Diffusion NMR spectroscopy applied to coordination and organometallic compounds

CHAPTER THREE

Diffusion NMR spectroscopy applied to coordination and organometallic compounds Álvaro Raya-Barón, Pascual Oña-Burgos, Ignacio Fernández Department of Chemistry and Physics, Research Centre CIAIMBITAL, University of Almerı´a, Almerı´a, Spain

Contents 1. Fundaments of the diffusion NMR methodology 2. Application to metal complexes 2.1 Transition metals complexes 2.2 Alkaline and alkaline–earth complexes 2.3 Main-group metals complexes 2.4 Rare earth complexes 3. Applications to cluster complexes 4. Applications to supramolecular structures 5. Conclusions References

127 138 139 152 161 162 168 172 180 181

Abstract This chapter illustrates an extensive review of the application of diffusion NMR techniques on coordination compounds and organometallic systems that gives an idea of the extraordinary progress that this field has achieved, whether using PGSE or DOSY methodologies. The estimation of diffusion parameters using all the advantages of highresolution NMR spectroscopy specially with modern probeheads, that allow the use of intense gradient fields and the tuning of less conventional nuclei, have begun new perspectives to determine the size and shape of many molecular systems in solution. In both, supramolecular architectures or smaller metallic complexes, this type of measurements allows one to assess their aggregation state, character of intermolecular interactions, stability or association constants between different hosts and guests, among many other interesting features. The main aim of this review is to present an overview of the PGSE and DOSY NMR mapping and its applications in inorganic systems, specifically coordination compounds based on transition metals, alkaline, alkaline-earth, maingroup, and rare earth metal centres, as well as cluster complexes and metal-based supramolecular structures. A brief introduction to pulse-field gradient NMR is also given, with special emphasis on the methodological procedures that can be used to obtain good quality data, providing different possibilities when choosing different variables,

Annual Reports on NMR Spectroscopy, Volume 98 ISSN 0066-4103 https://doi.org/10.1016/bs.arnmr.2019.04.004

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such as the correct pulse sequence or the right equation that govern both the friction and/or shape factor. The material given in this review are appealing in its simplicity, offer chemically useful results and we believe they should significantly boost the use of diffusion NMR measurements. Keywords: Diffusion NMR, PGSE, DOSY, Organometallics, Coordination compounds

Formation of intermolecular complexes, molecular recognition, association and/or aggregation, rearrangements towards the formation of supramolecular architectures, inclusion complexes, molecular vehicles, ion pairing, and generally speaking the study of molecular interactions, represents one of the most challenging and promising fields for chemists and biochemists. In parallel, the understanding of the structures involved in organic and organometallic reactions, homogeneous and heterogeneous catalytic systems, complex mixtures as well as ionic liquids (IL), is also an arena of tremendous projection, among other reasons due to their industrial implications. NMR represents one of the most important structural elucidation tools in organic and organometallic chemistry. Throughout the last decades, numerous experiments have been developed that make possible to obtain structural, spatial, and dynamic information of a vast variety of systems. However, in certain situations, conventional NMR does not allow obtaining all the information, in many cases crucial, for its complete understanding. At the dawn of the NMR, methods capable of obtaining diffusion coefficients were developed, although their greater use and exploitation had to wait until the 90s or perhaps somewhat later. In this context the present review is introduced and centred around the applications of multinuclear NMR, and in particular on the use of diffusion experiments based on magnetic field gradient pulses towards the study of molecular interactions in inorganic and organometallic systems. It does not pretend to be an NMR review per se, and for the fundamentals of NMR numerous excellent texts are currently available [1]. The literature reported until 2005 on the application of PGSE NMR to the determination of molecular volumes, hydrogen bonding and ion pairing of coordination compounds containing organic ligands have been nicely reviewed by Pregosin et al. [2] and recently updated by himself in 2017 [3]. The present chapter will review reports of the application of PGSE and DOSY NMR to coordination and organometallic compounds starting from 2005 until February 2019. The chapter includes >200 references that are distributed along four sections that are given below.

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1. Fundaments of the diffusion NMR methodology The estimation of molecular size also represents a topic of growing interest, since it allows to address the study of problems related to the degree of nuclearity and/or aggregation, ion pairing, hydrogen bonding strength, association constant, as well as molecular weight prediction. Diffusion is the result of the translational movement induced by the temperature in a stochastic random path experienced by molecules in solution. It can be thought of as a Brownian motion without an applied force and thus on the average no net movement is observed, so then molecules that start together in the same vicinity will be separated. In fact, this Brownian motion is one of the critical factors, other than activation energy and orientation, responsible for all chemical reactions since the reacting species must collide before they can react. Mathematically, in an isotropically homogeneous medium, the probability of finding a molecule in a given position rt when it started its movement in an initial position r0 after a time t, is given by Eq. (1).
 (1) P ðro , rt Þ ¼ ð4πDt Þ3=2 exp ðrt  ro Þ2 =4Dt The radial distribution of the molecules in a system of infinite length obeys to a Gaussian function, where its width increases within time. Again, in an isotropic medium and without gradients of concentration and/or temperature, the average displacement of a molecule in the three directions (n ¼ 2 or 4, and not 6, for movements in one or two directions of space) is given by the so-called Einstein’s relationship given by Eq. (2).  2 r ¼ 6Dt (2) The diffusion coefficients usually adopt values between 109 m2/s (small complexes in solutions of low viscosity) up to 1012 m2/s (usually coordination polymers or macromolecular clusters). Formally, the diffusion coefficient is given by Eq. (3). D ¼ kB T =f

(3)

where T represents the absolute temperature, kB the Boltzmann constant, and f the so-called friction factor. For a sphere of radius r in a continuous medium of viscosity η, the friction factor is given by the Stokes equation (Eq. 4). f ¼ 6πηr

(4)

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The combination of the above equations provides the Stokes-Einstein relationship given by Eq. (5). kB T D¼ (5) 6πηr This expression is commonly used in the calculation of the hydrodynamic radius. Initially, it was proposed that for small molecules the factor 6 in Eqs. (4) and (5) could be replaced by a factor of 4 [4]. However, this approach that maintains part of the Stokes model received over the years multitude of objections, and finally most of the scientist whether keep the number 6 or just replace the whole equation by some other alternatives. In this regard, it has settled other theories that describe the friction factor with geometries other than the spherical, or even assuming as spheres the solute and the solvent, describing the friction factor as a value dependent on the molecular size of both [5]. In this way, a coefficient c is usually incorporated into the previous expression, that is dependent on both the radius of the solute and of the solvent. The expression dependent on the quotient rd/rH comes from the theory developed by Wirtz (Eq. 6) [6], which was later on improved by Chen (Eq. 7) [7]. !1 3rd 1 c ¼6 +  rd  (6) rH 1 + =r H "  2:234 !#1 rd (7) c ¼ 6  1 + 0:695  rH It is therefore clear the importance of using expressions that regulate the magnitude of c, especially for organic and organometallic systems of smallmedium size. In fact, from analysis of the prerequisites underlying the Stokes-Einstein model it follows that the smaller the system under study (hydrodynamic radius of the system becomes comparable with the radius of solvent molecules) and/or the greater the deviation of its shape from a sphere (prolate/oblate ellipsoid or systems with long molecular chains) the greater the errors in the size determination using the Stokes-Einstein equation, what makes necessary the introduction of an fs factor which includes the deviation of the shape of the species under study from the spherical shape. A nonideal shape and size of a real molecule can be accounted for by modifying Eq. (5) as follows: [8] D¼

kB cfs πηr

(8)

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A more correct analysis requires models that take account of the shape and relative size of the molecule of the compound under study. In general, frictional coefficients are calculated with the help of the hydrodynamic equation, particularly the Stokes equation (Eq. 4) for low Reynolds numbers. Apart from the sphere, exact solutions for fs are only available for some other simple geometries such as cylinders and ellipsoids. The surface area of an ellipsoid, for instance, is greater than that of a sphere of the same volume, and therefore, its friction factor is larger for both prolate and oblate ellipsoids than for the equivalent spheres. These factors for cylinders and ellipsoids are given in Table 1. For ellipsoid type systems (prolate and oblate), this parameter fs, depends on the relationship between the semiaxes b and c [10]. Interestingly, if these semiaxes ratio b/c is higher than 3, the error in the results obtained using Eq. (5) will be >10%. Also, it is quite probable that the product of the coefficient c and the friction factor fs in Eq. (8) will be equal to 6, i.e., Eq. (5) will formally be valid. Thus, for most practically used molecular species in solutions, Eq. (5) should probably be used with care and only as a first approximation [8]. As already mentioned, the first theoretical and experimental demonstration of self-diffusion coefficient measurements by NMR is attributed to Stejskal and Tanner in 1965 [11]. Diffusion NMR methodology holds Table 1 Friction coefficients for three simple geometries (sphere, cylinder and ellipsoid) in the stick boundary conditions. Shape Parameters Friction factor (fs)a

a, radius

Sphere Cylinder

b

d, diameter; l, length; p, l/d; a, l  (3/16p2)1/3

Oblate ellipsoid

b, semi-major axes; c, semi-minor axes; p, b/c (<1); a, (b2c)1/3

Prolate ellipsoid

p, b/c (>1); a, (bc2)1/3

a

6πηa 

2 1=3 2 fsphere ln3pðpÞ + ϑ 2 ϑ ¼ 0:312 + 0:565 p  0:100=p pffiffiffiffiffiffiffi2ffi 1p pffiffiffiffiffiffiffi2ffi fsphere 1p 1=3 1 =p p tan pffiffiffiffiffiffiffi ffi 2 pp1ffiffiffiffiffiffiffi ffi fsphere p2 1 =p p1=3 tanh 1

The value of “a” given for each geometry it is used for calculating the respective value of fsphere. This formula is only valid for p in the range from 2 to 20 [9].

b

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nowadays a special position among the different experiments available to the NMR spectroscopist thanks to the continuous hardware and software improvements that make the measurements of diffusion coefficients a straightforward procedure. A scan of articles published in top journals that includes the terms “PGSE” or “DOSY” as topic shows that the majority comes from the chemistry arena and right after from the biochemistry molecular biology field. If one sorts out the results in terms of authors, the top three are Morris with 60 publications, Nilsson with 59 and Pregosin with 54. Fig. 1 shows these distributions out of an overall of 2528 publications. The evolution of publications reveals a year by year increasing trend with 2017 as the year with the maximum number of 193 publications. Again, the search topics were whether PGSE or DOSY (Fig. 2).

Fig. 1 ISI Web of Knowledge search results per research area (top) and author (bottom). The search words were “PGSE” or “DOSY” both as topic.

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Fig. 2 Evolution of publications (articles per year): 1967–2019. Source: Data collected from ISI Web of Knowledge. Computations by the authors.

The theoretical and methodological aspects of diffusion NMR have previously been covered in several reviews [12] and books [13]. In brief, it separates NMR signals according to diffusion coefficients which is finding increasing use for the analysis of mixtures of small to large-sized molecules. Diffusion NMR experiments contain a pair of gradient pulses as the medullar part of the sequence, which linearly vary the magnetic field along the longitudinal axis of the sample. The experiment provides a series of 1D NMR spectra in which the intensity of each signal experiences an attenuation (Ediff ¼ I/I0) according to the Stejskal-Tanner (ST) equation on increasing the magnetic field gradient strength G. Ediff ¼ eDγeff δ σ 2

2 2

G2 Δ0

(9)

The most common form of this equation, assuming free diffusion, is a Gaussian decay function in which D is the translational diffusion coefficient of the molecule to which the monitored signal belongs, γ eff is a linear combination of the gyromagnetic ratios of the nuclei studied depending on the coherence transfer pathway, δ is the PFG duration, and σ is the gradient shape factor. The diffusion delay Δ is the time between the two PFG pulses in which the molecular diffusion can induce its effect, while Δ0 is this same delay corrected by an amount that depends on the specific pulse sequence and gradient shape used [14]. For a continuous distribution of diffusion coefficients, A(D), Eq. (9) could be replaced by the following integral equation to describe the signal decay. ð∞ 2 2 2 2 0 Ediff ðgÞ ¼ AðDÞeDγeff δ σ G Δ dD (10) 0

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To measure the translational diffusion coefficient, several 1D spectra are recorded at various gradient strengths G, resulting in an attenuation for each signal. Fitting Eq. (9) to these signal attenuations then provides the diffusion coefficients of the molecules associated with these signals. When signals arising from molecules with different diffusion coefficients overlap in the spectrum, the process to resolve the multiple diffusion coefficients becomes significantly more complicated and over the years several processing techniques have been described to deal with this issue [15]. Fig. 3A and B illustrates the two basic pulse sequences based on the theory described previously. The first pulse sequence is based on a spin-echo (SE) while the second one it is recorded using a stimulated spin echo (STE). In both cases the first step is to excite the spins using a 90° radiofrequency (RF) pulse. Spins are now in the x,y-plane and relax according to the transverse relaxation time T2. After this RF pulse, a gradient pulse of intensity G1 and duration δ is applied. At the end of this gradient pulse, the spin spatial position is encoded inside the spin phase shift. The molecules are let to diffuse during a time interval Δ. During this diffusion time, the magnetization is either transversal or longitudinal for the SE or STE pulse sequence, respectively. At the end of the diffusion time Δ, a second gradient pulse having the same magnitude and duration as the first one is applied. This second gradient pulse rephase the spins since it has an ‘effective sign’ opposite of that of the first one. Usually, there are two options to produce a gradient pulse with an ‘effective sign’ opposite of that of the first pulse. Either it is a gradient pulse with indeed a current in the opposite direction

Fig. 3 Typical pulse sequences for the PGSE experiments: (A) the Stejskal-Tanner spinecho (SE) experiment; (B) the stimulated Stejskal-Tanner spin echo (STE) experiment modified via substitution of a single 180° pulse for two 90° pulses. The homospoil gradient pulse (Gh) during longitudinal storage is shown in solid black.

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(opposite sign) or, because the spins were inverted by an RF pulse, a gradient pulse having the same sign as the first one. However, all experimental methods including the NMR-based determination of self-diffusion coefficients have some limitations. Problems of diffusion NMR experiments are usually of hardware nature, where the most studied and basically solved are those derived from eddy currents, quality of the pulse field gradient generated and temperature gradients. Generation of gradient pulses is accompanied by fast switching of electric current in the gradient coil and induction of eddy currents in metallic parts of the probe around the NMR tube, which leads to distortions of the spin echo signal. Modern probes are equipped with active-shielding systems [16], which reduce the amplitude of eddy currents by a few orders of magnitude. However, when using large-amplitude PFG, the effect of eddy currents may be noticeable. There are few alternatives of minimization of this effect. One of them includes the modification of the shape of the gradient pulse in order to reduce the amplitude of eddy currents and minimize their effect on the spin echo signal. Since the amplitude of eddy currents is proportional to the rate of the change in electric current flowing through the gradient coil [16], the use of smoothly increasing/decreasing gradient pulses should lessen eddy currents. This is the reason why most of the spectrometers have already settled-up SMSQ (smoothed square shaped) instead of rectangular pulses in their diffusion methodologies. Alternative shapes are trapezoidal, sine or half-sine pulses, among others. A drawback of this approach consists in that, owing to the smaller area under the curve for non-rectangular gradient pulses compared to rectangular at the same amplitude, the action of the former on the system will be less pronounced; this can be critically important in the studies of systems with small self-diffusion coefficients such as high average-weight molecular weight polymers or supramolecular architectures. However, even non-rectangular PFG do not allow a full suppression of eddy currents. In this regard, pulse sequences based on the stimulated echo (STE, Fig. 3B) sequences including: STE-LED (stimulated echo with longitudinal eddy current delay, Fig. 4A) [17] and especially STE-BPP-LED (stimulated echo with bipolar pulse pair and longitudinal eddy current delay, Fig. 4C) have proved themselves to be robust alternatives to avoid eddy currents effects [18]. Suppression of eddy currents can be also achieved using an additional time delay Te (Fig. 4A and C) at the end of the pulse sequence. The essence is that the fourth RF pulse causes the magnetization vector to leave the xy

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Fig. 4 Typical pulse sequences for the PGSE experiments: (A) STE-LED (stimulated echo with longitudinal eddy current delay), (B) STE-BPP (stimulated echo with bipolar pulse pair), (C) STE-BPP-LED (stimulated echo with bipolar pulse pair and longitudinal eddy current delay), and (D) DSTE-BPP (double stimulated echo with bipolar pair pulses) for compensation of convective flow effects. Homospoil gradient pulses (Gh) during longitudinal storages are shown in solid black.

plane and become parallel to the z axis, thus no longer being affected by the shaded gradients induced by eddy currents. The magnetization vector retains its orientation over the time interval Te (usually 50 ms), which is long enough for eddy currents to decay [12b]. Then, under the action of the last 90° pulse the magnetization vector returns back to the xy plane, which is followed by detection of the FID during the acquisition time (AQ). The BPP module uses composite gradient pulses (two gradient pulses having halved duration and opposite signs separated by a 180° pulse). These opposite-signed gradient pulses make the eddy currents induced by them be cancelled [19]. An added value of this last module, is that the composite pulse field gradient pulses allow one to minimize the effects of inhomogeneity of the main magnetic field B0 and cross-relaxation [20]. As mentioned previously, temperature gradients within the sample can induce errors in the estimated self-diffusion coefficients. If the temperature of the sample placed into the probe of an NMR spectrometer is not stabilized, the sample could experience a nonuniform temperature, which creates a temperature gradient. If this gradient is rather large, longitudinal

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convective flows of the liquid along the sample appear which are superimposed with diffusion flows. This causes strong distortions of the diffusion decays (up to sinusoidal modulations of the decay curve) [21]. Most diffusion NMR experiments are carried out at ambient temperature. However, for some applications, it is necessary to measure at higher [22] or lower temperatures [23]. The latter would be the case for inorganic or organometallic complexes that are fluxional or unstable in solution at ambient temperature, a common observation. The heating or cooling of the sample may have, potentially, two negative effects on diffusion measurements. On one hand, it can affect the mechanical stability of the experimental setup, which is obviously detrimental, and in on the other, it may cause the formation of convection currents within the sample, which can be mistaken for faster diffusion, or even completely distort the shape of the intensity decays [21]. There is a number of methods for minimization of temperature gradients in the sample: (i) reduce the diameter of the sample by the use of commercially available coaxial NMR tubes [24], (ii) the height of the sample can be reduced [25], (iii) the viscosity of the sample can be increased, (iv) the air-gas flow velocity can be increased [26], (v) the temperature control system can be redesigned [27], or (vi) the sample can be spun at a rate synchronized with Δ [28]. Reducing the diameter of the sample minimizes longitudinal flows owing to friction on tube walls [21], but at the same time, it leads to a decrease in the signal-to-noise ratio due to a reduction of the volume sample. To solve this problem, one can use specially shaped tubes in which the volume of the sample is confined from both sides by two inserts whose magnetic susceptibility is chosen to be close to that of the solution [29]. However, when working at temperatures above or below room temperature it is increasingly difficult to control these currents and therefore new pulse sequences have been developed that compensate for these effects. Fig. 4D shows the so-called double stimulated sequence that looks to make the effective temperature gradient in the sample becomes equal to zero. A drawback of this double stimulated pulse sequence is the need for enhanced phase cycling. In addition, the overall sensitivity of this pulse sequence is somewhat lower than non-doubled sequences because of the longer duration of the DSTE sequence, i.e., when quadrupolar nuclei are measured such as lithium-7 [23,30], boron-11 [31], or chlorine-35 [32]. As a result, the corresponding relaxation decay is also longer. However, it is clear that in some cases the loss of sensitivity can be compensated by the gain from minimization of convection.

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Solvent suppression can be added to all these pulse sequences by either adding a module of excitation sculpting at the end of the diffusion encoding period [33] or combining the WATERGATE strategy within the bipolar gradient scheme [34]. For the latter, a LED delay can readily be added if necessary. From Eqs. (9) and (10) one can note that, with the exception of the diffusion coefficient D, all the other parameters are either fixed in the pulse sequence (G, δ and Δ) or measured (Ediff). To estimate the diffusion coefficient, one of the fixed parameters must be varied in discrete steps to then fit the experimental signals according to Eq. (10). To keep all the times similar from one experiment to the other, the experimentalist usually varies the intensity of the pulsed gradients G. Indeed, if a duration parameter is changed, then the effect of relaxation times must be included in the signal expression. Typical experimental times are in the range of minutes when the samples are concentrated or nuclei with high receptivity are the choice, to a few hours for diluted samples or when less active nuclei are monitored. Several pulse sequences have been proposed to decrease this experimental time based either on a decrease of the phase cycling [35] or on the recording of the diffusion information within one scan by spatial parallelization (SPEN) [36]. The former is probably the most used pulse sequences to save experimental time which is based on unbalanced bipolar gradient pulses that reduces the length of the phase cycling. In this pulse sequence, called Oneshot, coherence-selection and diffusion-encoding gradients are merged to reduce the number of required scans to one per increment. More recently a spatially encoded sequence has been introduced that makes the whole acquisition time being reduced to just 1 s. The new method developed by Dumez and coworkers relies on a spatial encoding of the diffusion dimension, for which convection-compensation is introduced [37]. For the fitting, the method of choice is usually the inversion of Laplace Transform (ILT). This ILT is classified as an ill-posed problem which were originally introduced by Hadamard [38]. Since the initial and boundary conditions are not well defined, eventually strong vulnerability to noise and numerical instability have induced the emergence of different approaches. These can be divided in those based on total band shape, known as multivariate methods, and those run by single channel methods. Representatives for multivariate methods are DECRA [12b], MCR [39], SCORE [40] and OUTSCORE [41]. As single channel, we can regard Levenberg-Marquardt statistical method [42] and SPLMOD [43]. All these approaches consider the diffusion coefficient as monodisperse. Instead, other approaches that consider the diffusion coefficient as a distribution are CONTIN [44], maximum entropy (MaxEnt) [45] and more recently PALMA [46]. Urbanczyk

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et al. have described a new method that uses a tailored regularization term designed to automatically tune to the different polydispersity of the sample [47]. We have recently introduced a genetic algorithm [48] and an algebraic reconstruction technique (dART) to solve this inversion problem specially in overlapped resonance signals [49]. As an example, Fig. 5A shows the NMR spectra recorded as a function of the gradient strength G for an unknown mixture of species in deuterated

Fig. 5 (A) Raw 1H NMR PGSE diffusion experiments in deuterated chloroform at room temperature, using the stimulated echo sequence, showing the signal attenuation of the different components of the mixture. (B) Stejskal-Tanner plots of some of the monitored signals. The solid lines represent linear least-squares fits to the experimental data.

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chloroform. It is clear that different NMR signals are attenuated at different rates and according to the signal expression, this is due to different diffusion coefficients, i.e., the signals at 0.24 (blue dot) and 1.36 ppm (white dot) do not belong to the same molecular entity. To extract the value of the diffusion coefficients, the logarithmic evolution of the signal as a function of the experimental conditions can be plotted as given in Fig. 5B. The experimental data points are aligned with the slope corresponding to the diffusion coefficient. As will be noted in some of the examples described below, PGSE NMR data have been also found useful to estimate molecular weights, owing that in some cases mass rather than geometrical features is often the parameter to be determined, and especially the empirically derived Flory scaling relationship [50] is probably the most straightforward relation between Mw and D (Eq. 3). D ¼ AMwα

(11)

Delsuc and coworkers have checked the validity of this power law equation for a large set of molecular types and molecular weights, introducing α as a measure of the fractal dimension dF (¼1/α) [51]. Further, Li et al. [52] have employed Eq. (4) derived for the first time by the Williard group [53], to linearly relate D and Mw, which incorporates the density of the molecule (ρ) and the Avogadro constant (NA).  1 1 1 1 162π 2 (12) log ðDÞ ¼  log ðMW Þ + logρ  log η  log k3B T 3 NA 3 3 3 3 In some cases, for this kind of determination, several standards of known formula weight (FW) must be placed together with the analyte within the same sample. Then, D values are calculated for all the components and the FW of the analyte can be estimated via extrapolation or interpolation from the D-FW correlation found for the standards [54].

2. Application to metal complexes In coordination chemistry, X-ray diffraction analyses of the crystalline products are often used to assess the coordination modes, nuclearity and 3D structures of the complexes under study. However, all these features can be dramatically altered upon dissolution. Since many of the coordination and organometallic compounds presented in the literature are employed as reactants or catalysts in solution-state, it is critical to know how they perform in solution, rather than that in the solid state, in order to better understand their

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chemical behavior. In this sense, diffusion NMR methodology constitutes a well-established analytical tool that provides valuable information about many of these aspects.

2.1 Transition metals complexes The group of Schubert has assembled poly-pyridyl ruthenium and iridium complexes of significance for their use in sensors and electronic devices employing a 2-ureido-4[1H]-ureidopyrimidinone ligand [55]. The Ru(II) complex was studied through 1H DOSY NMR in CD2Cl2 solution and in the presence of trifluoroacetic acid (TFA). The diffusion coefficient found in CD2Cl2 solution (0.676 times the one found for cyclodextrin, employed as internal standard) was smaller than that measured in the CD2Cl2-TFA mixture (0.965 times the D-value obtained for cyclodextrin), suggesting that the Ru(II) complex exists as a dimer in CD2Cl2 solution but dissociates to form a monomer in the presence of TFA. On the other hand, the Ir(III) complex was not subjected to these experiments because it decomposed in the presence of TFA during the long time (14 h) required to perform the DOSY measurements. Hijazi et al. reported in 2007 the use of 1H DOSY experiments to define the aggregation state of a dinuclear Ru/Cr complex (1) in DMF-d7 solution [56]. Complex 1 was found to form a tetranuclear chloro-bridged dimer ˚ , notably larger than that of (Fig. 6), as suggested by its rH value of 6.3 A ˚ 3.5 A found for the monomeric complex in CDCl3 solution. It is worth mentioning that an ellipsoid model treatment (see Table 1) was applied to ˚ the dimeric complex 1, allowing to calculate an equatorial length b of 14 A ˚ and a polar length c of 12A.

Fig. 6 Dimeric heterometallic Ru/Cr complex.

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Macchioni and co-workers have studied the ion pairing in solution of arene ruthenium complexes via DOSY in several reports, and disclosed interesting results [57]. The importance of 1H and 19F PGSE NMR experiments was highlighted when distinguishing aggregation states of ion pairs and quadruples of Ru(η6-arene) cationic complexes with different fluorinated anions [57a] as well as the identification of ion triples of Ru complexes with alkoxy-tailored ligands as a result of their ability to form intercationic hydrogen bonds [57b]. These ion triples consisted in two Ru complex cations aggregated with a BF 4 anion, resulting in a species of the type + [Ru]2BF4 , which was deduced from the molecular volumes (VH) calculated for the cationic and the anionic species in solution. PGSE NMR measurements also confirmed the formation of dications via intermolecular hydrogen bonding between protonated Ru(η6-arene) complexes with PTA (1,3,5-triaza-7-phosphaadamantane) ligands in acetone solution [57c]. The relationship between ion pairing of these type of Ru(II) complexes in solution and their catalytic performance was also investigated by Macchioni with the aid of PGSE NMR techniques [57d]. It was suggested that bulky and strongly ion pairing anions disfavoured the catalytic activity of the cationic Ru(III) complex. In a very recent work, Biancalana et al. studied the hemilabile character of (2-diphenylphosphino)phenol when coordinating to the ruthenium precursor [(η6-p-cymene)RuCl2], for what PGSE NMR measurements in combination with DFT calculations allowed to ascertain aggregation states in solution at different concentrations [57e]. They found that higher concentrations of the Ru precursor favoured the coordination of the alcohol in the (2-diphenylphosphino) phenol ligand to the metal centre, resulting in cationic complex 2 (Scheme 1), while at low concentrations of Ru the equilibrium was favourable to form complex 3, in which both chlorides remain attached to the metal (Scheme 1).

Scheme 1 Hemilabile behaviour of (2-diphenylphosphino)phenol ligand depending on the concentration of Ru precursor.

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The research of Macchioni and collaborators have also been focused on the synthesis and characterization of zirconium and hafnium metallocene complexes [58]. Solution-state studies using PGSE NMR spectroscopy provided useful information to determine ionic aggregation states and their dependence on ionic ratios, steric effects and solvent polarity. In the case of zirconaaziridinium ion pairs [58b] (Fig. 7) it was observed that the selfaggregation tendency of ion pairs containing the MeB(C6F5)3 anion was unaffected by the nature of the R substituent (phenyl or long alkyl chain), while the ion pairs containing the weakly coordinating B(C6F5)4 anion showed a slightly higher self-aggregation tendency when R is a long C18 alkyl chain rather than a phenyl group. In addition, the ionic aggregation of zirconaaziridinium ion pairs in cyclohexane solution was around 10 times greater than in benzene solution, and an increasing temperature clearly disfavoured the formation of aggregates greater than single ion pairs. Machioni’s group has also provided insights of the olefin polymerization reaction catalysed by zirconium metallocene in the presence of methylaluminoxane (MAO) additives [59]. 1H PGSE NMR measurements supported that mixed salts are formed between Zr complexes and MAO with no tendency to self-aggregation. Similarly, DOSY NMR has been applied by Quanten et al. to Zr(IV)-substituted Wells-Dawson polyoxometalate, which has been pivotal to understand its reactivity as metallopeptidase employing a surfactant medium [60]. 1H and 31P DOSY NMR spectra were acquired to determine the hydrodynamic radii of the surfactant (through 1H) and the polyoxometalate (through 31P), which were nearly identical along all the concentration range, thus confirming the encapsulation of the zirconium complex inside the micelles. The influence of solution ion-pairing in catalytic processes where arene–ruthenium complex salts are involved have also been studied by

Zr

N

R R

O

X

Inner-sphere ion pair

N

Zr

R R

Outer-sphere ion pair

R = Me, Ph or alkyl chain X = MeB(C6F5)3- or B(C6F5)4-

Fig. 7 Zirconaaziridinium ion pairs studied by Macchioni.

X

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the teams of Pregosin and Dyson [61]. They combined PGSE and 1H,19F HOESY (heteronuclear Overhauser effect spectroscopy) NMR in order to compare diffusion coefficients of the cation and the anion. Thus, if the ions are closely paired in solution, the D(cation) and D(anion) values found will be identical, on the contrary if the ions are separated, their D values will be appreciably different. They observed that the D values of small fluorinated anions (OTf, BF4, PF6) differed considerably of those of their corresponding Ru-based cations in THF solution, while large aromatic anions (BPh4, BArF (B((3,5-CF3)2C6H3)4)) provided D values consistent with close ion pairing. The catalytic performance of the cationic Ru(η6arene) complex in styrene hydrogenation was higher in the presence of small anions (OTf, BF4, PF6) that produce a lower degree of ion pairing and therefore the cationic Ru complex provides better access to catalytic sites. Pregosin and co-workers have studied ion pairing in palladium complexes in a number of reports [62]. Comparison of the hydrodynamic radii (rH) of cationic Pd(II) complexes with binaphthyl (BINAP) ligands and their corresponding counter-anions revealed different ion pairing extents with a strong dependence on the solvent [62b,c]. The tendency observed for ion pairing of Pd(II)(BINAP) cations and fluorinated anions, such as PF6, OTf and BArF, was CD2Cl2 < THF < CDCl3. PGSE NMR measurements were accompanied by 1H,19F HOESY spectra, since both type of experiments can provide information about cation–anion interactions across space. This same experimental approach allowed them to identify a significant degree of ion pairing between Pd-(η3-allyl) cationic complexes and anionic tetraaryl boranes in CD2Cl2 solution [62d]. The group of Sen has carried out diffusion NMR to measure the Brownian motion of second generation Grubbs’ catalysts in metathesis reactions while performing ring closing metathesis (RCM) and cross metathesis (CM) [63]. The main contribution of this work is that the diffusion coefficient of the ruthenium complex (Grubbs’ catalyst) is constant during CM reactions, but it is increased during RCM transformations and then decreased back to its original value for the catalyst when the process is finished. This effect was explained by phosphine dissociation during RCM reaction, which does not necessary occur in CM. The hypothesis was also supported by DFT calculations. Finally, these authors employed the same strategy to demonstrate that diffusion NMR is a powerful tool to measure in situ modifications of the catalyst in Angstrom scale [64]. Kunz and co-workers successfully employed DOSY NMR to distinguish coordination modes and aggregation states of a palladium(0)

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complexes incorporating a bis-NHC-type ligand whether in solution (4) or in crystalline state (5) [65]. While X-ray diffraction analysis revealed a dimeric heteronuclear (Pd/K) arrangement of 5 (Scheme 2), the D value calculated from 1H DOSY NMR measurements was consistent with a monomeric structure of 4 (Scheme 2) in THF-d8 solution, although the exact coordination mode could not be ascertained. Metal-centred heterocubanes (Fig. 8) have been obtained employing four metallaligands based on a lithium–silanide complex [66]. The interesting structure found in the solid state was corroborated in solution employing 1 H and 7Li PGSE NMR measurements. The hydrodynamic radii calculated ˚ (Pd, complex 3) and 6.1 A ˚ (Pt, complex 4) that via diffusion were 6.0 A ˚ (Pd) and coherently matched those calculated via X-ray diffraction: 6.4 A ˚ 6.5 A (Pt). Abramov et al. have described the grafting of [Cp*Rh]2+ complexes on the surface of Lindqvist-type Nb and Ta polyoxometalates (POM) [67]. 1H DOSY NMR experiments were performed to confirm that the general

Scheme 2 Different coordination modes in solution and in the solid state of a Pd(0) NHC-type complex.

Fig. 8 3D-Structure of palladium- and platinum-centred heterocubanes.

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structure [{Cp*Rh}2M6O19]4 (M ¼ Nb, Ta) found in the solid state, ˚. remained in D2O solution, with an hydrodynamic radius of 7.20 A 31 In 2010, the group of Williard reported the use of P DOSY NMR to calculate the formula weight (FW) of metal complexes with phosphine ligands [68]. Several samples of manganese complexes (Fig. 9) with phosphine ligands (PMe3, PBu3, PPh3) were prepared in regular 5 mm NMR sample tubes containing a “microtube” insert in which an internal reference for 31P NMR measurements (OP(OMe)3, OPPh3, OP(n-octyl)3) was placed, so that the analyte and the reference were physically separated. As shown in Table 2, excellent D and formula weight correlations were predicted using this method, which prevents undesired interactions between the analyte and the internal reference in the sample. Go´mes and collaborators have provided the role of cobalt complexes as mediators in polymerization of styrene and methyl methacrylate [69]. In this study, DOSY NMR measurements were employed to corroborate that copolymers are promoted instead of homopolymers.

Fig. 9 Manganese complexes with phosphine ligands.

Table 2 Formula weight estimations for manganese complexes via 31P DOSY NMR D-FW correlations. Entry Compound FW (g/mol) Estimated FW (g/mol) % error

1

OP(OMe)3

140.07

137

2.1

2

OPPh3

278.28

297

6.8

3

OP(n-octyl)3

386.63

370

4.4

4

6

391.39

419

7.2

5

7

375.28

360

4.1

6

8

531.46

509

4.2

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Ruiz-Muelle et al. have carried out a deep study of the reactivity of titanocene (III) with propargyl chlorides [70]. In this study, propargyl chloride (terminal alkyne) and 1-chlorooct-2-yne (internal alkyne) were used to evaluate the reactivity of the dimer [TiIIICl2]2. Interestingly, the terminal alkyne exclusively afforded the allenic intermediate 9 (Scheme 3) while internal alkyne promoted only the propargyl derivative 10. Both systems were fully characterized by 1D and 2D NMR, where PGSE and DOSY experiments proved to be key to determine that these complexes are monomers in solution with hydrodynamic radii of 4.1 and 3.5 A˚ for 10 and 9, respectively, thus indicating that no self-aggregation takes place.

Scheme 3 Synthesis of allenic and propargylic Ti(IV) complexes used in Barbier-type reactions.

Zinc-based coordination compounds are in general diamagnetic, and this fact has prompted researchers to exhaustively study these systems through spectroscopic methods, specially NMR. The group of Meyer has synthesized a family of zinc complexes based on dithiophenolate platforms that exist as monomers or dimers in the solid state, controlled by steric effects (Scheme 4) [71]. The complexes were examined by DOSY NMR in CD2Cl2 in order to ascertain their nuclearity in solution, and the results were compared to the solid-state structures determined by X-ray diffraction. For the complexes bearing chloro- and tert-butyl-substituted 2,20 -dithiobiphenyl ligands (Scheme 4), the hydrodynamic radii found were very similar to the radii calculated for a monomer from the crystal structure, therefore the dimeric structure in the solid state dissociated into monomers in CD2Cl2 solution. In the case of the Zn(II) complex bearing the methylene-bridged ligand 2,20 -methylenedibenzenethiol (Scheme 3) the results of room temperature measurements were not conclusive. Low temperature (95°C) DOSY experiments were therefore carried out showed the presence of two species with different D, which suggested the existence of an equilibrium between monomeric and dimeric forms.

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Scheme 4 Zinc(II) complexes with dithiophenolate ligands.

Scheme 5 Conditions employed by Ay et al. for the asymmetric conjugate addition of diethylzinc with cinnamaldehyde utilizing [2.2]paracyclophane ligands.

Ay et al. carried out mechanistic investigations on the asymmetric conjugate addition (ACA) reaction of dialkylzinc reagents with aldehydes (Scheme 5), for which DOSY NMR measurements provided crucial information [72]. The existence of (ZnL)n (L ¼ [2.2]paracyclophane ligand, see Scheme 5) complexes was supported by X-ray diffraction analyses, DFT calculations and 1H DOSY NMR experiments, and a dimeric (ZnL)2 species was proposed to act as pre-catalyst in the ACA process. DOSY NMR also revealed that the aggregation state of these (ZnL)n complexes is highly dependent on temperature and concentration.

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DOSY NMR has also provided important information about the intermediates formed in the reaction between Grignards reagents and ketones in the presence of ZnCl2 [73]. At low temperature (40 °C) only one species is observed that corresponded to the anion [Zn2Et5]. Diffusion NMR established a molar volume of 226 cm3 mol1 whereas the calculated through DFT was 232 cm3 mol1. Interestingly, at room temperature the alkyl species detected showed a clearly smaller volume of 160 cm3 mol1. The authors proposed that at room temperature exists an equilibrium between [Zn2Et5], [ZnEt3] and [ZnEt2] that is shifted to the former at very low temperature. Lewinski and coworkers have employed DOSY NMR to elucidate the role of zinc-alkoxide in the product distribution of the alky-transfer reaction (Scheme 6) [74]. DOSY NMR was employed to estimate the hydrodynamic radius and then the molecular weight of the intermediate 11-int (Scheme 6). ˚, The diffusion coefficient was consistent with a dimeric species of radius 4 A which corresponded to a molecular weight of 866 g/mol. The same group later focused on the reactivity between TEMPO and diethylzinc [75]. The reaction with one equivalent of TEMPO allowed the synthesis of species 12 that exists in solution as a monomer, as suggested ˚ determined by DOSY experiments. by its hydrodynamic radius of 4.86 A When two equivalents of TEMPO are used, species 13 was formed which was proven to be a monomer after applying diffusion NMR (rH ¼ 5.46 A˚) (Scheme 7).

Scheme 6 Zn(II)-mediated alkyl-transfer reaction and structure of the intermediate as elucidated from DOSY NMR.

Zn

Scheme 7 Different products from the reaction of ZnEt2 and TEMPO depending on stoichiometry.

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Consiglio et al. have studied the aggregation properties of zinc complexes based on Schiff-base ligands [76]. Formula weight estimation via DOSY experiments revealed that in DMSO-d6 (a coordinating solvent) all the complexes studied exist as monomers with a DMSO molecule coordinated, while in CDCl3 (non-coordinating solvent) the complexes are aggregated as dimers, except one of them, believed to form oligomers due to broadening of the NMR signals. The group of Oro described in 2013 the synthesis, characterization and reactivity of iridium(III) complexes bearing 8-oxidoquinoline-2-carboxylato as tridentate ONO-pincer ligand [77]. The behavior of some of these Ir(III) complexes, such as complex 14, as monomers or dimers in solution was found dependent on solvent polarity (Fig. 10), as deduced from their D values calculated from DOSY NMR measurements. In polar solvents, a solvent molecule binds to the metal centre, favouring the monomeric structure ˚ ), whereas in non-coordinating solvents the dimeric aggrega(14a, rH ¼ 5.94 A ˚ ) is favoured. tion of the complex (14b, rH ¼ 7.17 A Sierra and co-workers studied polyhydride osmium complexes with a 2-phenylimidazole ligand using 1H DOSY NMR in toluene-d8 in a temperature range from 296 down to 203 K and found a temperature dependence of ˚ the association degree [78]. At room temperature (296 K), the rH of 4.84 A calculated from the measured D value resulted notably lower than the rH of ˚ calculated from the X-ray structure of the osmium complex, which 5.15 A suggests that the intermolecular interactions between hydrides are inexistent at this temperature. However, the larger rH values found at lower temper˚ at 203 K) suggest the formation of aggregates. atures (i.e., rH ¼ 16.3 A

Fig. 10 Different aggregation states of ONO-pincer Ir(III) complex 14 depending on solvent polarity.

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The group of Xue have reported the synthesis of several tantalum alkyl imides and amide imides, which were structurally characterized in the solid and solution states and modelled by DFT calculations [79]. 1H DOSY experiments at room temperature in C6D6 solution employing SiMe4 as internal standard revealed monomeric or dimeric aggregation states in all the compounds studied, which matched the structures determined by X-ray diffraction in most cases. In 2016, Morisako et al. employed 1H DOSY NMR to study the solution structure of zincate complexes bearing piperidine-type ligands 15 and 16 (Fig. 11) [80]. These studies showed that complex 15 loses one of the THF molecules coordinated to the Li in THF-d8 solution, while complex 16 loses both of them. Aldrich et al. carried out an extensive study on ion pairing between cationic nitrido chromium(VI) complexes of the type [NCr(NiPr2)2(PR3)]+ and common weakly coordinating anions (BPh4, B((3,5-CF3)2C6H3)4, B(C6F5)4, PF6, SbF6, Al(OC(CF3)3)4) [81]. A clear dependence of the ion pairing on solvent polarity was observed in a combination of DOSY and ROESY (rotating-frame Overhauser effect spectroscopy) NMR experiments, indicating a larger ion separation in polar solvents (CD3CN) than in non-polar ones (CDCl3). DOSY measurements allowed a consistent estimation of the ion pairing extent from both the determination of molecular volumes and molecular weight. Multiplatform NMR measurements supported by DFT calculations also allowed them to distinguish preferred approaching sites of the anions to the cationic Cr(VI) complex. In this sense, while small anions, such as PF6, could approach to the Cr centre through the less congested area around the nitrido ligand (blue dashed line, Fig. 12), the bulkier anions (BPh4 or B((3,5-CF3)2C6H3)4) showed no spatial preference when pairing the complex cation. Gladysz and coworkers have synthesized a family of ovoid rhenium and osmium complexes by ring-closing metatheses of two phosphorus-based

Fig. 11 Heterobimetallic lithium zincate complexes with piperidine-derived ligands.

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ligands [82]. This work used DOSY NMR and ion mobility mass spectrometry (IMMS) to differentiate the generated isomeric compounds. In fact, it is proposed that IMMS has a higher resolution than DOSY, related to size and shape. The group of Barry synthesized a family of electron deficient complexes based on half-sandwich and dithiolato chelating ligands [83]. These authors carried out a wide structural study in solution, solid state and DFT/TDFT calculations. Monomeric structures were always found for rhodium, osmium and iridium metal precursors. However, a rhodium derivate bearing the less steric demanding dithiolato ligand was proved to exist as an equilibrium monomer: dimer while in solid state appeared only as a monomer. Galakhov et al. have reported the synthesis and characterization of half-sandwich tantalum complexes [84]. Mono- and di-nuclear tantalum complexes were obtained during the reactivity study carried out with [TaCp*Cl4]. Diffusion NMR experiments corroborated the structures found by X-ray diffraction, where no self-aggregation was detected. Consiglio et al. described in 2010 the synthesis of a zinc complex bearing a Schiff-base ligand, whose optical and fluorescent properties were studied, as well as its aggregation tendency in solution [85]. 1H DOSY NMR measurements were employed to confirm the dependence of the aggregation state of Zn(II) complex 17 (Fig. 13) on the solvent polarity, via estimation of the molecular weight of the species detected. The data gathered in Table 3

Fig. 12 Preferred approaching site for a PF 6 anion towards a nitrido Cr(VI) complex.

Fig. 13 Zinc(II) complex with a Schiff-base ligand.

151

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showed that the D values do not change significantly at different concentrations in polar solvents (DMSO-d6), and the estimated molecular weights of 815–832 g/mol were consistent with the presence of a monomeric species with axially coordinated DMSO. On the other hand, the MW values calculated in a non-coordinating solvent such as tetrachloroethane (TCE-d2) suggested the formation of Zn-O-Zn bridged aggregates whose size were concentration-dependent: at concentrations of 1 mM or lower, the MW indicated the formation of dimers, while at higher concentrations (5 mM) the formation of larger oligomers was observed. Marchio` and co-workers described the use of an heteroscorpionate ligand used in the preparation of copper and silver complexes and studied their aggregation states in solution by means of 1H PGSE NMR measurements [86]. Ligand 18 (Fig. 14) was employed as a trinuclear lithiated adduct and transmetallated with Ag(I) and Cu(I), yielding a trinuclear [Ag(18)]3 complex and a pentanuclear [Cu5(18)4]+ complex, respectively, as determined by their X-ray diffraction structures in the solid state. The identity of these oligonuclear structures was further studied in solution via 1H diffusion NMR using CD2Cl2 as solvent, which allowed to calculate the hydrodynamic volumes (VH) of the different species present in solution. ˚ 3 was consistent with the For the Ag(I) complex, the VH value of 1720 A conservation of the trinuclear structure determined by X-ray diffraction Table 3 Diffusion coefficients (D) and estimated molecular weights (MW) of Zn complex 17 in non-coordinating (TCE-d2) and coordinating (DMSO-d6) solvents at different concentrations. Estimated MW (g/mol) Solvent Concentration (mM) D (×10210 m2/s)

TCE-d2

5.0

2.37

1948

TCE-d2

1.0

2.88

1402

TCE-d2

0.5

3.11

1315

DMSO-d6

5.0

2.15

832

DMSO-d6

1.0

2.30

815

Fig. 14 Heteroscorpionate ligand bis(3,5-tertbutylpyrazol-1-yl)dithioacetate.

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without further aggregation in solution. For the Cu(I) complex, however, solution studies (ESI-MS, 1H NMR) evidenced the presence of two species in equilibrium. Via 1H PGSE NMR, VH were calculated for both species: the larger volume of 2630 A˚3 matched well with the pentanuclear structure ˚ 3 was consistent found in the solid state, while a smaller volume of 2330 A + with the formation of a tetranuclear species [Cu4(18)3] .

2.2 Alkaline and alkaline–earth complexes Due to their versatile application in synthetic chemistry, organolithium compounds have been the subject of numerous investigations, both addressing their structure in the solid state and their behavior in solution, aiming to find structure–reactivity relationships in this class of compounds. The group of Williard have presented a diffusion-related body of knowledge on lithium complexes during the last decade [87]. In 2009, they gathered in an account their most relevant works since 2000 on the application of PGSE and DOSY NMR to the study of organometallic reactive intermediates in solution, aiming to comprehend the differences between X-ray diffraction structures in the solid state and the aggregation states in solution, and how it can influence a reaction mechanism [88]. Among their most interesting advances, the development of an experimental procedure to establish a correlation between diffusion coefficient and formula weight, employing inert molecules of known FW as internal standards, is of special importance. Besides, most of their studies were carried out on compounds bearing enriched 6Li centres rather than the naturally abundant 7Li, as the lower quadrupole of the 6Li nucleus renders dipolar behavior and therefore narrower peaks, thus facilitating signal resolution and two-dimensional spectra acquisition [87c]. Several alkyl lithium/amide lithium mixed aggregates isotopically enriched with 6Li (Fig. 15) have been synthesized and studied by

Fig. 15 Organolithium aggregates studied by Williard and colleagues.

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multiple 1D and 2D NMR experiments (1H, 13C, 6Li, 15N, DOSY, HSQC, HMBC, EXSY, HOESY, low-temperature NMR) in toluene-d8 solution [e,87a–c]. These NMR-based investigations led to the determination of aggregation states and 3D-structures of the polynuclear lithium complexes in solution, which matched those found in the solid state by X-ray diffraction analyses. The calculation of molecular weights of the lithium complexes via D-FW (diffusion coefficient—formula weight) correlations in 6Li DOSY measurements with 6LiHMDS as internal standard was also possible, thus establishing new methodologies for the characterization of organolithium compounds in solution. Furthermore, the chirality of the amide lithium chiral complexes studied (Fig. 15, left) was revealed to persist in solution, which is thought to be responsible of the asymmetric induction of this system in the addition of the n-butyl moiety to aldehydes. Simple organolithium compounds, such as n-butyllithium [87f] and cyclopentyl lithium [87d], have also been characterized in solution in order to discern solventand temperature-dependent aggregation states and solvation degrees. The group of Maddaluno have also reported on the characterization of 6 Li labelled organolithium compounds via NMR spectroscopy, although 7Li compounds were employed for 1H DOSY experiments [89]. The establishment of a D-FW correlation in a mixture of MeLi and LiCl in THF-d8 solution at 170 K was performed in the presence of trimethyl-, tri-tbutyl- and triphenyl-benzene as internal standards. The formula weight of 277 g/mol obtained via interpolation from the logD—log FW plot suggested the presence of either a [(MeLi)(LiCl)] dinuclear species or a planar tetramer [(MeLi)2(LiCl)2], depending on the number solvation THF molecules considered. In order to infer the possible influence of their aggregation states in solution into their catalytic performance for the ring-opening polymerization of L-lactide, Roşca et al. studied several lithium and potassium phenolates using PGSE NMR techniques [90]. Three phenolate derivatives (Fig. 16) were

Fig. 16 Aminoether substituted phenolates employed for Li and K complexation.

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Table 4 Hydrodynamic radii calculated from 1H PGSE and from X-ray diffraction. rX-ray (Å) Complex Solvent rH (Å)

[Li(19)]

CD2Cl2

3.15

7.10

[Li(20)]

THF-d8

4.84

7.55

[K(21)]

THF-d8

4.98

7.88

deprotonated using either n-BuLi or KH, and the resulting complexes were crystallized and analysed by X-ray diffraction. Complexes [Li(19)], [Li(20)] and [K(21)] were subjected to 1H PGSE NMR measurements, from which their hydrodynamic radii were calculated. The resulting molecular radii were notably lower to those found in the solid state (Table 4), confirming a mononuclear motif in solution, in contrast with the dimeric structures found in the crystalline state. Stalke and co-workers have carried out several studies on coordination modes and aggregation states of lithium and other alkaline metals with simple and common bases and donors [54,91]. In 2010 they prepared a series of oligomeric aggregates through the reaction of [LiCH2SiMe3]6 with ether donors as Et2O, tBuOMe and dimethoxyethane (DME) [91a]. For the dimeric aggregate [(DME)(LiCH2SiMe3)]2, 1H DOSY NMR was employed to assess the possible deaggregation undergone in solution. The diffusion constants found for each part of the molecule were 8.868 log(m2/s) for the DME and 9.024 log(m2/s) for LiCH2SiMe3, from which a 73% aggregation in solution was calculated. In 2012, they described the crystalline product obtained from the reaction of tBuLi with dimethylaniline, where two distinct organolithium tetrameric molecules ([tBuLi]4 and [o-Me2N-C6H4Li]4) were found in the unit cell [91b]. This compound was therefore studied through NMR spectroscopy in toluene-d8 in order to ascertain if such unusual arrangement is conserved in solution state. Instead of only two signals, the 7 Li NMR spectrum of the compound showed up to five distinct peaks. 7Li DOSY measurements revealed different D values for each of the five species found in solution, which were finally determined to be all the possible tetrameric combinations of the monomeric organolithium compounds tBuLi and o-Me2N-C6H4Li ([tBuLi]4, [(tBuLi)3(o-Me2N-C6H4Li)], [(tBuLi)2(o-Me2NC6H4Li)2], [(tBuLi)(o-Me2N-C6H4Li)3] and [o-Me2N-C6H4Li]4). More recently, Neufeld and Stalke have developed an alternative methodology for the determination of molecular weights from diffusion coefficients, by

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employing an external calibration curve (ECC), which not only lowered considerably the errors in FW estimation but also allowed to use only one internal reference during the experiments, that could be the solvent itself [54]. Using this new methodology, the aggregation patterns of alkali metal cyclopentadienides (CpM; M ¼ Li, Na, K, Rb, Cs) in THF-d8 solution were investigated with the aid of DOSY NMR [91c]. Via ECC-MW estimations, it was determined that the predominant species in solution were monomeric aggregates with coordinated THF molecules ([CpM(THF)n]; n ¼ 2 for Li and Rb, n ¼ 3 for Na and K), except for caesium, which showed molecular weights higher than 1500 g/mol, consistent with the formation of cyclic pentamers or hexamers. CpLi was further studied by 1H and 7Li DOSY NMR, and the formation of CIP (contact ion pairs) in THF-d8 solution was confirmed as the D values obtained from the spectra of each nuclei (1H and 7 Li) were equivalent. The DOSY-ECC approach have also been used for the study of the solution behavior of amide-Mg-Li aggregates in THF [91d] and a heteroleptic potassium crown–ether complex with unusual stability against hydrolysis [91e]. Hevia and co-workers have investigated the synthesis, structure and stability of organometallic lithium and magnesium reagents [92]. In 2012 they studied the co-complexation reactions of Li(CH2SiMe3) and Mg(CH2SiMe3)2 in the presence of different oxygenated (THF and 1,4-dioxane) and nitrogenated (TMEDA (N,N,N0 ,N0 -tetramethylethylenediamine) and PMDETA (N,N,N0 , N00 ,N00 -pentamethyldiethylenetriamine)) donors, and analysed the products using X-ray crystallography and multinuclear (1H, 13C and 7Li) NMR spectroscopy [92a]. Employing oxygen donors such as THF and dioxane led to the formation of polymeric chains in the solid state, while the nitrogen donors TMDA and PMDETA afforded heterobimetallic complexes with discrete molecular structures in which the N-ligands showed a preference for Li coordination. The polymeric lithium magnesiates derived from the reactions with THF and dioxane were further investigated via 1H DOSY NMR in C6D6 solution to determine if the macromolecular structure was retained in solution. For the complex [(THF)LiMg(CH2SiMe3)3]n the diffusion coefficient and formula weight values estimated from the 1H DOSY spectra were consistent with a monomeric structure in solution, thus confirming the disaggregation of the 1D polymer in solution. In this case, equivalent D values were measured from the protons of THF and of CH2SiMe3 suggesting that both moieties form part of the same molecular species in solution. Similar findings for the dioxanebridged lithium magnesiates suggested that monomeric aggregates are also formed in solution, in which the polymeric structure is lost but a close interaction

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between dioxane molecules and the organometallic moiety is maintained. In a later study, Hevia et al. employed 1H DOSY NMR to determine the aggregation states of oligomeric (LiTMP)n (TMP ¼ 2,2,6,6-tetramethylpiperidine) aggregates in solution [92b]. The estimation of molecular weights were performed in C6D6 and in cyclohexane-d12 solutions, using SiMe4, 1-phenylnaphtalene and tetraphenylnaphthalene as internal standards in both cases. The estimated MW obtained were consistent with the relative size of the cyclotrimer and the cyclotetramer (Fig. 17) with respect to each other, however, the errors relative to the theoretical MW values (27% for (LiTMP)3 and 40% for (LiTMP)4 in C6D6; 15% for (LiTMP)3 and 6% for (LiTMP)4 in cyclohexane-d12) were considerably large, thus evidencing the limitations of the method. Their group also studied the transmetallation process of aryl organomagnesiates and zinc pivalate in the presence of LiCl to yield organozinc compounds [92c]. 1H DOSY NMR spectroscopy was useful in this case to distinguish between the different products of the reaction, including those derived from degradation via partial hydrolysis. Sattler et al. prepared a series of lithium complexes by reacting nBuLi with (Me3Si)2P–PtBu2 under different conditions and the products were extensively studied by X-ray diffraction and NMR spectroscopy, including 1 H, 13C, 31P, 7Li and 29Si measurements [93]. When the complex [Li(Me3Si)P–PtBu2]4, which showed a tetrameric structure in the solid state with a Li4P4 core, was dissolved in toluene-d8, two different set of signals were detected via 1H NMR at room temperature. In order to discriminate these two new species, 1H PGSE measurements were performed on the ˚ were calculated for the samples. Hydrodynamic radii of 5.9 and 10.3 A ˚ found two species in solution, none of which matched the rX-ray ¼ 7.4 A for the tetramer in the solid state. Therefore, they concluded that

Fig. 17 Trimeric and tetrameric structures of (LiTMP)n cyclooligomers.

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[Li(Me3Si)P–PtBu2]4 undergoes dissociation upon dissolution in toluene, ˚ ) which is in an aggregation equiresulting on a smaller species (rH ¼ 5.9 A ˚ ). librium with a much larger species (rH ¼ 10.3 A In 2013, Gallegos et al. also synthesized and studied the solid state and solution structure of an heterometallic Li/Mg complex, along with its homometallic Li and Mg homologues [94]. Employing 1-phenylazo-2naphthol as bidentate ligand and LiHMDS or Mg(nBu)2 as metal precursors, the corresponding homometallic complexes (Fig. 18, top) were synthesized, and the Li/Mg heterometallic complex (Fig. 18, bottom) was prepared from the Mg complex and LiHMDS or nBuLi. X-Ray diffraction analyses of the heterometallic complex revealed an asymmetric unit containing two Li and two Mg atoms together with six 1-phenylazo-2-naphthol ligand molecules. Remarkably, the rH value and formula weight calculated via 1H DOSY measurements agreed with the data from X-ray diffraction, confirming that the same structure and aggregation state is retained in benzene solution. All three Li and Mg complexes were found active for the initiation of lactide polymerization. O’Hara and co-workers synthesized a new homometallic lithium complex and a series of heterometallic lithium magnesiates with potential applicability as reagents for the halogen-metal exchange reaction, and studied

Fig. 18 Li and Mg homo- and heterometallic complexes.

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their structures in the solid state and in solution [95]. First, an homometallic lithium complex was prepared from a racemic biphenol ligand (BIPHEN) and two equivalents of n-butyllithium (Scheme 8) as an intermediate towards the synthesis of lithium magnesiates. The solid-state structure of this complex was analysed by X-ray diffraction and the asymmetric unit consisted of a tetranuclear lithium complex with two BIPHEN ligands and four coordinating THF molecules, in which three distinct Li atoms were present. NMR spectroscopy was then employed to elucidate the structure of the complex in solution. 7Li NMR spectra in perdeuterated cyclohexane (cyc-C6D12) or THF-d8 showed only one broad signal, suggesting rapid exchange of the distinct Li atoms in solution. Interestingly, 1H DOSY NMR experiments revealed the presence of two different species in cycC6D12 solution, in which the BIPHEN and the THF molecules were separated. The differences in the D values obtained from coordinated THF molecules and BIPHEN molecules together with molecular weight estimations, suggested that the [Li4(BIPHEN)2] structure stayed intact in solution, while the coordinating THF molecules showed a dynamic behavior of solvation/desolvation to the lithium centres. Next, heterometallic lithium magnesiates were prepared employing the tetranuclear Li complex and organomagnesium reagents as starting materials (Scheme 8). This new species

Scheme 8 Lithium and lithium organomagnesiate complexes synthesized by O’Hara and colleagues.

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was characterized in solid state (X-ray diffraction) and in solution (1H, 13C, 7Li and DOSY NMR), showing a similar labile behavior of the coordinated THF molecules in cyc-C6D12 solution. The group of O’Hara have also reported the synthesis of heterometallic sodium-magnesium complex [Na4Mg2(TMP)6(nBu)2] (TMP ¼ 2,2,6,6tetramethylpiperidide) and its use as a regio-controlling template for the dimetalation of aromatic rings [96]. Although the hexanuclear complex could not be crystallized, NMR spectroscopy provided insight into its structure in solution. Both DOSY and EXSY (exchange spectroscopy) showed two different set of signals for the n-butyl moiety which was attributed to an equilibrium between dimeric and monomeric ([Na2Mg(TMP)3(nBu)]) forms of the complex. Bauer et al. described in 2016 the synthesis and characterization, in solid state and in solution, of lithiated complex 22, bearing a bis(imidazole-2thione) ligand (Fig. 19) [30]. In order to discern the aggregation state of complex 22 in solution, PGSE diffusion NMR measurements (1H and 7Li) at room temperature were performed of both the lithium complex and the ligand, contained in separate samples, for comparison. The diffusion coefficients (D) for 22 calculated from its 1H spectra were nearly equivalent to those calculated from the 7Li spectra along the concentration range assayed (20, 60 and 120 mM). These results indicate that the organic ligand and the Li atoms are considerably close in space, and thus 22 can be defined as a contact ion pair in THF-d8 solution. Also, the hydrodynamic radius (rH) of ˚ calculated from its D-value at 20 mM concentration matches well with 6.0 A ˚ estimated from the X-ray structure of 22, confirming the monothe 6.2 A meric character of the organometallic compound in THF-d8 solution. In 2018, the group of Ferna´ndez presented a lithium complex with an anthraquinone-derived ligand highly active as catalyst for carbonyl

Fig. 19 Structure of 22 in THF solution, as elucidated from multinuclear and PGSE diffusion NMR measurements.

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Fig. 20 Solid-state and solution structures found in a lithium anthraquinoid derivative.

hydrosilylation, and an extensive structural study of the complex in both solid state and solution was carried out [97]. The X-ray diffraction analysis of the crystalline solid revealed a dimeric arrangement of complex 23a (Fig. 20, left). However, solution-state analyses, including multinuclear (1H, 13C, 15N) NMR and 1H and 7Li PGSE NMR diffusion measurements, as well as ESI(+)-MS, were consistent with a monomeric structure of 23b in solution, in which the pyridine moiety in the coordination sphere of the Li is replaced by a THF molecule (Fig. 20, right). The D values obtained from the 1 H and the 7Li PGSE NMR experiments were almost equivalent, which ˚ calcupoints to a contact ion pair in THF-d8 solution. Also, the rH of 5.2 A lated from those D values is notably lower than that estimated from the ˚ ), thus providing proof of the monoX-ray structure for the dimer 23a (6.2 A meric nature of the Li complex in THF-d8 solution. Crimmin et al. described in 2007 the preparation of diphenylphosphide adducts of the heavier alkaline-earth metals (calcium, strontium and barium) as well as their structural characterization in the solid state, via X-ray diffraction, and in solution [98]. For both the Ca and Sr complexes of general formula [M(PPh2)2(THF)4] (M ¼ Ca, Sr) the hydrodynamic radii calculated from PGSE NMR measurements in THF-d8 solution were in perfect agreement with the radii calculated from the X-ray structure for monomeric species. However, for the barium complex [Ba3(PPh2)6(THF)4]n, which showed a polymeric arrangement in the crystalline solid, PGSE measurements did not yield precise enough data to calculate accurate diffusion coefficient in solution. Breher and co-workers reported in 2008 structural and reactivity studies on magnesium and zinc complexes bearing tris(pyrazolyl)methanide ligands [99]. A zwitterionic magnesium complex and its corresponding protonated triflate salt (Scheme 9, 24 and 25, respectively) were both crystallized and

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Scheme 9 Zwitterionic magnesium complex 24 and its corresponding protonated triflate salt 25.

analysed by X-ray diffraction. PGSE NMR experiments were carried out on these magnesium complexes (in C6D6 solution for 24 and in acetone-d6 for 25), revealing in both cases that the monomeric structures found in the solid state were retained in solution, as very similar rH and rX-ray were calculated.

2.3 Main-group metals complexes A complex formed between 2-isopropylmalic acid and aluminum(III) was studied spectroscopically via multinuclear (1H, 13C, 27Al) NMR and DOSY, among other techniques, by the group of Yoshimura [100]. 1H DOSY NMR measurements of a mixture containing the 2-isopropylmalic acid ligand and AlCl3 in D2O solution allowed to unambiguously identify the signals for the free ligand and for the Al(III) complex. A larger diffusion coefficient of 3.91010 m2/s matched well with the D ¼ 4.11010 m2/s determined for the ligand when measured in the absence of Al(III), while a D value of 2.51010 m2/s in the mixture was attributable to the larger aluminum complex. Nurchi et al. carried out an extensive study on the coordinating properties of kojic acid-derived ligands with potential applicability for the chelation of Fe(III) and Al(III) in therapeutic treatments [101]. 1H PGSE (STE sequence) NMR experiments were key to discern coordination modes between ligand 26 (Fig. 21) and Al(III) in 1:1 stoichiometry within an acidic (pH 3.5) D2O solution. For ligand 26, quantum chemical calculations predicted a close resemblance with a sphere and a diffusion coefficient of 3.71010 m2/s which excellently matched the value of D ¼ 3.71010 m2/s measured, within the experimental error. For the case of the aluminum

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Fig. 21 Ligand used by Nurchi et al. in the synthesis of Fe(III) and Al(III) complexes.

Fig. 22 Different aggregation states of bimetallic organotin complex in solution (27a) and in solid state (27b).

complex, quantum chemical calculations modelled a dimeric structure [Al2(26)2] in the shape of a short rod with length of 19.0 A˚ and diameter ˚ , resulting in a D ¼ 2.961010 m2/s, which is close enough to the of 7.4 A experimental value of 2.61010 m2/s, what confirmed the dimeric structure of the complex in solution. The synthesis of a series of organotin compounds was described by Alashkar et al. in 2016, including an extensive characterization in both solid and solution state [102]. In the case of organotin complex 27 (Fig. 22), it was found to behave as a monomer in solution (27a), as deduced from the rH ˚ calculated from its 1H DOSY NMR spectrum, which value of 5.4–5.7 A was in contrast with the dimeric structure (27b) found in the solid state via X-ray diffraction analysis.

2.4 Rare earth complexes The group of Williams described in 2007 the synthesis and characterization of a series of phosphinamido yttrium complexes active in the initiation of

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lactide ring-opening polymerization [103]. The reaction between Y(HMDS)3 (HMDS ¼ bis(trimethylsilyl)amide) and a bis(thiophosphinamido) ligand afforded an heteroleptic Y(III) complex bearing the bis(thiophosphinamide) ligand and a HMDS ligand attached to the metal centre (Fig. 23, left), as determined by X-ray diffraction analyses of their crystals. The structure of this complex in THF solution was proven to be equivalent to that in the solid state, as its ˚ determined via 1H PGSE NMR measurements hydrodynamic radius of 5.27 A ˚ calculated from the X-ray structure. was in agreement with the rH ¼ 5.15 A However, when a bis(phosphinamido) ligand reacted with similar silylamide Y(III) precursors, the complex obtained (Fig. 23, right) exhibited a dimeric structure in the solid state, as revealed by X-ray diffraction. Once again, 1H PGSE NMR confirmed the retention of the dimeric structure in THF solution, deduced from the similarity of the rH values calculated from the diffusion coefficient (6.46 A˚) and the X-ray structure (6.28 A˚). Natrajan et al. synthesized a series of anionic homobimetallic lanthanide (neodymium, samarium, europium, terbium, dysprosium, holmium, erbium and ytterbium) complexes, which displayed a dimeric structure in the solid state, as showed by single crystal X-ray diffraction [104]. The 1H DOSY NMR spectra of the paramagnetic Nd, Sm and Tb complexes in D2O solution were measured and allowed the determination of the corresponding diffusion coefficients, from which molecular volumes were calculated. For the samarium and terbium complexes, the molecular volumes of 2679 and ˚ 3, respectively, compared well with the sizes of 2748 and 2732 A ˚3 2575 A found in the crystal structure, thus providing evidence that the dinuclear structure was retained in aqueous solution. The neodymium complex was not ˚ 3 suggested a similar structure crystallized, but its solution volume of 2575 A to those of the Sm and Tb complexes. The rest of the paramagnetic lanthanide complexes (europium, dysprosium, holmium, erbium and ytterbium),

Fig. 23 Yttrium(III) complexes with thiophosphinamido (left) and phosphinamido (right) ligands.

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however, showed proton resonances with line width too large (and therefore short T2 relaxation times) to allow accurate DOSY NMR spectra acquisition. Ruiz-Muelle et al. have recently described the synthesis of a family of isostructural 1D-coordination polymers from an anthraquinoid ligand (Fig. 24) and rare-earth metals (Y, La, Nd, Eu, Gd, Tb, Dy, Er) [105]. PGSE measurements (DMSO-d6) were performed on both the ligand and the yttrium(III) complex and the corresponding D and rH values were calcu˚ of the Y(III) complex was clearly lated. The hydrodynamic radius of 7.0 A ˚ ) and matched well the value calcularger than that of the free ligand (4.4 A ˚ ), thus proving that the struclated from the X-ray structure (rX-ray ¼ 6.5 A ture found in the solid state was retained in solution. Roesky and co-workers reported in 2012 the synthesis of several lanthanide (samarium, europium, lutetium) complexes bearing the hexadentate chelating ligand 1,4,7-tris(3,5-di-tert-butyl-2-hydroxybenzyl)-1,4,7-triazacyclononane, with the ability to reversibly bind to SO2 [106]. When treated with gaseous SO2 in THF solution, the samarium and europium complexes underwent coordination of a sulphur dioxide molecule on the metal centre, giving rise to a SO2-bridged dimer (Scheme 10), as revealed by its X-ray analysis in the solid state.

O

O

HN

O OH

Fig. 24 Anthraquinoid ligand employed for the formation of 1D-polymers with Y and lanthanides.

Scheme 10 Lanthanide complexes with SO2-binding ability at room temperature.

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Solution-state studies of the paramagnetic Sm complex via 1H PGSE NMR in THF-d8 confirmed the integrity of the SO2-bridged dimeric complex in solution, due the near equivalent value of the hydrodynamic radius ˚ to that calculated from the X-ray structure (rX-ray ¼ 9.8 A ˚ ). rH ¼ 9.7 A The group of Breher have presented various works on the structure and behavior of yttrium and rare earth complexes, featuring detailed NMR studies [107,108]. Using 1H and 19F PGSE NMR experiments, the ion pairing extent of three yttrium complexes were assessed by comparing the diffusion coefficients obtained from the 1H spectra attenuation for the polydentate ligands and from the 19F spectra of coordinating triflate (OTf¼ CF3SO3) anions [107]. As an example, the D and rH data for Y complex 28 (Fig. 25) are gathered in Table 5. The values obtained for the cationic (1H of ligand) and anionic (19F of triflate anions) are clearly different, indicating that ion pairing is not complete. However, the hydrodynamic radius of 5.2 A˚ calculated from 19F is ˚ radius found for a free solvated triflate notably larger than the usual 3 A anion, thus indicating that an important extent of ion pairing is taking place. Using the same hexadentate ligand as in 28, a series of rare earth (yttrium, lanthanum, samarium, lutetium, plutonium) complexes were later synthesized and subjected to structural characterization [108]. Multinuclear PGSE NMR (CD3CN solution) measurements revealed partial dissociation in all the complexes and that the ion pairing degree decreases with cation radius along the lanthanide series (ion pairing: La3+ > Sm3+ > Lu3+), while Pu complex shows the largest dissociation degree.

Fig. 25 Mononuclear Y(III) complex prepared and characterized by Breher and co-workers. Table 5 D and rH values for complex 28 in CD3CN at room temperature. rH (Å) Nucleus D (10210m2s21) 1

H

19

F

9.022

6.6

11.455

5.2

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The group of Parquette and RajanBabu described in 2014 the preparation of a series of yttrium and lanthanide homobimetallic complexes with catalytic activity for the enantioselective ring opening reaction of aziridines [109]. Two yttrium-salen complexes 29 and 30 (Fig. 26) were subjected to a stability study via DOSY NMR in CD2Cl2 solution. While the DOSY spectrum of bimetallic complex 30 stayed unaltered for >40 h, with a logD value of 8.40–8.45 during the time range measured, the monometallic complex 29 showed a dynamic behavior, with logD values oscillating between 8.4 and 8.75 in 12 h periods. Raya et al. reported in 2017 the preparation of two yttrium and dysprosium complexes with 5-nitropicolinic acid as ligand [110]. X-ray diffraction analyses of the Y(III) and Dy(III) complexes revealed that they are isostructural in the solid state, and that they form dinuclear structures in which each metal centre is bonded to two water molecules and four 5-nitropicolinate ligands, two of them bridging the metal centres (Fig. 27). In order to study the aggregation state of the yttrium complex in solution, 1H PGSE NMR

Fig. 26 Yttrium-salen complexes catalytically active for ring opening reaction of aziridines.

O N O O N O

O O H2O OH 2 O O

N

M

N O

O N O

N O

O

O N

O

N O O M

O H2O OH 2 O O

N N

N O

O

O N O

M = Y or Dy

Fig. 27 Dinuclear yttrium and dysprosium complexes bearing several units of 5-nitropicolinic carboxylates.

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diffusion measurements were performed on both separate samples of the 5-nitropicolinic acid ligand and of the Y(III) complex. Hydrodynamic radii of 3.1 and 6.5A˚ were calculated from the measured values of D for the ligand and the complex, respectively. Both rH values were consistent with those ˚ for the ligand and the complex deduced from the X-ray data (3.4 and 6.5 A respectively), suggesting that it retains its dinuclear structure in DMSO solution. Schelter and co-workers have studied very recently the solid state and solution structures, as well as the electrochemical properties, of cerium(IV) complexes with a tetradentate atrane-type ligand [111]. A chloride-bridged unsymmetrical dinuclear Ce(atrane) complex was prepared using an atrane ligand and Ce(HMDS)3Cl as Ce(IV) precursor (Scheme 11, top). Treating this complex with potassium 2,6-diphenylphenolate or with KHMDS afforded the corresponding dimeric [Ce(atrane)(L)]2 (L ¼ 2,6-diphenylphenolate or N(SiMe3)2) complexes (Scheme 11, bottom) after loss of KCl. All three Ce(IV) complexes were analysed by X-ray diffraction and displayed a dinuclear structure in the solid state. However, the 1H DOSY NMR measurements in THF-d8 solution revealed that both dimeric [Ce(atrane)(L)]2 type complexes underwent dissociation into monomeric entities, while the

Scheme 11 Synthesis of dinuclear Ce(IV) complexes with an atrane ligand.

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chloride-bridged precursor retained its dinuclear character. This latter species, however, presented a rH value of 4.9 A˚ consistent with a monomeric structure when the 1H DOSY NMR measurements were performed in a coordinative solvent such as pyridine-d5.

3. Applications to cluster complexes Scheele et al. reported in 2008 the use of multinuclear NMR (1H, 13 C, 15N, 109Ag) and DOSY measurements to ascertain molecular structures of silver(I) complexes with NHC (N-heterocyclic carbene) and pyrazole ligands in solution [112]. The X-ray diffraction analysis of complex 31 showed a octanuclear structure in the solid state (Scheme 12). However, when crystals of 31 were dissolved in acetone-d6 its 1H NMR spectra

Scheme 12 Proposed structures in acetone-d6 solution for polinuclear Ag complexes.

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revealed partial decomposition into two new species, 32 and 33. 1H DOSY experiments performed on the mixed sample allowed the measurement of their respective D values for all three components and to estimate their molecular sizes. The dimeric tetranuclear structure of 32 and that trimeric hexanuclear of 33 (Scheme 12) were also supported by 1H, 13C, 15N and 109 Ag NMR measurements. In 2010, Albinati et al. synthesized and characterized the platinum dicluster complex [Pt3(μ-PtBu2)3(CO)2]2(μ-10 ,1000 -diethynylbiferrocene) [113]. DOSY NMR in combination with 1D ROESY (rotating-frame Overhauser enhancement spectroscopy) measurements in C6D6 and in CD2Cl2 solutions, employing SiMe4 as internal standard, confirmed that the aggregation states and the most stable conformation of the platinum cluster in both solvents were in agreement with those determined in the solid state. To this end, the shape of the molecule was approximated to an ellipsoid of revolution and the hydrodynamic radii obtained from the measured D values were compared to those calculated for different conformations of the complex. Sokolov and co-workers described two new tantalum polyoxometalate (POM) clusters coordinated with a ruthenium half-sandwich [114]. Both POM complexes Na10[{(C6H6)RuTa6O18}2(μ-O)]39.4H2O and Na4(trans-[{(C6H6)Ru}2Ta6O19]20H2O had their structures determined by X-ray diffraction and ESI(-)-MS. The 1H DOSY NMR spectra in D2O solution in both cases provided D values from which hydrodynamic radii in the range of 6.75–6.96 nm were calculated. These values are consistent with the presence of solvated trans-[{(C6H6)Ru}2Ta6O19]4, cis[{(C6H6)Ru}2Ta6O19]4, and [{(C6H6)Ru}Ta6O19]6 monomeric anions in solution, but not with the dimeric [{(C6H6)RuTa6O18}2(μ-O)]10 anion, which must therefore dissociate in D2O solution. The group of Lalinde and Moreno reported the preparation and structural characterization of platinum-lead tetranuclear (Pt2Pb2) and trinuclear (Pt2Pb) clusters [115]. The solution behavior of one of the tetranuclear Pt2Pb2 complexes was studied by means of 1D 1H PGSE and 2D DOSY NMR, as well as variable-temperature 1H NMR, in CDCl3 solution. These experiments provided data consistent with an equilibrium between tetranuclear and binuclear (PtPb) entities in solution, which would be strongly displaced towards the binuclear species in the experimental conditions. Breher and collaborators described in 2011 the preparation of a triangulo palladium cluster (Fig. 28, 34) employing a tris(methimazolyl)silanide ligand [116]. Via PGSE NMR measurements, the diffusion coefficient of 34 in DMSO-d6 was obtained, from which hydrodynamic radius and volume

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˚ 3, respectively, were calculated. This latter value matof 6.9 A˚ and 1375 A ˚ 3), ched very well that found from X-ray diffraction analysis (VX-ray ¼ 1364 A thus proving that the integrity of the solid-state structure is retained in solution. The group of Finze have synthesized a family of dinuclear gold(I) complexes based on carba-closo-dodecaboranylethynido ligand and trialkylphosphine (Scheme 13) [117]. In the solid state, X-ray diffraction analyses revealed that the more sterically demanding phosphine P(iPr)3 induce the formation of dinuclear monomers while the less sterically hindered PMe3 and PEt3 promote dimerization, giving rise to tetranuclear gold clusters. DOSY NMR experiments using three different solvents (DMSO-d6, (CD3)2CO and CD2Cl2) demonstrated that when the phosphine used is trimethylphosphine the species exists as a dimer at room temperature in any of the three solvents

Fig. 28 Palladium cluster with a Pd3 triangular core.

Scheme 13 General structure of dinuclear (monomeric) and tetranuclear (dimeric) Au(I) clusters.

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˚ (monomer), tested and in DSMO-d6 up to 75 °C (rX-ray ¼ 4.75 A ˚ rH ¼ 5.25–6.65 A (dimer)). On the other hand, when the employed phosphine is P(iPr)3, the Au(I) complex exists as a monomer in solution within all conditions tested. However, for the complex bearing the PEt3 ligand, the structure is found to exist in an equilibrium between monomer and dimer at room temperature that completely shifts to the dinuclear monomer at 75 °C (DMSO-d6) with an hydrodynamic radius of 4.14 A˚, compared to the ˚ calculated for the dimer at 25 °C in the same solvent. 5.78 A DOSY NMR has been also applied in the nanoparticles field [118]. In this regard, the group of Thieuleux has employed in situ DOSY experiments to corroborate the formation of platinum nanoparticles covered with octylsilane fragments of an overall diameter of ca. 2.6 nm where the Pt core size ranges from 1.1 to 1.6 nm. DOSY methods have also been used by Arvelos et al. to study the self-assembly of polyethylene glycols (PEGs) on the surface of palladium nanoparticles [119]. In fact, it is demonstrated that the solvation of Pd2(dba)3 with PGEs entities modulates the size of the final Pd nanoparticles. Another example is the one described by Durant et al. where DOSY NMR spectroscopy were applied to study palladium nanoparticles systems dispersed in ionic liquids (ILs) and shown to be a helpful tool to understand the behavior of these systems. Even if the nanoparticles themselves cannot be detected through NMR, observation of the solvent (methanol) and the IL ([BMI][PF6] or [BMI][N(SO2CF3)2)]) via 1H, 19F, 31P and 11B DOSY experiments permitted to prove the presence of Lewis bases coordinated at the metallic surface by a significant decrease of IL diffusion coefficients relative to ligand free nanoparticles. This effect is better revealed by ILs showing a strong trend to form ion pairs in the presence of methanol as cosolvent, as observed for [BMI][NTf2]. This behavior was not observed for molecular precursors such as [PdCl2(cod)] or [Pd2(dba)3] of no IL nature [31a]. The group of Tilley reported in 2015 mechanistic investigations on the oxygen evolution reaction in artificial photosynthesis systems based on a cobalt cluster cubane with topology [Co4O4] where an oxo-cobalt(V) species has been proposed to mediate [120]. In this sense, 1H PGSE NMR measurements in D2O solution have supported that the integrity of the cubane remains during the reaction course while acetate ligands dissociate at basic pH and are consequently replaced by OH anions, as suggested by the similar rH values found for both species (7.0 A˚ for ˚ for [Co4O4(OAc)3(Py)4(OH)2]). [Co4O4(OAc)4(Py)4] and 6.8 A

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4. Applications to supramolecular structures W€ urthner and collaborators synthesized in 2006 a palladium-based fluorescent multichromophore metallosupramolecular square via metalion coordination self-assembly [121]. The resulting structures were characterized using elemental analysis, UV/Vis spectroscopy and a range of NMR experiments (1H, 13C, 31P, 1H DOSY) in CD2Cl2 solution. However, in order to minimize convection effects, the BPP-LED sequence together with CDCl3 as solvent was employed for the DOSY measurements of the palladium metallasquare 35 (Fig. 29), due to its higher boiling point relative to CD2Cl2. A diffusion coefficient D ¼ 5.11010 m2/s was calculated from various 1H signals of 35 and the results were compared to those of a previously described platinum analog [122], with a D value of 6.11010 m2/s. The molecular size ratio of 1.5 (from the calculated rH) between 35 and the Pt analog was coherent with a similar molecular weight ratio, which confirmed a similar structural arrangement on both Pd and Pt supramolecular metallasquares. A series of palladium(II) complexes with NHC ligands substituted with a poly(benzyl ether) dendron on one of the N positions were described and

Fig. 29 Fluorescent palladium metallasquare architectures.

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successfully employed as catalyst for the Heck reaction by Ortiz et al. in 2016 [123]. These dendrimers were measured via DOSY NMR using both DMF-d7 and acetone-d6 as solvents, finding comparable hydrodynamic radii for these supramolecular systems in either solvent. A reasonable correlation between rH values and the size of the dendron substituent was also found, which was similar enough to the estimations derived from molecular models and calculations. In addition, the catalytic activity of these Pd complexes towards Heck coupling reaction was not negatively affected by an increase of the dendrimer size. Samanta et al. reported a year later the preparation and application as drug delivery platform of a metal-organic polyhedron (MOP) by a selfassembly route from Pd(NO3)2 and a bidentate pyridine-based ligand [124]. The use of 1H DOSY NMR techniques in D2O solution was critical to confirm the formation of the palladium MOP as well as the attachment of the doxorubicin drug molecules to its surface. Also, the stability of the drugbearing MOP within 10 mM sodium phosphate buffer at pH 7.4 was confirmed by its 1H and DOSY spectra. The group of Chi recently reported the synthesis and characterization of heterometallic architectures based on a cobalt-containing tetratopic donor and palladium or ruthenium acceptors [125]. From a mixture of donor 36 and acceptor 37 (Fig. 30) in CD3OD/CD3NO2 (1,1) solution, a heterotrimetallic (Co(I)/Fe(II)/Pd(II)) supramolecular barrel was obtained, and its molecular structure in solution was elucidated from 1H and 13C NMR

Fig. 30 Tetratopic donor and Pd/Fe and Ru acceptors employed for the self-assembly of heterotrimetallic barrel and heterobimetallic cages.

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measurements, along with DOSY NMR, which showed the formation of a single product at D ¼ 4.61010 m2/s. Single-crystal X-ray diffraction analyses confirmed the structure of the product in the solid state. Following a similar experimental procedure, heterobimetallic (Co(I)/Ru(II)) cages were prepared from donor 36 and acceptors 38 or 39 (Fig. 30). 1H NMR and single-crystal X-ray diffraction analysis, among other techniques, evidenced the formation of a single product from the reaction between 36 and 39, however, 1H NMR measurements of the product of SM8 showed duplicated signals, all of them corresponding to the same D value of 5.81010 m2/s in the DOSY spectrum. A combination of 1H, DOSY and ROESY NMR experiments and ESI-HRMS analyses evidenced that this phenomenon was caused by the formation of two isomers: one of them in which the cyclopentadienyl of both 36 ligands of the cage were pointing outwards and another isomer in which one of the Cp moieties is placed inside the cage. Caskey and Michl described in 2005 the self-assembly synthesis of platinum-based prismatic molecular rotors, which were structurally characterized by mass spectrometry, elemental analysis and NMR (1H, 13C, 31P, 195 Pt, DOSY, etc.) in the absence of X-ray diffraction good-quality crystals [126]. From the computational modelling of the molecular architectures by universal force field (UFF) [127] molecular mechanics, the radii of the supramolecular prisms were estimated and then compared to the data obtained from 1H DOSY NMR in CD2Cl2 (Table 6). The experimental (DOSY) and theoretical (UFF) molecular sizes matched well for the expected three-dimensional structures. Stang and co-workers have employed DOSY and PGSE NMR measurements to characterize platinum supramolecular assemblies with pyridyl-type ligands [128,129]. In 2008, the molecular radii, R, of structures with a trigonal prism geometry were estimated from the D values obtained in 1H DOSY experiments in CD3NO2 solution [128]. The distance from the centre of the prismatic assemblies to the platinum atoms located at the vertices of the prism was considered to be equivalent to the radius of a sphere and so the Stokes-Einstein equation was employed to calculate a

Table 6 Molecular radii for trigonal and tetragonal molecular rotors. r from UFF (Å) Compound rH (Å)

Trigonal prism

17.6

15.2

Tetragonal prism

13.1

12.7

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˚ , which was similar enough to the value of 10.8 A ˚ estimated from R of 8.8 A UFF molecular mechanics computational modelling for a trigonal prism geometry. Later, in collaboration with Yang in 2010, a similar working approach was utilized to characterize the three-dimensional structure of platinumbased supramolecular dendrimers with an adamantanoid core [129]. 1H PGSE NMR measurements in acetone-d6 solution of several assemblies bearing different dendritic substituents on the same adamantanoid core were employed to determine the molecular radii of the structures, which were in good agreement with the R values estimated from computational molecular dynamics simulations. Yang and collaborators have also used DOSY NMR in CDCl3 solution to estimate the size of different platinum triangular metallodendrimers [130]. These dendrimers showed lower D values with increasing molecular weights, matching the structures modelled by semiempirical molecular orbital methods. In 2015, they employed a pyridyl-based ligand to synthesize new ring-shaped supramolecular assemblies from diplatinum(II)-based acceptors and spherical assemblies using palladium(II) as acceptor [131]. The 2D DOSY NMR spectra in DMSO-d6 of each one of the assemblies provided a single band at the logD dimension, confirming the discrete formation of only one product in each case. Similar pyridinebased ligands and platinum precursors were employed by Baba et al. in 2015 for the synthesis of a dodecanuclear Pt(II)-linked hexagonal macrocycle [132]. 1H DOSY measurements in CD3NO2 solution were found decisive to identify differently sized intermediates during the self-assembly process of the coordination architecture. The group of Das has synthesized different supramolecular metallacages [133] and macrocycles [134] using triptycene organoplatinum cores (Fig 31, 40)

Fig. 31 Organoplatinum building block employed by the group of Das for the construction of metallacages and macrocycles.

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or a dipodal pyrazine organoplatinum acceptor (Fig 31, 41). These architectures were then thoroughly characterized using various techniques (multinuclear NMR, mass spectrometry, X-ray diffraction, computational modelling, etc.). In both cases, 1H DOSY NMR spectroscopy revealed a single set of signals, thus ruling out the possibility of the formation of different oligomers in solution or larger supramolecular structures other than the expected. The group of Therrien have described in several occasions the preparation of cationic arene ruthenium trigonal metalla-prisms with the ability to encapsulate planar polyaromatic scaffolds (phenanthrene, triphenylene, pyrene, and photosensitizers such as porphyrin or phthalocyanine, among others) [135]. All structures were subjected to extensive characterization via NMR techniques, where again DOSY NMR experiments in CD3CN solution were crucial to confirm the encapsulation of the guest molecules into the metalla-cages. This was performed by determining the diffusion coefficients on both the metalla-cage host and the guest molecule, which turned out to be the same (within the experimental error) thus proving that they are part of the same entity in solution. Besides, almost identical hydrodynamic radii were calculated for the metalla-cages before and after the encapsulation process, showing that the structures undergo no relevant conformational change upon encapsulation of the guest molecule. On the other hand, Jin and co-workers proved via 1H DOSY measurements that their iridium-based metalla-rectangle did not encapsulate pyrene molecules in solution [136]. The DOSY spectra in CD3OH of a mixture of the iridium metalla-rectangle and pyrene showed the same diffusion coefficient than when they were measured in separated samples. X-ray crystallography further confirmed the outer interaction between the metalla-rectangle and pyrene, in which the cavity of the supramolecular structure was partially occupied by solvent (CH2Cl2) molecules, while pyrene molecules established π-stacking interactions in the outside of the structure. The group of Pluth presented in 2015 the synthesis of rhodium supramolecular structures assembled via a combination of hydrogen bonding and metal–ligand interactions [137]. These new architectures were analysed via X-ray diffraction in the solid state and further investigated via 1H DOSY NMR in CD2Cl2 solution. The DOSY spectra showed the formation of a discrete species for each of the assemblies studied, and the calculation of their hydrodynamic radii confirmed the retention in solution of the monomeric structure found in the solid state, thus ruling out both the dissociation of the supramolecular structures or the formation of higherorder aggregates.

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Laramee-Milette et al. prepared a luminescent tetraruthenium metallasquare via a photo-induced assembly pathway [138]. DOSY NMR experiments in acetone-d6 solution were conducted on either the mononuclear Ru precursor complexes and on the tetranuclear metallasquare (Fig. 32). The D values obtained were almost equivalent for the mononuclear Ru(II) complexes 42 (DX¼Cl ¼ 10.01010 m2/s, DX¼MeCN ¼ 9.931010 m2/s, DX¼Py ¼ 9.991010 m2/s), while a notably lower diffusion coefficient of 5.191010 m2/s was found for species 43, thus being coherent with its supramolecular nature. The structure of ruthenium metallasquare in the solid state was further confirmed by single-crystal X-ray diffraction analysis. Lozano-Cruz et al. synthesized and characterized a series of ferrocenederived dendrons with antibacterial activity [139]. The species prepared consisted of a ferrocene unit as focal point with a dimethylamino-terminated carbosilane dendrimer substituent of up to three generations (Fig. 33). These dendrimers were prepared in neutral form or protonated on the amine positions using HCl. In order to determine the size of the dendrons in solution, DOSY NMR measurements were carried out in different solvents; CDCl3 and CD3OD for the neutral molecules, and CD3OD and D2O for the protonated cationic species. The neutral dendrons showed similar hydrodynamic radii when measured in either solvent and only a slight increase in

Fig. 32 Ru(II) complex precursors and the resulting metallasquare after photo-induced assembly.

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R1 =

Fe

R3

Si R2

HN Si R1 R1

R2 = Me ; R3 =

N

or R2 = R1 ; R3 =

Si R1

R1

Fig. 33 General structure of Me2N-terminated carbosilane dendrons with ferrocene at the focal point.

size with higher generation. The cationic dendrons showed comparable rH values with respect to their neutral counterparts when measured in CD3OD, being only slightly larger, however, the rH values calculated from the DOSY measurements in D2O resulted notably larger and generation-dependent than those observed in CD3OD, thus evidencing the formation of aggregates in water solution. The extent of such self-aggregation tendency was found to be correlated to the antibacterial activity of these cationic dendrons, as those of first and second generation resulted more active than the third generations, which undergoes greater self-aggregation degree. Wang and co-workers described very recently the synthesis of several iron-based hemicages via coordination-driven assembly in which the presence of a ferrocene unit in the tripodal ligands facilitated the process due to the rotational dynamics of the system [140]. For all three structures prepared, 1 H DOSY spectroscopy in CD3CN confirmed the formation of a single discrete species in solution, provided all the 1H chemical shifts corresponded to ˚ calculated from the same D value. Besides, the hydrodynamic radius of 9.2 A the diffusion coefficient value for one of the structures matched that from computed molecular models. Using tripodal terpyridine ligands with an adamantane core in combination with zinc salts, Li and co-workers synthesized three different supramolecular architectures in 2014 [141]. Depending on the angle formed by the linker between the adamantane and the terpyridine moieties on each ligand, the 3D structures obtained from the reaction with Zn(NO3)26H2O were either a cube, a tetrahedron or a trigonal bipyramid (Scheme 14). DOSY NMR spectra in CD3CN solution revealed the formation of a single species in each case, with logD values of 9.96 (cube), 9.66 (tetrahedron) and

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Scheme 14 Precursor employed in the synthesis of different shape supramolecular architectures.

9.48 (trigonal bipyramid), allowing to calculate an edge length of 5.6 nm for the cubic structure. These results were consistent with the diameters of 6.9 (cube), 4.4 (tetrahedron) and 2.9 nm (trigonal bipyramid) estimated from molecular simulations. Ca´mara et al. reported the use of a series of gold(I) metallaligands with bipyridine donors to synthesize triple helicate supramolecular structures upon coordination of Fe(II), Zn(II) or Co(II) [142]. The resulting complexes, containing three molecules of Au(I) metallaligand (Fig. 34) and two centres of the divalent metal, were studied by 1H PGSE NMR in CD3CN solution at 2.5 mM concentration, and their diffusion coefficients and hydrodynamic radii calculated. The rH values found were very similar ˚ , except for those for all the complexes, ranging between 10.8 and 11.4 A ˚ containing the more rigid binaphthyl spacer in the metallaligand (11.8 A ˚ for the Fe(II) complex and 11.9 A for the Zn(II) complex). These results suggest that the ligand side chain remains folded in solution, and the complex adopts a compact structure similar to that of the solid state determined by X-ray diffraction.

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Fig. 34 Gold(I) metallaligands employed to form triple helicates.

5. Conclusions This chapter illustrates a considerable progress in the diffusion NMR field, whether using PGSE or DOSY methodologies, and using an increasing number of nuclei. The estimation of diffusion parameters using all the advantages of high-resolution NMR spectroscopy specially with modern probeheads, that allow the use of intense gradient fields and the tuning of less conventional nuclei, opens unique possibilities to determine the size and shape of many molecular systems in solution. In the case of supramolecular architectures, or in smaller metallic ion pairs for instance, this allows one to assess their state, character of intermolecular interactions, stability, association constants between different hosts and guests, etc. At the same time, in spite of the wider use of diffusion-ordered NMR spectroscopy, there are still many underlying chemical problems of unknown nature that diffusion NMR methodologies can help to unravel. It is important to mention that diffusion NMR methodology is not an universal tool and does not replace traditional NMR methods based on, for instance, analysis of the homo- or heteronuclear Overhauser effect and chemical shifts, which in some cases provide complementary information that allows to draw the real picture of the system under study. A joint analysis of the diffusion, relaxation and NMR spectral parameters is key when one goes from estimation of empirical parameters of the molecular system to fully characterize more subtle features such as the real shape or the mutual orientation of components in a specific system. The results given

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in this review are appealing in its simplicity, offer chemically useful results and we believe they should significantly boost the use of diffusion NMR measurements. The review has been written under financial support from Junta de Andalucı´a (Spain) under the project number P12-FQM-2668 and Ministerio de Ciencia, Innovacio´n y Universidades (Spain) under the project numbers CTQ2017-84334-R.

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