lecture25_2011 - 04Mar2011 Chemistry 21b – Spectroscopy...

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Unformatted text preview: 04Mar2011 Chemistry 21b – Spectroscopy Lecture # 25 – Nuclear Magnetic Resonance Spectroscopy Along with infrared spectroscopy, nuclear magnetic resonance (NMR) is the most important method available for the determination of molecular structure – particularly for large organic molecules and biopolymers. While infrared spectroscopy provides information about the functional groups that are present in a molecule, NMR yields the number of (and in certain cases the separations between) certain atoms in the sample. What is the basis of NMR spectroscopy? As we have seen in earlier lectures, electrons and many nuclei have magnetic dipole moments that lead to non-zero values of the spin nuclear angular momentum. By applying a magnetic field, it is possible to separate single axis components of this nuclear spin angular momentum and to induce transitions between them. Specifically, if a nucleus has an intrinsic spin angular momentum I with magnitude radicalbig I ( I + 1)¯ h , the nuclear magnetic dipole moment μ N is equal to μ N = g N e 2 m p c I , (25 . 1) where g N is the nuclear g-factor and m p is the proton mass. Because nuclear structure is complex, the values of g N are non-integer and are most easily determined experimentally. The absolute magnitude of the nuclear magnetic moment is | μ N | = | g N | e 2 m p c [ I ( I + 1)] 1 / 2 ¯ h = | g N | β p radicalbig I ( I + 1) , (25 . 2) where the nuclear magneton β p (commonly denoted β N ) is defined as β p ≡ e ¯ h 2 m p c = 5 . 051 × 10 − 24 erg / gauss . (25 . 3) Due to the increased proton mass, the nuclear magneton is (1/1836) th of the Bohr magneton (to which we’ll return in our discussion of ESR). The projected components of the nuclear angular momentum, denoted by M I ¯ h , obviously run from − I to + I in integral steps, and the z-component of the nuclear spin eigenfunctions follow ˆ I z | M I > = M I ¯ h | M I > . Only nuclei with either odd mass or odd atomic number, or both, have non-zero values of I . Thus, common nuclei such as 12 C and 16 O cannot be used in NMR spectroscopy, but 1 H (I=1/2), 2 D (I=1), 13 C (I=1/2), 14 N (I=1), 15 N (I=1/2), 17 O (I=3/2), 19 F (I=1/2) and 31 P (I=1/2) can. Magnetic Resonance and Selection Rules As we know from an analysis of the Zeeman effect, in the absence of an external magnetic field the different values of M I are degenerate, and no spectroscopy is possible. 190 Classically, the interaction between a nuclear magnetic moment and an external magnetic field B is μ N · B = − g N β p ¯ h − 1 I · B = − g N β p ¯ h − 1 BI z , (25 . 4) where we have chosen the z-axis to coincide with the direction of the applied magnetic field. Quantum mechanically we have ˆ H = − g N β p ¯ h − 1 B ˆ I z = − γ n B ˆ I z , (25 . 5) where γ N ≡ g N β p / ¯ h is the magnetogyric ratio. Thus, ˆ H | M I > = − g N β p BM I | M I > , M I = I, I − 1 , ..., − I (25 . 6) The application of the static magnetic field results in evenly spaced energy levels that...
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lecture25_2011 - 04Mar2011 Chemistry 21b – Spectroscopy...

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