Nuclear Overhauser effect

The nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity (positive or negative) of one NMR resonance that occurs when another is saturated by irradiation with an RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation. The nuclear Overhauser effect (NOE) is the transfer of nuclear spin polarization from one population of spin-active nuclei (e.g. 1H, 13C, 15N etc.) to another via cross-relaxation. A phenomenological definition of the NOE in nuclear magnetic resonance spectroscopy (NMR) is the change in the integrated intensity (positive or negative) of one NMR resonance that occurs when another is saturated by irradiation with an RF field. The change in resonance intensity of a nucleus is a consequence of the nucleus being close in space to those directly affected by the RF perturbation. The NOE is particularly important in the assignment of NMR resonances, and the elucidation and confirmation of the structures or configurations of organic and biological molecules. The two-dimensional NOE experiment (NOESY) is an important tool to identify stereochemistry of proteins and other biomolecules in solution, whereas in solid form crystal x-ray diffraction must be used to identify the stereochemistry. The NOE developed from the theoretical work of American physicist Albert Overhauser who in 1953 proposed that nuclear spin polarization could be enhanced by the microwave irradiation of the conduction electrons in certain metals. The electron-nuclear enhancement predicted by Overhauser was experimentally demonstrated in 7Li metal by T. R. Carver and C. P. Slichter also in 1953. A general theoretical basis and experimental observation of an Overhauser effect involving only nuclear spins in the HF molecule was published by Ionel Solomon in 1955. Another early experimental observation of the NOE was used by Kaiser in 1963 to show how the NOE may be used to determine the relative signs of scalar coupling constants, and to assign spectral lines in NMR spectra to transitions between energy levels. In this study, the resonance of one population of protons (1H) in an organic molecule was enhanced when a second distinct population of protons in the same organic molecule was saturated by RF irradiation. The application of the NOE was used by Anet and Bourn in 1965 to confirm the assignments of the NMR resonances for β,β-dimethylacrylic acid and dimethyl formamide showed that conformation and configuration information about organic molecules can be obtained. Bell and Saunders reported direct correlation between NOE enhancements and internuclear distances in 1970 while quantitative measurements of internuclear distances in molecules with three or more spins was reported by Schirmer et al. Richard R. Ernst was awarded the 1991 Nobel Prize in Chemistry for developing Fourier transform and two-dimensional NMR spectroscopy, which was soon adapted to the measurement of the NOE, particularly in large biological molecules. In 2002, Kurt Wuthrich won the Nobel Prize in Chemistry for the development of nuclear magnetic resonance spectroscopy for determining the three-dimensional structure of biological macromolecules in solution, demonstrating how the 2D NOE method (NOESY) can be used to constrain the three-dimensional structures of large biological macromolecules. The NOE and nuclear spin-lattice relaxation are closely related phenomena. For a single spin-​1⁄2 nucleus in a magnetic field there are two energy levels that are often labeled α and β, which correspond to the two possible spin quantum states, +​1⁄2 and -​1⁄2, respectively. At thermal equilibrium, the population of the two energy levels is determined by the Boltzmann distribution with spin populations given by Pα and Pβ. If the spin populations are perturbed by an appropriate RF field at the transition energy frequency, the spin populations will return to thermal equilibrium by a process called spin-lattice relaxation. The rate of transitions from α to β is proportional to the population of state α, Pα, and is a first order process with rate constant W. The condition where the spin populations are equalized by continuous RF irradiation (Pα = Pβ) is called saturation and the resonance disappears since transition probabilities depend on the population difference between the energy levels. In the simplest case where the NOE is relevant, the resonances of two spin-​1⁄2 nuclei, I and S, will be chemically shifted but not J-coupled. The energy diagram for such a system has four energy levels that depend on the spin-states of I and S corresponding to αα, αβ, βα, and ββ, respectively. The W's are the probabilities per unit time that a transition will occur between the four energy levels, or in other terms the rate at which the corresponding spin flips occur. There are two single quantum transitions, W1I, corresponding to αα ➞ αβ and βα ➞ ββ; W1S, corresponding to αα ➞ βα and βα ➞ ββ; a zero quantum transition, W0, corresponding to βα ➞ αβ, and a double quantum transition corresponding to αα ➞ ββ. While rf irradiation can only induce single-quantum transitions (due to so-called quantum mechanical selection rules) giving rise to observable spectral lines, dipolar relaxation may take place through any of the pathways. The dipolar mechanism is the only common relaxation mechanism which can cause transitions in which more than one spin flips. Specifically, the dipolar relaxation mechanism gives rise to transitions between the αα and ββ states (W2) and between the αβ and the βα states (W0). Expressed in terms of their bulk NMR magnetizations, the experimentally observed steady-state NOE for nucleus I when the resonance of nucleus S is saturated ( M S = 0 {displaystyle M_{S}=0} ) is defined by the expression: where M 0 I {displaystyle M_{0I}} is the magnetization (resonance intensity) of nucleus I {displaystyle I} at thermal equilibrium. An analytical expression for the NOE can be obtained by considering all the relaxation pathways and applying the Solomon equations to obtain