Interplay of Through-Bond Hyperfine and Substituent Effects on the

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Interplay of Through-Bond Hyperfine and Substituent Effects on the NMR Chemical Shifts in Ru(III) Complexes Lukaś ̌ Jeremias,† Jan Novotný,† Michal Repisky,‡ Stanislav Komorovsky,§ and Radek Marek*,† †

CEITECCentral European Institute of Technology, Masaryk University, Kamenice 5/A4, CZ-625 00 Brno, Czechia Hylleraas Centre for Quantum Molecular Science, Department of Chemistry, UiTThe Arctic University of Norway, N-9037 Tromsø, Norway § Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia Downloaded via UNIV OF CALIFORNIA SANTA BARBARA on July 14, 2018 at 08:29:36 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: The links between the molecular structure and nuclear magnetic resonance (NMR) parameters of paramagnetic transition-metal complexes are still relatively unexplored. This applies particularly to the contact term of the hyperfine contribution to the NMR chemical shift. We report combining experimental NMR with relativistic density functional theory (DFT) to study a series of Ru(III) complexes with 2-substituted β-diketones. A series of complexes with systematically varied substituents was synthesized and analyzed using 1H and 13C NMR spectroscopy. The NMR spectra recorded at several temperatures were used to construct Curie plots and estimate the temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the NMR shift. Relativistic DFT calculations of electron paramagnetic resonance and NMR parameters were performed to interpret the experimental observations. The effects of individual factors such as basis set, density functional, exact-exchange admixture, and relativity are analyzed and discussed. Based on the calibration study in this work, the fully relativistic Dirac−Kohn−Sham (DKS) method, the GIAO approach (orbital shift), the PBE0 functional with the triple-ζ valence basis sets, and the polarizable continuum model for describing solvent effects were selected to calculate the NMR parameters. The hyperfine contribution to the total paramagnetic NMR (pNMR) chemical shift is shown to be governed by the Fermi-contact (FC) term, and the substituent effect (H vs Br) on the through-bond FC shifts is analyzed, interpreted, and discussed in terms of spin-density distribution, atomic spin populations, and molecular-orbital theory. In contrast to the closedshell systems of Rh(III), the presence of a single unpaired electron in the open-shell Ru(III) analogs significantly alters the NMR resonances of the ligand atoms distant from the metal center in synergy with the substituent effect.

1. INTRODUCTION Nuclear magnetic resonance (NMR) spectroscopy is a widely employed method for characterizing the structures of new chemical compounds and biomolecular systems. However, this technique is generally less successful for open-shell molecules and metal complexes with unpaired electrons, which exhibit pronounced electron paramagnetism. In this case, both the NMR chemical-shift tensors and the indirect nuclear spin−spin coupling constants are significantly affected by paramagnetic effects.1 The resonance frequencies of paramagnetic species typically lie outside of the normal range of chemical shifts for their diamagnetic analogs as a result of the additional (de)shielding contributions caused by the paramagnetic center (e.g., transition metal). The NMR spectral window can expand to hundreds of ppm for 1H and even thousands of ppm for heavier ligand atoms such as 13C or 15N.1−3 At the same time, the presence of unpaired electron(s) induces a fast nuclear spin relaxation that results in significant broadening of the NMR resonances.4 Despite these difficulties, paramagnetic NMR (pNMR) spectroscopy is becoming very important in areas of © XXXX American Chemical Society

research such as the structural characterization of paramagnetic metalloproteins,5,6 magnetic resonance imaging,7−10 or the development of molecular magnets.11,12 However, the systematic investigation of even relatively simple paramagnetic transition-metal complexes that exhibit sufficiently resolved resonances remains a challenging task. The experimentally observed total NMR chemical shift of an atom L in a paramagnetic compound can be decomposed into two principal contributions:6 δ Ltot = δ Lorb + δ LHF

(1)

The orbital term, δorb L , is essentially temperature-independent (here, we neglect the rovibrational motions and the supramolecular association processes in solution), whereas the hyperfine term, δHF L , is temperature-dependent. These two terms can therefore be determined from several NMR Received: January 9, 2018

A

DOI: 10.1021/acs.inorgchem.8b00073 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

that for systems with ground-state multiples characterized by zero-field splitting, the NMR theory has matured only recently31,32 and has been used to calculate the NMR chemical shifts of some prototypical transition-metal complexes.33−35,39 In the present paper, the orbital and hyperfine contributions to the 1H and 13C NMR chemical shifts were determined experimentally for a series of ruthenium(III) compounds 1a-1e (for structures, see Figure 1) from NMR measurements at

measurements at different temperatures and analyzed in terms of a Curie plot (δtot L as a function of the reciprocal of the absolute temperature, 1/T).13,14 The orbital shift of the spectator ligand atom L is obtained theoretically as the difference between the shielding constants of a reference diamagnetic compound, σref, and the spectator atom, σorb L : δ Lorb = σref − σLorb

(2)

In parallel with the standard formalism for diamagnetic systems, the orbital NMR shielding constant can be further divided into orbital diamagnetic (σd) and orbital paramagnetic (σp) terms: σLorb = σLd + σLp

(3)

Traditionally, the hyperfine (HF) NMR shift term in eq 1 is separated into contact and pseudocontact contributions because the latter term provides useful geometrical information.15,16 However, this traditional separation loses its usefulness and applicability within the relativistic framework because there are additional relativistic contributions. In this work, we employed an alternative separation of δHF L into Fermicontact (FC), spin-dipole (SD), and paramagnetic nuclearspin−electron-orbit (PSO) terms that is governed by separation of the A-tensor, eq 4.17,18 δ LHF = δ LFC + δ LSD + δ LPSO

(4)

This separation is more appropriate for chemical interpretation because δFC L can be linked directly to the spin density at the position of the spectator nucleus L, regardless of the theoretical framework used. In addition to the terms in eq 4, there is one extra contribution (termed δREL L ), which is, however, negligible in most of the cases studied here (see Section 3.3).17,18 Note that eq 4 holds for the paramagnetic doublet systems studied in this work, vide infra. The development and application of theoretical approaches used to calculate the NMR properties of paramagnetic transition-metal systems have been discussed in a series of papers.2,19−30 The calculation of pNMR parameters can be directly related to the parameters of EPR spin Hamiltonian as shown for doublet systems by Moon and Patchkovskii22 and later extended to systems with an arbitrary spin degeneracy by Van den Heuvel and Soncini.31−35 The computational approaches used to predict the NMR and electron paramagnetic resonance (EPR) parameters in real-size systems (a few hundreds of atoms) rely mostly on density functional theory (DFT).36 For transition-metal complexes, the relativistic effects play an important role and can be incorporated into theoretical models by means of relativistic Hamiltonians, such as the two-component zeroth-order regular approximation Hamiltonian (SO-ZORA) or the four-component Dirac− Coulomb (DC) Hamiltonian, that involve the spin−orbit (SO) coupling.37 The SO-ZORA Hamiltonian19 has been used to calculate the NMR chemical shifts in some paramagnetic ruthenium(III) compounds, including NAMI-type systems and their pyridine analogs, Ru(acac)3, Ru(tfac)3, mer-Ru(ma)3 (acac = acetylacetonate, tfac = trifluoroacetylacetonate, ma = maltolate),4,18−20,38 and supramolecular host−guest complexes.30 Similarly, the DC Hamiltonian21 has been employed to assign and interpret the pNMR spectra of some previously mentioned compounds, namely NAMI and its pyridine analogs, as well as mer-Ru(ma)3.18,20,21 We note in passing

Figure 1. Structures and atom numbering scheme for complexes 1a− 1e (ruthenium) and 2a−2b (rhodium).

various temperatures. The previous characterizations of these compounds by NMR spectroscopy (see Table S1 in Supporting Information) relied mostly on 1H NMR experiments, whereas 13C NMR data were in most cases missing40,41 or incomplete.42 Here, we provide a full set of 13C NMR data recorded by using state-of-the-art cryoprobe NMR technology at high magnetic fields (resonance frequency 700 MHz and above for 1H). In addition, relativistic DFT calculations (twocomponent SO-ZORA43 and four-component Dirac-Kohn− Sham (DKS)21,44) were performed to assist in assigning the resonances and to interpret the electronic and spin structures of these compound in terms of the individual contributions to the NMR chemical shifts. The 1H and 13C NMR chemical shifts of two diamagnetic Rh(III) analogs, 2a and 2b, were determined for reference purposes and to assist in interpreting the NMR data.

2. METHODS 2.1. Materials and Synthesis. The starting compounds RuCl3· xH2O, RhCl3·xH2O, 2,4-pentanedione, 1,3-diphenyl-1,3-propanedione, 3-methyl-2,4-pentanedione, N-bromosuccinimide, NaHCO3, K2CO3, Cu(NO3)2·3H2O, acetic anhydride, and CH3COONa were used as obtained from our suppliers. The solvents in p.a. grade were used as received without further purification. B


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Inorganic Chemistry Ru(III) complexes Ru(acac)3 (1a),40 Ru(Br-acac)3 (1b),41 Ru(NO2-acac)3 (1c),41 and Ru(dbm)3 (1e)42 (acac = acetylacetonate, dbmH = dibenzoylmethane) were prepared according to published procedures. Ru(Me-acac)3 (1d) was synthesized using the same procedure as reported for Ru(dbm)342 by using 3-methyl-2,4pentanedione as the starting compound instead of 1,3-diphenyl-1,3propanedione. Single crystals of 1d suitable for X-ray analysis were obtained by slowly evaporating the solvent from a solution of 1d dissolved in a mixture of dichloromethane and hexane. For crystallographic data, see Table S2. The Rh(III) complexes Rh(acac)3 (2a) and Rh(Br-acac)3 (2b) were synthesized by the same procedures as reported for their ruthenium analogs using RhCl3·xH2O as the starting compound instead of RuCl3·xH2O. Single crystals of 2b suitable for X-ray diffraction analysis were obtained by slowly evaporating a chloroform solution of 2b. For crystallographic data, see Table S2. 2a: 1H NMR (292.1 K, CDCl3, in ppm): 5.50 (H2), 2.17 (H3); 13 C NMR (292.1 K, CDCl3, in ppm): 188.71 (C1), 99.30 (C2), 26.63 (C3). 2b: 1H NMR (292.1 K, CDCl3, in ppm): 2.53 (H3); 13C NMR (292.1 K, CDCl3, in ppm): 187.96 (C1), 96.06 (C2), 30.85 (C3). 2.2. NMR Spectroscopy. 1H and 13C NMR spectra of Ru(III) and Rh(III) complexes were measured on a Bruker Avance III HD 700 MHz spectrometer. The spectra were recorded in CDCl3, acetone-d6, toluene-d8, or N,N-dimethylformamide-d7 in the range of temperatures between 240.7 and 341.7 K. The exact temperature (T) of the sample was calibrated using the chemical-shift separation Δ (in ppm) between the OH resonance and CHn resonance of methanol in methanol-d4 (for the temperatures T′ below 300 K) and in 80% ethylene glycol in dimethyl sulfoxide-d6 (for the temperatures T′ above 300 K). All of the NMR spectra were referenced to TMS, and the NMR chemical shifts are reported in ppm. 2.3. X-ray Diffraction. Diffraction data for complexes 1a and 2b were collected on a Rigaku MicroMax-007 HF rotating-anode fourcircle diffractometer with Mo Kα radiation. The temperature during data collection was 120(2) K. The structures were solved by direct methods and refined by the ShelXTL software package.45 Crystallographic data and structural refinement parameters are listed in Table S2 in Supporting Information. 2.4. Quantum Chemical Calculations. Geometry. We used an approach calibrated in our previous studies of octahedral and square− planar transition-metal complexes20,46,47 to optimize the molecular geometry. The geometry of the Ru(III) and Rh(III) complexes was optimized using DFT with the PBE0 functional48,49 and the def2TZVPP50 basis set for all atoms, with the corresponding relativistic effective core potentials (def2-ECPs)51 for the metal center, as implemented in the Turbomole 7.0.0 program.52 The structures were optimized using the COSMO (conductor-like screening model; the same solvent as used in the NMR experiment)53 solvent model (for Cartesian coordinates, see Supporting Information). All calculations were performed with the m5 integration grid and the following convergence criteria: 10−6 for the energy change and 10−3 for the geometry gradient. The optimized and experimental interatomic distances are summarized and compared in Table S3 in Supporting Information. For the effects of optimization approach (dispersion correction and implicit solvent model) on the interatomic distances (Table S4) and NMR parameters (Table S5), see Supporting Information. Two-Component Calculations of NMR and EPR Parameters. The NMR and EPR parameters were calculated using the two-component ZORA54,55 Hamiltonian, as implemented in the ADF program package (versions 2016 and 2017).56−58 Limitations of the program meant that the NMR shielding constants of open-shell systems were determined only at the scalar (spin−orbit free) one-component ZORA level, using PBE, PBE0 (which has exact-exchange admixture of 25%), and PBE0−40 (PBE0 with the exact-exchange admixture increased to 40%) functionals,59−61 the TZ2P and QZ4P basis sets,62 and using either vacuum or the COSMO solvent model (the same solvent as used in the NMR experiment).53 Because the reference calculations (PBE0-40/QZ4P/solvent for 1a and 1b) showed that the

effect of the XC kernel (as implemented in ADF2017) on the orbital H and 13C NMR shielding values is vanishingly small (Δδorb XC < 0.02 ppm), all of the production calculations were performed without the kernel contribution. Note, however, that the effect of the XC kernel was found to be significantly larger in the diamagnetic Rh analog (ΔδXC < 2.02 ppm). The calculated NMR chemical shifts were referenced relative to benzene as a secondary reference: δref = 7.15 ppm for 1H and δref = 127.8 ppm for 13C.20,63,64 The hyperfine parameters were calculated at the 2c (SO-ZORA) level using the same functionals, basis sets, and solvent model as for the calculation of orbital contributions. The reported values of the hyperfine and orbital contributions to the 1H and 13C NMR shielding constants were obtained by averaging the corresponding values for all chemically equivalent atoms. Four-Component Calculations of NMR and EPR Parameters. NMR and EPR parameters were calculated using the program ReSpect (version 4.0.065) with four-component Dirac−Kohn−Sham (DKS) methodology44,66−69 along with Jensen’s uncontracted pc-1 (upc-1),70,71 pc-2 (upc-2),70,71 pcS-1 (upcS-1),72 pcS-2 (upcS-2),72 pcJ-0 (upcJ-0),73 pcJ-1 (upcJ-1),73 pcJ-2 (upcJ-2),73 and the uncontracted iglo-ii (uiglo-ii)74 and iglo-iii (uiglo-iii)74 basis sets for the light atoms, plus Dyall’s VDZ, cVDZ, VTZ, cVTZ, or VQZ basis sets75 for the Ru and Br atoms. PBE, PBE0, and PBE0-X (PBE0 with the user-modified exact-exchange admixture of X = 5, 10, 15, 20, 30, 35, 40, 45, or 50%) functionals59−61 were used (with a newly implemented GIAO approach to the orbital shielding). The calculations were carried out either in a vacuum (both NMR and EPR parameters) or in a solvent (only EPR parameters); the latter are represented by the PCM (polarizable continuum model)76 solvent model (the same solvent as used in the NMR experiment). The NMR shielding constants were converted into NMR chemical shifts using the same approach as for the two-component calculations mentioned above. The value of the temperature-dependent hyperfine shift (δHF L , sum of eqs 10 and 11 in ref 21) was obtained as the sum of the contributions from both the isotropic and the anisotropic FermiSD PSO contact (δFC L ), spin-dipole (δL ), and paramagnetic spin−orbit (δL ) SD PSO shifts is governed terms, where the separation into δFC L , δL , and δL by the separation of the hyperfine coupling tensor, A, presented in eqs 21−23 in ref 17. For more detailed explanation on splitting of δHF L , see ref 18. Bonding Analysis and Electronic Structure. Energy decomposition analysis (EDA)56,77 as implemented in the ADF 2017 program (ZORA/PBE0/TZ2P/vacuum) was used to analyze the bonding between 2-X-β-diketonate ligands (L) and the paramagnetic Ru center. Spin-restricted fragments were defined in two arrangements: Ru + 3L or RuL2 + L. The electron deformation density (EDD)78,79 was analyzed by using the EDA-NOCV approach.80,81 The spatial distribution of total spin density and spin populations for individual ligand atoms were calculated at the scalar-relativistic (ZORA/PBE0/ TZ2P) level either in a vacuum or by using the COSMO solvent model.18,20 1

3. RESULTS AND DISCUSSION 3.1. Experimental 1H and 13C NMR Chemical Shifts. The Ru(III) and Rh(III) complexes investigated in this study were prepared by the procedures described in Section 2.1. The crystal structures of compounds 1d and 2b were characterized by X-ray diffraction analysis; their molecular structures are shown in Figure 2 (for a comparison between the experimental and calculated interatomic distances, see Table S3 in Supporting Information). The deviation of the calculated interatomic distances (except the bonds with hydrogens) relative to the experimental solid-state structures is less than 3 pm (in most cases less than 1 pm), which substantiates the selection of the DFT method used in this study (PBE0/def2/ TZVPP/ECP).20,46,47 All of the Ru(III) and Rh(III) compounds were characterized by NMR spectroscopy. The C


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Inorganic Chemistry

Figure 3. Portion of the 13C NMR spectrum of compound 1a in CDCl3 plotted for temperatures 310, 292, 272, and 251 K. The 13C NMR signals are assigned to the individual atoms C1−C3 and the temperature-independent signals of the solvent (residual CHCl3) and reference standard (TMS) are highlighted in yellow.

Table 1. Experimental 13C NMR Chemical Shifts for Compounds 1a−1e, 2a, and 2b Measured in CDCl3 at 293 Ka compound

atom

δorb C

1a

C1 C2 C3 C1 C2 C3 C1 C2 C3 C1 C2 C3 C4 C1 C2 C1′b C2′b C3′b C4′b C1 C2 C3 C1 C2 C3

+175.8 +165.7 +30.1 +151.1 +222.4 +45.8 +135.0 +267.0 +34.1 +151.3 +187.8 +47.2 +4.1 +211.7 +96.6 +142.0 +131.4 +127.6 +131.4 +188.7 +99.3 +26.6 +188.0 +96.1 +30.9

1b

1c

Figure 2. Molecular structure of compound (a) 1d and (b) 2b as determined by X-ray diffraction. Thermal ellipsoids shown at the 50% probability level were plotted by the OLEX2 program.82 Positionally disordered atoms with minor occupancy and molecules of solvent in 2b have been omitted for clarity (for more details, see Supporting Information). Symmetry codes: (i) 1−x+y, 2−x, z; (ii) 2−y, 1+x−y, z.

1d

1e

NMR spectra of paramagnetic ruthenium compounds 1a−1e were measured at temperatures ranging between 240.7 and 341.7 K. An example of the 13C NMR spectrum for complex 1a, plotted at four selected temperatures, is shown in Figure 3. The previously reported 1H and rather incomplete 13C NMR data are summarized in Table S1 in Supporting Information. The full set of 1H and 13C NMR resonances for compounds 1a−1e recorded in this study at various temperatures (see Tables S6−S13 in Supporting Information) was assigned based on the correlation between the experimental and DFT calculated data (see Section 3.2) and the reference NMR data for the diamagnetic Rh(III) analogs, Table 1 and 2. It should be noted that our assignments of the 13C NMR resonances for the methine (C2) and carbonyl (C1) carbons in 1a are the reverse of those published previously.38 For compound 1d, there is a significant discrepancy between the 1 H NMR chemical shift of H4 published previously (−34.2 ppm at room temperature,83 Table S1 in Supporting Information) and our measurement (+56.5 ppm at 292 K, Table S12 in Supporting Information), which is supported by DFT calculations (Tables S19 and S24 in Supporting

2a

2b

slope of the Curie plot (prefactor c in c·1/T)

δHF C

δtot C

−11 268 +44 595 −16 080 −18 096 +113 458 −11 862 +8089 +69 521 −10 897 −34 811 +78 939 −13 006 −26 484 −40 384 +82 690 −12 319 −5105 +2312 −1831

−38.5 +152.2 −54.9 −61.8 +387.2 −40.5 +27.6 +237.3 −37.2 −118.8 +269.4 −44.4 −90.4 −137.8 +282.2 −42.0 −17.4 +7.9 −6.2

+137.3 +317.9 −24.8 +89.3 +609.6 +5.3 +162.6 +504.3 −3.1 +32.5 +457.2 +2.8 −86.3 +73.9 +378.8 +100.0 +114.0 +135.5 +125.2 +188.7 +99.3 +26.6 +188.0 +96.1 +30.9

a

HF The separate orbital (δorb C ) and hyperfine (δC ) contributions according to 1/T dependence (Curie plot, Figure 4) and the total chemical shifts (δtot C ) are given in ppm. The total NMR chemical shifts of C2 in 1a−1d, which are the most strongly influenced by the substituent effects, are highlighted in bold. bNote that the effect of the paramagnetic center on the carbons of the phenyl group in 1e is not monotonous.20,84

Information). The other previously reported NMR chemical shifts agree well with our current values. Determining the D


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Inorganic Chemistry Table 2. Experimental 1H NMR Chemical Shifts for Compounds 1a−1e, 2a, and 2b Measured in CDCl3 at 293 Ka compound

atom

δorb H

1a

H2 H3 H3 H3 H3 H4 H2 H2′ H3′ H4′ H2 H3 H3

+5.9 +2.7 +1.7 +0.9 +1.7 +8.4 +12.1 +7.9 +7.6 +6.9 +5.5 +2.2 +2.5

1b 1c 1d 1e

2a 2b

slope of the Curie plot (prefactor c in c·1/T)

δHF H

δtot H

−10 646 −2425 −2814 −1293 −3257 +14 015 −13 198 +1152 −258 +678

−36.3 −8.3 −9.6 −4.4 −11.1 +47.8 −45.0 +3.9 −0.9 +2.3

−30.4 −5.6 −7.9 −3.5 −9.4b +56.2b −32.9 +11.9 +6.7 +9.2 +5.5 +2.2 +2.5

a

The separate orbital (δHorb) and hyperfine (δHF H ) contributions according to 1/T dependence (for Curie plots, see Supporting Information), and the total chemical shifts (δtot H ) are given in ppm. b The total NMR chemical shifts of methyl groups in two structurally different positions of 1d are highlighted in bold.

differences is not straightforward because the exact temperature of the measurement is often not stated or a different solvent may have been used. However, the maximum difference is less than 2 ppm for 13C NMR chemical shifts and 0.2 ppm for 1H NMR chemical shifts. The NMR chemical shifts recorded at various temperatures are plotted versus the reciprocal of the absolute temperature (1/T). Example Curie plots for the 13C NMR of 1a and 1b are shown in Figure 4 (the remaining Curie plots can be found in Supporting Information, Figures S1−S7). The approximately temperature-independent orbital shifts (δorb L ) and the temperature-dependent hyperfine shifts (δHF L ) were estimated from these plots and are summarized in Table 1 (in CDCl3; the NMR values for 1a in acetone-d6, toluene-d8, and N,Ndimethylformamide-d7 can be found in Table S14 in Supporting Information). Whereas at lower temperatures, the carbon atom C2 in 1a and 1b is significantly deshielded (i.e., shifted to a higher frequency), the hyperfine contribution in these Ru(III) compounds typically induces additional shielding of the nuclei of the other carbon and the hydrogen atoms, see Figure 4. The electronic origins of the individual hyperfine contributions will be discussed in detail in Section 3.3. The effects of individual substituent on the total 13C NMR chemical shift of the methylene carbon, C2, are demonstrated in Figure 5. Substituting bromine for hydrogen at C2 results in an additional deshielding of C2 of almost 300 ppm (compare δtot C2 for 1a and 1b in Figure 5), accounted for mainly by the contribution of the hyperfine shift as will be discussed in detail in Section 3.3. As seen in Table 1, the total 13C NMR chemical shift for C3 of the methyl group in 1a (δtot C3 = −24.8 ppm) is very different from those in compounds 1b−1d (which range from +5.3 ppm to −3.1 ppm) with the spin density more delocalized toward the substituent at C2. The significant effect of the structural position of a methyl group on the 1H NMR chemical shift is seen by comparing the δtot H4 (+56.2 ppm) of H4 in 1d with the δtot H3 (ranging from −3.5 to −9.4 ppm) of H3 in 1a−1d. All the above-mentioned NMR effects originate in the Fermi-contact

Figure 4. Curie plots of the 13C NMR chemical shifts for compound 1a and compound 1b measured in CDCl3. The δorb C (temperatureindependent contribution) is estimated from an extrapolation to the limit 1/T = 0. The values of δHF C for individual atoms are shown for a temperature of 293 K.

Figure 5. Experimental total 13C NMR chemical shift of C2 for compounds 1a−1d measured in CDCl3 at 293 K. The substituent attached to C2 is depicted for each compound.

contributions related to the distribution of electron spin density in the β-diketonato moiety to be discussed in detail in Section 3.3. However, to investigate the factors influencing the orbital and hyperfine contributions to the total NMR chemical shifts in compounds 1a−1e using electronic structure calculations, the DFT method must be calibrated (Section 3.2). 3.2. DFT Calculations of NMR Chemical Shifts. To optimize the geometries of the ruthenium complexes, we followed the calibrated approach used in our previous studies on transition-metal complexes20,46,47 and described in Section E


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The effect of the solvent amounts to approximately 10−15 ppm for C2 in compound 1a (Figure 7).

2.4. The structures were optimized at the PBE0/def2-TZVPP/ def2-ECP level using an implicit solvent model (COSMO) of chloroform (and also acetone, toluene, and DMF in the case of 1a). Subsequently, relativistic DFT was used to calculate the NMR and EPR parameters at both the two-component (SOZORA in ADF, see Tables S15−S20 in Supporting Information) and four-component (DKS in ReSpect, see Tables S21−S24 in Supporting Information) levels. First, we calibrated the computational approach on the 13C NMR shift of C2 because it is particularly sensitive to the method selected. The effects of the basis set (from double-ζ to quadruple-ζ valence polarized) and the exact-exchange admixture used in the PBE0 functional (from 0 to 50%) on δHF C2 in compound 1a are shown in Figure 6. A comparison of the experimental values of the g-tensor with those calculated by using the VTZ/ upcJ-2 basis sets can be found in Table S25 in Supporting Information.

Figure 7. Total 13C NMR shift of atom C2 in 1a at 293 K, calculated by using different PBE-based functionals as the sum of the orbital (δorb C2 in red; solvent corrections from SO-ZORA were used for the values calculated in CHCl3, see Table S26 in Supporting Information) and hyperfine (δHF C2 in blue) contributions by using the DKS method. The experimental NMR chemical shifts for 1a and 2a are shown by green bars.

To further assess the DFT approach, we calculated the total C NMR shift of C2 in compound 1a (sum of the orbital and hyperfine contributions) as shown in Figure 7 (for full data sets, see Table S21 in Supporting Information). Whereas the orbital shift is rather insensitive to the computational level applied (red columns in Figure 7), the HF contribution is affected significantly (blue column) and can bring the total 13C NMR shift much closer to the experimental value (the last column, in green), especially when the hybrid GGA functional (PBE0) is used. This observation is related to the delocalization error in GGA functionals as discussed previously in connection with the ground-state spin density in open-shell systems and hyperfine interactions.20,38,85 Based on the total performance (for total RMSD values, see Figures S11 and S12 in Supporting Information), we selected PBE0/VTZ/ upcJ-2/CHCl3 for further calculations. The calculated and experimental total 13C NMR shifts for C2 in compounds 1a, 1d, and 1b are compared in Figure 8. A notable discrepancy between the calculated and experimental values was observed for both the orbital and hyperfine contributions to the 13C NMR chemical shifts. The source of this discrepancy is currently a mystery to us and could originate with decreasing probability from (i) an error in the experimental estimation of terms from the Curie plot, (ii) cancelation of errors between the orbital and hyperfine contributions in the DFT calculations, or (iii) possibly from neglecting the low lying excited states in the theoretical description. Despite this discrepancy between the calculated and experimental individual contributions to the total 13C NMR shift, a substituentinduced trend is reproduced sufficiently for both the total and hyperfine NMR shifts in this series, which justifies additional analysis of the magnetic resonance parameters in terms of the calculated spin density and atomic spin populations, Section 3.3. 3.3. Interpretation of Substituent Effects on the Hyperfine NMR Shifts: Distribution of Spin Density and Electronic Structure. To interpret the substituent effects on the hyperfine NMR shifts observed and discussed in Section 3.2, we first analyzed the individual contributions of the FC, SD, and PSO terms to δHF C2 . As expected, the hyperfine NMR 13

Figure 6. Hyperfine contributions to the NMR shift for C2 in 1a calculated by the DKS method (δHF C2 at 293 K) as a function of (a) basis sets and (b) exact-exchange admixture in the PBE0-X functional. For the DKS calculations of the NMR shifts for model compounds using larger basis sets (Figures S8 and S9) and for the basis-set dependence in the SO-ZORA method (Figure S10), see Supporting Information.

As demonstrated in Figure 6a (and Figures S8 and S9 in Supporting Information), the VTZ/upcJ-2 basis sets represent a combination that converges relatively well and has been used for the production calculations in the following parts. In passing, the smaller uiglo-iii basis set represents a very good alternative to upcJ-2 for large molecular or supramolecular complexes (see Tables S21−S23 in Supporting Information). F


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Figure 8. Total calculated (SO-ZORA values in orange, DKS values in violet: the PBE0 functional and the basis set of triple-ζ quality) and experimental (in green) NMR shifts for C2 in Ru(III) compounds 1a (X = H), 1d (X = Me), and 1b (X = Br) and Rh(III) analog 2b (X = Br) with HF HF their orbital (δorb C2 ) and hyperfine (δC2 ) contributions, shown below and above the black crossbar, respectively. The δC2 is calculated for temperature calculated by the DKS method (see Table S26 in of 293 K; solvent correction from the corresponding SO-ZORA calculation was used for δorb C2 Supporting Information).

shift of C2 is dominated by the FC contribution, see δFC C2 highlighted in bold in Table 3. The dominant role of the FC Table 3. DFT Calculated (DKS: PBE0/VTZ/upcJ-2/ CHCl3) Values of the g-Factor, Aiso (in MHz) and Hyperfine Contributions to the NMR Shift (in ppm) of C2 in Compounds 1a and 1ba parameter

compound 1a

compound 1b

giso Aiso δHF δFC δSD δPSO

2.030 +2.131 +223.3 +263.2 −6.3 −32.4

2.015 +4.873 +520.3 +538.2 −6.5 −9.2

Figure 9. Visualization of the total spin density (ZORA/PBE0/ TZ2P/CHCl3 level, isosurfaces at 0.0005 au) calculated for compounds 1a and 1b along with the total and AO-based spin populations at the Ru and C2 atoms, respectively. Note the differences between 1a and 1b in both 2pπ and 2s spin populations (shown for the C2 atom pointing toward the reader, not averaged value), where the later results in a different Fermi-contact contribution to the hyperfine NMR shielding at C2. The excesses of the α and β electronic spin states are shown in blue and red, respectively. For more details of the spin populations for individual atoms and different decomposition methods, see Table S31 in Supporting Information.

a

For NMR data of other atoms, see Table S27 in Supporting Information; for principal components of the g-tensors for compounds 1a−d, see Table S25 in Supporting Information; for hyperfine A-constants of C2 atoms in compounds 1a−d, see Table S28 in Supporting Information. Note the discrepancy between δHF and the sum of three individual terms (δFC + δSD + δPSO) amounting −1.2 ppm for 1a and −2.2 ppm for 1b, which arise from the minor neglected relativistic terms (see comments to eq 4).17,18

contribution is also evident from the sequential summation of the contributions of the molecular spin−orbitals (spinors, MSOs) to Aiso (Figures S13−S16 in Supporting Information), where the trend line for the FC contribution nicely parallels that for the total Aiso value, whereas the PSO and mainly the SD terms contribute only marginally. Therefore, only the FC contribution is analyzed and discussed in the following part. Because of the single-determinant DFT approach used in this study, three different values for C2 atoms in three ligand moieties have been observed. The values reported for the hyperfine and orbital contributions to the 1H and 13C NMR shifts were obtained by averaging the corresponding values for all chemically equivalent atoms (for individual values, see Table S28 and Figures S17−S20 in Supporting Information). As the Fermi-contact contribution to δHF is directly related to the distribution of spin density in the ligand (imbalance in the α vs β electron spin density),20,86 we plot the total spin density for compounds 1a and 1b in Figure 9. It is evident that the α-spin density is “propagated” from the transition-metal center (the source of α-spin density) through the metal−ligand

bond, with further polarization steps in the π-space of the unsaturated ligand moiety (O−C1−C2 fragment) to reach the π-space of the spectator atom C2.20,84 This α-spin polarization in the 2pπ AO induces α-spin polarization in the 2s AO of the C2 atom (Hund’s rule),6 which generates a deshielding (higher-frequency) Fermi-contact contribution. Note the slightly different distribution of spin density in compounds 1a and 1b. The polarizable Br atom alters the electronic structure in 1b in a way that allows for greater electron spin propagation from the Ru center (total Ru spin population 0.86, d-AOs 0.85) as compared to that in 1a (total 0.89, d-AOs 0.87), Figure 9. The calculated total spin populations at the spectator atom C2 in 1b and 1a are 0.043 (0.036 for 2pπ; 0.0037 for 2s) and 0.034 (0.029 for 2pπ; 0.0028 for 2s), respectively. The data summarized in the previous paragraph represent clear evidence that upon formation of the Ru−O bond, the spin density propagates via the π-space of the ligand before G


Article

Inorganic Chemistry

Figure 10. (a) Schematic graphical representation of the selected π-type spin−orbital interactions between the ligand (L) and the metal (M). (b) HOMO π-type orbitals for the anionic form of ligands a (left) and b (right) calculated at the ZORA/PBE0/TZ2P level. (c) The visualization of electron deformation density for, and electronic stabilization by, π-type β NOCV channel (for additional NOCV channels, see Supporting Information),80 which is the most important for the formation of the metal−ligand bond in 1a and 1b. Note a decrease in β spin density in the πspace of the C2 atom.

Table S32 in Supporting Information)56 of the bonding between the [RuL2]+ and L− fragments indicates a somewhat stronger covalent component of the Ru−O bond in compound 1b (ΔEorb = −141 kcal·mol−1) compared to 1a (ΔEorb = −136 kcal·mol−1), which is reflected in the ∼300 ppm larger δHF C2 for 1b (Table 3). As the central metal atom is identical in both compounds, the anionic forms of the ligands (2-X-βdiketonates; a: X = H, b: X = Br) were analyzed, and the HOMOs were found to be of the relevant π-symmetry relative to the M−L bond, Figure 10b. The HOMO is slightly more stabilized in the Br-substituted anionic ligand b compared to that in the reference unsubstituted anionic ligand a (ΔE = 0.25 eV, ZORA/PBE0/TZ2P/vacuum), and it can therefore be involved in a more efficient π-bonding metal−ligand interaction with the unoccupied d-orbital (β-spinor, SUMO in Figure 10) of the ruthenium atom. This phenomenon contributes to greater spin polarization of the somewhat more delocalized π-electrons in the ligand moiety of compound 1b compared to 1a. Note, however, that previously reported data for a series of Cr(III) β-diketonates have indicated a considerable π-type delocalization of the metal electrons through the π* orbitals of the ligands.89 In passing, the authors noted that the degree of back-bonding for β-diketonate is similar to that for cyanide. Although we cannot rule out the contributions of the LUMOs (π-accepting orbitals) of the anionic forms of the ligands90 to the spin-propagation mechanism, our analysis indicates the importance of the π-donating ligand → metal interaction in the ligand hyperfine NMR shifts. The dominant role of the π-

penetrating down to the 2s AO and reaching the nucleus of the NMR spectator atom C2. The propagation of the spin density from the metal center must therefore be related to the πcomponent of the metal−ligand bonding, particularly the πdonating/accepting ability of the ligand.87,88 How is this metal−ligand electron sharing realized? The σcomponent of the Ru−O bond is formed by classical donation of the lone pair of electrons of the negatively charged ligand to the vacant d-orbital of the positively charged ruthenium atom. However, the π-component of the Ru−O bond can be thought of as being formed in the following way. The β-spinor of the highest occupied molecular orbital (HOMO) of the ligand interacts with the singly unoccupied molecular orbital (SUMO, metal β-spinor) of the ruthenium; this represents L → M donation in the π-space (see Figure 10a). Note that this process leaves an overabundance of α-spin density in the πspace of the donating oxygen atom (cf. Figure 9). Simultaneously, the singly occupied molecular orbital (SOMO, metal α-spinor) of the ruthenium atom can interact with the α-spinor of the lowest unoccupied molecular orbital (LUMO) of the ligand. This M → L back-donation process also “generates” an overabundance of α-spin density in the πspace of the oxygen atom of the ligand. Although the relative roles of these two processes are not quantified here, they can synergistically generate α-spin density in the π-space of the oxygen atom that propagates further in the ligand fragment by spin-polarization mechanisms. What then is the difference between the π-type M−L bonds in 1a and 1b? In general, energy decomposition analysis (EDA, H


Inorganic Chemistry

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component of the M−L bonding for the α/β electron spin imbalance at the C2 atom has also been identified by EDANOCV analysis,80 where the most important β-unpaired NOCV channel represents the ligand → metal π-bonding interaction, see Figure 10c.18,20 In summary, we demonstrated that the substituentmodulated π-bonding ability of the ligand alters the extent of electron sharing between the metal and ligand atoms in πspace, a phenomenon reflected in the α/β electron spin imbalance in the ligand moiety and transcribed in the Fermicontact contribution to the hyperfine NMR shift of the C2 atom.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00073. Crystallographic data and structural parameters for compounds 1d and 2b, experimental and calculated NMR data, additional figures, and Cartesian coordinates (PDF) Accession Codes

CCDC 1812432−1812433 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

4. CONCLUSIONS A combined experimental NMR and relativistic DFT study of the 1H and 13C NMR chemical shifts in a series of synthesized paramagnetic Ru(III) and diamagnetic Rh(III) complexes with 2-substituted β-diketones was performed. Temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the total NMR shifts for the Ru(III) complexes were estimated from the Curie plots: NMR shifts (measured in the temperature range 241−342 K) plotted versus the reciprocal of the absolute temperature (1/T). DFT was used to calculate the EPR and NMR parameters at both the two-component (SO-ZORA in ADF) and fourcomponent (DKS in ReSpect) levels. The calculations were calibrated based on the 13C NMR shift of C2, which is significantly affected by the hyperfine contribution. The effects of basis sets, exact-exchange admixture in the PBE0 functional, and solvent (vacuum vs implicit solvent model) were examined, and the PBE0/VTZ/upcJ-2/PCM level was selected for further calculations using the DKS method. The total 13C NMR chemical shifts calculated using the DKS method at the above-mentioned DFT level are in excellent agreement with the experimental values, and significantly better than those calculated using the SO-ZORA approach with a similar triple-ζ basis set quality. A notable discrepancy between the calculated and experimental values was observed for both the orbital and hyperfine contributions to the 13C NMR chemical shifts. The source of this discrepancy is currently a mystery to us and could originate from an error in the experimental estimation of terms from the Curie plot, cancelation of errors between the orbital and hyperfine contributions in the DFT calculations, or possibly from neglecting the low lying excited states in the theoretical calculations. However, the theoretical calculations do provide an opportunity to interpret substituent-induced changes in the hyperfine NMR shifts in terms of electronic factors. The magnitude of the spin polarization in the ligand moiety is significantly modulated by the substituent bonded to the C2 atom. The polarizable substituent bromine modulates the electron density in the ligand in a way that allows for a more efficient spin polarization compared to hydrogen, which results in a greater α-spin population in the 2pπ AO at C2, subsequently a greater α-spin population in the 2s AO at C2 and leads to a larger contribution of the Fermi-contact term to the hyperfine NMR shielding of this carbon atom. Our results show that even for transition-metal complexes with the spin density highly localized at the central metal atom, the presence of a single unpaired electron inducing spin polarization in the ligand moiety significantly influences the NMR resonances of distant ligand atoms through the FC term.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Lukás ̌ Jeremias: 0000-0001-8744-6897 Jan Novotný: 0000-0002-1203-9549 Stanislav Komorovsky: 0000-0002-5317-7200 Radek Marek: 0000-0002-3668-3523 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Czech Science Foundation (Grants 15-09381S and 18-05421S) and by the Ministry of Education, Youth and Sports of the Czech Republic under the National Sustainability Program II (LQ1601). The CIISB research structure project LM2015043 funded by MEYS CR is gratefully acknowledged for the financial support of the measurements at the CF Josef Dadok National NMR Center and CF X-ray Diffraction and Bio-SAXS. Financial support was also received from the SASPRO Program (1563/03/02) cofinanced by the European Union and the Slovak Academy of Sciences, the Slovak Research and Development Agency (Contract APVV-15-0726), and the Research Council of Norway through its Centers of Excellence scheme (Grant 262695). Computational resources were provided by the CESNET (Grant LM2015042) and the CERIT Scientific Cloud (Grant LM2015085).

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REFERENCES

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