Chapter 1: Application of the Nuclear Overhauser Effect to the Structural Elucidation of Natural Products

Albert W. Overhauser, while holding a postdoctoral position at the Department of Physics of the University of Illinois at Urbana (IL), theoretically proposed in 1953 that if the electron spin resonance of the conduction electrons in metals is saturated, the nuclei of the metal will be polarized to the same degree they would be if their gyromagnetic ratio were that of the electron spin.¹  The nuclear spins would exhibit an enhanced polarization by a factor of ≅1000. Such a significant degree of polarization of the metal nuclei predicted by Overhauser was soon after experimentally demonstrated by Carver and Slichter in a sample of metallic lithium.²  This is the concept that led to a new field of study known as dynamic nuclear polarization (DNP),^3,4  in which the electron spin polarization is transferred to nuclei in order to significantly improve their sensitivity. Although not the topic of this chapter, it is important to highlight that DNP is slowly becoming a very powerful tool in the structure analysis of molecules in high-resolution, solid-state nuclear magnetic resonance (NMR) spectroscopy,^5,6  and led Professor Overhauser to receive the 1994 National Medal of Science.

Note, however, that the nuclear Overhauser effect (nOe), which is the nuclear–nuclear analog of the original electronic Overhauser effect, was first observed by I. Solomon in 1955.⁷  Following the studies on nuclear spin relaxation previously published by Bloembergen, Purcell, and Pound on a single-spin system, Solomon published a seminal article entitled “Relaxation Processes in a System of Two Spins”. He experimentally observed that the longitudinal magnetization of a dipolar-coupled pair of “unlike” spins (different resonance frequencies) does not show simple exponential decay as in the case of a single-spin system. The experiments were done in an anhydrous sample of hydrofluoric acid. Upon saturation (steady-state Overhauser effect) or inversion (transient Overhauser effect) of the ¹H resonance, a maximum increase of ∼30% of the ¹⁹F signal was observed. The same effect was observed on the proton signal when the ¹⁹F resonance was excited in a similar way. Although not explicitly stated in Solomon's paper, this was the first reported experimental observation of the Overhauser effect between nuclei, and the experiment was later called the “nuclear Overhauser effect” and gave origin to the nOe or NOE acronym. This acronym can also be found in the literature standing for “nuclear Overhauser enhancement” due to the fact that the experiment produces enhancements of the NMR signals. We particularly prefer to use the term “effect”. Solomon also set the theoretical basis of the NOE. He describes in his paper a set of modified Bloch equations that gives the correct equation of motion of the macroscopic magnetic moments for a system of two spins under the influence of dipole–dipole interaction. These equations are known today as the Solomon equations; the diagrams representing the Zeeman levels for a two-spin system are correspondingly known as the Solomon diagrams. Later in the chapter, we will come back to these equations and diagrams.

Intramolecular as well as intermolecular proton–proton NOEs were first reported by Reinhold Kaiser in 1963⁸  and 1965, respectively.⁹  In the former article, Kaiser reported how the Overhauser effect can be used to determine the relative sign of J coupling constants, and to assign spectral lines to transitions between energy levels in trans-crotonaldehyde and m-dinitrobenzene. In the second article, Kaiser reported the intermolecular NOE in the liquid state between the protons of chloroform and cyclohexane.

Anet and Bourn introduced the first application of the NOE to the configurational and conformational analysis of small organic molecules in a seminal paper published in 1965.¹⁰  In this ground-breaking paper, they observed NOE enhancements when irradiating a sample of 3-methyl-but-2-enoic acid (1) and dimethylformamide (2), as well as in the half-cage acetate 3 (Figure 1.1). Prior to this article, the assignment of proton resonances in high-resolution spectra was performed on the basis of chemical shifts and J couplings. Shortly thereafter, Nakanishi applied intramolecular NOE analysis to the structural determination of the ginkgolides, a series of polyhydroxylated terpenoids. Irradiation of the ginkgolide C t-butyl group resulted in clear intensity enhancements that allowed the determination of the configuration of the related stereogenic centers (Figure 1.2).¹¹  In the following year, the application of the NOE to taxane derivatives was also reported from the group of Nakanishi.¹²  With the addition of the NOE to the arsenal of analytical tools, it quickly became evident to chemists that NMR would become one of the most powerful tools for the structural analysis of molecules of any size. The application of the NOE in structural biology is outside the scope of this chapter, and most of the theoretical and practical aspects of the NOE in organic molecules have been covered in the monograph of Neuhaus and Williamson,¹³  as well as other reviews.^14,15  It is the purpose of this chapter to illustrate the use of not-so-common techniques, mainly involving quantitative aspects of the NOE for the determination of configuration and conformation in organic molecules. It will be assumed in our discussions that concepts such as chemical shift, J coupling, and NMR pulses, as well as the fundamentals of the T₁ and T₂ relaxation processes, are known by the reader.

In spite of the impressive technological advances that involve very high magnetic fields, cryoprobes, and digital consoles, among others, compared to other spectroscopic techniques, NMR is a horribly insensitive technique due to the very low energy difference between the spin energy states. For protons, the energy difference between the α (m=+1/2) and β (m=−1/2) states at 500 MHz (magnetic field of 11.75 Tesla) is merely 3.32×10⁻²⁵ Joules, leading to a Boltzmann population distribution of N_α/N_β=1.000080 (i.e. only 80 out of a million spins in excess at the α lower-energy state). That is why any ingenious experiments that help to significantly increase this population difference are always very welcome, and the Overhauser effect is also used for this purpose, apart from being a powerful technique in structural analysis.

Another consequence of such a low resonance energy is the very weak interaction of the nuclear spins with their surrounding medium, leading sometimes to considerably longer relaxation times. As stated by Abragam, the probability W per unit time of the nuclear spin-1/2 transition from the β into the α state through spontaneous emission of a photon appears to be a negligible phenomenon. For a ¹H spin resonating at 500 MHz, W would be ≈10⁻²⁵ s⁻¹. In addition, Abragam also showed that the transition probability for an induced emission or absorption under the effects of a radiation field involving photons would also be very small (W≈10⁻¹⁰ s⁻¹), concluding that the coupling with the radiation field is “hopelessly inadequate” as a viable relaxation mechanism. Hence, what would be a viable relaxation mechanism for nuclear spins?

In fact, since the only property of spin-1/2 nuclei that depends on orientation is their magnetic moment, transitions between nuclear spins can only be induced by magnetic fields. Let us first analyze the effect of a radiofrequency (rf) pulse on the macroscopic magnetization (M_z) of a sample of spin-1/2 exposed to a magnetic field B₀. At thermal equilibrium, the Boltzmann distribution will produce a population excess in the α state for nuclei with a positive gyromagnetic ratio, as is the case for protons. The sum of the projections of the individual spins’ magnetic moments onto the z-axis will build the macroscopic magnetization M_z. As we know from basic NMR concepts, no net magnetization is observed in the x, y-plane due to the random nature of the phase of the individual magnetic moments precessing around the axis of the applied magnetic field B₀. Since M_z is a macroscopic property, like temperature, it can be rotated at our whim around the rf field B₁ applied on the x-axis. Rotation at our whim means that we can take M_z from +z to +y (90° rotation). We can stop here, or we can continue to −z (180° rotation), or we can even continue to a total rotation of 360° and bring M_z back to +z as it was before we turned the rf on. If we pay attention to what happens to the populations as we rotate M_z, we will see that at a 90° or 270° rotation, the populations are equalized (N_β=N_α) since there is no longer net magnetization in the z-axis; at 180°, the populations are inverted (N_β>N_α); and after a total rotation of 360°, the populations are back in thermal equilibrium. This simple example experimentally demonstrates that a fluctuating magnetic field can stimulate the absorption of energy not only by the spins, but also by their relaxation. It is important to keep in mind that these processes only take place if the magnetic field oscillates at the same frequency as the spins.

In a real sample, the spins are not alone. They are surrounded by other spins from the same molecule, by solvent molecules, by impurities, and even by dissolved oxygen gas. These surroundings are known as the “lattice”, a term originating from the early studies of relaxation in solids, where the surroundings were a real solid lattice, and we can say that the spins are coupled and in equilibrium with this lattice. If the spins are driven out of equilibrium by excitation with rf power, once the rf power is turned off, they return to equilibrium by interacting with the lattice. As a result of the Brownian motions in the lattice, molecules randomly reorient in liquid solution, producing fluctuating magnetic fields. These oscillating magnetic fields are not coherent along the whole volume of the sample. Each spin in the sample is affected in a different way as a result of the random nature of the reorientation. However, the frequency of these fluctuating fields will depend on the correlation time (τ_c) of the molecules. The correlation time is defined as the time it takes a molecule to reorient 1 radian. The inverse of the correlation time (1/τ_c) represents the rotational molecular frequency (ω) in radians per second (rad s⁻¹). The lattice is composed of a continuum of energy levels with a distribution of frequencies described by a function known as the spectral density, J(ω). This spectral density function depends on the molecular correlation time, which in turn depends on the sample temperature and viscosity. Spins return to equilibrium via a dynamic interaction with microscopic magnetic fields that randomly turn on and off along the volume of the sample with different intensities and directions. The projections of these magnetic fields along the z-axis (parallel to B₀) will add or subtract to B₀, introducing acceleration or deceleration of the spins’ precession angular speeds that lead to random changes in their phases. This contribution does not involve energy exchange with the lattice (adiabatic), since no change in the population distribution takes place. This process only affects the loss of transverse magnetization (M_x and M_y) by dephasing the spins contributing to the coherences created in the x, y-plane after a rf pulse is applied.

On the other hand, the components perpendicular to B₀ will in fact produce an effect that is equivalent to that produced by the rf field B₁ by inducing transitions between spin energy levels (non-adiabatic) in both directions (α→β and β→α), leading to longitudinal relaxation. By longitudinal we refer to changes in the intensity of the magnetization in the z-axis (M_z). These random perpendicular fields also contribute to transverse relaxation. It is important to highlight that these transitions will only happen if these random fields oscillate at the corresponding nuclei Larmor frequencies. During the longitudinal relaxation process, the populations will change until they reach a Boltzmann distribution as predicted by the temperature of the lattice (i.e. the populations will continue to change until the spins reach thermal equilibrium with the lattice). Note that it is assumed that the lattice is always in thermal equilibrium with itself and that its specific heat is infinite.

It is experimentally found that the loss of transverse magnetization as well as the return of the populations follow first-order kinetics (eqn (1.1) and (1.2)). Two first-order rate constants are involved in the relaxation process. These are the longitudinal relaxation or spin–lattice rate constant R₁, governing the recovery of the equilibrium magnetization M₀ and the transverse, or spin–spin relaxation rate constant R₂, which dictates the disappearance of observable transverse magnetization. These rate constants will have the associated relaxation times T₁=1/R₁ and T₂=1/R₂:

Why does spin relaxation follow an exponential decay law? In principle, other temporal dependencies—for instance, a Gaussian decay —could be imaginable. Following an exponential dependence implies that the time evolution of magnetization depends only on its particular value at a given time t, as can be seen on the time derivative . However, other possible forms for magnetization evolution as for instance a Gaussian-like dependence will not fulfill this condition and will therefore imply a memory of the system. We want to thank Stan Sykora for making us aware of this issue.

If a strong rf is applied, as in the spin-lock conditions applied in the ROE experiments, the transverse magnetization is not exactly governed by the T₂ time, but is instead governed by the T_1ρ relaxation time.

As noted above, all magnetic field oscillations that can cause a transition between energy levels can be a source of relaxation. Besides the external field, all active nuclei in a molecule, or the surrounding solvent, unpaired electrons in the molecule or external agents (trace metal ions, oxygen, etc.) are capable of promoting relaxation since the Brownian motion of molecules and solvents changes the relative orientation of the molecular spins (note, however, that spins themselves are locked in the direction of the strong external field). We list here the sources for spin relaxation experienced by molecules in solution:

• Dipolar relaxation: the source of the NOE and the most effective source of relaxation in solution.

• Chemical shift anisotropy (CSA) relaxation. The chemical shielding is a tensorial orientation-dependent property. Therefore, the effective field B_eff experienced by a particular nucleus depends on molecular reorientation. For instance, the carbon nuclei in benzene are more shielded when the C₆ axis is collinear with the external field than in the case of a perpendicular orientation. Just as with dipolar coupling, the anisotropy effects vanish in isotropic conditions, but they are still a source of relaxation. However, CSA relaxation is only relevant for nuclei with large chemical shielding tensor anisotropies and at high fields, and it is therefore not so relevant to ¹H NOE experiments.

• Scalar coupling relaxation: contrary to the case of dipolar relaxation, J-coupling values are not affected by rotational motions, but only internal motions, so they are consequently a much poorer source of relaxation than the dipolar coupling. In the case of weak coupling, only the z-component of the local field is affected, producing only transverse relaxation. This is, however, not true in the case of strong coupling, and scalar relaxation may contribute to negative enhancements.

• Paramagnetic relaxation: similar in nature to dipolar relaxation, relaxation caused by interaction with magnetic moments of unpaired electrons is extremely effective due to the high gyromagnetic ratio of the electron being nearly three orders of magnitude larger than that of the proton (γ_e/γ_H=−657.42). Even small traces of paramagnetic agents may cause very effective relaxation of the nuclear spins.

The dipolar interaction between spin-active nuclei is governed by the distance separating the nuclei and the orientation of the internuclear vector with respect to the strong external field:

This direct interaction may have a magnitude of thousands of Hz, as can be observed in solid-state samples. However, under isotropic molecular tumbling conditions, as is commonly the case in liquid-state samples, the equally probable orientations of the internuclear vector in all directions will cause the angular term in eqn (1.3) to vanish (see Chapter 4 on residual dipolar couplings [RDCs]). However, although the D_IJ does not show as an observable splitting of spectral lines, the magnetic field oscillation caused by reorientation of the internuclear vector may still cause transitions between spin states. This dipole–dipole relaxation acting on systems driven out of thermal equilibrium is the source of the NOE.

The nOe η_I{S} can be defined as the fractional enhancement of the NMR signal integral of nucleus I when the magnetization of nucleus S is moved out of equilibrium either by saturation or inversion; if spin I is close in space to S, both nuclei will be involved in a significant dipole–dipole interaction. The perturbation on spin S will be transmitted to spin I, therefore modifying the intensity, measured as the value of the corresponding integral, of its NMR signal, with I^I and I$0I$ being the integral values of the NMR signal for nucleus I under perturbed and unperturbed conditions, respectively. If the intensity increases with the perturbation, then the NOE is defined as positive, and is conversely defined as negative in the case of a decrease in intensity:

For an NOE enhancement to be observed, the internuclear vector (r_IS) has to be reoriented in solution at a rate within the range of the resonance frequencies of the spins I and S, which can be bonded or non-bonded, and may belong to the same or to a different molecule. Note that this reorientation may be caused both by global molecular tumbling and intramolecular conformational changes.

In isotropic solutions, the dipolar coupling is manifested not as an observable splitting of the transition lines, but rather as NOE due to the dipole–dipole relaxation. The fact that the dipolar coupling (D) between two nuclei vanishes due to isotropic molecular tumbling in solution is the reason why the NOE is observed. If the molecule does not tumble (solid state), then the dipolar couplings have a finite value that depends on the internuclear distance and on the angle of the internuclear vector with respect to the axis of the external magnetic field, but the NOE disappears. It is the oscillating nature of the dipole–dipole interaction that produces an efficient cross-relaxation process between the interacting nuclei, giving rise to the NOE. In normal standard liquid NMR conditions (isotropic tumbling), both parameters (the NOE and the dipolar coupling, D) cannot be observed simultaneously. However, if the sample is exposed to an anisotropic environment such as liquid crystals, liquid crystalline solutions, or stretched polymer gels, fractions of the dipolar coupling (known as RDC, see Chapter 4) and NOE are simultaneously observable in solution. If the degree of alignment in the anisotropic media is weak (∼0.01–0.10%), then 99.90–99.99% of the molecules are still tumbling isotropically, thereby producing very homogenous NMR spectra with enough molecular tumbling to display a NOE.

It is beyond the scope of this chapter to treat the theoretical aspects of the nOe in detail. However, without being redundant, it is germane to briefly consider a few key equations, as well as several other basic concepts, in order to better understand the Overhauser effect and provide the reader who has an interest in natural product structure elucidation with an appropriate level of understanding to use these experiments in their research.

The energy level diagram for a system of two dipolar-coupled nuclei I and S is shown in Figure 1.3. We may distinguish in this scheme three types of transitions between energy levels: first, single-quantum transitions W_SQ, where either the spin I or spin S state is changed; second, zero-quantum or flip-flop transitions αβ↔βα; and finally, the double-quantum αα↔ββ W_DQ transitions. Whereas rf irradiation may cause only single-quantum transitions, giving rise to observable spectral lines, relaxation may take place through any of the three mechanisms.

Consider now what happens through a thermally equilibrated system upon selective irradiation of the spin S (Figure 1.4). Irradiation will cause equalization of the α and β states of spin S through the single-quantum transition processes. If relaxation is not taken into account, we would see how the signal from the S spin disappears while the total intensity of the I signal, defined by its integral, remains the same. However, relaxation-induced non-radiative double-quantum and zero-quantum transition processes are operative. If double-quantum transitions are much more efficient than the zero-quantum transition process (W_DQ≫W_ZQ), the population of the αα state will grow at the expense of the ββ state in an attempt to restore the Boltzmann relationship (2ΔN). Therefore, the differences between the energy levels for single-quantum transitions of spin I will grow by a factor Δ, increasing the intensity of the I signal. Conversely, if the zero-quantum transition is more efficient than the double-quantum transition, then the population will flow from the αβ to the βα state. This will therefore decrease the population difference by a Δ factor and the integrated intensity of signal I would decrease proportionally. Thus, we will have positive NOE (intensity increases) when double-quantum relaxation predominates over the zero-quantum process, but a negative NOE if the situation is reversed.

Inclusion of all processes in Figure 1.4 in the Solomon equations leads to eqn (1.5). The term σ_IS represents the difference between the double-quantum and zero-quantum relaxation rates and it will govern the sign of the NOE. ρ_IS is the total dipolar longitudinal relaxation rate constant experienced by spin I, due to the presence of spin S. Note that according to this expression, if the magnetogyric ratios of the coupled nuclei have the same sign, as in homonuclear experiments or ¹H–¹³C experiments, then the intensity of the signal is increased (positive NOE), but is reversed if the sign of the nuclei is different. This is an important issue in broadband decoupling, and while irradiation of ¹H increases the sensitivity of the ¹³C-detected experiments, it will cause a decrease in ¹⁵N experiments:

Note, however, that spin I can relax through other mechanisms such as CSA or scalar couplings or, in a very effective way, through nucleus–electron relaxation due to the presence of paramagnetic substances (e.g. oxygen) in the sample. All of these additional relaxation sources may cause decreases in the NOE enhancement or even cause it to vanish. These additional relaxation pathways can be included in eqn (1.6) by replacing the purely dipolar relaxation rate ρ_IS by an effective rate , which includes all of the additional relaxation effects on spin I:

The W_DQ, W_SQ, and W_ZQ rate constants correspond to transitions with very different associated frequencies. If we consider a pair of proton nuclei in a 500 MHz spectrum separated by 1 ppm, the W_DQ transition (ω_I+ω_S) will be of 500 500 MHz+500 000 MHz=1 000 500 MHz, whereas it will be only 500 Hz for the zero-quantum transition W_ZQ (ω_I−ω_S). Therefore, they will be induced by fields oscillating at very different frequencies (i.e. by molecular motions of very different speeds), and these frequencies will depend on the particular dynamics of the internuclear vectors in the molecule. As a first approximation, we may consider our molecule as a solid body where all of the internuclear vectors are fixed with respect to a rigidly attached molecular frame. The random nature of the molecular motion does not allow the quantification of a rotational speed of this solid body, but we may still define an average rotational speed in terms of the so-called rotational correlation function, τ_c. If we consider a vector r connecting two points of the body, it is clear that the coordinates of this vector, with respect to the external laboratory frame, will change during the period of time τ. The average speed at which this vector changes its orientation in space can be defined through a time correlation function g(τ):

This rotational correlation function takes the exponential form given in eqn (1.8) where τ_c is the rotational correlation time, defined as the time constant for the exponential decay of the correlation function:

In our solid body approximations, τ_c will be the same for all of the internuclear vectors considered; note, however, that the presence of internal motion movements may cause this approximation to break down, and very different correlation times may be observed for different parts of the molecule. As a very general rule of thumb, the rotational correlation time for small molecules in organic solvents is given by the expression:

where MW is the molecular weight of the given molecule in mass atomic units. Note, however, that τ_c is proportional to the viscosity of the solvent and decreases with increasing temperature.

The long τ_c of a slowly tumbling molecule will be associated with oscillating fields of low frequency, and a short τ_c will conversely be associated with high-frequency oscillating fields. The available power (i.e. how much energy can be retrieved by the lattice at a given frequency) can be quantified by just applying a Fourier transform to the rotational correlation function. This Fourier transform of the exponential correlation function is a Lorentzian function, known as the spectral density function J(ω):

When τ_c shortens, the spectral density function becomes broader and contributions from higher frequencies become important, as shown in Figure 1.5. The rates for the single-, zero-, and double-quantum processes can be cast now in terms of the spectral density function. For a dipolar-coupled spin pair, the rate constants W are given by the following expressions:

Inserting these equations into eqn (1.5), the theoretical stationary NOE for a homonuclear system is given by:

Plotting eqn (1.14) as a function of τ_c indicates that the NOE will be positive at short correlation times, a typical condition of small organic molecules. Around the cross-point, ωτ_c≈1.12 and the NOE falls rapidly until it reaches a maximum negative −100% enhancement. At higher fields, the null condition will be reached at lower τ_c values (Figure 1.6). Therefore, it could be the case that NOE experiments perform better at lower fields, as some complex organic molecules may enter the negative region in high-field instruments.

Things become more complicated, but also more interesting, in the case of a system with more than two coupled dipolar spins. In general, the presence of other X spins close to the observed nucleus I acts as an additional source of leakage, causing a reduction of the observed NOE. For a multispin system, the observed enhancement of I upon S irradiation is given by:

Looking at the numerator of eqn (1.15), one can see that the enhancement of spin I depends on the enhancements of the surrounding spins X suffer upon S irradiation. If we just irradiate spin A (Figure 1.7), the perturbation created in the populations of B will be transmitted to the population of C, disturbing its signal intensity. In the region of a positive NOE, when double-quantum cross-relaxation predominates, this disturbance can be observed as a negative NOE. Note, however, that in the region of negative NOE, all observed NOEs, either direct or indirect, are of negative sign.

In systems with many spins, the indirect effects may complicate the quantification of the values and a full treatment of the multispin Solomon equations could be needed. However, note that although in a stationary state experiment, the final enhancements are independent of the time, the indirect NOEs need much longer times to reach the stationary state. Thus, the use of non-stationary kinetic NOE experiments will allow easier quantification of the NOE.

We will see in this section that quantitative analysis of the NOE can be facilitated by the use of kinetic NOE experiments rather than stationary-state experiments. The most simple way to perform kinetic NOE measurements is to use the truncated NOE experiment (TOE), where the selective irradiation times are kept below the saturation values.¹⁶ 

For a multi-system, the Solomon equation takes the form:

When spin S is selectively irradiated, at the initial time t=0, the equation reduces to:

Therefore, the initial increase of the I_z population depends linearly only on the cross-relaxation with spin S. This is the basis of the initial rate approximation. However, at longer times, the relaxation of spin I with spins other than S becomes more important. Since for a rigid molecule we can define a global correlation time for the different spins, the NOE enhancements will be directly proportional to the r$IS−6$ distances. Hence, if a valid NOE within the initial rate approximation is measured between two probe nuclei with a well-known distance, it is possible to determine an unknown I–S distance:

where C is a proportionality constant depending on the Larmor frequency and on the rotational correlation time. Therefore:

The initial rate approximation is the basis of most of the NOE-based conformational analysis that is used due to its simplicity. Note that, similar to the stationary NOE, the TOE is a difference experiment, and therefore has associated with it all of the practical problems inherent to difference spectroscopy.

Most of the modern applications of NOE are based on the use of transient NOE techniques. In the 1D transient NOE or 1D-NOESY experiments, the spin S is driven out of equilibrium by selective inversion. After that, a mixing time period τ_m is allowed to elapse before the application of the observation pulse and acquisition.

Since the system is not saturated in the NOESY experiment, the magnetization enhancement on spin I depends now on the relaxation rate of the inverted spin S, denoted as R_S. Near the extreme narrowing limit, this rate is competitive with the cross-relaxation term and the maximum positive enhancement that can be obtained in a transient experiment is only 38.5%. In the ωτ_c≫1 region, enhancement it is still around 100% as cross-relaxation is the most efficient process. Transient NOE measurements can be performed in a 2D fashion in the extremely popular NOESY experiments. In NOESY, the inversion pulse is split into two 90° pulses and a t₁ chemical shift evolution is inserted between them (Figure 1.8). After the second 90° pulse, z-magnetization is created for all spins, depending on their respective chemical shifts. During the mixing time τ_m, cross-relaxation effects will give rise to NOE enhancements. Note, however, that several artifacts may arise in this experiment. If a scalar coupling exists between the spins, then zero-, single-, and double-quantum coherences evolve during the experiment. Also, axial peaks may arise due to spin relaxation during the t₁ period. These artifacts can be removed using an eight-step phase cycle. Since cross-peaks may have either negative or positive signs with respect to the diagonal, the NOESY spectra should be acquired in phase-sensitive mode using TPPI, States, or States-TPPI protocols.

The advent of pulsed field gradients (PFGs)¹⁷  allowed purging of undesired coherences in a reduced number of scans. By inserting a weak gradient during the whole mixing time τ_m, the number of scans can be reduced to just two (Figure 1.9). Alternatively, a 180° pulse can be flanked by two strong PFGs to suppress the evolution of coherences during the PFG period, with the purpose of the 180° pulse being to refocus the evolution of coherences taking place during the gradient period. Echo–antiecho phase-sensitive NOESY spectra can be recorded by the insertion of a PFG during the evolution period.¹⁸ 

When molecules reach a motion regime in which the resonance frequency (ω_o) is in the order of the inverse of their molecular correlation time (ω_oτ_c≅1.12), the NOE enhancement is null and/or very weak. This is a situation that is observed for molecules in a range of molecular weights, reported by some authors to be 1000–2000 or 1000–3000, but a recent review article by Breton and Reynolds¹⁹  mentioned that it can start from molecular weights of ∼700. The molecular weight at which the NOE enhancement in small molecules starts to decrease depends on many factors, such as molecular shape (affecting its tumbling rate), solvent viscosity, temperature, and spectrometer frequency. However, it is a situation that has to be judged by the chemist experimentally. Many natural compounds fall into this category, particularly glycosides with several sugar units, peptides, macrocyclic natural compounds, dimers of diterpenes, triterpens, steroids, or large alkaloids.

Since this undesired phenomenon occurs at ω_oτ_c≅1.12, one of the experimental alternatives is to manipulate ω_oτ_c to move it away from the null NOE enhancement point. Around the null point, for a given molecule (constant value of τ_c), the NOE enhancement (η) shows a sharp change as a function of the spectrometer frequency (ω_o). For example, a null NOE at 500 MHz can be turned into an enhancement of +0.10 at 400 MHz and +0.22 at 300 MHz, or −0.10 at 600 MHz and −0.18 at 700 MHz. However, not every laboratory around the world has the luxury of having many NMR spectrometers to manipulate the NOE enhancement as a function of the spectrometer frequency. Nevertheless, for a given spectrometer, it is also possible to manipulate the molecular tumbling rate or correlation time (τ_c), which strongly depends on the solvent viscosity. Since temperature affects viscosity, changes in temperature and/or in the type of solvent will also help to move the experimental conditions away for the null NOE point. These were the only options available to chemists until 1984, when Bothner-By and colleagues introduced a rotating frame NOE experiment that was published with the name CAMELSPIN (Cross-relaxation Appropriate for Mini-molecules EmulLated by SPIN-locking) and was later renamed to rotating frame Overhauser enhancement spectroscopy (ROESY).²⁰  In the rotating frame NOE experiment, the cross-relaxation process occurs under the effect of a spin-lock, and the NOE enhancements (also referred to as ROE) are always positive, regardless of the tumbling rate of the molecules. There is not such an NOE null point at ω_oτ_c≅1.12. In addition, direct NOE enhancements have opposite signs to those from spin diffusion, saturation transfer, and exchange for all molecules (small and large).

Similarly to most NMR experiments, the rotating frame NOE can be performed as a selective 1D (selective ROE) or as a 2D (ROESY) experiment. In Figure 1.10, the basic ROESY pulse sequence is shown. Although the experiment does not show an NOE null point as a function of the molecular tumbling rate, leading to a significant advantage over traditional NOE, the ROE experiment presents a series of experimental complications. Since the experiment involves a spin-lock that is not as strong as the one used by TOCSY, in-phase TOCSY transfer peaks are observed and they are not distinguishable from real ROE peaks. In addition, these TOCSY transfers also lead to TOCSY-ROE transfers of magnetization, which give origin to “false” cross-correlation peaks for protons that are far from each other.²¹  The spin-lock is not uniform over the whole proton chemical shift range, leading to non-uniform enhancement and making the experiment not recommendable for quantitative purposes. Finally, anti-phase COSY-like peaks between J-coupled spins are also observed, but their intensity is very weak. Further modifications to minimize these unwanted experimental complications were reported. Hwang and Shaka introduced a variant of the experiment that minimizes the TOCSY contributions.²²  Its name is transverse ROESY (T-ROESY or Tr-ROESY), and the mixing period consists of a train of 180° with alternate phase . The pulses are given with no time between them. We strongly recommend this version of ROESY, which significantly reduces the unwanted TOCSY and false ROE peaks. The only shortcoming of this experiment is that the intensities of the cross-peaks are smaller than in the original ROESY experiment. From a conceptual standpoint, NOE and ROE experiments are based on the same physical phenomenon and provide the same structural information. Due to the fact that ROE experiments present so many experimental complications, it is important to be aware of these interferences when the experiment is used. A series a potential cross-peaks not related to the purpose of the experiment (no ROE peaks) may be observed and can mislead the users regarding their structural problem. Therefore, we strongly recommend not using the ROE experiments if there is no need for them. We fully agree with the following statement from Timothy Claridge, which clearly summarizes the problem:²³ 

We have performed a full-text search of the entire online collection of the Journal of Natural Products using the keyword “roesy” and we found 1156 articles. Surprisingly, more that 90% of these articles report the use of ROESY for molecules that do not really need it! And those that use it do not even mention or justify the reasons why. It seems that many natural products chemists use ROESY by tradition without being aware of the differences with regards to a NOESY experiment. If signal overlapping or sensitivity does not become a critical issue, the use of relatively low-field spectrometers (∼300–400 MHz) may be considered in order to avoid the use of the ROESY experiment. As a final note, ROE builds twice as fast as NOE, hence shorter mixing time values are recommended (300–400 ms).

If scalar coupling is present between protons, the corresponding term will evolve during the mixing time as a sum of zero- and double-quantum coherences, which will be manifested as antiphase peaks in the 1D- or 2D-NOESY/ROESY spectrum. Although the double-quantum component may be filtered by phase cycling or application of a PFG during the mixing time, this is not possible in the case of the zero-quantum component, as it has the same coherence order as the observed longitudinal magnetization. This zero-quantum component will evolve during the mixing time as the difference Ω_ZQ between the offsets of the scalar coupled nuclei, giving a peak of intensity I_ZQ:

Although the total integral of these antiphase peaks will be zero, they may obscure the presence of a true NOE correlation, making the observation of weak correlations difficult and the quantification of the integrals inaccurate. A simple procedure for minimization of the zero-quantum peaks in NOESY experiments is to introduce a small random variation of the mixing time, or either to randomly move the placement of a π pulse in the middle of the mixing time, between each t₁ increment. The magnitude of the true NOE peak will be minimally affected, especially at long mixing times, whereas the phase of the ZQ peak will differ from experiment to experiment and most of the signal will cancel out. Note that the degree of variation Δτ_m should cover at least one cycle of the zero-quantum coherence, which makes the elimination of ZQ peaks between protons that are very close in chemical shift more difficult to accomplish (see Figure 1.11). However, this procedure introduces some degree of t₁ noise into the spectrum since the ZQ peak is spread out along the F₁ dimension after Fourier transformation. These effects can be clearly shown in the NOESY 2D spectrum of a synthetic isoquinoline derivative, recorded with a 500 ms mixing time delay (Figure 1.12), which clearly shows zero-quantum correlations between vicinal and germinal protons. The introduction of a 30 ms random variation between either scans or experiments effectively removes the zero-quantum peaks.

A 3D-based approach was proposed to suppress ZQC coherence without introducing additional t₁ noise by smearing out the ZQC peak over the third dimension. Clean NOESY spectra are obtained with this methodology, although at the cost of somewhat reduced sensitivity.²⁴  Based on previous work, Howe presented a ZQ filter based on spin-echo evolution inside a z-filter element. A 180° pulse is placed inside the z-filter block and moved through it in t₁ increments. As ZQ is refocused at 2T-t₁, the ZQ will evolve during a t₁ time. Typically, 12 increments were needed for a clean elimination of the ZQ peak.²⁵ 

In 2003, Thrippleton and Keeler²⁶  proposed a ZQC filter based on generating a phase difference between the ZQC magnetizations for different positions of the NMR tube by simultaneous application of a PFG on the z-axis and a swept-frequency 180° pulse (Figure 1.13).

If τ_f is the duration of the gradient/swept-frequency pair, a particular point on the tube will experience the 180° pulse at a time at xτ_f where 0<x<1. Thus, ZQC is refocused over a time 2τ_f, but still evolves for the remaining (1−2x)τ_f time. As x is a function of the position in the tube, the ZQ contribution is effectively dephased over the sample, leading to ZQ signal attenuation in a single scan. The attenuation A suffered for a I_ZA peak between I and J spins is:

Typically, τ_f is in the range of ∼30–50 ms. Although this can become problematic for studies where very short mixing times are needed, it is perfectly acceptable for standard small-molecule NOESY experiments. Note, however, that for coupled spins with closely similar chemical shifts, longer τ_f delays may be necessary. As an alternative, Keeler and Shaka later proposed the use of not one, but a cascade of z-filters, which leads to improved signal suppression.²⁷ 

Dimeric natural products are frequently encountered in nature. Greer and coworkers analyzed a large database of literature entries and estimated that nearly 7% of the papers reported full bilaterally symmetric dimeric structures.^28,29  NOE experiments in dimeric compounds are difficult to interpret. First, NOEs between equivalent protons are in principle hidden, and second, ambiguities between intra- and inter-monomer correlations can also be present. A way to circumvent the first problem is to exploit the asymmetry found in the ¹³C isotopomers, as only one of the two equivalent carbons attached to the proton nuclei of interest will be a ¹³C nucleus, while the other will be attached to ¹²C. Thus, the ¹³C filtering of the NOESY experiment, through an HSQC or HMQC step, may allow for differentiation of the two nuclei.³⁰  Editing can be done either prior to the NOE block, as in the case of a HSQC-NOESY,³¹  or after, as in the NOESY-HSQC or NOESY-HMQC experiments.³²  If there is an NOE between chemically equivalent protons, the use of F₂- or F₁-coupled HSQC experiments allows the observation of a diagonal peak on the ¹²C isotopomer between the two halves of the doublet split by ¹J_CH (Figure 1.14).

In the 800 ms HSQC-NOESY spectrum of carbazol (Figure 1.15), the NOESY peak between the equivalent protons 4 and 4′, as well as the cross-peak between 3 and 4, and 3′ and 4′ can be seen. Note that the rest of the cross-peaks between close protons are not observed in this spectrum, likely due to different correlation times about the molecular axes.

The intensity of the cross-peaks is, in principle, the same if the carbon editing is done either before (HSQC-NOESY) or after (NOESY-HSQC) the NOESY block. However, experimental intensities may differ due to relaxation effects. Gschwind et al.³³  analyzed the effect of diffusion in the gradient-selected HSQC-NOESY and NOESY-HSQC experiments. In the first experiment, the mixing time is placed in the middle of the gradient refocusing, whereas in HSQC-NOESY, refocusing of gradients is separated by short delays. Hence, diffusion may severely decrease signal intensity in the HSQC-NOESY experiment, especially if very long mixing times are employed. Theoretically estimated attenuation factors range from 0.8 at a 0.5 s mixing time to 0.25 for a 3 s mixing time.

With respect to the practical application of these techniques, it should be noted that these are rather insensitive experiments, typically requiring samples in a 0.1–1 M concentration range using standard 5 mm probes, and therefore are only helpful for synthetic compounds where typically larger amounts of sample are available. However, the large boost in sensitivity provided by 3 or 1.7 mm cryoprobes may certainly make this experiment feasible for natural compound elucidation. As an example of this, Buevich et al. applied HSQC-NOESY experiments, along with J-coupling analysis of ¹³C satellites, to the determination of the conformation in a dimeric benzamide.³⁴  The relative intensity of the cross-peak between the equivalent methine protons (Figure 1.16) showed a preference for a gauche rather than an anti-conformation of the dimer, in agreement with a J-coupling of ∼4 Hz between these protons observed through the ¹³C satellites. Generation of artificial HSQC-NOESY data sets, obtained through covariance processing of individual HSQC and NOESY spectra,³⁵  can be useful in structural elucidation, but since the generated spectra does not contain any information present in the parent spectra, they will not show cross-peaks between equivalent protons.

Traditionally, organic chemists have employed NOE in a qualitative way where the observation of an NOE correlation simply informs that the two nuclei of interest must be close enough to give an appreciable dipolar interaction, and the quantitative or semi-quantitative use of NOE experiments is relatively scarce.

Very recently, the Butts group has tried to bring NOE in small molecules to a fully quantitative level (FQ-NOE).³⁶  Their proposal involves the use of techniques that are already known for ameliorating the quantification of NOEs in biopolymers. The proposed methodology involves several procedures that can be summarized in two principal points:

1. Use of 1D-NOESY DPFGSE experiment rather than 2D-NOESY experiments, as they provide more reliable integrals.

2. Calibration of integral areas against irradiated peak areas. This procedure extends the linear behavior of the NOE. After acquisition of the experiments, the integral of the irradiated proton is set to an arbitrary fixed number and all correlation integrals are further related to this integral for each experiment.

Interproton distances are then computed according to:

The r_ref value is then taken from an internuclear pair that is minimally affected by conformational mobility as a methylene pair or two ortho aromatic protons. Thus, once this reference distance is determined, either from tables or a molecular modeling structure, all interproton distances can be obtained if the corresponding cross-relaxation peaks are observed. A very complete set of 1D-NOESY data was obtained for strychnine, where the average absolute error between interproton distances was below 5% as compared to high-quality DFT and X-ray structures.

However, the use of 2D-NOESY experiments degrades the quality of the fit, especially if short d1 relaxation delays are used; relaxation delays up to ∼5 s are necessary in order to improve the quality of the data. However, long delays between transients greatly increases the necessary acquisition time without achieving the accuracy of the 1D procedure. Other sources of error in the 2D-NOESY experiments arise from t₁ noise, which makes the extraction of data very dependent on processing procedures. One could, in principle, argue that many of the sources of t₁ noise (e.g. temperature variation) are still present in the 1D experiment in the form of spectral noise; however, the short acquisition time of the 1D experiment lowers the impact of error sources.

Butts and coworkers also observed that degassing the sample did not improve the accuracy of the NOE-determined distances. This is due to a very similar impact of paramagnetic relaxation on the intensity of all observed correlations. Even the presence of oxygen shortens the t₁ relaxation time, allowing the safe use of short d1 delays in the 1D-NOESY experiments.

The accuracy in the experimentally determined interproton distances allowed the authors to experimentally prove the existence of a minor second conformation of strychnine. They observed a much larger deviation for the protons H_11β and H_23β as the NOE-determined distance, 3.49 Å, compared poorly to DFT and X-ray distances 4.10 Å and 4.12 Å, respectively (Figure 1.17). Further, molecular modeling studies suggested that this effect can be explained by the contribution of a second conformation of strychnine, arising from pseudo-rotation of the C₂₂–C₂₃ bond, with a low population that should lie 9.4 kJ mol⁻¹ over the basal form according to ab initio studies. In this higher-energy conformation, the H_11β–H_23β distance is shortened to 2.11 Å according to a computation that, according to Boltzmann-computed populations, corresponds to an average distance of 3.60 Å, very close to the 3.49 Å of the NOESY-determined distance. This neatly shows how the highly non-linear nature of the NOE can be exploited for unraveling low-population conformations that can be very difficult to detect using more linear techniques such as scalar coupling analysis or even RDCs.

The use of quantitative NOESY or ROESY may extend the applicability of NOE experiments to natural products with many stereogenic quaternary centers where no obvious NOE or ³J analysis is possible. By making use of FQ-NOE and ¹³C DFT chemical shift predictions,^37,38  Butts and Bifulco determined the relative configuration of conicasterol F,³⁹  a new compound isolated from a Theonella marine sponge. 2D-NMR determined the structure to be either the cis-diepoxide or the trans form (Figure 1.18).

A series of 1D- and 2D-ROESY 300 ms mixing time experiments were conducted and 18 internuclear proton distances determined. The distance between the geminal vinylic protons was taken as a reference. 3D structures were generated at DFT level for the two possible configurations of conicasterol F. The fit between the structures and the data set was expressed in terms of the maximum absolute error (MAE; eqn (1.24)).

The differences between the ROE-determined and the DFT-computed proton–proton lengths were determined. MAEs of 2.6 and 5.9 were obtained for the trans and cis configurations of conicasterol F, respectively. This result was in agreement with ¹³C chemical shift DFT GIAO/MPWPW91/6-31G* predictions, which furnished MAE deviations of 0.8 and 3.7 for the trans and cis forms, respectively.

FQ-NOE and quantum mechanical ¹³C chemical shift predictions were also applied to the determination of the relative configuration in plakilactones G (4) and H (5) (Figure 1.19).⁴⁰  Upon an exhaustive force-field conformational search, structures were refined at the DFT level and ¹³C shifts computed at the DFT-GIAO level. Boltzmann populations were computed according to the relative energies. The computed Boltzmann populations were then employed to get averaged 〈r⁻⁶〉 distances and chemical shifts. Both methodologies agreed in the configurational assignment for plakilactone G (5). The determination of configuration in the diol 4 was more cumbersome. As a first step, 4 was determined to possess a 7,8-erythro relative configuration by chemical derivatization to the 7,8-O-isopropilidene compound and chemical shift analysis of the acetonide methyl groups.⁴¹  Whereas ambiguities arose when determining the relative configuration of the two remaining centers when using the FQ-NOE or chemical shift ¹³C prediction methodologies, the combination of these two methods provided results with higher confidence. Chemical derivatization of the diol moiety in 4 following the Riguera double derivatization method⁴²  afforded the absolute configuration of the molecule.

The analysis of NOE experiments in the presence of molecular flexibility is a challenging problem since the very nature of the dipolar relaxation relies on the relative movement of nuclear spins. The analysis of molecular flexibility depends strongly on the ratio between the conformational exchange rates and the global molecular tumbling correlation times, τ_C. In general, NOEs can be only linearly averaged when the conformational exchange rates are lower than NOE buildup rates. In this case, the observed NOE enhancement is a simple linear combination of the enhancements for every single contribution:

where η_i are the individual enhancements and w_i are the corresponding normalized populations. However, only very slow conformational processes such as peptide bond rotations lie in this regime.

Most of the interesting conformational movement types involve rotation around one or more single bonds. These processes generally have low activation barriers and correspondingly high conformational exchange rates. In these cases, conformational exchange is faster than NOE buildup, but still slower than global molecular tumbling. This involves the averaging of auto- and cross-relaxation rates, which are therefore given by:

and result in a 〈r⁻⁶〉 averaging of the internuclear distances over the different conformations.

Finally, some molecular conformational movements with very low barriers, such as methyl group rotation, take place at a rate that is even higher than overall tumbling and, in this case, the correlation function is a complex function of spherical harmonics and internuclear distances. Analytical expressions for NOE enhancement between a single proton and a rotating methyl group,⁴³  as well as for intra-methyl relaxation,⁴⁴  are available and have been implemented in the FIRM program.⁴⁵ 

From this point forward, we will focus on the case of medium-rate 〈r⁻⁶〉 averaged processes where relaxation contributions from different conformations need to be taken into account and NOE enhancements explained (deconvoluted) in terms of a discrete conformational distribution. In this respect, different proposals can be found in the NMR literature, such as MEDUSA,⁴⁶  CPA,⁴⁷  or PEPFLEX-II.⁴⁸ 

Forster proposed a full-relaxation matrix deconvolution approach.⁴⁹  Assuming a jump-model where the conformational averaging can be described by a combination of discrete geometries, the averaged relaxation matrix is given by:

where w_i are the weights of each population. In this procedure, the effects of spin diffusion are taken into account through the use of relaxation matrix computations. Populations are computed by applying a non-linear fitting scheme to the experimentally determined NOESY volumes, similar to the Levenberg–Marquardt procedure.^50,51  The authors applied the developed algorithms to the conformational analysis of the O-methyl-α-l-iduronate sodium salt using data from a 3 s mixing time NOESY experiment. Three static conformations (Figure 1.20) consisting of two chair forms, ¹C₄ and ⁴C₁, and one skew form, ²S_O, were employed in the analysis. The computed populations were in good agreement with those obtained from J-coupling analysis of full MD trajectories using the Haasnoot–Altona equation.⁵²  Note, however, that this procedure has rarely been further used for quantitative analysis, and the general viability of this approach still needs to be confirmed, although very recently new software packages have appeared that make use of full relaxation matrix approaches.⁵³ 

The most widely used approach in conformational analysis of small organic molecules has been the NMR analysis of molecular flexibility in solution (NAMFIS) methodology developed from Cicero, Barbato, and Bazzo.⁵⁴  As a proof of concept, they analyzed the conformation of a cyclic peptide in which previous conformational clustering was done using the MEDUSA procedure. The NAMFIS approach is based on several steps. First, a conformational ensemble should be built using an appropriate force-field and a stochastic conformational search procedure. Since force-field-computed relative energies may have a significant error, care should be taken in order not to lose any structure that is significantly represented in the experimental ensemble. A recommended procedure would be to keep all conformations below ΔE∼3 kcal mol⁻¹ (∼1% Boltzmann population at 298 K). However, depending on the force-field chosen and the functionality present in the molecule, the necessary energy threshold can be increased to safer limits in the range of 10–12 kcal mol⁻¹.

The key of the NAMFIS method lies in summing up all of the available NMR restraints in a single penalty function P as shown in eqn (1.29). These restraints include not only NOE-estimated distances, but also ³J_HH scalar couplings. The penalty function is then built as a sum of square differences:

The dⁱ-calculated distances correspond to r⁻⁶ averages of the internuclear distances of individual geometries as obtained from molecular modeling; in other terms:

The ³J_calc values are obtained using the simple three-term Karplus equation:

or the more complex Haasnoot–Altona equation,⁵²  which takes into account the electronegativity of the substituents, as well as their relative orientations. Many molecular modeling packages implement routines for the computation of these couplings from a given 3D structure.

It should be noted that the merit function in NAMFIS weights every NOE and ³J contribution according to their associated error. The use of NOE errors shown in Table 1.1 and a 1.5 Hz general error for ³J_HH couplings, computed with the Haasnoot–Altona equation, was recommended.⁵⁵  Once eqn (1.29) is set up, the populations are determined by a linearly constrained non-linear least-squares optimization procedure.

NAMFIS is intended to overcome a general problem with modern computational methods: although they can provide sufficiently accurate geometries, prediction of relative energies in solution can only be considered as a semi-quantitative procedure. Therefore, in the original NAMFIS implementation, computed relative energies are used only to define the threshold for conformer selection.

NAMFIS has been used profusely for the determination of conformational space in tubulin ligands of a macrocyclic nature, such as taxol and its derivatives, discodermolide, laulidamide, and epothilone A (Figure 1.21).

NAMFIS analysis can be performed using scalar couplings other than ³J_HH. Monteagudo and coworkers⁵⁶  analyzed the conformation of a doxorubicin disaccharide (Figure 1.22) by combination of NOE-derived distances and three-bond proton–carbon ³J_CH couplings. The proton–carbon couplings were calculated by using a tailored Karplus relationship.⁵⁷ 

A graphical frontend for the NAMFIS program has been made available in the Janocchio software package.⁵⁸  Another NAMFIS-like implementation is the DISCON program.⁵⁹  As an additional advantage over the original NAMFIS implementation, DISCON employs a clustering algorithm, based on experimental NOE and scalar coupling data, prior to the NMR data deconvolution step, in this way avoiding the presence of many nearly degenerate solutions of the population determination problem. DISCON was successfully employed in the conformational analysis of (+)-spogistantin-1 (Figure 1.23)⁶⁰  and its analogs⁶¹  using a combination of long-range NOEs, retrieved from a 600 ms NOESY experiment, and ³J_HH couplings.

Griesinger and coworkers employed NOESY-determined distances, in combination with RDCs, for the complete determination of the configuration at the C20,C25,C24′ positions of fibrosterol sulfate A, a polysulfated steroid isolated from the sponge Lissodendoryx fibrosa.⁶²  The authors employed a RDC-based approach where, previous to the RDC fitting step, the conformational space of the molecule was determined by using NOESY-based distances, as well as ³J_CH and ³J_HH couplings, as time-averaged restraints during a MD run.^63,64  RDC fitting provided strong evidence for the C20,C25,C24′-(SSS) configuration shown in Figure 1.24.

The NOE family of experiments is still nowadays essential for the configurational/conformational analysis of natural products. The use of PFG-based pulse sequences provides cleaner spectra in a reduced number of scans and they should be the option of choice. ¹³C-filtered experiments, such as HSQC-NOESY, may be crucial for the analysis of dimeric structures. By using carefully tailored experimental conditions, the NOE can be brought to a nearly quantitative level, allowing the determination of internuclear distances with high accuracy. In combination with other observables such as scalar couplings, NOE-obtained distances can be employed in NAMFIS and related conformational deconvolution techniques to ascertain the conformational state in solution of highly flexible molecules.