheme 2c).30 When a single-crystal X-ray diffraction (XRD) analysis is lacking, further tools to support EPR assignment appear to be necessary. Nowadays, density functional theory (DFT) B


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Inorganic Chemistry

The optimized Cartesian coordinates are reported in Tables S1−S20 in the Supporting Information, and the comparison between the calculated and experimental X-ray structures available in the literature (complexes [V(cat)3]2−, [V(bdt)3]2−, [V(dmit)3]2−, [V(mnt)3]2−, [V(LN)2], [V(LS)2], [V(mmp)3]2−, [V(pdbh)2], [V(dhab)2], [V(taci)2]4+, [V(L1)2], and [V(L2)2]) is presented in Tables S21−S32 in the Supporting Information. As it can be observed, the agreement between the experimental and calculated structures is very good and the percentage deviation from the experimental bond lengths and angles is usually < 2%, and only in three cases (two lengths and one angle) exceeds 5%. The 51V HFC tensor A was calculated according to the procedures reported in the literature,44 with the exchange-correlation functional BP86 (Becke ‘88 exchange and Perdew ‘86 correlation),45,46 the hybrid meta-GGA functional TPSS0 (25% exchange of TPSSh, the hybrid version of TPSS meta-GGA functional),47 the one-parameter hybrid functionals B1LYP48,49 and PBE0 (the hybrid version of Perdew− Burke−Erzerhoff GGA functional),50 the three-parameter hybrid functionals B3LYP (the popular functional that includes 20% HF exchange),51,52 B3P (the hybrid version of P86),46a,51 and B3PW (the hybrid version of PW91),51,53 the Handy hybrid functional O3LYP,54 the half-and-half hybrid functionals BHandHLYP and BHandH,40 and the double hybrid functionals B2PLYP (that includes a second-order perturbation correction for nonlocal correlation effects).55 The basis sets 6-311g(d,p)56 and VTZ57 were used for all the 20 VIV complexes. Preliminary calculations on [V(axhm)3]2− and [V(taci)2]4+ were carried out also with other basis sets, such as cc-pVTZ,58 def2TZVPP,57,59 6-311++g(d,p),56 and a general set obtained using ORCA “core properties” CP(PPP)41a on V and VTZ on the other atoms (indicated with CP(PPP)/VTZ). The ratio between the computational time compared with VTZ is ∼100 for cc-pVTZ, ∼40 def2-TZVPP, ∼10 for 6-311++g(d,p), ∼3 for 6-311g(d,p) and ∼2 for CP(PPP)/ VTZ. For all the functionals, spin contamination was found to be small and the eigenvalue of the spin operator ⟨S2⟩ was always TPSS0 ≈ O3LYP > PBE0 ≫ B3P > B3PW ≫ B1LYP

(16)

> BHandH > BHandHLYP > B3LYP > BP86

where N is the number of HFC constants examined (N = 20 for Ai and N = 14 for Aiso).

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whereas, based on the MAPD, the ranking is

RESULTS AND DISCUSSION Twenty VIV complexes with different donors (O, N, S), coordination mode (bidentate or tridentate), electric charge (−8, −2, 0, +1, +4), and coordination geometry (octahedral or trigonal prismatic) were studied. The structure of the ligands is represented in Scheme S1 in the Supporting Information, whereas that of VIV species in Schemes S2−S5 in the Supporting Information. For all these compounds, the 51V anisotropic HFC constants (Ax,y,z) were available, whereas the isotropic constants (Aiso) were reported for only 14 of them (Table 1). In Table 1, the experimental g factors and A constants are listed; however, the present work has been limited to the calculation of A and its comparison with the experimental values, while the accurate calculation of the g tensor for these complexes is currently in progress. 1. Prediction of the 51V A Tensor as a Function of the Functional and the Basis Set. The best DFT method to predict the 51V HFC A tensor for VIVO complexes uses halfand-half functionals such as BHandHLYP or BHandH, and a triple-ζ basis set plus polarization functions such as 6311g(d,p).35a Therefore, as a first step, the basis set 6311g(d,p) was fixed and functionals were varied. Several types of functionals were used: exchange-correlation functionals such as BP86,45,46 the hybrid meta-GGA functional TPSS0,47 the one-parameter hybrid functionals such as B1LYP48,49 and PBE0,50 the three-parameter hybrid functionals such as B3LYP,51,52 B3P46a,51 and B3PW,51,53 the Handy hybrid functional O3LYP,54 half-and-half hybrid functionals such as BHandHLYP and BHandH,40 and the double hybrid functional B2PLYP.55 The values of Aiso, and of Ax, Ay, Az calculated with these functionals are reported in Tables S33−S44 in the Supporting Information.

B2LYP > TPSS0 ≈ O3LYP ≈ PBE0 ≫ B3P > B3PW ≫ BHandH ≈ B1LYP > BHandHLYP > B3LYP ≫ BP86

(see Figure 1 and Figure S1 in the Supporting Information).

Figure 1. Mean absolute percentage deviation (MAPD) from experimental Aiso calculated with ORCA software using several functionals and the 6-311g(d,p) basis set. B2PLYP* refers to the calculation performed with the B2PLYP functional and VTZ basis set.

As mentioned in the Introduction, EPR spectra of hexacoordinated VIV complexes can be divided into those with Az ≫ Ax ≈ Ay (geometry close to the octahedron) and those with Ax ≈ Ay ≫ Az (geometry close to the trigonal prism).28 Therefore, if the axis with the highest symmetry is the z axis, in the transformation from an octahedron to a trigonal prism, the largest value of A changes from Az to Ax (this is due to the E


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Inorganic Chemistry elements in the diagonalized tensor AD: ADz , the highest value of the tensor, is negative in the first case and adds to Aiso, whereas it is positive in the second case and subtracts from Aiso). When an anisotropic spectrum is considered, the most important datum is the highest value of A, Ax or Az, depending on the type of spectrum. In Table S46 in the Supporting Information, the values of Ai calculated with the functionals tested are listed. Based on the MPD, the order of accuracy of the functionals in the prediction of Ai is

PBE0 has been already discussed in the literature.30,31,37,38 (7) The double hybrid B2PLYP behaves better than all of the other functionals, in terms of prediction of Aiso and Ai. It allows calculating Aiso with MPD and MAPD values of −4.1% and 8.2%, and Ai with MPD and MAPD values of −0.9% and 3.3% (see Figures 1 and 2 and Figures S1 and S2). Therefore, the functional with the best performance, in the prediction of both the isotropic or anisotropic 51V HFC constants, is the double hybrid B2PLYP;55 the technical details about it are given in the Computational Section. It gives encouraging results in the prediction of thermodynamic data:62,65a,c,76 for example, barrier heights,65b isomerization energies,77 and transition-metal reactions78 were well-simulated. Moreover, it has been also applied to the prediction of circular dichroism (CD) spectra79 and magnetic coupling constants,80 and to the calculation of excited states of polycyclic aromatic hydrocarbons.79 Neese and co-workers investigated, with good results, the performance of this functional in the prediction of molecular hyperfine couplings for a series of small radicals and transition-metal complexes.81 In Table 2, all the components of the 51V A tensor calculated with the B2PLYP functional and the 6-311g(d,p) basis set for 20 VIV complexes are reported. Note that the prediction of Ai is particularly good with PD values (eq 13) between −8.4% and 5.3% (excluding the rather large value of 10.4% for [V(mnt)3]2−). One must remember that, until now, the best results obtained in the literature with PBE0 functional and VTZ basis set allowed a prediction of Ai with APD values (eq 14) no less than 6% and with an MPD value of −9.1%.30,31,37,38 After determining the best functional, we compared the prediction obtained fixing B2PLYP and varying the basis set. In particular, beside 6-311g(d,p), we tested VTZ, which, for VIVO complexes, gave better performance than other sets.35b Preliminary calculations on [V(axhm)3]2− and [V(taci)2]4+ with other basis sets, such as cc-pVTZ,58 def2-TZVPP,57,59 6311++g(d,p),56 and a general set obtained using ORCA “core properties” CP(PPP)41a on V and VTZ on the other atoms (CP(PPP)/VTZ), did not give significant improvement in the prediction of the 51V HFC A tensor. For example, for is 18.5 × 10−4 cm−1 (wrong algebraic [V(axhm)3]2−, Acalcd iso sign) with cc-pVTZ, 19.5 × 10−4 cm−1 (wrong algebraic sign) with def2-TZVPP, −63.1 × 10−4 cm−1 with 6-311++g(d,p), and −64.4 × 10−4 cm−1 with CP(PPP)/VTZ, whereas they are −64.0 × 10−4 cm−1 with 6-311g(d,p) and −67.5 × 10−4 cm−1 with VTZ, to be compared with an experimental value of −68 and Acalcd are, respectively, × 10−4 cm−1; for [V(taci)2]4+, Acalcd x y −4 −1 108.4 × 10 cm (wrong algebraic sign) and −27.7 × 10−4 cm−1 with cc-pVTZ, 110.5 × 10−4 cm−1 (wrong algebraic sign) and −26.9 × 10−4 cm−1 with def2-TZVPP, −95.2 × 10−4 cm−1 and −91.9 × 10−4 cm−1 with 6-311++g(d,p), and −96.6 × 10−4 cm−1 and −93.6 × 10−4 cm−1 with CP(PPP)/VTZ, whereas they are −95.5 × 10−4 cm−1 and −92.0 × 10−4 cm−1 with 6311g(d,p) and −98.8 × 10−4 cm−1 and −96.0 × 10−4 cm−1 with VTZ, to be compared with experimental values of −99.4 × 10−4 cm−1 and −97.2 × 10−4 cm−1. From these data, it emerges that 6-311g(d,p) behaves better than 6-311++g(d,p) among the Pople basis sets, and VTZ better than the “general” CP(PPP)/ VTZ set among those developed by Ahlrichs; instead, cc-pVTZ and def2-TZVPP did not give encouraging predictions. The

B2LYP ≫ TPSS0 > PBE0 > O3LYP > B3P ≈ B3PW > B1LYP ≈ BHandH > BHandHLYP > B3LYP ≫ BP86

whereas, based on the MAPD, the ranking is B2LYP ≫ TPSS0 > O3LYP > PBE0 > B3P ≈ B3PW > BHandH > B1LYP ≈ BHandHLYP > B3LYP ≫ BP86

(see Figure 2 and Figure S2 in the Supporting Information).

Figure 2. Mean absolute percentage deviation (MAPD) from experimental Ai calculated with ORCA software using several functionals and the 6-311g(d,p) basis set. B2PLYP* refers to the calculation performed with B2PLYP functional and VTZ basis set. (It must be taken into account that Ai is related to Aiso through eqs 8−11.)

From these data, it emerges that (1) All the functionals underestimate both Aiso and Ai, with MPD values from −27.6% to −4.1% for Aiso and from −24.1% to −0.9% for Ai (see Figures S1 and S2). (2) The MAPD values go from 27.6% to 8.2% for Aiso and from 24.1% to 3.3% for Ai (see Figures 1 and 2). (3) The exchange-correlation functional BP86 gives the worst results, with the MPD larger than 20% both for Aiso and Ai. It should not be used for computations of the EPR parameters of a VIV species. (4) The two half-and-half functionals, which give the best performance in the prediction of Aiso and Az for VIVO complexes, fail with “bare” VIV species. The main reason is the underestimation of Aiso (MAPD of 23.1% and 21.5% for BHandHLYP and BHandH, respectively). (5) The popular B3LYP functional does not perform very well and cannot be recommended for such types of calculations. (6) Only the functionals PBE0, TPSS0, O3LYP, and B2PLYP give an absolute value of MPD and MAPD below 10% for Aiso and Ai. The good performance of F


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Inorganic Chemistry

Table 2. Components of the 51V HFC A Tensor for VIV Complexes Calculated with ORCA Software Using the B2PLYP Functional and the 6-311g(d,p) Basis Seta complex 2−

[V(cat)3] [V(dhp)3]+ [V(dhm)3]8− [V(hpo)3]+ [V(mpo)3]+ [V(bdt)3]2− [V(dmit)3]2− [V(mnt)3]2− [V(LN)2] [V(LS)2] [V(mmp)3]2− [V(pdbh)2] [V(axhm)3]2− [V(sal-NSO)2] [V(dhab)2] [V(hypPh)2] [V(bhpp)2] [V(taci)2]4+ [V(L1)2] [V(L2)2]

AFC

ADx

ADy

ADz

ASO x

ASO y

ASO z

Aiso

PD (Aiso)b

Ax

Ay

Az

PD (Ai)b,c

−59.5 −59.1 −63.3 −57.8 −58.8 −56.7 −85.5 −61.9 −63.4 −53.8 −61.5 −51.8 −55.1 −59.0 −57.1 −63.2 −64.7 −44.0 −65.1 −47.0

−33.9 −51.8 −37.2 −33.1 −31.5 −28.9 −20.1 −26.6 36.1 49.2 −31.4 50.1 −32.4 −47.5 −55.6 32.9 32.0 −37.7 −39.5 33.9

−31.8 −9.8 −25.7 −33.0 −31.2 −27.5 −14.6 −24.1 33.2 12.8 −31.3 10.8 −32.2 −10.5 0.0 35.9 32.4 −33.9 −19.6 31.1

65.7 61.6 62.9 66.0 62.7 56.4 34.7 50.7 −69.3 −62.0 62.7 −61.0 64.5 58.0 55.6 −68.8 −64.4 71.6 59.1 −64.9

−14.3 −13.9 −13.2 −12.7 −11.4 −12.2 −13.5 −12.0 −8.0 −3.5 −13.9 −4.7 −12.6 −11.8 −9.0 −9.8 −12.0 −13.8 −13.9 −6.8

−14.3 −13.8 −11.5 −12.7 −11.3 −12.2 −15.6 −12.1 −9.0 −8.1 −13.9 −5.5 −12.6 −7.2 −9.8 −8.2 −3.0 −14.1 −6.7 −4.0

−1.6 −2.1 −2.2 −1.2 −3.0 −7.0 21.1 −13.0 −10.4 −12.2 −3.6 −10.3 −1.7 −4.1 −2.5 −10.2 −12.2 −0.9 −4.7 −9.7

−69.6 −69.0 −72.2 −66.7 −67.4 −67.1 −88.1 −74.3 −72.5 −61.7 −71.9 −58.7 −64.0 −66.7 −64.2 −72.6 −73.8 −53.6 −73.6 −53.8

−8.5 −9.2 d −5.0 4.0 11.9 d d d d 1.3 −10.8 −5.8 d −4.2 −11.8 −6.7 −11.0 11.9 −12.9

−107.7 −124.8 −113.6 −103.6 −101.7 −97.8 −119.0 −100.5 −35.2 −8.1 −106.7 −6.4 −100.0 −118.3 −121.7 −40.1 −44.7 −95.5 −118.5 −19.8

−105.6 −82.7 −100.5 −103.5 −101.4 −96.4 −115.7 −98.0 −39.2 −49.1 −106.7 −46.5 −99.8 −76.7 −66.8 −35.6 −35.4 −92.0 −91.4 −19.9

4.6 0.4 −2.6 7.0 0.9 −7.3 −29.7 −24.3 −143.1 −128.0 −2.3 −123.1 7.8 −5.1 −4.0 −142.2 −141.3 26.7 −10.8 −121.6

0.6 4.0 −3.7 −8.4 −2.2 2.9 5.3 10.4 −2.7 −0.9 −7.2 −1.4 0.0 −4.6 −0.5 −0.7 −0.5 −4.0 −0.9 −4.2

a All the values reported in units of 10−4 cm−1. bPercentage deviation (PD) defined in eq 13. cAz for [V(LN)2], [V(LS)2], [V(pdbh)2], [V(hypPh)2], [V(bhpp)2], and [V(L2)2], and Ax for all the other compounds. dValues of Aexptl iso not reported in the literature.

inclusion gives a more complete and physically meaningful description of the HFC A tensor for a transition-metal complex. The values of MPD from the experimental Aiso and Ai without the inclusion of the second-order SO term in the eqs 8−11 are reported in Figures S3 and S4 in the Supporting Information. It is evident that such a term allows for significant improvement in the prediction of Aiso and Ai (for example, if functional B2PLYP is taken into account, MPD for Aiso goes from −15.3% without SO contribution to −4.1%, and, for Ai, it goes from −10.5% without SO to −0.9%). As a second comment, a double hybrid functional such as B2PLYP must be used. It is well-known that many GGA functionals overestimate the covalency of M−L bonds, transferring too much spin density to the ligands and giving an absolute value of the HFC constant that is too small; in contrast, HF terms acts in the opposite direction and predicts M−L bonds that are too ionic, resulting in a large absolute value of A.34d,82 Therefore, the high fraction HF exchange in double hybrid functionals such as B2PLYP produces a better prediction of the Fermi contact term AFC (and, hence, of Aiso) than the other functionals (note that this term is significantly underestimated by most of the DFT calculations).34d,83 Now, it can be interesting to compare the experimental EPR spectrum of [V(taci)2]4+ with those predicted by B3LYP, PBE0, and B2PLYP functionals (with the 6-311g(d,p) basis set fixed). As it is known, B3LYP is the most popular and most used functional, PBE0 gives, until now, the best results for nonoxido VIV species,30,31,37,38 and B2PLYP is the most promising functional, based on the data of this work. The results are shown in Figure 3. It is evident that all three functionals give a qualitative representation of the spectrum, but B2PLYP also allows one to obtain a good quantitative agreement and the spectrum predicted is almost superimposable to the experimental one. In particular, B2PLYP simulates better than the other functionals Ax and Ay, which account for the total width

results obtained with B2PLYP functional and VTZ basis set are shown in Table S47 in the Supporting Information. Overall, the data can be represented graphically plotting the values of MPD and MAPD for Aiso and Ai in a histogram. This has been shown in Figures 1 and 2, as well as Figures S1 and S2. Note that the performances of the two basis sets are comparable, with VTZ and 6-311g(d,p) being the best in the prediction of Aiso and Ai, respectively. From an examination of Figure 1, it is possible to notice that the MAPD from the experimental value of Aiso is ∼8% and 170°. In these cases, the SOMO is based mainly on the V-dxy orbital (>90%) with a small contribution ( Az, with Az or Ax in the approximate range of (120−135) × 10−4 cm−1. In the next paragraphs, the electronic structure and the MOs composition, as well as their relationship with the experimental EPR spectrum and the HFC constants, will be discussed. Two groups of three “bare” VIV species were chosen: [V(hyphPh)2] (“type 1” spectrum), [V(dhp)3]+ (“type 2”) and [V(LS)2] (“type 3”) are debated in the main text, whereas [V(bhpp)2] (“type 1” spectrum), [V(hpo)3]+ (“type 2”), and [V(L2)2] (“type 3”) are illustrated in the Supporting Information. The EPR spectra of [V(hyphPh)2], [V(dhp)3]+, and [V(LS)2] are shown in Figure 5, and those of [V(bhpp)2], [V(hpo)3]+, and

Figure 6. Singly occupied molecular orbitals (SOMOs) for (a) [V(dhp)3]+, (b) [V(LS)2], (c) [V(hyphPh)2], and (d) amavadin. The position of the three Cartesian axes is indicated close to each structure. In [V(hyphPh)2], Ph indicates the phenyl rings, whereas in [V(LS)2], tBu indicates the tert-butyl groups; neither of them contribute to the SOMO. SOMOs were calculated with ORCA software, using the B2PLYP functional and the VTZ basis set.

that, whereas for [V(hyphPh)2] and amavadin (spectra of “type 1”) the SOMO is based essentially on V-dxy, for [V(dhp)3]+ (spectrum of “type 2”) it is very different and has components not only on the xy plane but also on the xz and yz planes; even if it resembles the V-dz2, it is a composite orbital generated by the mixing of V-dxy (accounting for the electron density in the xy plane) with V-dxz and V-dyz (accounting for the electron density along the z axis and the peculiar shape, similar to the simple dz2 atomic orbital). The SOMO for [V(LS)2] (spectrum of “type 3”) is located mainly on the xy plane, because the main contribution comes from V-dxy, but the non-negligible mixing with the V-dxz, V-dyz, and V-dz2 orbitals accounts for the part along the z axis. The SOMOs for the other three nonoxido VIV complexes that were taken as examples ([V(bhpp)2], [V(hpo)3]+, and [V(L2)2], which give EPR spectra of “type 1”, “type 2”, and “type 3”) are reported in Figure S7 in the Supporting Information. To account for the reduction of HFC constant along the z axis (this case is taken as an example) for “bare” VIV species when the mixing of V-dxz, V-dyz, V-dx2−y2, or V-dz2 orbital with V-dxy occurs, the complexes for which the largest A is Az (i.e., [V(LN)2], [V(LS)2], [V(pdbh)2], [V(hyphPh)2], [V(bhpp)2], and [V(L2)2]; see Table 1) were considered. A similar discussion can be applied also to explain the small values of Ax for the other compounds examined in this work (i.e., those for which the largest value of A is Ax; see Table 1). The equations that relate the value of Az with the dipolar term Pd (∼128 × 10−4 cm−1 for VIV 87), the Fermi contact κ (∼0.85 for VIV 87), the spin−orbit coupling constant λ (∼250 cm−1 for

Figure 5. Experimental EPR spectra of nonoxido VIV complexes: (a) [V(dhp)3]+ (“type 2”); (b) [V(LS)2] (“type 3”), and (c) [V(hyphPh)2] (“type 1”). The experimental MI = −7/2, 7/2 resonances along the x or z axes are indicated by the dotted lines.

[V(L2)2] are shown in Figure S6 in the Supporting Information. From an examination of Figure 5 and Figure S6, it can be observed that a “type 1” spectrum closely resembles that of a VIVO complex, whereas the small value of Ax or Az and the spectral pattern for “type 2” and “type 3” are, instead, indicative of the formation of a “bare” VIV species. The spectrum of amavadin belongs to “type 1” and, for this reason, resembles that of a VIVO compound; in fact, the geometry is close to an octahedron and the contribution of Vdxy in the SOMO approaches 100% (it is 99.4% for amavadin and, for example, 100% for [VO(H2O)5]2+; see Table 4). The data of our calculations confirm the similar spectral and electronic properties of VIVO species and amavadin, already suggested by discrete variational (DV Xα) calculations.86 As pointed out by Armstrong et al.,86 such a similarity is related to the strong ligand field in the axial direction, because of the VO bond in the first case and the two donors of the η2-NO− group in the second one. Of course, the deepest reason resides in the electronic structure and, in particular, in the contribution of V-dxy orbital to the SOMO. As a final comment, it is not surprising that the value of Az is larger than ∼(135−140) × 10−4 cm−1 for the spectra of “type 1” (the contribution of V-dxy in the SOMO is >90%) and that for amavadin is >150 × 10−4 cm−1 (the contribution of V-dxy in the SOMO is ∼99%). In J


Article

Inorganic Chemistry

value of ∼127 × 10−4 cm−1, which is a reasonable result for “bare” VIV species. At a first approximation, in eqs 17−21, the terms multiplied by ±(3/7)λ can be neglected because the denominator is much larger than the numerator; in fact, for VIV, λ ≈ 250 cm−1 85 and the energy differences Δ(x2−y2), Δ(xy), Δ(xz), Δ(yz), and Δ(z2), which fall in or near the visible region of the electromagnetic spectrum, are about two orders of magnitude greater, in the range of 10 000−30 000 cm−1 (we call this form of the equations without the terms multiplied by the ±(3/7)λ the “approximate form” and the value of Az estimated, Aestmt ). z Let us consider the six VIV complexes mentioned above (it must be highlighted again that eqs 17−21 are valid only in this case and that they would be different for the species with Ax as the largest value of A), plus amavadin and [VO(H2O)5]2+. Now, let from eqs 17−21 in us plot, for these species, the value of Aestmt z the “approximate form” (using the experimental gz, Pd = 128 × 10−4 cm−1, κ = 0.85, the coefficients α, β, γ12, γ22 and δ from the SOMO calculated by DFT methods in this work and neglecting the terms multiplied by ±(3/7)λ), as a function of the experimental Az (Aexptl z ). In other words, the contribution of each V-d orbital to Az was “weighted” using its coefficient in the linear combination of the SOMO through the “approximate form” of eqs 17−21. Since it is possible to observe in Figure 7

VIV 85), and the coefficients of V-d orbitals in the SOMO are as follows:85 SOMO V-dxy: ⎡ ⎛ 4⎞ A z = Pd⎢β 2⎜ −κ − ⎟ + (gz − 2.0023) ⎝ ⎢⎣ 7⎠ −

2 2 β 2γ2 2 ⎫⎤ 3 ⎧ β γ1 ⎬⎥ λ⎨ + 7 ⎩ Δ(xz) Δ(yz) ⎭⎥⎦ ⎪

⎪

⎪

⎪

(17)

SOMO V-dx2−y2: ⎡ ⎛ 4⎞ A z = Pd⎢α 2⎜ −κ − ⎟ + (gz − 2.0023) ⎢⎣ ⎝ 7⎠ −

2 2 α 2γ2 2 ⎫⎤ 3 ⎧ α γ1 ⎬⎥ λ⎨ + 7 ⎩ Δ(xz) Δ(yz) ⎭⎥⎦ ⎪

⎪

⎪

⎪

(18)

SOMO V-dxz: ⎡ ⎛ 2⎞ A z = Pd⎢γ12⎜ −κ + ⎟ + (gz − 2.0023) ⎢⎣ ⎝ 7⎠ α 2γ12 β 2γ12 δ 2γ12 ⎫⎤ 3 ⎧ ⎨ ⎬⎥ + λ + − 7 ⎩ Δ(x 2 − y 2 ) Δ(xy) Δ(z 2) ⎭⎥⎦ ⎪

⎪

⎪

⎪

(19)

SOMO V-dyz: ⎡ ⎛ 2⎞ A z = Pd⎢γ2 2⎜ −κ + ⎟ + (gz − 2.0023) ⎝ ⎢⎣ 7⎠ +

2 2 β 2γ2 2 δ 2γ2 2 ⎫⎤ 3 ⎧ α γ2 ⎬⎥ λ⎨ + − 7 ⎩ Δ(x 2 − y 2 ) Δ(xy) Δ(z 2) ⎭⎥⎦ ⎪

⎪

⎪

⎪

(20)

SOMO V-dz2: 2 2 ⎡ ⎛ δ 2γ2 2 ⎫⎤ 4⎞ 3 ⎧ δ γ1 ⎬⎥ + Az = Pd⎢δ 2⎜ −κ + ⎟ + λ⎨ ⎢⎣ ⎝ 7⎠ 7 ⎩ Δ(xz) Δ(yz) ⎭⎥⎦ ⎪

⎪

⎪

⎪

(21) Figure 7. Estimated absolute value of Az (Aestmt ) as a function of the z N S experimental absolute value of Az (Aexptl z ) for [V(L )2], [V(L )2], Ph 2 [V(pdbh)2], [V(hyph )2], [V(bhpp)2], and [V(L )2] (blue diamond), amavadin (pink square), and [VO(H2O)5]2+ (green triangle). Aestmt z was determined from eqs 17−21 in the “approximate form” (taking −4 −1 the experimental gz, Pd = 128 × 10 cm , κ = 0.85, the coefficients α, β, γ12, γ22, and δ from the SOMO calculated by DFT methods in this work and neglecting the terms multiplied by ±(3/7)λ). The value of R2 for linear fitting is 0.974. The difference between the values of Aestmt z and Aexptl is due to the uncertainty on the values of Pd and κ, and is due z to the fact of having neglected the terms multiplied by ±(3/7)λ. Calculations were carried out with ORCA software using the B2PLYP functional and the VTZ basis set.

where α, β, γ1 , γ2 , and δ are the coefficients of V-dx −y , V-dxy, V-dxz, V-dyz, and V-dz2 orbitals in the SOMO, and Δ(x2−y2), Δ(xy), Δ(xz), Δ(yz), and Δ(z2) are the energy difference between the specific V-d excited orbital and the SOMO.85 2

2

2

(

In these equations, (i) A z ∝ Pd × β 2 −κ −

4 7

2

) when the

SOMO is a pure V-dxy orbital (an analogous equation is valid

(

for V-dx2−y2), (ii) A z ∝ Pd × γ12 −κ +

2 7

) when the SOMO is a

pure V-dxz orbital (an analogous equation is valid for V-dyz);

(

and (iii) A z ∝ Pd × δ 2 −κ +

4 7

) when the SOMO is a pure V-

dz orbital. It must be observed that, in the first case, −4/7 (i.e., −0.57) is added to −κ to give a negative term with a large absolute value, whereas in the second and third cases, 2/7 (i.e., 0.29) or 4/7 (i.e., 0.57) must be added to −κ to give a negative term but with a small absolute value. If, for Pd and κ, we use the values reported by Pecoraro and co-workers,87 Az ∝ −β2 × 182 × 10−4 cm−1 when SOMO is based on the V-dxy orbital, and Az ∝ −γ12 × 72 × 10−4 cm−1 and Az ∝ −δ2 × 36 × 10−4 cm−1 when it is based on V-dxz or V-dz2 orbital. As an example, if SOMO is composed by 50% V-dxy and 50% V-dxz, Az assumes a 2

85

that a linear relationship is obtained, this is a further demonstration that the mixing among the five V-d orbitals in the SOMO is the reason for the decrease of the absolute value of Az and that greater is such a mixing greater is the lowering of Az. With increasing the “weight” of V-dxy in the SOMO, Az

(

increases significantly because the term Pd × β 2 −κ −

4 7

) in eq

17 has the largest absolute value among the corresponding ones contained in eqs 17−21. K


Article

Inorganic Chemistry According to other studies in the literature,88 the electronic structure and MO composition of [V(dhp)3]+ (“type 2” spectrum), [V(LS)2] (“type 3”), and [V(hyphPh)2] (“type 1”) were evaluated choosing a coordinate system in which the molecular axis with the highest symmetry is oriented along the z direction and the two other axes roughly occupy the x and y directions. The energy levels of the MOs derived from V-d orbitals are shown in Figure 8. For clarity, the energy of the MOs is relative to the SOMO, set as reference at 0.0 eV. The energy order of V-d orbitals is as follows:

be assumed that LUMO+9 for [V(dhp)3]+ derives exclusively from V-d orbitals and, in particular, from V-dz2 (shown in red in Figure S8). It is noteworthy that the mixing of V-d orbitals decreases from a trigonal prismatic geometry to an octahedral geometry, and this is in agreement with other results in the literature that reported the mixing of V-dxy and V-dz2 in the SOMO for distorted “bare” VIV species.14b,90,91 For [VO(H2O)5]2+, the order V-dxy < V-dxz ≈ V-dyz < V-dx2−y2 < V-dz2 is found, in agreement with the discussion of Ballhausen and Gray,92 and no mixing is observed (Figure S8). The energy levels of the MOs based V-d orbitals for the other group of three “bare” VIV species[V(bhpp)2], [V(hpo)3]+, and [V(L2)2]are represented in Figure S9 in the Supporting Information, whereas the total percentage of these orbitals, with respect to the total V contribution in the MOs, is shown in Figure S10 in the Supporting Information.

Figure 8. Relative energy levels of V-d orbitals for [V(dhp)3]+, [V(LS)2], and [V(hyphPh)2]. The position of the three Cartesian axes is also indicated. In [V(hyphPh)2], Ph indicates the phenyl rings, whereas in [V(LS)2], tBu indicates the tert-butyl groups; neither of them contribute to the SOMO. The MOs composition was calculated with ORCA software, using the B2PLYP functional and the VTZ basis set.

for [V(dhp)3]+: V‐dxz < V‐d x 2 − y2 ≈ V‐d yz < V‐dxy ≈ V‐d z 2

for [V(LS)2]: V‐dxy < V‐dxz < V‐d yz < V‐d x 2 − y2 < V‐d z 2

for [V(hyphPh)2]: V‐dxy < V‐d yz ≈ V‐dxz < V‐d z 2 < V‐d x 2 − y2

The total percent contribution of the V-d orbitals with respect to the total percentage of V in the specific MO for [V(dhp)3]+, [V(LS)2], and [V(hyphPh)2]and for amavadin and [VO(H2O)5]2+is reported in Figure S8 in the Supporting Information and has been calculated according to the procedure established in the literature.89 To interpret Figure S8, one must recall that (i) only the MOs derived from V-d atomic orbitals were considered; (ii) for each MO, only the total contribution of the V-d orbitals was taken into account; (iii) the percent amount reported refers to the weight of the specific V-d orbital, with respect to the total V-d orbital contribution. For example, in the LUMO+9 of [V(dhp)3]+, the total percent contribution of V-d orbitals is 70.4 and, of this amount, 53.8 belongs to V-dz2, 14.9 to V-dx2−y2, 1.2 to V-dxz, and 0.5% to V-dxy (i.e., the relative contribution of V-dz2, V-dx2−y2, Vdxz, and V-dxy orbitals, with respect to the total V contribution, is 76.4%, 21.2%, 1.7%, and 0.7%, respectively). Therefore, it can

Figure 9. MOs for amavadin: (a) SOMO (V-dxy); (b) LUMO (mixing of V-dxz and V-dyz); (c) LUMO+1 (mixing of V-dyz and V-dxz); (d) LUMO+2 (V-dz2) and (e) LUMO+3 (V-dx2−y2). The position of the three Cartesian axes is also indicated. MOs were calculated with ORCA software, using the B2PLYP functional and the VTZ basis set. L


Article

Inorganic Chemistry For amavadin, the order V-dxy < V-dxz ≈ V-dyz < V-dz2 < Vdx2−y2 is predicted, which is comparable with the results reported by Kaupp and co-workers.39 V-dxy is SOMO (and HOMO), and the excited V-dxz, V-dyz, V-dz2, and V-dx2−y2 orbitals are LUMO, LUMO+1, LUMO+2, and LUMO+3, respectively. These five MOs are represented in Figure 9. It must be observed that the electronic structure of amavadin is very similar to that of a VIVO complex.

The results of this work indicated that the formation of nonoxido VIV complexes can be inferred by their Ai value and spectral pattern. Conversely, the EPR spectrum of such species can be predicted based on the MOs composition, which is easily calculable by DFT methods (see Figures 6 and 8). Depending on the SOMO shape and composition, the spectrum can be classified as “type 1”, “type 2”, or “type 3”. Also, the examination of the vanadium coordination environment can provide information on the experimental EPR spectrum: when the geometry is trigonal prismatic, the spectrum will be of “type 2”; when it is intermediate between the trigonal prism and octahedron, the spectrum will be of “type 3”, whereas when the geometry is close to the octahedron, the spectrum will approach the “type 1” and will resemble that of a VIVO species (both for the large value of Az and spectral pattern). The analysis of the electronic structure of amavadin suggested the order V-dxy < V-dxz ≈ V-dyz < V-dz2 < V-dx2−y2 among the five MOs based on V-d orbitals. Such an electronic structure is comparable to that of a VIVO complex and, for this reason, Aiso and Az measured in the isotropic and anisotropic EPR spectra are larger than 80 × 10−4 cm−1 and 150 × 10−4 cm−1, and the structure of amavadin was initially described as an “usual” oxidovanadium(IV) complex.

■

CONCLUSIONS In this work, the 51V HFC A tensor has been calculated for 20 “bare” VIV complexes with different donor sets, electric charges, and coordination geometries, using ORCA or Gaussian software and several functionals and basis sets. The data indicated that the best functional to predict Aiso or Ai (i = x, z, depending on the geometry and electronic structure of the complex) is the double hybrid functional B2PLYP,55 which gave a mean percentage deviation (MPD) from Aiso and Ai of −4.1% and −0.9% (for basis set 6-311g(d,p)) and −0.3% and 2.3% (for basis set VTZ). The MAPD from Ai is 3.3% (for basis set 6-311g(d,p)) and 3.8% (for basis set VTZ), which is comparable with the results obtained for VIVO complexes. With the functional B2PLYP and the basis set VTZ, the percentage deviation from experimental Aiso and Az for amavadin is −1.1% and −2.0%, respectively (the calculated Aiso and Az value are −80.1 × 10−4 cm−1 and −150.0 × 10−4 cm−1 vs the experimental values of −81.0 × 10−4 cm−1 and −153.0 × 10−4 cm−1 25). The high fraction of HF exchange in B2PLYP (53%), which balances the overestimation of the covalency of V−L bonds, improves the prediction of Aiso significantly with respect to the hybrid meta-GGA functionals, one- and threeparameter hybrids, and half-and-half hybrid functionals. The results allowed us to divide the spectra of nonoxido VIV compounds in three types: “type 1”, “type 2”, and those intermediate, which, in this work, are called “type 3”. The spectra of “type 1” are detected for VIV species formed by tridentate ligands with rigid structure and meridional coordination. In these complexes, the SOMO is based mainly on the orbital V-dxy with a small contribution ( Ay > Ax or Ax > Ay > Az (depending on the geometry and electronic structure of the complex), with Az or Ax in the range of (120−135) × 10−4 cm−1, is revealed.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00409. Schemes with the structure of ligands and complexes (Schemes S1−S5); figures with mean percentage deviation and mean absolute percentage deviation from experimental Aiso, Ai, and Ai,anis (Figures S1−S5); experimental EPR spectra, SOMOs and energy levels of V-d orbitals for VIV species (Figures S6−S10); tables with optimized Cartesian coordinates (Tables S1−S20); comparison of optimized and experimental X-ray structures (Tables S21−S32); values of Aiso, Ax, Ay, Az calculated with all the functionals and basis sets (Tables S33−S47) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Fondazione Banco di Sardegna for the financial support (project Prot. U924.2014/AI.807.MGB; Prat. 2014.0443).

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REFERENCES

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