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This book is dedicated, first and foremost, to my wife Carole-Joyce, without whose support and understanding, it would never have appeared and also to the memory of Prof. L. M. Venanzi.

Multinuclear NMR spectroscopy is without doubt a major contributor to elucidating molecular structure in solution. Coordination and organometallic chemists routinely measure hundreds (if not thousands) of NMR spectra every day. Nevertheless, there are very few books devoted to the NMR characteristics of these metal complexes. Further, although many of the NMR details connected with these measurements are closely related to those associated with the ¹H and ¹³C characteristics of organic or biological molecules, there are some important and unique differences arising due to complexation of an organic molecule to a transition metal.

In this text, designed for PhD and postdoctoral chemistry students, I discuss many (but certainly not all) of the multinuclear NMR parameters that are most relevant for transition metal organometallic chemists. There will be a strong emphasis on routine measurements, that is, ¹H and ¹³C NMR, but there are a number of readily measurable spin = 1/2 nuclei such as ¹⁵N, ¹⁹F or ³¹P, that afford structurally valuable chemical shifts, plus diagnostic spin-spin coupling constants. Measurements on these nuclei are important since coordination chemists need to understand the immediate environment of the metal center, and ¹H and ¹³C NMR alone may not be sufficient, as these probes can be somewhat remote from the metal. Frequently, ³¹P and/or other spin I = 1/2 nuclei such as ²⁹Si, ¹⁰³Rh, ^117,119Sn or ¹⁹⁵Pt will prove to be a better choice. Some of the model transition metal compounds chosen for the chemical shift and coupling constant discussion will often be either directly involved with, or related to, some aspect of homogeneous and enantioselective catalysis. There will be an emphasis on metal phosphine and carbene complexes as these are fairly important ligands in this area.

Somewhere in an old cookbook I remember reading ‘‘the first thing one needs to do in order to make rabbit stew is to catch the rabbit”. First one needs to obtain the various spectra so that these NMR techniques make up the first part of the book. Although many young researchers measure NMR spectra, it is important to think not only about ‘‘routine measuring’’ but also a bit about how one might improve the quality of the spectra obtained. In my experience, we are a little spoiled, in that modern NMR spectrometers often deliver good quality spectra without much effort on the part of the user. Of course once the spectrum is present, there is the question of assignment. Since it may prove necessary to assign modestly complicated spectra, a few words on current two-dimensional methods are appropriate. Some of these 2-D methods are fairly straightforward, whereas others require more effort on the part of the user. All of the NMR techniques presented are fairly standard (and available on all modern spectrometers) so that I will not review the theory associated with these methods.

A major part of this text, chapter 11, is devoted to solving structural and other NMR problems concerned with transition metal coordination and organometallic compounds. The reader will be shown a reaction followed by the kind of NMR data that one normally finds in a preparative experimental section. Using these chemical shifts and coupling constants one is asked to propose a structure. In chapter 12 the solutions to the problems will be provided, together with a literature citation and some subjective commentary.

In order to prepare the reader for these problems, a schematic very brief introduction to selected organometallic reaction mechanisms and the syntheses of several classes of metal complex will be given. This will hopefully direct the reader’s thinking when confronted with the problems.

This text is not designed to be comprehensive, but rather to emphasize-as briefly as possible-what one needs to know in order to obtain the most useful spectra and then using the NMR data that one can derive from them, to solve routine research problems in coordination and organometallic chemistry.

Abbreviations

Introduction

Just as in organic chemistry or biochemistry, it is now routine to measure ¹H, ¹³C, and, often, ³¹P NMR spectra of diamagnetic organometallic and coordination compounds. Many NMR spectra are measured simply to see if a reaction has taken place as this approach can take sometimes take <5min. Having determined that something has happened, the most common reasons for continuing to measure are usually associated with

1) Confirmation that a reaction has taken place and, by simply counting the signals, deciding how to proceed

2) The recognition of new and/or novel structural features via marked changes in chemical shifts and/or J-values, and

3) The need for a unique probe with sufficient “structural resolution” to follow the kinetics or the development of a reaction.

When a P atom is present, proton-decoupled ³¹P NMR often represents one of the simplest analytical tools available as the spectra can be obtained quickly and do not normally contain many lines.

Figure 1.1 shows the ³¹P NMR spectra for aqueous solutions of the Pt(0) and Pt(II) complexes Pt(TPPTS)₃, D, and Pt(H)(TPPTS)₃⁺, A, respectively, as a function of pH (TPPTS is the water-soluble triphenyl phosphine derivative P(m-NaSO₃C₆H₄)₃). At pH 13, the Pt(0) complex is stable, while at pH 4, the hydride cation is preferred. The lowercase letters indicate the ¹⁹⁵Pt satellites. One isotope of platinum, ¹⁹⁵Pt, has I = 1/2 and 33.7 natural abundance, and the separation of these satellite lines represents ¹J(⁹⁵Pt, ³¹P), another useful tool. Using ³¹P rather than ¹H or ¹³C provides a quick and easy overview of the changes in the chemistry and corresponds to point 1.¹⁾

Figure 1.1 ³¹P NMR spectra recorded on the same solution after 10 cycles between pH 4 and 13: (a) recorded at pH 13, showing the Pt(0) complex, D, Pt(TPPTS)₃, and (b) recorded at pH 4, showing Pt(H)(TPPTS)₃ cation, A. Traces of the hydroxide-bridged dinuclear complex, C, as well as the phosphine oxide, OTPPTS, are marked [1].

Apart from recognizing the number of different chemical environments, many times the important clue(s) with respect to the nature/and or source of the reaction products stem from specific chemical shifts.

Reaction of Ru(OAc)₂(Binap) with 2 equivalents of the strong acid CF₃SO₃H affords the product 1.2 in high yield. Superficially, complex 1.2 appears to arise as a result of the addition of H₂O across a Binap P-C bond. But what is the water source? The ¹³C spectrum of the reaction solution, see Figure 1.2, reveals that acetic anhydride is produced (and thus water) from the two molecules of HOAc produced from the protonation. Further, the spectrum shows a C=O signal for the novel intermediate 1.1.

This reaction represents an example of point 2, in that the product reveals an unexpected feature.

Figures 1.3 and 1.4 demonstrate point 3. The ¹H NMR spectrum of the deuterated rhodium pyrazolylborate isonitrile complex, RhD(CH₃)(Tp′)(CNCH₂Bu^t), in the methyl region, slowly changes to reveal the isomer in which the deuterium atom in now incorporated in the methyl group to afford RhH(CH₂D)(Tp′)(CNCH₂Bu^t). In this chemistry, the deuterium isotope effect on the ¹H methyl chemical shift is sufficient to allow the resolution of the two slightly different methyl groups and thus allow the ¹H(²H) exchange to be followed.

Figure 1.4 shows the intracellular and extracellular exchange of cesium, via ³³Cs NMR (I = 7/2, 100% abundant), as a function of time. Although this subject does not involve transition metal chemistry, it does demonstrate how NMR can shed light on a potentially complicated biological subject. Both Figures 1.3 and 1.4 represent examples of the use of NMR to follow a slowly developing chemical transformation (point 3).

To be fair, a unique structural assignment cannot usually be made by counting the number of ¹H, ¹³C, or ³¹P signals and/or measuring their chemical shifts. X-ray crystallography remains the acknowledged ultimate structure proof. However, for monitoring reactions, identifying mixtures of products and detailed mechanistic studies involving varying structures, NMR has proven to be a flexible and unique methodology. Apart from ¹H, ¹³C, ¹⁵N, ¹⁹F, or ³¹P, already mentioned, there are many other possibilities, including ²H, ²⁹Si, one of the Sn isotopes, and ¹⁹⁵Pt, to mention only a few.

Figure 1.2 Section of the ¹³C spectrum of the reaction solution after 30min at 353 K with peaks for the acetate moiety of 1.1, acetic acid, and acetic anhydride. The expanded section shows the P C coupling, ²J = 2 Hz (75MHz in 1,2-dichloroethane solution) [2].

Figure 1.3 Methyl region as a function of time (minutes) of the ¹H NMR spectrum from the rearrangement of RhD(CH₃)(Tp′)(CNCH₂Bu^t), to RhH(CH₂D)(Tp′)(CNCH₂Bu^t) in benzene-d₆ at 295 K [3].

Figure 1.4 ¹³³Cs NMR spectra of human erythrocytes suspended in a buffer containing 140 mM NaCl and 10 mM CsCl. The origin of the chemical shift scale is arbitrary [4, 5].

In addition to chemical shifts, the observed signal multiplicity (as in Figures 1.2 and 1.3) can be useful, as the observation of a coupling constant (J-value) can help to confirm that a fragment is within the coordination sphere. In Figure 1.2, an acetate carbon is coupled to the ³¹P. In Figure 1.3, the ¹⁰³Rh (I = 1/2, 100% natural abundance) couples to the ¹H of the methyl group. Apart from these routine parameters, organometallic chemists need to occasionally use slightly more specialized NMR tools. Spin–lattice relaxation times, T₁’s, for example, are now used to characterize metal molecular hydrogen complexes. All these, and others, together with the ability to detect and measure solution dynamics over several orders of magnitude, contribute to making NMR an indispensable technique. However, modern NMR spectrometers are not always simple to use and obtaining good quality NMR spectra can require some effort.

References

2. Geldbach, T.J., den Reijer, C.J., Worle, M., and Pregosin, P.S. (2002) Inorg. Chim. Acta, 330, 155.

3. Wick, D.D., Reynolds, K.A., and Jones, W.D. (1999) J. Am. Chem. Soc., 121, 3974.

4. Davis, D.G., Murphy, E., and London, R.E. (1988) Biochemistry, 27, 3547.

1) Although not always specified, the ¹³C and ³¹P NMR spectra that follow throughout this text (and in the literature) are almost always measured with broad band ¹H decoupling, so that ⁿJ(¹H,X) coupling constants are not present and this helps to simplify the spectra. Occasionally, this will be indicated as “¹³C(¹H)” or “³¹P{¹H}.” Unless otherwise specified, the reader should assume broad-band proton decoupling.

Routine Measuring and Relaxation

2.1 Getting Started

Preparing the sample may not be trivial (many organometallic complexes are air and water sensitive); but assuming that one has prepared circa 0.7 ml of a clear solution containing 5–10mg of sample,¹⁾ in the usual 5 mm NMR tube, one is ready to measure a spectrum.

Most beginning researchers place the sample in the magnet, stabilize the magnetic field via a ²H lock (frequently no longer necessary), call up a simple measuring program, and type, “go.” For a standard one-dimensional proton ¹H NMR measurement, a few minutes (or less) of accumulation time are often sufficient to obtain a ¹H free induction decay (FID) that, after Fourier transformation, affords a spectrum with sufficient signal-to-noise (S/N) ratio. After a phase correction, the spectrum is plotted.²⁾

Typically, these operations are followed by an integration procedure to determine the relative number of protons in the various groupings of resonances, and this may be where a problem arises. The integration obtained may indicate that, instead of, for example, a 2 : 1 ratio, one finds a 1.7 : 1 ratio or 2.3 : 1 ratio. There may be a structural reason for the observed results, but sometimes, the problem is simply one of “relaxation.”

The NMR program may already contain a “recommended” ¹H pulse length (or it may simply be what the last researcher found to be optimal for his or her chemistry). If the chosen pulse length and/or the acquisition time (the time used by the computer to collect the FID) have not been properly considered, the integrals may not (and usually do not) correctly reflect the relative populations. Moreover, the S/N ratio may not be optimal.

Scheme 2.1 shows a cartoon of a routine measurement (note that the horizontal axis is not to scale). We will assume that the pulse length chosen (in microseconds) corresponds to a 90° pulse. A 90° pulse is defined as that pulse length that tips the magnetization vector 90° from its equilibrium position on the z-axis (A) and affords the maximum signal after one pulse (B). Less than 90° will afford a vector whose projection on (for example) the x-axis, will not be quite so large (C).

After the excitation via the 90° radio frequency pulse, an FID is collected in the chosen number of memory points. If there is no relaxation (post) delay, the experiment is repeated “N” times until sufficient signal is obtained. The acquisition time is determined by the number of data points in the FID (chosen by the operator), multiplied by the time the computer “resides“ in each channel (the dwell time, DT). The value of DT is set by the computer and is related to the selected spectral width. The simple relation is spectral width = 1/2(DT)³⁾, so that for large spectral widths the computer spends less time in each data point. Since the spectral width chosen is normally much larger for ¹³C or ³¹P, than for ¹H, for the same number of data points, the DT will normally be much shorter for these nuclei relative to ¹H. Since, as we will learn in the chemical shift section, the range of ¹H and ¹³C shifts in organometallic species is larger than for routine organic compounds, there is a tendency to “play it safe” and choose a relatively large spectral width. As we will see, this is acceptable provided that one adjusts the acquisition time accordingly.

Before discussing relaxation phenomena, it is useful to think, briefly, about the subject of spectral resolution and especially the accuracy of measured coupling constants. If one selects, for example, a spectral width of 20000 Hz and places the spectrum (after transformation of the FID) into 32 K data points, the resolution cannot be better than circa 0.62 Hz. If we assume that an error of ±1 channel is reasonable, rather than just 1 channel, then the J-values will not be better than about 1.2 Hz. Of course, one can use 64 K points, but this will still not allow the J-values to be determined to ±0.1 Hz. The student might keep this in mind when reading the literature.

2.2 Relaxation

Returning to relaxation, what happens after the first 90° pulse? It is often the case that the various protons (or carbons) to be measured have not had sufficient time to completely relax to their equilibrium positions during the acquisition time chosen. Consequently, in a multipulse experiment, the amount of signal obtained for each of the individual protons of the molecules under consideration will vary with their ¹H relaxation characteristics. It is sufficient to note that, to obtain a spectrum with the correct relative integrals, one either reduces the length of the pulse and/or one adds a relaxation delay at the end of the FID accumulation. An alternative to a relaxation delay involves the use of more data points during the accumulation of the FID. This adds more time in the gathering of the data (not always desirable) and improves the spectral resolution. It is not normally necessary to add a paramagnetic relaxation reagent.

Usually, a smaller pulse angle, perhaps, between 30° and 45°, will most likely afford correct integrals. But how do we know whether 30° or 45° corresponds to the correct choice?⁴⁾ Generally speaking, if one plans to work on a given set of molecules for a prolonged period (for example, for the length of a Ph.D. research project), it is advisable to measure the spin lattice relaxation times, T₁ for the protons of the class of compounds to be studied, and then to set up the experiment with a suitable acquisition time and/or postdelay.

is a straightforward process and affords a series of spectra as a function of the different waiting times, τ. The 180° pulse inverts the magnetization. After short τ values, the magnetization is still inverted and, after the 90^° pulse, transformation of the FID affords a “negative” signal. As the waiting time τ increases, the spins relax more and more toward their original equilibrium positions and the 90° pulse results in a “positive” signal.

Figure 2.1a shows an inversion-recovery T₁ measurement for the two types of hydride ligand in

(2.1). Note that with a τ value of 2000ms, the central proton is “positive” whereas the outer two hydride signals have close to zero intensity. For the two separate ¹⁹⁵Pt measurements on Pt{P(t-Bu)₃}₂ at 310 K, given in Figure 2.1b, one sees the effect on the signal intensities of altering the waiting time and of changing the magnetic field strength and we shall come back to this field dependence shortly. The T₁ values can be calculated from the experimental data via a well-known regression analysis. The waiting time that corresponds to “zero” signal is circa T₁(ln2) and although this may prove a useful relation for estimating T₁ it is not usually very accurate.

An understanding of the factors affecting the spin–lattice relaxation times, T₁’s, will help to solve the ¹H integration problem, and also can be of value in connection with optimizing S/N ratios and/or mixing times in 2-D ¹H,¹H nuclear Ovehauser effect (NOE) experiments. Moreover, there are some subtle problems concerned with integrals and intensities for ¹³C and ³¹P, involving T₁ so that a brief discussion on NMR relaxation is useful.

One can summarize the longitudinal relaxation rate of a nucleus, R₁(= 1/T₁), as resulting from the sum of a number of contributions and these are shown in Eq. (2.2).

The various contributions [3] to the overall relaxation rate are defined as follows: DD, dipole–dipole; CSA, chemical shift anisotropy; SR, spin rotation; SC, scalar coupling; Q, quadrupole; and EN, electron–nuclear. For our purposes, it is useful to discuss only two of these contributions,

and

Figure 2.1 (a) Inversion-recovery experiments to determine the relaxation times of the hydride ligands for

in CF₃CO₂H at 298 K. The waiting times are in milliseconds. The weak resonances surrounding the main bands stem from ¹⁸³W [1]. (b) ¹⁹⁵Pt T₁ measurements on Pt{P(t-Bu)₃}₂ at 310 K at 7.0 T (left) and 9.4 T (right) using the inversion-recovery pulse sequence. The variable delays between the 90” and 180” pulses were varied between 0.001 and 0.4 s. The spectral width corresponds to 12 000 Hz [2].

2.2.1 Dipole–Dipole Relaxation

Dipole–dipole relaxation, in which one of the two dipoles is ¹H, represents an important (and usually dominating) contributor to the relaxation of the two

important nuclei ¹H, ¹³C, and occasionally for ¹⁵N and ³¹P. In the equation above, γ is the gyromagnetic ratio and is directly proportional to the magnitude of the magnetic moment of the nuclei A and ¹H, S is the spin quantum number, h is Planck’s constant, τ is a molecular correlation time, and r is the distance between the two dipoles. Often, a number of proximate dipoles (for example, a set of protons in an aliphatic chain and/or the protons of an aromatic moiety) will contribute to the relaxation of a given ¹³C, ¹⁵N, or (sometimes) ³¹P. The values of τ and r represent two very important factors that vary with molecular structure. Large molecules move slowly (large τ) and some ¹³C or ¹⁵N spins have the protons directly bonded (short r-values).

where N in Eq. (2.4) represents the number of protons attached to the carbon in question. Clearly, a short r-value (e.g., a hydrogen atom directly bound to the ¹³C in question) will afford a shorter T₁. However, the τ value can be quite important. Anything that changes molecular motions (different solvents, via their viscosities, variable temperature experiments – again through a change in viscosity –, large vs small molecular size, or perhaps steric crowding) can affect τ and thus T₁.

The ¹³C T₁ values given below (in seconds) for 1-decanol, represent a classical example of how τ can be important for relaxation

The OH group provides a molecular anchor in that there is H-bonding to another alcohol (or solvent). This leads to different local τ-values along the chain with more freedom for movement (shorter τ-values) as one moves down the chain away from the OH group. A very similar effect is found for the ¹³C T₁’s in P(n-Bu)₃ complexes of palladium such as trans-PdCl₂L₂, L = P(n-Bu)₃. Here, the metal and its halogen and phosphine ligands function as the anchor, and once again, the ¹³C T₁’s increase as one moves down the phosphine chain [4b].

Changing nucleus, Table 2.1 shows some ³¹P T₁ values for P(Aryl)₃ complexes of iridium and gold, plus T₁’s for several alkyl phosphine complexes of palladium, in CDCl₃ solution. The T₁ values for the Ir and Au complexes decrease as the molecular weight of the P(Aryl)₃ increases due to the differing τ-values. Note that PPh₃ itself (not complexed, and thus presumably with a shorter τ-value⁵⁾) has a relatively long T₁, 26.0 seconds. The same trend for the ³¹P T₁’s is found when the R group of the trans-PdCl₂(PR₃)₂ is made larger by increasing the chain length. Since dipole–dipole relaxation is important for these alkyl phosphines (the methylene protons on the adjacent carbon are not too far away), the observed changes in the T_I’s are reminiscent of what we have seen for the ¹³C T₁ values shown above, for trans-PdCl₂L₂, that is, an increasing correlation time leading to a shorter ¹³C T1.

Where dipole–dipole relaxation is important (as in ¹H and ¹³C NMR), NOEs, that develop due to relaxation effects, can result in signal enhancement. The theoretical maximum is 50% for ¹H and almost a factor of 2 for ¹³C. Although not widely recognized, there is a dipole–dipole contribution to the ³¹P relaxation in metal phosphine complexes, and especially in alkyl phosphine complexes. Indeed, the dipole–dipole contribution can amount to between 70 and 100% of the relaxation [5]. Since a substantial dipole–dipole contribution exists, Overhauser effects between ³¹P and ¹H can have a marked effect on the ³¹P signal intensity when the phosphorus spectrum is measured with ¹H decoupling.

such as that indicated in Eq. (2.5). Simple integration of the ³¹P spectra will most likely not lead to the correct relative populations, unless both T₁’s and NOE’s have been considered. Measuring and using integrals in ³¹P spectra can be quite challenging!

Although technically important, there are not too many areas of organometallic chemistry where measuring T₁’s is necessary to understand the chemistry. However, in the discussion of the NMR parameters of molecular hydrogen complexes, to follow later on, ¹H T₁ data for both the hydrogen and hydride ligands are suggested to afford a diagnostic tool for these complexes in solution. The short H–H distance in the complexed η²-H₂ ligand (short r-values) results in extremely short ¹H T₁ values, (usually <20ms) relative to those T₁’s for terminal hydrides (often several hundred milliseconds). A review by Morris [6] includes more than 100 representative examples of these very short T¹’s.

An example is illustrative. At 198 K, the proton NMR spectrum of the Ru-carbene complex 2.2, exhibited two low-frequency signals in a 2 : 1 ratio. One finds a broad singlet for the η²-H₂ hydrogen ligand at δ = –4.1 and a much sharper singlet for the classical hydride at δ = –8.7. The T₁ value measured for the η²-H₂ resonance was found [5] to be much shorter (36 ms: 223 K) than the value found for the terminal hydride signal (241 ms: 253 K).

2.2.2 Chemical Shift Anisotropy

The CSA mechanism, R₁^CSA, is an important contributor to the relaxation of heavy nuclei, and particularly for the transition metals. This

aspect of relaxation is readily recognized due to its unique B₀² dependence (see Eq. (2.6)). Once again, r is a molecular correlation time. A comparison of the two inversion-recovery experiments in Figure 2.1b, above, for ¹⁹⁵Pt (I = 1/2,33.7% abundance) shows this type of field dependence. The ¹⁹⁵Pt T₁ for the two-coordinate Pt(0) complex, Pt{P(t-Bu)₃}₂ at 7.0T, 46ms, is longer than that at 9.4T, 25ms.

Figure 2.2 ¹⁹⁵Pt relaxation effects on the methyl ¹H line shapes for (a) PtCl(CH₃)(1,5-COD) at 200, 400, 500, and 700 MHz and (b) trans-PtCl₂{As(CH₃)₃}₂ at 200, 400, and 700 MHz. Notice the increasing line width as the B₀ field is increased. (A. Moreno, P.S. Pregosin 2010, unpublished results.)

In Chapter 7, the reader will find comments concerned with metal-to-proton and metal-to-carbon coupling constants. Sometimes, and especially where high-field magnets are employed, these ⁿJ(M, ¹H or ¹³C) values are not observed. The source of the problem is the B₀² dependence of the metal relaxation. Increasing the magnetic field strength, from, for example, 300 MHz (7.04T) to 700 MHz (16.4T), will (i) drastically shorten the metal T₁’s and (ii) broaden the proton or carbon line widths (a T₂ effect). As noted above, the ¹⁹⁵Pt metal T₁’s can be of the order of milliseconds. The long-range proton or carbon J-values are often <50 Hz, so that the fast metal relaxation can cause the connected ¹H or ¹³C resonances to almost or indeed completely “disappear.” Figure 2.2 give examples of ¹H spectra of two Pt-complexes, PtCl(CH₃)(1,5-COD) and trans-PtCl₂(As(CH₃)₃)₂, at different field strengths. In both cases, the ¹⁹⁵Pt satellite resonances broaden markedly as the field increases.

2.2.3 Passing Comments

1) Not all metals relax rapidly. Trivalent complexes of ⁸⁹Y (I = 1/2,100% natural abundance) possess quite long T₁ relaxation times (600 s or longer). This very long T₁ combined with a favorable spin quantum number affords sharp lines in the region of 3–5 Hz [7].

2) R₁^q usually represents the dominating (and very efficient) relaxation pathway for quadrupolar nuclei so that both ¹⁴N and ⁷⁵As are often effectively decoupled from spin I = 1/2 nuclei due to the fast relaxation. Not all quadrupolar nuclei relax so rapidly! For example, ²H with its relatively small quadrupole moment readily reveals J-values with both ¹H and ¹³C.

3) R1^SR relaxation involves molecules or fragments that rotate rapidly with the result that a coupling exists between the nuclei and the magnetic moment generated by rotating charge distribution. This process can be important for ¹⁹F and ³¹P among others.

4) R₁^EN is responsible for the rapid relaxation of the nuclei in a paramagnetic complex and depends strongly on the number and relaxation rate of the unpaired electrons.

2.2.4 Useful Tips

1) It will be easier to set up an NMR experiment correctly, and obtain good integrals, if the T₁’s are known.

2) For low-temperature measurements, if dipole–dipole relaxation dominates, the S/N ratios can sometimes be improved by using a larger pulse angle, since the T₁’s will be shorter (viscosity effects).

3) One should be careful when using ³¹P integrals to determine equilibrium constants.

4) Sometimes, it is wiser to measure ¹J(Metal,¹H) values at lower field.

References

1. Henderson, R.A. and Oglieve, K.E. (1993) J. Chem. Soc. Dalton Trans., 3431.

2. Benn, R., Reinhardt, R.D., and Rufinski, A. (1985) Magn. Reson. Chem., 23, 259.

3. See (a) Liu, M. and Lindon, J.C. (1996) Concepts Magn. Reson., 8, 161, for a review on NMR relaxation; See also (b) Bakhmutov, V.I. (2004) Practical NMR Relaxation for Chemists, John Wiley & Sons, Ltd.

4. (a) Jans-Burli, S. and Pregosin, P.S. (1985) Magn. Reson. Chem., 23, 198; (b) Bosch, W. and Pregosin, P.S. (1979) Helv. Chim. Acta, 62, 838.

5. Burling, S., Haller, L.J.L., Mas-Marza, E., Moreno, A., Macgregor, S.A., Mahon, M.F., Pregosin, P.S., and Whittlesey, M.K. (2009) Chem.-Eur. J., 15, 10912.

6. Morris, R.H. (2008) Coord. Chem. Rev., 252, 2381, and references therein.

7. Jindal, A.K., Merritt, M.E., Hyun Suh, E., Malloy, C.R., Sherry, A.D., and Kovacs, Z. (2010) J.Am. Chem. Soc., 132, 1784.

1) The amount necessary to obtain excellent signal-to-noise in a short period of time, will depend on the molecular weight and of course the nucleus to be measured amongst other parameters.

2) No longer carried out at the NMR console, but rather at some remote PC station so that others can efficiently utilize the machine time.

4) This problem has been studied at length. The optimum angle (the so-called Ernst angle) depends on T₁. For T₁ values between 0.4 and 4.0 s this angle changes from 53° to 86° assuming an acquisition time of 1 s.

COSY and HMQC 2-D Sequences

3.1 Tactics

Assuming that one has measured a routine ¹³C and/or ¹H spectrum, these spectra now need to be properly assigned and interpreted. For a routine ¹H spectrum of a simple complex, it is often sufficient to inspect the chemical shifts (as these may be diagnostic for a structure type), the individual integrals, and the various ⁿJ(¹H,¹H) interactions.

A somewhat lengthy strategy to assign spectra and subsequently solve the structure for complicated problems might involve

One rarely needs all the above, especially as the entire set can easily consume 24 h or more of machine time; however, for some particularly tricky problems, many (or all) of the above will prove necessary. How does one decide which of these methods to use?

3.2 COSY

Occasionally, the ¹H spectrum of an unknown is sufficiently complicated such that one cannot easily find which spins are coupled to one another, perhaps due to signal overlap. This is often the case where structurally complicated phosphine ligands (such as a tricyclohexyl phosphine, PCy₃, derivative) and/or large organic substrates (perhaps as part of a chiral auxiliary) are in play. In these cases one might wish to measure one or more 2-D NMR spectra, the simplest of these being a ¹H,¹H COSY spectrum. Equation (3.1) shows the basic two-pulse sequence (there are many variations on this theme), and Figure 3.1 provides a trivial example concerned with the CH₃O-Biphep salt, [Pt(CH₃CN)₂(P,P)](CF₃SO₃)₂.

Normally, the diagonal (whose projection on the axes affords the chemical shifts) runs from the top right to the bottom left and the cross-peaks arising from the proton-proton coupling constants, appear as off-diagonal signals. The COSY spectrum for this simple Pt-dication contains cross-peaks connecting H³ and H⁴, H⁴ and H⁵ plus H³, and H⁵. The H³ and H⁵ cross-peaks are relatively weak due to the small value of ⁴J. Although COSY represents a valuable tool, many times the proton spectra of the ligands employed are sufficiently simple so that this measurement is not necessary. Alternatively, the ¹H assignment can be made via an equally useful method, for example, one or more ¹³C,¹H correlations.¹⁾

Figure 3.1 Section of the COSY spectrum for the three biaryl protons H3–H5 in [Pt(CH₃CN)₂(P, P)](CF₃SO₃)₂ [1].

3.3 HMQC and HMBC

3.3.1 Methods

The ability to recognize how many H atoms are attached to a given carbon, together with the corresponding ¹H and ¹³C chemical shifts, provides powerful tools with respect to assigning both spectra and structure. Given the extensive literature ¹³C chemical shift database (there are commercially available programs that calculate ¹³C chemical shifts in organic compounds), it is useful to correlate the measured ¹H signals to their corresponding ¹³C (or ³¹P or ¹⁵N) absorptions. For ¹³C, one-dimensional methods such as attached proton test (APT) fulfill this function [3].

However, a variety of two-dimensional HMQC pulse sequences [4], based on using one, two, or three-bond coupling constants, not only can achieve the goal but also allow the X-nuclei data to be obtained efficiently. Obviously, the success of this technique depends on the presence of a spin–spin interaction between the X resonances and a suitable proton. For ¹³C [5], these coupling constants are usually present in either the ligands and/or from a reagent that has entered the coordination sphere. Fortunately, there is a substantial literature concerned with ⁿJ(¹³C,¹H) over one, two, and three bonds.

Given that related HMQC pulse sequences are also in use for measuring ¹H correlations to main-group nuclei, such as ²⁹Si, ⁷⁷Se, and ^117,119Sn, as well as transition metal nuclei such as ¹⁸³W or ¹⁰³Rh, Figures 3.2 and 3.3 give pulse sequences for a selection of these methods [5].

The basic sequence, given in Figure 3.2a, involves four pulses: two pulses, a 90° and 180°, on the I-channel and two 90° pulses on the S-channel, followed by collecting the free induction decay. These sequences represent sensitive, routinely used tools, and involve double-polarization transfer (I → S → I), with the I spins representing a high-sensitivity nucleus, most often ¹H, but occasionally ¹⁹F or ³¹P, and the less sensitive, S-spin (¹³C or ²⁹Si, etc.). The time, Δ, in Figure 3.2a, is critical and should be set close to 1/2{ⁿJ(S, I)}, whereas the time t₁ represents the time variable for the second dimension and is much shorter. The less sensitive nucleus data are detected using the proton signals (the two nuclei share common energy levels because of the coupling constant), and the spectra are usually presented as contour plots. Other ¹³C,¹H, correlation methods are available, but currently, the HMQC approach is favored due to the S/N advantage provided by these methods. This signal enhancement is proportional to the ratio (γI/γS)^5/2 where γ is the gyromagnetic ratio of the nucleus (and is directly related to the nuclear magnetic moment). Enhancement factors for a few other nuclei are indicated in Table 3.1.

Figure 3.2 Heteronuclear multiple quantum correlation (HMQC) pulse sequences. (a) Sequence for small J(I,S) values, (b) for larger, resolved J(I,S) values and phase-sensitive presentation, (c) zero- or double-quantum variant for the determination of the I-spin-multiplicity, and (d) with refocusing and optional S-spin decoupling. The broad bars indicate 180°, and the narrower bars indicate 90° pulses.

Figure 3.3 Heteronuclear single-quantum correlation (HSQC) pulse sequences with optional decoupling of the S-spin. (a) Standard sequence and (b) modified for the I-spin-multiplicity determination. The broad bars indicate 180°, and the narrower bars indicate 90° pulses.

Since the potential signal-to-noise gain can be of the order of 10³ or more, for very insensitive nuclei, the use of HMQC methods allows one to obtain relatively insensitive “X” nuclei chemical shift data in a reasonable period of time. Practically speaking, for about 10–20 mg of a complex of molecular weight circa 500, one can obtain reasonable quality data for many (but not all) less sensitive nuclei in 1 h or less. This methodology is not new. Early on, Benn, Brevard, and von Philipsborn, among others, have advocated their use in the measurement of, for example, ⁵⁷Fe, ¹⁰³Rh, and ¹⁸³W spectra. The reader is recommended to consult the literature [7–9] for an explanation of why and when one would use the more complicated sequences.

3.3.2 One-Bond 2-D ¹³C,¹H Correlations

For organometallic problems, the most frequently used HMQC method will involve ¹³C. The one-bond ¹J(¹³C,¹H) values for routine sp³ and sp² carbons often fall in the range 125–170 Hz so that a choice of Δ corresponding to circa 130–140 Hz (that is, 1/2(135) = 3.7 ms) is satisfactory.

Table 3.1 Enhancement factors, via HMQC methods, for selected nuclei [6, 7].

Having established the method of choice, a few examples involving both assigning carbon resonances and recognizing structure are illustrative. The dialkyl Ru-arene complex (3.1), in Figure 3.4, and the dinuclear Pd(I) diene salt (3.2), in Figure 3.5, represent examples where one-bond ¹³C,¹H correlations helped to assign the carbon spectra. Only a section of the total spectrum is shown in both cases. In the Ru complex (3.1), the three protons of the coordinated arene, H3–H5 (already assigned via spin-spin multiplicities and NOE effects), are correlated to their ¹³C signals via ¹J(¹³C,¹H). The separation of the two cross-peaks in the horizontal direction for each carbon represents the one-bond J-value. These cross-peaks have different phases (indicated by the open and closed circles) and knowing the phases can be helpful when the structure in question is much more complicated and there are many cross-peaks in the map, some of which overlap. Note that these three carbons are found at relatively low frequency, due to the complexation of the arene. Further, both H3 and C3 do not appear at the lowest frequency so that an assignment based on literature “organic substituent effects” would not be correct.

Figure 3.4 Section of the phase-sensitive HMQC, ¹H-detected ¹³C,¹H correlation for the Ru(arene complex (3.1), in the region of the complexed arene. The fourth, weaker ¹³C signal represents one of the complexed fully substituted carbons. R¹ = CH₃, R = 3,5-di-t-butylphenyl. The open and closed cross-peaks reflect the phase (¹³C at 100.6 MHz, ¹H at 400 MHz, CD₂Cl₂) [10].

Figure 3.5 Section of the ¹³C,¹H HMQC spectrum of the isoprene complex (3.2). The intense triplet stems from CDCl₃ [11].

Figure 3.5 shows a section of the one-bond ¹³C,¹H HMQC spectrum containing the five ¹H resonances of the complexed isoprene for the bridging Pd(I) dimer

(3.2). This 1-D ¹H spectrum is not trivial due to a number of long-range ³¹P,¹H coupling constants. Once again, the open and filled-in cross-peaks indicate the phases for each of the two ¹³C spin states. Note that isoprene carbon C3 correlates to a single-proton H3 at 2.96 ppm, whereas the CH₂ carbons C1 and C4 each show cross-peaks (near 2.8 ppm and 4.9 ppm, for C1 and 2.8 ppm and 4.2 ppm for C4) for the two attached protons. Apart from connecting the protons to their carbons, this C,H correlation is helpful as it confirms the overlap near 2.8 ppm and pinpoints the methine isoprene CH proton, thereby providing a starting point for the ¹H assignment. The distinction between the protons of the two isoprene =CH₂ groups (and thus the two ¹³C resonances) can be made via an analysis of the ³J(¹H,¹H) values since H3 will couple to the H4 protons, together with NOE results. The spectrum also contains a cross-peak connecting H1E (that trans to the C2-C3 single bond) to C3, and this is due to a long-range correlation. These can also be quite useful as we will see shortly.

Figure 3.6 Section of the ¹³C,¹H HMQC spectrum of the rhodium 1,5-COD oxazoline cation shown below. The anion is BF₄. THF solution [12].

Often enough, this type of one-bond carbon–proton correlation is just as important for the ¹H assignment as it is for the ¹³C assignment. Figure 3.6 shows part of the correlation for a rhodium 1,5-COD oxazoline salt in THF solution. The distinction between the 1,5-COD olefinic protons and the OCH₂ oxazoline protons for the BF₄ salt is complicated by signal overlap. However, since the ¹³C spectrum, in the vertical direction, shows the 1,5-COD olefinic carbons as doublets (¹⁰³Rh has I = 1/2 and 100% natural abundance), the cross-peaks point clearly to the ¹H signals of the olefin.

3.3.3 One-Bond 2-D ¹⁵N,¹H Correlations

The same type of HMQC sequence can be used in connection with one-bond coupling constants involving N-H protons. The ¹J(¹⁵N,¹H) values are quite substantial and for sp³ and sp² N atoms often fall in the range circa 65–80 and 85–100 Hz, respectively. The bridging amide ligand in palladium complex (3.3), in Figure 3.7, is representative, and in this example, one would like to distinguish between the two broad OH and NH absorptions. If the NH proton does not exchange rapidly, it can be correlated to the ¹⁵N resonance. The observed 70–75 Hz ¹J(¹⁵N,¹H) value falls in the expected range and assigns the single-proton signal at 0.69 ppm as that bound to nitrogen.

Figure 3.7 ¹⁵N,¹H HMQC spectra for dinuclear complex 3.3. δ¹⁵N = 28.5. The uncomplexed aniline, p-CH₃O-C₆H₄NH₂, has δ¹⁵N = 52.5 so that the ¹⁵N chemical shift difference between the aniline and the coordinated [ArNH]- is circa 24ppm (CD₂Cl₂, 500 MHz, 213 K) [13].

3.3.4 Two and Three Long-Range Bond ¹³C,¹H Correlations

Long-range HMQC correlations (sometimes named HMBC, for “multiple bond” correlations) are extremely valuable as they can be used to measure many different nuclei, for example, when a nitrogen atom is fully substituted, as in a (CH₃)₂NCH₂CH₂N(CH₃)₂, TMEDA, or Schiff’s base, R₁CH = NR₂, type complex. However, the most common of these measurements involves a long-range proton–carbon correlation [5].

For aliphatic compounds, ³J(¹³C,¹H) shows a dihedral angle (Karplus-type) dependence with maxima at circa 7–9 Hz. For routine aryl sp² carbons, the values for ²J(¹³C,¹H) are often <5 Hz and those for ³J(¹³C,¹H) a little larger between 6 and 10 Hz; however, there are exceptions.

Since these ²J(¹³C,¹H) and ³J(¹³C,¹H) values for sp³ and sp² carbons vary quite a bit, a choice of 10 Hz, Δ = circa 50 ms, although somewhat biased toward ³J(¹³C,¹H) is often sufficient to obtain good quality spectra. Moreover, if the measurement is planned such that the Δ value chosen does not favor the two-bond interactions, and this might be the case for aryl sp² carbons, the 50 ms choice can often suppress the cross-peaks from ²J(¹³C,¹H), thereby providing a useful simplification of a frequently complicated 2-D map. Of course depending on their magnitudes, it may not be possible to eliminate all the cross-peaks arising from ²J(¹³C,¹H) since each class of compound is somewhat different. However, when the optimum Δ value is known, these long-range ¹³C,¹H correlations are especially valuable for locating and assigning fully substituted ¹³C signals. The four examples that follow use these long-range ³J(¹³C,¹H) correlations and are taken from organometallic carbene, hydride, aryl, and olefin chemistry.

Figure 3.8 The long-range HMQC ¹³C,¹H correlation for the Pd–carbene complex (3.4) with the intense cross-peak due to the N-CH proton between 7 and 7.5 ppm. Note also the interaction of the carbene carbon with the anti-allyl proton trans to the carbene donor [14].

Although carbene complexes are increasingly in use in organometallic chemistry, the ¹³C signal intensity from a fully substituted carbene of an N-heterocyclic carbene can be weak, due to a relatively long T₁. However, several possible long-range J-values can be used to detect this carbene absorption using HMBC methods. In the Pd-carbene complex (3.4), the carbene carbon, at 186–187ppm, couples to the heterocyclic =CH protons via three bonds and this correlation is often strong, as seen in Figure 3.8.

Alternatively, one can sometimes use the N-substituent, rather than the proton of the heterocyclic ring, if a suitable ³J-value is present. The aliphatic region of 3.5 (Figure 3.9) displays two isopropyl methine septets, due to restricted rotation about the Ru–C_NHC bonds. A ¹³C–¹H long-range correlation reveals that both these methine protons couple to the carbene resonance at δ = 199.1.

Figure 3.9 Section of the ¹³C,¹H HMBC spectrum for Ru complex 3.5 arising from the three-bond correlation between the methine protons and the carbene carbon atom (CD₂Cl₂, 400 MHz, 298 K) [15].

Long-range ¹³C,¹H correlations are especially useful for finding the fully substituted aryl ipso carbons. In the Pd-aryl complex (3.6a) (Figure 3.10), the three-bond correlation from the aryl methyl ¹H signal to the meta carbon assigns C3 (and thus H^m, via the one-bond correlation). In Figure 3.10, this meta proton, H^m3.6b¹³² interactions are absent.

Me	methyl
Et	ethyl
i-Pr (or Prⁱ)	iso-propyl
t-Bu (or Bu^t)	tert-butyl
Cy	cyclohexyl
p-Tol	para-methyl phenyl
Mes	2,4,6-trimethyl phenyl
Triflate	CF3SO3⁻ anion
OAc	acetate anion
acac	acetyl acetonate anion
DFT	density functional theory
DMSO	dimethyl sulfoxide
DMF	dimethyl formamide

The Author

Abbreviations

1

Introduction

References

2

Routine Measuring and Relaxation

2.1 Getting Started

2.2 Relaxation

2.2.1 Dipole–Dipole Relaxation

2.2.2 Chemical Shift Anisotropy

2.2.3 Passing Comments

2.2.4 Useful Tips

References

3

COSY and HMQC 2-D Sequences

3.1 Tactics

3.2 COSY

3.3 HMQC and HMBC

3.3.1 Methods

3.3.2 One-Bond 2-D 13C,1H Correlations

3.3.3 One-Bond 2-D 15N,1H Correlations

3.3.4 Two and Three Long-Range Bond 13C,1H Correlations

3.3.2 One-Bond 2-D ¹³C,¹H Correlations

3.3.3 One-Bond 2-D ¹⁵N,¹H Correlations

3.3.4 Two and Three Long-Range Bond ¹³C,¹H Correlations